PRO?r;~ÏV OF s r i t - *--•->- -• -^ - INTERNATIONAL LABOUR OFFICE THETi^--i Ai-!3 UGC?. CO-.íuESS ©i? e ^ ^ Ä O Ä S T U D I E S AND R E P O R T S Series M (Social Insurance) No. 17 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION OF SOCIAL INSURANCE Compulsory Pension Insurance Lucien FÉRAUD Agrégé de l'Université, docteur es sciences GENEVA, 1940 Published in the United Kingdom For the INTERNATIONAL LABOUR OFFICE (LEAGUE OF NATIONS) By P. S. KING & SON, Ltd. Orchard House, 14 Great Smith Street, Westminster, London, S.W.l PRINTED BY ALBERT K U N D I » GENEVA PREFACE Compulsory social insurance, and, in particular, those branches which deal with risks that may not materialise for some considerable time, such as insurance against invalidity, old age and death, have from the outset been obliged to take account of technical considerations in organising their finances. Originally they made use of the actuarial technique which had previously been developed for. the requirements of commercial insurance and pensions funds. It was soon found that the methods so far applied had to be extensively changed in order to meet the special problems arising out of the wide scope and special characteristics of social insurance. As social insurance spread to increasingly large sections of the community and to a growing number of countries, the actuarial studies required gradually evolved a special technique. This technique, like that of other actuarial operations, is based on probabilities, and makes it possible in any given case to deduce the most accurate and reliable conclusions from the existing demographic statistics and financial data. This actuarial technique has played a fundamental part not only in the current supervision of the working of insurance institutions, but also in the inauguration of new schemes or the reform of existing ones. It has often been found that the fate of some proposed legislation depended very largely on the possibility of finding a satisfactory technical solution whereby the desired aims could be reached with the available means. At other times, technical arguments have proved to be the only ones that provide a final answer to the criticisms directed against insurance schemes. In all circumstances experience shows that the development of social insurance is closely linked up with the evolution of its technique. The International Labour Office, in its studies, has thus had to devote attention to the actuarial technique of social insurance. PREFACE IV The present volume deals with the technique of compulsory (contributory) invalidity, old-age and widows' and orphans' insurance schemes, on the subject of which the International Labour Conference adopted six Draft Conventions (Nos. 35 to 40) and one Recommendation (No. 43) at its Seventeenth Session in 1933. This work is not intended to be a handbook or a systematic treatise on the subject; the financial organisation of social insurance schemes depends so largely on economic, social and even political conditions that it was felt essential to deal with the question in a more concrete manner. A survey has therefore been given of the most representative insurance schemes in various countries, and the technical mechanism of each has been studied as it works in the operation of the scheme, not merely at one given date or at a few dates, but throughout the whole course of its development. It was therefore impossible to include in a single volume more t h a n a few schemes; among those which have the widest scope, the following were selected, the list being given in the chronological order of the introduction of the schemes. Invalidity, Old-Age and Widows' and Orphans' Insurance Part I: 1891 to 1914. Part II: after 1924. GREAT BRITAIN AND NORTHERN IRELAND: Part I: National Health Insurance (1912). Part II: Widows', Orphans' and Old-Age Contributory Pensions (1926). ITALY: General Scheme of Compulsory Insurance against Invalidity, Old Age and Death (1920). BELGIUM: Old-Age and Widows' and Orphans' Insurance for Workers (1926) and Old-Age, Widows' and Orphans' Insurance for Salaried Employees (1927). CZECHO-SLOVAKIA: Invalidity, Old-Age and Widows' and Orphans' Insurance for Workers (1926). FRANCE: General Scheme of Social Insurance (1930). GERMANY: for Workers. Each of these schemes is dealt with in a separate study, based mainly on the actuarial work which played an actual part in the preparation, application and reform of the legislation in question. These studies will not always absolve the reader from the necessity of studying the legislative texts and certain original memoranda, but they do at least provide a summary of the available information and a clue to guide the reader through a mass of documents, which are generally very numerous and scattered. The reader will also find an outline of the main provisions of the legislation, the basic numerical data (mortality, invalidity and annuity tables, etc.) and a bibliography. PREFACE V Most of the studies were submitted in manuscript to the competent national authorities, and the Office wishes to pay a tribute to the invaluable assistance these authorities granted it, and to express its deep gratitude, while naturally itself taking the full responsibility for the published text. * * * The general plan of this work was evolved and drawn up several years ago by Mr. Adrien Tixier, now Assistant Director, and at that time Chief of the Social Insurance Section, who in that capacity prescribed the method to be followed in analysing the financial organisation of insurance schemes. The carrying out of the plan was entrusted to the actuary of the Social Insurance Section, Mr. Lucien Féraud, D.Sc, who prepared all the actuarial monographs in this volume, and also the general introduction bringing out the actuarial technique peculiar to compulsory invalidity, old-age and survivors' insurance schemes. It would have been possible to divide the analysis of the financial organisation chronologically according to the dates of the more important reforms in the insurance legislation. That is the simplest method for a single insurance scheme, but it was not thought to be the best in a work of an international character. It was felt that if all the studies were drawn up in accordance with a uniform plan—subject to certain inevitable variations—the volume would gain in homogeneity and could be more easily consulted as a work of reference. The plan followed falls under four main heads: I. Demographic elements (biometrie tables, data concerning the insured population and changes in that population, etc.). II. Financial elements (contributions, State aid, benefit, administrative expenses, etc.). III. The financial system proper—that is, financial equilibrium and stability. IV. Financial administration—that is, the investment of funds, the organisation of actuarial and financial control, and the statistical methods employed for recording results. \I PREFACE A general introduction indicates, from the financial and technical point of view, the fundamental characteristics of the insurance schemes analysed in this volume, bringing out the differences between their financial systems, and thus facilitating correlation and comparisons. With the exception of the paragraphs intended more particularly for actuaries, in which mathematical symbols are used, the volume should be perfectly comprehensible to any person with some knowledge of the working of social insurance. This work is a technical and purely objective contribution to the study of social insurance, bringing out the structure of its financial organisation, indicating the methods and purposes of its peculiar actuarial technique, and thus contributing to the improvement and development of that technique 1 . 1 For the English translation the thanks of the International Labour Office are due to Mr. W. E. P. Loraine, F.I.A., of the Government Actuary's Department. CONTENTS Page PREFACE INTRODUCTION m 1 L I S T OF MONOGRAPHS: Belgium 47 Gzecho-Slovakia 83 France 167 Germany 271 Great Britain 443 Italy 517 INTRODUCTION Of all the risks that can be covered by social insurance, only three are considered in this volume, those of invalidity —however defined *—old age, and death ; in the last case the insurance benefit consists of a lump sum or a pension paid to the insured person's surviving dependants. A scheme of social insurance provides as a rule for all three of these risks together, or for only two of them. None of the schemes is ever completely independent, whether administratively or financially, of co-existing schemes with a different scope or covering a different risk. But for the present purpose an attempt is made, for each of the schemes considered, to ignore whatever is not essential to its real aims. Only compulsory (contributory) schemes are discussed, without reference to any of the optional provisions or voluntary schemes that often accompany a compulsory scheme. An examination of the financial problems of social insurance may be undertaken from various points of view, among which distinctions may be drawn between the economic, the social, and the technical. The immediate and the more remote effects of the changes produced in the distribution of goods through the action of social insurance form the subject of very interesting economic studies. The social purposes of insurance and the conditions that must be satisfied in order that these purposes may be fulfilled have been described in particular in several publications of the International Labour Office 2. These two standpoints are left out of account here, that adopted being a third. The problems are 1 The definition used in each of the insurance schemes studied is indicated in the separate monographs. For a general review of the various conceptions of invalidity, cf. INTERNATIONAL LABOUR OFFICE: The Evaluation of Permanent Incapacity for Work in Social Insurance, Studies and Reports, Series M (Social Insurance), No. 14, 1937. 2 See the volumes dealing with the various branches of social insurance in Studies and Reports, Series M (Social Insurance), especially Compulsory Pension Insurance (No. 10), 1933. 2 INTRODUCTION considered in the light in which they appear, for example, to the management of a social insurance scheme concerned solely with the working of the scheme. Consequently, the laws, regulations, and judicial practice underlying the scheme, as also its administrative arrangements, are described only to the extent that is necessary for a proper understanding of its financial organisation. The problems discussed here may be divided into three groups. The first arise before legislation has been enacted and are connected primarily with its preparation; they form the subject of technical work, usually known as the preparatory work. A further distinction may be made after, the scheme has been put into force : on the one hand, there are the problems arising out of the technical operations that are necessary for its working (statistical returns and enquiries, technical accounting, estimates, actuarial balance-sheets, etc.) and are carried out at regular or irregular intervals ; and on the other, those connected with the planning and application of reforms. It is obviously impossible to take each scheme and study it as it was organised and worked at a particular date. The end in view is to consider not only the problems arising out of the development, adjustment or reform of a social insurance scheme, but also the problems—often entirely different from the first—with which the expert is faced who is consulted on the preparation of new legislation. For this reason, although the history of each scheme is not recounted, an attempt is made to bring out those events in its evolution which have been of essential importance from the technical standpoint. It is hardly necessary to point out that in no case has the mechanism described been an unchanging one, working in close conformity with a specified plan. On the contrary, there have been incessant modifications; it seems, in fact, that the reason why the financial organisation of social insurance must rest on a technical basis is not so much to prevent any alteration of the scheme as to facilitate the reforms and adjustments that are found to be necessary during its actual operation. Wherever occasion arises, account is taken here of this constant process of adjustment, which is no doubt the most important function of the technique now under consideration. This study obviously cannot claim to provide a fuller and more detailed analysis of any of the schemes studied than those already made in the country concerned. The only end in view here is to bring out the essential factors and characteristics of financial organisation, an attempt being made to present them in the form that appears to be best suited to a reader familiar with the insurance INTRODUCTION 3 schemes of his own country, but not acquainted in detail with those in force elsewhere. The various technical conceptions met with in the course of these analyses are all placed on the same footing, whether they belong to the technique of private insurance or of pension funds or have been introduced for the special purpose of solving a social insurance problem. By way of a general introduction, each of the headings of the plan adopted for the preparation of the monographs will now be discussed in turn, with a view to bringing out the main features of the many problems raised by the financial organisation of social insurance. I. — DEMOGRAPHIC ESTIMATES, BASES AND EXPERIENCE Chapter I of each monograph covers all the technical factors which are not financial in character and can be sufficiently defined by the statistics without recourse to the accounts. The first section deals with the biometrie data that do not depend on absolute figures relating solely to the insured group ; the next two sections, on the contrary, relate to the particular group considered and discuss respectively the insured population and the number of beneficiaries. The figures corresponding to these two factors are both considered with reference, not to a particular date alone, but to their movement during as long a period as possible. Biometrie Tables The general title " biometrie tables " covers a certain number of statistical results of a demographic nature, which have been put into such a form that they can be applied to other groups than those from which they are derived. At the inception of any social insurance scheme, there is nearly always a complete lack of statistics concerning the group which it is proposed to insure. Recourse is therefore had to observations made under other social insurance schemes in the same country or abroad, to the data derived from pension funds, or to the results of general or occupational censuses or special enquiries. Once the scheme has been put into force, the insurance institution usually tries to make statistical returns, from which biometrie tables can be compiled for the insured group itself, and these gradually take the place of the tables that served as a basis for the preparatory work. 4 INTRODUCTION To be complete, the study oî a biometrie table should provide exact information on: (1) the observations made (definition of the group under observation, period of observation, definition and number of persons exposed to the risk, definition of the risk, and number of cases in which the risk materialises); (2) the recording and examination of the observations (bodies responsible for operations, methods employed); (3) the construction of the table (essential formulae, adjustments) ; (4) the use made of the table and the reasons leading to its selection ; (5) bibliographical references (original publications, reproductions in full or in part). The above summary is in itself sufficient to show that a detailed study of biometrie tables would call for a whole series of volumes. Here, only those tables arc considered which played a direct part in the preparation or reform of social insurance legislation, to the exclusion of those which were used for purposes of comparison but which were not finally adopted. Leaving out of account the many theoretical researches into the construction or properties of the various classes of biometrie tables, attention is paid here chiefly to their application to social insurance technique. In a number of cases numerical data are reproduced in full. For other tables references are given by means of which recourse may be had to the original documents ; owing to the difficulty that may sometimes be met with in procuring these, reference is also made to the more widespread reproductions, in particular those to be found in standard works. The biometrie tables are divided into several classes according as they relate to: (a) mortality; (b) invalidity or invalidity and mortality together; (c) morbidity (owing to its indirect effects, even though sickness is not one of the risks considered in this study); (d) marital condition and composition of the family. The essential features of the tables in each of these classes will now be reviewed. 5 INTRODUCTION Mortality is no doubt the demographic phenomenon which was studied first and which has been the subject of the largest number of publications. In social insurance use is nearly always made of the mortality tables compiled for the population as a whole from the returns of one or more censuses and from the statistics of deaths. As a rule these tables are prepared, for each sex separately, by the central administrative authority responsible for the compilation of statistics, and their construction has given rise in each country to detailed research. The figures appearing in mortality tables are not the direct result of observations: by means of various methods—into the details of which it is not possible to enter here—gross figures are first determined, from which the final figures are obtained by a process, of " adjustment ". To bring out the significance of the figures contained in mortality tables and to run over briefly the terms and symbols usually employed, we may have recourse to a theoretical pattern. Take a group of persons all of a certain (initial) age, exactly x0 years, and let lx be the number of these persons. At the end of a year the survivors of the group will be aged x0 + 1 and their number will be lXo+i- Similarly, at the end of two years there will be lXo+ 2 survivors aged xQ + 2 years, and so on, up to an extreme age co, for which la = 0 (w varies according to the tables and usually lies between 95 and 105 years). The discontinuous sequence 'nco ' *'xa+ h ••• ) ^u constitutes a life table. As a matter of fact, life tables are not constructed as easily as this, because the statistical material does not possess all the various features which have been assumed here. Nevertheless, the result which it is sought to obtain is in fact that corresponding to the above pattern. When applying a life table (which may be briefly designated lx), the number of survivors at age x + a of a group J\lx persons aged x is obtained by the rule of three: '•x The ratios ~^ introduced in this way are treated as probabil- ities of survival; the ratios - y ^ are represented by the symbols px, whose complements qx = 1 — px constitute the annual mortality 6 INTRODUCTION rates. A mortality table may thus be defined by any one of the discontinuous sequences lx, px or qx. The application of a mortality table to an insured group can be justified only by a detailed discussion, which may. be carried out from several standpoints. It will be sufficient here to note a few aspects. The groups to be considered will not be composed of persons who at a specified date are all aged so and so many years exactly. Consequently, the discontinuous figures of the mortality tables must be used to obtain appropriate averages by recourse to hypotheses—as simple as possible—concerning the distribution of dates of birth during the year. For any particular calculation, a mortality table only is nearly always used ; the assumption is thus that during the whole period covered by the calculation, " mortality at any age remains constant". As regards social insurance in particular, the application of a mortality table drawn from observations concerning the population as a whole is in itself an approximation, the degree of which is ODen to discussion, in the schemes discussed here which cover a large proportion of the occupied population, it will be- seen that the mortality rates applied to the whole insured population are not drawn from observations effected in the insurance scheme itself, but have always been assimilated to the general mortality rates. On the other hand, when, instead of the whole insured population, a particular group of insured persons is considered, defined with reference to another criterion, for example invalidity or marital condition, the definition of mortality rates is frequently based on observations made during the operation of the scheme itself. Before turning to the tables which involve the conception of invalidity (or validity), it may be noted that this conception depends on legislation, administrative regulations, and judicial practice and is-therefore not invariable in its significance. Tables concerning invalidity were first prepared by pension funds for particular classes of workers. But later they have been based, where possible, on the statistics derived from compulsory insurance in order that they may be exactly suited to the scope of the insurance scheme. The tables showing mortality rates for invalids, mortality rates for healthy persons, the probability of becoming invalid, and validity rates are considered in turn. INTRODUCTION / , The mortality rates for invalids have been the subject of many researches, which have led to a variety of tables: Tables of aggregate values, which depend only on the age reached by the invalid and are constructed in accordance with a pattern similar to that introduced above for general mortality tables. Tables of selected values, obtained by taking into account both the duration of invalidity and the age reached by the invalid, or, which comes to the same thing, the age of becoming invalid and age reached by the invalid. These tables are no longer mere lists of figures, but comprise both rows and columns, the former corresponding to the age of becoming invalid and the latter to the duration of invalidity as long as it is less than a certain limit, ordinarily not exceeding ten years. Tables of ultimate values, which depend only on the age reached by the invalid but do not apply until the invalidity has lasted long enough for selection to have ceased having any appreciable effect. There are also tables (compact) showing the cessation of invalidity pensions, in which the figures depend neither on the age of becoming invalid nor on the age reached by the invalid, but only on the duration of invalidity. As a rule the mortality rate of invalids and their rate of withdrawal from insurance are assimilated, although the latter may depend on various causes other than death. In certain cases, however, a correction is made to take into account the discrepancy between the two phenomena. Further, only permanent invalidity is considered, the assumption being that a person who has become invalid will never return to a state of health. The deaths of healthy persons which take place without any previous invalidity have also been the subject of researches, which have led to the compilation of tables of mortality rates for healthy persons. The tables showing the probability of becoming invalid are derived either from the observations of pension funds or from social insurance statistics. These invalidity tables—as they are known for short—provide " invalidity rates", which are in fact the annual rates of becoming invalid, and therefore represent the average number of healthy persons aged x years (in a given group of 100,000, for example) who become invalid during a year, that is, before reaching the age x -j- 1. If the probability of becoming invalid and the cessation of invalidity are taken together, the pattern previously introduced with reference to mortality alone must be generalised. Again, we 8 - INTRODUCTION take a theoretical initial group of lXo persons, all of a certain (initial) age, x0 years exactly. At the end of a year the survivors of this group include ZÄ"+1 healthy persons and lXo+t invalids, or in all there are tXo+i -f tx\+i — lXo+l survivors. By this process two discontinuous sequences of figures, lxa and l", are obtained, which summed in pairs reproduce for any one value of x the life table /,. for the group taken as a whole. The three sequences lx, Z"", and lx form a validity table, which represents in schematic form the evolution of mortality, of invalidity, and of the relation between them. The data obtained directly from observations may be used to define the mortality of the total group composed of healthy persons and invalids, the mortality of invalids, the mortality of healthy persons, and the probability of becoming invalid. These data are not all independent: a knowledge of three of them is sufficient to determine the combined evolution of mortality and invalidity. It will be seen that in every case the observations have been used to provide figures concerning the probability of becoming invalid and the mortality of invalids, but that in some cases recourse is had to experimental mortality rates for healthy persons, while in others, on the contrary, these rates are calculated with reference to the mortality rates applicable to the whole group of healthy persons and invalids together. The morbidity rates of the insured group have an effect on the financial situation of a pension insurance scheme. When an insured person falls ill, he is no longer in receipt of wages, and consequently his contribution to the scheme is not paid, unless its place is taken by a payment from some other source. It will therefore be necessary, as a rule, to take into account the average number of days of sickness per insured person and per annum, that is to say the " annual morbidity rate ". Further, it may happen, as in Great Britain, that sickness insurance and invalidity insurance are closely connected and that the financial equilibrium of the two schemes cannot be separated. It is considered sufficient to indicate, in each of the monographs, which morbidity tables have been taken into account in the studies for the pension insurance scheme *; in the case of Great Britain, tables relating to both morbidity and invalidity are taken into account. 1 For a systematic study of morbidity tables, reference may be made to à previous publication of the INTERNATIONAL LABOUR OFFICE: Compulsory Sickness Insurance, Studies and Reports, Series M, No. 6, 1927, pp. 437-445. INTRODUCTION 9 In many calculations it has been necessary to have recourse to data concerning the marital condition of insured persons and the composition of their families. This has involved the introduction of a great variety of statistical bases, comprising among others : mortality tables for single insured persons and" married insured persons separately (males and females separately); marital coefficients (males and females separately), indicating at each age the proportion of married insured persons; probability of marriage for females; average age of the wife in relation to husband's age; number and distribution by class (healthy, invalid, pensioned, not pensioned, insured, not insured) of wives of insured persons; number and distribution by class (healthy, invalid, pensioned, not pensioned, insured, not insured) of widows of insured persons; mortality rates for children; average number of children dependent on insured persons (according to the age of the children and the age of the father); average number of children dependent on widows of insured persons (according to the age of the child and the age of the mother). These data have not always been as adequate and complete as might have been desired and they have had to be taken from the most varied sources: some are derived from general censuses, others from special enquiries and sometimes from social insurance statistics proper. Insured Population The description of the insured population relates not only to its total number but also to its distribution by sex and by age. A distinction may be made between two main problems, relating respectively to the insured population at a given date and to the movement of that population. When an insurance law is being prepared, no direct information is available concerning the group that it is proposed to insure. Consequently, reference must be made either to general censuses and for preference occupational censuses, or to data drawn from other insurance schemes already in force in the country, subject to corrections if the scope of the schemes is not the same. While the scheme is actually in operation, the insurance institutions try to record exact information on the number of insured 10 INTRODUCTION persons and their distribution by sex and by age. These investigations raise a difficult statistical problem, because the insured group is large, scattered, and constantly liable to variation owing to a number of causes, chief among which is that the status of the insured person is not always defined with sufficient exactitude. The statistics of entrants are easier, but provide only a maximum figure for the number of insured persons. A brief analysis is given later of the principal methods used for obtaining as reliable an estimate as possible of the number of insured persons and their distribution by sex and by age. In a certain number of cases the number of insured persons at each age has been estimated over a series of years in order to obtain a table showing the probable evolution of the insured population. Two quite different methods have been used. According to the first, the insured population at a given date is to begin with considered as a " closed group " ; that is to say, it is assumed that there are no additions to the group and that the only decreases to which it is liable are due to causes covered by the biometrie tables (invalidity, death). By applying these tables to the age distribution adopted for the initial date, the evolution of the closed group is found without difficulty. Account must next be taken of the contingent ' entering into insurance each year and the departures produced by causes which are not taken into account in the biometrie tables. For the contingent entering into insurance each year, the age distribution is determined with reference to observations made during one or more years, and it is next assumed that this will remain unchanged. As a rule, it is assumed by approximation that all the entrants into insurance belong to the lower ages, for example, 16, 17 and 18 years. For the evolution of the total entrants, recourse is had to one or other of the following hypotheses: (a) the total number of entrants remains constant; {b) it increases regularly in such a way that the transition from one year to the next is obtained by multiplying it by a " co-efficient oí annual increase " which is higher than unity. Thus an attempt is made to obtain an estimate of the entrants into insurance corresponding to the new generations entering active working life. Further, the insurance scheme may receive or lose insured persons who, whatever their age, may change their employment and consequently enter or leave its scope. These two movements and also their resultant—which is all that is of importance to the insurance scheme—are difficult to determine exactly, and still INTRODUCTION li more difficult to forecast, for they are subject to wide variations when there are changes in the complex of economic and social conditions. The financial consequences of these variations depend essentially on the provisions adopted concerning the maintenance of the rights of persons leaving insurance, concerning the qualifying period to be completed by new insured persons, and concerning the maintenance of rights of insured persons transferring from one scheme to another. Finally, with regard to the scope of social insurance, migration movements involve a problem which it has not as a rule been possible to solve satisfactorily from the statistical point of view. It will be seen, however, t h a t a certain number of insurance institutions have recognised the importance of this problem and tried to collect information with a view to obtaining a sufficiently approximate solution for use as a basis for actuarial calculations. With the other method, which is quite different, an estimate, made in advance on the basis of the results of general censuses and of certain demographic hypotheses, is used as the startingpoint for representing the evolution of the total population by sex and by- age during a series of years. For each group and each sub-group the transition from the total population to the occupied population is effected by means of an " occupation ratio ", and t h a t from the occupied population to the insured population by means of an " insurance ratio ". The occupation and insurance ratios are obtained by means of special enquiries. Number of Beneficiaries It will be seen that the calculations for demonstrating financial equilibrium may call for estimates of the annual " contingents " of persons who are granted the various kinds of benefits or of the number of persons in receipt of the various benefits at a specified date, for example at 31 December. The contingents and numbers of persons in receipt of benefit are calculated each year on the bases mentioned above—that is to say, on the one hand the biometrie tables and on the other the data defining the insured population and its evolution. The statistics concerning persons in receipt of benefit are among the fullest and most exact compiled by social insurance institutions. They relate either to the contingents which in each year of operation (or in each financial year) joined the number of beneficiaries or left them, or to the number of persons in receipt of the various classes of benefit at the end of each year (or of each financial year). 12 . INTRODUCTION They may be recorded in various ways, according as the date chosen as the initial (or final) date for each class of benefit is: (1) that at which the conditions defining the materialisation of the risk are fulfilled (or cease to be fulfilled); (2) that of the decision to award benefit (or of the notification of cessation of the risk); (3) that of the first (or the last) payment made to the beneficiary. The monographs show examples of the use of all these various methods; and in some cases two different types of statistics may be found side by side in the same scheme, for the same benefits. II. — FINANCIAL ESTIMATES, BASES AND EXPERIENCE The second chapter of each monograph brings together the data which are immediately financial in character and therefore depend directly on the monetary unit. These data obviously relate to the fundamental factors of financial organisation: contributions, subsidies, benefits, and accumulated funds. They are considered here in turn, and for each of them an attempt is made to bring out its essential characteristics as necessitated by the nature and functions of social insurance, to show the significance of the calculations involved, and to set forth the bases adopted and experience gained in actual practice. Contributions In the compulsory (contributory) insurance schemes considered here, a large part of the financial resources, sometimes practically the whole, is derived from periodical payments, the cost of which is shared between insured persons and employers, as a rule in equal parts. These payments, which are given the name of contributions or may be regarded as equivalent to contributions, must satisfy certain conditions as to uniformity which are necessitated not by the actual financial mechanism but by the nature and purposes of the insurance scheme. The point is that social insurance must make no distinctions between workers that might tend to influence their employment. The rate of contribution must thus be independent of the insured person's age; in the schemes considered here it is also independent of occupation, except in a few cases. Further, it has been recognised as desirable for economic reasons 13 INTRODUCTION that the rate of contribution should remain unchanged from year to year, since the employer wishes to know in advance what his share will be in order to include it in his estimate of production costs. Nevertheless, while the rate of contributions ought not to be liable to constant and abrupt changes, it need not necessarily be invariable; it is considered permissible for it to rise at long intervals, for example every ten years. The various methods of determining contribution rates rest on one or other of the following three conceptions: flat rate of contribution for all insured persons of the same sex (i.e. contribution independent of wages) ; division of wages into classes, and flat rate of contribution within each class; rate of contribution equal to a fixed proportion of wages between certain limits. This is not the place to examine the various processes or to discuss their respective advantages and drawbacks *. It will be sufficient to note that as a rule the section dealing with contributions in the monographs discusses a certain number of related data such as: the sex and age distribution of the wages on which the calculation of contributions is based, and the distribution of the same wages according to their amount or the class in which the contribution is paid; the average number of contribution days or weeks per year; the number of " contributors "—that is, of insured persons who have paid at least one contribution during a specified period or have contributed at a given date; the number of " full contributors "—that is, the imaginary number of insured persons who, if they had contributed without interruption, would together have paid during the year in question the total sum actually derived from contributions; the average daily, weekly, monthly or yearly wage; the average daily, weekly, monthly or yearly contribution. The estimates of contribution income are obtained by two methods. The first takes as a starting-point the evolution of the insured population year by year and arrives at an evaluation of 1 Cf. INTERNATIONAL- LABOUR OFFICE: Compulsory Pension Studies and Reports, Series M, No. 10, 1933, pp. 450-467. Insurance, 14 INTRODUCTION the total annual income from contributions. The second involves a calculation of the probable present value 1 of the contributions expected in the future from all the insured persons or only from a fraction of their total number. The most usual system is to distinguish between (a) insured persons belonging to the scheme at a given date and (b) those entering after that date. For an annual amount equal to the monetary unit— that is to say, for an annual " unit " contribution—it is enough to take for each insured person aged x at the date of calculation the probable present' value of a temporary annuity equal in amount to unity, and to sum the results so obtained for all insured persons in the group considered. In order that this first result may be used to obtain the result corresponding to the absolute amounts of contributions, it is indispensable 1 The notion of probable present value may be illustrated with only slight recourse to mathematical language. To begin with, it should be remembered that in the case of capital bearing interest, if it is assumed that the interest is added as soon as earned to the capital and thus itself begins to bear interest —in other words in the case of capital at compound interest—the amount of the capital is no longer a constant but must be regarded as a quantity that varies with the date at which it is considered. Hence, when the calculations relate to large capital sums or to a period of several years—as is often the case in insurance—it is important to define not only the amount of the sum but the date at which it is to be paid. Its present value is defined as the amount which, if paid at once, could take the place, account being taken of the accumulation of interest at a given rate, of the payment of one or more sums of a given amount at one or more future dates. The compound interest formula immediately gives the present value A (o) at date t = 0 of a payment A {t) made at date t A(i) A <°> = trrj' = A(i> •v I i being the annual interest on a monetary unit and v the discount factor 1 + l) To arrive at the notion of probable present value, the Eulerian method may be used and a group taken of lx0 persons aged x0 years, to which no additions are made but which suffers withdrawals for various reasons. Let lx equal the number of persons who still belong to the group at age x. If a sum A («) is to be paid each time t h a t a person in the group reaches age x, the total of these claims may be regarded as equivalent to the payment at the initial date of as many times a certain amount A (x0) as there are persons in the initial group. The amount A (x0) is called the probable present value at the initial date of the payment A (x) and is obtained, account being taken of the deductions that have occurred in the group and the accumulation of interest, from the formula A (*o) lx0 v*° = A W lx "X If, instead of taking a single payment A (x) due at age x, a series of payments A (xi) is taken, due at ages xi respectively, the probable present value of these payments is defined in a similar manner. It is on probable present values of this kind that nearly all the actuarial calculations are based. INTRODUCTION 15 to combine the biometrie and demographic hypotheses already accepted with certain new hypotheses of an economic character. One of these relates to the average number of paid-up contributions, which cannot be estimated without taking into account the degree of employment and possibly the rate of sickness. The second, which applies when the contribution depends on wages, relates to the amount of wages, their variation with the insured persons' age, and their fluctuations, with changes in" economic and social conditions. The very important question of the choice of the rate of contribution is regularly left to the third chapter in all the monographs, for it is felt that it cannot be separated from the study of the financial system proper, owing both to its importance and to the technical character of the methods (calculation • of theoretical premium) which have had to be used in many cases. The statistics compiled by the insurance institutions may relate to all the data referred to above. They can thus provide figures for estimating the degree of employment and level of wages of the insured population. If the insurance scheme is wide enough in scope, the figures may thus provide valuable information—failing a better approximation—on the degree of employment and level of wages of the occupied population as a whole. Public Subsidies A separate section is devoted to a second source of income for most insurance schemes, namely the subsidies provided by the State or other public authorities. The need for financial participation by the public authorities and the part this plays necessarily enter into the examination of the mechanism by which financial equilibrium is established and are therefore discussed in the third chapter of each monograph x. Here it will be sufficient to note that, considered as a whole, the financial participation of public authorities and in particular of the State may be conceived under different aspects, ranging from one to the other of two extremes. At one extreme, for example, the State may be called upon to provide a full and direct guarantee of the financial equilibrium 1 In particular, it will be seen that the participation of the public authorities is usually connected with the burden assumed by the insurance scheme during the " transitional " period (see p. 23)—that is to say, its essential purpose is the paying off of the " initial liability " (see p. 30). 16 INTRODUCTION of the insurance scheme ; in this case, the national budget for each financial year must include the sums needed to bring the income of the insurance scheme to the same level as its expenditure. Preference is usually given, however, to the other extreme, based on the idea of self-sufficiency in social insurance, according to which the insurance budget is drawn up separately from the national budget, though this does not necessarily prevent the inclusion in the latter of subsidies, fixed in advance, for the benefit of the insurance scheme. Which of these two tendencies prevails will be determined by considerations that are not connected solely with social insurance but relate to the organisation of public finance and ultimately to the economic functions assigned to the State and other public authorities. However, in considering the financial problems of social insurance it is nearly always desirable to assume conditions of self-sufficiency—that is to say, to take each institution or each scheme as a separate accounting unit. It may also be noted that the financial participation of the State sometimes takes forms that do not appear at all in the accounts of the compulsory insurance scheme; for example, the State may assume the cost. which need not be small, of a system of non-contributory benefits to buttress the contributory scheme. The amount of the financial participation of the State or other public authorities may vary so considerably from one scheme to another that it escapes all argument of a general character. At the most one may note a constant tendency to avoid large-scale occasional subsidies and to prefer regular payments that remain practically, if not altogether, constant in amount. Chapter II of each monograph reviews the data and factors which serve to define and evaluate the income of the insurance scheme derived from public subsidies. The participation of the public authorities may take a variety of forms \ the commonest of which are the following: payment of a lump sum; allocation of the proceeds of certain taxes or dues; temporary or exceptional subsidies; payment of a contribution or a fraction of the contribution; payment of a fraction of total benefits or the whole of certain benefits; payment of a supplement to the insurance benefits: the individual amount of the supplement may be uniform, but it may also 1 Gf. Compulsory Pension Insurance, pp. 473-482. INTRODUCTION 17 depend on the time spent in insurance and the amount of contributions paid; payment of certain expenses (administrative expenses, etc.); guarantee with respect to any deficit that may occur in a particular financial year; guarantee with respect to the " uncovered actuarial liability " 1 ; guarantee limited to an amount fixed in advance. When the amount of the subsidy depends either on the number and amount of contributions or on the number and amount of benefits, the estimates concerning contributions or benefits immediately lead to an estimate of the charge assumed by the public authorities, and the statistics concerning subsidies may be incorporated with the figures obtained from the actual payment of contributions or benefits as the case may be. • Benefits The benefits provided by a pension insurance scheme consist in the main of: temporary or permanent pensions for invalidity; treatment for the prevention and cure of invalidity; old-age pensions (or the capital sum representing the cover for such pensions); lump sums at death and temporary or permanent pensions for widows (or widowers), orphans, and in some cases other surviving dependants. All or part of the payments made in respect of old-age insurance may be reserved for the insured persons' surviving dependants. In some cases an allowance is added to the amount of the benefit when the beneficiary has one or more dependent children, until they reach the age at which their education is deemed to be completed. The various rules which have been applied for defining the conditions of award or withdrawal of benefits and calculating their amount are systematically studied in the volume published by the International Labour Office previously mentioned 2, which brings out in particular their economic effects and social significance. 1 2 This expression will be defined later, see p. 30. Compulsory Pension Insurance, pp. 168-226. 2 18 INTRODUCTION From the point of view of financial organisation alone, the components of benefits, apart from certain supplementary or optional benefits the amount of which is not determined in advance, may be divided into two groups: (1) Components whose amount is fixed and is consequently uniform for a group of insured persons (in particular the basic amounts). (2) Components calculated with reference to the contributions paid on the insured person's behalf or to his wages or to the contribution period, or to a combination of these data. This group may in turn be subdivided into two. The first sub-group comprises benefit components corresponding to the contributions paid on behalf of the insured person in virtue of the actuarial formulae customarily serving as the technical basis for individual life insurance or invalidity insurance policies; the calculation of the amount of the benefit is then obtained by equating the probable present value of the benefit component in question to the probable present value of the fraction of the contribution devoted to covering that component. In the second sub-group the calculation is based on a different principle, and as a rule the benefit component is computed by means of a linear equation, the terms of which include both its amount and the data on which it depends. It should be noted that social insurance contributions and benefits do not as a rule correspond to each other in the same way as premiums and annuities under individual life insurance or invalidity insurance policies. In other words, the relations between income and expenditure which arise from individual life insurance policies do not constitute a sufficient mechanism to enable social insurance to achieve its proper ends. A social insurance scheme cannot in fact fully carry out its purpose unless it is able to grant, in the event of the materialisation of one of the risks it covers, benefits at such a level that they can guarantee the " social security " of the recipients. Moreover, it is essential to note that there must be no delay in fulfilling this purpose. The financial problems would appear in an altogether different light if only those workers who had been insured since the beginning of their working life could claim benefits. This distinction will be shown later to play a fundamental part in the study of financial systems 1 . 1 See below, p. 23. INTRODUCTION 19 The evolution of the cost of benefits depends in the first place on the number of beneficiaries and the method of calculating each benefit. The total annual expenditure nearly always rises during the first years of operation of the scheme. At the beginning it is usually nil, owing to the qualifying period that must be completed before a claim to benefit can be made. After that it remains fairly small during a certain period, even though the maximum rate of benefit may be applied at once. The reason is that during the first year after the completion of the qualifying period, benefits are paid only to a single annual contingent (though this may be unusually large); in the second year a further contingent of beneficiaries is added to the remainder of the first, and so on. By this process of accumulation the annual cost of benefits rises from year to year, whatever the effects of the various factors that can make their influence felt. It may therefore be concluded that for any particular insurance scheme taken from its inception the expenditure corresponding to benefits is characterised mainly by the level about which the annual total tends to stabilise itself and by the rapidity of the rate of increase during the first decades of working. As in the case of contributions, the estimates are obtained by two quite different methods of calculation. The first starts with a preliminary estimate (made, as already indicated, on the basis of the biometrie tables and the composition of the insured population) of the number of persons in receipt each year of the various benefit components. The numbers so calculated are multiplied by the average value of the benefit component in question. This average value is obtained either by the formula which is prescribed by legislation for determining the amount of the benefit component, or by data derived from the biometrie tables and the composition of the insured population, or by an enquiry or partial return made during, the actual operation of the scheme. This method leads to an annual estimate of the cost of each benefit component. The second method consists essentially in the calculation of:: (1) the probable present value of acquired rights, that is to say,. of the benefits still due to a beneficiary aged x; (2) the probable present value of rights in course of acquisition, that is to say, of the benefits to be paid, in the event of materialisation of the risk,, to an insured person aged x or his dependants. The calculation of these present values is by no means without theoretical interest, since the classic actuarial formulae used for the purpose have to be 20 INTRODUCTION specially adapted, on the one hand, in order to turn the available biometrie data to the best possible account, and on the other, to find a solution for the special problems arising out of the technique of social insurance. An account is given in each monograph of the formulae used for obtaining the probable present values of the principal benefit components on the basis of a unit amount; with these fundamental formulae there is no difficulty in deducing the probable present values of all the benefits. As in the case of contributions, the final results are obtained by summing the present values for the whole group of insured persons, a distinction being made, if necessary, between the initial insured population and the persons joining the scheme after its coming into force. During the working of an insurance scheme the amount of a particular benefit is determined either, as in the case of a pension or a capital sum resulting from individual payments, by recourse to schedules similar to those used for individual life insurance or invalidity insurance policies, or by recourse to à simple arithmetical calculation when as already indicated the calculation is based upon a linear equation 1. The experience of the scheme as regards each benefit or benefit component relates essentially to its average value and the total annual expenditure. In this connection two remarks made above with regard to the statistics of beneficiaries may be repeated: the observations may relate either to pensions whose payment begins or ends within a given period or to pensions in course of payment at a given date; the figures arrived at differ with the definition adopted for the dates of commencement and cessation of benefits. Other Income and Other Expenses For several schemes there is occasion to consider other sources of income and other items of expenditure, including the following: (1) interest on accumulated funds, which is taken into account separately in cases where the evolution of the different items of income and expenditure are examined year by year; (2) initial and exceptional endowments; 1 See above, p. 18. INTRODUCTION 21 (3) administrative expenses which it is not always possible to estimate exactly; (4) special kinds of benefit (benefits in kind, cash grants, etc.). Another item of income and of expenditure results from the provisions adopted for the maintenance of the rights of insured persons who transfer from one insurance scheme to another. The transfer may take place within a country or, on the contrary, be the effect of migration. It raises a very important but also very difficult problem, the solution of which depends on the financial systems of the schemes concerned. This study is not the place for examining the technique on which the maintenance of rights of workers who insure successively with several schemes may be based 1. All that is given is a. few brief indications, devoted solely to the effects on the financial equilibrium of the schemes considered of the entrance and withdrawal of insured persons coming from or going to other social insurance schemes. Accumulated Funds When an insurance scheme is put into operation, it has no capital, except in a few rare cases. It has been seen that in general the rates of contribution are at once fixed at their normal level while the cost of benefits, which to begin with is nil, gradually rises. This being so, surpluses will automatically accumulate from the date when the scheme is put into operation and during a certain number of years. The accumulation of funds may thus be regarded as a direct consequence of the rules fixing the rates of contribution on the one hand and the conditions of award and amount of benefits on the other. The accumulated funds are in the first place the protective reserves that an insurance scheme needs as much as any other undertaking. They may comprise, in addition, either the whole 1 The maintenance of rights in course of acquisition and acquired rights under invalidity, old-age and widows' and orphans' insurance on behalf of workers who transfer their residence from one country to another is the subject of international Convention No. 48, adopted by the International Labour Conference in 1935 at its Nineteenth Session. The Convention came into force on 10 August 1938. A systematic study of the question was made by the International Labour Office in two preliminary reports: Maintenance of the Rights in Course of Acquisition and the Acquired Rights of Migrant Workers under Invalidity, Old-Age and Widows' and Orphans' Insurance, International Labour Conference, Eighteenth Session, Report IV, 1934; Maintenance of Rights in Course of Acquisition and Acquired Rights under Invalidity, Old-Age and Widows' and, Orphans' Insurance on behalf of Workers who Transfer their Residence from one Country to Another, International Labour Conference, Nineteenth Session, Report I, 1935. 22 INTRODUCTION or a part of the actuarial liability 1 . The part played by accumulated funds in the maintenance of financial equilibrium 2 and the questions arising out of their investment 3 are examined later. III. — FINANCIAL SYSTEM In each of the monographs composing this volume the first two chapters are devoted to a description of the factors and data used in actuarial technique or statistics which together form the fundamental bases of the financial organisation of the insurance scheme. The third chapter discusses, under the heading financial sijstem, this financial organisation itself, with special attention to its essential function, the realisation and maintenance of financial equilibrium. It is thus necessary, for each of the schemes considered, to bring out one or more conceptions of equilibrium between resources and charges and to examine the necessary and sufficient conditions for establishing such equilibrium and keeping it stable. In studying the financial system of insurance schemes, particular and constant attention is given to the problem of financial equilibrium. Accordingly, any researches made with a view to estimating the economic or social effects of the working of a scheme as a whole or of a particular provision are left out of account, even though they may be definitely technical in character 4. Only in a few cases is it possible to distinguish between the three risks, invalidity, old age, and death, for in most of the schemes studied financial equilibrium is not established or even considered for each risk separately, but only for all three or for two of them together. The presentation of the technical problems arising directly out of the establishment and maintenance of financial equilibrium differs according as they are met with during the preparatory work for the introduction of a new insurance scheme or during the working of an existing scheme in connection with a proposed reform, and according as they relate to operations connected with the working of the scheme or to its actuarial control. These various alternatives are discussed in turn. Before any study of financial equilibrium can be made, it is indispensable to note t h a t a precise and full statement of the 1 2 3 4 The definition of this term is given below, p. 26. See below, p. 31. See below, p. 37. It is not considered that the distribution of charges over the various generations calls for a general discussion, since it depends essentially on the financial system, of which it is an immediate consequence. INTRODUCTION 23 problem to be solved necessarily includes a certain number of facts on which the acceptable solutions depend. Thus before looking for a solution, it is necessary to know whether the public authorities participate financially in the scheme, and if so to what extent; further, whether the financial administration of the scheme is centralised or, on the contrary, divided among several large or small institutions; and lastly, what the functions of the scheme are with regard to persons insured during the transitional period. In the evolution of an insurance scheme, a distinction must as a rule be drawn between the initial period, known as the transitional period, and the subsequent period, known as the normal period. From the theoretical point of view the normal period is reached when a sufficient number of years have elapsed after the scheme has been put into operation for it to include only persons who could have belonged to it from the age fixed as the lower limit for admission to insurance. Until that date, a certain number of workers completing a normal working life will have been obliged to enter the scheme when older than that age limit. It is clear that the problem of financial equilibrium is altogether different according as it is considered in relation to the one or the other of these two periods. Obviously it is in the normal period that the simplest and in every respect the most satisfactory methods can be adopted. In actual fact, however, the only important problem for social insurance is found to be that of the transitional period. For there is no social insurance scheme in existence which has operated without modification long enough to include only persons (among workers having had a normal working life) who have been subject to the same legislation since they were at the lowest age limit for entering insurance. A social insurance scheme cannot remain unchanged in the midst of the variations that economic and social conditions undergo. It therefore has periodically to be reformed. The financial problems that arise in connection with each of these reforms can never be treated fully with reference to the normal period alone. The study of financial equilibrium must therefore always be undertaken with reference to a scheme that is still in the transitional period. Hence it is indispensable to examine the provisions adopted on behalf of the insured persons who were unable to join the scheme at the lower age limit, and in particular their period of employment before the scheme was put into operation, to the extent that this period is taken into account for the purpose of establishing a claim to benefit or of increasing the amount of benefit. 24 INTRODUCTION The necessity of founding pension insurance schemes on a technical basis was- evident from the outset. It is true that certain benefit funds tried to work on purely empirical lines, so that the amount or even the award of benefits depended on the financial situation of the moment. But the results obtained were unsatisfactory, even though as a rule the only risk involved—that of sickness—was one for the near future and of short duration. When it was proposed to cover the risks of invalidity, old age and death, account had to be taken of obligations to be met at a comparatively remote date, which meant that a financial system based on technical calculations at once became indispensable. In the search for a suitable technique for social insurance, several tendencies have been displayed. One idea has been to employ the methods used in private insurance for the provision of life annuities or invalidity pensions; in this case, the system known as that of individual accumulation is adopted, contributions paid on behalf of each insured pei son being entered into an individual account for the puipose of accumulating the sum needed for the payment of benefit, account being taken of compound interest and withdrawals from the scheme owing to death or invalidity. A second method' has been to have recourse to a system of collective accumulation such as had previously been employed by pension funds; here the cost of benefit is covered by requiring all insured persons to pay the same average premium. In yet other cases recourse has been had to a so-called assessment system: the contributions paid during a year or other specified period cover either the benefits paid during the year or period (assessment proper) or the capital corresponding to the pensions awarded during the year or period (assessment of capital cover). In most cases, however, recourse has been had to a mixed financial system based, from the technical standpoint, on several methods. As a matter of fact, the financial systems on which the social insurance schemes covering the risks of invalidity, old age and death—and in particular the schemes described in this volume— are actually based show at once on more detailed investigation that each of them constitutes a highly complex whole, subject to numerous modifications. The study of financial systems is thus a somewhat difficult one; in particular it is impossible to classify them in clearly defined groups 1 or to distinguish between them 1 Several classifications are conceivable according to various criteria, such as the ratio of the yield from contributions to the cost of benefits in each year, the amount of accumulated funds, etc.- INTRODUCTION 25 merely by nomenclature. No doubt the expressions " accumulation ", " assessment ", etc., are classical and for this reason cannot be left out of account, but it must be noted that they are not sufficient in themselves to describe a financial system. In the course of a discussion on any one insurance scheme, these expressions may explicitly or implicitly be given a meaning on which all are agreed. But when the discussion extends from one scheme to another, and even more from one country to another, the significance given to the same expression may vary considerably. It will be seen in fact that in the financial organisation of a single scheme several of these terms are used, being applied to the various technical mechanisms entering into the scheme. In point of fact the financial system of a social insurance scheme covering the risks of invalidity, old age and death involves, from the actuarial point of view, a number of calculations based on different methods. This is not the place for a systematic examination of these methods ; it is considered preferable to abstract from the many conceivable financial systems three patterns, and, by way of introduction to this study, to describe each of the three. Although in practice the whole structure of the financial organisation of a social insurance scheme is never built up on one such pattern alone, it is hoped that this procedure will make the mechanism of the principal methods of calculation employed for the actuarial work as clear as possible, since they are described with reference to the actual conditions in which they have been used. The first schematic financial system considered is that in which financial equilibrium is established individually for each insured person. It is called here for short the " individual accounts pattern ". Its description is followed by that of two other schematic financial systems, in which financial equilibrium is established collectively for all insured persons together, or for a group of insured persons ; they are called here the " average premium pattern " and the " annual estimates pattern ". For each of these patterns, an account is given of the principle on which financial equilibrium is based, the mechanism by which it is established, and the operations carried out in the actual working of the scheme, in particular those for the technical control of the financial situation. Individual Accounts Pattern The essential principle on which this pattern is based rests on an individual conception of financial equilibrium: at the date 26 INTRODUCTION when a worker enters insurance, the liabilities x and expectations 2 of the scheme with respect to him are equivalent in the actuarial sense, or in other words their probable present values are equal. From this equality it at once follows that there is a very close connection between the contributions paid for each insured personand the amount of the benefits that he may be granted; benefits are related to contributions in much the same way as annuities or capital sums insured by private insurance companies are related to the premiums paid under individual policies. In fact, the benefit amounts are determined according to schedules similar to those which serve as the technical basis for individual life insurance or invalidity insurance policies. It has already been seen 3 that benefits cannot depend on contributions in this way if the scheme is to fulfil its function completely and in particular provide adequate protection for insured persons during the transitional period. It follows at once that the individual accounts pattern is not in itself sufficient for the financial system of a social insurance scheme. Let us consider the working of this pattern more closely. The contributions paid in the name of each insured person are registered (in an individual account) with a reference to his age at each payment, and the amount of benefits to be granted if the risk materialises is calculated directly from these entries. As a rule the payment of a constant contribution is effected at regular intervals for each insured person. At any age x + t after the age x at which a person enters insurance the probable present value of the expectations of the insurance institution is usually, for each risk and each insured- person, lower than the probable present value of its corresponding liabilities. The difference between the probable present value of the liabilities of the insurance scheme with regard to all the insured persons and the probable present value of all its expectations is called the actuarial reserve or premium reserve or again the actuarial liability4. This " prospective " definition of the actuarial liability is equivalent to the 1 2 3 4 These comprise all or part of the benefits and the administration expenses. That is, the contributions and, possibly, public subsidies. See above, p. 18. It will be seen that the actuarial reserve appears on the liabilities side of the balance-sheet, whereas other reserves, such as the contingencies reserve, appear on the assets side. The expression " actuarial liability " removes all risk of confusion. Cf. H. GA.LBR.UN: De l'organisation des caisses de retraites (Gauthier-Villars, Paris, 1939), p. 12; and S. DUMAS: Répartition ou capitalisation dans l'assurance des personnes (Librairie de l'Université, Lausanne, 1937), p. 33. 27 INTRODUCTION " retrospective " definition obtained by taking the difference between the probable present values of liabilities and expectations relating to the period between the age of admission x and the subsequent age x + t. The individual accounts pattern calls for a process of technical accounting by means of which the results of each financial year can be analysed at first sight 1 . At the end of each financial year, nearly always at 31 December, a valuation is made. The value of the actuarial liability at t h a t date is calculated; the knowledge of this liability makes it possible to analyse the results for the financial year in question. Within the " profit and loss " account, several separate accounts are opened, for each of which the probable value of the balance is zero; these accounts are defined in such a way t h a t the values of their balances bring out separately the financial effects of variations in mortality or invalidity rates or in the yield of accumulated funds 2 . When the balances in these different accounts are known, the balance-sheet at the date of the valuation can be drawn up, showing essentially on the assets side an estimated value of the investments and on the liabilities side the amount of the actuarial liability as calculated. With a financial system of this pattern, a number of operations calling for actuarial technique are required, chief among which are establishment of the benefits schedule, organisation of the technical accounting, calculation of the actuarial liability, valuation of the investments, calculation of the rates of yield, selection of the rate of interest serving as a basis for calculation (the actuarial rate), organisation of the statistical work and comparison of its results with the biometrie tables adopted as a basis. Average Premium Pattern Here, financial equilibrium is again defined by the relation between the probable present values of the liabilities and expectations of the scheme; but the liabilities and expectations are no longer considered for each insured person separately, b u t only for the whole insured group or for certain subdivisions. It is clear that, corresponding to each subdivision, there will be a different 1 As proof that such accounts, while respecting the general rules for all accounting, are of a special nature owing to their very purpose, it is sufficient to note that the actuarial liability is as a rule much the largest item on the liabilities side of the balance-sheet (it often exceeds three-quarters of the total). 2 For a detailed study of this technical accounting, cf. H. GALBRUN, op. cit., pp. 14-31. 28 INTRODUCTION definition of financial equilibrium. I t will be Sufficient here t o recall the divisions into financially independent groups most usually employed. Sometimes t h e liabilities and expectations are considered for a limited ' period only, a t t h e end of which t h e problem of equilibrium has t o come up for reconsideration either by t h e same method or by another. Sometimes t h e insured persons are divided into " generations ", or groups consisting of persons born in the same years; an important special case, described in more detail later, is t h a t in which a distinction is made between the insured membership on a particular date and the contingents t h a t enter insurance in each of t h e following years. Finally, when insured persons are divided into classes according t o the amount of their wages, financial equilibrium m a y be considered separately for each class. The pattern considered here is based mainly on an actuarial calculation for determining t h e value of an average premiumx —that is to say, of the annual premium which satisfies the condition of financial equilibrium for a n insured group assumed t o be financially independent, either indefinitely or over a specified period. The average premiums may b e calculated for different groups and for different periods. If all insured persons, present and future, are taken together, a general average premium is obtained. These theoretical results can serve as a guide for selecting the rates of contribution. In fact, with such a pattern, the rate of contribution actually applied is fixed a t a value approaching the figure obtained from t h e calculation of t h e average premium. It may happen t h a t reference is also made t o t h e individual premium t h a t t h e insured person would have had t o pay under an individual policy in order t o acquire t h e same rights as those guaranteed by t h e social insurance scheme; sometimes it is held t o be indispensable that t h e rate of contribution should not exceed this premium, and sometimes it is considered sufficient t h a t the difference between the two should not be great. 1 The calculation of average premiums has been the subject of many actuarial studies. There is no room here to enumerate them all; it will be enough to mention three standard works, which may be said to have laid the foundation on which all subsequent study of the question has been or must necessarily be based: J. KAAN: "Die Finanzsysteme in der öffentlichen und in der privaten Versicherung " in Mitteilungen des österreichisch-ungarischen Privat-Versicherungsanstalten, 1909 (Vienna). Verbandes der L. VON BORTKIEWICZ : " Die Deckungsmethoden der Sozialversicherung " in Report of the Sixth Congress of Actuaries (Vienna, 1909). F. CANTELLI: " S u i metodi di calcolo nelle assicurazioni sociali", in Le Assicurazioni Sociali, Voi. I I , No. 2 (Rome, 1926). INTRODUCTION 29 The calculation of average premiums is combined, in the preparatory work undertaken before the introduction of the social insurance scheme, with a preliminary valuation, which consists, in fact, in comparing the probable present values 1 of the financial resources and charges of the scheme. A separate valuation is made for each financially independent group, and includes: on the assets side, the probable present values of contributions and of State subsidies; on the liabilities side, the probable present values of benefits and of administrative expenses. It may happen t h a t the State subsidies do not appear in the preliminary valuation either because they are incorporated directly with contributions or because they do not enter into the financial mechanism proper—as, for instance, when their object is the payment of a supplementary benefit. For the calculation of the probable present values of liabilities and expectations, it becomes necessary to take account of insured persons who leave the insurance scheme for reasons other than those covered by the biometrie tables. It has been seen that it is difficult to estimate the movement of withdrawals in advance. In some cases it has been considered sufficient to fix a maximum limit for its financial consequences, and in others it has been incorporated in the calculation of the general average premium by recourse to certain hypotheses 2. The control of the financial evolution involves mainly the establishment of an accounting balance-sheet each year and an actuarial balance-sheet at intervals of several years, as a rule two, three, four or five. The actuarial balance-sheet resembles the preliminary valuation; but the latter includes an estimated value of investments in exceptional cases only, while the former always includes this item among its assets. The actuarial balance-sheet takes into account a certain number of new data brought out by the statistics of the working of the scheme, and also shows the probable present value of acquired rights. The very important questions of the technical reserve and the amount of accumulated funds in a schematic financial system of this pattern may now be considered. 1 These are calculated on the basis of a single rate of interest called the actuarial rate. 3 One of the questions on the agenda of the Twelfth International Congress of Actuaries is that of abnormal withdrawals and their influence on the calculation of premiums and actuarial reserves. 30 INTRODUCTION The difference at any date between the probable present value of the liabilities and expectations of the scheme in respect of insured persons gives, by means of a prospective definition 1 , the amount of the collective technical reserve. If the group for which the average premium is calculated includes only persons belonging to the scheme at the date of calculation, the collective technical reserve coincides with the actuarial liability as defined above in the section dealing with the individual accounts pattern. But it is lower than that reserve if, in virtue of the lasting and compulsory character of insurance 2 , the average premium has been calculated for a group comprising both present and future insured persons. In order to make the position clear, we may consider the working of the scheme from its inception and assume t h a t the financial system is based on a general average premium. The actuarial liability calculated for the initial membership could be covered at the outset only by a large initial endowment; as a rule, the greater part, if not all, of this actuarial liability remains uncovered, and constitutes the initial liability. The contingent of insured persons entering in any particular year normally comprises a large proportion of the younger generation, and the corresponding premium would therefore be lower than the general average premium. Consequently, for this contingent taken separately, the probable present value of expectation exceeds that of liabilities, and the operation of insurance begins not with a liability, as in the case of the initial membership, but with an asset. An insurance scheme a t its outset may roughly be regarded as the amalgamation of (1) a scheme limited to the initial membership, and (2) a series of schemes limited respectively to the first, second, etc., annual contingents. Each of these schemes applies to a closed group. The first shows an initial liability, while each of the others begins with an asset, and financial equilibrium is established in such a way t h a t the sum of the assets balances the initial liability. By definition, the general average premium is higher than the premium corresponding to t h e contingent entering insurance each year, but lower than t h a t which should be applied to the initial 1 The collective technical reserve may also be defined retrospectively; the two definitions lead to the same result if, when the average premium is put into operation, the group considered is financially independent. 2 If the scheme is administered by several financially independent institutions, the compulsory character of insurance applies to each separate institution, so that the insured community may in each case be regarded as a group which is necessarily renewed. INTRODUCTION 31 membership if it were treated as a closed group a . It immediately follows that the general average premium leads to a smaller accumulation of funds than in the case of the average premium calculated for the initial membership. In other words, the collective technical reserve is lower than the actuarial liability. This leads to a distinction between two different conceptions of the function of the funds accumulated as technical reserves. According to one conception, the object is to safeguard the theoretical possibility of liquidating all the operations undertaken by the insurance institution: the probable present value of the liabilities may not exceed the probable present value of the expectations plus the total amount of the accumulated funds. It is admissible that from the inception of the scheme the payment of a surcharge on the premium should be required for the purpose of constituting a reserve equal to the actuarial liability. According to the other conception, on the contrary, it is considered that, owing to the permanence of social insurance and the compulsion to insure, there is no occasion to contemplate the liquidation of all the liabilities and expectations at a particular date. The accumulated funds ought never to reach the figure for the amount of the actuarial liability, but the income they produce is nevertheless sufficient to fulfil their function of maintaining financial equilibrium, in combination with the other fundamental factors of the scheme. Both these conceptions may be employed in the technique of social insurance, but it may be remarked that the amount of the accumulated funds, while always remaining—as already seen—lower than the actuarial liability, may reach a variety of values. For example, to take a scheme in which the cost of benefits, starting at nil, rises gradually up to a maximum, at which it becomes stabilised. When the general average premium is introduced at the inception of the scheme, funds are accumulated as long as the cost of. benefits is lower than the income from contributions in each year. It will at once be seen that the accumulation of funds will be smaller during the period of application of the general average premium if that premium is adopted only after a certain time has elapsed since the inception of the scheme. The longer this time is, the smaller will the accumulation of funds be; and in the extreme case, in which the calculation 1 To take this premium as the rate of contribution is implicitly to assume that the age distribution of the persons entering insurance each year is the same as that of the initial membership. In compulsory insurance it is certain that the age distribution of the annual contingents is more favourable than that of the initial membership. 32 INTRODUCTION and introduction of the general average premium do not take place before the cost of benefits has reached its maximum, it will be nil. It may therefore be concluded that the amount of the funds accumulated in consequence of the adoption of a general average premium depends in the main on the increase in the cost of benefits after the general average premium has been put into operation. "With the average premium pattern, the principal task of actuarial technique is to calculate the average premium, make the preliminary valuation, and prepare the actuarial balance-sheets. In order that these balance-sheets may be drawn up with all possible precision and exactitude, the insurance institution usually tries to compile the statistics of working of the scheme on the lines indicated by the actuarial services. The actuarial balance-sheets and the technical work for which they call allow not only the control of the financial evolution of the scheme, but also a critical analysis of the sources of profit and loss. Consequently, they may lead their authors to suggest measures likely to restore a sound financial situation or to extend the social utility of the scheme. In actual fact, the conclusions drawn from the actuarial balance-sheets have very often played a decisive part in the reforms made in social insurance legislation. Annual Estimates Pattern The annual estimates pattern, like the average premium pattern, rests on a collective conception of financial equilibrium. The total resources are made at least equal to the total charges either for each financial year or for a period comprising several consecutive years. If equality of the two totals is regularly achieved, the obvious result is equality in the probable present values that would have been established with the average premium pattern. In addition, it affords a guarantee that the scheme will at any time be able to meet its financial obligations. The definition shows that this pattern must be based on a table giving for each financial year an estimate of probable resources against one of probable charges. This annual estimate table may be compiled either for the whole of the insurance scheme or only for a part—a special fund whose situation is considered separately. As a rule it covers only a certain number of consecutive financial years, and consequently does not fully solve the problem of financial INTRODUCTION 33 equilibrium. It may happen in some cases t h a t , by taking other considerations into account, it becomes possible by affirm t h a t from the last date of the period onward, financial equilibrium will be easy, or at least comparatively easy, to establish. In the other cases, the conclusions to be drawn from this table must be combined with a comparison of the probable present value of liabilities in respect of an unlimited period with t h a t of the corresponding expectations. This comparison in effect is simply an actuarial balance-sheet (or a preliminary valuation) identical with those required by the average premium pattern. It may be made, moreover, for any one of the years covered by the annual estimates table x. This being the principle on which the annual estimates pattern rests, it should be noted t h a t it is not incompatible with the accumulation of reserves, whether temporarily or even permanently. It may happen that during a certain number of years resources exceed charges and funds accumulate, and t h a t during the following years the contrary takes place, and the accumulated funds are gradually absorbed in order to meet the annual deficits. In other cases, equilibrium is established, during a particular financial year or other period, between financial resources and the capital sum representing cover for the pensions awarded during the year or period in question, plus the cost of benefits other than pensions and of administration. In t h a t case the system involves an accumulation of funds to an amount representing the probable present value of acquired rights; in other words, the acquired rights reserve is actually constituted. Sometimes, instead of providing for equality between total resources and total charges, it is considered sufficient to take only the resources and charges for a fund separate from the rest of the insurance scheme. As already mentioned, public subsidies are included in resources unless they can be distinguished from the financial system proper. If, when an insurance scheme is being drawn up, this third pattern is used, it follows from what has been said above t h a t an initial annual estimates table must be made, and at the same time, in most cases, a preliminary valuation. The control of the financial situation during the working of the scheme will require, in addition to an accounting balance : sheet, the following operations : the initial annual estimates table must be reviewed periodically with reference to the recently compiled statistics, and must at the 1 The annual estimates table and the calculation of the probable present values are based on a single interest rate, which is called the actuarial rate. 3 34 INTRODUCTION same time be extended by a certain number of years; periodically prepared balance-sheets must take the place of the preliminary valuation. In many cases an annual estimates table and an actuarial balance-sheet are drawn up at the same time at regular intervals. An examination of the insurance schemes studied in this volume will show that the financial system of each is based mainly on a combination of the principles and methods brought out by the above description of three 'typical patterns. The conceivable systems are infinite in number, and it is clear that the financial results of an insurance scheme depend not only on the combination of technical methods which form its financial system but on the numerical values adopted for the basic data. Different results may be obtained by the use of the same methods and, conversely, different methods may lead to the same results. It would therefore be meaningless to make a comparison of financial systems without reference to the circumstances and conditions that led to their adoption or maintenance. The comparison can be stated as a well-defined problem only when the adoption of certain bases and the choice of certain numerical values are taken as postulates and when the surrounding economic and social conditions and the results which it is intended to achieve are known at least approximately. There are thus as many problems as there are admissible conditions; a number of them have been treated in purely theoretical works or in relation to the factors of a particular insurance scheme. The financial organisation of each scheme raises a special problem, which differs at least in some subsidiary aspects from all those that have been solved in the past. Further, it is not difficult to realise that two different financial systems may produce the same results when certain conditions are fulfilled. From the purely technical point of view the following may be deemed to be essential qualities of the financial system: easy and reliable control of the financial situation and its evolution; simple financial organisation; low cost of the administrative operations involved by its working. To conclude this brief analysis of financial systems in social insurance, an attempt may now be made to bring out the nature and scope of the part played by the actuary in preparing a plan for the introduction or the reform of a social insurance scheme. INTRODUCTION 35 The actuary's work may be divided into two stages, though they cannot always be distinguished clearly. In the first place, he examines the conditions to be fulfilled by contributions, subsidies, benefits, and the accumulation of funds, with reference on the one hand to the special aims and characteristics of social insurance andón the other to data that do not belong exclusively to insurance. He must take into account a host of financial, economic, social, and even political considerations and, in particular, the conditions in which accumulated funds may be invested1, and he must respect the rules adopted in regard to public finance. The numerical values of the basic data are selected as judiciously as possible, but it may also be necessary to consider their stability, for example, as regards the level of wages and the purchasing power of benefits. In the second stage of his work, the actuary takes the conditions and data so defined as part of the terms of the problem to be solved. With these premises he tries to discover a mechanism suitable to serve as a basis for the financial organisation. As a rule recourse is had to an appropriate combination of the classic technical methods. Lastly, this combination must be adapted to the numerical data peculiar to the insurance scheme which it is pro^ posed to introduce or reform—that is to say, numerical values must be calculated for certain basic factors as a function of the values adopted for the rest. This brief outline cannot claim to be a survey of all the many and various tasks to be carried out by the actuary 2, but it brings out the complexity of his main function. In that connection, two further remarks may be made, one of them in order to make the significance of the actuarial calculations clearer and the other to show the position which the actuary is nearly always led to adopt. The actuarial calculations call for a number of hypotheses, some of which necessarily relate to the distant future; the estimates to which they lead may thus ultimately prove at variance with the facts. These estimates must therefore be regarded, not as forecasts, but as the best indications that can be obtained in the existing uncertainty as to the evolution not only of the insurance scheme but of the economic and social conditions of the country as a whole. The trustworthiness of these estimates increases if a 1 2 These considerations are dealt with below. See pp. 37-41. In particular, the choice of the basic rate of interest, the calculation of the rate of yield on invested funds, the valuation of investments for the balance-sheet, and the organisation of statistics raise actuarial problems which are distinguished from the framing of the financial system itself; they are discussed later. 36 INTRODUCTION maximum limit for the probable error is calculated, or if several successive figures are given, each of them more approximate than the preceding one but depending on a larger number of hypotheses. On the other hand, it is often possible and therefore expedient to calculate a lower or higher limit for the desired result by a rough approximation, calling only for a small number of hypotheses. From this point of view the best financial system is not that which is based on the most successful estimates but that which is sufficiently flexible to allow the financial organisation to be adjusted, without upsetting its structure, to any transformation of economic and social conditions. The second remark to be made is intended to bring out the position that the actuary must nearly always adopt in tackling his part of the work of preparing or reforming the financial organisation of a social insurance scheme. The conditions to be fulfilled by the fundamental factors of the financial organisation are not all equally absolute; as a rule it is impossible to realise all of them at once. Take, for example, the case of an insurance scheme about to be put into operation. It appears desirable that the following conditions should be met: claims to substantial benefits should be allowed without delay or after only a brief delay, contribution rates should never reach too high a level, and yet they should not be too low during the first period of operation; the participation of the State should not be too burdensome; the accumulation of reserves should be limited to the minimum. No solution can satisfy all these requirements at once. If it approaches some of them, it will inevitably depart from the others. The actuary is therefore nearly always led either to propose a compromise not deviating too much from any of the ends in view, or to indicate several possible solutions, mentioning their respective advantages and drawbacks and leaving it to the lawgiver' to choose which he prefers. IV. — FINANCIAL ADMINISTRATION The last chapter of each monograph in this volume deals with. the problems arising out of the investment of accumulated funds and gives a few brief indications concerning actuarial control, accounting operations, and the collection and compilation of statistics. INTRODUCTION 37 Investment of Accumulated Funds At the beginning of the working of a pension insurance scheme some time passes, as a rule several years, before all the income is absorbed by the expenditure. The result is an accumulation of funds. These funds constitute on the one hand the technical reserves and on the other the contingencies, compensation, temporary and special reserves. It has been seen that the amount that the total technical reserve may reach and the rate at which they are accumulated are determined by the financial system. The size of the other reserves differs considerably from one insurance scheme to another. The technical reserves, owing to the part they play in the financial system, must necessarily bear interest. As a rule all the reserves are invested together. The total constitutes the mass of accumulated funds, and this mass is invested according to the principles, rules and methods which will now be analysed. No account is here taken of the short-term investment of working capital, consideration being given only to investments proper made for a medium or long term. In the foregoing pages it is implicitly assumed that the questions arising out of the investment of social insurance funds have been solved 1. In particular it is assumed that the technical reserves bear interest at a rate at least equal to the actuarial rate and that no loss can be suffered on the amount of the invested capital. The same questions bear quite a different aspect if the size of the available funds and the rate at which they are accumulated are taken as data resulting from the financial system chosen, and if the main problem under consideration is that of the selection of investments. In this case they go beyond the field of social insurance proper, and it becomes necessary to examine them in relation to financial problems, especially as regards their effect on the capital market, and also in relation to the general economic and social situation. Owing to the importance óf these questions 2 they have attracted the notice of the International Labour Office, which, after a preliminary study, submitted them to an international 1 It is obvious that the replies given to these questions for any particular insurance scheme play an important part in the framing and choice of its financial system. 2 The investment of capital in life insurance is one of the items on the agenda of the Twelfth International Congress of Actuaries. 38 INTRODUCTION committee of experts. This committee held a first meeting in December 1937 and a second from 5-9 December 1938 and adopted a series of conclusions, which have been published in a volume in the same series as the present one 1 , together with the main lessons to be drawn from the consultation of the experts and the preliminary work. It will therefore be sufficient to make only a few brief observations here. Among all the considerations by which the selection of investments may be determined, it is customary to pick out—somewhat arbitrarily perhaps—the three general conditions of safety, liquidity and yield. The safety of an investment may be regarded, in the first place, as a contractual matter—that is to say, the clauses of the loan must be strictly observed in the present and the future; next, there is the question of real safety—that is to say, of avoiding or reducing losses in purchasing power, especially in the case of depreciation of the currency. Normally, the technical reserves are required to be liquid only to the extent that the financial system calls for their absorption. In some cases, however, liquidity can be very useful by facilitating the transformation of the financial system if in unforeseen circumstances the scheme is suddenly faced with considerable difficulties. It should, of course, be possible to realise the contingencies reserves at any time. Since the income from funds invested as technical reserves plays an essential part in the maintenance of financial equilibrium, it is indispensable that the rate of yield on their total should not fall below the minimum adopted for fixing the rate of interest which serves as a basis for the calculations. If this condition is realised, there can be no objection to allowing part of the accumulated funds to bear a lower rate of interest, provided that the investments have advantages irom other points of,view. It may in fact be expedient, when selecting investments, to take into account their social and economic utility as well as the conditions of safety, liquidity, and yield. In favourable circumstances the funds of the social insurance scheme may thus help towards national economic development and, in particular, towards the 1 INTERNATIONAL LABOUR OFFICE: The Investment of the Funds of Social Insurance Institutions, Studies and Reports, Series M, No. 16, 1939. INTRODUCTION 39 improvement of the conditions of life of the insured community, not to say the national community as a whole. In all the schemes studied here, it will be seen that the investment of accumulated funds is governed by a certain number of legislative provisions supplemented by regulations. In some cases social insurance funds are treated on the same footing as other classes of investments for which rules that have stood the test of time already exist. In general, however, a series of special provisions are adopted for application to the social insurance scheme. The regulations generally enumerate : (1) the classes of investments which are permissible for the insurance institutions without restriction; (2) the classes of investments which are permissible for the insurance institution, provided that their total does not exceed a certain proportion, fixed in advance, of the value of the total holding, or that their yield is not less than a rate fixed in advance (for each class of investment), or that a special permit is obtained from the supervisory authority ; (3) the classes of investments which are compulsory for the insurance institution up to a certain proportion of the total value of the holding. The selection of the investments, made in accordance with the provisions of laws and regulations, may be entrusted to a central body or, on the other hand, may be regarded as a prerogative of the managers of each institution. Both methods have their advantages and their drawbacks; it will be seen that they can be applied at the same time, each of them to a part of the funds to be invested. In some cases the selection is left to the initiative of the insurance institution, but the rates of yield may not fall below the minima fixed periodically by the central body. Whatever method is adopted, it is certain that the selection of investments is a difficult and responsible task, which cannot be carried out successfully without extensive knowledge. The decisions concerning investments are rightly considered to be so important that nearly always representatives of the insured persons and employers are required to take part in them. In order that a coherent financial policy may be followed, the body responsible for selecting 40 INTRODUCTION investments is often led to draw up in advance an investment scheme, applicable during a specified period unless unforeseen circumstances intervene. The execution of orders to buy and sell securities may itself be made subject to supervision or may be compulsorily entrusted to a national institution. Each insurance institution must necessarily establish and, as a rule, publish each year a description of its property and, in particular, of its investments. The tables so drawn up are used to prepare a series of annual figures, which provide information not only on the total amount of the funds invested at the end of each year but also of the distribution of the funds among the different classes of investments. The annual return on the assets of an insurance institution is not in itself sufficient to calculate the rate of yield on investments. Account must also be taken of repayments of capital, of the gradual depreciation of real estate, and in some cases of clauses special to each investment. The rate of yield is calculated for each class of investment, and especially for the different kinds of bonds, according to the rules accepted for long-term financial operations, no modification being made in these rules because the securities in question are held by social insurance funds. An average rate of yield having been determined for the whole holding, it must be ascertained that it is at least equal to the actuarial rate of interest—that is to say, the rate of interest serving as a basis for the actuarial calculations. In actual fact, provision is always made for a safety margin between the two rates. The choice of the actuarial rate raises a very important, but also very difficult question which has so far been treated as settled. In fact, whatever the financial system adopted, it becomes necessary to admit that the technical reserve should bear interest at a rate at least equal to the actuarial rate and should do so not only during a few years but in theory during the whole period covered by the calculations, not to say indefinitely. This hypothesis, which is indispensable in all life insurance or invalidity insurance calculations, is not, in fact, as arbitrary as it might seem at first sight. It is largely justified by the two following observations 1. In the first place, the yield of that part of the holding which consists of negotiable securities redeemable at a fixed rate—and this is : Cf. H. GALBRUN, op. cit., pp. 124-126. INTRODUCTION 41 often the largest part—usually undergoes only comparatively slight and small fluctuations. Secondly, when the insurance scheme has passed through the initial period of accumulation of reserves, the amount of the reserves remains stationary or at least varies very slightly, and in consequence new investments and changes of investments have only a small effect on the rate of yield. In other words, the yield displays a certain " inertia ". Further, as regards social insurance, an adequate rate of yield is all the less important when the financial system calls for a smaller quantity of technical reserves. Lastly, provision may be made against losses of interest by constituting in advance a special reserve for compensating such losses. The calculation of the rate of yield is bound up with another technical problem which has already been mentioned: the determination of the value at which the holding is to appear in the balance-sheet. Here again social insurance schemes apply all or some of the various methods employed in private undertakings. The value at which each investment is recorded on the assets side of the balance-sheet is obtained by reference to one or more of the following figures : nominal value, purchase price, market quotation at a given date, average market quotation during a given period, actuarial quotation 1. It will be seen later that a great variety of methods have been adopted in the different insurance schemes. For the moment it is sufficient to note that one example will be found of a special fund created to counteract fluctuations in the quotations of negotiable securities and even of real estate, and thus to stabilise the value at which investments figure in the balance-sheet. Actuarial Accounting and Control A reference was made in the study of financial systems to the important part played within each by actuarial accounting and control. In each monograph an attempt is made to bringo ut the essential principles on which the accounting of the insurance institutions are based, and a few brief indications are given as to 1 The actuarial quotation or value of a security at a given date is simply the present value at that date of all the sums still due to the person holding the security; for the calculations, use is made either of the yield on the security under consideration or of the actuarial rate or of a figure obtained from one of these by the addition of a safety margin. 42 INTRODUCTION the carrying out of actuarial control, the frequency of such control, and the publication of the results. Organisation of Statistics Among social insurance statistics a distinction may be made between : (1) those established regularly in order to record the working of the scheme; (2) researches for the purpose of constructing new biometrie tables (mortality rates, probability of becoming invalid, cessation of invalidity, etc.) on the basis of observations made during the working of the scheme itself; (3) special enquiries undertaken to provide, on any given point, a more precise basis for the actuarial calculations, and especially for the actuarial balance-sheet; (4) special enquiries for studying the expediency and possibility of introducing administrative reforms. It should be observed that after several years of working, the figures collected by an insurance scheme are often of intrinsic statistical value. In particular, if the scope of the scheme coincides with one or more occupational groups, the observations recorded for the insured population form an important contribution to the demographic study of the occupied population. Conversely, cases may be found in which the general census forms include a special question for the purposes of the social insurance scheme. It is therefore necessary, in organising the statistics of social insurance, to take into account the connections that it may be expedient if not indispensable to establish between these statistics and other statistics compiled in the country. It has been seen that one of the most important statistical problems with which insurance institutions have to deal consists in determining the number of insured persons and their age distribution. It is necessary to revert to this problem in order to recall the two principal methods that have been applied—not without difficulty—for its solution. In some cases, a direct enumeration is made, based on the records of entries and with. drawals or on the movement of the documents issued to insured persons for the purpose of the collection of contributions (cards, INTRODUCTION 43 sheets) or on the inventory of the individual files kept by the institutions (to which are often added perforated cards suitable for mechanical classification and counting). In other cases, recourse is had to indirect methods based on the following principle: the number of daily contributions paid during the " observation period " appears in the returns of the institutions or is deduced —when the same rate is applicable to all insured persons in a group—from the total yield of the contributions. In order to obtain the insured population the total number of contributions is divided by the average number of contributions, this last figure being obtained by means of a partial enquiry. Either of these methods can be applied to different groups or sub-groups of the insured population and can thus provide information, in particular, on the distribution by wage classes or by age groups. In the following monographs an attempt is made to emphasise the features special to the statistics established in each scheme and references are given to the documents in which these statistics are published. NOTE ON THE NATIONAL MONOGRAPHS Each of the following studies is devoted to a single social insurance scheme; it forms a whole and can therefore be read separately from the rest of the volume. It is preceded by a detailed table of contents and concludes with a bibliography which does not claim to include all the publications relating to the scheme but only the documents and texts used here. It seemed neither possible nor very useful to make a general list of the works and articles dealing with the actuarial technique and financial organisation of social insurance. Such a list would be excessively long and would include a great variety of works; moreover, in most cases the interest of each work mentioned would be fully evident only when considered with reference to the particular insurance schemes the author had in mind. When a study is divided into two parts, there is a separate bibliography for each. In the text, the bibliographical references are made by means of figures in square brackets—e.g. [5]—sometimes followed by a page number—e.g. [5; page 112]. In every case the figures refer to the bibliography immediately following the monograph or part of a monograph in which they appear. 44 INTRODUCTION In each chapter, and often in the same section, a distinction is made wherever possible between: (a) the estimates prepared in connection with a proposal for the introduction of new legislation or for the reform of existing legislation; (b) the data which served as a basis, at least during a certain period, for the working of the insurance scheme; (c) the experience of the scheme. The terminology employed in the publications of the International Labour Office on social insurance, especially in the other volume of this series, is used throughout. On the other hand, no attempt has been made to standardise the actuarial notation; for ease of reference it has seemed preferable, except for a few old memoranda, to retain the symbols adopted in the original works. The following is the list of national monographs in alphabetical order. Page BELGIUM: Old-Age and Widows' and Orphans' Insurance for Workers and for Salaried Employees Table of Contents and Index of Tables Text and Tables Bibliography 47 47 49 81 CZECHO-SLOVAKIA: Invalidity, Old-Age and Widows' and Orphans' Insurance for Workers Table of Contents and Index of Tables Text and Tables Bibliography 83 83 86 165 FRANCE: General Scheme of Social Insurance Table of Contents and Index of Tables Text and Tables Bibliography 167 167 170 268 GERMANY: Invalidity, Old-Age and Widows' and Orphans' Insurance for Workers Table of Contents and Index of Tables 271 271 Part I. — From 1891 to 1914 Text and Tables Bibliography 277 277 396 INTRODUCTION 45 Page Part II. — 1924 Onwards Text and Tables Bibliography GREAT BRITAIN AND NORTHERN IRELAND: National Health 399 399 439 Insurance and Contributory Pensions Scheme Table of Contents and Index of Tables Introduction Part I. — National Health Insurance Text and Tables Bibliography Part II. — Widows', Orphans'and Old-Age Contributory Pensions Text and Tables Bibliography ITALY : General Scheme of Compulsory Insurance against Old Age and Death Table of Contents and Index of Tables Text and Tables Bibliography 443 443 447 449 449 483 487 487 514 Invalidity, 517 517 519 564 BELGIUM Old-Age and Widows' and O r p h a n s ' Insurance for Workers and for Salaried Employees CONTENTS Page INTRODUCTION • 49 CHAPTER I: Demographic Elements and Experience 1. 2. 3. Mortality Tables Insured Population Statistical Experience Annual Numbers of Beneficiaries , CHAPTER II : Financial Elements and Experience 1. 2. 3. 4. 5. Contributions Amount of Contributions in Workers' Scheme Amount of Contributions in Salaried Employees' Scheme. Number of Contribution Units Sundry Receipts Benefits Benefits of Workers' Scheme Benefits of Salaried Employees' Scheme Experience State Subsidies State Subsidies proportionate to Annuities Additions to Old-Age and Widows' Annuities Orphans' Allowances Cost of Administration CHAPTER I I I : Financial System 1. 2. Individual Accumulation Male Insured Persons: Workers aged 18 and over and Salaried Employees Male Insured Workers under age 18 and Insured Females . Insured Females who Insure a Life Annuity for Dependants General Indications on Accumulation Operations . . . . Central Funds 51 54 54 55 56 56 56 57 58 58 59 59 60 62 62 63 63 69 70 71 71 71 74 74 77 77 48 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Page CHAPTER IV: Financial Administration 1. 2. Investment of Funds Statutory Provisions. Various Categories of Investment Authorised Statistics of the Funds Invested in the Various Categories by the General Savings and Pension Fund Financial Results BIBLIOGRAPHY 80 80 80 80 81 81 INDEX OF TABLES I. II. HI. IV. V. Annual Number of Contributions Number of Beneficiaries in Receipt of Annuities Average Joint Contributions Total Annual Amount of Contributions Total Amount of Annuities Constituted by Individual Accumulation . . . . * VI. State Subsidies Proportionate to Annuities Constituted by Individual Accumulation VII. State Subsidies: Total Annua! Grants Between 1926 and 1930 m Respect Oi. -LtGn-v^ontriuutory Pensions, ¿vuditums ör Allowances VIII. Maximum Rates of State Additions to Annuities IX. Table for Use in Calculating Annuities Constituted by Individual Accumulation X. Statement of the Investments of the Pension Fund 55 55 58 59 62 63 64 65 75 81 INTRODUCTION The old-age and widows' and orphans' insurance schemes, which apply compulsorily to workers and salaried employees, are based on Acts of 10 June 1930, 14 July 1930 and 15 December 1937. This legislation must be regarded not as an innovation, but as the point which has now been reached in the course of an evolution in which three main stages are prominent. In the first period insurance was not yet compulsory and its development was marked by the following legislative measures: i. Act of 8 May 1850 establishing the General Pension Fund; 2. Parliamentary resolution granting, as from 1891 and within the limits of the credit voted each year, bonuses to persons insured with the General Pension Fund; 3. Act of 10 May 1900 establishing a scheme of voluntary insurance subsidised by the State; 4. Act of 20 August 1920 granting a non-contributory pension to all persons aged at least 65 whose means are below a prescribed level. The second phase is characterised by the introduction of compulsory schemes and by the addition of widows' and orphans' insurance. The insurance schemes for workers and for salaried employees were governed by the Acts of 10 December 1924 and 10 March 1925 respectively, which came into force on 1 January 1926 and Î January 1927 *. The third stage began with the reorganisation of the compulsory schemes—that of the workers by the Act of 14 July 1930 (in force 1 January 1931) and that of the salaried employees by the Act of 18 June 1930 (in force 1 January 1932). These measures were completed by the Act of 15 December 1937, the various parts of which became operative on 1 July 1937, 1 October 1937 and 1 January 1938. The following chapters deal almost exclusively with this stage. The two schemes of compulsory insurance against old age and death covering workers and salaried employees are very much alike. The method of individual accumulation, according to which the contributions paid give rise to annuities which vary with the duration of insurance, is identical in both schemes apart from some differences of secondary importance. The two schemes also have in common the non-contri1 The Act of 10 March 1925 aroused numerous protests, even before it came into force and was never applied except partially; an immediate revision was undertaken, the contributions were reduced and it was decided that they should be paid provisionally to the General Pension Fund, there to be accumulated in individual accounts under the provisions of the Act of 10 December 1924. 50 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION butory additions granted to insured persons of the transitional period, i.e. those born before 1 January 1908. The two financial systems are so closely linked together that very often the statistics do not give separate figures for each scheme, but only totals for the two together. Accordingly, a simultaneous analysis, in a single monograph, has been undertaken of the financial organisation and technique of both the workers' and the salaried employees' schemes. CHAPTER I DEMOGRAPHIC ELEMENTS AND EXPERIENCE § 1. — Mortality Tables The Belgian table F. 1904 was first resorted to for both sexes and for all categories of insured persons. This table, for females, was constructed at the same time as two others for males and for both sexes respectively, by the Actuarial Department of the General Savings and Pension Fund. The three tables were published in a special pamphlet [5] together with details of the data and the methods of construction employed. The statistical data comprised: (1) The results of the general censuses of the Belgian population for 1880, 1890 and 1900. (2) Statistics of deaths, according to age, for each of the years 1892, 1893 to 1901. (3) Statistics of births during the period 1891-1900. In the absence of migration statistics according to age, no account was taken of migratory movements : the Belgian population is considered as a " closed group ". It should be mentioned also that the death statistics include all deaths occurring in the country, while the census data refer only to persons having their residence in Belgium. The probability of death at age x is calculated by an approximate formula deduced from the formula of Zeuner and Knapp: 1891, 1900.- PX = . . , , , . . 1 1892, 1901 j 1-1 ^x + 77 2" ' 1891, 1900T . . 1893, 1901 j a x 1891, 190OT m which the two condensed expressions fined as follows: First 1891, 1900 ft=10 ^ n ^x = 2u Lx , 1890 + ftT x 1892, 1901 7 . dx are de- 52 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION and the approximate value of the expression is obtained from the results of the three general censuses of 1880, 1890 and 1900 by means of graphic interpolation of the second order, which, using Woolhouse's formula. gives : 1891 190 ' °L:c = 6.15 1 8 % -f 4.675 19 °°L, - 0.825 im Lx . (where *LX represents the number of persons aged over x but under x + 1 at 31 December in year t). Further 1882,1901, ft=n ^ t 1890 + fe, ft=2 ' where im+kdx represents the number of deaths during year 1890+Ä of persons aged over x but under x -f- 1. The probabilities of death for the first years of life are determined by the use of special formulae resulting from an approximation analogous to that which produced the general formula, viz: ?0 = d„ N ' _ q i = d, W=J0 ' ?a = d2 N-d0-¿; ' etC '' where N represents the mean annual number of births. The results obtained from these formulae merge with those obtained from the general formula as from age 4 or 5. After the crude rates had been calculated they were graduated by an analytical method based on Makeham's formula. The 72 equations corresponding to the integral ages from 20 to 91 aie divided into three groups, each covering 24 consecutive years. If the equations of each group are added together there remain only three equations and these will fix three of the constants of Makeham's law. Also the graduated and the crude values can be equated at age 20, so that the crude curve and the graduated curve have at least four points in common, corresponding to ages 20, 44, 68, 92. Below age 20 the table cannot be graduated by Makeham's law, but its progression was so regular that it did not seem necessary to graduate it. It was simply adjusted to the curve for higher ages at age 20 by fixing a suitable value for the fourth constant of Makeham's law. The table produced in this manner for females has been used for all the annuity calculations in the schemes of insurance against old age and death (both compulsory and voluntary) whatever the sex, age and occupation of the insured person. In 1939 it was decided to substitute a more recent table (F. 1928-1932) for mortality table F. 1904 where the rates for females (insurance schemes for workers and salaried employees) and the rates for workers aged under 18 were concerned. The 1928-1932 tables were constructed [6] from the following statistical data: (1) The results of the general census of 31 December 1930 (age distribution of the population resident in Belgium): 53 BELGIUM (2) The distribution of actual deaths (i.e. including deaths of aliens resident in Belgium) by: (a) age at death for the years 1928, 1929, 1930; (b) age at death and year of birth for the years 1931, 1932. (3) The annual numbers of emigrants and immigrants. The following formula, derived from Zeuner and Knapp's formula, was used: A ¡ = 1932 " : (=1932 2J (=1928 (=1929 A (=1930 L X+ — ^ (=1932 dx + ^ •" (=1928 A ( = 1932 t_xdx (=1931 7 ^ A (=1933 ' - À + "7 ^ j * i = 1928 * t-x-Jx (=1929 where Lx represents the number of persons aged over x but under x + 1 at 31 December in year t; dx the number of deaths during year t of persons aged over x but under x + 1 ; t_xdx the number, of deaths during year t of persons aged over x but under x + 1 who were born during year t — x ; t_xix the excess of immigrants over emigrants during year t in the case of persons who were born during year t — x (it being assumed that the age distribution of the excess of emigrants over immigrants corresponded to that of the alien population recorded at the census of 31 December 1930). An analogous formula was used for the first year of life: (=1932 0.65 1928 iZ0 + 2 ^» + "32^0 (=1928 ( = 1932 A (=1932 (=1932 ( = 1928 * ( = 1928 ( = 1928 where hN represents the number of births during year t, assuming that 65 per cent, of the deaths between ages 0 and 1 relate to births of that year. The crude table so obtained was adjusted: (1) for ages 24 and over, by means of Makeham's formula, using King and Hardy's method; (2) for ages under 24, by means of graphic interpolation. 54 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION § 2. — Insured Population The insurance of workers covered, under the Act of 14 July 1930, two categories of compulsorily insured persons, defined as follows. The first category, that of wage earners, includes all workers of both sexes aged at least 14, provided that they are employed in Belgium or abroad in the service of an employer and in the employment of an undertaking with its head office established in Belgium. There is no limit fixed to the amount of remuneration. The obligation to insure applies, not only to wage earners in commerce, industry and agriculture, but also to domestic servants. The following are excepted: miners and seamen (who are covered by special schemes), and persons employed by public authorities, provided that they are entitled to pension by virtue of their employment. The second category, that of independent workers, includes any person performing manual or intellectual labour on his own account who is thereby subject to the professional tax and whose professional income does not exceed 18,000 francs per annum. This category was transferred to voluntary insurance by the Act of 15 December 1937. Under the Act of 18 June 1930, the following are subject to the insurance scheme for salaried employees: (1) salaried employees of both sexes, of Belgian nationality, who are employed and paid in Belgium or abroad, by a Belgian firm or by a brarch of a foreign firm established in Belgium; (2) salaried employees of both sexes, of foreign nationality, who are employed and paid in Belgium by a Belgian firm or by a branch of a foreign firm established in Belgium; (3) salaried employees of both sexes in the service of the State, the provinces and the communes, public i istitutions and public utility companies, whose terms of service do not provide for an old-age pension, a widow's pension and an allowance to orphans aged under 18; (4) the following classes are assimilated to salaried employees: (a) professional journalists; (b) members of the teaching staff attached to a private educational establishment who are not covered by the teachers' pension laws; (c) persons who carry on in Belgium the profession of lyric or dramatic artist or instrumentalist under a business contract which is binding for at least a month. Provision is also made for voluntary insurance attached to the workers' insurance scheme and for. " continued insurance " and voluntary insurance in conjunction with the salaried employees' insurance scheme. STATISTICAL EXPERIENCE The number of individual accounts is no clear indication of the insured population. Each insured person may have opened in his name, in fact, several accounts appearing in different categories: workers, salaried employees, optional payments, or voluntarily insured persons. Moreover, in the course of each accounting period a number of accounts 55 BELGIUM entail no financial operation. More informative are the numbers of annual contributions for each category as shown in table I. TABLE I . — ANNUAL NUMBER OF CONTRIBUTIONS (in thousands) Year 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 . . . . x . . . . 2 . . . . Workers' insurance Optional Voluntary Compulsory ofcontributions compulsorily insurance insurance insured persons 41 1,276 419 1,358 39 447 1,414 36 455 1,431 34 468 1,391 31 592 1,285 546 25 1,296 20 475 1,305 15 384 1,348 14 338 317 1,451 14 1,553 13 319 employees' insurance 199 205 230 240 438 235 221 224 225 238 252 i T h a t is, for workers, a total of 1,856,000 contributions, viz. 1,076,000 for males and 780,000 for females. 2 T h a t is, for workers, a total of 1,791,000 contributions, viz. 1,088,000 for males and 703,000 for females. § 3. — Annual Numbers of Beneficiaries The portion of the old-age pension or widow's pension which is related to the accumulation of the contributions paid (old-age annuity or widow's annuity) is subject to no qualifying period. On the other hand the payment of additions and allowances the cost of which is borne by the State is subject to a complex system 1of conditions as to contributions and needs which will analysed later . The figures of the number of beneficiaries given in the following table relate to the portions of pension constituted by accumulation, and are obtained by counting the number of " annuity orders " current at the end of each year. TABLE NUMBER OF B E N E F I C I A R I E S IN R E C E I P T OF II. ANNUITIES (in thousands) At the end of year 19321 1933 1934 1935 1936 1937 . . . . . . . . . . . . . . . . . . . . . . . Workers' insurance Old-age ' Widows' annuities annuities 135 33 158 35 191 51 222 60 246 68 289 88 Salaried employees' insurance Old-age Widows' annuities annuities 0.9 0.6 2.4 1.4 4.1 2.3 4.9 3.3 7.9 4.4 9.7 5.5 i Figures before 1932 do not distinguish between workers' insurance and employees' insurance. i See Chapter II, 4, pp. 62-70. salaried CHAPTER II FINANCIAL ELEMENTS AND EXPERIENCE § 1. — Contributions AMOUNT OF CONTRIBUTIONS IN WORKERS' SCHEME The wage earners are divided into eight classes, to each of which there corresponds a rate of contribution fixed in accordance with the following scale, irrespective of sex: • Amount, of weekly wage (francs) Class I n in IV v VI VII VIII . U n d e r 50 50.01-75 75.01-100 100.01-125 125.01-150 150.01-175 175.01-200 Over 200 Amount of the monthly joint contribution (francs) 5 7 10 13 16 19 22 25 The contribution of the insured person, which is equal to that of the employer, is fixed monthly on the basis of the wage at the rate represented by the first payment to the insured person in the current month. Independent workers who, under the Act of 14 July 1930, constituted a second category of insured persons, were required to contribute on the basis of their professional income in the previous year. Before the contributions are credited to the individual accounts opened with the Pension Fund there is deducted, in the case of all male persons born before 1908, a levy for the benefit of the Widows' and Orphans' Fund 1. These deductions were fixed formerly at: («) 10 francs per annum for male insured persons born before 1 January 1888; (b) 5 francs per annum for male insured persons born between 1 January 1888 and 31 December 1907. 1 The purpose and the function of this Fund are indicated below, p. 77. BELGIUM 57 As from 1 October 1937 these rates were reduced as follows: (a) (A) (a) (b) where t h e annual amount of t h e contributions is less t h a n 60 francs and equal to or greater t h a n 30 francs: 5 francs per annum for male insured persons born before 1 January 1888; 2 francs per annum for male insured persons born between 1 January 1888 and 31 December 1907; where t h e annual amount of the contributions is less t h a n 30 francs: 2 francs per annum for male insured persons born before 1 January 1888; 1 franc per annum for male insured persons born between 1 January 1888 and 31 December 1907. Since 1 July 1937 every worker over 21 is required to p a y 5 francs for each complete month of unemployment or sickness. AMOUNT OF CONTPIBUTIONS IN SALARIED E M P L O Y E E S ' SCHEME The Act makes a distinction between two kinds of contribution, one going to the insurance institutions to accumulate in a personal account, the other serving to maintain t h e Salaried Employees' Allowances Fund. (a) Contributions paid to Insurance Institutions The amount of t h e contributions paid to the insurance institutions is fixed in proportion to salaries, t h e m a x i m u m remuneration taken into account for this purpose being 18,000 francs a year. The employee's contribution is fixed at 3 per cent, of his remuneration. The employer's contribution is fixed at t h e following proportions of t h e same remuneration: Until From From From (b) 1960 1961 to 1975 1976 to 1990 1 January 1991 onwards . . . . Contributions paid to Salaried 4 per cent. 4i/ 3 „ 4% „ „ 5 „ „ Employees'1 Allowances Fund Only salaried employees b o m before 1 J a n u a r y 1895, for whose benefit the Salaried Employees' Allowances F u n d is established, contribute to this Fund. The amount of the annual contribution is fixed according to t h e following t a b l e : Date of birth, of insured person Before 1 January 1875 From 1875 to 1879 „ 1880 „ 1884 „ 1885 „ 1889 „ 1890 „ 1894 Francs 90 75 60 45 30 All employers must p a y to t h e Salaried Employees' Allowances Fund an annual contribution, amounting t o : 120 francs until 1960, 80 francs from 1961 to 1975, 40 francs from 1976 to 1990, 58 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION in respect of each insured person employed on 31 December of the current year. When an insured person is employed on 31 December by several employers, each employer must make the payment specified above, except in the case of an employee earning less than 3,600 francs, in which case the contribution is reduced by a half. NUMBER OF CONTRIBUTION UNITS The numbers of annual payments for each category of insured persons are given in table I above '. The mean values of the annual payments given below have been obtained by dividing the total amount of joint contributions by the number of annual payments, but in the case of salaried employees the figures relating to 1932 onwards have been calculated by reference to the monthly payments. TABLE I I I . — Year 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 AVERAGE JOINT Workers' insurance Average annual contribution (francs) CONTRIBUTIONS Salaried employees' insurance Average Average annual monthly contribution contribution (francs) (francs) 48 47 47 49 66 152 157 151 146 154 164 597 674 713 775 671 75 78 78 77 78 82 .. Table IV gives in round figures the total annual amount of joint contributions for each category. In considering these figures it should be noted that, up to 1 January 1932, the voluntary contributions of salaried employees are included with those of the workers under the heading " voluntary insurance ". § 2. — Sundry Receipts Each of the two insurance schemes receives either the total or only a part 2 of the capital sums accumulated for the purpose of a widow's pension whenever a male insured person dies a bachelor, widower, or divorced. The amounts credited under this head are paid over definitively, at the death of the insured, either to the Widows' and Orphans' Fund for workers or to the Salaried Employees' Allowances Fund. 1 2 See p. 55. See pp. 72-74. 59 BELGIUM TABLE IV. TOTAL ANNUAL AMOUNT OF CONTRIBUTIONS (in thousands of francs) Workers' insurance Year 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 . . . . . . . Salaried employees' insurance Optional contribuCompulsory tions of Voluntary insurance corapulsorily insurance insured persons 60,679 63,908 67,116 70,194 92,158 195,680 203,417 197,570 196,271 223,187 255,337 1,074 9.85 1,037 984 1,229 1,234 1,209 765 655 638 674 11,224 13,072 13,904 14,776 23,131 37,707 33.308 27,397 24,131 23,267 24,331 Compulsory Salaried and employees' voluntary allowances insurance fund 119,000 138,000 164,000 186,000 294,000 210,598 208,099 208.881 208,442 222,015 248,936' • — — — — 28,855 29,311 31,186 30,844 32,712 33,300 § 3. — Benefits In this section are described the benefits of the workers' and salaried employees' schemes ; the next section deals with the additions to old-age and widows' annuities and the orphans' allowances, the cost of which is borne entirely by the State. BENEFITS OF WORKERS' SCHEME The pensionable age is fixed, at the option of the insured person, for males, at any birthday between the 60th and the 65th; for females, at any birthday between the 55th and the 65th. The old-age annuity includes (a) a retiring annuity corresponding to the amount shown in the personal account of the insured person and (b) a proportionate State subsidy equal to 50 per cent, of this retiring annuity with a maximum of 1,200 francs a year (this maximum being reduced if the pension commences before 65)1. The amount of the widow's annuity is assessed: (1) by taking a varying percentage of the retiring annuity corresponding to the amount shown in the personal account of the husband at the date of his death; (2) by increasing the amount so obtained by 50 per cent, in respect of the proportionate State subsidy1. 1 These State subsidies, proportionate to the old-age or widow's annuity, are granted to foreigners only if a treaty of equality of treatment has been concluded with their country of origin. For insured persons born between 1867 and 1884 the proportion may exceed 50 per cent, (see p. 63) and for the oldest of these it may reach 100 per cent. 60 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION If husband and wife are the same age, the varying percentage mentioned above depends only on the age of the husband at death, in accordance with the following scale: Percentage (hx) for assessing widow's annuity (husband and wife of the same age) Less t h a n 41 35 41 36 42 37 43 38 44 39 45 40 46 r 41 47 .,,... 42 48 43 49 44 50 45 . 51 46 52 47 53 48 54 49 1 55 and o v e r 50 1 The percentage remains fixed at 50 when the insured person dies after having entered upon his old-age pension. Age of husband at death If husband and wife arc of different ages, these proportions must be multiplied by a conversion factor: in this case the amount of the widow's annuity is obtained by two successive operations: (1) calculation of the widow's annuity that would have been payable if husband and wife had been of the same age ; (2) conversion of this annuity by means of the coefficients from two scales [7] dependent on the age of the husband at death and the difference in ages (to the nearest integral number of years). The application of the first scale reduces the annuity when the wife is younger than the husband, while the second on the other hand increases the annuity when the wife is older than the husband x. The contributions credited to the personal account of a female insured person are in principle applied entirely to the purchase of a retiring annuity, but a part of these contributions may, at the request of the insured, be reserved for the purpose of providing at her death a life annuity for certain persons named in advance. This life annuity becomes payable only if the death of the insured occurs before entering on the old-age pension. A lump-sum death benefit is payable, when the insured person dies without leaving a widow, either to his children aged less than 16 or to his parents. BENEFITS OF SALARIED EMPLOYEES' SCHEME The pensionable age is fixed, at the option of the insured, for males at any birthday between the 55th and 65th, and for females between the 50th and 60th. 1 So t h a t the p r e s e n t value r e m a i n s t h e s a m e : see below Chapter I I I , 1, p . 72. BELGIUM 61 The old-age annuity and the widow's annuity are composed, in accordance with the same rules as in the workers' scheme, of two portions derived respectively from the accumulation of contributions and the proportionate State subsidy. Under the same conditions as in the workers' scheme, part of the contributions credited to the personal account of a female insured person may, at her request, be reserved for the purpose of providing a life annuity for persons named in advance, such life annuity becoming payable only in the event of the death of the insured before entering on the old-age pension. A lump-sum death benefit is paid to children, parents or other persons named in advance, when the insured dies without leaving a widow (except in the case where the insured dies after having entered on his old-age pension and after having used his option of converting the lumpsum death benefit corresponding to his contributions into a life annuity for himself). Besides the benefit payments just enumerated, which correspond to the payments under the workers' scheme, the Salaried Employees' Allowances Fund provides for the following allowances: (a) Old-age allowances granted to male insured persons who have attained age 65 and females who have attained age 60, where the following conditions are fulfilled: (i) The insured was born before 1 January 1895; (ii) The insured was born after 31 December 1861, for males, or after 31 December 1866, for females; (iii) The insured has paid statutory contributions as from 1 January 1926, or from the date when the law applied to him, whichever is the later; ; (iv) The insured has made all the statutory payments to the Salaried Employees Allowances Fund as from 1 January 1932, or from the date when the law applied to him, whichever is the later (if all the payments have not been made, the allowance is proportionately reduced). The annual amount of these allowances varies, according to the year of birth of the insured, between 200 and 1,500 francs for men and between 130 and 770 francs for women. An insured person who opts to draw his annuity before the limiting age (65 for men and 60 for women) may obtain a reduced allowance, but no such allowance will be granted if the pensioned person is still working for an employer. (b) Widows' allowances granted approximately under the same conditions as old-age allowances, viz: (i) The husband must have been born after 31 December 1861, and before 1 January. 1895; (ii) The husband must have paid statutory contributions as from 1 January 1926, or from the date when the law applied to him, whichever is the later; (iii) The husband must have made all the statutory payments to the Salaried Employees' Allowances Fund as from 1 January 1932, or from the date when the law applied to him, whichever is the later. The amount of the widow's allowance is derived from the old-age allowance to which her husband would have been 62 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION entitled at age 65 by applying on the one hand the percentages used in calculating widows' annuities 1 , and on the other hand, to take account of differences of age between husband and wife, special scales fixed by Royal Order. (c) Orphans' allowances, payable to the surviving parent or, after the death of both parents, to the person in charge of the orphan, of 300 francs per annum for each child aged less than 18. (d) Invalidity allowances insuring 1,500 francs a year for permanent total invalidity (until the coining into force of a compulsory invalidity insurance scheme). EXPERIENCE The following table shows the sums paid by way of annuities constituted by individual accumulation: TABLE V. — TOTAL AMOUNT OF A N N U I T I E S CONSTITUTED BY I N D I V I D U A L ACCUMULATION (in thousands of francs) Workers' insurance Current at the end of the year 19321 1933 1934 1935 1936 1937 . . . . Salaried employees"' insurance For insured pensions (old-age) For widows For insured pensions (old-age) 6,557 7,460 11,023 14,174 17,560 15,744 1,445 1,691 4,142 5,296 6,535 14,279 124 496 1,055 1,890 2,837 3,948 For widows 521 1,327 2,134 2,903 3,903 • 4,928 i Returns before 1932 do not distinguish between workers and salaried employees. § 4. — State Subsidies State grants are made on behalf of workers and salaried employees in accordance with regulations laid down in the legislation governing the workers' insurance scheme, which automatically extends to salaried employees' insurance. Such grants are intended to cover expenditure incurred under three heads: (a) The subsidies proportionate to annuities constituted by individual accumulation; (6) The additions to old-age and widows' annuities; (e) Orphans' allowances. 1 See above, pp. 59-60. 63 BELGIUM STATE SUBSIDIES PROPORTIONATE TO ANNUITIES The payment under this head has already been described in the preceding section. Normally it is fixed at 50 per cent, of the retiring annuity or of that part of the widows' annuity which is constituted by individual accumulation, subject to prescribed maxima (e.g. 1,200 francs per annum in the case of a pension commencing at age 65). In the case of certain " transitional " insured persons the State subsidy under the same conditions is increased to the following percentages (subject to the same maxima): 100 per cent, for insured persons born between 1867 and 1874. 75 „ „ „ „ „ „ „ 1875 and 1879. 60 „ „ „ „ „ „ „ 1880 and 1884. The following table shows the annual charge falling on the State in respect of payments under this head: TABLE VI. — STATE SUBSIDIES PROPORTIONATE TO ANNUITIES CONSTITUTED BY INDIVIDUAL ACCUMULATION (in thousands of francs) Workers' insurance Year 1932l 1933 1934 1935 1936 1937 1 . . . . For insured pensions (old-age) 1,186 1,909 3,168 4,620 6,438 10,784 Salaried employees' insurance For widows For insured pensions (old-age) For widows 976 1,557 2,264 2,618 3,233 5,243 486 1,236 1,965 3,253 4,723 5,908 377 744 1,661 1,760 2,222 2,662 Returns before Í932 do not distinguish between workers and salaried employees. ADDITIONS TO OLD-AGE AND WIDOWS' ANNUITIES The additions to old-age and widows' annuities form a complicated system which is common to both insurance schemes. This system was introduced by the Act of 14 July 1930 in substitution for previous provisions, which granted: (1) A non-contributory pension under the Act of 20 August 1920; (2) An addition to old-age and widows' annuities under the Act of 10 December 1924; (3) A non-contributory old-age allowance under the Act of 10 December 1924; (4) Supplementary non-contributory pensions, supplementary additions to old-age annuities and supplementary non-contributory old-age allowances, under the Acts of 20 Julv 1927 and 2 April 1929. 64 ACTUARIAL T E C H N I Q U E AND ' FINANCIAL ORGANISATION The following table shows the State grants made between 1926 and 1930 jointly to the workers' and salaried employers' insurance schemes to cover the charges in respect of the items mentioned above. TABLE V I I . — STATE S U B S I D I E S : TOTAL ANNUAL GRANTS B E T W E E N AND 1 9 3 0 IN RESPECT O F NON-CONTRIBUTORY P E N S I O N S , A D D I T I O N S OR ALLOWANCES 1926 (in thousands of francs) Non-contributory pensions Additions to old-age annuities Additions to widows' annuities Non-contributory old-age allowances Supplementary non-contributory pensions . . Supplementary additions to old-age annuities . Supplementary non-contributory old-aee allow- 1926 1927 1928 1929 1930 194,119 197,293 196,789 200,006 18.5,573 — — 46 1,416 515 1,699 2,924 4,610 174 2,281 5,319 157,461 135,755 9,555 18.693 1,187 3,141 — — — 130,260 116,399 — — — — • 17,583 ' 32,429 The State payments which were gradually introduced into the scheme from 1920 to 1930 were all intended to protect the " transitional " insured persons, who under the application of the normal rules alone would obtain insufficient pensions. With the same object in view the 1930 Acts reduced the categories of payments to two—additions to old-age annuities and additions to widows' annuities. After 1930 the method of granting these two additions was frequently modified1 before being thoroughly amended by the Act of 15 December 1937. Provisions in force 1931-1937 Under the system of State additions to annuities in force from-1931 to 1937, " transitional " pensioners were divided into four categories, according as their date of birth was: 1. Before 1 2. In 1863, 3. Between 4. Between January 1863; 1864 or 1865; 1866 and 1870 inclusive: 1871 and 1907 inclusive. The payment of these additions was subject to the fulfilment of conditions in respect of contributions and of need which became more stringent as the date of birth grew later. The Act of 1930 fixed a maximum scale depending on the date of birth of the beneficiary, which is given below. 1 Under the Acts of 23 July 1932,17 May 1933 and 31 July 1934, and numerous Royal Orders. 65 BELGIUM TABLE VIII. — MAXIMUM RATES OF STATE TO ANNUITIES ADDITIONS Additions to old-age annuities Year of birth, of insured person j 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 ...- . . . . . . . . - Additions Married male insured persons 3,200 3,200 3,100 3,100 3,000 3,000 2,900 2,900 2,800 2,700 2,600 2,600 2,600 2,500 2,400 2,400 2,300 2,300 2,200 2,100 2,000 1,900 1,800 1,800 1,700 1,600 1,500 1,400 1,300 1,200 1,100 900 800 700 600 500 400 300 200 100 Other beneficiaries 2,100 2,100 2,000 2,000 1,900 1,900 1,800 1,800 1,700 1,600 1,500 1,500 1,500 1,400 1,300 1,300 1,200 1,200 1,100 1,000 900 800 700 700 600 500 400 300 200 100 to widows' annuities 540 540 540 540 540 480 480 480 480 480 420 420 420 420 420 360 360 360 360 360 300 300 300 300 300 240 240 240 240 240 180 180 180 180 180 120 120 120 120 120 The above rates underwent a temporary cut of 5 per cent, during the period 1 July 1933-30 November 1936. They were payable only if all the statutory contributions had been made. j Where this was not the case, the addition was reduced in the ratio of the number of contributions paid to the number which should have been paid, but no addition was granted if the insured person had not paid half the statutory contributions. On the basis of the table of maxima reproduced above, the amount 5 r 66 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION of the addition was calculated from schedules * graduated according to the means of the beneficiary. The choice of the schedule to be used in any particular case depended upon 1. The category to which the beneficiary belonged (unmarried, widowed, or divorced persons living alone or in institutions at the public expense; married men; wives who are sole beneficiaries; unmarried, widowed or divorced persons living with other claimants or in institutions not at the public expense); 2. Year of birth; 3. Contributions paid. With a view to applying the schedules for assessing the benefit payable according to the means of the beneficiary, it is necessary to define precisely the resources which must be taken into account, the method of calculating the income and the conditions under which certain items are to be disregarded. The statutory rules on these points and the numerous amendments which have been made to them are not relevant to a technical consideration of the financial organisation of the scheme and do not lend themselves to the drawing up, of estimates. It may however be remarked that they can nevertheless exert an appreciable influence both on the practical bearing and on the financial equilibrium of the insurance scheme. experience Under the scheme introduced by the 1930 Acts, the total amounts paid under the heading of additions to old-age annuities, for the workers' and salaried employees' schemes combined, were as follows: 519,814 thousand francs in 1931 989,146 „ „ „ 1932 1933 714,202 1934 439,215 1935 499,144 1936 494,261 The total amounts paid under the heading of additions to widows' annuities, for the two schemes, were: 10,122 thousand francs in 1931 16,816 „ „ „ 1932 20,532 1933 30,024 1934 1935 27,989 1936 26,268 Measures introduced by the Act of 15 December 1937 As from 1 October 1937, under the Act of 15 December 1937, the grant of additions to annuities is subject to new rules, the most important of which from a financial point of view are as follows. Additions to old-age annuities without means test Additions to old-age annuities are granted without a means test, at or after the age of 65 years, to insured men, and to insured women who These schedules were amended by several Royal Orders. BELGIUM 67 are unmarried, widowed, divorced or under a judicial separation, provided such persons were born on or after 1 January 1867 and that the contributions indicated below have been made on their behalf, as employed, unemployed or sick persons, from the age of 51 to that of 65 years. Nevertheless, no contribution is required in respect of any period before 1 January 1926. The conditions relating to contributions mentioned above are considered as fulfilled if, between the ages of 51 and 63, there was only one break in payment, as follows: 1. One year at the most for insured persons born in the years 18701874 inclusive; 2. Two years at the most for insured persons born in the years 18751879 inclusive; 3. Three years at the most for insured persons born on or after 1 January 1880. Payments made under the special Acts relating to old-age and widows' and orphans' insurance for salaried employees, mine workers and seamen are included for determination of contributions as indicated above. Payments made as voluntarily insured persons, in Belgium, by employed persons who were at the same time paying contributions under the legislation of a country party to a reciprocity agreement with Belgium are also taken into account. As regards persons compulsorily insured under the Act relating to old-age and widows' and orphans' insurance for salaried employees, only those insured persons whose annual average salary during the five years preceding their sixty-fifth birthday did not exceed 21,000 francs may receive additions to annuities without a means test. An addition is also payable at the age of 65 years, without a means test, to the widow of an insured person who also received the addition, provided such widow has made, as a voluntarily insured person, the payments required of persons of her age and provided the marriage was contracted before the husband reached the age of 60. Each insured person, and his (her) spouse if any, must sign an undertaking definitively to stop all occupational activity on applying for the grant of an addition payable without means test, whatever is the age of the spouse at that time. In order that payment of contributions shall not be considered as interrupted for application of the above conditions, at least nine monthly contributions, with a total not inferior to 50 francs, must have been paid each year. Nevertheless this condition is regarded as fulfilled if: 1. As regards the period 1 January 1926-31 December 1931, contributions have been paid totalling 72 francs for males or 24 francs for females; 2. As regards the year 1931-32, a contribution has been paid of 50 francs for males or 24 francs for females; 3. As regards each of the insurance years 1932-33, 1933-34, 1934-35, 1935-36, 1936-37, 1937-38, 1938-39, a contribution of at least 50 francs has been paid. Additions to old-age annuities with means test An employed person who has not fulfilled the conditions required for entitlement to an addition to an old-age annuity without means test may become entitled to this addition on the following conditions. 68 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The maximum addition (see table VIII) is granted when the insured person's means, together with those of his (her) spouse if any, are not above 2,800 francs for a married insured person or 1,900 francs for an insured person who is unmarried, widowed, divorced or under a judicial separation. If the total means exceed the above figures, the addition is equal to the difference between the maximum appropriate to the insured person and the part of his (her) means exceeding 2,800 or 1,900 francs as the case may be. There are exact rules governing the determination of that part of the applicant's means which must be taken into account for grant or calculation of the addition; but such rules do not fall within the scope of this volume and will therefore not be examined here. A person born before 1 January 1867 may'receive an addition to his old-age annuity after a means test and provided the following contributions have been paid on his behalf: 1. 2. 3. For persons born before 1 January 1863, no payment required; For persons born in 1863, 1864 or 1865, any payment; For persons born in 1866, a payment of 108 francs for males or 36 francs for females. The maximum addition which may be granted is fixed at 3,200 francs if the applicant is a married man, and 2,100 francs if the applicant is unmarried, widowed, divorced or under a judicial separation. A person born in 1863, 1864 or 1865 who has made no payment at all. or a person born in 1866 who has made payments amounting to less than 108 francs but not less than 54 francs (insured man) or to less than 36 francs (insured woman), may claim an addition to his old-age annuity not exceeding 2,900 francs if the applicant is a married man or 1,900 francs if the applicant is unmarried, widowed, divorced or under a judicial separation. No addition to an old-age pension is granted to insured persons born in 1866 by or on behalf of whom a contribution of at least 54 francs (insured men) or 18 francs (insured women) has not been paid. For insured persons born on or after 1 January 1867 who have not made all the payments required for grants of the maximum addition, the annual amount of the addition is reduced by the following amounts for each missing or insufficient annual contribution: 300 francs for married men; 200 francs for insured persons who are unmarried, widowed, divorced or under a judicial separation; 150 francs for married women. If the number of annual payments made amounts to less than half the number which the insured person ought to have made no addition is allowed. Additions to widows' annuities An addition of 540 francs is allowed to the widows of insured persons born in the years 1861-1866 inclusive, by or on behalf of whom the following contributions have been paid: 1. 2. For persons born in the years 1861-1865 inclusive, any payment; For persons born in 1866, a payment of 108 francs. Widows of Belgian nationality of insured persons born in 1867-1907 inclusive receive an addition the amount of which is determined in accordance with the date of birth of the insured person (see table VIII BELGIUM 69 above), provided the contributions required for grant of the maximum addition to an old-age annuity have been made. If not, the amount of the addition is reduced by 60 francs a year for each missing or insufficient annual contribution. No addition is granted if the number of contributions paid is less than half as great as the number which the insured person ought to have paid, up to and including the year of insurance in which death occurred. A widow who remarries loses her right to the addition from the month following that of her remarriage. ORPHANS' ALLOWANCES Under the Act of 1930, the award of these allowances was subject to the rules indicated below. An annual allowance of 240 francs was granted to the widow (or widower) for each dependent child under 16 years of age. On the death of the widow or widower, this allowance—increased to 420 francs—was paid to the person or organisation supporting the child. On the death of a female insured person, unmarried, widowed or divorced, leaving children under 16 years, an allowance of 240 francs was paid to the person or organisation supporting such a child; this allowance was not payable in addition to that mentioned in the preceding paragraph. As from 1 October 1937, under the Act of 15 December 1937, the provisions governing the grant of orphans' allowances have been as follows. On the death of a male insured person (married), an annual allowance of 240 francs is granted to the widow for each child under 16 years of age who was dependent on the insured person at death. On the death of the widow, this allowance—increased to 420 francs—is paid to the person or organisation supporting the child. On the death of an insured person of either sex, unmarried, widowed or divorced, leaving children under 16 years of age who were dependent on such person at death, an allowance of 420 francs per child is paid to the person or organisation which supports the child; this allowance is not payable in addition to that mentioned in the preceding paragraph. In the case of insured persons born in the years 1861-1866 inclusive, orphans' allowances are granted on the following conditions: 1. For insured persons born in 1861-1865 inclusive, provided some payment has been made; 2. For insured persons born in 1866, provided a payment of 108 francs (men) or 36 francs (women) has been made. In the case of insured persons born in the years 1867-1907 inclusive, no orphans' allowance can be granted if the number of contributions paid amount to less than half the number which the insured person ought to have paid, up to and including the year of insurance in which death occurred. Conditions of Nationality and Residence attached to Grant of Additions and Allowances The grant of additions and allowances has always been subject to conditions of nationality.and residence. Under the Act of 15 December 1937, additions and allowances are granted in principle to insured persons of Belgian nationality residing in Belgium. 70 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Where an insured person receives an old-age pension under the legislation of a country which has concluded a reciprocity agreement with Belgium, the amount contributed to the pension by the foreign State is deducted from the addition normally allowable. In determining whether an insured person has made at least half the number of annual contributions required, i.e. whether he is entitled to an addition, the payments made by him as an employed person under the legislation of a country which has concluded a reciprocity agreement with Belgium are taken into account. Where the addition is granted in view of the contributions paid as an employed person under the legislation of a country which has concluded such an agreement, the amount of the addition is reduced in accordance with the ratio between the number of contributions actually paid in Belgium and the number required of insured persons of the same age. Foreign nationals may receive additions and allowances if a reciprocity agreement has been concluded with their country of origin 1. § 5. — Cost of Administration The cost of administration is borne: (1) By the insurance institutions: (2) By the Ministry of Labour and Social Welfare, for the organisation and supervision of compulsory insurance and for administering the additions to old-age annuities; (3) By the Workers' Widows' and Orphans' Fund; (4) By the Salaried Employees' Allowances Fund. The tables on which are based the calculations of the annuities constituted by the individual accumulation originally included a uniform loading for administration expenses fixed at 3.5 per cent, of the total contributions paid. The tables brought into force for females and for workers under 18 years of age by the Royal Order of 28 April 1939 were drawn up with a loading of 6 per cent, for workers' insurance and 4.5 per cent, for salaried employees' insurance. 1 Two such agreements, with the Netherlands and France respectively, had been concluded by the end of 1937. CHAPTER III FINANCIAL SYSTEM As was indicated in the introduction, the financial organisation of the workers' scheme and that of the salaried employees' scheme are so similar that they can be considered together. Both schemes include individual accumulation in personal accounts, and also a system whereby the charges due to the " transitional " period are covered by one or more central funds. § 1. — Individual Accumulation Individual accumulation is operated according to the methods employed in life assurance by private companies. The scales were originally calculated on a uniform basis for both sexes and for all categories in accordance with a single mortality table (Belgian F 1904). The Royal Order of 28 April 1939 introduced for females and workers under 18 years of age new scales based upon a more recent mortality table (Belgian F 1930). Briefly the actuarial operations are characterised by two essential features: (i) The contributions credited to the individual account of an insured person are considered as premiums paid for a capital sum assured on his life. (ii) The capital sum assured is in every case converted into an annuity. In all these calculations the rate of interest is fixed at 3.75 per cent. The contributions credited to the personal accounts are intended for the purchase of retiring annuities and annuities for widows. For this purpose they are disposed of in the manner indicated below, according to the category "of the insured person. The principal scales to be used for assessing in the various cases the amount of that portion of the pension which is constituted by individual accumulation are also reproduced. MALE INSURED PERSONS: WORKERS AGED 18 AND OVER AND SALARIED EMPLOYEES The following is a description of the actuarial method employed in calculating the annuities. 72 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION The contributions credited to each personal account are applied to assure: (i) A capital sum payable on survival to age 65; (ii) A capital sum payable on death before reaching age 65 (death benefit). These capital sums are compulsorily converted into annuities payable either to the insured person (in which case they revert, to the extent of one-half, to the widow on his death) or to the widow. The capital sums assured are such that,, if the wife is the same age as the husband, the portion of the widow's annuity constituted by individual accumulation is equal to a percentage 1 (depending on the age of the husband at death) of the retiring annuity earned by the husband at the moment of death. The following formulae express, as á single premium, the present value of the benefits due to the contributions credited to the personal account of an insured person aged x (in this category) on the basis of a unit retiring annuity commencing at age 65: For the retiring annuity itself: D, aw For the reversionary annuity: D„ 1 D„ ' 2 * 66/66 ' For the death benefit: *-*x x where hx represents the percentage 2, according to the age at "death, for calculating the widow's pension, on the basis of equal ages of husband and wife. Or for all benefits : pu 1 64 , ri 2X 0.01 hx Cx af+i + D65\ < + '65/65 The retiring annuity commencing at age 65 which is purchased by a single premium of one franc is thus (taking into account a loading of 3.5 per cent, for administration expenses) 3 : 0.965 pu 1 2 3 These percentages are reproduced above: Chapter II, 3, pp. 59-60. See above: Chapter II, 3, p. 70. The numerical values are reproduced below in the second column of table IX (p. 75). BELGIUM 73 Finally, the retiring annuity, commencing at age 65, purchased by constant premiums of one franc a year payable in twelfths at the end of each month (premiums ceasing on attainment of age 65 or prior death), is obtained, with the aid of the numerical factors described above, by applying the formula 0.965 r = •, am). pU 165-1 X The tabular results of this calculation are shown in the.third column of table IX. A number of provisions have now to be considered which are closely connected with the method of calculating the annuities and which govern the manner of disposing of the death benefit where a single, widowed or divorced insured person dies or enters upon his old-age pension. As these provisions are not identical for workers and salaried employees, they must be considered separately. (a) Workers In the event of the insured dying before entering on his old-age pension, half of the death benefit—that is, the part corresponding to his own contributions—is payable to those entitled (children under 16 or parents), the other half being paid to the Widows' and Orphans' Fund. If there are no persons entitled, the whole of the death benefit is paid to the Widows' and Orphans' Fund. When a single, widowed or divorced insured person enters on his old-age pension, the sum accumulated to provide the death benefit is paid to the Widows' and Orphans' Fund. Consequently, this Fund assumes the following obligations: (i) In the event of the insured marrying and subsequently dying, the Widows' and Orphans' Fund pays to the widow an annuity calculated on the basis of a capital sum equal to half the capital sum corresponding to the old-age pension which the husband was drawing; (ii) In the event of the insured dying without leaving a widow, the Widows' and Orphans' Fund pays to those entitled—if there are any—half the capital sum, without interest, which was transferred to it. (b) Salaried Employees In the event of the insured dying before entering on his old-age pension, three-sevenths of the death benefit—that is, the part corresponding to his own contributions—is payable to those entitled (children, parents or persons nominated by the insured), the remainder being paid to the Salaried Employees' Allowances Fund. If there are no persons entitled the whole benefit is paid to the Salaried Employees' Allowances Fund. When a single, widowed or divorced insured person enters on his old-age pension, the sum accumulated to provide the death benefit is paid to the Salaried Employees' Allowances Fund; but a part of this sum, up to three-sevenths of it, may, at the request of the insured, be converted into a life annuity for his benefit. Consequently the Salaried Employees' Allowances Fund assumes the following obligations: 74 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION If the conversion option has not been used: (i) In the event of the insured marrying and then dying, the Allowances Fund pays to the widow an annuity calculated on the basis of a capital sum equal to half the capital sum corresponding to the old-age pension which the husband was drawing; (ii) In the event of the insured dying without leaving a widow the Allowances Fund pays to those entitled—if there are any— three-sevenths of the capital sum, without interest, which was transferred to it. If the conversion option has been used, the Allowances Fund undertakes, in the event of his marrying and then dying, to pay to the widow an annuity calculated on the basis of a capital sum equal to half of foursevenths of the capital sum corresponding to the old-age pension which the husband was drawing. MALE INSURED WORKERS UNDER 18 AND INSURED FEMALES The contributions credited to each personal account are applied entirely to the purchase of a retiring annuity. In workers' insurance the pension annuity is calculated on the basis of the formula: 0.94 66-* | X which represents the annuity deferred to age 65 purchased by a single premium of one franc. The numerical values of this deferred annuity, calculated on the basis previously indicated, are given below in the fourth column of table IX. The scale used under the salaried employees' scheme for the calculation of annuities of insured females is obtained by a similar formula: 0.955 The numerical values corresponding to this formula can be calculated from the figures in the fourth column of table IX by means of a constant factor: 0.6258. INSURED FEMALES WHO INSURE A LIFE ANNUITY FOR DEPENDANTS An insured female may have part of her contributions applied to the purchase of a life annuity for the benefit of persons whom she supports and who are designated by her. In these cases the actuarial method employed in the calculation of the annuities differs from that indicated ahove for insured females generally, and is as follows: The contributions credited to each personal account are applied to assure: (i) A capital sum payable on survival to age 65 (this capital sum is compulsorily converted into an annuity); TABLE I X . — TABLE FOR USE IN CALCULATING A N N U I T I E S CONSTITUTED BY I N D I V I D U A L ACCUMULATION Age at payment of contribution (1) 14 years 15 " 16 " 17 " 18 " 19 » 20 " 21 " 22 » 23 » 24 " 25 » 26 " 27 " 28 » 29 » 30 " 31 » 32 " 33 » 34 » 35 " 36 " 37 » 38 " 39 » 40 " 41 » 42 " 43 » 44 " 45 » 46 » 47 » 48 » 49 » 50 » 51 » 52 » 53 » 54 » 55 » 56 " 57 » 58 » 59 » 60 » 61 » 62 » 63 » 64 " 65 » Annuity commencing at age 6 E purchased Male insured workers aged 18 and over Male insured By fixed workers under premiums of By a single 1 franc a year premium payable in twelfths by a payment of 1 franc at the end of each of 1 franc month until age 65 or previous death (2) (3) (4) 0.989 — — 0.951 — — 0.914 — — 0.879 — — 0.452 8.926 0.845 0.440 8.619 0.811 8.327 0.779 0.429 0.419 8.063 0.748 7.802 0.718 0.409 0.400 7.539 0.690 0.390 7.279 0.662 0.380 7.022 0.636 0.370 6.766 0.611 0.360 6.513 0.586 0.351 6.262 0.563 0.341 6.015 0.540 0.332 5.771 0.519 0.322 5.530 0.498 0.313 5.293 0.478 0.304 5.059 0.459 0.295 4.830 0.440 0.286 4.604 0.423 0.278 4.383 0.405 0.269 4.166 0.389 3.953 0.261 0.373 0.253 3.746 0.358 0.245 3.543 0.343 0.237 3.343 0.329 0.229 3.151 0.315 0.221 2.964 0.302 0.214 2.782 0.290 0.207 Z.ÜU; 0.277 0.200 2.435 0.266 0.193 2.269 0.254 0.187 2.108 0.243 0.181 1.952 0.233 0.174 1.800 0.223 0.168 1.653 0.213 0.162 1.510 0.203 0.157 1.371 0.194 0.151 1.237 0.185 0.145 1.106 0.176 0.140 0.980 0.168 0.135 0.857 0.159 0.129 0.737 0.151 0.124 0.621 0.144 0.119 0.508 0.136 0.113 0.399 0.129 0.108 0.294 • 0.121 0.103 0.192 0.114 0.098 0.094 0.108 0.093 0.101 — 76 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION (ii) A capital sum payable on death.before entering on old-age pen- ¡ sion equal to 30 per cent, of the capital value, at the age of death, of the annuity formed in the insured person's personal account; this capital sum is converted into a life annuity for the benefit of persons designated in advance by the insured. The following formulae express, for workers' insurance, as a single premium, the present value of the benefits due to the contributions credited to the personal account of an insured person aged x (who has requested the formation of a life annuity for the benefit of persons whom she supports)—on the basis of a unit retiring annuity commencing at age 65: ' For the retiring annuity itself: Bx * • ' For the death benefit: D, •^ 0.30 CL a" x+i Or in total: 0.30 C fl(4> + D„, «' (4) * X D, X X+i ' 63 The retiring annuity commencing at age 65 which is purchased by a single premium of one franc is thus (taking into account a loading of 6 per cent, for administration expenses): 0.94 •IJC Finally, the retiring annuity, commencing at age 65, purchased by constant premiums of one franc a year payable in twelfths at the end of each month (premiums ceasing on attainment of age 65 or previous death) is obtained, with the aid of the numerical factors described above, by applying the formula: 0.94 ,(12) | 65-1 In the salaried employees' scheme analogous formulae are used which may be deduced from the above by altering the age of commencement of old-age pension from 65 to 60 and the loading for administrative expenses from 6 to 4.5 per cent. BELGIUM 77 GENERAL INDICATIONS ON ACCUMULATION OPERATIONS On the same bases as the above tables, scales have been constructed giving the coefficients to apply, for each category of insured person, in order to reduce the amount of the old-age pension where this is drawn before the normal age of 65 or 60 as the case may be. In the workers' insurance scheme all the operations of individual accumulation are carried out by the Pension Fund, which forms part of the General Savings and Pension Fund. The Pension Fund still contains the personal accounts of all salaried employees who joined before the coming into force of the Act of 18 June 1930. Under this Act salaried employees could insure either with the Pension Fund or with the National Pension Fund for Salaried Employees or with other institutions. The latter may be either autonomous, or employers' funds, or legally constituted insurance companies. The conditions which they must fulfil in order to obtain approval have been fixed by Royal Orders1. Membership of an institution has for consequence the opening of a personal account and therefore the accumulation of the contributions paid to that account. § 2. — Central Funds Under the 1930 Acts the additions to widows' annuities and the orphans' allowances 2 were charged to the Widows' and Orphans' Fund, in the case of both the workers' and the salaried employees' schemes. This Fund had to receive on the one hand an annual grant from the State, and on the other hand: (1) Capital sums accruing on the death of single, widowed and divorced insured persons; (2) Employers' contributions in respect of wage earners over 65 years ; (3) A contribution from male insured persons fixed at the rates which have been indicated above 3 ; (4) Interest earned by the investment of sums produced by the sale of insurance stamps. These last four items of receipts should allow the Widows' and Orphans' Fund to pay supplementary additions and supplementary allowances—subject to parliamentary approval. A Royal Order of 30 March 1936 withdrew all State aid from the Widows' and Orphans' Fund as far as the workers' scheme is concerned. On the other hand, as concerned that scheme, the Fund had to bear only the cost of supplementary additions and supplementary allowances. In addition, the Widows' and Orphans' Fund is granted the status of a legal person and can therefore receive gifts and bequests 4, subject to previous authorisation by the Ministry of Labour and Social Welfare. 1 2 3 4 Dated 10 June 1930 and 26 November 1931. Other than those payable from the Salaried Employees' Allowances Fund. See Chapter II, 1, pp. 56-57. The Act of 15 December 1937 assigns as further resources to the Widows' and Orphans' Fund insurance reserves which have ceased to have any purpose. 78 ACTUARIAL T E C H N I Q U E AND F I N A N C I A L ORGANISATION The cost of the additions to old-age and widows' annuities and of the orphans' allowances, in the workers' scheme, is borne by án autonomous fund which has been granted the status of a legal person. This " Appropriation Fund " is guaranteed by the State and is under the control of the Audit Office. It is attached to the Ministry of Labour and Social Welfare and is administered by a management committee composed of officials nominated respectively by the Minister of Labour and Social Welfare and the Minister of Finance. The preceding chapter showed how the benefits of the workers' scheme will be provided, in the normal period, as to two-thirds by the accumulation of the joint contributions, and as to one-third by State subsidies chargeable at the date of payment of benefit, the total amount of which is included in the budget each year. The additions to oldage and widows' annuities and the orphans' allowances were instituted for the transitional period to take the place of the contributions which would have been paid if the law had come into force at an earlier date. The charge falling on the State on this account can therefore be included, as to one-third, in the annual budget in the same way as the State subsidies proportionate to annuities constituted by individual accumulation. The other two-thirds are treated as a State liability, amounting at 1 January 1936 to approximately 7 thousand million francs. The State discharges responsibility for the payment of interest on, and the liquidation of, this debt by paying a fixed annuity to the Appropriation Fund. Consequently the resources of the Appropriation .Fund are provided in the following manner: 1. An annual appropriation borne by the State is made equal to one-third of the additions to old-age and widows' annuities and of the orphans' allowances paid in the course of the year. The amount of this grant is not finally determined until the year following that during which the payments have been made. In the budget for the current financial year an approximate amount is credited, and after the auditing of the accounts and the drawing-up of the annual balance sheet there is made either a refund to the Treasury or a supplementary credit to the Appropriation Fund. 2. A constant annuity payment is made, the amount of which is calculated so as to liquidate in 99 years a capital sum equal to the present value (at a rate of interest fixed by Royal Order) of two-thirds of the probable expenditure of the Appropriation Fund. Whenever the Minister of Labour and Social Welfare thinks fit, and at least once in five years, a new estimate is made of the probable expenditure of the Appropriation Fund; the subsequent annuity payments are determined by the actual expenditure in past financial years since 1 January 1936, and by the new estimate. 3. Supplementary annuity payments may be made permitting the reduction of the annuities still outstanding, either by the repayment of loans before their time or by setting up reserves. For a period the resources of the Appropriation Fund will fall short of its expenses and the difference will be met by borrowings from the General Savings and Pension Fund. This institution will be obliged to grant loans, by way of investment, for a term of years ending in every case on 31 December 2034. The rate of interest on these loans BELGIUM 79 will be deduced from the rate of interest in force for the calculation of insurance annuities (at the present time 3.75 per cent.) by adding a loading which will be fixed by Royal Order. After a certain number of years part of the resources of the Appropriation Fund will be used to provide the interest and capital repayment of these loans. When all the additions and allowances have been paid, the remaining annuity payments to be received by the Appropriation Fund up to the end of the ninety-ninth year will be set oft—on the assumption that all the adjustments provided have been effected—against those in respect of which the Fund itself is indebted to the General Savings and Pension Fund. It will then need only a simple transfer of credit in order to liquidate the Appropriation Fund at the end of the transitional period. The Salaried Employees' Allowances Fund bears the cost of old-age, widows' and orphans' allowances granted under the conditions indicated above x. This Fund is supported by: (1) A contribution payable by all employers and all salaried employees who were born before 1 January 1895 2 ; (2) The capital sums which revert to it in the event of the death of single, widowed or divorced insured persons 3. 1 2 3 See Chapter II, 3, pp. 61-62. See Chapter II, 1, pp. 57-58. See Chapter III, 1, pp. 73-74. CHAPTER IV FINANCIAL ADMINISTRATION § 1. — Investment of Funds STATUTORY PROVISIONS. VARIOUS CATEGORIES OF INVESTMENT AUTHORISED Each insurance institution administers the funds which correspond to its accumulation operations, the total of which is at least equal to the total of the mathematical reserves corresponding to its insured members. The authorised categories of investment for the National Pension Fund for Salaried Employees and for approved insurance institutions uicluue : (1) Belgian or Colonial Public Funds and other securities guaranteed by the State; (2) Loans to provinces and communes; (3) Mortgage-bonds on lands or mortgage loans; (4) Debentures of Belgian companies which for at least five years have met their liabilities from their ordinary resources; (5) Loans for land purchase, for the construction or purchase of property situated in Belgium, and for the setting-up or equipment of health establishments for the use of salaried employees. The investments which the Pension Fund is authorised to make by the law governing i t x are approximately the same as those enumerated above. STATISTICS OF THE FUNDS INVESTED IN THE VARIOUS CATEGORIES BY THE GENERAL SAVINGS AND PENSION FUND The moneys of the Pension Fund and the other institutions which combine to make up the General Savings and Pensions Fund are administered jointly. The Pension Fund draws up separately at the end of each year a statement of its investments and their distribution among the various authorised categories. The reserves of the Pension Fund result from the accumulation operations carried out for a population of insured persons including all the workers, the salaried employees who are members of the Pension Fund, and other classes of insured persons 1 Law of 16 March 1865. 81 BELGIUM (miners, and voluntarily insured persons). T h e following table gives the statement of t h e investments of t h e Pension F u n d at t h e end of 1931 and of each subsequent year. TABLE X. — STATEMENT OF T H E INVESTMENTS OF THE P E N S I O N FUND (in thousands of francs) At 31 Dec- At 31 Dec- At 31 Dec- At 31 Dec- At 31 Dec- At 31 Dec- At 31 December ember ember ember ember ember ember 1937 1931 1932 1933 1934 1935 1936 Direct Belgian Rentes . . Indirect Belgian Rentes and securities guaranteed by the State Communal, provincial and municipal bonds . . . . Debentures of Belgian companies Mortgage loans Workers' dwellings: advances to authorised societies Advances to public moneylending offices Totals 340,657 388,082 385,244 676,973 1,043,158 1,244,996 1,649,487 524,435 665,575 254,323 306,750 753,233 793,403 892,291 1,016,307 1,271,214 397,955 395,854 393,670 452,840 275,665 109,543 426,484 135,374 530,115 138,303 474,534 583,504 142,210 567,735 129,340 570,178 122,799 671,313 123,116 743,895 887,994 39,500 38,800 997,687 1.005.162 948,554 907,924 571,472 32,500 32,550 32,650 2,288,018 2,849,059 3,240,387 3,634,606 4,006,998 4,347,594 ¿,793,786 37,850 37,500 § 2. — Financial Results The General Savings and Pension F u n d publishes each year a report in which are shown t h e situation a n d t h e operations of t h e Pension Fund [4]. BIBLIOGRAPHY Legislation Act of 14 July 1930, relating to the insurance of workers. INTERNA- TIONAL LABOUR OFFICE: Legislative Series, 1930, Bel. 7. Act of 18 June 1930, relating to the insurance of salaried employees. INTERNATIONAL LABOUR OFFICE: Legislative Series, 1930, Bel. 6. Act of 15 December 1937, relating to insurance against old age and premature death. INTERNATIONAL LABOUR OFFICE: Legislative Series, 1937, Bel. 7. Publications of the Insurance 4. 5. Institutions Comptes rendus (annuels) des opérations et de la situation de la Caisse générale d'épargne et de retraite. Tables belges 1934. Mortality tables constructed by the Actuarial Department of the General Savings and Pension Fund. 6 82 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION 6. MINISTÈRE DE L'INTÉRIEUR ET DE LA SANTÉ PUBLIQUE, Office central 7. de Statistique: Tables de mortalité de la population belge 1928-1932. La Caisse générale d'épargne et de retraite et ses différents services. Brussels, 1930. 8. CAISSE GÉNÉRALE D'ÉPARGNE ET DE RETRAITE, SERVICE DE LA CAISSE DE RETRAITE: Rentes viagères, pensions des salariés, travailleurs indépendants et assurés libres. Brussels, 1934. 9. CAISSE GÉNÉRALE D'ÉPARGNE ET DE RETRAITE, SERVICE DE LA CAISSE DE RETRAITE: Pensions des employés. Brussels, 1932. 10. CAISSE NATIONALE DES PENSIONS POUR EMPLOYÉS: Renseignements généraux. Tarifs et applications. Books and Surveys 11. 12. 13. H. VELGE: Les lois belges d'assurance et de prévoyance sociales. L'Edition universelle, 53, rue Royale, Brussels, 1933. E. MELOT: Les pensions de vieillesse. Editions de la Société d'études morales, sociales et juridiques, 9, rue de Namur, Louvain, 1934. DEROOVER and THÉ ATE: New Social Insurance Laws in Belgium. Transactions of the Eighth International Congress of Actuaries, London, 1927. Vol. I l l , pp. 92-107. GZEGHO-SLO VARIA Invalidity, Old-Age and Widows' and O r p h a n s ' Insurance for Workers CONTENTS Page 86 INTRODUCTION CHAPTER I: Demographic Estimates, Bases and Experience 1. 2. 87 Biometrie Tables Mortality and Invalidity Tables for Insured Persons . . . Tables on Marital Status and Family Statistics Insured Population . Preparatory Estimates Experience 3. Number of Beneficiaries 106 . . . . Table of Symbols introduced in Chapter I CHAPTER I I : Financial Estimates, Bases and Experience 1. 87 87 94 104 104 Contributions ' Wage Classes and Rates of Contribution Calculation of the Present Value of the Contributions which the Scheme should receive under the Terms of the Legislation Total Present Value of All Contributions and Estimate of Their Annual Amount Experience 110 113 115 115 115 116 118 119 2. State Grants 125 3. Benefits Conditions of Award and Computation of Benefits . . . . Essential Factors in the Calculation of the Present Value of Benefits Total Present Value of Benefits and Total Annual Emerging Cost Experience 127 127 Other Expenditure . . . • Medical Assistance Administration Expenses 145 145 146 4. Table of Symbols introduced in Chapter II 133 143 144 147 84 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Page CHAPTER III : Financial System 149 1. Calculation of the General Average Premiums 149 2. Preliminary Valuation and Table of Annual Estimates . . . 152 3. Actuarial Balance-Sheets and Financial Development of the Central Institution 154 CHAPTER IV: Financial Administration 158 1. Investment of Funds. Statutory Provisions and Regulations Prescribed Classes of Securities Authorised Classes of Securities Other Statutory Provisions Selection of Investments The Investment of Funds in Practice 158 158 159 159 160 161 2. Statistics of Investments Composition of the Funds Income from Investments Rate of Interest Yielded 161 161 161 163 3. ' Accounting and Statistics. Actuarial, and Financial Control . Statutory Provisions Statistical Returns Publication of Statistics BIBLIOGRAPHY . . . . . ' 163 163 163 165 165 INDEX OF TABLES I. II. HI. IV. Probabilities of Becoming Invalid Validity Table Probabilities of being Married Distribution of Wives of Insured Men according to Category V. Average Age of Wife VI. Exit from Insurance and Marital Status of Women . . VII. Widows' Dependent Children VIII. Initial Insured Population IX. Male Insured Population. Female Insured Population X. Insured Population as at 1 January 1930 XI. Numbers of Beneficiaries (Estimates) XII. Invalidity Pensions. Old-Age Pensions XIII. Widows' and Widowers' Pensions. Orphans' Pensions XIV. Dowry and Lump-Sum Payment on Death XV. Average Daily Wage (Males and Females) XVI. Average Weekly Contribution (Males and Females) . . XVII. Annual Numbers of Full Contributors XVIII. Average Annual Number of Contribution Days 89 92 94 Age . . . . . . . . 97 99 101 104 105 107 109 110 Ill 112 113 120 122 123 124 CZECHOSLOVAKIA 85 Page XIX. XX. XXI. XXII. XXIII. XXIV. XXV. XXVI. XXVII. XXVIII. XXIX. Annual Amounts of State Individual Subsidies (Estimates) . 126 State Individual Subsidies 127 Invalidity Pension: Amount and Percentage of Average Wage 133 Supplementary Benefits in Respect of Insured Persons born before 1 January 1899 133 Annual Emerging Cost of Benefits (Estimates) 143 Amount of Benefits Paid each Year. Average Amount of Pension Paid each Year 144 Preliminary Valuation Sheet 153 Table of Annual Estimates: Probable Progress of Income and Outgo — Growth of Funds 154 Actuarial Balance-Sheet of the Central Institution as at 1 January 1930 156 Financial Progress of the Central Institution from 1926 to 1937 157 List of Investments of the Central Institution as at 31 December in each Year 162 INTRODUCTION The compulsory .insurance of workers against invalidity, old age and death was initiated in the Republic of Gzecho-SIovakia by the Act of 9 October 1924; it came into force on 1 July 1926. The original legislation was amended as from 1 January 1929, by the Act of 8 November 1928 [5], which extended the scope of the benefits and increased their amount. The Government Order of 15 June 1934 l had as its principal object the improvement of the financial condition of institutions effecting sickness insurance, which had suffered from the decrease in membership and the fall in wages caused by the economic crisis. It reduced various sickness benefits, but on the other hand made certain improvements in the benefits of the insurance scheme against invalidity, old age and death. The improvements, which operated as from 1 July 1934, included the following principal amendments: (1) the lowering of the pension age for widows from 65 to 60; (2) the addition of supplementary benefits to insured persons born before 1 January 1899; (3) the extension of the period during which the right to all benefits is maintained. The compulsory insurance of workers against invalidity, old age and death, to which this anatysis is devoted and the scope of which will be defined later, is administered by the Central Social Insurance Institution, which is established at Prague. It delegates to sickness insurance institutions—which are under its control—certain administrative functions, such as the fixing and receipt of contributions, the admission, cancellation and changes in class of insured persons, the receipt of applications for benefit, and the acceptance of such applications after investigation, with supporting- documents. The Central Institution also acts as co-ordinating medium between the various sickness insurance organisations, whose administrative technique it strives to unify and improve. It was impossible to include within the scope of this volume the studies of a purely technical nature which accompanied the preparation of the Czecho-Slovak legislation. The documents' which seemed to show most clearly the technique underlying the system of insurance which is the subject of this monograph—and to which reference is constantly made—are, on the one hand, the reports leading up to the 1924 Act, more particularly the explanatory memorandum of 1924[2], and, on the other hand, the parliamentary document [6] which reproduces the conclusions arrived at in the investigations. leading up to the 1934 Act and in which are included the actuarial balance-sheet of 1 January 1930 and the data on which it is based. Finally, this, like the remaining sections of the volume, is confined to compulsory insurance, leaving aside voluntary insurance as far as was possible to do so 2 . 1 To which legal force was given by another legislative document (Act No.2 146 of 1934): Bibliography No. 1. . Although they do not come within the scope of this volume, marriage allowances could not be disregarded, because they form an integral part of the financial organisation of the system, because they, together with the other benefits, are covered by a single inclusive contribution, and finally because they figure in the actuarial balance sheet. CHAPTER I DEMOGRAPHIC ESTIMATES, BASES AND EXPERIENCE § 1. — Biometrie Tables This section is divided into two parts devoted respectively to: (a) The tables of mortality and invalidity which constitute the essential technical bases of insurance against invalidity and old age. (b) The tables of dependency statistics to which recourse must be made in the insurance of benefits on behalf of members of the insured person's family. MORTALITY AND INVALIDITY TABLES FOR INSURED PERSONS The demographic bases underlying the system of insurance against invalidity and old age may be considered as centred around two " validity tables " (Aktivitätsordnung) which give for males and females respectively the subdivision into healthy and invalid lives of the survivors of an initial group of healthy persons of the same age. These validity tables are not produced directly from the statistical material obtained from actual observations; they are deduced, by methods which will be described later, from the following data: General life probabilities (healthy and invalid lives together); Rates of cessation of invalidity (according to age and duration of invalidity) ; Probabilities of becoming invalid. General Life Tables In the investigations leading up to the 1924 Act use was made of the life table for males and females constructed for the general Austrian population by means of: The general Census of 31 December 1910; The records of deaths during the 1years 1906 to 1910, and Graduation by the Bruns method . These two life tables, which are denoted by Zx, are reproduced below in columns 4 and 7 of table II. For the actuarial valuations as at 1 January 1935 the Austrian table appeared to be too high and for it was substituted the mortality table which had just been constructed for Czecho-Slovakia on the basis of the deaths registered in the years 1929 to 1932 and of the general Census of the population on 1 December 1930. 1 Oesterreichische Statistik, Neue Folge, I. Band, 4. Heft, Karl Gerold's Sohn, Vienna, 1917. 88 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Rates of Cessation of Invalidity Use has been made of " select " rates of cessation of invalidity CO tO 1-* p p o o p p tO tO tO i o tO tO •O VX OX £ - CO CO CTï H» CA Hi» IO £> en no os to ^ O O O O. O "tOfcObO IO "to CO tO tO I-* H* ^ O l tO v j t o CO iO CO CO O 0.2120 0.2173 0.2223 1 1 11 1 1 " O CTS CTS CTS CTS CTS CTS CTS CTS CTS O co o en m ¡t> co io H* CTS en en en en O O 00 <1 OS en en en en en hi> co io CTI tO IO CO O WOOÜlvJsO p ^ Ca vj 00 p o p p ' p , ^ l^> ^ }£* t o i-5- O t o (O O rf> O O O O o o to co o p o vj h* o p p o o CTÌ en H* to o o p p p p p p p p p p ö o © o o o ö o ò ö rf> CO CO IO bO CO v.) tO 00 rfS O 00 en >í> CTS H* OO O rf O O i t - ^ O O o O O O O O o o o t-A H* O o o co 00 H* CO 0 5 0 « o o o O O co o OS v j w y \ o o o o o o CTs en * co co e*? o o e« p o p p © IO "»-** Î-S* H* Ï-* o o o o O t û O C D v J Ca h(> co t o i-* CT» CO tO CO Ova jí> M* to en «!»v3CDO\ p o oo to o o o #" H> co o o Co en #•* ó o co O «O o o to vj O o o o o to to CO i-* CTs - ^ o o H O e 91 CZECHO-SLOVAKIA When the actuarial balance-sheet as at 1 January 1935 was being drawn up it was found that the rates of invalidity which had been in use up to then were too low: consequently it was decided to substitute new figures based on the experience during the years 1925-1930 of the insurance of workers in Germany against invalidity, old age and death 1. Construction of Validity Tables For each sex a group of 100,000 healthy persons is observed from age 20, and the numbers laa and ln of survivors who are healthy and invalid respectively are calculated for all ages x. From the rates of cessation of invalidity o n + f e it is possible to obtain the probability fi% ? that an insured person who became invalid at age Z, will be living and still an invalid at age x, thus: PU = (* - °J (* - w ) • • • ( ! - ' r a + ^ J • Using continuous expressions and instantaneous rates of becoming invalid i (x), the number of invalids at age x produced by the initial group at age 20 is expressed by the formula t; = fr^i^f di The numbers lx are calculated from the life table lx, from the rates of becoming invalid ix and from the rates of cessation of invalidity <*R]+ft by means of approximate methods which are equivalent to the solution of Volterra's integral equation of the second degree: laa[v\ — nv\ - j rr(Ç)*(5)^(*,ç)rfç. For ages less than 20 the validity table is extended by means of the formula ¿x+i = ''x V1 aa 9x *x) in which the rates of mortality q of healthy persons are merged with the rates qx applicable to the general mortality. The two validity tables which were constructed, by the method which we have just given in principle, in the course of the studies preparatory to the 1924 Act are reproduced below: 1 See the section of this volume devoted to the insurance of workers in Germany against invalidity, old age and death, p. 401. 92 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION TABLE I I . V A L I D I T Y TABLE Females Males Age (1) Healthy lives Invalids Total (4) = (2) Healthy lives (2) (3) + (3) (5) Invalid (6) Total (7) = (5) + (6) 20 21 22 23 24 25 . . . . . . .. .. .. .. .. .. 100,000 99,299 98,576 97,853 97,130 96,410 36 69 103 141 183 100,000 99,335 98,645 97,956 97,271 96,593 100,000 99,289 98,547 97,778 96,966 96,119 26 27 28 29 30 . . . . . .. .. .. .. .. 95,693 94,977 94,258 93,538 92,814 229 279 334 390 449 95,922 95,256 94,592 93,928 93,263 95,238 94,337 93,416 92,462 91,489 1,054 1,275 95,752 95,008 94,264 93,516 92,764 31 32 33 34 35 . . . . . .. .. .. .. .. 92,080 91,334 90,570 89,784 88,971 515 582 650 719 791 92,595 91,916 91,220 90,503 89,762 90,496 89,486 88,466 87,434 86,392 1,511 . 1,759 2,009 2,266 2,525 92,007 91,245 90,475 89,700 88,917 36 37 38 39 40 . . . . . .. .. . . . . .. o o .1 o n 864 940 85,337 84,268 83,174 82,060 80,910 2,790 3,058 3,342 3,639 3,963 88,127 87,326 86,516 85,699 84,873 41 42 43 44 45 . . . . . 46 47 48 49 50 45 99 164 256 373 514 671 848 100,000 99,334 98,646 97,942 97,222 96,492 87,250 86,335 85,373 84,368 1,022 1,112 1,207 88,991 88,190 87,357 86,485 85,575 .. .. .. .. .. 83,319 82,234 81,111 79,945 78,726 1,318 1,441 1,578 1,728 1,898 84,637 83,675 82,689 81,673 80,624 79,727 78,519 77,281 76,013 74,713 4,309 4,675 5,060 5,465 5,892 84,036 83,194 82,341 81,478 80,605 . . . . . .. .. .. .. .. 77,545 76,116 74,692 73,184 71,583 2,082 2,284 2,524 2,797 3,110 79,536 78,400 77,216 75,981 74,693 73,383 72,007 70,575 69,077 67,483 6,338 6,814 7,326 7,880 8,498 79,721 78,821 77,901 76,957 75,981 51 52 53 54 55 . . . . . .. .. .. .. .. 69,891 68,098 ' 66,195 64,180 62,030 3.457 3,848 4,288 4,778 5,341 73,348 71,946 70,483 68,958 67,371 65,770 63,941 61,964 59,844 57,545 9,196 9,961 10,819 11,750 12,785 74,966 73,902 72,783 71,594 70,330 56 57 58 59 60 . . . . . .. .. .. .. .. 59,749 57,302 54,688 51,906 48,962 5,968 6,691 7,515 8,433 9,440 65,717 63,993 62,203 60,339 58,402 55,042 52,331 49,367 46,139 42,599 13,935 15,199 16,613 18,183 19,953 68,977 67,530 65,980 64,322 62,552 61 62 63 64 65 . . . . . .. .. .. .. . . . 45,829 42,487 38,978 35,341 31,633 10,562 11,820 13,170 14,576 15,985 56,391 54,307 52,148 49,917 47,618 38,823 34,926 31,019 27,222 23,584 21,846 23,750 25,554 27,145 28,479 60,669 58,676 56,573 54,367 52,063 UOjlii / 93 CZECHOSLOVAKIA TABLE II. VALIDITY TABLE (continued) Females Males Age (1) Healthy lives (2) Invalids (3) Total (4) - (2) + (3) Healtny lives (5) Invalids (6) Total (7) = (5) + (6) 66 67 68 69 70 . . . . . . . . . . . . . . . 27,942 24,356 20,917 17,682 14,709 17,309 18,470 19,429 20,141 20,559 45,251 42,826 40,346 37,823 35,268 20,160 16,977 14,069 11,419 9,021 29,512 30,221 30,585 30,628 30,369 49,672 47,198 44,654 42,047 39,390 71 72 73 74 75 . . . . . . . . . . . . . . . 11,997 9,631 7,602 5.928 4,570 20,695 20,478 19,935 19,064 17,922 32.692 30,109 27,537 24,992 22,492 6,921 5,127 3,640 2,455 1,530 29,774 28,843 27,587 26.028 24,224 36,695 33,970 31,227 28,483 25,754 76 77 78 79 80 . . . . . . . . . . . . . 3,481 2,614 1,929 1,394 973 16,576 15,092 13,532 11,948 10,389 20,057 17,706 15,461 13,342 11,362 820 282 22,238 20,137 17,982 23,058 20,419 17,858 81 82 83 84 85 86 . . . . . . . . . . . . . . . . . . 645 399 215 88 10 8,893 7,485 6,188 5,017 3,984 3,094 :— — — — — — — ~ — — — — — — — ~ ~ 9,538 7,884 6,403 5,105^ 3,994 3,069 — — — — — — — M. Tauberes adjusting Coefficients The probabilities of cessation of invalidity a refer to exits from invalidity which are due not only to death but also ,to other causes. In a certain number of cases it is necessary to have probabilities which refer only to exits due to death. For this purpose use is made of M. Tauber's coefficient TX, which shows, according to the German experience and for quinquennial ages of entry on invalidity, the proportion of cessations of invalidity which is due to death. Age at entry on invalidity 20 25 30 35 40 45 Coefficient 0.800 0.825 0.850 0.875 0.900 0.925 Age at entry on invalidity 50 55 60 65 70 . . . . . . Coefficient 0.950 0.975 1.000 1.000 1.000 94 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION TABLES ON MARITAL STATUS AND FAMILY STATISTICS Probability of being Married, Males The probability Çm that a male insured person aged x is married is derived from the Census taken in Gzecho-Slovakia on 15 February 1921 [1]. These results, for quinquennial age groups, have been adopted after comparison with figures which had been obtained in respect of Austrian workers during the year 1896. By graphic interpolation the following probabilities of being married applicable to each age have been obtained: TABLE I I I . — Age Age Males 15 . . . 0.0004 16 . . . 17 . . . 18 . . . 20 . .. 0.0007 .0.0011 0.0019 0.0036 0.0108 21 22 23 24 25 . .. ... ... . .. . .. 0.0373 0.0842 0.1456 0.2108 0.2761 26 27 28 29 30 . .. .... . .. . .. . .. 0.3414 0.4066 0.4718 0.5225 0.5802 31 32 33 34 35 . . . . . 36 37 38 39 40 ... . .. . .. ... . .. 4 f\ 13 P R O B A B I L I T I E S OF B E I N G . . . .. .. .. .. .. 0.6319 0.6791 0.7221 0.7556 ' 0.7822 0.8018 0.8177 0.8297 0.8380 0.8443 MARRIED Males 'Age Males 41 42 43 44 45 . . . . . .. .. .. .. .. .0.8498 0.8546 0.8565 0.8584 0.8592 66 67 68 69 70 . .. . .. ... . .. . .. 0.7406 0.7275 0.7141 0.6990 0.6839 46 47 48 49 50 . .. . .. . .. . .. ... 0.8598 0.8603 0.8606 0.8592 0.8576 71 72 73 74 75 . . . . . . . . . . 0.6688 0.6537 0.6386 0.6224 0.6062 51 '52 53 54 55 . .. ... . .. . .. . .. 0.8558 0.8527 0.8493 0.8448 0.8387 76 77 78 79 80 ... . .. . .. . .. . .. 0.5899 0.5737 0.5575 0.5457 0.5338 56 57 58 59 60 ; . . . . .. .. .. .. .. 0.8321 0.8246 0.8166 0.8095 .0.8014 81 82 83 84 85 . . . . . .. .. .. .. .. 0.5220 0.5101 0.4983 0.4796 0.4610 61 62 63 64 65 ... . .. . .. . .. . .. 0.7933 0.7847 0.7756 0.7644 0.7525 86 87 88 89 90 . . . . . . ; . . . 0.4423 0.4237 0.4050 0.3988 0.3855 . . . . . . . . . . These probabilities of being married enable the number 0\tx of married insured men to be calculated at each age from the total number of insured men JRX, thus: 0f]ll = JR* • C 95 CZECHO-SLOVA.KIA Probabilities of being Married, Females The probability XJ that a woman aged y is married has also been derived from the results of the Census taken in Gzecho-Slovakia on 15 February 1921; it has only been used in calculations referring to marriage allowances. Marriage Rates, Females The probability ¡x that a woman aged y will marry during the year has been constructed by graphic interpolation from quinquennial figures obtained from Austrian statistics l relating approximately to the territory of the Gzecho-Slovak Republic. Distribution of Wives of Insured Men according to Age and Category Calculation was first made of the numbers V of women aged y, who are wives of insured men, by the following procedure. In the course of the work on the 1921 Census an investigation into 746,551 marriages was made at Prague and its suburbs. These marriages were classified according to age of husband x and age of wife y, in both cases in quinquennial age groups. The resulting double-entry table has been used in the following manner. If we denote by ffljy the number in this table which corresponds to the group whose mean ages are a:' and y' and if we assume that nú, = 2 ^ > then the number of wives of insured men y=y'+2 V V = ¿i ^v y=y'-2 is calculated, in each quinquennial age group, from the number of insured married men by means of the formula: x v i _ 'S mc V„ i/,l y' ^ j x' '' '3c' > j ^ J2J m x'y' V' From the resulting values V , the numbers V corresponding to each individual age y is obtained by means of graphic interpolation. 1 Oesterreichische Statistik, Neue Folge, 14. Band, 1. Heft (p. 22 Übersicht 8; column headed " Sudetenländer "), Karl Gerold's Sohn, Vienna, 1918. 96 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The total number of women aged y who are wives of insured men was then divided into categories in accordance with the following table and formulae: Healthy persons, themselves insured: Tpa Healthy persons: V — — — — __ — — — — — v „ V 70 38Ò 790 ' 1,360 2,270 1 2 6 11 2 9 30 52 3,700 6,400 10,800 21,400' 24,100 20,528 20,898 21,093 21,172 21,130 19 27 ' 36 45 56 79 113 150 193 241 25,400 26,000 26,280 26,400 26,380 4,908 4,858 4,805 4,751 4,696 21,050 20,922 20,753 20,554 20,296 68 81 94 • 108 122 294 349 408 467 526 26,320 26,210 26,060 25,880 25,640 . . . . . . . '. '. \ . . . 4.640 4,582 4,518 4,371 20,000 19,568 19,085 18^527 17,930 136 150 164 179 194 584 640 693 744 795 25,360 24,940 24.460 23,900 23,290 . . . . . ;. . . . . . . . 4,289 4,201 4,114 4,026 3,938 17,313 16,633 16,074 15,580 15,140 210 227 250 264 283 848 899 952 1,020 1,089 22,660 21,960 21,390 20,890 20,450 . . . 4¡450 45. 46 . 47 . 48 . 49 . . . . . . . . . . . '. . . . . 3,851 3,763 3,675 3,587 3,500 l'4,743 14,389 13,947 13,427 12,890 304 . 326 348 372 399 1,162 1,242 1,320 1,394 1,471 20,060 19,720 19,290 18,780 18,260 50 51 52 53 54 . . . . . . . . . . . . . . . 3,390 3,230 2,969 2,662 2,437 11,860 10,772 9,940 9,359 8,847 427 452 463 469 478 1,493 1,506 1,548 1,630 1,738 17,170 15,960 14,920 14,120 13,500 . . . . . 7 98 ACTUARIAL TECHNIQUE AND FINANCIAL TABLE IV. ORGANISATION DISTRIBUTION OF WIVES OF INSURED MEN TO AGE AND CATEGORY (continued) ACCORDING Wives of insured men 0 Invalid Healthy Age Total Themselves insured v V pa V Not themselves insured Pensioned "pa vt(p) v y V Not pensioned v t uip) V V V 55 56 57 58 59 . . . . . . . . . . . . . . . . . . 2,251 2,105 1,969 1,837 1,708 8,320 7,726 7,082 6,393 5,680 500 533 572 619 673 1,849 1,956 2,057 2,152 2,239 12,920 12,320 11,680 11,000 10,300 60 61 62 63 64 . . . . . . . . . . . . . . . 1,584 1,460 1,336 1,212 1,088 4,913 4,066 3,277 2,582 2,021 742 822 908 998 1,085 2,301 2,289 2,229 2,128 2,016 9,540 8,640 7,750 6,920 6,210 . . . . . e ecf\ . . . f\C r a u i X ETC C 1,OUO A M r r 1,1^1 A onn J.,OZ / O,OVJ\* 66 67 68 69 . . . . . . . . . . . . . . . . 840 716 610 517 1,157 831 553 330 1,230 1,275 1,326 1,387 1,693 1,478 1,201 886 4,920 4,300 3,690 3,120 70 71 72 73 74 . . . . . . . . . . . . . . . . . . . . 430 360 260 167 100 175 44. 587 187 —• — — 1,448 1,549 1,460 1,263 1,060 •— — — 2,640 2,140 1,720 1,430 1,160 75 76 77 78 79 . . . . . . . . . . . . . . . . . . . . 53 23 7 — — — —. — — 847 637 473 370 280 — — — — 900 660 480 370 280 80 81 82 83 84 . . . . . . . . . . . . . . . . . . . . — — — — — — — — 210 160 120 80 60 .—. — — — 210 160 120 80 60 85 86 87 88 . . . . . . . . . . . . . . . . — — — — — — 40 30 20 10 — — — 40 30 20 10 CC yj*j . 99 CZECHOSLOVAKIA Probability that at the Moment of Death of an Insured Man his Widow (aged j), who is not Herself Insured, will never enter into Insurance These probabilities wnp have been borrowed from data used in Germany for the technical calculations relating to the insurance of workers against invalidity, old age and death 1. Probability that the Widow of an Insured Man will not Herself be Insured at Age y For these probabilities ü n p there have been adopted the figures representing, according to the general census of the Czecho-SIovak population on 15 February 1921, the ratio of widows who are not employed to the total number of widows. Average Age of Wife The average age of the wife for each age of busband has been calculated with the help of the table mentioned above 2 which gives the distribution of marriages according to the ages of husband and wife (for quinquennial age groups). By using the formulae y = JL 2i ™x>v y and by interpolation, the age yx corresponding to each age x has been obtained: TABLE V. Age of husband 15 16 17 18 19 20 21 22 23 24 AVERAGE AGE OF WIFE Age of wife . . . . . . . . . . . . Age of husband 21 21 21 22 22 25 26 27 28 29 23 23 24 24 24 30 31 32 33 34 Age of wife 25 25 26 26 27 0 . . . . . . . 28 28 29 30 31 1 See the section of this volume devoted to this insurance scheme, pp. 331332 and 334. 2 See p. 320. lOO ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION TABLE V. — AVERAGE AGE OF W I F E Age of husband Age of wife (continued) Age of husband Age of wife 35 36 37 38 39 32 33 34 35 36 65 66 67 68 69 40 41 42 43 44 37 37 38 40 70 71 72 73 74 63 64 65 65 66 45 46 47 48 49 41 42 43 43 44 75 76 77 78 79 67 67 68 69 69 50 51 52 53 ÇA 45 46 47 48 80 81 82 83 70 70 71 72 55 56 57 58 59 50 51 52 53 54 85 86 87 88 89 73 73 74 74 75 60 61 62 63 64 55 56 57 58 59 90 75 . 38 60 60 61 62 63 ...>... rtn Cessation of Insurance and Marital Status of Insured Women Data collected by the Central Irstitution during the years 1926-30 provided material for constructing the table reproduced" below which gives, for an initial group of 103,045 insured women at age 15, the number (P^Ja) who remain in insurance, subdivided into married, widowed or divorced (¿° a ) and spinsters (l^^). The calculations have been based on the following formulae [6]: aaivp) Pjaa +K ;aay reproduced below: TABLE V I I I . — Age INITIAL I N S U R E D POPULATION Males Females .... .... .... .... .... 27,348 26,773 26,230 25,757 25,398 10,072 9,865 9,668 9,496 9,342 46 47 48 49 50 ... ... ... ... ... . . . . . 25,096 24,747 24,358 23,943 23,505 9,187 9,016 8,828 8,634 8,379 28,488 24,892 21,724 19,361 17,645 51 52 53 54 55 .... .... .... .... .... 23,032 22,504 21,906 21,200 20,392 8,121 7,838 7,530 7,192 6,847 37,412 34,814 33,078 31,917 31,013 16,357 15,263 14,316 13,455 12,734 56 57 58 59 60 .... .... .... .... .... 19,341 17,979 16,765 15,774 6,500 6,204 5,966 5,779 A K CiCC. K till 30,311 29,717 29,126 28,534 27,945 12,108 11,551 11,047 10,643 10,324 Age Males Females 15 55,728 30,974 16 17 18 . . . . . 19 20 71,507 83,661 85,326 85,114 84,071 43,798 50,451 54,600 53,034 49,646 41 42 43 44 45 21 22 23 24 25 81,653 77,706 70,168 60,186 51,504 46,094 42,716 39,423 35,997 32,288 26 27 28 29 30 47,795 46,465 45,023 43,252 40,828 31 32 33 34 35 36 37 38 39 40 . . . . . Total . . 1,790,968 1,111.857 Annual Numbers of Entrants It was observed first of all that: (1) Workers usually enter into employment before the age of 20 and consequently entry into insurance will take place almost always before that age; (2) Insured persons who enter after age 20 will for the most part have already been employed in an insured occupation; in most cases these insured persons will bring with them a capital sum and their movement should be considered, from the point of 106 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION view of the financial stability of the scheme, not as an entry but as a transfer. (3) Insured persons who enter after age 20 without bringing a capital sum as transfer value will be very few in number and the losses due to such entrants will be more than compensated by the reduction in liabilities consequent upon persons leaving the scheme. As a result of these considerations it was assumed that entry into insurance would always take place between the ages of 15 and 19. The number of insured persons entering at each of these five ages has been deduced from the figures relating to the initial population in the case of men by the formula ,aa l'x-í and by an analogous formula in the case of women. The annual coefficients of increase cx were first calculated by means of the 1900 and 1910 Censuses. However, for the calculation of the annual number of entrants 2 t m and 2 1 , as a safety measure and on the assumption that the population would not continue to increase at a rate as rapid as that during the decennium 1900-1910, all the coefficients cx were reduced to unity. The followingMale» are the results obtained in this manner: Females 21™ = 55,728 2 l ( 6 = 30,1 21™ = 16,013 21' 16 = 12,! 21™ = 12,483 Srt„ = 6,1 21™ = 2,092 K= *.' 21™ = 274 EXPERIENCE The insured population is the subject of two series of statistics, the most important of which will now be indicated, with the significance of each, but the summary analysis of the processes by which they are constructed will be reserved for Chapter IV. Each sickness insurance institution follows the movement of its membership from day to day by means of the admissions and cancellations which it registers. From the daily figures thus obtained are calculated monthly averages which are sent (on monthly returns) to the Central Institution, which arranges for their publication [11, 12]. By means of counterfoils detached from folios which the sickness insurance institutions send annually to the Central Institution an enumeration of the insured membership took place on 30 June and 31 December of each year up to 1932 and on 30 June 1933 and 1934. The results are tabulated separately for the different types of sickness insurance institution in quinquennial age groups and for each sex [10, 12]. The following table reproduces the figures relating to the total insured population: 0 107 CZECHO-SLOVAKIA TABLE IX (à). — 1927 Year of birth 30.VI 1916 and later 1911-1916 1906-1910 1901-1905 1896-1900 1891-1895 1886-1890 1881-1885 1876-1880 1871-1875 1866-1870 1865 and earlier. Not stated MALE I N S U R E D POPULATION 31.XII 30.VI 1930 1929 1928 31.XII 30.VI 31.XII 30.VI 31.XII 121,420 329,113 263,468 194,178 132,726 105,314 91,364 81,502 71,163 49,616 146,063 241,118 212,918 163,619 109,128 86,750 74,746 66,117 57,768 40,101 196,503 323,650 275,933 197,790 133,485 105,912 92,620 82,160 71,370 48,410 201,510 223,467 217,862 160,177 107,462 85,328 73,260 .64,335 56,025 38,197 251,140 315,332 275,319 195,764 132,750 106,207 92,662 82,079 70,770 47,515 202,381 211,459 216,213 156,886 106,327 84,349 71,396 65,236 55,138 36,622 260,447 275,699 248,897 180,344 123,322 98,472 85,839 74,714 63,504 41,450 205,810 177,379 191,144 140,217 94,341 75,275 64,861 56,136 47,067 30,608 784 3,773 639 2,863 712 3,204 589 2,525 495 2,919 348 2,239 403 1,116 301 699 T o t a l . . 1,444,421 1,201,830 1,531,749 1,230,737 1,572,952 1,208,594 1,454,207 1,083,838 1932 1931 Year of birth 30. V I 31.XII .30.VI 31.XII 1933 1934 30.VI 30. V I 1916 later . . 1911-1916 . 1906-1910 . 1901-1905 . 1896-1900 . 1891-1895 . 1886-1890 . 1881-1885 . 1876-1880 . 1871-1875 . 1866-1870 . 1865 and earlier. . Not stated. 297 295,261 261,619 241,540 177,160 119,377 96,515 82,428 69,438 58,378 35,519 223 205,386 155,580 164,077 121,936 81,603 64,520 55,172 47,177 38,968 23,512 18,111 265,822 228,477 213,939 156,543 105,098 82,594 70,635 59,288 46,799 25,607 27,547 164,791 138,220 143,016 105,987 70,507 55,335 46,627 39,127 31,191 16,985 49,038 217,787 198,567 188,569 137,836 92,441 71,970 60,447 49,015 37,015 17,889 81,998 192,472 210,912 187,136 138,010 92,064 71,059 58,228 46,150 32,751 13,323 322 723 209 489 187 487 135 286 136 729 109 865 T o t a l . . 1,438,577 958,852 1,273,587 839,754 1,121,439 1,125,077 108 ACTUARIAL T E C H N I Q U E AND F I N A N C I A L ORGANISATION TABLE IX (b). — F E M A L E I N S U R E D POPULATION 1928 1927 1929 1930 Y e a r of birth 31.XII 30. V I 1916 and later . . . 1911-1916 . 1906-1910 . 1901-1905 . 1896-1900 . 1891-1895 . 1886-1890 . 1881-1885 . 1876-1880 . 1871-1875 . 1866-1870 . 1865 and earlier . . Not stated . 31.XII 30.VI 30.VI 31.XII 31.XII 30.VI . . 71,378 90,038 121,173 134,265 161,560 148,596 183,247 160,033 . 246,879 219,463 240,767 210,896 233,546 199,690 207,232 170,672 . 160,757 141,450 148,498 128,079 140,047 120,156 122,738 100,709 . 98,519 88,229 94,981 82,800 92,986 80,339 84,222 69,675 . 65,707 60,084 65,576 57,822 66,273 57,129 62,171 51,276 . 50,663 45,982 50,422 44,583 50,726 44,053 47,423 38,921 . 39,615 35,571 39,123 34,136 39,348 33,888 37,247 29,961 . 31,282 27,980 30,908 26,637 30,835 26,270 27,871 22,420 . 24,853 21,776 24,136 . 20,575 23,586 19,979 21,931 17,085 . 15,253 13,168 14,472 12,306 13,557 11,338 12,531 9,523 . . 296 2,437 UU / jUU./ 232 1,850 <-} f. K OO O 242 2,009 o o o OAn 211 1,583 30.VI 1916 and later . . 218 1911-1916 . 219,232 1906-1910 . 188,474 1901-1905 . 112,936 1896-1900 . 81,179 1891-1895 . 60,143 1886-1890 . 45,512 1881-1885 . 35,230 1876-1880 . 26,617 1871-1875 . 20,212 1866-1870 . 10,945 1865 and earlier. . 209 Not stated. 309 Total. . 801,216 152 1,626 296 604 nnn r * n 225 377 /»n/\ / o ö , o vo 1931 Year of birth 246 1,955 1932 1933 1934 31.XII 30.YI 31.XII 30.VI 30.YI 167 189,346 148,510 85,246 63,194 47,119 35,327 26,988 20,100 15,001 7,765 11,762 215,350 159,183 96,837 70,646 52,109 38,825 29,830 22,457 16,528 7,941 18,897 178,904 128,112 78,032 56,364 41,715 30,869 23,246 17,167 12,270 5,513 34,056 207,369 145,491 90,953 67,481 50,039 36,805 27,948 20,481 14,450 5,943 62,217 197,076 136,994 88,413 67,108 49,811 35,982 26,566 18,915 12,377 4,273 141 240 144 293 98 171 90 424 82 651 639,144 721,905 591,358 701,530 700,465 nnn 109 CZECHO-SLOVAKIA For the actuarial balance-sheet as at 1 January 1930 the following figures taken from the registration statistics [6] have been used to ascertain, at the valuation date, the insured membership, and its distribution by age: TABLE X. — INSURED POPULATION AS AT 1 JANUARY 1 9 3 0 Age Males 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 18,820 81,797 94,407 93,984 92,837 90,143 82,250 84,290 81,718 74,127 73,443 70,995 69,548 64,117 61,076 55,305 48,054 45,891 41,359 38,957 35,479 34,399 30,896 31,743 28,282 28,282 27,562 26,995 26,224 ZO,;B; Age Females 14,035 62,039 73,030 71,384 68,793 63,67356,528 50,381 46,587 39,609 38,016 34,519 33,389 29,582 28,427 26,278 24,194 22,837 21,866 20,726 19,131 17,989 15,974 15,579 13,896 13,787 13,807 12,567 12,107 11,695 45 .... 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 Total Males Females 25,455 24,403 24,296 22,411 21,834 22,573 22,094 20,689 20,524 20,127 20,195 19,747 17,274 17,383 16,384 14,860 13,390 11,299 5,377 11,065 10,257 10,101 9,031 8,504 8,677 8,257 7,667 7,461 7,283 6,903 6,789 5,951 5,470 5,119 4,481 3,986 3,269 1,771 273 152 104 87 93 91 255 105 51 33 45 14 2,019,891 1,104,970 In the same balance-sheet the annual numbers of entrants into insurance were estimated [6] by means of the formulae—and consequently on the same assumptions—previously adopted in the preparatory investigations \ The entry ages are limited to 16 to 19 for males and 16 to 18 for females and the annual numbers are estimated as follows: Females . Males 1 dl™e = 71,507 9Vw = 43,798 SI™ = 12,483 9t[7 = 6,881 SI™ = 2,092 Si' 4,431 SI™ = 274 See above, p. 106. = 110 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION T h e annual average of t h e whole insured membership was as follows: 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 •. . • . . 2,142,926 2,330,932 2,287,896 2,172,857 2,062,475 1,881,244 1,710,383 1,680,787 1,692,104 1,850,797 2,041,454 § 3. — Number of Beneficiaries In the preparatory estimates may be found t h e table reproduced below, which gives for a n u m b e r of years (from five to t w e n t y years after the commencement of t h e scheme) t h e number of pensioners in each of the principal categories 1. TABLE X I . — NUMBERS OF BENEFICIARIES (Estimates in the preparatory investigations) Number of years since coming into operation of the scheme 5 6 7 8 9 10 11 12 13 14 ' 15 16 17 18 19 20 Number of beneficiaries Invalidity pension Old-age pension 9,069 26,193 41,750 56,362 70,259 83,545 96,281 108,514 120,284 131,124 141,993 153,010 163,302 173,327 183,133 192,783 3,187 10,122 18,028 26,616 35,631 44,789 • 53,786 62,407 70,475 77,879 84,608 90,656 96,029 100,739 104,813 108,277 Widows', 1 widowers' and orphans' pension | 4,371 13,008 31,605 61,975 83,157 101,164 117,515 133,750 148,926 163,906 177,491 191,263 204,127 216,658 228,917 240,978 T Lmm t , 16,627 49,323 91,383 144,953 189,047 229,498 . 267,582 304,671 339,685 372,909 404,092 434,929 • 463,458 490,724 516,863 542,038 1 A subsequent estimate modified slightly the columns of this table referring to beneficiaries in receipt of invalidity, widows', widowers' and orphans' pensions. See Bibliography, No. 3, p. 165. 111 CZECHO-SLOVAKIA The statistics of the Central Institution show, for each year and for each class of pension: (1) The number of claims paid and the number of claims rejected, whence may be found the number of pensions awarded; and (2) The number of new pensioners and of cancellations, whence may be deduced the number of pensions in force at the end of the year. The results appear, for each class of pension, in tables XII and XIII below, which begin with the year 1929 because, on account of the waiting period, no pension could be awarded during the preceding years. TABLE XII (a). INVALIDITY PENSIONS Number of Year 1929x 1930 1931 1932 1933 1934 1935 1936 1937 . . . . claims decided by the Central Institution pensions granted coming into payment pensions current at the end of the year 1,069 7,725 19,880 35,915 48,681 58,175 61,618 50,649 40,427 604 6.031 16,329 28,183 34,962 38,475 38,170 26,961 21,384 613 6,012 16,123 27,685 35,379 38,625 39,570 27,261 21,313 604 6,062 20,495 44,801 73,330 102,077 129,654 141,407 147,803 i On account of the qualifying period no invalidity pension could be paid before 1929. TABLE XII (b). OLD-AGE PENSIONS Number of Year claims decided by the Central Institution pensions granted pensions coming into pensions current at the end of the year 1929 * . . . . 1930 1931 1932 1933 1934 . . . . . 1935 1936 1937 16 17 1,086 5,692 8,469 9,617 10,346 9,484 9,022 1 14 951 4,951 7,266 8,433 8,187 7,720 7,452 1 11 921 4,906 7,314 8,451 8,684 7,719 7,400 1 11 916 5,661 12,375 19,705 26,936 32,834 37,945 i On account of the qualifying period no old-age pension could be paid before 1929. 112 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XIII (a). WIDOWS' AND WIDOWERS' PENSIONS Number of Year 1929 * . . . . 1930 1931 . . . . . 1932 1933 1934 1935 1936 1937 claims decided by the Central Institution pensions granted coming into payment pensions current at the end of the year 1,395 3,609 4,710 5,291 5,895 6,502 7,529 8,259 8,949 1,007 2,565 3,572 4,063 4,510 4,951 5,668 5,881 6,459 1,043 2,568 3,577 4,007 4,572 5,128 6,067 5,842 6,318 1,007 3,399 6,680 10,263 14,171 18,274 23,191 27,226 31,262 " i On account of the qualifying period no widow's or widower's pension could be paid before 1929. TABLE XIII (b). — ORPHANS' PENSIONS Number of Year 1929l 1930 1931 1932 1933 1934 1935 1936 1937 0 . . . . claims decided by the Central Institution pensions granted coming into payment the end of the year pensions 1,610 4,053 4,990 5,160 5,580 5,623 6,296 6,847 6,896 1,444 3,618 4,463 4,676 5,056 5,144 5,673 6,153 6,173 1,503 3,666 4,498 4,679 . 5,262 5,309 6,292 6,409 6,471 1,444 4,752 8,712 12,736 17,327 21,845 27,282 31,906 35,753 i On account of the qualifying period no orphan's pension could be paid before 1929. 113 , CZECHO-SLOVAKIA The number of cases entailing t h e p a y m e n t of a marriage allowance or the payment of a capital sum on death are shown below: TABLE XIV. — D O W R Y AND LUMP-SUM P A Y M E N T ON DEATH Number of payments Year 1926 1927 1928 1929l 1930 1931 1932 1933 1934 1935 1936 1937 Of a dowry Of a lump-sum payment on death 22,238 41,291 46,535 48,335 44,958 45,567 45,215 48,331 52,168 655 5,086 6,300 5,706 6,624 6,510 6,671 7,204 7,067 7,347 7,982 8,256 i The dowry was instituted by t h e 1928 Act. TABLE OF SYMBOLS INTRODUCED IN CHAPTER I = General life table. "X jCLCt -jli L x ^c CT KJ+ft = Number of healthy and invalid persons in the validity table (4 = C + Q. = Probability of cessation of invalidity (Ç being the age at becoming invalid and k the duration of invalidity). = Invalid life table. = Annual rate of becoming invalid. K*,5 "X c = Probability that an insured person who became invalid at age .Ç will still be an invalid and living at age x. = M. Tauber's adjusting coefficients. = Probability of being married, males. = Probability of being married, females. 3RX = Probability that a woman aged y will marry within the year. = Number of insured men in the initial population. = Number of insured women in the initial population. o 114 £fLm x £fV v 5ît î " tnx v \ "Va = Number of males who enter into insurance each year. = Number of females who enter into insurance each year. = Number of insured married men. = Number of marriages at age x for husband and age y for wife. = Total number of wives of insured men. = Number of healthy wives of insured men. 1 V y v „rpa Vy ~,npa *y •cri

v •yUnp) v np w v np a ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION y = Number of invalid wives of insured men. = Number of healthy wives of insured men, who are themselves insured. = Number of healthy wives of insured men, who are not themselves insured. = N u m b e r of invalid wives of insured m e n , in receipt of pension. — N u m b e r of invalid wives of insured m e n , n o t in receipt of pension. = Probability, at the moment of death of an insured man, that his widow (aged y) who is not herself insured will never enter into insurance. = Probability that the widow of an insured man will not herself be insured at age y. yx — A v e r a g e a g e of wife of insured m e n aged x. jauvp) jcuxs) p,aa = N u m b e r of w o m e n r e m a i n i n g in insurance (out of an "v ' y ' v initial group of insured females at age 15) married, spinsters and total respectively. 0 = Probability that an insured woman marrying at age y v will not exit from insurance. / = Life table of children up to age 17. i/ K x j£ LW v = Number of children for age of father x and age of child z. = Probability that an insured man aged x will be the father of a child under age 15. = Numbers of insured men corresponding to numbers kx of children. = R a t i o of n u m b e r of widows h a v i n g t w o or m o r e dependent children to the total number of widows. = Number of children aged z who are dependent upon a widow aged y. Cx~ = Annual coefficient of increase for age x. * L * S v CHAPTER II FINANCIAL ESTIMATES, BASES AND EXPERIENCE This chapter deals with the resources and the liabilities of the insurance scheme. The resources are constituted by contributions from insured persons and their employers, interest on accumulated funds and subsidies from the State. The liabilities comprise expenditure on benefits and administration. Each of the categories of receipt and expenditure which have just been enumerated will be examined in turn. Remarks on the interest on accumulated funds, however, will be relegated toI the following chapter, where the preparatory estimates (table XXVI) and the actual income (table XXVIII) 2 will be shown. § 1. — Contributions Contributions are payable in equal parts by the insured person and his employer. They are uniform for each of the wage classes into which insured persons are divided. WAGE CLASSES AND RATES OF CONTRIBUTION In the technical investigations which led up to the 1924 Act, insured persons were divided into four wage classes. The rates of contribution were uniform for each class and were based on the " general average premiums " brought out by the actuarial calculations which will be considered in the following chapter 1 . Below are reproduced the weekly contributions originally estimated and the contributions fixed by the 1924 Act, which are about 1.8 per cent, smaller. This reduction i2 Page 154. Page 157. 3 Chapter III, § 1, pp. 150-151. 116 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION was introduced to counterbalance the interest profit due to the excess of the rate of interest on the accumulated funds over the basic rate 1 . Total weekly contribution (in crowns) Limits of daily wage (in crowns) Wage class A B C D Rate originally considered in the preparatory investigations Reduced rates fixed by the 1924 Act 4.40 5.80 7.20 9.00 4.30 5.70 7.10 8.80 14 to 22 22 t o 28.50 More t h a n 28.50 The 1928 Act increased to five the number of wage classes and fixed the rates of contribution as follows: Wage class Aa Ab B G D Limits of daily wage (in crowns) 10 t o 14 t o 22 to More Total weekly contribution (in crowns) 14 22 28.50 t h a n 28.50 2.60 3.60 5.10 6.60 8.40 CALCULATION OF THE PRESENT VALUE OF THE CONTRIBUTIONS WHICH THE SCHEME SHOULD RECEIVE UNDER THE TERMS OF THE LEGISLATION Each of the basic elements which appear in this calculation will be reviewed. Distribution of Insured Persons by Wage Class In the preparatory investigations use was made first of all of the distribution by wage class which was indicated by the statistics regarding wages as at i January 1923 [2]. Later, recourse was had to other 1 See later, pp. 153 and 163. 117 CZECHOSLOVAKIA figures supplied by the wages statistics as at 1 January 1924 [3]. two series of figures are reproduced below: The Percentage of insured persons in each class, from the statistics of wage earners as at 1 January Wage class 1924 1923 A B . C D 41.10 19.36 11.34 28.10 • 52.75 21.65 10.87 14.73 100.— 100.— Average Number of Contribution Weeks Per Annum In the investigations preparatory to the 1924 Act it was assumed, on the basis of statistics prepared in the scheme of insurance of workers in Germany against invalidity, old age and death l , that the average number of contribution weeks per annum would be In class A, 42 weeks „ ,. B, 44 „ » » C, 46 „ . „ „ D, 48 „ In the preparation of the 1930 balance-sheet recourse was had to new figures calculated by the Central Institution by relating the contribution days in the year 1929—divided according to age and wage class—to the population registered in the middle of the same year. The double-entry table obtained in this manner is shown at the" end of this section among the statistics of operation of the scheme. Present Value of a Unit Contribution The essential element in the calculation of the present value of contributions is the present value a a a which is calculated from the ± X column I™ in the validity table by means of the commutations 2 : D aa v 1 = jaa x K V N 2» aa x See the section of this volume devoted to the insurance of workers in Germany against invalidity, old age and death, pp. 327, 329 and 384. 2 v represents the discount factor -rrr-,' i the annual interest on a monetary unit and w the limiting age. 118 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION A unit contribution payable by an insured person aged x as long as he is healthy and not later than age 65 is a temporary annuity the present value of which is calculated by the formula * : -N: N aX, 65-3c| Á clause in the Act provides that the payment of the old-age pension may be postponed .when the insured person continues to earn a certain minimum wage. Denoting by aft the proportion of the pensions commencing at each age, the present value a^g^^r must be replaced by the following, in order to take into account the option to postpone: afe N N (p) aa fe = 65 D In the investigations preparatory to the 1924 Act the coefficients 45.00 41.32 1927 1928 1929 1930 1931 1932 1933 1934 1935 | 14.36 14.75 15.67 17.02 18.11 17.91 18.25 The average daily wage, on which is based the distribution of insured persons by wage class, has been obtained at 30 June and 31 December of each year up to 1932 and at 31 December 1933 and 1934 for the different types of sickness insurance institutions, for quinquennial age groups and for each sex. The averages for the total insured population are grouped in the following table: 1 2 3 See later, Chapter III, p. 153. See later, Chapter III, p. 156. Table XXVI, p. 154. 120 ACTUARIAL T E C H N I Q U E AND F I N A N C I A L ORGANISATION TABLE XV (a). — AVERAGE DAILY W A G E : MALES (In crowns) 1928 1927 Year of birth 1929 1930 30.VI 31.XII 30.VI 31.XII 30.VI 31.XII 30.VI 31. X I I 6.74 14.27 22.14 24.27 25.40 25.28 25.25 24.76 23.79 22.68 6.54 15.08 22.63 24.63 25.55 25.40 25.18 24.53 23.54 22.34 7.69 18.35 24.15 25.73 26.48 26.26 26.16 25.65 24.55 23.44 7.84 19.05 24.59 25.91 26.49 26.21 25.93 25.26 24.16 23.00 9.60 21.78 25.95 26.96 27.46 27.13 26.89 26.32 25.16 23.97 10.08 21.79 25.88 26.96 26^7 26.64 26.16 25.63 24.27 23.18 11.90 23.12 26.48 27.14 27.53 27.14 26.85 26.22 24.77 23.63 11.47 22.21 25.53 26.18 26.36 25.95 25.57 24.73 23.33 22.25 earlier . . . Not stated . . 19.85 15.21 19.28 14.65 19.94 15.93 19.04 15.54 20.51 18.49 20.31 18.34 17.48 19.25 16.05 17.40 Total . . . 20.29 20.17 21.54 21.31 22.80 22.64 23.29 22.27 1916 a n d later . . . . 1911-1916 . . 1906-1910 . . 1901-1905 . . 1896-1900 . . 1891-1895 . . 1886-1890 . . 1881-1885 . . 1876-1880 . . 1871-1875 . . 1866-1870 . . 1865 and 1932 1931 Year of birth 1934 30.VI 31.XII 30. V I 31.XII 30.VI 30.VI . . . . . . . . . . . . . 9.47 13.29 23.25 26.01 26.62 26.86 26.22 26.10 25.24 24.01 22.73 16.32 20.34 8.05 11.91 22.17 24.89 25.44 25.50 25.01 24.54 23.73 22.47 21.37 15.05 19.94 6.15 13.97 22.58 24.84 25.26 25.46 25.00 24.69 24.06 22.67 21.62 16.94 16.49 5.50 13.01 21.44 23.91 24.27 24.28 23.78 23.22 22.46 21.05 20.38 15.77 16.59 6.00 14.72 21.34 23.64 24.12 24.38 23.90 23.57 22.72 .21.43 20.54 16.97 20.43 . 6.96 15.59 20.79 23.06 23.45 23.63 23.13 22.82 21.88 20.49 19.74 17.82 19.63 . . . . 22.85 21.53 21.82 20.54 20.70 20.10 1916 and l a t e r . 1911-1916 . . 1906-1910 . . 1901-1905 . . 1896-1900 . . 1891-1895 . . 1886-1890 . . 1881-1885 . . 1876-1880 . . 1871-1875 . . 1866-1870 . . 1865 a n d earlier Not stated . . Total 1933 . . . . . . . . . . . . . 121 CZECHO-SLOVAKIA TABLE XV (b). AVERAGE DAILY W A G E : FEMALES (In crowns) 1927 Year of birth 30. V I 1929 1928 31.XII 1930 30.VI 31. X I I 30.VI 31.XII 30.VI 31. XII 1916 and later . . . . 1911-1916 . . 1906-1910 . . 1901-1905 . . 1896-1900 . . 1891-1895 . . 1886-1890 . . 1881-1885 . . 1876-1880 . . 1871-1875 . . 1866-1870 . . 1865 and earlier . . . Not stated . . 8.75 8.95 11.73 12.47 13.98 14.64 14.91 15.66 15.57 16.37 15.76 16.66 15.65 16.52 15.35 •16.19 14.81 15.65 14.42 15.11 9.76 13.03 14.92 15.75 16.35 16.49 16.34 15.91 15.37 14.81 10.01 13.62 15.45 16.27 16.90 17.06 16.88 16.45 15.89 15.21 10.31 13.24 14.82 15.68 16.30 16.40 16.22 15.67 15.10 14.62 10.68 13.52 15.09 16.07 16.72 16.89 16.70 16.14 15.51 14.99 11.02 13.66 15.01 15.62 16.11 16.23 15.87 15.41 14.57 14.14 11.05 13.50 14.89 15.64 16.16 16.31 15.98 15.40 14.73 14.15 11.98 11.72 12.40 11.30 12.58 11.44 12.33 11.80 14.52 13.17 13.20 13.21 13.04 12.20 13.15 12.22 Total . . 13.35 13.88 14.03 14.36 13.93 14.24 14.01 13.93 1932 1931 Year of birth 30.VI 31.XII 10.02 1916 and later . . 1911-1910 . . 1906-1910 1901-1905 1896-1900 1891-1895 1886-1890 1881-1885 1876-1880 1871-1875 1866-1870 1865 and earlier Not stated . . 13.66 14.73 15.21 15.51 15.62 15.16 14.59 13.93 13.42 12.83 11,24 9.85 11.00 13.36 14.48 15.09 15.45 15.44 15.02 14.50 13.89 13.38 12.90 10.93 Total 13.64 13.37 A A A Ci Í ± .X if 1933 1934 30.VI 31.XII 30.VI 30.VI 8.07 12.95 13.80 14.11 14.34 14.32 13.87 13.34 12.78 12.46 13.13 9.78 8.00 10.99 12.84 13.75 14.14 14.39 14.32 13.90 13.39 12.87 12.56 13.10 11.15 8.18 10.96 12.59 13.23 13.49 13.62 13.52 13.19 12.74 12.21 12.10 12.63 11.84 8.39 11.28 12.76 13.35 13.54 13.66 13.56 13.14 12.63 12.08 12.03 12.98 11.58 12.69 12.61 12.20 12.20 in ST 122 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION The average contributions calculated by the Central Institution each year, for quinquennial age groups and for each sex, arc reproduced below: TABLE XVI ( a ) . AVERAGE W E E K L Y CONTRIBUTION - . MALES (In crowns) Year of birth 1916 a n d later . . 1911-1916 1906-1910 1901-1905 1896-1900 1891-1895 1886-1890 1881-1885 1876-1880 1871-1875 1866-1870 1865 a n d earlier . Not stated . . . . . . . . . . . 1927 . . . . . . . . . . . . . Total . . . 1928 1929 1930 1931 1932 1933 1934 1935 4.51 5.74 6.67 6.96 7.09 7.06 7.03 6.92 6.74 6.55 3.51 5.75 6.59 6.80 6.88 6.82 6.76 6.64 6.41 6.08 3.90 6.02 6.69 6.84 6.88 6.79 6.73 6.60 6.35 6.10 — 3.21 4.11 6.04 6.59 6.70 6.73 6.63 6.56 6.43 6.15 5.91 2.85 4.20 5.91 6.39 6.48 6.53 6.40 6.32 6.18 5.91 5.70 2.86 4.31 5.66 6.15 6.24 6.27 6.16 6.08 5.91 5.65 5.49 2.93 4.30 5.43 5.92 6.01 6.04 5.92 5.84 5.66 5.39 5.31 2.98 4.28 5.29 5.75 5.82 5.84 5.72 5.61 5.42 5.17 5.28 5.93 6.03 5.22 . 5.44 5.76 4.80 5.08 4.57 5.45 4.55 4.82 KAA O.\J\J f r o 5.13 5.18 4.87 4.44 6.32 5.99 '6.08 5.97 5.78 5.55 5.34 5.16 — 4.40 5.20 6.31 6.69 6.90 6.88 6.87 6.78 6.60 6.41 6.11 TABLE XVI (b). — • — AVERAGE W E E K L Y C O N T R I B U T I O N : FEMALES (In crowns) Year of birth 1916 a n d later . . 1911-1916 1906-1910 1901-1905 1896-1900 1891-1895 1886-1890 1881-1885 1876-1880 1871-1875 1866-1870 1865 a n d earlier . Not s t a t e d 1927 1928 1929 1930 1931 1932 1933 1934 1935 . . . . . . . . . . . 4.43 4.66 4.92 5.08 5.20 5.25 5.24 5.20 5.14 5.09 4.51 4.80 5.04 5.20 5.32 5.36 5.33 5.28 5.22 5.16 3.39 3.94 4.30 4.50 4.66 4.71 4.67 4.55 4.42 4.31 3.50 4.03 4.33 4.50 4.62 4.65 4.58 4.45 4.32 4.19 — 3.17 3.51 4.01 4.26 4.39 4.47 4.49 4.39 4.28 4.13 4.02 2.96 3.46 3.90 4.11 4.21 4.26 4.27 4.17 4.06 3.93 3.85 2.95 3.44 3.81 3.98 4.06 4.10 4.09 4.00 3.90 3.78 3.75 2.78 3.30 3.66 3.83 3.89 3.93 3.92 3.85 3.72 3.64 3.69 2.60 3.12 3.49 3.62 3.66 3.69 3.67 3.59 3.48 3144 3.63 . . . . 4.76 4.57 4.80 4.65 4.30 3.82 4.01 3.61 3.98 3.47 4.03 3.39 3.93 3.63 3.94 3.53 4.28 3.25 Total . . . 4.89 4.98 4.13 4.13 4.03 3.87 3.75 3.57 3.35 . . . . . . . . . . . — — — 123 CZECHO-SLOVAKIA The annual number of contributing days, divided by 365 (or 366), gives the number of " complete contributors ", that is to say the hypothetical number of insured persons contributing every day in the year which corresponds to the given number of contributing days. The number of " complete contributors " is calculated each year, on the one hand for each of the quinquennial age groups and for each sex and on the other hand for each wage class and for each sex. Only the total figures for each sex are reproduced below. TABLE X V I I . ANNUAL NUMBERS OF FULL Year 1927 1928 1929 1930 1931 1932 1933 1934 1935 CONTRIBUTORS Males Females Total 1,361,775 1,462,026 1,444,207 1,368,274 1,299,587 1,152,815 1,030,335 1,021,001 1,032,875 788,151 824,732 825,787 793,462 765,185 712,635 675,928 673,227 674,895 2,149,926 2,286,758 2,269,994 2,161,736 2,064,772 1,865,450 1,706,263 1,694,228 1,707,770 There have also been calculated for the " complete contributors " of each sex: (1) The distribution according to wage class 1 ; and (2) The average annual contributions, which are reproduced below: Average annual contribution l'or à " complete contriti litor " Year 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1 • Men Women Total 327 339 312 317 311 302 289 279 269 (in crowns) 259 265 215 216 210 203 196 186 175 302 312 277 280 274 264 252 242 232 See Bibliography, No. 9, table V, p. 158. • 124 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION The average annual numbers of contributing days have been calculated by relating the number of contributing days paid each year to the registered population *. In the course of the preparation of the actuarial balance-sheet at 1 January 1930, the average numbers given below were calculated, for each wage class, on the basis of the contributions paid in 1929 and the age distribution of the registered population 2 . TABLE AVERAGE XVIII. ANNUAL NUMBER OF CONTRIBUTION DAYS Average contribution days per insured person and per annum in class Year of birth Aa Ab B . C D Total Males L a t e r t h a n 1910. . 1906-10 1901-05 1896-1900 1891-95 1886-90 1881-85 1876-80 1871-75 1866-70 1865 a n d earlier . Total . . . . 190.77 31.72 14.55 11.91 12.69 13.45 14.47 16.92 19.65 26.59 47.67 30.25 28.75 23.60 21.95 20.41 21.56 21.70 22.66 25.92 29.60 29.65 46.91 65.09 54.94 50.18 ' 45.89 47.43 46.95 49.85 54.57 61.18 51.63 15.31 47.71 52.82 48.31 44.75 44.57 43.53 44.77 45.83 48.02 35.65 9.74 61.78 116.46 134.95 141.27 137.17 130.59 122.74 105.81 86.49 82.53 292.98 235.05 262.37 267.30 265.01 264.18 257.24 256.94 251.78 251.88 247.13 43.78 25.22 53.59 43.14 95.23 260.97 Females L a t e r t h a n 1910. . 1906-10 1901-05 1896-1900 1891-95 1886-90 1881-85 1876-80 1871-75 1866-70 . . . . . 1865 and earlier . Total 1 2 . . . . 151.77 112.68 85.87 72.35 63.24 64.82 65.70 73.09 77.57 83.78 68.09 55.96 73.01 69.61 59.36 53.61 51,39 48.79 48.55 46.57 47.41' 36.59 43.68 73.17 80.43 79.41 79.49 85.30 85.84 85.21 79.75 77.95 66.75 7.78 23.11 35.50 40.13 43.93 47.44 46.20 43.55 37.83 33.95 22.00 1.58 6.49 11.55 15.16 18.07 18.93, 16.77 13.68 11.00 9.29 9.12 260.77 288.46 282.96 266.41 258.34 267.88 263.30 264.08 252.72 252.38 202.55 99.94 61.54 71.81 29.57 9.91 272.78 Bibliography, No. 10, years 1931-1932, p. 46. ' The actuarial balance-sheet at 1 January 1930, is based on the average figures for each year of age, deduced by interpolation from thefiguresin table XVIII. See Bibliography, No. 6, pp. 67-68. CZECHO-SLOVAKIA 125 The sums of money corresponding to the registered contribution days are calculated each year for each sex, in quinquennial age groups and for the various types of sickness insurance institution. The annual total of the contributions actually received by the Central Institution, excluding the contributions paid by the State in respect of insured persons carrying out their military service, amounted to: Year Thousand crowns 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 332,086 655,539 721,305 634,526 614,511 573,575 496,467 429,313 415,493 408,080 454,094 535,229 § 2. — State Grants A State subsidy is added to every payment made under the head of pensions for invalidity, old age, widows, widowers or orphans, subject to the following conditions: The State subsidy is not paid if, during the preceding fiscal year, the pensioner's income, excluding the social insurance pension, exceeded the sum exempt from income tax (7,000 crowns). When the pensioner, in addition to receiving the social insurance pension, is in receipt of a pension under the Act relating to the compensation of men disabled in the war or of any other pension from a public fund, the State subsidy is only granted to the extent of its excess over such further pension. Aliens are entitled to the State subsidy only if their country of origin has a scheme of insurance against invalidity, old age and death and if in this country the State pi ovides supplementary pensions tho benefits of which are available to Czecho-Slovak citizens. State subsidies are calculated on the basis of fixed annual amounts according to the category of pension, as follows: ANNUAL AMOUNT OF S U B S I D Y Crowns Invalidity or old-age pension Widow's or widower's pension Half-orphan's pension Full orphan's pension ' 500 250 100 200 Since the State subsidies are proportional to that element entering into the constitution of all classes of pension which is independent of 126 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION the duration of insurance, it is evident that the methods and formulae which are employed in calculating the present values in respect of the various elements of benefit give also the present values of the State subsidies. Reference should therefore be made to section 3 below. The annual sums payable by the State on account of the subsidies were estimated in the investigations preparatory to the 1924 Act as indicated in the table below 1 : TABLE XIX. ANNUAL AMOUNTS OF STATE INDIVIDUAL SUBSIDIES (Estimates in the investigations preparatory to the 1924 Act) Number of years since coming into operation of the scheme 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 Subsidies added to Invalidity pensions 4,535 13,097 20,875 28,181 35,130 41,773 48,141 54,257 60,142 65,562 70,997 76,505 81,651 86,664 91,567 96,392 Widows' and orphans' pensions In thousands of crowns 1,594 535 5,061 1,611 9,014 3,689 13,308 6,980 17,816 9,385 22,395 11,506 26,893 13,492 31,204 15,533 35,238 17,385 38,940 19,341 42,304 20,944 45,328 22,569 48,015 24,087 50,370 25,566 52,407 27,012 54,139 28,436 Old-age pensions Total i 6,664 19,769 33,578 48,469 62,331 75,674 88,526 100,994 112,765 123,843 134,245 144,402 153,753 162,600 170,986 178,967 i It was also estimated that the annual total of State individual subsidies would reach 508,529 thousand crowns after 50 years. In addition the State undertakes the payment of contributions during periods of military service: according to estimates included in the investigations mentioned above, this will entail an annual expenditure of 17.4 million crowns. The State also helps by bearing the cost of setting up and administering the insurance courts (including the Superior Insurance Court) and by granting various privileges such as the exemption from taxes. 1 A second estimate brought out figures slightly different from these in respect of the subsidies to invalidity, widows', widowers' and orphans' pensions. See Bibliography, No. 3, p. 163. 127 CZECHOSLOVAKIA EXPERIENCE The State subsidies which have been added to the various classes of pension have entailed the payment by the State of the following annual sums: TABLE X X . STATE I N D I V I D U A L SUBSIDIES (Annual amounts in thousands of crowns) Year 1929 1930 1931 1932 1933 1934 1935 1936 1937 Invalidity pensions Olfl-age pensions Widows' and widowers' pensions Orphans' pensions Total 172 2,355 8,580 19,336 32,232 46,505 60,346 67,395 70,500 1 5 230 2,136 5,320 8,967 12,507 15,438 17,947 159 744 1,461 2,310 3,224 4,272 5,359 6,434 7,419 188 836 1,519 2,241 3,065 4,005 4,903 5,870 6,502 519 3,939 11,790 26,023 43,841 63,749 83,116 95,137 102,368 § 3. — Benefits First of all the various species of benefit will be passed in review, and in each case the rules will be set forth which determine the conditions of award and the amount of the sums granted. CONDITIONS OF AWARD AND COMPUTATION OF BENEFITS Invalidity Pension Title to pension is determined on the basis of loss of earning capacity: an insured person who, by reason of sickness or infirmity, is incapable of earning at least one-third of the sum usually earned by a healthy person in the same district, acquires the right to an invalidity pension. The invalidity pension consists of a fixed sum and additions varying with the duration of insurance. The invariable sum, which was fixed at 500 crowns per annum by the 1924 Act, was increased by the 1928 Act to 550 crowns per annum. The additions in each class are proportionate to the number of weekly contributions. The 1924 A c t 1 fixed the addition in respect of each weekly contribution at 20 per cent, of it, that is to say at: In class A, 0.86 crowns ,. „ B, 1.14 „ „ „ G, 1.42 „ » » D, 1-76 „ 1 The technical investigations which led up to this Act are based on additions which bear to the contributions the ratio of 20 to 100. 128 ACTUARIAL T E C H N I Q U E AND F I N A N C I A L ORGANISATION The additions have been modified by the 1928 Act which laid down the following rates, as from 1 January 1929: Wage class Aa Ab B C . . D Addition in respect of each weekly contribution . 0.60 0.85 1.15 1.40 1.75 Old-Age Pension The old-age pension normally falls due at the age of 65. However, postponement has been provided for in the following cases: (1) Under the 1924 Act, when the insured person continues to earn a wage equal to one-third of the sum usually earned; (2) As from the date of coming into force of the 1928 Act, when the wage equals one-half of the sum usually earned. The amount of the old-age pension is calculated in the same way as the amount of the invalidity pension. Widow's Pension Under the 1924 Act a widow is entitled to a pension when she is suffering from invalidity which is defined as either general incapacity for work to the extent of at least two-thirds, or inability to attend to her household duties. The 1928 Act extends the title to pension to: (1) a widow who maintains not less than two children under age 17 of the insured person; (2) a widow who has reached age 65. This age limit was reduced from 65 to 60 by the 1934 Act. The amount of the widow's pension is equal to half the invalidity or old-age pension. In the event of the widow remarrying she forfeits her title to pension but receives a lump sum payment equal to three times the yearly amount of her pension. Widower's Pension A widower is not entitled to pension unless he was incapacitated at the date of the death of his wife so that the maintenance of the family fell principally on her shoulders. The amount of the widower's pension is calculated in the same way as that of the widow's pension. Orphan's Pension Every half-orphan is entitled, up to age 17, to a pension whose amount is equal to two-tenths of the pension which the insured person received or could have claimed in case of invalidity. The amount of the pension is doubled in the case of a full orphan. Lump Sum Benefit at Death The lump sum payment at death is made when the insured person leaves no widow (or widower) entitled to a pension, either because death occurred before the expiration of the qualifying period or because she (or he) did not fulfil the statutory conditions. CZECHOSLOVAKIA 129 The payment is made in the following order of priority: husband or wife; children, including grandchildren, illegitimate children, adopted children, foster-children and step-children; parents or brothers and sisters of the deceased. Under the 1924 Act the capital sum payable on death was equal to ' one year's amount of the invalidity or old-age pension which the insured person was receiving or could have claimed. By virtue of the 1928 Act, when the insured person dies before the expiration of the qualifying period, the capital sum payable on death is fixed' at: In class Aa, 550 crowns' „ Ab, 600 „ „ B, 650 „' ,, C, 700 „ „ D- '50 „ . If the qualifying period has been completed the capital sum payable on death is assessed, as under the former Act, at one year's amount of the invalidity or old-age pension, provided that it is not less than the amounts mentioned above (550 — 750). Educational Allowance Every invalidity or old-age pension is increased by 10 per cent, for each child aged less than 17 years maintained by the pensioner (the term " children " includes legitimate and illegitimate children, adopted children, foster-children, grandchildren and step-children). Dowries Since the coming into force of the 1928 Act, every insured woman who has completed the waiting period is entitled on marriage to a dowry whose amount is fixed at: In class Aa, „ „ AÔ, „ B, „ „ C, „ „ D, 400 crowns 450 „ 500 550 600 In the event of remarriage an insured woman is entitled to a further dowry provided that she was insured for not less than five years before the second marriage. Supplementary Pensions in Respect of Insured Persons who were Born before 1 January 1899 By virtue of the 1934 Act a supplementary invalidity or old-age pension is granted to every insured person born before 1 January 1899, on whose behalf there have been paid up to 31 December 1931 at least 700 daily contributions (or 100 weekly contributions). This supplementary pension is equal to one-third of the average annual addition which could have been acquired between the attainment of age 27 and 1 July 1926. The calculation of this average annual addition is made on the basis of the additions actually acquired between 1 January 1927 and 31 December 1931. Benefits whose amount is assessed as a fraction of the invalidity or old-age pension are increased pro rata to the supplementary invalidity or old-age pension defined above. 9 130 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Qualifying Period Title to all benefits, except to the lump sum death benefit, is subject to the serving of a qualifying period. This qualifying period, which in the preparatory investigations consisted of 200 contribution weeks, was fixed by the 1924 Act at 150 contribution weeks and reduced to 100 contribution weeks by the 1928 Act. Under the 1934 Act it is no longer based on the number of contribution weeks but on the number of contribution days, which must be at least equal to 700. Periods of military service, as well as those during which the insured person has contributed to other schemes of insurance against invalidity, old age and death (miners, salaried employees or public officials) are deemed to be contribution periods for the purpose of the qualifying period. Maintenance of Right to Benefits The maintenance of benefit rights in the insurance against invalidity, old age and death, which in the initial legislation was provided for the period of one year, was extended to eighteen months by the 1928 Act. The insured person still had the option of preserving indefinitely his benefit rights, in the insurance scheme against invalidity, old age and death, up to the amount corresponding to the contributions paid, provided that he paid a renewal fee of 10 crowns a year. By virtue of the 1934 Act benefit rights are maintained for a period equal to one-fourth of the period corresponding to the contributions paid, with a minimum of two years; this minimum is extended to five years in case of unemployment. The provisions regarding renewal fees do not apply after 1 July 1934, except in cases where such payments were made before that date. Maintenance of Rights of Insured Persons who Pass from the Workers' Scheme of Insurance against Invalidity, Old Age and Death to another Scheme of Social Insurance or vice versa By virtue of the 1924 Act, when a worker changes his employment and consequently ceases to be insurable in the workers' scheme of insurance against invalidity, old age and death, the Central Institution shall pay to the new insurance institution a "transfer value " representing the value of the rights acquired by the insured person in so far as these are covered by the insurance contributions paid on his account. In consideration of this transfer value the insured person is granted a reduction of waiting period in the new insurance scheme and eventually the right to increased benefits. Similar provisions apply when the movement is in the reverse direction, that is to say when a worker leaves another scheme of social insurance and becomes insured under the Central Institution. In order to calculate the transfer value use is made of the formula introduced by Küttner 1 for. obtaining the value of a reduced valuation reserve : í z 1 " Die Rückkaufs- und Abfmdungswerte bei vorzeitiger Lösung des Versicherungsverhältnisses." Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker. 7. Heft, Berne, 1912. CZECHOSLOVAKIA 131 where tV- represents the premium reserve in respect of an insured person who entered at age £ and who has paid a premium P 5 for t years ; tWs represents the reduced premium reserve by Kiittner's method ; -P represents the general average premium 1 which has actually been paid on behalf of the insured person; and P ç represents the fixed premium calculated individually for an insured person entering at age \ The reserves are calculated in two portions: corresponding to the fixed portion of the pension, that is to say the basic sum; and Ps corresponding to an addition which increases by unity for each contribution year that has been completed. The final figure adopted as the transfer value is given by the formula 2 where * represents the total contributions paid, n the total number of contribution weeks, and where, in estimating on average the additions s to one-fifth of the relative contributions 3, — represents the average 5» value of the addition corresponding to one contribution week, and 10 s represents the average value of the addition corresponding to n 50 contribution weeks, or one contribution year. In order to facilitate the application of this formula scales 4 have been constructed which give for each sex separately: (1) The value of tWc corresponding to a basic sum of 500 crowns, according to the number of completed contribution years (of 50 weeks) and according to the quinquennial age group within which the insured person falls at the date of calculation of the transfer value. 1 2 See later, pp. 149-152. Prof. V. LENZ: O Pfevedních Cástkách v Sociálním Pojistëni. Rozpravy Jednoty pro vëdy Pojistné. Cislo 4. Prague, 1928. 3 Under the 1924 Act the addition in respect of each weekly contribution is exactly equal to one-fifth of the contribution : this proportion was maintained only approximately as from the date of coming into force of the 1928 Act. 4 Regierungsverordnung vom 29. November 1928. (Sammlung der Gesetze und Verordnungen des ¿echoslovakischen Staates. 1928, 69. Stück.) 132 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION (2) The values of t W | corresponding to addition which grow by 10 crowns for every completed contribution year, according to the number of contribution years (of 50 weeks) and according to the quinquennial age group within which the insured person falls at the date of calculation of the transfer value. Because of the amendments introduced by the 1928 Act these scales have ceased to operate as from 1 January 1929. It was found that the number of transfers was very large and, since it was feared that the calculation of the transfer values would become more and more .onerous, efforts were made to simplify the original method while at the same time adapting it to the provisions of the new Act. It was noticed that the figures in the scales used before the end of 1928 varied comparatively little with the age of the insured person at the moment of transfer. This led to the construction of a new scale 1 from which could be calculated (for each sex separately) an approximation to the transfer value by taking into account only the number of contribution weeks in respect of each wage class. As a further simplification of the administrative processes consideration has been given to a more fundamental reform of the financial mechanism relating to transfers: the abandonment of transfer values and the sharing of the cost of benefits, at the moment of the occurrence of the event insured against, among the various institutions to which the insured person belonged. This reform has been the subject of various investigations but at the present time it still remains no more than a proposal. Lapse of Rights The period beyond which right to claim lapses is five years for all classes of pension and two years for marriage allowances and lump-sum payments on death. Amounts of Invalidity and Old-Age Pensions and Percentages of Wages which they Represent The amounts of invalidity or old-age pensions depend on the duration of insurance and their calculation follows directly from the legislative provisions which we have enumerated above. By way of example we reproduce in table XXI below: (1) The amounts of the invalidity pension after a given number of years each containing 50 weekly contributions, including the State subsidy, but excluding other allowances and additions which may be added to it: (2) The percentages which these amounts bear to the average wage on the. basis of an average wage of: In class Aa, 2,600 crowns „ „ *A.b, 4,200 „ „ B, 5,400 „ „ G, 7,650 ,, » D, 9,450 „ 1 Regierungsverordnung vom 18. Februar 1937. (Sammlung der Gesetze und Verordnungen des Cechoslovakischen Staates. 1937, 10. Stück.) 133 CZECHOSLOVAKIA TABLE X X I . — c I N V A L I D I T Y P E N S I O N : AMOUNT A N D OF AVERAGE WAGE PERCENTAGE Number of contributions paid 100 500 1,000 1,500 2,000 2,500 Amount of invalidity pension in crowns Aa Ab . . . . B . . . C . . . D . . . 1,110 1,135 1,165 1,190 1,225 1,350 1,475 1,625 1,750 1,925 1,650 1,900 2,200 2,450 2,800 1,950 2,325 2,775 3,150 3,675 2,250 2,750 3,350 3,850 4,550 2,550 3,175 3,925 4,550 5,425 Percentage ratio oí invalidity pension to average wage Ao Ab B . C . D . . . . . . . . , . . 42.6 27.0 21.6 15.6 13.0 51.9 35.1 30.1 22.9 20.4 63.5 45.2 40.7 32.0 29.6 75.0 55.4 51.4 41.2 38.9 98.1 75.6 72.7 59.5 57.4 86.5 65.5 62.0 50.3 48.1 The supplementary pensions granted in respect of insured persons born before 1 January 1899, which correspond to the contributions paid, continuously in the same class, between 1 January 1927 and 31 December 1931, are also given. TABLE XXII. —• S U P P L E M E N T A R Y B E N E F I T S I N R E S P E C T PERSONS BORN B E F O R E 1 J A N U A R Y 1 8 9 9 OF INSURED (In crowns) Age of insured pension on January 1926 30 35 40 45 50 55 60 Amount of supplementary benefit on the basis of continuous contributions between 1 January 1927 and 31 December 1331 in class Aa Ab B C D 36.57 97.52 158.47 219.42 280.37 341.32 402.27 44.37 118.32 192.27 266.22 340.17 414.12 488.07 60.03 160.08 260.13 360.18 460.23 560.28 660.33 73.08 194.88 316.68 438.48 560.28 682.08 803.88 91.35 243.60 395.85 548.10 700.35 852.60 1,004.85 ESSENTIAL FACTORS IN THE CALCULATION OF THE PRESENT VALUE OF BENEFITS The essential factors which enter into the calculation of the present value of benefits may be expressed as a certain number of unit present values the method of calculation of which will now be considered. 134 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION The unit present values will be classified according to the nature of the benefit principally concerned. , Old-Age Pension The present value of the right to an old-age pension—of one unit, payable as from age 65—to an insured person now aged x is given by the expression aa 65 aa If the payments are monthly or weekly the commutation function N"a must be adjusted in accordance with the formula NT' = N where 8 is calculated by the formula % = 1 -(- i 2 ? + hi and consequently has one of the following values: Rate of interest (4 per cent.) Rate of interest (4% per cent.) - For monthly payments For weekly payments S12 = 0.4648 S62 = 0.4969 Si2 = 0.4656 In the case of postponed pensions, for the unit present value is substituted the following expression a aa(p) x ns-x\ax aa 2^N^ = = D To take the case of an insured person who each year acquires the right to a unit addition by virtue of the payment of his contributions. The present value of the right to such additions, for an insured person aged x, is calculated by the formula <65 aa es-xi^x (66 - x) C 5 _ x | ar if the age at which the old-age pension is granted is fixed at 65; or 135 CZECHO-SLOVAKIA 2.(Ä + I-X) aa(p) a. 0LhK Ä=65 = — aa if postponement of pensions is taken into account. Invalidity Pension The present value of a unit invalidity pension in course of payment may be obtained by two methods which will now be described. In the first method the basic function is the probability of cessation of invalidity ^m+h mentioned in Chapter 1 1 . It is necessary to make a distinction between two cases. (1) Where the duration of invalidity exceeds 10 years, the calculation is made by the continuous application of the formula a* = 1 + v (1 — ax) a.lx+1 starting from a*101 which is taken to be equal to unity. (2) Where the duration of invalidity is not greater than 10 years, the use of the identity a j x ] + u = &x+11 and of the continuous formula a M + ft = 1 + W (1 Gixi+k) a [ x ] + ft+i will finally produce a M which represents the present value at the moment when the unit pension is granted. The second method is based on the table ¿ ra+fe of survivorship of invaliditv pensions corresponding to the rates of cessation of invalidity The commutation columns are constructed in the usual way p.i U [s]+h — Tt [x]+k l X+k lyji W+ft V iN ~ ^ ^ ¿¿¿ k „ t [i]+fi U and finally the present value of unit pension is obtained by the formula NÍ. a [acJ+ft — i [x] + k n u The values of a M calculated on the basis of the probabilities of cessation of invalidity mentioned above, with interest at 4 per cent., show a clearly defined maximum between ages 55 and 60 for males and 1 2 See p . 88. See C h a p t e r I, p . 88. 136 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION about age 45 for females. Certain values of a ^ which are sufficient to demonstrate the variations in value are reproduced below. Present value of unit invalidity pension at date of grant Age at grant Males 3.4623 . 4.6623 5.7921 6.2925 6.71587.0149 7.0339 6.0584 4.3460 2.7234 1.4288 1.0000 20 30 '40 45 50 55 60 70 80 90 100 101 Females 5.4544 9.1799 10.6842 10.7995 10.6384 10.2130 9.5118 7.2959 4.7399 2.8620 1.4490 1.0000 The intermediate present values a^+j] are obtained by taking the mean 1 / í 2 VaM + a [x+i]) Account is taken of the frequency of payments by applying the coefficients 8„ defined above. «12) a __ i L [x+i) — a[x+i) The present value of a unit invalidity pension in the course of being acquired is obtained in the following manner: The commutation functions Da aa I • x l x+i V a i(i2> [x+i] are first obtained and then the corresponding values of N"' and Sx are calculated. The present value of a unit invalidity pension in the course of being acquired is then obtained immediately by the formula ai • D: As a result of the 1934 amendments an adjusting coefficient has been introduced into the calculation of SLJ [6]. It was necessary to take into account the suspension of the right to an invalidity pension for periods during which the insured person was in receipt of sickness insurance benefit. By means of statistical investigations dealing with 25,000 invalidity pensions paid during the years 1929 to 1932 the Central CZECHO-SLOVAKIA 137 Institution calculated the following values of the average number of months during which paymenf of the invalidity pension was suspended —so as to avoid duplication of benefits: Average number ol months during which the right to invalidity pension is suspended Males | Females Age 7.68 7.50 7.23 7.05 6.65 6.65 5.82 4.58 3.23 2.41 U n d e r 20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 56-60 61 and over . 9.22 8.31 8.39 7.28 6.52 5.61 4.75 3.43 2.38 2.20 • These averages, expressed as fractions of a year and rounded off to the nearest unit, have been taken as adjusting coefficients ? and applied at the same time as the factors 8 in order to obtain from a M a new function , a M in which account is taken of the average suspension of the invalidity pension and at the same time of the payment by monthly instalments. The calculation is made by means of the following formula: »| a W „ (1 — o) 4] + ? hW + i = (l — ? ) a w + ? ii a w I,M in which S12 has the value of 0.4656 on the basis of interest at 4% per cent. Starting from the value thus obtained for „¡aL, the commutation functions D"1 N" 1 S^1 and, from them, the present value of the unit annuity SLX1 were obtained by the formulae which we have mentioned above. In order to give effect to the deferment of the right to invalidity pension during the waiting period of t years the following formula was used: Nai 'I' aa To take again the case of an insured person who acquires each year, after the end of the waiting period, the right to a unit addition by virtue of the payment of his contributions. The present value of the right to such additions, for an insured person aged x, is calculated by means of one of the following formulae: (1) On the assumption that all insured persons claim their old-age pension and consequently cease to contribute at age 65: <65 (+ll c ai —s J x+t+ D1 "S' • 138 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION (2) Taking into account the insured persons who postponed the claiming of their old-age pension and who consequently continue to contribute after age 65: ^ ¿ K ft ft=65 ^X + t + l aUp) „-IB) t + l|a.V ö ft + l aa "x which may otherwise be written <05 ai(p) t+i|ax m t+i|ax — J ¿ | ^ft + 1 fk + 1 ft=65 I aa introducing the coefficients yk obtained from the coefficients aft by the following linear equations: Y„ = 1 — (66 , OÍ 65 y ' = 1 — a 1 67 — a 65 , 66 etc. ' Widow's Pension The present value of the right to unit pension or to a lump sum on death in respect of the wife of an insured man who becomes a widow at age y is represented by the formula Fy = ~ (v; 60 Fv - JV - 1 lvy a„ -t- \y T v J + vy (a„ + ay ) (2) for y < 60 aa F, = i - 1 2 (1 - *„) v ; + 2 V f + v r p ) a r + 5y ^ ay(z> . + in which a a » ,-npa r ainp . np / * _i_ aa(i2)\ ] ) V y [|60-y a y + ^60 W - y | a y + <¡o-y|ay jj j , (z) is given by the weighted average % ¡ J T 2*? ' 2 5 represents the ratio of the number of widows maintaining two or more children to the total number of widows 2 , and k indicates the number of children aged z maintained by a widow aged y3. Orphan's Pension The calculations relating to orphans' pensions rest essentially on formulae analogous to those applicable to widows' pensions, the most important of which have just been described. The present value of a unit orphan's pension in the course of payment, for a child aged z, is calculated in the usual way from the life table lz, thus N r — N„ D, The present value, at the death of an insured person aged x, of the right to unit orphans' pensions is on the average . ^ 1 Rx |l7-z a z 17„ 1 a 3 See above, p. 128. See Chapter I, p. 103. See Chapter I, p. 103. _ 2= 0 141 CZECÌiO-SLOVAKfA where the function k~ represents the number of children living corresponding to t h e number of insured males L^. 1 . The present value of the right to unit orphans' pensions acquired by an insured person aged x is calculated, as in the case of widows' pensions, by distinguishing between two alternative assumptions: (1) If the insured person dies in good health: t h e following expression is valued Ma aa x+ì 17 (12> a ¿a Qx V x+è(z) 'i (2) tf the insured person dies an invalid: we start with the expression 24 [x}+h v D [x] X + k+i 17 (12) à-x+k+Hz) where d\,+k and D[ x] have the same meaning as in t h e calculations for widows' pensions. After applying M. Tauber's adjusting coefficients, thus "A* — "(SC T •"*«> — x *^x(z) j values of the following expression are obtained 1 Ma • ~2 I'x l x V x+i / « . i . w.i A \ oc(z) + v AK+KZ>J • The results corresponding to these two assumptions are added together, thus 17 na "xw — 7 aa a a — "x Çx *"*"* 17 v <12> Jaa ' sc+i(z) + ~2 "x 'lx 3C+ ^ _L a v /17A' _L \ A«z> + 17 i' s i+iw) • A Thence is deduced 17 Na = 2 "Da and finally a ^Xjzi _ aa 1 x IT 17 a x . 142 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Since the education allowance is cancelled if the pensioner dies or ceases to be an invalid there must be deducted from the preceding expression • jaa Î4 17 ¿y i % xV ''x ^x+Jiz) • The present value of the right to a unit education allowance, added to an invalidity pension, acquired by an insured person aged x, is consequently calculated by means of the commutation functions i7_ai jaa • i i11 <12> 17 ~ i 17 -, ivrai V 17 r\ai and is represented by the formula n (2) ai IN* 'wa Education Allowance added to an Old-Age Pension The present value of the right to a unit education allowance, added to an old-age pension, acquired by an insured person aged T, is represented by 17 a 17 aa y^aa Í-J a '-'s 17 (12) a<*g(-?\ s(z) -\T 17-.aa lV<;/r> -L^fiirl where s represents the age at which the old-age pension is granted. To allow for cases where the benefit to be valued covers education allowances added to invalidity pension as well as those added to old-age pensions, the differences N . , -— N",\ must be substituted for the commutation functions N .2) . In this way is avoided the duplicate reckoning of the present values of education allowances which are payable to insured persons who become invalid after having passed the age s at which the old-age pension is granted. Dowries In the investigations preparatory to the 1928 Act, the present value of dowries is calculated by means of the following commutation functions nav 7aa y+i , . r A ,.av v rav where £y and V- represents (for females) the probabilities of being married and the marriage rates already mentioned in Chapter 11. The investigations preparatory to the 1934 Act [6] are based on the table reproduced above (table VI) which was constructed by the Central Institution from the data regarding cessations of insurance and matrimonial status derived from persons insured during the years 1926-1930. The following new commutation functions have been constructed with the help of the columns vl and /" a s which appear in this table: p-.aa pjaa y D„ -= ly v ; p^av 7 aa(s) C„ = ly P*/ras y+i v ¡xy ; "S^ Pnao My = ^ fc=o 1 See p. 95. ty+k . 143 CZECHO-SLOVAKIA From these the present value of the right to unit dowry in respect of an insured woman aged y is immediately obtainable by the formula: *-* it TOTAL PRESENT VALUE OF BENEFITS AND TOTAL ANNUAL EMERGING COST In the course of the investigations preparatory to the 1924 Act, the present value of all benefits in respect of the initial insured population and also of future entrants were calculated separately for basic amounts and for additions depending upon duration of insurance. The totals obtained appear in the liabilities of the preliminary valuation reproduced below 1. The actuarial balance-sheet as at 1 January 1930 2 necessitated the calculation of the present value of (1) benefits in the course of payment; (2) the various benefits in the course of being acquired (in respect of the present insured population) ; (3) the various benefits in respect of future entrants into insurance. The following figures give the estimate, for the principal categories, of the total annual emerging cost of benefits 3 : TABLE X X I I I . ANNUAL EMERGING COST O F BENEFITS (Estimates in the preparatory investigations, in thousands of crowns) Number of years since coming into operation of the scheme 5 6 7 8 9 10 11 12 13 14 15 16 . . . . 17 . . . . 18 19 20 1 2 3 . . Invalidity pensions Old-age pensions Widows' and orphans' pensions and educational allowances 6,802 20,692 34,653 49,035 63,936 79,368 95,318 111,769 128,704 145,548 163,292 182,082 200,861 220,125 239,904 260,257 2,390 7,996 14,963 23,156 32,424 42,550 53,248 64,279 75,408 86,446 97,299 107,881 118,116 127,939 137,305 146,174 938 2,960 6,817 13,126 18,360 23,448 28,620 34,232 39,777 45,848 . 51,437 57,356 63,270 69,339 75,570 81,980 See Chapter III, p. 153. See Chapter III, p. 156. A second estimate produced slightly different results. No. 3, p. 163. Total 10,130 31,648 56,433 85,317 114,720 145,366 177,186 210,280 243,889 277,842 312,028 347,319 382,247 417,403 452,779 488,411 See Bibliography 144 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION EXPERIENCE The most important results of the operation of the scheme concerning payments made in respect of benefits are (1) the total amount paid each year for each benefit; (2) the average pension paid each year (for each benefit). These two series of results appear in table XXIV below, which demonstrates the effect of the increase in benefits which came into force on 1 July 1934. TABLE XXIV (a). AMOUNT OF B E N E F I T S PAID EACH YEAR (In thousands of crowns) Widows' Invalidity Old-age or wid- Orphans' Total pensions pensions owers' pensions pensions pensions ~Yp*r 1926 1927 1928 1929 * 1930 1931 1932 1933 1934 1935 1936 1937 471 6,278 23,561 54,348 91,968 148,320 212,166 237,825 248,768 2 16 625 5,835 14,663 29,296 47,062 58,780 68,883 416 1,917 3,989 6,261 8,982 13,382 18,837 22,746 26,416 504 2,171 4,153 6,177 8,550 11,634 15,165 18,135 20,096 1,393 10,381 32,328 72,622 124,163 202,632 293,231 337,486 364,163 Lump sum payments* on death 463 3,551 4,398 4,042 5,037 5,150 5,551 6,212 6,499 7,444 8,222 8,769 Dowries — — Grand total 10,742 19,252 21,657 22,128 21,058 20,448 20,243 21,427 23,339 463 3,551 4,398 16,178 34,671 59,135 100,301 151,434 229,578 320,918 367,135 396,271 i On account of t h e qualifying period t h e only p a y m e n t s made before 1929 were the lump sum p a y m e n t s on d e a t h . TABLE XXIV (h). AVERAGE AMOUNT OF P E N S I O N PAID EACH YEAR (In crowns) Year Invalidity pensions Old-age pensions 1 9 3 1 . . . '. . 1932 1933 1 9 3 4 (1st half) . 1 9 3 4 ( 2 n d half) . 1935 1936 1,276 1,305 1,326 1,343 1,649 1,661 1,660 1,297 1,317 1,335 1,791 1,817 1,838 Widows' or widowers' pensions 632 643 655 668 834 838 • 843 Orphans' pensions 495 497 503 507 568 573 573 145 CZECHOSLOVAKIA The supplementary pensions instituted by the 1934 Act for the benefit of insured persons who were born before 1 January 1899 have given rise to the following total payments: about 22 million crowns during the second quarter, 1934; about 55 million crowns during the year 1935; about 68 million crowns during the year 1936; about 81 million crowns during the year 1937. Jubilee Fund On the occasion of the tenth anniversary of the Czecho-Slovak Republic, a special fund, called the Jubilee Fund, was created by an initial grant of one million crowns. It was increased by two millions in 1930 and by one million in 1935 on the occasion of President Masaryk's 80th and 85th birthdays. This fund is used to provide help to insured persons who become invalid or are without resource or medical assistance and who do not fulfil the qualifying conditions for receipt of benefit in the scheme of insurance against invalidity, old age and death. The following sums have been distributed: Voar Thousands of crowns ïedT 1929 1930 1931 1932 1933 1934 1935 1936 1937 198 424 323 325 365 343 750 420 393 § 4. — Other Expenditure M E D I C A L ASSISTANCE The Act passed in 1934 provides that: (1) The Centra] Institution may at any time, at its own expense, grant an insured person curative treatment for the purpose of averting or postponing an impending invalidity (this treatment may be granted to a widow only if she is sick) ; (2) Within the limits of the sums allocated to curative treatment and in accordance with a plan which shall be approved each year by the Ministry of Social Welfare in agreement with the Ministry of Public Health and Physical Culture, the Central Institution may carry out and promote general or special measures and schemes for the prevention of premature invalidity among insured persons and their families, the combating of social diseases (tuberculosis, nervous disorders, venereal disease, alcoholism, cancer, etc.) or the raising of the general level of health among insured persons and their families. The technical investigations undertaken preparatory to the 1924 Act allocated 3 per cent of the contribution income to medical assistance [3]. The sums which have been actually used for the prevention and cure of invalidity, principally in sanatoria, hospitals, thermal establishments 10 146 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION and nursing homes, amounted to the following totals, in thousands of crowns: Year Cost of medical assistance 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 914 8,654 19,009 26,013 30,894 23,646 25,533 24,825 26,899 23,057 21,797 ADMINISTRATION EXPENSES In the investigations preparatory to the 1924 Act, a fraction of the contributions, fixed at 11 per cent of the total, was prescribed for covering administration expenses [3]. The expenditure of the workers1 scheme of insurance against invalidity, old age and death under the heading of administration includes both the cost of maintaining the Central Institution and also the repayment to sickness insurance institutions of the expenditure in respect of local financial operations entrusted to them. The repayments to sickness insurance institutions and the total expenditure amounted to the following figures, in millions of crowns: Year 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 . . Repayments to sickness insurance institutions Total administration expenses 10.9 25.0 24.7 30.9 30.4 29.2 28.4 28.-0 27.5 27.2 27.6 28.7 12.2 30.3 33.5 42.3 58.4 50.3 50.6 51.4 53.3 54.5 54.5 56.0 The figures appearing in table XXVI below show the charge in respect of medical assistance and administration expenses, according to calculations made in the course of the investigations preparatory to the 1924 Act. For the actuarial balance-sheet as at 1 January 1930 the emerging cost has been estimated for medical assistance and administration expenses together, in accordance with data collected by the Central Institution from 1926 to 1933, at an annual total commencing at 85 millions and increasing annually by one per cent, of this initial figure up to a maximum reached after twenty-five years. CZECHOSLOVAKIA 147 Since these estimates were in excess of the a m o u n t s actually realised, it was decided that, for the balance-sheet as at 1 J a n u a r y 1935, t h e same mitial total and the same rate of increase should b e maintained b u t t h a t t h é initial year should be changed from 1930 to 1935. TABLE OF SYMBOLS INTRODUCED IN CHAPTER II (0 Limiting age. i Annual interest on a monetary unit. 1 Discounting factor 1+ i Proportion of old-age pensions which begin to be payable at age k. «ft Proportion of old-age pensions not in payment at the beginning of the kth year of age. Present value of a unit contribution payable in respect of an insured person aged x so long as he remains healthy and not later than age 65. aa a *,65-."c| = Premium reserves calculated by the normal method. &S2 , aaipi <65 aa e5-x| sc a aaipi = Present value of the right to unit old-age pension, payable from age 65, acquired by an insured person aged x. Adjusting coefficient to allow for monthly or weekly payments. Present value of the right to unit old-age pension, with postponable commencing age, acquired by an insured person aged x. Present value to an insured person aged x of the right to additions of old-age pension, on the assumption that these additions increase the amount of pension by a unit for each completed contribution year before age 65. Present value to an insured person aged x of the right to additions of old-age pension, on the assumption that these additions increase the amount of pension by a unit for each completed year before the date of commencement of payment of pension. Present value of a unit invalidity pension when invalidity commenced at age x and has a duration of k years. i(tt> x -p v a d-xiv) |i7-z a z it***<» i7 a °-x{z) 17 a ai * "aaa s-x\ x(z) p Aav v — Present value of a unit invalidity pension in t h e course of being acquired, in respect of an insured person aged x . = p r e s e n t value of a unit invalidity pension i n - t h e course of being acquired, in respect of an insured person aged x , taking into account a waiting period of t years. = present value to a n insured person aged x of the right to additions of invalidity pension, on t h e assumption t h a t these additions increase the a m o u n t of pension b y a unit for each completed contribution year from t h e end of t h e waiting period until age 65. = Present value to a n insured person aged x of the right to additions of invalidity pension, on t h e assumption t h a t these additions increase the amount of pension b y a unit for each completed contribution year from t h e end of t h e waiting period until t h e date of commencement of p a y m e n t of oldage pension. = Present value of t h e right to a unit pension or to a lump sum on death in respect of the .wife of a n insured m a n who becomes a widow a t age y . — Present value of t h e right t o a unit widow's pension or t o a lump sum on death acquired b y a n insured m a n aged x . = Present value of a unit pension paid to an orphan aged z. = Present value oí the right to unit orphans' pensions on the death of a n insured man aged x . — Present value of t h e right t o unit orphans' pensions acquired b y an insured m a n aged x . = Present value of t h e right to a unit education allowance, added to an invalidity pension, acquired by an insured m a n aged x . = = P r e s e n t value of t h e right to a unit education allowance, added t o an old-age pension, acquired b y an insured man aged x (the old-age pension being payable as from age s). Present value of t h e right to a unit dowry on marriage in respect of an insured woman aged y . CHAPTER III FINANCIAL SYSTEM The financial system which, after thorough technical research, was adopted as the basis for the scheme of workers' insurance against invalidity, old age and death, satisfies certain essential requirements which must first be summarised. Financial equilibrium is secured between contributions on the one hand and benefits on the other. The individual State subsidies do not, strictly speaking, enter into the financial mechanism and entail only simple accounting operations \ The rates of contribution are based on general average premiums (the calculation of which will be analysed in the first section of this chapter). In each wage class a uniform rate of contribution is fixed, applicable to all present and future insured persons. Future entrants into insurance will bear a part of the burden in respect of the initial population. However, the ratio of contributions to benefits is so arranged that thé cost to future entrants is not excessive and cannot exceed that required to purchase the same benefit rights from private assurance companies. The accumulation of reserves is limited to those required to safeguard the actuarial equilibrium of the system. A rate of interest of 4 per cent, was used as the basis for the calculations made in the investigations preparatory to the 1924 Act; the basic rate of interest was increased to 24% per cent, by the 1928 Act when itwas found that the interest yield was appreciably in excess of the latter rate. § 1. — Calculation of the General Average Premiums In § 3 of the preceding chapter prominence was given to certain expressions which represent the probable present values of unit contributions or of unit payments for the various classes of benefit and which constitute the essential theoretical bases on which depends the calculation of the present value of the total liabilities and assets of the insurance scheme. 1 A valuation has, however, been made of the annual charge falling on the State in respect of the payment of individual subsidies: see Chapter II, § 2, pp.2 125-127. See later, Chapter IV, § 2, p. 163. 150 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION If a denotes any one of these expressions, the present value to which it leads may be calculated as follows: (1) in respect of the initial male population (2) in respect of the initial female population ^ 1 y ^'y a y ") (3) in respect of future male new entrants 3C=15 where c represents an annual coefficient of increase of the population l, independent of age, which is taken to be equal to 1.01 a . This formula may be written 19 by letting k = v1'* clh + v3h c3U + ... that is to say by taking k = 34.16301 for a rate of interest oí 4 per cent., k = 29.35288 for a rate of interest of 4 % per cent.; (4) in respect of future female new entrants k2 Dl l a. • y=i5 From the comparison of the liabilities and the assets of the scheme are immediately obtained average premiums in respect of the various classes of insured persons and the various types of benefit. These average premiums were at first obtained by means of the formulae reproduced in Chapter II, which are based on the assumption that throughout his career each insured person receives a constant i l 2 See Chapter I, § 2, p. 106. The formulae and hypotheses adopted for the first calculations of general average premiums during the preparatory work have here been followed. For instance, it is supposed that the contingents becoming insurable each year include persons of all ages from 15 to 19. In the subsequent calculations of general average premiums, a number of data were modified, but the principle has remained the same. 151 CZECHO-SLOVAKIA wage. They were recalculated on the assumption that the wage increases regularly each year by 10 per cent, of its initial value between the ages of 15 and 25 and then remains constant at double its initial figure. Since the increase of wages is of consequence only in so far as it entails transfer from one wage class to another, there was calculated, in each case, a weighted average of the premium P corresponding to the first assumption and the premium P is) corresponding to the second assumption. The weighting coefficients were determined in the investigations preparatory to the 1924 Act at first on the basis of statistics of wages at 1 January 1923: Wage class Weighted average premium A 0.6 P™ + 0.4 PA B . . . 0.4 P * + 0.6 P B C 0.2 P™ + 0.8 P c D Px, and then on the basis of statistics of wages at 1 January 1924: Wage class Weighted average premium A 0.4 P f + 0.6 P A B 0.26 P * + 0.73 P B C • D 0.13 PÍf + 0.86 P„ c PD On the basis of the average annual numbers of contribution weeks, which have been indicated above, namely: In class A ., >. B „ „ G • „ „ D 42 weeks 44 „ 46 „ • 48 „ the investigations preparatory to the 1924 Act calculated, for each type of benefit, average premiums relating respectively to: (1) Males, females and both sexes combined; (2) The initial population, future entrants and all contributors. Below are reproduced the average premiums obtained, in each wage class for all benefits combined and for both sexes, from two series of calculations based respectively on wages statistics as at 1 January 1923, and as at 1 January 1924. 152 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Wage class Average annual premium for the initial population Average annual premium (or future entrants Average annual premium for all contributors (general average premium) First series of average premiums [2] (based on wages statistics as at 1 January 1923) A B G D 226.77 279.48 335.91 410.34 154.29 194.34 236.11 290.38 176.96 220.91 267.09 327.41 Second series of average premiums [3] (based on wages statistics as at 1 January 1924) A B C D 219.38 270.60 325.56 394.82 146.46 185.78 227.37 279.16 169.15 212.12 257.79 314.86 § 2. — Preliminary Valuation and Table of Annual Estimates The first series of average premiums relating to all contributors (general average premiums) was used as the basis for the rates of contributions in the first technical valuations which preceded the 1924 Act. The rates assumed * in these valuations corresponded t o annua] contributions—reproduced below—which were in excess of the theoretical general average premiums: Wage class A B C D Annual contribution corresponding to the rates assumed in the first investigations preparatory to the 1924 Act 184.80 crowns 255.20 331.20 „ • 432.00 The difference between these annual contributions and the general average premiums represented a margin which was to be used t o cover administration expenses and t h e cost of medical assistance and finally t o maintain a special guarantee fund. The investigations preparatory to the 1924 Act concluded with the construction, on t h e bases just described, of a " preliminary valuationsheet " demonstrating the solvency of the system at the time of its coming into force. This is reproduced below: 1 Which have been referred to above: Chapter II, § 1, p. 116. 153 CZECHO-SLOVAKIA TABLE XXV. PRELIMINARY VALUATION SHEET (at 4 per cent, interest) (In millions of crowns) ASSETS LIABILITIES Contributions : Wage class A „ B „ C „ D 13,380 8,198 5,599 15,821 Basic amounts Additions: Wage class „ „ „ „ 7,179 A. B. C. D. . . . . 9,877 5,626 3,631 9,973 -29,107 Administration expenses, medical assistance and grant to guarantee fund: Wage class A . . 629 „ B . . 1,150 „ „ C . . 1,103 „ D . . 3,830 6,712 Total Total . 42,998 42,998 It has already been seen that the rates of contribution which came into operation on 1 July 1926 are 1.8 per cent, less than those which were at first taken into consideration. This reduction is due to the fact that during the first ten years the insurance scheme will benefit by reason of the interest yield being in excess of the basic rate of interest. It was assumed that the interest yield would be 5 per cent, during the first five years and 4% per cent, during the next five years. The reduction in the rates of contribution corresponding to this assumption was calculated in such a way that the total amount of the reserves at the end of each year would not be increased. This condition enables a direct calculation to be made of the amount P n of the contribution income to be substituted for the amount P n calculated on the basis of interest at 4 per cent. The proportionate reduction of the rates of contribution is then given by the formula [3] > P p' 1.05 5 + 1.05* 2 fa' p p' 1.045 p 2 " tZ 1-05" + 1.05e Z* 1.045" The excess of the rates of contributions actually put into operation over the theoretical average premiums still represented a margin. This margin, estimated to be 15.3 per cent, of the total contributions, was apportioned as follows [3]: 11 per cent, for administration expenses; 3 per cent, for medical assistance; 1.3 per cent, for the guarantee fund. 154 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION On the bases adopted for the second series of calculations made in the course of the preliminary investigations there was drawn up a table of annual estimates—reproduced below—which shows the probable financial development of the system: TABLE XXVI. — TABLE OF A N N U A L ESTIMATES—-PROBABLE OF INCOME AND O U T G O — G R O W T H OF F U N D S PROGRESS (In thousands of crowns) Income Year of operation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total accumulated fund at beginning of year Contributions 482.95 989.96 1,527.50 2,089.49 2,669.61 3,235.54 3,797.39 4,350.13 4,895.40 5,433.89 5,949.85 6,467.32 6,987.29 7,510.26 8,037.98 8,566.75 9,097.18 9,629.92 10,165.57 10,704.73 11,248.07 11,794.81 12,345.27 12,899.40 13,457.00 14,019.76 14,587.31 15,158.90 15,733.48 577.00 601.04 626.05 650.30 674.27 678.81 683.14 687.26 691.18 694.93 717.75 739.42 761.22 783.12 805.10 827.15 849.28 871.50 893.79 916.14 938.59 960.97 983.57 1,006.11 1,028.65 1,051.02 1,073.51 1,095.94 1,118.29 1,140.56 Outgo Total Adminis- accumulated tration at expenses fund end of Interest Benefits Transfer and values medical year assistance 12.41 37.07 62.96 90.36 118.97 133.27 158.82 184.18 209.13 233.74 229.70 250.71 271.79 292.96 314.26 335.75 357.28 378.88 400.57 422.38 443.33 466.45 488.71 511.12 533.67 556.36 579.25 602.34 625.59 648.96 25.68 46.95 63.82 81.53 6.10 97.67 21.05 40.65 110.47 64.42 120.05 92.16 130.32 119.97 138.30 148.80 144.09 178.62 152.38 209.54 159.60 240.78 165.69 272.75 170.72 304.27 174.66 336.12 182.21 368.04 189.19 400.01 195.62 432.05 201.53 464.22 206.88 496.47 211.71 530.14 216.00 564.36 219.76 599.27 222.97 635.08 225.63 669.76 227.72 705.65 229.27 743.02 230.24 782.10 230.64 823.18 233.48 80.78 84.15 87.65 91.04 94.40 95.03 95.64 96.22 96.77 97.29 100.49 103.52 106.57 109.64 112.71 115.80 118.90 122.01 125.13 128.26 131.40 134.54 137.70 140.86 144.01 147.14 150.29 153.43 156.56 159.68 482.95 989.96 1,527.50 2,089.49 2,669.61 3,235.54 3.797.39 4;350.13 4,895.40 5,433.89 5,949.85 6,467.32 6,987.29 7,510.26 8,037.98 8,566.75 9,097.18 9,629.92 10,165.57 10,704.73 11,248.07 11,794.81 1-2,345.27 12,899.40 13,457.00 14,019.76 14,587.31 15,158.90 15,733.48 16,306.66 § 3. — Actuarial Balance-Sheets and Financial Development of the Central Institution The actuarial balance-sheet which the Central Institution must draw up every five years makes use of the theoretical factors, which were previously used for determining the general average premiums, for the purpose of calculating the assets and liabilities of the insurance scheme. 155 CZECHO-SLOVAKIA The actuarial balance-sheet drawn up as at 1 January 1930 introduces a certain number of new factors of which we shall describe the most important: 1. The distribution of the contribution days, according to age and wage class, based on the experience of the year 1929 1. This distribution made it possible to take account of the growth of wages with age without having recourse, as hitherto, to the premiums P. At each age the average value of the daily contribution and the average value of the addition corresponding to a day's contribution were calculated by the following formulae: PT = y [d(x> A °) • 2 - 6 + d(x>A») •3-6 + + d ( * , B ) . 5 . 1 + á ( * , C ) . 6 . 6 + á ( * , D ) . 8.4J ; i j[d{x, A 0 ) . 0.60 + d{x,Ab). + d(x, B) . 1.15 +d(x, 0.85 + G) . 1.40 +d(x, D) . 1.75], where d (x, Aa) , d (x, Ab) , d (x, B ) , d (x , C) , d (x , D) represent the percentages of contribution weeks in respect of each wage class. 2. The present value of the rights to supplementary benefits in the case of insured persons born before 1 January 1899, which is calculated by means of the following formula [6J (in the case of males): N 30-34 . 35-39 ' 40-44 45-49 ' 50-54 ' 55-59 ' 50 59 95 152 198 231 247 251 250 247 100 100 100 100 100 95 90 80 60 40 50 59 95 152 198 219 222 201 150 99 § 2. — Population of Insured Persons and Contributors Under the Legislative Decree of 28 October 1935 the scheme for insured persons in commerce and industry covered compulsorily, up to the age of 60, all employed persons and, generally, all persons of French nationality, male and female, in whatever capacity and wherever they might be working, and whether for one or several employers, as long as their total annual remuneration, excluding family allowances, did not exceed 15,000 francs. (This limit was increased to 18,000 francs 1 GENERAL la 2population, STATISTICAL OFFICE OF FRANCE: Statistique du mouvement de 1911, 1912, 1913, p. LVI. 3 Annuaire statistique de la France, 1921, Part II. GENERAL STATISTICAL OFFICE OF FRANCE. 12 178 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION in towns of more than 200,000 inhabitants and in certain industrial areas. It was increased by 2,000 francs if the employed person had one child dependent on him,'by 4,000 francs if he had two children, and if he had three or more it was increased to 25,000 francs.) To these provisions, which appear in almost the same form in the 1930 Act and in the Legislative Decree of 28 October 1935, the latter adds the following stipulations. Compulsory insurance is extended to the following classes of workers: persons working at home; commercial travellers and agents who are not licensed; employees in hotels, restaurants and cafés; drivers of public vehicles who do not own their vehicle; luggage porters working under contract; attendants and other employees in theatres or places of amusement. Compulsory insurance does not cover persons whose normal wage is less than 1,500 francs per annum, nor children who are subject to compulsory school attendance or who work in the homes and for the account of their parents. The scope of the legislation does not include officials employed by public authorities or public services, railwaymen, miners, seamen, tramway workers, etc., who are covered by special schemes. Foreign workers are compulsorily insured under the same conditions as French workers. They and their dependants, if they are domiciled in France, are entitled to the benefits due in respect of the contributions credited to their account. Other benefits are only granted if an agreement to this effect has been concluded with their country of origin. The Act of 26 August 1936 substituted, for the remuneration limits (above which the obligation to insure ceases) hitherto in force, two limits uniformly applicable in all areas: 21,000 francs per annum, if the employed person has no child dependent upon him; 25,000 francs per annum, if the employed person has at least one child dependent upon him. The same Act reduced from 1,500 to 1,000 francs per annum the lower remuneration limit below which the obligation to insure ceases. An Act of 31 December 1937 provided that all workers registered on 31 December 1937 should provisionally remain in insurance. As from 1 October 1938 the upper limit of remuneration for liability to insurance was fixed by the Decree of 14 June 1938 [23] at a uniform figure of 30,000 francs a year irrespective of the family responsibilities of the insured person. The same Decree extended compulsory insurance to: brokers, inspectors and other unlicensed agents of insurance companies ; the. managers of co-operative societies and the branch managers of multiple shops or of other commercial or industrial establishments. The scheme applicable to agricultural workers includes compulsorily: persons employed in occupations in agriculture and forestry; persons employed by rural craftsmen, and contractors for threshing and other agricultural work; 179 FRANCE persons employed by agricultural trade unions and organisations carrying on agricultural social insurance; persons employed by mutual agricultural credit funds and co-operative agricultural funds; persons employed by agricultural family allowances funds, and, in general, persons employed by any regularly constituted agricultural occupational organisations. Compulsory insurance covers also share-farmers who ordinarily work only with the help of members of their family (wife, parents, children, brothers, sisters or collateral relatives) and who do not own a share of the stock of greater value than 10,000 francs at the time,of becoming oècupiers of the undertakings. Children are not deemed to be wage earners as long as they are subject to compulsory school attendance or when they are employed by their parents and work for them without receiving any money wage. The members of a farmer's family, when they live with him and ordinarily work with him and for his account, become compulsorily insurable as soon as they come within the scope of the legislation relating to accidents in agriculture. ESTIMATES OF THE INITIAL INSURED POPULATION The principal estimates of the initial insured population made in the course of the preparatory investigations will now be reviewed. A first estimate [2, p. 138], based on the result of the general census in 1911 and on the losses caused by the war, included all wage-earners between 16 and 60, agricultural and others, who did not earn more than 10,000 francs per annum and came within the scope of compulsory insurance. It gave the following figures for the total number and its distribution into age groups. TABLE IV. ESTIMATED INITIAL POPULATION OF INSURED PERSONS (in thousands) Age (years) Men Women 16-19 20-24 25-29 30-34 35-39 . . . . . 40-44 45-49 50-54 55-59 1,081 857 759 563 480 459 415 343 274 667 642 427 321 277 245 216 179 161 1,748 1,499 1,186 Total 5,231 3,135 8,366 884 757 704 631 522 435 At the same time it was estimated that the number of wives, not being wage earners, of compulsorily insured men would reach 1,359,000 and that the number of children under age 16 (not being wage earners) of compulsorily insured men would be 3,131,000. 180 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION When share-farmers and their wives were transferred from compulsory to voluntary insurance the above figures had to be reduced [38]. The total of the compulsorily insured persons then became about 8 million (5,009,000 men and 3,002,000 women). In a later investigation [3, p. 161] the estimated compulsorily insured population of 8,011,000 was distributed into age groups by means of proportions obtained from a Ministry of Labour enquiry, as at 1 November 1922, concerning persons insured for workers' and peasants' pensions. In 1926 the knowledge of the partial results of the census at 6 March 1921 enabled a new estimate to be made, which produced a total compuleorily insured population of 8,310,000 [4, p. 68]. In the final preparatory investigations [7, p. 26] the age distribution shown in table V was adopted for a total compulsorily insured population of 8,310,000, based on the final results of the 1921 census. TABLE V. ESTIMATED I N I T I A L POPULATION OF I N S U R E D PERSONS (in thousands) Age (years) U n d e r 20 20-24 oc fln 30-34 35-39 40-44 45-49 50-54 55-59 Total Men Women Total 1,015 590 625 540 515 500 455 405 325 710 685 455 350 290 245 220 205 180 1,725 1,275 1,080 890 805 745 675 610 505 21 15 13 11 10 9 8 7 6 4,970 3,340 8,310 100 Percentage In 1930 [9, p. 41] the total number of insured persons was estimated to be 834 millions (5% millions in commerce and industry and 3 million in agriculture). All these estimates were provisional and were subject to alteration as long as the provisions defining the scope of the Act were not finally settled. EXPERIENCE Statistics obtained during the operation of the scheme do not enable the total number of the insured to be fixed with precision. The number of contributors, which can be estimated with greater precision from the numbers of quarterly contribution sheets, was as follows (in thousands): Commerce and industry Agriculture 1933 1934 1935 1936 5,621 473 5,582 523 5,487 552 5,844 579 As a result of statistical researches [31] based on the analysis of a considerable number of records relating to insured persons in commerce and industry, the following age.distribution of contributors has been obtained: 181 FRANCE TABLE VI. — DISTRIBUTION BY OF CONTRIBUTORS: EXPERIENCE Distribution of 100,000 contributors from analysis of 4,911,100 6,348,486 25,173,707 records records records relating relating relating to to 1933 tO 1935 1930 and 1931 Age (years) U n d e r 15 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 Total AGE . . . . . . 1,182 13,869 16,219 15,599 12,825 9,680 8,379 7,658 7,117 6,453 1,019 2,536 12,521 15,890 15,199 13,260 10,147 8,343 7,724 6,845 5,998 1,537 693 9,074 14,535 16,129 14,396 11,772 8,610 7,408 6,721 6,170 4,492 100,000 100,000 100,000 § 3. — Annual Number of Benefieiaries INVALIDITY PENSIONS The first estimate [2,. p. 145] divided the invalid pensioners into two groups according as the duration of invalidity was less or more than five years. The first group was expected to number 28,000 from the beginning of the third year (after a qualifying period of two years) and to reach a constant maximum of 99,000 after the seventh year. The second group would commence at 13,000 in the eighth year and would continue to increase up to the figure of 182,000 at the end of 45 years. The total number of invalidity pensions current each year was then estimated [3, p. 193], on the basis of Zimmermann's invalidity table * and the German invalid life table ', to be 32,814 for the first year of benefit and 430,000 when a stationary position would be reached. A subsequent estimate based on the table 2 of the railway pensions fund of Prussia and Hesse (1908-1912) and on a total of 8,742,000 compulsorily insured persons produced an annual crop of 59,000 invalids aged less than 60. Applying to this supposedly constant crop the invalid life table constructed by the Actuarial Department of the Ministry of Labour, the following forecasts were obtained: the number of pensions in payment would commence at 59,000 at the beginning of the second year (after a qualifying period of one year) and would reach 316,000 at the end of 10 years, 506,000 at the end of 20 years, 590,000 at the end of 30 years, 611,000 at the end of 40 years and finally a maximum of 613,000 as from the forty-third year [5, pp. 83, 87]. In 1929, the crop of invalids was estimated to be 30,000 for the year 1932 and 60,000 for each year following [8, p. 240]. 1 2 See above, p. 175. See the section devoted to invalidity, old-age and widows' and orphans' insurance for workers in Germany, table V, p. 289. 182 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION TABLE V I I . OBSERVED N U M B E R S OF I N S U R E D P E R S O N S E N T E R I N G ON INVALIDITY ( I N S U R A N C E FOR COMMERCE AND I N D U S T R Y ) Age a t e n t r y on invalidity (years) 16 and under. Year of entry on invalidity 1933 1935 1934 | 1936 17 18 19 20 36 55 109 206 222 38 98 121 198 383 39 106 147 188 312 69 116 184 224 266 21 22 23 24 25 254 190 156 172 184 387 317 283 245 311 406 450 402 380 393 384 512 451 514 446 26 27 29 30 209 232 180 198 191 314 286 301 280 359 383 386 360 363 344 449 499 433 439 412 31 32 33 34 35 198 179 159 172 161 282 306 267 262 238 381 389 368 350 327 461 417 422 480 442 36 37 39 40 144 117 140 117 136 230 223 206 213 196 348 290 317 305 24-7 460 458 402 404 357 41 42 43 44 45 135 119 121 133 105 177 172 195 155 171 273 247 268 240 260 330 300 314 300 306 46 47 48 . . . 49 50 136 104 118 126 117 178 202 200 176 212 253 279 264 281 277 325 332 305 317 327 51 52 53 54 55 127 126 122 150 168 226 222 238 228 257 279 297 318 329 331 348 385 389 381 425 56 57 .58 . . 59 60 189 191 81 1! 270 318 360 403 432 418 418 483 529 491 286 28 38 67 1 71 i Total I n c o m p l e t e figures. 6,623 316 151 ! 177 i 10,585 159 1 13,949 16,992 Total 183 PRANCE Experience Scheme for commerce and industry Cases of invalidity. — Table VII opposite shows the number of persons becoming invalid in each age group in the years 1933, 1934, 1935 and 1936. Cessation of invalidity pensions. — The statistics of pensions which lapsed because of death or the return of the pensioner to health cover only a small number of years. It will suffice to reproduce the following table which shows, in the case of 10,000 invalids whose pensions began during the years 1933,1934 and 1935, the number of those still in a state of invalidity after a certain number of months or years (no account being taken of cases in which the pension was suspended). TABLE V I I I . Year of entry on invalidity 1933 . . 1934 . . 1935 . . CESSATION OF INVALIDITY Initial Number of invalids after number of invalids 3 months 16 months 19 months | 1 year | 2 years | 3 years 10,000 10,000 10,000 9,547 9,473 9,463 9,054 8,997 9,037 8,566 8,540 8,785 8,187 8,225 8,700 7,158 7,301 6,486 i i i i Not established. The number of current pensions at the end of 1936 was 37,272. Agricultural scheme Table IX below shows the number of persons becoming invalid in each age group during the years 1933, 1934, 1935 and 1936. The total number of invalids is still too small for the statistics of cessation of pensions to provide any conclusive evidence. On 31 December 1936 the number of current pensions was 1,662. OLD-AGE PENSIONS The application of the 1911 tables P.M. (males) and P.F. (females) to a" population of 7,800,000 compulsorily insured persons produced [38, p. 72] an annual crop of 73,000 old-age pensions commencing at age 60. On the basis of the age distribution resulting from the 1911 census (adjusted for war losses) and the mortality table P.M.F. 1901, the oldage pensions arising from a population of 8,742,000 compulsorily insured persons were estimated as follows [5, pp. 121, 125]: 470,000 for the 5 years' crops coming into payment simultaneously in the sixth year (after a 5 years' qualifying period) : 82,000 for each subsequent annual crop; 721,000 for the total number of pensions in payment at the beginning of the tenth year; 960,000 for the total number of pensions in payment at the beginning of the fifteenth year ; 1,100,000 for the total number of pensions in payment at the beginning of the twentieth year; 1,200,000 for the total number of pensions in payment when a stationary position would be reached. 184 ACTUARIAL TECHNIQUE AND FINANCIAL TABLE I X . ORGANISATION OBSERVED NUMBERS OF INSURED PERSONS ENTERING ON INVALIDITY (INSURANCE FOR AGRICULTURE) Age at entry on invalidity (years) Year of entry on invalidity 1933 _ 1935 | Total 1936 7 3 8 14 1 8 4 11 12 1 6 • 9 12 11 4 22 18 36 49 3 4 1 5 3 17 11 9 5 21 18 19 16 9 12 15 13 17 26 21 53 47 43 45 57 2 2 9 6 6 23 17 9 5 16 18 20 17 13 14 18 23 25 18 15 61 62 60 42 51 31 . . . 32 Q 3 34 35 5 5 7 3 4 16 17 10 18 20 17 25 19 19 30 16 22 12 20 18 54 69 48 60 72 36 37 38 39 40 2 2 4 3 5 8 12 13 6 7 19 19 14 11 12 22 17 15 18 14 51 50 46 38 38 41 42 43 44 45 3 7 2 5 7 9 5 8 12 8 17 10 10 16 13 11 8 15 10 16 40 30 35 43 44 46 47 48 49 50 3 7 1 3 3 13 7 16 12 17 13 11 19 16 15 15 10 13 19 20 44 35 49 50 55 51 52 53 54 55 8 4 2 1 8 11 12 14 12 25 18 12 20 26 18 15 11 24 26 28 52 39 60 65 79 56 57 58 59 60 5 17 2 — — 24 35 41 4 11 29 37 28 42 7 32 54 51 50 18 90 143 122 96 36 191 588 754 850 2,383 16 a n d 17 18 19 20 under 21 22 . . . 23 24 25 2 1 2 5 12 1934 . 26 27 28 29 30 • Total 185 FRANCK Experience The amount of the old-age pensions which began to be paid before 1 July 1935 could not be fixed at the guaranteed minimum x but had to remain below that figure because the pensioners had not paid five years' contributions. The number of these pensions current on 31 December 1936 was 59,650. Insured persons who began to draw their pension after 1 July 1935 are, if necessary, granted supplements bringing the pension up to the minimum guaranteed under the Social Insurance Act. Insured persons born between 1 July 1865 and 1 July 1875, who had reached the age of 60 years or over on 1 July 1935 and requested the payment of their pension as from that date, form what is known as the " exceptional crop ". This group is very large because it includes the elderly insured persons who joined the scheme on 1 July 1930 and waited until they had completed the five contribution years required by the legislation. On 31 December 1937 the number of old-age pensions granted could be classified as follows, according to the date at which they begin; the figures concern the scheme for commerce and industry and the agricultural scheme. Date of beginning of pension 1 J u l y 1935 1 October 1935—1 J u l y 1936 1 October 1936—1 J u l y 1937 Total number of pensions granted Number of pensions granted including a supplement 268,045 77,174 71,962 218,389 58,783 45,249 . . . . . . On 31 December 1937, for the same dates of beginning of pension, 48,762 claims were still under consideration (in the scheme for commerce and industry and in the agricultural scheme). 1 Cf. below, Chapter II, section 5, p. 202. CHAPTER II FINANCIAL ESTIMATES, BASES AND EXPERIENCE The resources of the insurance scheme are constituted by the contributions levied on insured persons and their employers, grants from public authorities and miscellaneous receipts. In paragraphs 1 to 3 below each of these classes of receipts is dealt with separately, with mention of the essential provisions which mark the various stages in the progress of the legislation. The liabilities of the insurance scheme include the cost of benefits and administrative expenses. In sections 4-10 below, each of the main items of expenditure will be examined separately. In each case the principal clauses governing the award and calculation of benefits under the 1930 legislation, as amended since that date, in particular by the Decrees of October 1935 and of June 1938, will be successively indicated. § 1. — Contributions of Insured Persons and Employers METHOD OF FIXING AND SCALES OF CONTRIBUTIONS The method of fixing the contributions of insured persons and employers in relation to wages and, in particular, the limits of the wage taken into consideration for this purpose have been modified from time to time. Government Bill, 1921 The 1921 Government Bill [1] divided insured persons into six wage classes, in each of which a basic wage was fixed, 5 per cent, of this being taken as the contribution of the insured person and also as that of the employer. Above a uniform limit fixed at 10,000 francs per annum an employed person was not subject to compulsory insurance. Chamber of Deputies Bill, 1924 The Chamber of Deputies Bill of 1924 [2] maintained the provisions of the Government Bill of 1921 as regards the calculation of contributions, but widened the scope of the scheme by increasing the upper limit of the sixth class by 2,000 francs for each dependent child under the age of 16. Act of 5 April 1928 The 1928 Act provided that the joint contribution, payable in equal parts by the insured person and employer, should be fixed at 10 per cent. 187 FRANCE of the total amount of wages up to a maximum of 15,000 francs. The maximum annual remuneration compatible with liability to insurance was fixed at 18,000 francs, excluding family allowances. This figure was increased by 2,000 francs for each dependent child after the first, and decreased by 3,000 francs for persons with no dependent child. In studying the legislation which came into force in 1930 and its amendments, a distinction must be made between insurance in commerce and industry and agricultural insurance. Insurance for commerce and industry Act of 30 April 1930. — In order to fix the rates of contribution the Act of 30 April 1930 divided insured persons into five wage classes. The contribution of the insured person, still equal to that of the employer, was fixed in each class according to the basic wage. The five wage classes, the basic wage, the rates of daily, weekly, monthly, and annual contributions were determined, until 1 April 1934, for non-agricultural insurance as follows: Limits of wage class t. Under 8 francs (1 to 2,399) 2. 8 frs. to 14 fr. 99. (2,400 to 4,499) 3. 15 frs. to 19 frs. 99 (4,500 to 5,999) 4. 20 frs. to 31 frs. 99. (6,000 to 9,599) 5. 32 frs. and over (9,600 and over) Daily basic wage Contribution of insured person, equal to that of employer per day per week per month per annum (francs) (francs) (francs) (francs) 6 0.25 1.50 6 72 12 0.50 3.00 12 144 18 0.75 4.50 18 216 24 1.00 6.00 24 288 36 1.75 10.00 40 480 (francs) The annual joint contribution represents 8 per cent, of the annual basic wage. The fifth class has as its upper limit a wage of 15,000 francs per annum. This maximum is increased to 18,000 in towns of more than 200,000 inhabitants and in a certain number of industrial areas, the list of which is fixed by Decree. It is increased by 2,000 francs if the insured person has one dependent child, by 4,000 if he has two, and it is increased to 25,000 francs if the insured person has three or more dependent children. In this fifth class the annual basic wage remains fixed in all cases at 12,000 francs. In order to cover the cost of the invalidity risk these rates of contribution are increased by one-eighth as from 1 April 1934, and by another eighth as from 1 April 1940. Modification of the 1930 Act. — The Finance Act of 28 February 1934 deferred the date of coming into force of the increase by one-eighth of the rates of contributions which it had been provided should take place as from 1 April 1934. Decree of 28 October 1935. — The Decree of 28 October 1935, substituted from 1 January 1936 for contributions fixed by wage classes contributions proportional to the actual wage of the individual. The actual wage is defined as the total cash remuneration—excluding family 188 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION allowances—increased by the amount of tips and payments in kind valued as a lump sum. The contribution is payable as to one-half by the insured person and as to one-half by the employer 1 . It is fixed at 8 per cent.2 of the insured wage, that is to say 8 per cent, of the actual wage to the maximum amount of: 1,000 500 ' 240 40 5 francs a month in the case of monthly wages; francs a fortnight in the case of fortnightly wages; francs a week in the case of weekly wages; francs a day in the case of daily wages; and francs an hour in the case of daily work of less than the legal duration. Act of 26 August 1936. — The upper wage limits on which the contributions are calculated were modified from 1 January 1937 by the Act of 26 August 1936. The remuneration of the insured person is taken into account in calculating the contribution to the maximum amount of 1,250 625 315 50 8 francs a month in the case of monthly wages; francs a fortnight in the case of fortnightly wages; francs a week in the case of weekly wages; francs a day in the case of daily wages; and francs an hour in the case of daily work of less than the legal duration. In the case of wages less than 1,500 francs a year (and greater than 1,000 francs a year), the contribution is calculated on the basis of an annual amount of 1,500 francs. Decree of 14 June 1938. — The raising of the limit of remuneration for liability to insurance resulted in raising the upper wage limit for the purpose of calculating contributions. These upper wage limits were fixed, as from 1 July 1938, as follows: 1,500 francs a month in the case of monthly wages; 750 francs a fortnight in the case of fortnightly wages; 380 francs a week in the case of weekly wages; 72 francs a day in the case of daily wages; 9.50 francs an hour in the case of daily work of less than the legal duration. The maximum amount for every half-day of employment of less than five hours is 36 francs. Agricultural insurance Act of 30 April 1930. — The Act of 30 April 1930 contains certain provisions applicable only to insured persons in agricultural occupations. The division into five wage classes specified for industry and commerce is maintained for agriculture. The contribution of the insured person, and the equal contribution of the employer, each consist of two parts: (1) a portion, used to cover the risk of old age, which is fixed at a quarter of the contribution payable by an insured person in industry or commerce in the same wage class; 1 The employer's share only is payable where the employed person is over 602years of age or a pensioner, and consequently is not liable to insurance. As a transitional measure the rate of contribution was reduced to 7 per cent, of the insured wage for the year 1936. 189 FRANCE (2) a portion, used to cover the risks of sickness, maternity and death, which is compulsory up to 5 francs a month. The wage which is taken into consideration in dividing the insured persons into classes, and which consequently enters into the calculation of the contribution, is not the actual wage but a mean daily wage which is fixed in each department. Decree of 30 October 1935. — The Decree of 30 October 1935 relating to insured persons in agricultural occupations fixes in a uniform manner as from 1 January 1936 the rates of the joint contribution, payable in all cases as to one-half by the insured person and as to one-half by the employer, in the case of children under 16, women and men respectively : Contribution of insured person, equal to that of employer Class of insured person in agriculture Children under 16 Men daily monthly annual (francs) (francs) (francs) 0.30 0.40 0.50 6 8 10 72 96 120 These contributions are used partly to cover the risks of sickness and maternity and partly for 1 old age, in accordance with coefficients which will be dealt with later . Decree of 15 June 1938. — The number of classes of insured persons was increased from three to four. The first now includes not only children up to the age of 16 years but also apprentices, probationers and workers with reduced working capacity; a new class was introduced for workers of both sexes whose annual remuneration exceeds 12,000 francs. The contribution rates for the first three classes remain the same and a higher rate was introduced for the fourth. The classes of insured persons and the contributions for each class are shown in the following table: Contribution of insured person, equal to that of employer Class 1. Children under 16, apprentices, probationers and workers with reduced 2. 3. 4. Women . . . . ' . • Men Men and women whose annual salary i Page 221. daily monthly annual (francs) (francs) (francs) 0.30 0.40 0.50 6 8 10 72 96 120 0.75 15 180 190 ACTUAKIAL T E C H N I Q U E AND FINANCIAL ORGANISATION The apportionment of these contributions between the various risks will be considered later l. ESTIMATES RELATING TO INSURED WAGES AND CONTRIBUTION YIELD In the Statement [2] on the financial and actuarial bases of the Social Insurance Bill made on 23 February 1922 by Mr. Cahen-Salvador before the Social Insurance Commission of the Chamber of Deputies, the estimated population of 8,366,000 compulsorily insured persons is subdivided into six wage classes as follows: Wage class (francs) 1. 2. 3. 4. 5. 6. Less t h a n 1,200 1,200 to 2,400 2,400 t o 4,000 4,000 to 6,000 6,000 to 8,000 8,000 t o 10,000 Total . . . . . . Men Women Total (in thousands) 145 657 2,250 1,613 411 155 380 1,561 771 392 22 9 525 2,218 3,021 2,005 433 164 5,231 3,135 8,366 In 1925, the Report [3] of the Senatorial Commission on Hygiene had as its principal object the estimation of the total of insured wages. After the necessary adjustments had been made to the statistics resulting from the operation of the 1898 Act on workmen's compensation, it was considered that the annual total of wages would be between 45 and 50 thousand million. Accordingly the average annual wage, on the assumption of 8 million 2 insured persons, was taken to be 5,000 francs. In the Recommendation [5] submitted in 1927 by the Senatorial Finance Commission the total amount of insured wages was estimated first at 42 thousand million by an optimistic estimate and then at 38.3. thousand million by a more cautious estimate, the latter relating to 8,742,000 compulsorily insured persons divided in the following manner: Thousands 1st 2nd 3rd 4th 5th 6th class: class: class: class: class: class: less than 1,200 francs 1,200 to 2,400 francs 2,400 to 4,000 francs 4,000 to 6,000 francs 6,000 to 8,000 francs 8,000 francs and above 268 1,403 2,681 2,573 1,241 576 These figures were borne out by the results of two investigations: one relating to 608,000 workers in the metallurgical, machine and electrical 1 2 Page 221. . . . From the preceding estimate (8,366,000) was deducted the number of share-farmers (566,000) who were assumed to be no longer compulsorily insured, and the result was increased to 8 million to allow for the movement towards industrialisation and for the increasingly important factor of the immigration of foreign workers. 191 FRANCE industries (226,000 in the district of Paris and 382,800 in the rest of France), the other arising out of the results obtained from 1922 to 1925 by the local general (sickness insurance) fund of the City of Strasburg. In 1929, as the result of a rise of wages—as was proved by the statistics of insured wages from companies officially authorised to effect insurance against industrial accidents—the Senatorial Commission on Hygiene [8, pp. 227-230] substituted for the preceding estimates the figures of 64 thousand million for the total of insured wages (46 thousand million in commerce and industry and 18 thousand million in agriculture). Finally the Recommendation [9, p. 41] submitted in 1930 by the Senatorial Finance Commission, on the basis of the following distribution by wage class: Per cent. 1st class: less than 4,500 francs 35 2nd class: 4,500 to 6,000 francs 15 3rd class: 6,000 to 9,600 francs 25 4th class: 9,600 to 15,000 francs 25 Total 100 arrives at an average daily wage of 21.90 francs, with 300 days in thé year, and consequently brings out an annual total of insured wages of 52 thousand million (36 thousand million in commerce and industry and 16 thousand million in agriculture). To support the estimates drawn up in the course of the preparatory investigations, the annual contribution yield has been deduced, either in total or for one or more of the risks, from the total of the insured wages by applying the appropriate factors, which will appear in the following chapter when the various apportionments which have been successively applied to the total contribution come to be reviewed. EXPERIENCE AS REGARDS INSURED WAGES AND CONTRIBUTIONS COLLECTED Distribution of Contributors by Wage Class Reference has been made in the preceding paragraphs to the results that can be deduced from the actual experience of the operation of the scheme as regards the total number of contributors and their age distribution 1. For the purpose of ascertaining the amount of wages, analyses have been made of numbers of quarterly contribution sheets amounting to 25,173,707 for the years 1930 and 1931, to 6,348,486 for the year 1933 and to 4,911,100 for the year 1935 2. Both these came from the non-agricultural scheme and had been apportioned by departmental offices. In this way were obtained [31, p. 220] the figures of the following table, which shows for each age group the proportion of insured persons whose remuneration is less than the respective limits of the various wage classes: 1 2 See p. 181. Up to 1 January 1936 stamps representing the contributions in respect of sickness and maternity were affixed to quarterly sheets. 192 ACTUARIAL T E C H N I Q U E TABLE X. DISTRIBUTION AND FINANCIAL ORGANISATION OF CONTRIBUTORS BY AGE GROUP AND WAGE CLASS Percentage of contributors whose annual wage was Age (years) in 1930-1931 less t h a n in 1935 less t h a n in 1933 less t h a n Fr. Fr. Fr. Fr. Fr. Fr. Fr. Fr. Fr. Fr. Fr. Fr. 2,400 4,500 6,000 9,600 2,400 4,500 6,000 9,600 2,400 4,500 6,000, 9,600 Under 1 15-19 . 20-24 . 25-29 . 30-34 . 35-39 . 40-44 . 45-49 . 50-54 . 55-59 . 60-64 . 28.5 8.9 3.4 3.2 3.8 5.1 5.9 7.2 8.8 10.9 13.0 All ag(;s 77.5 36.6 14.8 9.9 10.4 12.9 14.6 17.0 19.7 23.2 26.6 91.5 59.8 29.2 19.2 18.8 22.4 24.4 27.2 30.0 34.0 37.8 97.7 91.0 68.8 53:8 51.0 54.0 56.2 59.7 63.5 68.5 72.2 6.1 18.2 30.5 64.1 54 27 6 4 5 6 7 9 11 15 19 94 70 25 13 12 13 16 19 23 28 34 98 87 42 24 21 22 26 29 33 39 45 99 99 83 64 57 57 60 63 66 72 77 7.1 19.8 31.5 66,0 10 24 35 69 35.9 9.5 3.6 3.3 3.9 5.1 6.3 7.6 10.0 13.6 16.9 87.1 39.0 15.5 10.3 10.3 12.7 14.9 16.9 20.8 26.1 31.2 96.2 61.7 29.5 19.6 18.6 21.7 24.4 26.5 30.8 36.5 42.2 99.0 92.7 71.5 57.2 53.8 55.5 57.4 59.2 63.3 70.2 75.4 Average Daily Wage The two statistical analyses which have just been mentioned have also rendered possible the calculation of the average daily wage for each age group. In this way the three columns in table XI have been constructed, which show that wages increase with age up to a maximum value corresponding to the group of insured persons aged 30 to 34, and thereafter diminish slowly but continuously. TABLE X I . Age (years) 15-19 20-24 25-29 . . . . 30-34 35-39 40-44 45-49 50-54 55-59 . . . : 60-64 AVERAGE DAILY WAGE Year 1930-1931 Year .1933 Year 1935 Fr. Fr. Fr. 12.43 18.76 24.91 27.60 27.90 27.10 26.56 25.76 24.86 • 23.68 22.68 10.98 18.27 24.51 27.16 27.58 26.97 26.38 25.84 24.70 23.01 21.53 9.36 13.08 21.66 25.86 26.88 26.70 25.86 25.02 24.06 22.44 , 20.88 193 FRANCE Total Amount of Contributions Collected Since the inauguration of the scheme the contributions of compulsorily insured persons, agricultural and non-agricultural, have yielded the following annual amounts: 1,496 million francs in 1930 (second half-year) 3,562 3,261 3,271 3,176 3,086 2,640 4,186 „ „ ., „ „ „ „ „ „ 1931 1932 1933 1934 1935 1936 1937 To these~figures must be added the yield of the contributions paid in cash directly by the organisations effecting agricultural social insurance, which amounted to 35.1 million francs from 1.VII.30 to 31.III.32 20.5 28.5 28.7 28.5 23.1 „ ,. „ „ 1.IV.32 11-33 1.1.34 1-1-35 1.1.36 „ „ „ „ „ 31.XII.32 31.XII.33 31.XII.34 31.XII.35 31.XII 36 § 2. — State Aid The various successive plans which were drawn up during the course of the preparatory investigations each entailed a new estimate of the burden to be borne by the State. These estimates depend on the particular terms of the plan concerned and are not, in general, comparable inter se. Moreover, the State subsidies are not always fixed in advance: in certain cases it has been provided only that eventual deficits would be made good by the public authorities. For this reason the object of this paragraph is limited to a consideration of the subsidies which have been included in the legislation subsequent to and including the 1930 Act and which consequently became effective. Among these the following are the most important: (1) a fixed scheme (2) a grant insured subsidy to be used, in particular to wind up the 1910 of workers' and peasants' pensions 1, to cover the additional benefits payable to agricultural persons. Each of these two State contributions will be examined in turn. FIXED SUBSIDY BY THE STATE According to the 1930 Act a sum of 540 million francs was to be paid by the State each year. The purposes of this subsidy—which are revealed by a study of the financial scheme—are the winding-up of the 1 See Introduction, p. 170. 13 194. ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION 1910 scheme of workers' and peasants' pensions and the guarantee of the financial stability of the insurance scheme. The Decree of 16 July 1935 reduced this fixed annual payment to 140 million francs as from 1 July 1935, subject to a State guarantee. The Decree of 28 October 1935 confirms this reduction and formulates the accompanying guarantee in the following terms: " Nevertheless, if a deficiency is disclosed in the Augmentation Fund it will be immediately made good by a payment from the general budget. The total of payments of this nature may not exceed the sum represented by the capitalisation of an annuity of 400 million francs as from 1 July 1935 at a rate of interest fixed for each year retrospectively 1 by agreement between the Ministers of Labour and Finance,-in accordance with that applicable to the calculation of the old-age insurance scales." On account of the reduction which it has suffered, the fixed State subsidy is no longer sufficient to cover the cost of winding up the workers' and peasants' pensions scheme. This insufficiency will-continue for a certain number of years, after which the deficit which will have accumulated should be made good by annual surpluses. Thus the efficacy of the State subsidy in establishing the financial equilibrium of the insurance scheme has disappeared for a period which will certainly extend beyond a decennium. The sums actually paid by the State, under the heading of this fixed subsidy, since the inauguration of the scheme are indicated by the following figures, against which is shown the actual expenditure on workers' and peasants' pensions: Year Payment made by the State Actual expenditure on workers' and peasants' pensions (million francs) 1930 (second half) 1931 1932 1933 1934 1935 1936 1937 270.0 540.0 540.0 508.5 540.0 340.0 140.0 140.0 85.5 527.0 415.6 384.1 349.7 323.6 288.8 262.5' GRANTS ADDED TO CONTRIBUTIONS OF AGRICULTURAL INSURED PERSONS Under the 1930 Act the State must make an annual grant to guarantee the payment of additional benefits to insured persons in agricultural occupations. This grant is used: (1) to increase the contribution paid for old-age insurance by each insured person over age 30 by adding thereto 80 percent.; 1 4.40 per cent, for the year 1 July 1936-30 June 1937. 195 FRANCE (2) to increase each contribution paid for insurance against sickness, maternity and death, by a fixed amount of 10 francs a month. The Decree of 30 June 1934 reduced the increase—payable by the State—of the contribution for insurance against sickness, maternity and death to 8 francs a month but, on the other hand, added to it an increase of 1 franc a month for the insurance of agricultural workers against invalidity. As from 1 January 1936, the increase of 9 francs a month has been replaced, according to the Decree of 30 October 1935, by 90 per cent, of that fraction of the contribution allocated to sickness and maternity insurance. This increase is applied as to two-thirds (60 per cent.) to sickness and maternity insurance and as to the other third (30 per cent.) to the insurance against invalidity and death. According to the Decree of 15 June 1938, this addition is fixed as from 1 January 1939 at 80 per cent, of the fraction of the contribution allocated to sickness, maternity and invalidity. Since 1 January 1936 there has been no increase in the old-age contributions of insured persons over the age of 30 years, but the State, in order to guarantee the minimum pensions, makes a grant equal to 40 per cent, of the total amount of contributions credited in the preceding year to the individual old-age insurance accounts. The sums paid by the General Guarantee Fund to the agricultural insurance funds in compensation for the supplements paid to insured persons reached the following amounts: 1930-31 1932 1933 1934 1935 1936 • Thousand francs 8,138 87,478 70,326 65,164 65,619 43,815 1 i Not including the increase of contributions paid under the Decree ol 30 October 1935. The following amounts were reimbursed by the State to the General Guarantee Fund: Thousand francs 27,355 61,328 98,048 120,705 1933 1934 1935 1936 OTHER STATE CONTRIBUTIONS Savings on Cost of Assistance The 1930 Act provided for the annual payment'by the^State, the departments and communes, for the benefit of the insurance scheme, of one-half of the savings which they had made, owing to the Operation of the social insurance scheme, on the average credit made to cover the cost of assistance during the five years immediately preceding the coming into force of the Act. Kffl,íáB*'^ This item gave rise to no payments. The Decree of 28flOctober 1935 did away with it. 196 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION (2) Reimbursement of Expenses in Respect of Workers aged 60 to 65 at the Date of coming into Force of the Act This reimbursement, which was prescribed by the 1930 Act, was not altered by the Decree of 26 October 1935. (3) Grant in Aid of the Sickness Insurance of Old-age Pensioners This grant was transferred to mutual-aid societies when sickness insurance for old-age pensioners was detached from the compulsory insurance scheme by the Decree of 28 October 1935. § 3. — Sundry Resources The 1930 Act, like the Decree of 28 October 1935, allocates to the social insurance scheme a certain number of other permanent resources1: (1) The unused portion of the annual revenue fixed by Article 4 of the Act of 31 December 1895 (product of the sale of the Grown jewels). Under this heading there were paid: 167 thousand francs for the year 1931 128 „ „ „ „ 1932 136 „ „ „ „ 1933 151 „ „ „ „ 1934 140 „ „ „ two years 1935 and 1936. (2) The total amount of fines (basic amount and additional tenths). Under this heading the following sums have been paid to the fund: 5 thousand francs in 1933 73 „ „ „ 1934 127 „ „ „ 1935 241 „ „ „ 1936 (3) A special payment fixed annually by the Finance Act to be made out of the Treasury's share of the supplementary royalties payable by the Bank of France and out of the State's share of gaming revenue. The payments made under this heading have been 5 million francs in 1932 and 3 million francs for each of the following years. (4) Pension instalments lapsing under the five-year period of prescription and repayable capital sums which are not claimed by dependants of insured persons who have been dead for more than five years. § 4. — Invalidity Benefits INVALIDITY PENSIONS 1930 Act and Decree of 30 June 1934 The 1930 Act defines as follows the conditions of award and the amount of the invalidity pensions in the compulsory scheme applicable to industry and commerce: " an insured person who, on the expiry of 1 Interest on accumulated funds forms part of the financial mechanism; see Chapter III. FRANCE 197 the time limit of six months covered by sickness insurance or, in the event of an accident not covered by the Industrial Accidents Act, after healing of the injury, is medically certified to be still suffering from a disorder or infirmity which reduces his working capacity by at least two-thirds shall be entitled to an invalidity pension." An insured person has the right to benefit from invalidity insurance when he has been registered for at least two years and has to his credit a minimum of 480 daily contributions paid during the two years preceding the commencement of the sickness or the accident. A person who entered into insurance before the age of 30 is entitled to a pension equal to at least 40 per cent, of the average wage calculated from the compulsory contributions paid each year (from the age of 16 if he is over that age). This percentage is increased, up to a maximum of 50 per cent., by 1 per cent, of the wage for each year of insurance beyond the thirtieth during which at least 240 daily contributions were paid. For a person who entered into insurance after the age of 30 the rate of 40 per cent, is reduced by one-thirtieth for each year between 30 and the age of entry into insurance, with a guaranteed minimum. This minimum is fixed at 1,000 francs if the insured person has contributed for at least six years; it is 600 francs when the qualifying period has been completed and increases by 100 francs for each subsequent year during which 240 daily contributions were paid. In all cases the pension is increased by 100 francs a year for each child under 16 years of age. The Decree of 30 June 1934 extends the benefit of invalidity pensions to insured persons in agricultural and forestry occupations. The invalidity pensions are calculated according to the same rules as in the nonagricultural scheme and on the basis of the contributions actually credited to the individual accounts for old-age insurance. Decrees of October 1935 As from 1 January 1936, by virtue of the Decrees of October 1935, the invalidity pensions are subject to the following rules: Insurance for commerce and industry In order to claim benefits under the invalidity insurance system, the insured person must have been registered for at least two years before the beginning of the quarter in which the sickness or accident occurred and must have had deducted from his salary a sum of at least sixty francs for each of those years. 1 For an insured person who entered before the age of 30, the invalidity pension is equal to 40 per cent, of the average annual wage on the basis of which were calculated the contributions paid since his entry into insurance. For an insured person registered after age 30, this pension is reduced by one-thirtieth for each year or fraction of a year of age between thirty 1 Under the Decree of 14 June 1938, an insured person who ceases to be liable to insurance before having acquired his right to old-age insurance benefits and who is not receiving invalidity insurance benefit retains his right to a possible invalidity pension on condition that he asks for the final settlement of this pension before the end of the 18 months following the date on which he ceases to be liable to insurance. 198 ACTUARIAL T E C H N I Q U E and the age at entry. case be less than: AND FINANCIAL ORGANISATION Nevertheless the invalidity pension can in no 1,000 francs if the insured person proves 6 or more contribution years, 900 „ „ „ „ „ „ at least 5 contribution years, 800 „ „ „ „ „ „ „ „ 4 700 „ „ „ „ „ „ „ „ 3 600 „ „ „ „ „ „ „ „ 2 Only those years are deemed to be contribution years during which the deductions from wages on account of contributions total at least 60 francs. ' From age 60 the invalidity pension is replaced by the old-age pension to which the insured person is entitled by virtue of the payments made by his successive employers as well as by virtue of the contributions paid annually in their stead by the invalidity fund for the purpose of old-age insurance. These contributions are fixed in conformity with a scale constructed by the Minister of Labour according to the wage on the basis of which the invalidity pension had been calculated. The invalidity pension continues to be increased by 100 francs a year for each child under 16 years of age. Agricultural insurance In order to claim benefit when he becomes invalid an insured person must have been registered for at least two years before the beginning of the quarter in which the sickness or accident occurred, and for each of these two years his individual old-age insurance account must have been credited with contributions totalling at least 100 francs for men, 60 francs for women and 20 francs for children up to the age of 16. For an insured person registered before the age of 30, the pension is equal to ten times the average annual contribution appearing in his individual account. For an insured person registered after the age of 30, it is reduced by one-thirtieth for each year or fraction of a year of age between 30 and the age at entry, but the invalidity pension can in no case be less than: 800 francs if the insured person proves 4 contribution years Only those years are deemed to be contribution years during which the insured person's individual account is credited with at least 100, 60 or 20 francs, respectively for men, women, and children under 16. Decree of 15 June 1938 From 1 January 1939 onwards, the amount of contributions which must have been credited to the individual old-age insurance account during each of the two years of the qualifying period for invalidity insurance is reduced: from 20 to 16 francs for children under 16 years (being fixed at 16 francs for all insured persons in the first class); from 60 to 48 francs for women (second class) ; from 100 to 80 francs for men (third class). It is fixed at 100 francs for insured persons in the fourth class. FRANCE 199 The rate of individual pension granted to an insured person registered before the age of 30 years is increased from 10 to 15 times the average annual contribution standing to his account; it automatically follows that the invalidity pensions granted to insured persons registered after the age of 30 are increased by half their original value (the minimum rates applicable when the number of years of payment is less than five remain unchanged). Estimates made in the Course of the Preparatory Investigations The Government's Bill of 1921 [1] distinguished pre-invalidity, which was deemed for five years to be a continuation of sickness (after the sixth month), and permanent invalidity beginning at the expiration of the period covered under the heading of sickness and pre-invalidity. In the Statement on the financial and actuarial bases of the Social Insurance Bill [2, pp. 138 et seq.] already cited the costs of pre-invalidity and permanent invalidity are estimated to be as follows, for a total of 8,366,000 compulsorily insured persons: Temporary payments for pre-invalidity (from 7th to 66th month) ranging from 45 to 250 francs a month according to wage class: 26.4 million francs for the 3rd year of operation 93.4 „ „ „ „ 7th and subsequent years of operation. State contribution to pre-invalidity (20 francs a month for the first three wage classes in cases of total incapacity): 3.6 million francs for the 3rd year of operation 12.9 „ „ „ „ 7th and subsequent years of operation. Pensions for permanent invalidity are constituted by the sums accumulated in the individual old-age insurance accounts, with the following additions: (1) a complementary pension, the charge of which is borne by an assessment fund and is estimated to be: 16.1 million francs for the 8th year of operation 23.5 million francs for the 9th year of operation (in which year it attains its maximum) 1.9 million francs for the 15th year of operation. (2) complementary pensions provided by the State (250 francs in cases of total incapacity), representing in total: 0.5 million francs for the 8th year of operation 8.9 million francs for the 24th year of operation (when it attains its maximum) 2.9 million francs about the 45th year of operation; (3) pension supplements paid by the State, during the transitional period, to allow the minimum of 500 francs to be reached, the total of which is estimated to be: 1.5 million francs for the 8th year of operation 5.1 million francs for the 14th year of operation (when it reaches its maximum) 0.2 million francs at the end of 45 years. In the subsequent investigations [3,- 5, 7] pre-invalidity was no longer separated from permanent invalidity. It was assumed that the annual 20O A C T U A R I A L T E C H N I Q U E AND FINANCIAL ORGANISATION crop of invalids would remain approximately constant. An annual levy on the total amount of contributions would enable capital sums to be set aside to cover all the invalidity pensions which emerged during the year. Several estimates of this levy were made, and they all produced the figure of approximately 2 per cent, of wages. Experience Scheme for commerce and industry The invalidity pensions granted before 31 December 1935 involved an expenditure for the General Guarantee Fund amounting to the following figures up to 31 December 1937: 41,056 thousand francs for pensions in the strict sense; 1,272 thousand francs for children's supplements. The average value of the pensions being paid at 31 December 1936 was 2,121.75 francs. Agricultural scheme The invalidity pensions granted before 31 December 1935 involved an expenditure for the General Guarantee Fund amounting to the following figures up to 31 December 1937: 979,000 francs for pensions in the strict sense; 89,000 francs for children's supplements. The average value of the pensions being paid at 31 December 1936 was 991 francs. MEDICAL GARE OÏ INVALIDS The 1930 Act, which was extended by the Decree of 30 June 1934 to cover agricultural occupations, and likewise the Decrees of 1935, grant during a period of five years the medical benefit for insured persons in receipt of an invalidity pension. The Decrees of October 1935, with a view to the prevention of invalidity, establish a liaison between the sickness and invalidity insurance schemes. When a sickness which has been certified for more than two months foreshadows a future invalidity or appears to need special care, such as a course of treatment in preventive or curative establishments or a surgical operation, the sickness insurance fund notifies the regional federation of sickness and maternity funds, or the invalidity insurance fund to which it is attached. The special care may be provided by the sickness insurance fund and repaid to it by the institution responsible for the cost of invalidity insurance, without thereby occasioning a diminution of the expenses incurred under the heading of sickness insurance. In the Statement on the financial and actuarial bases mentioned above [2, p. 146], the cost of medical, pharmaceutical and special treatment for temporary invalids is estimated, for 8,366,000 compulsorily insured persons, at a figure which increases from 6.4 million francs in the third year to a constant maximum of 22.6 million francs from the seventh year onwards. The portion of the contribution required to cover the cost of the care of invalids was estimated in several subsequent estimates [3, 4, 7] at 0.1 per cent, of salary. The expenditure of the General Guarantee Fund in respect of the care of invalids before 31 December 1935 amounted at 31 December 1937. to: 38,307 thousand francs in the scheme for commerce and industry; 1,075 thousand francs in the agricultural scheme. 201 FRANCE § 5. — Old-Age Pensions 1930 ACT In accordance with the 1930 Act, old-age pensions are governed by the following clauses, which refer to the scheme for industry and commerce as well as to that for agriculture. Old-age insurance guarantees a pension on retirement at age 60. However, the payment of the pension may, on the request of the insured person, be anticipated from age 55 onwards or postponed. The old-age pension is in principle constituted by the accumulation, under the alienated capital system 1 or the repayable capital system at the option of the insured person, of the fraction of contribution which is credited to each individual account. This fraction is fixed as follows: 2 per cent, of basic wage for insured persons aged less than 30; 3.6 per cent, of basic wage for insured persons aged 30 or more 2. Normally, every insured person who can prove, at the age of 60 or up to the age of 65, at least 30 contribution years, each with a minimum of 240 daily contributions, is entitled to an old-age pension at least equal to 40 per cent, of the average basic wage as ascertained from the compulsory contributions paid each year from- the- age of-16. The pension is increased by a tenth for an insured person of either sex who has brought up at least 3 children until the age of 16. When the father and mother are both at the same time entitled to this 10 per cent. increase, it is only granted once and is based on the higher of the two pensions. Insured persons aged more than 30 at the date of the Act's coming into force have the benefit of " transitional " provisions. In the " transitional period " each insured person who, since the Act's coming into force, has paid continuously 240 daily contributions each year, is entitled to a pension at least equal to as many thirtieths of the normal pension as he has contribution years to his credit, subject to a minimum pension of 600 francs. DECREES OF OCTOBER 1935 The Decree of 28 October 1935 made no essential modification of the method of constituting old-age pensions in the non-agricultural scheme. Nevertheless, the average wage on which is based the calculation of the guaranteed minimum depends no longer upon the contributions paid from the age of 16 but upon all contributions.. Moreover, contribution years are defined not by the payment of a minimum of 240 daily contributions but by a deduction of at least 60 francs from the insured person's wages. 1 When accumulation is effected under the alienated capital system, the insured person may still, by express declaration, at the moment of entering on his pension, give up part of his own pension in exchange for the right to a reversionary pension in favour of his wife. 2 In the agricultural scheme contributions payable by an insured person aged more than 30 do not exceed 2 per cent, of basic wage, the additional 1.6 per cent, being paid by the State. 202 A C T U A R I A L T E C H N I Q U E AND FINANCIAL ORGANISATION In accordance, with the Decree of 30 October 1935 the constitution of the old-age pensions in the agricultural scheme is governed by the following regulations. Life annuities are constituted in individual accounts by crediting therein a fraction of contribution fixed at 24 francs per annum for children under age 16; 72 „ „ „ „ women; and 120 „ „ „ „ men. Minimum pensions are guaranteed under the following conditions: When the individual account has been credited each year, for at least 30 years, with contributions of a minimum of 100 francs for men and 60 francs for women, the old-age pension shall not be less than twenty times the average annual contribution allocated to old-age insurance; In the case of insured persons aged less than 30 on 1 July 1930, who have until 31 December 1935 fulfilled the conditions required by the 1930 Act, and whose individual account has been credited each year from 1 January 1936 with contributions of at least the minima mentioned above (100 francs for men and 60 francs for women), the old-age pension shall be equal to as many thirtieths of the normal pension as there are annual payments credited to the account, subject to a minimum pension of 600 francs. DECREE OF 15 JUNE 1938 From 1 January 1939 onwards insured persons in agriculture are divided into four classes and consequently the fractions of the contribution allocated to the individual old-age insurance accounts are fixed as follows: First class 24 francs a year; Second class 72 ,, „ „ Third class 120 „ „ „ Fourth class 180 „ „ „ ESTIMATES MADE IN THE COURSE OF PREPARATORY INVESTIGATIONS In the preparatory investigations attention was given to estimating the expenditure involved in the payment of complementary old-age pensions, that is to say the excess of the guaranteed fixed minima over the pensions constituted by the contributions credited in individual accounts. The Report of the Senatorial Commission on Hygiene [3], dated 1925, adopts as its bases on the one hand an average wage of 5,000 francs and the average individual account credit of 175 francs (i.e. 3.5 per cent, of the wage) and on the other hand a guaranteed minimum fixed in the following mariner: after thirty contribution years, 40 per cent, of the average wage over the last ten years; before thirty contribution years, as many thirtieths of the normal pension as the insured person has contribution years to his credit, subject to a minimum of 600 francs. On these bases the complementary old-age pensions appeared to be equal to a perpetuity of 282.5 million francs, with interest at 5 per cent. 203 FRANCE The second supplementary Report of the Senatorial Commission on Hygiene [4, pp. 62 et seq.], dated 1926, amends the estimate of the same charge, on the basis of a new age distribution of insured persons deduced from the results of the 1921 Census, to a perpetuity of 218 millions (with interest at 5 per cent.). The Recommendation of the Senatorial Finance Commission of 1921 [5, pp. 120-122] adopts for workers earning less than 4,000 francs an average wage of 2,607 francs, and for workers earning more than 4,000 francs an average wage of 6,149 francs. On the basis of a contribution of 4 per cent, of average wage to old-age insurance and assuming the same method of constituting old-age pensions as that considered above, the following annual figures represent the emerging cost of complementary old-age pensions: Year of operation 6th 7th 8th 9th 10th ' 11th 12th 13th 14th 15th 16th 17th 18th 19th 20th - 21st 22nd 23rd 24th 25th . . . . . Cost of bringing pensions up to the guaranteed minima (million francs) 218 245 271 295 319 341 362 380 396 410 421 429 435 438 439 437 433 426 416 401 Year of operation 26th . 27th 28th 29th 30th 31st 32nd 33rd 34th 35th 36th 37th 38th 39th 40th 41st 42nd 43rd 44th 45th Cost of bringing •pensions up to the guaranteed minima (million francs) 384 362 337 309 282 256 231 208 186 165 146 128 112 96 82 70 59 49 41 34 The Report of the Senatorial Commission on Hygiene [8, pp. 234-236], dated 1929, estimates that the cost of guaranteeing minimum old-age pensions to non-agricultural insured persons and agricultural insured persons in the transitional period could be covered by a perpetuity of 513 million francs, on the assumption that the average wage is 8,000 francs and the rate of interest 5 per cent. 1 The Recommendation of the Senatorial Finance Commission of 1930 [9, pp. 45-46] adopts as bases: an average daily wage of 21.9 francs and an average number of contribution days in the year of 270. On these bases the average cost per pension of guaranteeing the minimum 1 On the assumption that: 2 per cent, of the wages of insured persons aged at least 30, 3.50 „• „ „ „ .. „ „ „ „ over are devoted to old-age insurance. 204 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION old-age pensions is estimated as follows for non-agricultural insured persons : Group 1935 1940 1945 1950 1955 1960 Francs 450 517 674 735 (maximum) 674 454 In addition it is estimated that for an insured person who has paid contributions for 35 to 40 years the cost of the complementary old-age penfcion is zero, the guaranteed minimum pension being in this case provided entirely by the payments credited to the individual account. § 6. — Payments on Death 1930 ACT In the scheme for commerce and industry the insurance against death guarantees the payment of a lump sum to the dependants (surviving wife or husband, or descendants, or in default of such to the relatives in the ascending line who were dependent upon the insured person at the date of his death) of every insured person who has been registered for at least one year and who has completed 240 contribution days during the 12 months preceding death or 60 days during the last three months. This lump sum is fixed at 20 per cent, of the average annual wage, but it may not be less than 1,000 francs in the case of an insured person who has contributed regularly nor more than two-thirds of the deceased person's yearly wage. The lump sum payable at death is increased by 100 francs for each child aged less than 16 left by the deceased. The widow of an insured person having at least three children living, legitimate, recognised or adopted, of less than thirteen years of age, who were dependent on the insured person and who remain dependent on her, is entitled to a temporary orphan's pension for each child of less than thirteen years of age beginning with the second. When the children of an insured man or woman have lost both parents, each child under thirteen years of age is entitled to a temporary orphan's pension. The orphan's pension may not be less than 120 francs a year in respect of each child. The 1930 Act left the funds administering agricultural insurance free to fix the amount of the payments to be made in case of death. DECREES OF OCTOBER 1935 The Decree of 28 October 1935 made the following provisions governing the payments on death in the non-agricultural insurance scheme. In order to establish a right to death benefit the insured person must have been registered for at least one year and contributions amounting to at least 60 francs must have been deducted from his wages during the last four quarters preceding that of death, if it is sudden, or of the sickness or accident which resulted in death, if the deceased was an insured person at the date of death. 205 FRANCE The lump sum payable at death is no longer fixed at 20 per cent, of the average wage but at 20 per cent, of the wage corresponding to the joint contribution actually paid during the last four quarters preceding that of death, if sudden, or of the sickness or accident which resulted in death, if the deceased was an insured person at the date of death. The guarantee of a minimum of 1,000 francs is abolished. The lumpsum payment at death is, as before, increased by 100 francs for each child under age 16 left by the deceased. The temporary orphan's pensions are granted under the same conditions as in the 1930 Act but they are increased to 240 francs a year for each child. In the agricultural scheme, by virtue of the Decree of 30 October 1935, the dependants of the insured person receive on his death a lump sum equal to ten times the amount of the contributions credited to his oldage insurance individual account during the last four quarters preceding that of death, if it is sudden, or of the sickness or accident which resulted in death, if the deceased was an insured person at the date of death. The right to this payment is dependent upon the insured person's old-age individual account having been credited, in respect of the abovenamed period, with: at least 20 francs in the case of a child under 16, at least 60 francs in the case of a woman, and at least 100 francs in the case of a man. DECREE OF 14 JUNE 1938 In the scheme for commerce and industry the right to an orphan's pension is extended from the age of 13 to the age of 14 as from 1 July 1938. DECREE OF 15 JUNE 1938 In the agricultural scheme the amount which must stand to the credit of the individual old-age insurance account during the specified four calendar quarters in order to entitle the insured person to a lump sum at death is fixed as follows as from 1 January 1939: not ,, » ,, less than 16 francs ,. ,. 48 „ .. .. 80 ,, ,, „ 100 ,, for „ ,, „ an insured person of the first class; ,, „ ,, ,, „ second ,, ,, ,, ,, ,, ,, third „ ,, ,, „ „ fourth ,, ESTIMATES MADE IN THE COURSE OF PREPARATORY INVESTIGATIONS The Statement on the financial and actuarial bases [2] already mentioned deals with the granting to the dependants of compulsorily insured persons of a payment on death ranging from 150 to 1,500 francs, according to the wage class, conditional on the .insured person's having paid in the course of the twelve months preceding death a minimum of 240 daily contributions. It estimates that the cost of these payments would begin at 24,392 thousand francs for the first year and would reach 46,772 thousand francs in the ultimate position (towards the 45th year). The Senatorial Commission on Hygiene in its 1925 Report [3] values 206 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION at 0.3 per cent, of wages the fraction of contribution required to cover the cost of insurance against death. This figure was obtained on the following bases: a lump sum payment on death fixed at 20 per cent, of the average wage, subject to a guaranteed minimum of 1,000 francs; an average wage of 5,000 francs. The second supplementary Report [4] of the same Commission, dated 1926, by a new calculation based on the results of the 1921 Census reduces this fraction from 0.3 to 0.2 per cent. The Recommendation of the Senatorial Finance Commission [5], dated 1927, gives the following estimates: For the emerging cost of payments on death of an amount fixed at 20 per cent, of the average wage, an annual figure of about 73 million francs, representing 0.19 per cent, of the total wages; For the complementary payments on death, to bring them up to the guaranteed minima, an annual cost of about 19.8 million francs, representing 0.05 per cent, of the total wages. EXPERIENCE Under the heading of compulsory insurance against death there have been paid : t ' • (a) In the scheme for commerce and industry [30, 31, 32]: Thousands of francs 6,824 28,980 31,580 32,557 31.901 23,230 1930-1931 1932 1933 1934 1935' 1936_ (b) In the agricultural scheme [30, 31, 32]: 1930-1931 1932 1933 1934 1935 1936 Thousands of francs 187 1,397 1,893 1,750 1,943 1,096 1 * The two Decrees of 1935 involved a delay in the payment of lump sums in the event of death. In addition, the guarantee of the minimum benefit has~given rise, under both schemes, to expenditure borne by the General Guarantee Fund, and shown as follows in the accounts of that Fund [33]: Thousands of francs 1930-1931 1932 . . . 1933 1934 1935 1936 ; 17 481 700 805 1,060 587 1 i The guarantee of a minimum was abolished as from 1 January 1936. 207 FRANCE Furthermore, with the help of two partial analyses referring to documents of the years 1931 and 1932 respectively preliminary figures have been obtained [30] for some of the essential statistical elements of insurance against death. In particular the average amount of the lump sum payable at death has been estimated at: (1) In 1931, for ,, ,, ,, (2) In 1932, for ,, ,, ,, males, females males, females 1,575 francs; 1,249 ,, 1,525 „ 1,083 ,, § 7. — Family Maintenance Expenses Under this head are dealt with the additions which fall to be made, when the beneficiary has a dependent family, to the benefits applicable to the various risks. These additions have already been mentioned above; in this paragraph they are treated together, and likewise the estimates which have been made concerning them. 1930 ACT In the non-agricultural scheme, under the 1930 Act, the contributionmade by the social insurance scheme towards family maintenance expenses includes, as regards the risks of invalidity, old-age and death: (1) an increase of the invalidity pension by 100 francs a year for each child aged less than 16 years; (2) an increase of ttíe lump sum payment on death by 100 francs for each child aged less than 16 years. Moreover, the widow of an insured person having at least three children living, legitimate, recognised or adopted, of less than 13 years of age, who were dependent on the insured person and who remain dependent on her, is entitled to a temporary orphan's pension for each child of less than thirteen years of age beginning with the second. When the children of an insured man or woman have lost both parents, each child under thirteen years of age is entitled to a temporary orphan's pension. The amount of the orphan's pension may not be less than 120 francs a year in respect of each child entitled thereto. DECREES OF OCTOBER 1935 Under the Decrees of October 1935, the provisions mentioned above apply at the same time to the scheme for industry and commerce and to the agricultural scheme, and the amount of the orphan's pension is increased as from 1 January 1936 to 240 francs a year for each child entitled thereto. DECREE OF 14 JUNE 1938 From 1 July 1938 onwards, orphans' pensions are granted for one year longer—that is, up to the age of 14 years. 208 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION ESTIMATES MADE IN THE COURSE OF PREPARATORY . INVESTIGATIONS In the Statement on the Financial and Actuarial Bases [2] already referred to, the family maintenance expenses to be paid by the State are evaluated as follows: (a) additions to the monthly allowances for pre-invalidity from the 7th to the 66th month, inclusive (to the extent of 10 francs a month per child in cases of total incapacity). 1,005 million francs in the 3rd year, 3,554 ,, ,, ,, ,, ultimate position; (b) increase of the permanent invalidity pensions (beginning at the 67th month inclusive) to the extent of 100 francs a year for each child in cases of total incapacity: 389 million francs in the 7th year; 5,745 ,, ,, ,, „ 45th year; (c) payments on death (100 francs per child): 3,343 million francs a year. The Senatorial Commission on Hygiene in its Report, dated 1925, estimates at 0.1 per cent, of wages the fraction of contribution required to cover the cost of family maintenance expenses. In the Recommendation of the Finance Commission of the Chamber of Deputies [7], 1928 session, may be found detailed estimates of the cost of family maintenance expenses: (a) invalidity insurance 1 : 4 million francs the 1st year; 12 „ „ „ 6th year; 21 „ „ „ 11th year; 28 „ „ „ 16th year; 41 ,, ,, in the ultimate position ; (b) insurance against death: 8.3 million francs a year; (c) orphan's pensions 1 (90 francs a year for each child) : an annual expenditure commencing at 4 million francs in the 3rd year'and increasing to a constant maximum of 16 million francs reached in the 15th year. EXPERIENCE The expenditure resulting from the supplements for family responsibilities added to invalidity pensions, lump sums paid in the event of 1 The annual figures are reproduced in the Recommendation of the Senatorial Finance Commission for the year 1930. See Bibliography No. 9, p. 20. 209 FRANCE death and orphans' pensions is shown as follows in the accounts of the General Guarantee Fund 1: Supplements Supplements to invalidity to lump sums paid on death pensions Supplements to orphans' pensions Thousands of francs 1930-31 1931-32 1932-33 1933-34 1934-35 1935-36 1936-37 125 483 565 188 54 1,116 1,337 1,631 1,663 938 101 78 500 1,069 1,923 1,247 2,202 § 8. — Special Insurance of Wives of Insured Men 1930 ACT Under the 1930 Act, the wives, not being wage earners, of insured men are admitted to a special scheme of insurance defined as is indicated below, on condition that they apply within six months after 1 July 1930 or after the date of their marriage if they are aged less than 35 years, or after their exit from compulsory insurance. They are then deemed to be compulsorily insured persons receiving a hypothetical annual wage of 1,200 francs, subject to the following differences: their contribution is fixed at 10 francs a month, they are not entitled to the daily sickness benefit, they have no right to the guaranteed minimum of 1,000 francs in case of death, the payment of the invalidity pension operates only in cases of total incapacity to carry out household duties, and half of the contribution is applied to constitute an old-age pension in an individual account. The guaranteed minimum for the invalidity or old-age pension in the transitional period is fixed at 250 francs and is granted under the conditions regarding number and duration of contributions which are applicable to insured men. Women insured in this way who become widowed or divorced may continue to benefit from this special insurance. They have the option of maintaining for themselves and their children the rights to benefits in kind which they previously enjoyed by virtue of their husband's insurance, in return for a supplementary contribution independent of the number of children. DECREE OF 28 OCTOBER 1935 The Decree of 28 October 1935 imposed the following modifications on thé special insurance of wives of insured men: the hypothetical annual wage was increased from 1,200 to 1,500 francs, and 1 This Fund, the working of which will be considered later, took upon itself to refund to the insurance institutions up to 1 April 1936 the supplements paid by them to insured persons. The figures refer only to reimbursements by the General Guarantee Fund, that is, to supplements in respect of pensions which began to be paid not later than 1 April 1936. 14 •210 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION ' the contribution was fixed at 8 per cent, of this hypothetical wage, i.e. 30 francs a quarter. ESTIMATES MADE IN THE COURSE OF PREPARATORY INVESTIGATIONS The Report of the Senatorial Commission on Hygiene [3, p. 205], dated 1925, estimates the emerging cost of the special insurance for wives of insured men at 2 million francs on account of family maintenance expenses, and 14 million francs on account of old-age insurance, or a total of 16 million francs, which should be provided for, to the extent of a total of 7 million francs, by the payment of an annual contribution of 20 francs. The Recommendation of the Senatorial Finance Commission [5, p. 127] for 1927 estimates the expenditure on the special insurance for wives of insured men (additional payments for family maintenance, guaranteed minimum old-age pensions, and administration expenses) at a total commencing at 4 million francs for the first year and attaining 16 millions the 6th year, 24 millions the 15th year, thereafter decreasing until it reaches 5 millions towards the 45th year. This estimate has been adhered t o in the investigations which followed1. § 9. — Maintenance of Insurance Rights of Persons suffering from Sickness, Industrial Accident or Unemployment 1930 ACT The rights of an insured person suffering from sickness are maintained under the following conditions: When the sickness has lasted more than fifteen days, the sickness insurance fund pays for each working day from the sixteenth day, in respect of the insured person to whom it is paying pecuniary benefit, half the fraction of the contribution which must be assigned to old-age insurance. This fraction is fixed according to the basic wage upon which the daily pecuniary sick benefit is calculated. An insured person who is involuntarily unemployed, who registers at an employment exchange, who has completed a full year of uninterrupted membership of the social insurance scheme immediately before the period of unemployment, and who fulfils the same conditions in respect of contributions as are required for sickness insurance 2 , is entitled for a maximum period of four months in every twelve months to the payment of the joint contribution corresponding to his wage class for the purpose of maintaining his rights. 1 Recommendation of the Finance Commission of the Chamber of Deputies, 1928 (Bibliography No. 7, p. 65) ; and Recommendation of the Senatorial Finance Commission, dated 1930 (Bibliography No. 9, p. 20). 2 The insured person must have contributed for 60 days during the three months or 240 days during the twelve months preceding the sickness—days of sickness for which pecuniary benefit is paid being deemed to be contribution days. 211 FRANGE DECREE OF 28 OCTOBER 1935 With a view to maintaining the insured person's rights the following payments are made on his behalf: (1) by the sickness and maternity fund: as from the beginning of the second month of sickness (or of pathological pregnancy) a prescribed contribution for each fortnight in which cash benefits are granted, whatever the number of days for which benefit is paid. This prescribed benefit contribution is equal to the amount of the daily pecuniary benefit paid to the insured person, subject to a minimum of 6 francs; in cases of maternity a prescribed contribution of 24 francs ; (2) by the employer, or the insurer substituted therefor, as from the beginning of the second month of incapacity for work resulting from an industrial accident, a prescribed monthly contribution of 12 francs; (3) by means of a levy on all contributions in case of involuntary unemployment in respect of an insured person of French nationality registered at an employment exchange, a prescribed contribution of 30 francs for each quarter which includes at least 50 days of certified unemployment—but this contribution may not be paid for more than two consecutive quarters in the same civil year. ESTIMATES MADE IN THE COURSE OF PREPARATORY INVESTIGATIONS Contributions for Insured Persons while Sick The Statement on the Financial and Actuarial Bases, of 1923 [2, p. 146], estimates that the payment of all the contributions for insurance against old age and death, during days of sickness, will entail a constant expenditure of 33.6 million francs in respect of the compulsory insurance scheme. The Recommendation of the Senatorial Finance Commission, dated 1927 [5, pp. 92-93], estimates that the payment of the half-contribution for old-age insurance of sick persons will be equivalent to a levy of 0.05 per cent, of wages. This estimate has not been modified in later investigations. Maintenance of the Rights of Insured Persons while Unemployed After the abandonment of the unemployment insurance scheme, the inclusion of which had been considered in the Report of the Senatorial Commission on Hygiene, 1925 [3], the cost of the measures needed to maintain the rights of insured persons during involuntary unemployment was estimated at the constant figure of 0.1 per cent, of the total wages [5, 7]. 212 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION EXPERIENCE The payments made under the heading of half-contribution for old age in respect of sick insured persons, in the scheme for commerce and industry, reached the following totals: Period Cases ' of maternity Cases of sickness 1,132 1,385 1,169 1,292 1,804 6,015 8,749 7,344 9,587 14,914 Cases of maternity Cases of sickness 10 38 27 33 46 48 80 60 107 223 1930-31 1932 . . • 1933 1934 From 1.1.35 to 31.iu.36 and in the agricultural scheme: Period 1930-31 1932 . 1933 1934 F r o m 1.1.35 to 31.lil.36 ' . . . . The contributions in respect of unemployed insured persons could not be paid except after a long delay. They appear in the accounts of the General Guarantee Fund for the first time in 1934, and their amounts have been shown as follows: 1934 1935 1936 •. . 7,823 11,718 9,949 § 10. — Administration Expenses 1930 ACT The 1930 Act provided that insurance funds could not allocate to administration expenses a higher percentage than that which would be fixed, for the various funds, by a Decree issued on the recommendation of the Minister of Labour, and which would reach at its maximum 3.5 per cent: of the contributions received. Furthermore, it made provision for resources to meet the cost of operating the various services and funds in connection with the application of the Act, within the maximum limit of 5 per cent, of the total amount of all contributions and grants in aid. 213 FRANCE DECREES OF OCTOBER 1935 As from 1 January 1936, the payment of administration expenses is made directly by a deduction from the investment revenues in the case of the old-age and death funds or the invalidity, old-age and death funds and of the regional federations (Unions Régionales) of sickness and maternity funds. These deductions may not exceed maxima fixed by order of the Minister of Labour in such a manner that the total administration expenses of the funds and the regional federations of sickness and maternity funds cannot exceed, on a yearly average, 5 per cent, of the total resources provided for the operation of the social insurance scheme. For the years 1937 and 1938 the administrative expenses of the social insurance funds were subject to the following rules. Old-Age and Death Funds or Invalidity, Old-Age and Death Funds for Commerce and Industry The maximum for the administrative expenses of these funds was fixed at the aggregate of the following four amounts: (Í) an amount calculated on the basis of the contributions actually credited to the fund during the year in respect of old-age and . death insurance at the rate of: 6 per cent, of the contributions credited below 16 millions; 4.5 per cent, of the contributions credited between 16 and 32 millions; 2 per cent, of the contributions credited over 32 millions; (2) an amount equal to 8 francs per pensioner; (3) an amount equal to 6 per cent, of the contributions actually credited to the fund during the year in respect of invalidity insurance; (4) an amount equal to 5 francs per insured person or per pensioner who during the year requested the transfer of his contribution from the repayable capital system to the alienated capital system. Regional Federations for Commerce and Industry The maximum for the administrative expenses of the Regional Federations was fixed at the aggregate of the following two amounts : (1) an amount equal to 6 per cent, of the contributions actually credited to the Federation during the year; (2) an amount equal to 8 francs per pensioner. 214 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Compulsory Insurance Sections of Independent Agricultural Funds and Special Agricultural Insurance Section of the National Old-Age Pension Fund The maximum for the administrative expenses of these sections was fixed at the aggregate of the following four amounts: (1) an amount equal to 6.25 per cent, of the contributions and increase in contributions actually credited to the fund during the year in respect of old-age and death insurance; (2) an amount equal to 8 francs per pensioner; (3) an amount equal to 6.25 per cent, of the additional contributions actually credited to the fund during the year in respect of invalidity insurance; (4) an amount equal to 5 francs per insured person or per pensioner who during the year requested the transfer of his contribution from the repayable capital system to the alienated capital system. National Reinsurance Federations in the Agricultural Scheme The maximum for the administrative expenses of these federations was fixed at the aggregate of the following two amounts : 1. 2. an amount equal to 6 per cent, of the fraction of the contributions and State grants received during the year either in respect of reinsurance or in respect of invalidity insurance; an amount equal to 8 francs per pensioner. When the administrative expenses of any of the bodies mentioned above exceed the maximum in the course of any given year the difference is included in the administrative budget and must be worked off in subsequent budgets. ESTIMATES MADE IN THE COURSE OF PREPARATORY INVESTIGATIONS The 1923 estimates [38] relate on the one hand to the allowances and payments assigned to the insurance funds and on the other hand to the administration expenses of the offices. The first give a total of 88 million francs for the first year and 92 millions in the ultimate position, i.e. an average of about 11 francs per insured person. The second produce a constant total of 65 million francs. The Report of the Senatorial Commission on Hygiene [3, p. 195] dated 1925 arrives at an annual expenditure of 225 million francs which could be covered by a levy of 0.5 per cent, on wages. This figure is reduced to 191.7 millions in the Recommendation of the Senatorial Finance Commission [5, p. 129], of 1927. The Recommendation of the same Commission [9, p . 44], dated 1930, rounds up this figure to 200 millions! EXPERIENCE Until 1 January 1936 insurance funds received their administration allowances from a central organisation (the General Guarantee Fund), whose functioning will be examined below.- 215 FRANCE The total amount of the administration allowances assigned to each risk is shown by the following table (in thousands of francs) : Year 1930-1931 Medical care of invalids Old-age insurance 14 8,151 6,533 12,264 15,543 . . . 1935 Invalidity insurance 1,836 5,031 45,513 Liquidation of workers' and peasants' pensions scheme 253 6,532 4,436 4,754 l i Separate ligures for the different items not available. To the administration expenses mentioned above there must be added the cost of administration of the General Guarantee Fund, the administrative services and, finally, the repayment of postage in respect of franked correspondence. Under these three headings are entered the following amounts of expenditure, in thousands of francs : Year 1929 1930 1931 1932 1933 1934 1935 1936 1937 General Guarantee Fund 393 1,538 2,910 3,312 3,307 3,689 4,224 3,988 4,105 Administrative Repayment services to the of social Post Office insurance Administration 81,481 20,000 [ 148,662 47,850 75,779 71,841 78,129 74,968 89,185 24,000 24,000 20,000 24,100 24,100 CHAPTER III FINANCIAL SYSTEM The 1928 Act, like the preparatory investigations which preceded it, established a single financial system for the whole insurance scheme. In the 1930 Act, on the contrary, there appears a distinction between the insurance of workers in commerce and industry and that of agricultural workers. This distinction has been maintained, and it is impossible to confuse the two financial systems, which were instituted for the commerce and industry scheme by the Decree of 28 October 1935, and for the agricultural scheme by the Decree of 30 October 1935 respectively. With regard to the insurance against invalidity—which is analysed in detail in § 3—it must be noted that the financial mechanism provided for meeting expenditure has not yet been put into operation: only provisional measures have been taken, which have allowed the postponement of a permanent solution to the problem. § 1. — Essential Features of the Financial System With a view to facilitating the reading of this chapter and at the same time summarising the financial organisation on the one hand of the scheme for commerce and industry and on the other hand of the agricultural scheme, the various insurance institutions will be enumerated, with the indication of the principal roles which have successively been assigned to them. The institutions created by the 1930 Act, the modifications which they have undergone and the forms in which they exist as a result of the Decrees of October 1935 will be considered for each scheme separately. SCHEME FOR COMMERCE AND INDUSTRY The assessment funds instituted by the 1930 Act to administer the so-called assessment risks (sickness, maternity, death and care of invalids) became, as from 1 January 1936, old-age and death funds or sickness and maternity funds. The accumulation funds, on which, in accordance with the 1930 Act, depend the insurances against old age and invalidity, have been transformed by the Decree of 28 October 1935, into invalidity, old-age and death funds and they have been charged with the administration of orphans' pensions. The reinsurance federations of the 1930 Act, having for their object on the one hand the reinsurance of the risks of sickness, maternity and FRANCE 217 death and on the other hand the equalisation of the costs of the medical care of invalids, have been replaced, pursuant to the Decree of 28 October 1935, by regional federations of sickness and maternity funds. These have as their essential functions: (1) the equalisation of the risks of sickness and maternity, and the guarantee of the liability they involve; (2) participation in the supervision of sick persons and a share in the work of social hygiene and prevention; (3) the provision of medical treatment for invalids and the payment of invalidity pensions during the first five years from the date of entry on pension. The 1930 Act created within the central institution (General Guarantee Fund) two funds between which were shared the financial operations in respect of insured persons in commerce and industry: the Augmentation and Joint Business Fund and the Guarantee and Equalisation Fund. The Decree of 28 October 1935 defines the operation of the General Guarantee Fund as that of an Augmentation Fund and of a Guarantee Fund, which carry on respectively the work of the two pre-existing Funds. The invalidity risk, which up to 1 April 1934 had been provisionally made chargeable to the Augmentation and Joint Business Fund, was as from that date transferred to the Guarantee and Equalisation Fund. As from 1 January 1936 the cost of the invalidity risk falls partly on the regional federations, as regards the medical care of invalids and the payment of invalidity pensions during five years from the date of entering on pension, and partly on the invalidity, old-age and death funds, as regards the payment of invalidity pensions after 5 years until age 60. AGRICULTURAL SCHEME Mutual benefit societies or branches of such societies composed exclusively of insured persons in agricultural occupations, which undertook, under the 1930 Act, insurance against sickness, maternity and death, have been preserved by the Decree of 30 October 1935, but their operations have been limited to sickness and maternity. The independent old-age insurance funds of the 1930 Act continue to operate, but they extend their functions to cover invalidity and death: the National OlcUAge Pension Fund continues to take the place of the independent funds as regards insured persons who are not affiliated thereto. The agricultural reinsurance federations, which under the 1930 Act reinsured the risks of sickness and maternity, have been replaced, under the Decree of 30 October 1935, by the National Reinsurance Federations which have as their objects: (1) reinsurance of the risks of sickness and maternity; (2) participation in the supervision of sick persons and a share in the work of social hygiene and prevention ; (3) the provision of medical treatment for invalids and the payment of invalidity pensions during the first five years after entry on pension. 218 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The special agricultural fund and the agricultural relief fund which, under the 1930 Act, were charged respectively with the payment of complementary old-age pensions and with the guarantee of the solvency of the funds covering the risks of sickness and maternity, were abolished by the Decree of 30 October 1935. The two funds of the General Guarantee Fund mentioned above play a part in the administration of the agricultural scheme as well as in that for commerce and industry. With particular reference to the technical structure on which the financial system rests, a synthetic, outline will now be given of the principal mechanisms which play a part in the operation of both the insurance scheme for commerce and industry and the agricultural scheme. The description is confined to the features which are absolutely indispensable : (1) An " assessment ", which provides for the annual expenditure relating to certain risks by ¡means of a levy on the contributions of the same year. These risks, which at first included sickness, maternity, death, and medical care of. invalids have been limited as from 1 January 1936 to sickness and maternity. (2) An " accumulation " of sums entered in the individual account of each insured person, with the object of constituting a life annuity for him. (3) An " assessment to meet the capital value of pensions ", according to which the present values of the invalidity pensions which become current during the year aré debited each year. (4) A system of central funds in which a distinction is made (as indicated above) between: (a) " federations ", sometimes national, sometimes regional, (b) a central institution: the General Guarantee Fund. § 2. — Apportionment of the Total Contribution In this section will be examined the apportionment in accordance with which the total contribution is divided between the various risks and also between the various institutions. A certain number of the figures which will be reproduced have already been mentioned in the preceding chapter. It has seemed expedient, nevertheless, having regard to their importance, to bring them together in a special paragraph before entering into a detailed study of the financial system. ACCORDING TO THE PREPARATORY INVESTIGATIONS The coefficients of apportionment (including their sum, which defines the total contribution) have been the subject of a very important part of the preparatory investigations. In the table below are reproduced the principal apportionment scales which have been successively taken into consideration for the risks of invalidity, old age and death., They include most of the figures which have resulted from the estimates of expenditure calculated separately for each risk. 219 FRANCE TABLE X I I . — APPORTIONMENT OF TOTAL CONTRIBUTION AMONG I N V A L I D I T Y , OLD-AGE AND DEATH R I S K S : P R E P A R A T O R Y I N V E S T I G A T I O N S (as a percentage of basic wage) Finance Senatorial Commission SenaFinance of Chamber torial Commission of Deputies Health 1927 Recom1928 RecomCommendation [5] mendation [7] mission 1925 [3] Report Before After Before After age 30 age 30 age 30 age 30 ^ ^ y { Medicare f Accumulation^ for lifeOld-Age i annuity [ Guaranteed m i n i m a . . f L u m p sum p r o p o r t i o n a t e t o D e a t h •! basic wage 1 Guaranteed minima . . . Half contribution for old-age insurance of sick persons Family maintenance Maintenance of rights of unemployed Administrative expenses 2.00 0.10 2.23 0.20 1.81 0.16 2.00 0.10 2.00 0.10 3.50 2.00 0.66 4.00 2.00 1.25 4.00 0.21 0.17 0.19 0.05 0.19 0.05 0.05 0.05 0.10 0.05 0.04 0.05 0.10 0.05 0.05 0.05 0.10 0.05 0.05 0.05 0.10 0.05 0.30 0.10 0.10 0.50 SINCE THE COMING INTO FORCE OF THE 1930 ACT The apportionment coefficients prescribed by the 1930 Act are given first and then the more complete tables which have resulted from the Decrees provided for in the Act. Insurance for Commerce and Industry Under the provisions of the 1930 Act, the total contribution is fixed at 8 per cent, of the basic wage and it is divided into two equal parts allocated, subject to certain deductions, one to provide for the risk of old age, the other to guarantee the risks of sickness, maternity and death and the medical care of invalids. Out of the amount allocated to the provision for old age, there is assigned to the constitution of an old-age pension in the accounts of individuals a sum fixed each year by decree, which may not be less than 3.6 per cent, of the basic wage for insured persons aged 30 years or more and 2 per cent, of the basic wage for insured persons aged less than 30 years. The difference between the total part allocated to the provision for old age and the sum fixed by decree is paid to the General Guarantee Fund. Out of the total of the contributions allocated to the primary funds in respect of the insurance against sickness, maternity and death and medical care of invalids, there is retained, under the heading of guarantee and equalisation, 5 per cent, for the benefit of " Reinsurance Federations " and 5 per cent. for the benefit of the General Guarantee Fund (Guarantee and Equalisation Fund). A payment of 2 per mille of all contributions received by the insurance funds is deducted for the benefit of the Guarantee and 220 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Equalisation Fund (General Guarantee Fund), but the rate of this deduction may be decreased by decree in the event of the assets of the Guarantee and Equalisation Fund reaching 100 million francs. The so-called " accumulation contribution " has always been apportioned as follows (as a percentage of the basic wage): - Before age 30 After age 30 2.00 3.60 1.60 0.40 Accumulation Fund f Augmentation and Joint General J Business Fund . . . Guarantee F u n d 1 Guarantee and Equalisa- . 0.40 As from 1 August 1934, the fraction (0.4 per cent, of the basic wage) deducted for the benefit of the Guarantee and Equalisation Fund from the contributions of insured persons aged less than 30 years has been assigned by priority to the expenses of the insurance against invalidity. As regards the insurance against death, the medical care of invalids and the General Guarantee Fund, the following apportionment scales have been successively put into force, by the decrees provided for in the Act: Decree of Decree of 5.7.1930 21.7.1931 (years (year 1932) 1930-1931) Decrees of 12.4.1931 Decree of and of 3.5.1935 3.1.1934 (year (years 1935) 1933-1934) (Pe rcentage of the basic w age) Care of invalids : Assessment Fund . . . . Reinsurance Federation . . - ~ 0.120 0.008 — Insurance against death: Assessment Fund . . . . Reinsurance Federation. . 0.1684 0.0092 0.1684 0.0092 0.120 0.008 0.100 0.008 0.2948 0.280 0.440 ! 0.0800 0.080 0.080 General Guarantee F u n d : Reinsurance and guaranteed Maintenance of rights of * unemployed insured persons lo.2988J i Including cost of administration and expenditure relating to family maintenance. The Decree of 28 October 1935 confines itself, on the one hand, to fixing at 8 per cent, the ratio of the total contribution to the wage 1 , and, on the other hand, to stipulating the minimum fractions of this contribution which should be assigned to the individual accounts: 45 per cent, for insured persons aged 30 years or more and 25 per cent. 1 This percentage was reduced to 1 per cent, as an exceptional measure for the year 1936. 221 FRANCE for insured persons aged less than 30 years. The remainder of the apportionment is determined by order. The coefficients reproducep below determine, in thousandths of the total contribution, the apportionments applicable to contributions in the years 1936, 1937 and 1938 respectively. . Year 1937 Year 1936 Insured persons aged less than 30 years Accumulation Fund: Individual account. . Death and orphans' pensions Invalidity General Guarantee Fund : Complementary oldage pensions. . . . Insured' Insured persons persons aged aged 30 years less than or more 30 years Year 1938 Insured persons aged 30 years or more Insured persons aged less than 30 years Insured persons aged 30 years or more 250 450 250 450 250 450 15 15 12 13 12 13 20 30 20 30 250 50 250 50 250 50 Regional Federations : Invalidity and care of invalids Guarantee and equalisation -. 5 5 41 41 69 69 40 40 34 34 31 31 Assessment Fund. . . 440 440 400 400 350 350 1,000 1,000 1,000 1,000 1,000 1,000 Agricultural Insurance The apportionment of the contribution applicable to an insured person employed in agriculture is determined partially by the rules which define this contribution separately for old-age insurance and for insurance against sickness, maternity and death. A certain number of deductions are provided for, but they affect, not the contributions, but only the grants in aid assigned to the agricultural insurance scheme as an increase of contributions. It will be seen from the figures given above that under the Decree of 30 October 1935 the fraction of the total contribution apportioned -to the individual old-age insurance account was fixed at: Via for children under 16 years of age; women ; men. 6 /ie for 10 /2o for The fraction of the additional contribution (paid by the State) apportioned to the risks of invalidity and death was distributed as follows: during 1936: 2.60 francs a month to the National Reinsurance Federation and 0.40 franc a month to the Independent Invalidity, 222 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Old-Age and Death Fund or to the National Old-Age Pensions Fund (for the risk of death); during 1937 and 1938: 2 francs a month to the National Reinsurance Federation and 1 franc a month to the other fund (0.20 for invalidity and 0.80 for death). It follows from the figures given above that from 1 January 1939 onwards, under the Decree of 15 June 1938, the fraction of the total contribution apportioned to the individual old-age insurance account will be: 2 /12 for insured persons of the first class ; Vie >. .. » .. second „ /ao ,. .. » .. t h i r d .. "/so ,. .. .. », fourth „ . The remainder of the contribution is apportioned jointly to the risks of sickness, maternity and invalidity. The distribution of this second fraction is determined solely by Interdepartmental Order. The fractions of the additional contribution paid by the State which are allocated to the risks of sickness, maternity and invalidity are also determined by coefficients laid down by Interdepartmental Order. 10 § 3 . — Financial Equilibrium of Invalidity Insurance INTRODUCTION Since the coming into force of the scheme insurance against invalidity has undergone numerous modifications, which have largely disturbed the financial organisation which had been provided for it. The inconsiderable expenditure during the first years of operation was covered by exceptional receipts, but the normal method of covering the risk of invalidity has not been determined precisely. The total contribution had been fixed by the 1928 Act at 10 per cent. of the amount of wages, on the assumption, in conformity with the results obtained in the preparatory investigations, that a fraction of 2 per cent., of the amount of wages would be necessary to cover the cost of invalidity pensions. The legislative provisions which were subsequently adopted are no longer common to insured persons in commerce and industry and to insured persons in agriculture. As regards insured persons in commerce and industry,' the 1930 Act, in principle, does not deviate from the conception contained in the 1928 Act; nevertheless, the payments assigned to the insurance against invalidity have been deferred: until 1 April 1934, as regards a first fraction of 1 per cent, of the basic wage; until 1 April 1940, as regards a further fraction of 1 per cent, of the basic wage. Consequently, the expenditure on invalidity insurance has been provisionally charged to the Augmentation and Joint Business Fund. The FRANCE 223 Finance Act of 28 February 1934 deferred the payment of the first fraction of 1 per cent, of the basic wage which was due to commence on 1 April 1934, and at the same time transferred the charge in respect of the invalidity risk from the Augmentation and Joint Business Fund to the Guarantee and Equalisation Fund. As from 1 January 1936, in pursuance of the Decree of 28 October 1935, the cost of invalidity insurance is taken over: (1) by the regional federations as regards the care of invalids and the payment of pensions during the first five years after entering on pension; (2) by the invalidity, old-age and death funds as regards the cost of pensions from the end of the fifth year of pension until age 60. The 1930 Act entirely excluded from invalidity insurance all insured persons engaged in agricultural occupations. The Decree of 30 June 1934 extended invalidity insurance to agriculture and placed the resulting cost on the Agricultural Relief Fund. The Decree of 30 October 1935 divided the expenditure on invalidity between the National Reinsurance Federations (as regards the care of invalids and the payment of pensions during the first five years) and the independent invalidity, old-age and death insurance funds (as regards the cost of pensions after five years). PREPARATORY INVESTIGATIONS The choice of the most suitable financial mechanism to use for invalidity insurance has been considered repeatedly during the course of the preparatory investigations and on this subject various proposals were put forward. First of all a distinction was made between pre-invalidity, which was considered to be for five years a prolongation of sickness (after the end of the sixth month), and permanent invalidity which commenced at the end of the period of sixty-six months covered by sickness and then pre-invalidity. According to this conception, the risk of pre-invalidity was assimilated to the risk of sickness and should, therefore, like the latter, be amenable to an assessment scheme. Permanent invalidity, on the contrary, was regarded as a risk involving long-dated obligations, which should on this account be treated as of the same character as old-age insurance. From the commencement of pre-invalidity an individual invalidity insurance account should be substituted for the individual old-age insurance account and it should receive the actuarial reserve credited to the latter. In cases of partial incapacity for work the two individual accounts existed side by side. If the insured person regained his health the invalidity account disappeared in favour of the old-age account which was re-established. To the annuities produced by the accumulation of the contributions credited to the individual accounts had to be added, in certain cases and under well-defined conditions, complementary pensions the total amount of which would be obtained each year from a guarantee fund. Finally, provision was made for State contributions for the benefit of temporary as well as of permanent invalids. The subsequent investigations brought forward a different technical conception: pre-invalidity was no longer separated from permanent invalidity and together they had to cover their expenditure—separate from that of the risk of old age—by means of a levy on contributions. It was assumed that the annual crop of invalids would remain approximately constant and consequently recourse was had to the system, 224 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION called " assessment to meet capital value of pensions ", which was previously adopted in France for life annuities in respect of persons suffering from industrial accidents. An annual levy on the total contribution income was used for the purpose of setting up capital sums representing the actuarial reserve for all invalidity pensions which emerged during the year. Several calculations were made in order to determine this levy; they all resulted in approximately [3, 5, 7] 2 per cent, of wages. As regards medical care of invalids, the preparatory investigations all produced an estimate [3, 5, 7] of the cost corresponding to 0.1 per cent. of the total amount of wages. INSURANCE FOR COMMERCE AND INDUSTRY 1930 Act According to the second conception considered in the preparatory investigations, invalidity pensions constitute a risk distinct from that of old age. For the purpose of establishing the financial solvency of the insurance of this risk the Act provides two increases in contributions dating, the first from 1 April 1934, and the second from 1 April 1940, both, being fixed at one-eighth of the initial contribution, or one per cent, of the basic wage. As from 1 April 1934, the actuarial reserve for the invalidity pensions granted each year is to be provided in a special account, by means of a levy on contributions, the percentage to be fixed by decree each year. As a provisional measure, until 1 April 1934 the expenditure due to the payment of invalidity pensions is borne by the General Guarantee Fund (Augmentation and Joint Business Fund). The same applies to the cost of the medical care of invalids, subject to a counterbalancing payment made by the Reinsurance Federations. The actuarial reserves are calculated by means of a table constructed for an annuity payable until cessation by reason of death or return to health, receivable quarterly in arrear with proportion to date of death. This table is based on the table of cessation of invalidity pensions mentioned in Chapter I, with interest at a rate fixed according to the following rules: (1) if the rate of interest applicable to the calculation of reserves for old-age insurance * is greater than 5 per cent., it is reduced by 1.40 per cent.; (2) if the rate of interest applicable to the calculation of reserves for old-age insurance is equal to or less than 5 per cent., recourse is had to the following table: Rate of interest applicable to the calculation of actuarial reserves for old-age insurance (per cent.) 5.00 4.80 4.60 4.40 4.20 1 See below, p p . 228-229. Rate of interest applicable to the calculation of present values of invalidity pensions (per cent.) 3.60 3.40 3.40 3.20 3.00 FRANCE 225 (3) if the rate of interest applicable to the calculation of reserves for old-age insurance is equal to or less than 4 per cent, it is reduced by 1 per cent. From the total of the present values of pensions thus calculated is deducted the actuarial reserve corresponding to the old-age pensions which appear in the individual accounts of the invalids. In the case of a person in receipt of an invalidity pension, the life annuity under the old-age insurance system is payable either normally as from age 60, or for a reduced amount as from the definitive grant of the invalidity pension in case of permanent and total incapacity for work. The increase by one-eighth of the contributions, specified by the 1930 Act as from 1 April 1934, has been deferred, and at the same time the invalidity risk has been provisionally transferred, within the General Guarantee Fund, from the Augmentation and Joint Business Fund to the Guarantee and Equalisation Fund. As from 1 April 1934, and until January 1937, the latter fund repays to the old-age insurance funds the total amount of the invalidity pensions payable by them. To these repayments was assigned as a first charge the levy made, for the benefit of the Guarantee and Equalisation Fund, on the old-age insurance contributions of persons who have not attained age 30 (0.4 per cent, of the basic wage). The cost of the medical care of invalids was also charged to the Guarantee and Equalisation Fund. Decree of 28 October 1935 Since 1 January 1936 a distinction is made, as in the first preparatory investigations, between the first five years of invalidity and the subsequent years. During the first five years of invalidity the cost of pensions, and also the cost of the medical care of invalids, falls on the regional federations of sickness and maternity funds. At the expiration of the fifth year of invalidity, the invalidity, old-age and death insurance fund sets up, by means of its annual resources, the actuarial reserve corresponding to each invalidity pension. The invalidity pension ceases at age 60. As from this age it is replaced, in accordance with the mechanism called " supplementary insurance ", by the old-age pension to which the insured person is entitled by reason, on the one hand, of the payments made by his successive employers and, on the other hand, of the contributions paid each year to the old-age insurance scheme in their stead by the invalidity fund or by the regional federation of sickness and maternity funds. The contributions paid to the old-age insurance scheme by the invalidity fund or by the regional federation of sickness and maternity funds are fixed according to the average wage1 which served as basis for the calculation of the invalidity pension ; they are apportioned between the individual old-age insurance acpount of the beneficiary and the Augmentation Fund in accordance with the rules applicable to ordinary contributions. If the insured person is still, at the age of 60, in receipt of an invalidity pension, the General Guarantee Fund makes up to the amount of that pension the annuity entered (calculated under the alienated capital system) in his individual old-age insurance account. Each year an Order fixes the fraction of contribution which should be assigned to cover invalidity pensions in accordance with tables constructed by taking into account the pro1 According to a scale prescribed by Orders of 20 June 1936 and 27 April 1937. 15 x 226 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION bability of becoming an invalid at the various ages and the mortality of invalid persons. The rate of interest on which is based the calculation of the capital value of invalidity pensions is equal to 80 per cent, of the rate of interest applicable to the calculation of the actuarial reserves for old-age insurance for the same financial year *. For the purpose of covering the cost of the invalidity risk the following resources have been allocated: (a) to be assigned to the Regional Federations as exceptional items : a payment of 400 million francs from the General Guarantee Fund; an exceptional levy on the surplus receipts on 31 December 1935 in the assessment funds 2 ; the allocation of a fraction, equal to not more than '/ 12 , of the assets of the Reinsurance Federations at 31 December 1935. (b) to be assigned to the Regional Federations as normal items: an annual levy fixed at 20 per cent, of the surplus receipts of the sickness-maternity funds; a contingent levy on the total contributions (fixed for the year 1936 at 5 41 r /IOOOJ for the year 1937 at /iooo and f ° the year 1938 69 at /iooo of the total contributions). (c) to be assigned to the invalidity, old-age and death funds : one-half of the profits realised each year by these funds under the heading of old age and death, when the previous balancesheet shows a surplus. It is provided, moreover, that a fraction of contribution shall be assigned, by Order each year, to cover the cost of invalidity pensions: it was fixed for 1937 at 13/iooo> and for 1938 at 30/iooo of the total contributions. AGRICULTURAL INSURANCE Decree of 30 June 1934 The invalidity insurance system has been extended, with retrospective effect, to wage earners in agriculture and forestry. The invalidity pensions in the agricultural scheme, as well as the cost of the medical care of invalids, are charged to the Agricultural Relief Fund. This Fund receives a levy of 1 franc a month on the addition which the State makes, under the 1930 Act, to each contribution of agricultural insured persons in respect of the risks of sickness, maternity and death. This Fund also receives, in capital and interest, the balance of the proceeds of the sale of stamps for workers' and peasants' pensions to the maximum amount of 10 million francs. Decree of 30 October 1935 As for commerce and industry invalidity insurance is treated as supplementary to old-age insurance: the invalidity pension is replaced at the age of 60 by an old-age pension. During the first five 1 2 See below, p. 229. The amount of which was fixed at 300 millions by the Decree of 7 October .1936. 227 FRANCE years of invalidity, the cost of pensions and also the cost of the medical care of beneficiaries fall on the National Reinsurance Federations. The independent invalidity, old-age and death insurance funds set up, at the end of the fifth year from the date of entering on invalidity pension, the actuarial reserve for this pension. The resources specified for covering the cost of invalidity insurance, for the National Reinsurance Federations as well as for the independent invalidity, old-age and death insurance funds, are included in the levies, fixed by Decree, on the additional contributions payable by the State 1 . Decree of 15 June 1938 This Decree provides that from 1 January 1939 onwards that fraction of the contribution which is not allocated to the individual old-age insurance account shall be distributed over the risks of sickness, maternity and invalidity. For the first time a fraction of the contribution may be used for the invalidity risk. ESTIMATE OF THE COST OF INVALIDITY PENSIONS The Committee of Experts, appointed in 1935, valued, on the bases indicated above 2, the annual emerging cost of the capital reserves required to cover the temporary invalidity pensions and of the payments resulting from the operation of the supplementary insurance (payment of an old-age contribution on behalf of invalids). It produced the following results [30]: 0.08 per cent, of the wages of insured contributors for the 1st year 0.27 1.02 1.22 1.28 1.33 „Î) „ti „it •>•} „ „1 „Jï „ÏÏ » 11 ») Í> 11 Í )» 11 1 „ 1) )J )i )1 1 Î1 13 1 11 )) 11 51 1 11 lì i „ „ 5th „ „ „ 10th „ » » 15th „ „ „ 20th „ from the beginning of the 25th year. At the same time it estimated that the cost of the medical care of invalids would normally be equivalent to 0.22 per cent, of the wages of insured contributors. § 4. — Financial Equilibrium of Old-Age Insurance CONSTITUTION OF OLD-AGE PENSIONS Preparatory Investigations In the first Bill [1], presented by the Government in 1921, the fractional contributions which were to be capitalised in individual accounts differed as between different wage classes [2]. Subsequently this idea was completely abandoned. The Senatorial Commission on Hygiene in its 1925 Report [3] took into consideration only one percentage, which it fixed at 3.5 per cent, of wages; later investigations [5, 7] introduced 1 2 See above, pp. 194-195. Pages 200-201. 228 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION two percentages, applicable according to the age of the insured person at the moment of payment: 2 per cent, if this age is less than 30 years, and 4 „ „ ,, „ „ ,, more „ Act of 1930 An old-age annuity is constituted in favour of each insured person, in an account opened in his name, by the accumulation of a fractional contribution fixed by Decree but which, according to the Act, may not be less than 2 per cent, of the basic wage when the insured person has not attained age 30 and not less than 3.6 per cent, of the basic wage in the contrary case. In fact the percentages remained constantly fixed at their respective lower limit: 2 per cent, and 3.60 per cent. The accumulation operations are carried out by means of old-age insurance scales, in accordance with the following provisions: The old-age annuity corresponding to the payments received for the account of an insured person between 1 January and 31 December of any given year is calculated according to the scale applied in the course of the said year by the old-age insurance organisation responsible for constituting the annuity and in accordance with the age attained by the insured person during the same year. Each scale is calculated on the basis: (1) of a rate of interest fixed according to the rules set out later 1; (2) of annual rates of mortality provisionally taken from the table P.M.F. 1921 2; (3) of the repayment, without interest, on the request of the' insured person, of the payments made to his individual old-age insurance account; (4) of payments being made quarterly in arrear; (5) of the proportionate payment to the dependants of an insured person in case of death, the death being deemed to occur in the middle of the quarter, and the scale consequently allowing for the payment of a capital sum equal, on the average, to one-eighth of the annuity at the date of death of the annuitant. In pursuance of these provisions, the deferred life annuities produced by a single premium of 1 franc, the annuity being payable quarterly in arrear with proportion to date of death, are obtained: under the alienated capital system by applying the formula 3 1 under the repayable capital system by applying the formula r = • 3- j , where x represents the age of the insured person at the moment of payment of the single premium, x -f- n represents the age of the insured 1 2 Page 229. See p. 173. FRANCE 229 person at the time of payment of the pension and D, N, and M the usual commutation symbols 1. The scales have been constructed by making the calculations to the fourth decimal place and rounding off to the nearest tenth of a thousandth. Special provisions and special scales have been fixed for anticipating —as from age 55—the date of entering on pension or for postponing it or again for providing for the reversion of the old-age pension under the alienated capital system in favour of the surviving partner. The following are the rules governing the determination of the rates of interest to be used in the old-age insurance scales: A Decree issued in the course of the third quarter of each year fixes for the following year the maximum rate of interest to be used as a basis for the scales of all the funds which effect old-age insurance. Subject to this maximum the rate of interest for the scale of each fund is fixed in accordance with the average rate earned, as at 31 December of the year of the last account, by the total of the funds invested at that date". The rate adopted by a fund must be less than the maximum rate fixed by Decree to the following extent: the 'difference must be at least equal to 40 centimes if the average rate of interest of the investments is not more than 5 per cent. If, however, this average rate is more than 5 per cent, the minimum difference is increased by half the difference between 5 per cent, and the average rate, with a maximum difference of 2 per cent. These provisions apply to insured persons in agriculture as well as those in commerce and industry. In the agricultural scheme, as we have indicated above, the fractional contribution allocated to the individual old-age insurance account is fixed for all insured persons at 2 per cent, of the basic wage: in the case of insured persons aged more than 30 years the complement, corresponding to 1.60 per cent, of the basic wage, is paid by the State. Decree of 28 October 1935 (insurance for commerce and industry) The method of constituting old-age life annuities has remained approximately the same as that defined in the initial legislation. It has already been stated that the minimum which is to be allocated to the individual account is no longer fixed as a fraction of the basic wage but as a fraction of the contribution (45 per cent, or 25 per cent. according as the age of the insured person at the moment of payment is at least equal to or is less than 30 years). The rate of interest of the scales to be used in calculating the annuities is still defined by the rules summarised above; nevertheless the mortality table P.M.F. 1921 has been replaced by the table P.M.F. 1931. For the sake of example table XIII below reproduces from these scales the columns which correspond to the normal age of entering on pension, with interest at 4 per cent, and 5 per cent, respectively. In addition, the Decree which indicated in the course of the last quarter of each year the maximum rate of interest for the following year is replaced by an Order which prescribes the upper and lower limits to the rate of interest to be used for the old-age insurance scales. (For the years 1936, 1937 and 1938 the maximum has always been fixed at 4.80 per cent, and the minimum at 4 per cent.) 4=0 230 A C T U A R I A L T E C H N I Q U E AND FINANCIAL ORGANISATION TABLE X I I I . — L I F E A N N U I T I E S D E F E R R E D TO AGE 6 0 PR O D U C ED BY A SINGLE PAYMENT OF 1 FRANC Age at moment of payment (years) 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 9Q 30 31 32 33 34 35 36 37 38 39 40 41 , 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Alienated capital system 4 % 0.8912 0.8554 0.8206 0.7868 0.7541 0.7224 0.6917 0.6620 0.6333 0.6058 0.5795 0.5543 0.5303 0.5073 0.4853 0.4642 0.4441 0.4248 0.4063 0.3885 0.3715 0.3552 0.3395 0.3245 0.3101 0.2962 0.2829 0.2701 0.2578 0.2460 0.2346 0.2237 0.2132 0.2030 0.1933 0.1839 0.1749 0.1662 0.1579 0.1498 0.1421 0.1346 0.1274 0.1204 0.1137 0.1072 0.1010 0.0950 5 % 1.5065 1.4321 1.3609 1.2924 1.2268 1.1641 1.1040 1.0465 0.9917 0.9395 0.8902 0.8434 0.7992 0.7572 0.7175 0.6798 0.6441 0.6102 0.5781 0.5476 0.5186 0.4911 0.4650 0.4401 0.4166 0.3942 0.3729 0.3526 0.3334 0.3151 0.2976 0.2811 0.2653 0.2503 0.2360 0.2224 0.2095 0.1972 0.1855 0.1744 0.1638 0.1537 0.1441 0.1349 0.1262 0.1178 0.1099 0.1024 Repayable capital system 4 % 5 % 0.7300 0.6957 0.6629 0.6314 0.6011 0.5722 0.5445 0.5179 0.4925 0.4682 0.4450 0.4228 0.4015 0.3812 0.3617 0.3431 1.3075 1.2358 1.1677 1.1030 1.0415 0.9832 0.9279 0.8755 0.8258 0.7787 0.7340 0.6917 0.6517 0.6137 0.5778 0.5437 A OOCO A cr A A v.ox 0.3082 0.2919 0.2763 0.2614 0.2472 0.2336 0.2206 0.2081 0.1962 0.1849 0.1740 0.1637 0.1538 0.1444 0.1354 0.1268 0.1187 0.1109 0.1035 0.0965 0.0898 0.0834 0.0774 0.0717 0.0662 0.0611 0.0562 0.0517 0.0473 0.0432 0.0394 0.4808 0.4518 0.4244 0.3984 0.3737 0.3504 0.3283 0.3074 0.2877 0.2690 0.2513 0.2345 0.2187 0.2038 0.1897 0.1763 0.1638 0.1519 0.1407 0.1302 0.1203 0.1109 0.1022 0.0939 0.0862 0.0789 0.0721 0.0657 0.0598 0.0542 0.0491 f± r. The rate of interest to be used in calculating the actuarial reserves is obtained b y taking the arithmetic mean of the rates of interest for the 231 FRANCE scales used in calculating the annuities during the five years preceding the date of the account. Furthermore, the following rules have been laid down in regard to the transfer of actuarial reserves. When an insured person who has belonged successively to different funds claims the payment of his old-age pension, the transfer of the actuarial reserves for the old-age annuities to the fund which undertakes thé payment of the pension is effected within one month. The total amount of the said reserves is determined as at the effective date of transfer fixed by Order of the Minister of Labour, in accordance with the scale of the transferor fund in force at that date and with the age attained or to be attained by the insured person in the course of the year during which the transfer takes place. The fund which pays the old-age pension guarantees, as regards the payment resulting from the transfer of the said actuarial reserve, the amount of the annuity in accordance with its own scale. Finally, it must be noted that, if a fund undertaking old-age and death insurance experiences, in two successive years, a surplus in respect of these risks, half the surplus for the second year is applied to .covering the invalidity risk 1. Where a pension is granted at an earlier age, the pension as payable at age 60 is reduced by the following coefficients: Coefficient of reduction Age 55 years. 56 57 58 59 » » » » . . . . 0.6433 0.6993 0.7618 0.8324 0.9105 Decree of 30 October 1935 and Decree of 15 June 1938 (agricultural insurance) The old-age pension in the agricultural scheme is still constituted by the same method and on the same basis as in the scheme for commerce and industry. It is formed by the accumulation in the individual account of each insured person of that fraction of the contribution allocated to old-age insurance. It was pointed out above 2 (1) that the fraction of the contribution allocated to old-age insurance was fixed from 1 January 1936 to 1 January 1939 at the following figures: Children under 16 years w women M men 1 2 See p . 226. P a g e s 221-222. Viaths of the total contribution, or 24 francs a year; J 6/16ths of the total contribution or francs na ,year; i n72 o f«««,™ rrtrt „. J "/îoths of the total contribution, or \ 120 francs a year; 232 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION (2) that the fraction of the contribution to be allocated to old-age insurance as from 1 January 1939 was fixed by Decree of 15 June 1938 as follows: Insured persons of the first class . \ V h s of the total contribur I tion, or 24 francs a year; Insured persons of the second class. I V 1 « of the total contribur I tion, or 72 francs a year; ths f tribu r Insured persons of the third class . iI 1 0 /« ™ francs V**1 c a° n year; tion, °or Ü 120 Insured fourth class of the total contribulnsurea nersons persons of oi the tneiounn class. Ì^ "Aoths ^ Qr l g Q f r a n c g a y e a r GUARANTEE OF THE LEGAL MINIMA Under the 1930 Act the cost of the complementary old-age pensions, which increased up to the guaranteed minima the annuities entered in the individual accounts, was charged in the scheme for commerce and industry to the central institution (General Guarantee Fund) which embodied it in the financial mechanism of one of its Funds (Augmentation and Joint Business Fund *). This Fund received in compensation a levy made on the old-age insurance contribution. In accordance with the rules governing the apportionment of the contributions summarised above, the said levy was defined as follows : (a) for each insured person aged 30 years or more: the whole of that part of the old-age insurance contribution which is not entered in the individual account—i.e. not more that 0.40 per cent, of the basic wage; (b) for each insured person under age 30: a fraction of that part of the old-age insurance contribution which is not entered in the individual account, up to a maximum of 1.60 per cent, of the basic wage. It has already been shown, moreover, that during the years 1930-1935 the percentages of the levies made on the old-age insurance contributions in favour of the Augmentation and Joint Business Fund have always been fixed at the maxima authorised by the Act, that is to say, at 0.40 per cent, and 1.60 per cent, of the basic wage respectively. In the agricultural scheme the mechanism is the same in principle. However, a special fund (Special Agricultural Fund) was created to meet the supplementary cost of old-age pensions and to receive in compensation a State grant equal to 80 per cent, of the old-age insurance contributions (i.e. 1.60 per cent, of the basic wage) applicable to insured persons aged more than 30 years. In pursuance of the Decree of 28 October 1935, the fraction allocated to the individual account is no longer defined as a function of the basic wage but as a function of the total contribution 2. Furthermore, the whole of that part of the old-age insurance contribution which is not entered in the individual account is paid in all cases to the Augmentation Fund 3 of the General Guarantee Fund. In applying the above 1 2 3 See pp. 238-243. See p. 220. See p. 245. 233 FRANCE clauses the following were the percentages of contributions assigned to the,Augmentation Fund for the years 1936, 1937 and 1938 for the purpose of meeting the cost of complementary old-age pensions: 25 hundredths when the age of the insured person is less than 30; 5 hundredths when the age of the insured person is equal to or more than 30. The Decree of 30 October 1935 abolished the Special Agricultural Fund and at the same time the allocation of 80 per cent, of the old-age insurance contributions which was being made to this fund. As a set-off the State is obliged to pay each year to the Augmentation Fund a subsidy equal to 40 per cent, of the total amount of the contributions entered in the preceding year in the old-age insurance individual accounts of agricultural insured persons. The financial system of the complementary old-age pensions operates within the General Guarantee Fund, and the annual totals of the levies which have been assigned thereto appear below in section 6 of this chapter, which is exclusively devoted to the financial organisation of that Fund. The Committee of Experts appointed in 1935 has valued, as regards old-age insurance, the liabilities of the General Guarantee Fund not covered by the fractions of contributions assigned thereto for this insurance. The calculations have been based on the wages corresponding to 3 different hypotheses and with a constant rate of interest equal to 4 per cent. The following are the results obtained [30, p. 2] for the present value of the liabilities as at 1 July 1935: Average wage (francs) 5,800 6,500 7,200 Scheme for commerce and industry (million francs) 11,160 12,239 13,318 Agricultural scheme (million francs) 1,652 1,810 1,968 The same Committee adopted for the liability in respect of workers' and peasants' pensions as at 1 July 1935 a present value of 1,776 million francs. § 5. — Financial Equilibrium of Death Insurance SCHEME FOR COMMERCE AND INDUSTRY Under the 1930 Act the insurance of a capital sum payable at death is entrusted to assessment funds which receive for this purpose a levy on the so-called assessment contributions. Nevertheless the charge which thereby falls on the assessment funds is limited to a proportion of the basic wage (20 per cent.). The complementary amount required to raise this amount to the minimum guaranteed by the Act falls on the General Guarantee Fund. Furthermore, the risk of death, like the other assessment risks, is subject to a compensation and a guarantee which operate in two stages, firstly by the intervention of the Reinsurance Federations and then by a call on the General Guarantee Fund. 234 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION The portions of contribution assigned respectively to the assessment funds, the reinsurance federations and the General Guarantee Fund have been fixed and then modified by various Decrees1. The additions to the lump sum on death granted for family maintenance, like the orphans' pensions and the other additions for family maintenance, are charged to a special fund, within the General Guarantee Fund, which is supported by a levy of 6 per mille on the contributions. On the coming into force of the Decree of 28 October 1935 the guaranteed minimum of a thousand francs disappeared. The lump sum on death is limited to 20 per cent, of the basic wage and its administration, together with that of the orphans' pensions is entrusted to the accumulations funds which receive for this purpose a fractional contribution. This fraction has been fixed for 1936 at 15/1000 of the total contributions, reduced to 12/1000 for 1937 and raised to 20/1000 for 1938. The. additions granted in respect of family maintenance, for the insurance against death, as for the other risks, remain charged to the insurance funds which enter them for purposes of accounting with the benefits t o which they relate. The insurance funds set up a special reserve for the insurance against death: this reserve grows each year by one-fifth of the amount of the expenditure on insurance against death during the preceding financial year, until it reaches the total amount of the expenditure on insurance sgainst death «urmg tue preceuing îinanciai year. AGRICULTURAL SCHEME Under the legislation of 1930, the cost of the lump sums on death falls on the mutual benefit societies, on agricultural branches of mutual benefit societies or on departmental funds. By the Decree of 30 October 1935, it is transferred to the independent old-age insurance funds. The income to meet their cost, as well as that of orphans' pensions, continues to be constituted by a levy fixed by Order on the additional contributions paid by the State for the benefit of insured persons in agriculture. The following amount was deducted from each monthly- additional contribution for this purpose: 0.40 franc during 1936; 0.80 „ „ 1937 and during 1938. § 6. — Financial Equilibrium of Central Institutions This section deals with: (a) the " Federations ", whose rôle and powers have been profoundly modified by the Decrees of October 1935; (b) the central institution proper, that is, the General Guarantee Fund. 1 See pp. 219-220. FRANCE 235 THE " FEDERATIONS " Under the 1930 legislation, the scheme for commerce and industry necessitated institutions of departmental or inter-departmental scope, called Reinsurance Federations, whose function was: (1) to reinsure the assessment risks; (2) to equalise the cost of the medical care of invalids. In the agricultural scheme the Reinsurance Federations were intended to effect a second degree reinsurance for the risks of sickness, maternity and death. The Decree of 28 October 1935 substituted, for the Reinsurance Federations, Regional Federations of Sickness and Maternity Funds. The essential functions of these Regional Federations were: (1) the guarantee and equalisation of the risks covered by the sickness and maternity funds; (2) participation in the control of sick persons and collaboration in the work of social hygiene and prevention; (3) the administration of insurance against invalidity,- as far as concerns the care of invalids and the payment of invalidity pensions during the first five years of drawing the pension. Leaving on one side the guarantee and equalisation of the sickness and maternity risks, the resources will be indicated that are provided for the purpose of meeting the cost of the two other classes of expenditure, which figure in the accounts as " Social Hygiene and Prevention " and " Invalidity " respectively. To the account of " Social Hygiene and Prevention " are credited: (1) an initial grant fixed at one-sixth of the sums received by the Regional Federation out of the assets of the Reinsurance Federations as at 31 December 1935; (2) a levy, fixed by annual Decree 1, on the surplus receipts of the other accounts of the Regional Federation; (3) a contingent share from the sickness and maternity funds. As regards the " Invalidity " account, a distinction must be made between the normal resources and the exceptional resources intended to form an " Initial Grant Fund ". The " Initial Grant F u n d " is constituted by: (1) a payment from the General Guarantee Fund, fixed at 400 million francs ; (2) an exceptional levy on the surplus receipts of the assessment funds. This levy is equal to the smaller of the following two amounts: (a) the general reserve of the assessment funds appearing in the balance-sheet of 31 December 1934; (b) the average of 1 For the financial year 1936 this levy was fixed at one-half of the surpluses in the equalisation and guarantee accounts and one-quarter of the surplus in the " income " account. The balance of the surpluses is paid to the invalidity account. 236 ACTUARIAL T E C H N I Q U E AND F I N A N C I A L ORGANISATION the general reserve and the special reserve of the assessment funds appearing in the balance-sheet of 31 December 1934. Nevertheless, in the case of assessment funds whose profit and loss account for the financial year 1935-36 shows a debit balance, the reserves which are brought into play are taken not from the balance-sheet of 31 December 1934, but from that of 31 March 1936. Moreover, in the case of assessment funds whose profit and loss account for either 1934 or 1935-36 shows a debit balance, the levy is limited to not more than the amount of the general reserve or of the average of the special and general reserves appearing in the balance-sheet of 31 December 1933; (3) the allocation of seven-twelfths of the assets of the Reinsurance Federations as at 31 December 1935 1 . The normal resources include: (1) an annual levy fixed at 20 per cent, of the surplus receipts of the . assessment funds; (2) contingently, in case the resources previously mentioned prove to be insufficient, a levy on the total contribution income. The following amounts have, in fact, been allocated to the Regional Federations under the heading of " invalidity and care of invalids": in 1936, 5/1000 of the total contribution income; in 1937, /JOOO ii >i M in 1938, 69/iooo „ „ ., s> >i In the agricultural scheme the Decree of 30 October 1935 instituted National Reinsurance Federations whose functions correspond with those of the Regional Federations for commerce and industry with, however, important differences in the manner in which they carried them out. The following three duties are imposed on the National Reinsurance Federations (for each of which a special account is kept) : (1) reinsurance of the sickness and maternity risks; (2) participation in the control of sick persons and collaboration in the work of social hygiene and prevention; (3). the provision of medical care of invalids and invalidity pensions during the first five years after the date of entering on pension. The following resources are allocated to social hygiene and prevention: (1) a fraction of the assets of the Agricultural Reinsurance Federations which were replaced by the National Reinsurance Federations; (2) contingently, the balance of the annual surpluses of the reinsurance account after allocation of 35 per cent, to reserve; (3) contingently, subsidies from the sickness and maternity funds or a share in the cost of control services. 1 To these resources must be added a part of the surplus receipts for 1936 appearing in the other accounts of the Regional Federation. (See above.) 237 FRANCE To invalidity there is allocated a permanent receipt defined as a fraction, fixed by Order, of the additional contribution paid by the State. The following amounts were paid to the National Reinsurance Federations to be allocated to the invalidity risk: In 1936 2.60 francs per insured person per month; In 1937 and 1938. 2 ,, G E N E R A L GUARANTEE FUND Preparatory Investigations In the Bill [1, 2] brought forward by the Government in 1921 provision was made for the creation of a General Guarantee F u n d comprising: an equalisation fund designed to counteract the consequences of the inequality of the risks in the various regions; a reinsurance or reserve fund to cover exceptional risks; and a fund intended to contribute to the payment of complementary pensions, receiving for this purpose a p a r t of the employers' contributions relating to pensioned or alien employees, fines and double duties, and the State's contribution t o the guarantee of the minimum invalidity and old-age pensions. The subsequent investigations gave great prominence to a fund called " Augmentation and Joint Business F u n d ", which was intended t o support very varied charges arising out of practically all the risks and developing independently from each other: this fund would form a large central institution, playing an essential part in the financial equilibrium of the system considered as a whole. As from 1926 the preparatory investigations laid great stress on the financial equilibrium of this fund, by considering either the present values (or their expression in perpetual annuities) of its liabilities and its expected income or the probable progress of the fund during a certain number of years, t h a t is to say, by calculating annual estimates of its receipts and expenditure. In chronological order the first1 to appear was a budget of the Augmentation and Joint Business Fund in the form of perpetual annuities w i t h interest at the rate of 5 per cent. It is to be noted t h a t this budget covers b o t h compulsorily and voluntarily insured persons and it includes a scheme of insurance against unemployment which disappears in the later forecasts. The annual estimates of the progress of the Augmentation and Joint Business F u n d include on each occasion a table of receipts and of expenditure and the comparison of the total results obtained from these two tables. These estimates are not reproduced here; t h e y are very voluminous and relate to the provisions taken into consideration in the preparatory investigations which have for the most p a r t been profoundly modified before being included in the legislation 2. 1 Report of the Senatorial Committee on Hygiene, 1925, see Bibliography, No. 3, pp. 214-215. 2 Reference may be made to the following Parliamentary Reports: Recommendation of the Senatorial Finance Commission, 1927 : Bibliography, No. 5, pp. 143 et seq. Recommendation of the Finance Commission of the Chamber of Deputies, 1928; Bibliography, No. 7, pp. 62 et seq. Recommendation of the Senatorial Finance Commission, 1930: Bibliography, No. 9, pp. 21 et seq. 238 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION From 1 July 1930 to 31 December 1935 The 1930 legislation instituted the General Guarantee Fund as a central institution whose operations are shared between four funds: on the one hand the Augmentation and Joint Business Fund and the Guarantee and Equalisation Fund, which are common to the schemes for commerce and industry and for agriculture, on the other hand the Special Agricultural Fund and the Agricultural Relief Fund which are peculiar to the agricultural scheme. Each of these funds will be considered separately: their principal items of receipt and expenditure will be reviewed and their role and the powers attributed to them by law will be indicated. Augmentation and Joint Business Fund (1) Receipts. — The Augmentation and Joint Business Fund was constituted by an initial grant provided by: the Reserye Fund accumulated under the scheme of workers' and peasants' pensions; and a levy fixed at one-half of the surplus assets in the workers' and peasants' pension funds and, in particular, in the workers' and peasants' pensions section of the National Old-Age Pensions Fund. This fund was also credited during the financial year 1934 with a fraction of the balance of the Stamps Fund for Workers' and Peasants' Pensions. The normal resources of the Augmentation and Joint Business Fund may be divided into three groups according as they are derived from (i) public moneys; (ii) a levy on contributions or surplus assets, or (iii) miscellaneous sources: (i) Resources derived from the State, departments and communes: a State subsidy, payable in quarterly instalments, amounting to 540 million francs a year; the payment of the savings effected on the expenditure on relief, to the extent of the total in the case of the State and one-half in the case of the departments and communes; a special appropriation, fixed annually by the .Finance Act, out of the share of the supplementary royalty on the profits of the Bank of France accruing to the Treasury and out of the share of the proceeds of games of chance accruing.to the State; the repayment of expenditure relating, on the one hand, to the complementary old-age pensions granted to wage earners aged from 60 to 65 years at the date of coming into force of the Act, and, on the other hand, to the subsidies of 6 francs a month which augment the contributions paid by pensioners who wish to preserve for themselves and their wives the benefit of the insurance against sickness; the repayment of the additional benefits paid to insured persons in agriculture. (ii) Levies on contributions and on surplus .assets: levies made on all contributions in accordance with the proportions fixed each year by Decree 1-, 1 See p. 219. FRANCE 239 the employers' contributions in respect of insured persons whose wage exceeds the limit, employees who are in receipt of a pension or aged more than 60 years, and alien employees who are excluded from the benefit of the Act; a levy of 3 per cent, on the surplus receipts of the assessment funds; the levy of 6 per cent., provided in the Act as from the tenth year, on the surplus assets shown in the balance-sheets of the invalidity and old-age insurance funds; a levy on voluntary insurance contributions and a levy of 20 francs a year on the contributions of the wives of insured men who, not being themselves wage earners, are admitted to the benefit of the special insurance. (iii) Miscellaneous resources: The unutilised portion in each year of the income from the proceeds of the sale of the Grown jewels (Act of 31 December 1895) ; the arrears lapsing under the five-year period of prescription and the repayable capital sums not refunded to the dependants of insured persons who have been dead for more than five years; the total proceeds of fines in basic amount and additional tenths, and donations and bequests. To these resources must be added the interest on the investments allocated to the Augmentation and Joint Business Fund. Table XIV below shows in respect of the principal items of receipt the results of the operation of the Augmentation and Joint Business Fund from 1 July 1930 until 31 December 1936. (2) Expenditure. — Up to 1 April 1934 all the expenditure on invalidity insurance was charged to the Augmentation and Joint J3usiness Fund. As from that date only the following items of payment were charged to it under the heading of invalidity insurance: (1) the complementary pensions required to bring the pensions u p to the guaranteed minima; (2) additions in respect of family maintenance. The duties entrusted to the Augmentation and Joint Business Fund include essentially: the guarantee of the legal minima for old-age and invalidity pensions and for lump sums payable on death; a share, eventually assigned to the assessment funds, in the cost of reducing the percentage of medical and pharmaceutical expenses left charged on the insured person; an increase of 6 francs a month to be added to the contribution of insured persons in receipt of pension who maintain the benefit (as well as that of their wives) of insurance against sickness; the repayment of expenditure consequent on the winding-up of the workers' and peasants' pensions scheme; the payment of the employer's contribution, in the place of the employer, for insured persons registered on account of their family charges; the payment of all additional sums consequent on family maintenance expenses; 240 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION TABLE X I V . — RECEIPTS 1 OF T H E AUGMENTATION AND JOINT BUSINESS FUND (in thousands of francs) 1930 1931 1932 1933 Exceptional Winding-up of t h e Pension Scheme for Workers and Peasants Assets of t h e Reserve Fund Surplus assets of t h e Pensions F u n d s for W o r k e r s and Peas a n t s and- of t h e N a t i o n a l Old-Age Pension Fund (workers' and peasants' pensions section) 1934 -14,951 Resources provided Fixed State Subsidv Special appropriation from t h e profits of the B a n k of F r a n c e and proceeds from games of c h a n c e Increase of contribution granted for insured persons in agriculture . . Grant in aid of medical benefits for old-age pensioners 5,435 27,711 36 7,560 3,331 16,157 10 by the State ü'lUjUD'l J'1U,UUU 8,000 2,893 61,621 98,048 120,705 173 Levies on contributions Old-age, death, family maintenance a n d administration allowance . . . . Maintenance of rights of unemployed insured persons . . E m p l o y e e s whose wages exceed the Employers' limit for compulsory insurance. . contributions in respect of Employees in receipt of pensions or aliens Levies on surplus assets of assessment funds Levies on t h e contributions assigned to 351,368 — 41,915 — — — • assets 411,001 1,004,201 >46,804 35,864 27,116 33,378 27,977 54,068 33,286 '66,150 43,439 63,356 95,464 66,306 53,780 45,637 6,087 16,090 13,339 15,438 — . and surplus 61,628 Miscellaneous Totals 1936 resources L e v y on t h e balance of t h e S t a m p s F u n d for workers' and p e a s a n t s ' pensions Unutilised portion of t h e income produced b y t h e sale of Crown jewels " . . . Proceeds of fines I n t e r e s t on i n v e s t m e n t s Miscellaneous 1935 — 3,633 —' 167 — — 128 4 •— 21,274 39,501 5,792 resources 287 73 153,812 93 127 107,306 88,267 141 298,627 270,868 986.361 743,452 764,680 1,359,043 1,693,977 821,179 1 The receipts in respect of voluntary insurance and of t h e special insurance for wives of insured m e n , not being themselves wage earners, are not included in this table. 241 FRANCE TABLE XV. —• EXPENDITURE OF THE AUGMENTATION AND JOINT BUSINESS FUND 1 (in thousands of francs) Nature of expenditure 1930 Orphans' pensions . . . Payment of the contribution in the place of the employer for insured persons registered on account of their family charges . Increases granted for insured persons in Family charges: Sickness and maternity Death Invalidity Complementary payments on death . . . Grand in aid of medical benefits for old-age pensioners Invalidity : Complementary penCare of invalids and miscellaneous . . . Maintenance of rights of unemployed insured persons Complementary old-age : ' 1931 1932 1933 1934 1935 1936 78 500 1,069 1,923 1,247 196 77 16,312 16,769 17,371 11,678 8,138 94,607 88,817 68,295 157,529 77,354 9,078 54 — 17,254 1,116 — 16,994 1,337 — 17,204 1,631 125 20,597 1,663 468 11,504 938 511 17 481 700 805 1,060 587 9 43 .77 341 112 590 420 1,713 1,948 307 826 7,823 11,718 9,949 — — — — — — 35 — 163 Administration expenses of General Guarantee Fund 1,797 37,745 5,410 3,305 8,695 4,224 238 Administration expenses of central services . . 868 6,453 — — 59,417 — — Allowance for administration expenses . . . 480 56,906 90,742 95,886 96,501 116,443 36,346 Winding-up of pension scheme for workers and peasants . . . . 85,504 529,056 415,923 384,286 349,563 323,430 — Contribution to volun-. tary i n s u r a n c e . . . . — — — 4,500 6,000 — — Various expenses . . . — 9 8 132 320 4,970 1,000,506 Totals . . . . 88,649 647,652 625,696 612,813 634,680 665,246 1,153,085 i Expenditure due to voluntary insurance and special insurance of insured persons' wives who are not themselves wage earners are not included in this table. a contingent share—to be fixed annually by Decree—in the payment by the assessment funds of the half-contribution for old-age on behalf of insured persons who are sick; all the expenses of management and operation of all the institutions; 16 242 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION the reimbursement of the payments made by the funds in the place of unemployed insured persons; expenditure relating to family maintenance expenses in the special insurance scheme-, and the increases granted for insured persons in agriculture. For a certain number of these charges the Act imposes on the Augmentation and Joint Business Fund only a contingent share: according to the funds available and in conformity with a percentage to be fixed annually by Decree. The expenditure undertaken by the Augmentation and Joint Business Fund since the coming into force of the Act until 31 December 1936 has amounted to the'figures shown in table XV above. Guarantee and Equalisation Fund 1. Receipts. — The resources of this Fund comprised: a levy of 2 per cent, on all the contributions (this rate being subject to abatement when the assets of the Fund have reached 100 million francs) ; a contingent levy, which may reach 0.40 per cent, of the basic wage, on the old-age contributions of insured persons aged less than 30 years; a levy of 5 per cent, on the portions of contributions assigned to the assessment risks ; a levy of 2 per cent, on the annual surplus receipts of the assessment funds; 4 per cent, of the levy, provided by the Act as from the tenth year, on the surplus assets disclosed in the balance-sheets of the invalidity and old-age insurance funds. 2. Expenditure. — The Guarantee and Equalisation Fund was instituted essentially in order to make good any deficit of the receipts of the insurance funds and to prevent their becoming insolvent. As from 1 April 1934, to this function has been added that of the invalidity insurance (excluding the complements necessary to bring the pensions up to the guaranteed minima and the additions in respect of family maintenance expenses). Table XVII summarises the results of the operation of the Guarantee and Equalisation Fund. Special Agricultural Fund The Special Agricultural Fund was intended to guarantee the payment to agricultural insured persons of minimum old-age pensions. Its resources were constituted by a payment from the Augmentation and Joint Business Fund equal to 80 per cent of the contributions of the insured persons aged more than 30 years and by its own interest: they have attained the totals shown on p. 243. The Fund was charged for the first time in 1936 with the supplements to old-age pensions, amounting to 123,000 francs. The complete figures for the administration of the Special Agricultural Fund are given in table XVII below. Agricultural Relief Fund The purpose of the Agricultural Relief Fund was to allocate, as exceptional payments, grants to the agricultural insurance funds which 243 FRANCE in consequence of epidemics or other unavoidable cause find themselves unable to carry out their engagements. It also had to meet the expenditure consequent upon the extension of invalidity insurance to wage earners in agriculture or forestry. Originally it was maintained by a State grant equal to 80 per cent. of contributions of insured persons over 30 years of age (thousands of francs) 1932 1933 1934 1935 1936 7,004' 18,169 3,033 86,640 28,381 Total Interest on investments (thousands of francs) 3,330 4,725 5,732 143,227 13,787 payment equal to 5 per cent, of the total amount of contributions and increases allocated to the institutions which carry on agricultural insurance. There were assigned to it for the purpose of covering the cost of invalidity pensions: (1) a sum of 10 million francs levied on the workers' and peasants' pensions Stamps Fund (this sum was credited in 1934); (2) a levy equal to one-ninth of the increase of contribution paid for agricultural insured persons under the heading of assessment risks. Its receipts have been constituted in the following manner: TABLE XVI. — RECEIPTS OF THE AGRICULTURAL RELIEF FUND (in thousands of francs) 1931 1 1932 1933 5,794 5,001 1934 1935 1936 5,989 5,014 3,469 1,834 7,092 4,738 10,000 3,364 1,788 2,048 21,187 13,894 10,255 Levy of 5 per cent, on contributions and in814 Levy to cover invalidity expenses Portion of workers' and peasants' Pension Stamps Fund . . . . Interest on investments . 8 Total receipts 822 . . 5,794 5,001 Its expenditure, which was devoted entirely to covering the invalidity risk, amounted to: 186,000 francs in 1935; 691,000 francs in 1936. 244 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The total results of the administration of the Agricultural Relief Fund are shown in table XVII below. Summary of the Administration of the General Guarantee Fund Table XVII shows the annual totals of receipts and expenditure for each of the Funds just considered and consequently summarises the administration of the General Guarantee Fund from the date of its creation to 31 December 1936. TABLE X V I I . GENERAL SUMMARY OF RECEIPTS AND OF THE GENERAL GUARANTEE FUND EXPENDITURE (in thousands of francs) Name of fund Year Receipts Expenditure Surplus ( + ) or deficiencies (—) Augmentation and Joint Business Fund ' . . . . ' 1930 1931 1932 1933 1934 1935 1936 270,868 986,365 743,632 769,528 1,378,453 1,710,830 845,290 88,650 647,716 629,913 625,643 645,229 692,230 1,163,841 + 182,218 . + 338,649 + 113,719 + 143,885 + 733,224 + 1,018,600 — 318,551 6,704,966 4,493,222 +2,211,744 Total Guarantee and . . . . 20 635 9,474 535,564 + + + + + — 75,656 90,939 142,857 217,548282,268 430,143 545,693 + 379,125 822 5,794 5,001 21,187 13,895 10,255 186 691 + + + + + + 822 5,794 5,001 21,187 13,709 9,564 56,954 877 + 56,077 7,004 18,169 6,363 91,366 34,113 123 + + + + + 7,004 18,169 6,363 91,366 33,990 . . . . 157,015 123 + 156,892 . . . 7,843,753 5,039,915 Equalisa- Total . . . . A g r i c u l t u r a l Relief F u n d Total . Grand total 1930 1931 1932 1933 1934 1935 1936 . . . . Special Agricultural F u n d . Total 1930 1931 1932 1933 1934 1935 1936 1930 1931 1932 1933 1934 1935 1936 75,656 90,939 142,877 218,183 291,742 105,421 924,818 + 2,803,838 FRANCE 245 Decrees of October 1935 By the Decrees of October 1935 the administration of the General Guarantee Fund has come to mean that of an Augmentation Fund and that of a Guarantee Fund: subject to a certain number of modifications made at the same time to their respective functions, the first takes the place of the Augmentation and Joint Business Fund and the second that of the Guarantee and Equalisation Fund. The Augmentation Fund supports, on the one hand, the expenditure entailed by the winding-up of the workers' and peasants' pensions scheme, and, on the other hand, the complementary pensions designed to bring up to the legal minima the amounts of the old-age pensions paid by the insurance funds, both in the scheme for commerce and industry and also in that for agriculture. It was also made responsible for increasing by 15 per cent, the actuarial reserves for voluntarily insured persons when these reserves are transferred to an independent mutual aid fund or to the National Old-Age Pensions Fund. It is maintained by: an annual contribution from the State, whose amount is specifically fixed at 140 million francs *; the employers' contributions relating to wage earners aged more than 60 or in receipt of a pension; the portion of the old-age insurance contribution which is not credited to the individual account; a levy of 20 francs a year on the contributions of all wives of insured persons who are not themselves wage earners; the total amount of fines in basic amounts and additional tenths ; the unutilised portion in each year of the income from the proceeds of the sale of the Crown jewels (Act of 31 December 1895) ; the arrears lapsing under the five-year period of prescription and the repayable capital sums not refunded to the dependants of insured persons who have been dead for more than five years ; the payments out of the surplus assets of the workers' and peasants' pension Funds; the repayment by the State of the expenditure charged to the Fund in respect of pensions guaranteed to wage earners aged between 60 and 65 years at the date of coming into force of the Act; the balance of the account " proceeds of the sale of stamps for social insurance " instituted by the 1930 Act, which had to be woundup as at 31 December 1936; an appropriation, at a rate which is fixed annually by the Finance Act, out of the share of the supplementary royalty on the profits of the Bank of France accruing to the Treasury and out of the share of the proceeds of games of chance accruing to the State (provided that the total appropriation shall not exceed a maximum of 5 million francs); and an annual grant, out of the general budget, equal to 40 per cent, of the total amount of contributions credited in the preceding year 1 The State may be required to make a supplementary contribution under the conditions and within the limits defined by a guarantee clause reproduced above (pp. 192-193). 246 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION to the individual old-age insurance accounts of insured persons in agriculture. T h e operations of t h e Augmentation F u n d during 1936 are shown in Table X V I I I . TABLE XVIII. AUGMENTATION FUND RECEIPTS AND EXPENDITURE FOR 1936 (in thousands of francs) Receipts Share of balance of the Augmentation and Joint Business Fund Employers' contributions in respect of employed persons over 60 or pensioners Surplus assets of the workers' and peasants' pensions funds Fixed State subsidy Proceeds of fines Unutilised portion of the income from the proceeds of the sale of Crown jewels Levy on old-age contributions Various receipts Interest on investments Total 1,000,000 36,478 3,994 140,000 241 140 58,096 2,854 24,464 1,266,267 Expenditure Winding up of the pension scheme for workers and peasants -. . Guarantee of minimum old-age pension Orphans' pensions Augmentation of actuarial reserves of voluntarily insured persons Various Total 288,825 308 805 6,637 300,083 596,658 The purpose of the Guarantee Fund is to make grants or advances to the Regional Federations in cases where these are not able to guarantee the risks of sickness and maternity. There m a y also be made, out of the resources of this fund, exceptional appropriations in favour of the Regional Federations for the purpose of meeting expenditure on invalidity insurance. Each year it furnishes the amount necessary to defray the cost of administration of the General Guarantee Fund. The Guarantee F u n d received on 1 J a n u a r y 1936 an initial grant of the assets of t h e pre-existent Guarantee and Equalisation Fund. Its resources normally include: an appropriation out of the surplus receipts of the assessment funds and in the event of its assets falling below 200 million francs, an exceptional a n d temporary levy on the contributions assigned to the assessment risks. 247 FRANCE The Decree of 30 October 1935 involves the winding-up of the Special Agricultural Fund and of the Agricultural Relief Fund: it stipulates that the assets of the latter fund shall be divided among the National Reinsurance Federations for the purpose of the payment of invalidity pensions. The Guarantee Fund received in 1936: Thousands of francs As a fraction of the balance of the Guarantee and Equalisation Fund As interest on investments Total 500,000 18,815 518,815 During the same year it had to meet the administration expenses of the General Guarantee Fund, amounting to 3,750,000 francs. CHAPTER IV FINANCIAL ADMINISTRATION § 1. — Investment of Funds: Statutory Provisions and Regulations METHOD OF INVESTMENT Pursuant to the 1930 Act the insurance funds deposit either with the Deposit and Trust Fund or with the Bank of France any moneys in excess of the amount of cash which they are authorised to keep in hand. The Deposit and Trust Fund must utilise these moneys with due regard to the nature and extent of the risks insured by the funds: (1) to the extent of one-half at the instance of the funds and subject to certain approvals; (2) as regards the portion remaining to be invested, on its own initiative. ". The Decree of 15 May 1934 withdrew from this arrangement for the period 1 June 1934-31 December 1940 three-quarters of the disposable moneys of the accumulation funds and of the Augmentation and Joint Business Fund, but allowed the earlier provisions to remain as regards the other quarter. The Decrees of October 1935 maintained it, while stipulating, however, that the investments made on the initiative of the insurance funds or of the Federations—that is to say at the instance of the management committee of the Fund (or of the Federation) or of a committee authorised by it—must receive the endorsement of the management committee of the General Guarantee Fund or of a committee authorised by it, if it is a question of investments other than in State securities, securities of the " Caisse autonome d'amortissement ", or negotiable securities quoted on the Paris Stock Exchange. NATURE or THE INVESTMENTS AUTHORISED OR PRESCRIBED 1930 Act The investments made directly by the Deposit and Trust Fund on its own initiative are limited to State securities or securities guaranteed by the State, foreign securities under conditions to be laid down by a Decree issued on the recommendation of the Ministers of Finance, Labour and Foreign Affairs, land or communal bonds issued by the Land Bank (Crédit Foncier), the acquisition of real estate, and bonds of the principal public railway companies. FRANCE 249 The investments made at the instance of the social insurance funds include besides various categories which may be grouped as follows: 1. Investments of a social character, including: (a) loans to departments, communes, federations of communes, colonies, protectorates, chambers of commerce, chambers of agriculture, chambers of handicrafts or any other public institutions, or in securities guaranteed by these institutions; (b) loans to offices, societies and charitable trusts for workers' dwellings, real estate credit societies, societies and institutions for mutual credit and co-operation in agriculture, and provident and public health institutions recognised as being of public utility; (c) underwriting debentures and bonds of the National Agricultural Credit Fund and of various other societies eligible to obtain a. subsidy from the State or to obtain a loan at a reduced rate of interest from the State or from the National Agricultural Credit Fund. 2. The acquisition of land or buildings, subject to the approval of the General Guarantee Fund and the acquisition of land for re-afforestation or of existing forests, subject to the previous approval of the Superior Insurance Council. 3. All securities accepted as collateral by the Bank of France, as well as first mortgages in property in France, up to a total amount of 50 per cent, of the value of the property, subject to the approval of the General Guarantee Fund. Decree of 15 May 1934 The Decree of 15 May 1934 introduced into this initial system two series of important modifications: 1. It decided, as a transitional departure from the provisions of the Act, that the accumulation funds and the General Guarantee Fund should pay, from 1 June 1934 until 31 December 1940, 75 per cent, of their available moneys for the purpose of constituting a joint fund managed by the Deposit and Trust Fund; 2. it modified the normal list of authorised investments, A summary analysis of each of these modifications is given below. Joint Works Fund The Joint Fund instituted by the Decree of 15 May 1934 for the purpose of carrying out an extensive programme of public works to relieve unemployment by utilising the available moneys of the social insurance funds has received the name of " Joint Works Fund ". The available moneys of this fund are invested by preference in loans to the bodies which participate in the carrying out of works for the purpose of reducing unemployment, in accordance with the programme drawn up by the National Board of Public Works to Relieve Unemployment. These bodies may be departments, communes, federations of communes, national railway systems, public institutions, colonies, protectorates, holders of concessions for specially approved public works, and all other duly constituted bodies which have secured the guarantee of a department or commune. 250 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Loans are subject to the following rules. The contracts are drawn up in accordance with a uniform type adopted by the National Board: they are concluded by the Deposit and Trust Fund. The duration of the loans may not exceed 30 years, except in the case of loans to national railway systems in respect of which it may be specially increased to 50 years. Each year the Deposit and Trust Fund collects the annual payments due at the times stated in the contracts; after collection it credits the account of each fund with the portion of the annual payment due to it in accordance with the sums paid to the Joint Fund out of its available moneys. Each fund also has the right to a share of the other income of the Joint Fund which is derived in particular from the short-term investments which the Deposit Fund may be led to make provisionally. With a view to providing for the liquidity of their finances in the face of any contingency, funds are authorised as from 31 December 1940 to transfer among themselves the debts due to them. In default of a direct agreement, the Deposit and Trust Fund acts ex officio with the portion of the funds for the investment of which it is directly responsible. Modifications made in the list of authorised investments The bonds of departments, communes and federations of communes and the loans to these bodies are included among the investments which can be made directly by the Deposit and Trust Fund on its own initiative. - On the other hand, the following categories of investment cease to be authorised: stocks, bonds and shares and loans in respect of societies for workers' dwellings and institutions of mutual credit and co-operation in agriculture ; foreign securities; the acquisition of forests and lands for re-afforestation; loans to public health and provident institutions recognised as being of public utility. Moreover, mortgage loans and the acquisition of buildings are limited to buildings built and completely finished and situated in towns of more than 100,000 inhabitants or in the department of the Seine. For any one fund the total of the investments in real estate must not exceed 10 per cent, of the total amount of its investments. Decree of October 1935 Pursuant to the Decree of 28 October 1935, the authorised investments are all included in one list which limits the choice in all cases, that is to say when they are made at the instance of the social insurance funds as well as when they depend on the sole initiative of the Deposit and Trust Fund. Nevertheless, in the first case, investments in certain categories are authorised only after approval, as indicated above, by the governing body of the General Guarantee Fund or by a committee authorised by it. The investments which appear on this limiting list may be grouped in broad categories in the following manner: (1) Slate securities or negotiable securities which are quoted on the Paris Stock Exchange: State securities or those guaranteed by the State, securities of the " Caisse autonome d'amortissement ", FRANCE 251 bonds and debentures of the National Credit Fund, bonds and debentures of the principal public railway companies, land, communal or maritime bonds issued by the Land Bank, bonds and debentures of departments, communes, federations of communes, public institutions, colonies, protectorates, or mandated territories, securities guaranteed by these bodies or institutions, bonds and debentures of the National Agricultural Credit Fund, and any other bonds accepted as collateral by the Bank of France. (2) Simple loans: loans to departments, communes, federations of communes, public establishments, colonies, protectorates or mandated territories. (3) Mortgage loans: first mortgage loans on buildings completely finished and situated in towns of more than 100,000 inhabitants and in the department of the Seine, up to a total maximum of 50 per cent, of the value of the building. (4) Acquisition of buildings: acquisition of buildings completely finished and situated in towns of more than 100,000 inhabitants or in the department of the Seine. Nevertheless, the social insurance funds* may be authorised by the General Guarantee Fund, by way of exception, for the purpose of installing their administrative machinery, to acquire land or completed buildings and to erect buildings and fit them out. The total of the investments of any one fund or federation in buildings, including those made for the purpose of installing its administrative machinery, may not exceed 15 per cent, of the total amount of its invested assets. No new investment in buildings may be made by a fund for which the proportion mentioned above has already been exceeded, nor may it be made for the account of such a fund so long as its position is not in conformity with the regulations. .Apart from the acquisition of house property, securities quoted on the Paris Stock Exchange or loans to the Joint Works Fund, social insurance funds and their regional federations are not permitted to make any investments for a period of more than 30 years. Social insurance funds and their regional federations may be authorised by the Ministry of Labour, on their request and in view of justifiable cash requirements, to transfer to each other securities, title deeds to property, or other documents of title held by them. The nature of the investments that may be made by employers' pensions funds, and more generally by works insurance institutions, are subject to the special provisions laid down in public administrative regulations issued under the Decree of 14 June 1938. These regulations stipulate in particular: (1) the maximum proportion of the funds which may be invested or deposited in the establishment or undertaking in which the insured persons work; (2) the proportion of the investment's which must necessarily be in Government securities. Provisions peculiar to the Regional Federations of sickness and maternity funds In the investment of the available moneys of the Regional Federations a distinction may be made between true investments and the use of a part of the available moneys for works of prevention and cure. 1 And also the Regional Federations, under the Decree of 14 June 1938. 252 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The true investments of the Regional Federations are subject to the same rales as the investments of the invalidity, old-age and death funds, with the exception of two special provisions: (1) The proportion of the available moneys of the Regional Federations which must be invested exclusively either in State Securities or those of the Autonomous Amortisation Fund or in negotiable securities quoted on the Paris Bourse, is fixed by an Order of the Ministers of Labour and Finance l . (2) The Regional Federations as a whole are obliged to pay to the Joint Works Fund a sum at least equal to 300 million francs; they may later transfer their credits on this Fund to the invalidity, old-age and death insurance funds for the purpose of constituting actuarial reserves for the pensions paid by these institutions. The utilisation of a portion of the available moneys for the supervision of sick persons and for the prevention and cure of sickness is provided for under the following conditions. With a view to reducing the later expenditure of the insurance schemes and in particular of the invalidity insurance, the Regional Federations may, in agreement with the funds, on the recommendation of- the Minister of Public Health and on the authorisation of the Minister of Labour, initiate or subsidise works of common interest, such as: maternity and infant welfare centres, dispensaries and other institutions or establishments for ' promoting public health and the prevention of disease in general, holiday settlements, establishments for prevention and cure, sanatoria, convalescent homes and homes for the aged, and societies which organise admissions to preventive or curative institutions. Expenditure incurred under this heading, even if it involves the acquisition of buildings, is not classed as investments. The Regional Federations may also, with the consent of the Minister of Labour, grant loans to bodies or establishments mentioned in the list of investments authorised for the purpose of carrying out works for the purpose of the control of sick persons, and the cure and prevention of sickness. The rate of interest on these loans is fixed by an Order of the Ministers of Labour and Finance; another Order of the Ministers of Labour and Finance fixes each year the maximum total of the sums available to the Federations for applying to their programme of control, cure and prevention 2. Decree of 7 September 1936 According to this Decree all sums remaining available in the Joint Works Fund after the necessary deductions have been made to cover 1 An Order of 28 May 1938 stipulates that this proportion must be not less than three-quarters of the invested assets, no account being taken of the outstanding balance of the special account for social hygiene and prevention. 2 An Order of 21 June 1938 provides that this maximum will depend on the figures in the accounts of the Regional Federations (see p. 264): the sums left at the. disposal of the Federations for the purposes in question are limited to: (1) The outstanding balance of the account for social hygiene, prevention and supervision; (2) One-eighth of the invalidity reserve fund. TRANCE 253 commitments in connection with the plan of extensive public works to relieve unemployment are advanced to the National Credit Fund for the departments and communes. The amounts to be repaid annually in respect of these advances are calculated at a rate fixed from time to time ; the whole amount must be paid off within 30 years. Decree of 24 May 1938 This Decree made some considerable changes in the rules which will govern the investment of social insurance funds after 1 January 1941, that is to say, when the clauses concerning the Joint Works Fund cease to apply. As from 1 January 1941 the sums available in each invalidity, old-age and death insurance fund or old-age and death fund will be employed as follows : (a) A quarter will be advanced as a loan to the National Credit fund for the departments and communes, for financing departmental and communal works and the work of public establishments administered by these bodies; (b) A quarter will be invested, by decision of the Governing Body of the fund or of a committee of the Governing Body with powers from it, in the form of loans to departments, communes and public establishments for financing their work; (c) A quarter will be invested directly by the Deposit and Trust Fund ; (d) A quarter will be invested by the Deposit and Trust Fund in securities selected by the Governing Body of the insurance fund or by a committee of the Governing Body with powers from it. The assets of the Regional Federations will continue to be directly invested as formerly, half being invested directly by the Deposit and Trust Fund and the other half invested through it in securities selected by the Governing Body of the Regional Federation or by a committee of the Governing Body with powers from it. Investments made at the suggestion of the Regional Federations must be approved either by the National Credit Fund for the departments and communes in the case of loans to departments, communes and public establishments administered by them, or by the Governing Body of the General Guarantee Fund (or a committee having powers from it) in the case of investments other than those mentioned above and other than investments in Government securities, the Autonomous Amortisation Fund or negotiable securities quoted on the Paris Stock Exchange. RATES OF INTEREST OF INVESTMENTS Pursuant to the Act of 1930 the rate of interest of investments 1 made on the initiative of the insurance funds may not be less than a minimum rate fixed at the beginning of each year by a Decree issued on the recommendation of the Ministers of Finance and Labour. This minimum ratej which was at first fixed at 3.75 per cent for securities accepted as 1 Calculated in accordance with the rules which are reviewed in the next section (see p. 260). 254 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION collateral by the Bank of France and at 4.70 per cent, for the other categories of investment, was raised by the Decree of 2 June 1933 to 4.25 per cent, for securities 'accepted as collateral by the Bank of France and to 5.25 per cent, for the other categories of investment. The Decree of 15 May 1934 stipulates that the rate of interest of the loans which may be granted by the Joint Works Fund is fixed periodically by an Order of the Ministers of Labour and Finance after consultation with the National Board of public works to relieve unemployment. This rate was fixed for the first time on 14 September 1934 at 5.35 per cent. ; since 1 January 1935 it has remained at 5 per cent. Pursuant to the Decree of 28 October 1935, the rate of interest on long and short term investments 1 of the social insurance funds may not be less than the minimum rates fixed periodically by an Order of the Ministers of Labour and Finance. This Order also determines a minimum rate of interest for the investments authorised by way of exception for the purpose of installing the administrative machinery of the funds. In the application of these clauses an Order of 14 September 1936, which applies at the same time to the scheme for commerce and industry and also to that for agriculture, subjects the rates of interest on investments to the following rules. (1) For the investments of social insurance funds and their federations the minimum rates in force are maintained, namely: 4.25 per cent, for securities accepted as collateral by the Bank of France ; 5.25 per cent, for the other categories of investment. (2) Short term investments of the social insurance funds and their federations, when they are made in ordinary Treasury bonds, must carry a rate of interest at least equal to that of the National Defence Bonds issued at the same time. (3) The minimum rate is reduced to 3 per cent, in the case of the acquisition, construction or equipping of buildings for the purpose of installing the administrative machinery of the funds or of their federations. (4) The loans granted by Regional Federations to bodies or establishments for the purpose of carrying out works of social hygiene and of prevention, must carry a rate of interest at least equal to 4.50 per cent. (5) Loans granted by Federations of funds with the authorisation of the Minister of Labour up to a maximum fixed by Order 2 and intended for social hygiene and preventive work must bear interest at not less than 2 per cent. An Order of 6 February 1937 reduced from 5.25 to 5 per cent, the minimum rate of interest for the investments of social insurance funds or their Federations other than those in securities guaranteed by the Bank of France. The rate of interest applicable to the annual repayments of advances from the Joint Works Fund to the National Credit Fund for the departments and communes was fixed at 5 per cent, by an Order of 20 May 1937. 1 2 See footnote on previous page. See above, p. 252. 255 FRANCE § 2. — Statistics of Investments ACCUMULATION FUNDS The amounts of the investments made annually in each category on behalf of accumulation funds, either on their own initiative or through the Deposit and Trust Fund, appear in t h e reports published annually [30, 34, 32]. These same documents contain a detailed description of, the holdings of the accumulation funds, showing separately: (1) investments selected b y the funds themselves; TABLE XIX. — INVESTMENTS M A D E ON BEHALF OF THE ACCUMULATION FUNDS BUT SELECTED BY THEM l Title of securities held by the Deposit and Trust Fund As a t 31 December 1932 As at 31 December 1933 As a t 31 December 1934 As at As at 31 Dec- 31 December ember 1936 1935 Miscellaneous securities (nominal value in thousands of francs) Bons de la Défense nationale and Bons du Trésor . . . 670 28,177 41,956 10,000 13,855 Obligations du Trésor 4% pour cent 1932 (outillage national) 13,688 14,418 15,665 — — Obligations du Trésor 4% pour cent 1933 9,236 9,672 10,552 — — Obligations du Trésor redeemable in 15 years . . 12,664 13,343 14,248 — — Obligations sexennales de la Défense nationale . . . . 1,357 — — — Obligations du Trésor 4 pour cent 1934 450 450 — — — Obligations du Trésor 5 pour cent 1935 225 1,225 —— — Bons du Trésor 7 pour cent 1926 19 — 49 — Bons du Trésor 4% pour cent 1933 for 10 years . . . . 3,246 2,285 3,547 — — Bons du Trésor 5 pour cent 1933 for 5 years 570 833 1,577 — — Bons du Trésor 4 % pour cent 1934 2,591 3,802 10,976 — — Bons du Trésor 5 pour cent 1934 2,007 1,578 2,455 — — Bons du Trésor 4 pour cent 1935 7,796 9,843 Titres de dommages de guerre 116,795 140,300 145,088 160,903 171,985 Obligations de la caisse autonome d'amortissement . . 3,537 5,169 5,889 6,302 6,471 Carried forward . . . 148,509 187,425 204,995 236,871 249,664 i This table does not include loans to departments and communes or real estate investments. 256 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XIX. — INVESTMENTS MADE ON BEHALF OF THE ACCUMULATION FUNDS BUT SELECTED BY THEM Title of securities held by the Deposit and Trust Fund As at 31 December • 1932 As at 31 December 1933 (continued) As at 31 December 1934 As at 31 December 1935 As at 31 December 1936 Miscellaneous securities (nominal value in thousands of francs) Brought forward . . . 148,509 187,425 204,995 236,871 249,664 Obligations des Postes, Té6,840 7,406 légraphes et Téléphones . 3,245 4,917 8,418 Obligations and Bons du Crédit National 6,302 8,233 10,228 13,500 17,502 Obligations and Bons des 45,216 51,185 55,668 chemins de fer de l'Etat . Debentures and Bonds of various railway companies 161,682 237,746 226,822 270,514 303,183 State-guaranteed debentures of various shipping companies 15,259 16,474 16,559 Bonds issued by Colonies and Protectorates 10,376 22,195 32,810 41,668 46,981 Loans on the security of Government annuities . . . 25,640 44,778 48,516 52,114 58,516 Crédit foncier bonds . . . . 13,753 23,497 29,034 31,774 34,113 Bonds issued by departments and municipalities . . . . 14,319 21,026 25,605 32,153 37,628 Bons du port autonome du Havre 180 180 180 Miscellaneous shares . . . . 631 631 ' 3,185 Government stock and foreign bonds guaranteed by the French Government . 3,720 3,620 400 3,255 3,45.5 Bons de la Caisse nationale de crédit agricole 561 Total . . . . 384,227 553,254 649,593 758,089 835,698 " Rentes ' French Government " rentes " (thousands of francs) . . . " Rentes " issued by Colonies or Protectorates (thousands of francs) French Government " rentes " issued in U.S.A. (thousands of dollars) 3,029 4,093 4,495 5,344 7,087 0.8 0.8 0.8 1.1 0.9 . — > — — 6 Securities issued in dollars (nominal capital) " Messageries maritimes " debentures issued in Canada . 2,200 100,000 98,000 98,000 98,000 257 FRANCE (2) investments selected by the Deposit and Trust Fund; TABLE XX. — INVESTMENTS SELECTED AND TRUST FUND ON BEHALF Title of securities held by the Deposit and Trust Fund As at 31 Dec- As at 31 Dec- CIL1UCL pm hpr 1932 AND MADE BY THE OF THE ACCUMULATION 1933 DEPOSIT FUNDS * As at As at As at 31 Decem- 31 Decem- 31 December 1934 ber 1935 ber 1936 Various securities (nominal capital in thousands of francs) Obligations du Trésor 4 y2 pour cent 1932 (outillage national) . Obligations du Trésor 4 % pour cent 1933 . Obligations du Trésor redeemable in 15 years Bons du Trésor 4 % pour cent 1933 for 10 years Obligations de la Caisse autonome d'amortisseObligations du — 66 66 66 66 — 23,919 23,909 23,632 23,534 2,822 3,092 3,247 6,578 6,520 — 3,712 3,712 3,712 3,712 114,772 104,772 104,772 104,712 104,631 285 285 Crédit Obligations et bons des chemins de fer de l ' E t a t Debentures and bonds of various railway State-guaranteed debent u r e s of various shipping companies . . . Bonds issued b y Colonies and P r o t e c t o r a t e s . . Loans on the security of Government annuities ^reuìL loncìer JJÖÜUS . Bonds issued b y d e p a r t ments and municipal- — — — — 230,761 254,123 273,500 292,929 547,884 469,357 692,196 779,765 831,951 421 62,383 89,861 128,404 50 50 579 643 643 70,775 22,002 90,671 22,904 114,040 22,993 127,911 28,917 137,757 34,895 99 99 99 7,060 7,013 — Foreign S t a t e loans and bonds guaranteed b y t h e F r e n c h Govern- — Total . . . . — — — 5 758,405 949,824 1,282,120 1,446,641 1,572,344 " Reiites " (in thousands of francs) French G o v e r n m e n t 181 19,450 25,598 25,598 25,135 i This table does not include loans to departments and communes or real estate investments. 17 258 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION (3) Investments of the National Old-Age Pensions Fund (Social Insurance Section). TABLE XXI. INVESTMENTS MADE BY T H E NATIONAL OLD-AGE P E N S I O N FUND (Social Insurance Section) At 31 At 31 At 31 At 31 At 31 Decem- Decem- Decem- Decem- December 1932 ber 1933 ber 1934 ber 1935 ber 1936 " Rentes " (in thousands of francs) Title of securities — Net revenue J 3,510 | 5,125 | 4,607 | 4,144 Number of securities Obligations de la Caisse autonome de gestion des bons de la Défense nationale 4i/ 2 % 46,422 46,422 — 46,422 46,632 Bons du Trésor 4 y 2 % 1933 . — — — — 100 » » » 5% 1934 . . — — 748 1,392 1,392 Obligations du Trésor 4% 1931-1946 (2nd half-year) . — — — — 458 Obligations du Trésor 4 % % 1932-1947 (1st half-year) . — — — — 1,000 Obligations du Trésor 4 % % 1932-1942 (2nd half-year) . — — — •— 117 Obligations P.T.T. 5% redeemable 1928 — — — — 60 Obligations du Crédit national — — 219 Obligations de la Ville de Paris — — — — 170 Obligations du Crédit foncier de France 25,008 25,004 25,000 24,995 25,016 Obligations des chemins de fer de l'Etat 59,918 73,986 151,755 158,344 216,172 Debentures of various railway companies 378,377 566,031 700,410 823,064 894,036 Loans on the security of Government annuities (Act of 31 July 1920) . . . . . 290 28,671 33,500 33,614 33,871 State-guaranteed debentures of various shipping corn47,272 48,874 14,084 24,890 33,820 Obligations du gouvernement 5,328 5,328 général de l'Algérie, 4 % % — 5,328 5,328 , Obligations du gouvernement 3,363 3,463 général de l'Algérie, 5 % . . —— — State-guaranteed bonds of 2,860 3,073 various colonies — — — • — • • — Loans (amou nt in thousands of francs) Loans to departments (cost) Railway annuities guaranteed by State (cost) . . . . . Various loans . General Labour Fund (cost) . 77,557 124,700 121,802 118,762 115,572 44,142 175,764 172,328 168,703 164,878 — — 108,112 410,713 673,715 259 FRANCE THE GENERAL GUARANTEE FUND The investment operations of the General Guarantee Fund and the composition of its hoJdings are described in its annual report [33]. The investments of this fund amounted on 31 December 1936 to 2,749,379 thousands of francs, distributed as shown in table XXII. TABLE XXII. INVESTMENTS OF THE GENERAL GUARANTEE FUND AT 31 DECEMBER 1936 Sums invested Percentage per (in thousands category of francs) Nature ol holdings Transferable securities Short-term securities French Government securities French Government securities issued abroad State-guaranteed debentures of 100,000 484,195 21,078 668 961 shipping Departmental and municipal loans . . . . Debentures of "Crédit foncier" Railway securities Total transferable s e c u r i t i e s . . . . Loans 5,762 2,246 687 1,257,669 1,873,266 68.14 Loans to public undertakings Various loans Loans to colonies ,, ,, communes ,, ,, departments 72,836 35,265 164,803 74,238 188,181 271,722 Total loans 807,045 29.35 69,068 2.51 Read estate Grand total ' 2,749,379 100 JOINT WORKS FUND The Joint Works Fund received the following sums : From June During to During December 1935 1936 1934 in millions of francs From the accumulation funds . . . . • From the National Old-Age Pensions Fund From the General Guarantee Fund . . Total 414 889 703 183 231 828 272 146 1,307 266 969 260 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION At 31 December 1936 the Fund had granted loans: To departments, communes and. public establishments (and miscellaneous loans) amounting in all to 1,890 million francs; To the State for a total of 989 million francs. At the same date 28.5 million francs had been invested in short term securities and there was a credit balance of 197 million francs. RATE OF INTEREST YIELDED The average rate of interest on the investments is calculated according to the purchase price and by taking into account the receipt of eyentual premiums on redemption and the particular factors relating to each investment. The interest on intercalated and temporary investments of which the duration does not exceed one year are not taken into account. The application of these rules respectively to the two broad classes of investments, which have already been distinguished, produces the following results: Investments made on the initiative of the Deposit and Trust Fund During the financial year 1931-1932 During the financial year 1933 . . Existing at 31 December 1933 . . Investments made at the instance of the funds (except direct investments such as: purchase of buildings, loans, etc.) During the financial year 1931-1932 During the financial year 1933 Existing at 31 December 1933 Average rate of interest yielded (per cent.) 5.18 5.80 5.46 5.10 6.15 5.36 § 3. — Accounting, Statistics and Financial Control The rules relating to the accounting and statistics of social insurance funds, which were defined first of all by a Decree of 25 July 1930, subsequently underwent axertain number of modifications. The rules applied as from 1 September 1936 were formulated in a new Decree 1 relating to accounting, dated 29 July 1936 [22]. Its principal provisions are reviewed below, with special reference to those concerning the invalidity, old-age and death funds, the regional federations and the General Guarantee Fund ; particular attention is paid to the rules which define the technical accounting of the insurance against old age and death and of the invalidity insurance. RULES FOR ACCOUNTING OF ALL THE FUNDS AND FEDERATIONS The governing body of each fund or federation appoints a standing management committee which shall include at least two members of 1 The provisions concerning invalidity, old age and death were extended almost unchanged to the agricultural insurance scheme by Decree of 26 January 1937. FRANCE 261 the governing body and which shall be entrusted with the audit of the accounts. This committee must present to the governing body a report on the financial working during the past year and on the position of the fund or federation at the end of the year, before the balance-sheet is submitted to the Minister of Labour. Moreover the committee must at least once a year make a surprise examination of the fund and the accounts. The accounts of the social insurance funds and of the federations show all the items of receipt and expenditure and enable the allocation of the surplus receipts to be determined. They are drawn up in such a way that the amount of the expenditure relating to each benefit may be isolated. They take account only of financial operations actually affected and of credits and debits resulting from liabilities definitely incurred at the date at which the accounts are made up. RULES FOR ACCOUNTING OF THE INVALIDITY, OLD-AGE AND DEATH INSURANCE FUNDS The accounts of the insurance funds for invalidity, old-age and death include, on the one hand, the documents relating to the financial transactions and, on the other hand, the documents for use in investigating the actuarial position of the fund, in fixing the bases of its scales and in defining the rights of each member. The documents which relate to the items of receipt and expenditure and which enable the allocation of the surplus receipts to be determined constitute the financial accounting of the fund. The documents which are used for the determination of the rights of each member, for fixing the bases of the scales and for investigating the actuarial position of the fund constitute the technical accounting. Technical Accounting of the Funds effecting Insurance against Old Age and Death The technical accounting of the funds effecting insurance against old age and death include compulsorily: (1) (2) (3) (4) (5) (6) (7) an alphabetical index of members compiled on cards; the individual accounts of insured persons; a roll-book of annuities and old-age pensions; a roll-book of orphans' pensions; a card index of the pensions and annuities in force; a book of actuarial reserves; a list of attachments. The individual accounts of insured persons are kept in the form of folios classified according to year of birth under the four headings: contributors, pensioners, deceased and exitants. These individual accounts show, opposite the contributions, the interest due and the actuarial reserves which the fund has actually received during each year, the corresponding portions of annuity calculated according to the scale in force at the moment of crediting the amount. They must set forth the total amount of the annuities to be borne by the fund and the total amount of the repayable lump sums to be repaid in case of death. The individual accounts of pensioners must show, as regards the amount of the actuarial reserves transferred by other funds, the 262 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION name of the funds concerned and the date of transfer. The individual accounts of pensioners whose pensions are paid by another fund are classed under the heading " exitants " ; these individual accounts must show the amount of the actuarial reserves transferred to the fund which pays the pension, the name of that fund and the date of transfer; the amount of the actuarial reserves so transferred and the amount of the corresponding annuities are determined in accordance with rules laid down by Order. The individual accounts of deceased persons must show the date of decease, the amount of the lump sums paid to dependants of the insured person and the date of the payment. Entries in the roll-book of annuities and old-age pensions are made in chronological order according to the dates on which the annuities and. pensions were awarded. The same applies to the roll-book of orphans' pensions. The book of actuarial reserves is compiled at each valuation which necessitates the calculation of new actuarial reserves. The social insurance annuities and the workers' and peasants' pensions are calculated separately. Furthermore, a distinction is made between the annuities in course of payment and the annuities which are in the process of being constituted. For the annuities in course of payment, insured persons are grouped according to year of birth. For each group so formed the book of actuarial reserves shows: (a) (b) (c) (d) (e) the total number of beneficiaries; the total amount of annuities; the total amount of repayable capital sums; the present value of an immediate annuity of one franc; the actuarial reserve corresponding to the total amount of the annuities; (/) the actuarial reserve for a sum assured of one franc payable on death; (g) the actuarial reserve for the repayable capital sums. The reversionary annuities (with reversion to the surviving widow) are calculated separately. For the annuities in course of acquisition, the insured persons are grouped according to year of birth and also according to the age fixed for entry into pension. For each group so formed the book of actuarial reserves shows: (a) (b) (c) (d) (e) (/) the total number of members; the total amount of eventual annuities; the total amount of repayable capital sums; the present value of a deferred annuity of one franc; the actuarial reserve for the annuities; the actuarial reserve for a whole-life insurance of one franc payable on death; (g) the actuarial reserve for the repayable capital sums. Technical Accounting of the Funds effecting Insurance against Invalidity The technical accounting of the funds effecting insurance against invalidity include compulsorily: (1) a roll-book of invalidity pensions; FRANCE 263 (2) a list of the individual accounts of persons in receipt of invalidity pensions; (3) a book of capital values of invalidity pensions in course of payment. Entries in the roll-book of invalidity pensions are made in chronological order according to the dates on which the pensions were awarded. The individual accounts of persons in receipt of invalidity pensions are kept at the offices of the fund and are classed under six headings: pensions due by the federation; pensions due by the invalidity insurance fund; pensions taken over by the old-age pension fund; suspended pensions; cancelled pensions; deceased pensioners. The individual accounts of pensioners whose pension is payable by the federation or by the invalidity insurance fund are classified according to the year of birth of the pensioner and also according to the year in which he became an invalid. The book of actuarial reserves is compiled at each valuation which necessitates the calculation of new capital vaiues. The pensioners are grouped according to year of entry into pension and for each group so formed the book of capital values shows: (a) the total number of pensioners; . (b) the total amount of the invalidity pensions, excluding increases for family maintenance expenses; (c) the capital value of an invalidity annuity of one franc; (d) the capital value corresponding to the total invalidity pensions granted to the pensioners in the group. The percentage addition to be made to the capital value to take account of the increases for family maintenance expenses is fixed periodically by ministerial Order. The Minister of Labour constructs the table of cessation of invalidity pensions,1 and also the scales corresponding to the various rates of interest which give the capital value of an invalidity annuity payable to age 60 or until the pension is cancelled on account of death or return to health. Provisions Com.m.nn to Insurances against Invalidity. Old Age and Death Every year a balance-sheet is drawn up showing the assets and liabilities of the fund as at 31 December. This balance-sheet is submitted, before 1 July of the following year, to the scrutiny of the Minister of Labour. The balance-sheet reveals the factors which enable the apportionment of the assets and the determination of the average rate of interest of the investments to be made 2. Buildings belonging to the fund are included in the assets of the balance-sheet at a figure which may not in any case exceed the net cost as shown by the expenditure on purchase and on works of construction and improvement, excluding the cost of upkeep. As à counterbalancing item to the figure appearing on the assets side, the funds must include in the liabilities a reserve for the amortisation 1 For the choice of the rate of interest on which the amount of the capital values is to be calculated, see Chapter III, § 3, p. 224. 2 For the calculation of the average rate of interest on investments, see the preceding section, p. 260. 264 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION of buildings, which increases by one-hundredth of the net cost thereof for each complete year passed. The annuities and securities in the list of investments are valued both at the purchase price and at the Paris Stock Exchange market price for the last day of the year of account. If the total produced by the valuation at the Stock Exchange market price for the last day of the year of account is less than the total purchase price, the difference is carried to the expenditure side of the " Profit and Loss Account " (the difference of the preceding year being carried to the receipts side of the same account). In order to determine the rate of interest yielded by investments in buildings account is taken of the average net income received since purchase when this took place within less than five years, otherwise account is taken of the average net income of the last five years. The net annual income is obtained by deducting from the total rents and other charges paid by the tenants, on the one hand the expenditure on management and the costs paid by the fund and on the other hand an allowance for depreciation equal to one per cent, of the net cost of the building. • The rate of interest is found by dividing the average net income by the net cost of the building. The balance-sheet must show among the liabilities a special reserve for the insurance against death, which increases each year by one-fifth of the total expenditure of the insurance against death during the last financial year until it becomes equal to the total expenditure of the insurance against death in the last financial year. To the balance-sheet relating to each valuation are annexed separate tinancial accounts for the insurance schemes against invalidity, old age and death which show on the one hand the variations in the assets and liabilities and on the other hand the total receipts and expenditure since the date of the preceding valuation. The funds which effect insurance against invalidity must carry to*the credit of the " invalidity insurance " account half the annual profits derived from the insurances against old age and death whenever these two insurance schemes have disclosed profits at the end of the preceding financial year. This duty must be carried out within one month following the date at which the valuation of the fund receives the approval of the Minister of Labour. The funds which do not effect insurance against invalidity and whose previous balance-sheet discloses a surplus of assets must pay the half of the annual profits in the financial accounts to the invalidity insurance fund to which their members are attached. This payment must be made within three months following the date at which the balance-sheet of the fund receives the approval of the Minister of Labour. RULES FOR ACCOUNTING OF REGIONAL FEDERATIONS The Regional Federations open the following six general accounts in their books : an " invalidity " account for the payment of cost of treatment of invalids and invalidity pensions ; a " guarantee " account and an " equalisation " account; an account for " social hygiene, prevention and control " ; a " revenue " account and an " administration " account. Sums collected in respect of the exceptional levy on the surplus receipts of assessment funds are credited to an invalidity reserve fund. Regional Federations close their books at 31 December in each year, and submit to the Minister of Labour for approval before 31 March a balancesheet and a financial account showing the total of the receipts and expenditure since the date of the preceding balance-sheet. They also draw 265 FRANCE up a statement of the negotiable securities, loans and properties held by them at the date of the balance-sheet. The technical accounting of the Regional Federations include compulsorily: (1) a roll-book of invalidity pensions; (2) a list of the individual accounts of persons in receipt of invalidity pensions ; (3) a list of attachments. RULES FOR ACCOUNTING OF THE GENERAL GUARANTEE FUND 1 It was mentioned already that the two funds managed by the General Guarantee Fund contain a number of different items of income and expenditure. It will therefore be realised that it is impossible to give a brief summary of the regulations concerning the books and accounts of the General Guarantee Fund. It must suffice to mention that the Director of the Fund is required : (1) to submit annually to the members of the governing body an estimate of the probable income and expenditure for all the funds and accounts for which he is responsible during the following year; (2) to submit a general report [33] annually on the operations of the General Guarantee Fund, together with; (a) a general balance-sheet showing the situation of the different funds and special accounts at 31 December; (b) a return drawn up in accordance with the latest known statistics and showing, for the Augmentation Fund, the actuarial estimates of the probable charges for the following 30 years. These documents are submitted to the governing body along with the report of the chief accountant; they are then transmitted to the Minister of Labour and the Minister of Finance with the comments of i l . . • 1 J„ tue guvernuig ¿>uu\. R U L E S RELATING TO STATISTICS The old-age insurance funds submit to the Minister of Labour every year, before 1 July, a statement showing in respect of the penultimate year: (1) at each age, the number of individual accounts opened in the name of insured persons entitled to a pension: (a) who were living on 1 January, (b) whose pension was awarded during the year, (c) who died during the year, (d) who were living on 31 December; 1 These were laid down by Decree of 1 January 1.937. 266 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION (2) at each age, the number of individual accounts opened in the name of insured persons aged less than 60 years: (a) {b) (c) (d) (e) who who who who who were living on 1 January, were living on 31 December, died during the year, became members of the fund during the year, ceased membership of the fund during the year. The invalidity insurance funds submit to the Minister of Labour each year, before 1 July, a statement of insured persons entitled to invalidity pensions which have been in payment for not more than five years and showing in respect of the preceding year: (a) the distribution according to age and duration of pension, of invalids living on 1 January; (b) the distribution according to age of invalids whose existing pension has been in payment for five years and has been taken over during the year by the invalidity insurance fund; (c) the distribution, according to age and original year of entry on pension, of invalids whose pension, which had been suspended, has been reinstated during the year; (a) the distribution according to duration of pension of invalids who attained age 60 during the year; (e) the distribution, according to age and duration of pension, of invalids whose pension has during the year been cancelled by death or suspended or cancelled by reason of their return to health; (/) the distribution, according to age and duration of pension, of invalids living on 31 December. The Regional Federations submit to the Minister of Labour each year, before 1 July, a statement showing for the preceding year: (a) the distribution, according to age and duration of pension, of invalids living on 1 January whose pensions are paid by them; (b) the distribution according to age of invalids who entered on pension during the year; (c) the distribution, according to age and original year of entry on pension, of invalids whose pension, which had been suspended, has been reinstated during the year; (d) the distribution according to age of invalids whose existing pension has been in payment for five years and has been taken over by an invalidity insurance fund during the year; (e) the distribution, according to age and duration of pension, of invalids whose pension has during the year been cancelled by death or suspended or cancelled by reason of their return to health; (/) the distribution, according to age and duration of pension, of invalids living on 31 December whose pensions are paid by them. FRANCE 267 FUNDAMENTAL PROVISIONS DEALING WITH THE FINANCIAL CONTROL OF SOCIAL INSURANCE FUNDS AND THEIR FEDERATIONS The social insurance funds and Regional Federations function under the double control of the Minister of Labour and the Finance Minister. In the first place, the Minister of Labour exercises control over the documents which relate particularly to the valuations which the funds make at the end of a year. The control of these valuations, entrusted to the Department for Accounting, Statistics and Actuarial Technique (Direction de la Comptabilité des Assurances, de la Statistique et de l'Actuariat), allows first of all the elimination of mistakes and administrative errors. It also gives prominence to questions, which have not been correctly understood, and points on which the regulations have not been observed, and thus gives the central administrative authority the opportunity of imparting to the funds the supplementary instructions which they need. Moreover, the care devoted to the presentation of the valuations and the rapidity with which they are submitted give the central administrative authority indications which enable it to direct the attention of its inspectors toward those organisations in respect of which an investigation on the premises is particularly urgent. The inspectors and assistant inspectors carry out their investigations on the premises. They are obliged to advise the chairman of the board of management of the fund, society or federation, before beginning their work. The agents, officials and accountants of the fund must allow the inspectors access to the accounts and lists of assets and must show them the investments of every type which the fund may be holding, as well as the vouchers, books, registers, correspondence and other documents needed to give a complete insight into the administration of the fund. The control exercised by the Finance Minister includes, on the one hand, a constant supervision by the local Treasury officials (paymaster generals and Treasury collectors) and on the other hand occasional inspections by Treasury inspectors. The supervision by the local Treasury officials is constant. Every month the various institutions must submit to them a copy of their balance of account. These officials are also invited at least once a year to carry out an inspection on the premises. Every investigation carried out on the premises by the Treasury collector must be followed by a report submitted to the accountant, to the chairman of the board of management and to the managing director of the fund concerned, and a summary of the report in duplicate is sent through the official channels to the Public Accounts Department. In addition, Treasury inspectors may be sent out on a commission of investigation and control in respect of a particular institution indicated by the Finance Minister. In these cases investigation is necessarily much more detailed and extends over all the operations of the fund. The Treasury collectors are entrusted with the duty of ensuring that the irregularities discovered by the Treasury inspectors are put right. 268 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION BIBLIOGRAPHY I. — Parliamentary Documents 1. Projet de loi sur les assurances sociales, présenté au nom du Président de la République française (Chambre des députés, I 2 m e législature, session de 1921, n° 2369). 2. Rapport au nom de la Commission d'assurance et de prévoyance sociales (Chambre des députés, 12 m e législature, session de 1923, n° 5505). 3. Rapport au nom de la Commission de l'hygiène, de l'assistance, de l'assurance et de la prévoyance sociales (Sénat, année 1925, session ordinaire, n° 435). 4. Deuxième rapport supplémentaire au nom de la Commission de l'hygiène, de l'assistance, de l'assurance et de la prévoyance sociales (Sénat, année 1926, session extraordinaire, n° 628). 5. Avis au nom de la Commission des finances (Sénat, année 1927, session ordinaire, n° 213). 6. Rapport au nom de la Commission d'assurance et de prévoyance sociales (t. I : Etude générale, et t. II : Prestations pour la maladie, la maternité et l'invalidité) (Chambre des députés, 13 m e législature, session de 1928, n° 5496). 7. Avis au nom de la Commission des finances (Chambre des députés, 1 3 m e législature, session de 1928, n° 5727). 8. Rapport au nom de la Commission de l'hygiène, de l'assistance, de l'assurance et de la prévoyance sociales (Sénat, année 1929, 2 m e session extraordinaire, n° 750). 9. Avis au nom de la Commission des finances (Sénat, année 1930, session ordinaire, n° 16). 10. Rapport supplémentaire au nom de la Commission de l'hygiène, de l'assistance, de l'assurance et de la prévoyance sociales (Sénat, année 1930, session ordinaire, n° 37). 11. Rapport au nom de la Commission d'assurance et de prévoyance sociales (t. I: Etude générale, et t. I I : Prestations pour la maladie, la maternité, les charges de famille, les soins aux invalides et le décès) (Chambre des députés, 14 r a e législature, session de 1930, n° 3187). IE — Legislative Texts 12. 13. 14. 15. 16. 17. 18. 19. 20. Act of 5 April 1928. L. S.\ 1928, Fr. 9. Act of 30 April 1930. L. S., 1930, Fr. 5. Finance Act of 28 February 1934. L. S., 1934, Fr. 5. Decree of 15 May 1934. L. S., 1934, Fr. 5. Decree of 30 June 1934. L. S., 1934, Fr. 5. Decree of 16 July 1935. L. S., 1935, Fr. 8. Decree of 28 October 1935. L. S., 1935, Fr. 12. Decree of 30 October 1935. L. S., 1935, Fr. 13. Décret portant règlement général d'administration publique pour l'application du décret-loi du 28 octobre 1935. Journal officiel, 22 March 1936. 21. Décret portant règlement général d'administration publique pour l'application du décret-loi du 30 octobre 1935. Journal officiel, 25 March 1936. 1 L. S. = Legislative Series of the International Labour Office. 269 FRANGE 22. Décret du 29 juillet 1936 sur la comptabilité des caisses d'assurances sociales et de leurs unions. Journal officiel, 10-11 August 1936. 23. Decree of 14 June 1938. L. S., 1938, Fr. 7. 24. Decree of 15 June 1938. L. S., 1938, Fr. 10. III. — Administrative Documents 25. Table de mortalité de la Caisse nationale des retraites pour la vieillesse. Notice et tableaux. Paris, 1905. 24. Tarifs d'assurance-vieillesse. Capitaux de couverture des pensions d'invalidité. 2 m e édition. Paris, Imprimerie nationale, 1931. 27. Tarifs d'assurance-vieillesse. Table P.M.F. 1931. 3 m e édition. Paris, Imprimerie nationale, 1937. 28. " Rapport du ministère du Travail sur l'application de la loi des assurances sociales (statistiques du 1 e r juillet 1930 au 31 décembre 1932)" (Journal officiel, 8 March 1934). 29. " Rapport du ministère du Travail sur l'application de la loi des assurances sociales (statistiques du 1 e r janvier 1932 au 31 décembre 1933) " (Journal officiel, 12 March 1935). 30. " Rapport du ministère du Travail sur l'application de la loi des assurances sociales (statistiques du 1 e r janvier 1933 au 31 décembre 1934) " (Journal officiel, 1 March 1936). 31. " Rapport du ministère du Travaile r sur l'application de la loi des assurances sociales (statistiques du 1 janvier 1934 au 31 décembre 1935) " (Journal officiel, 18 April 1937). 32. " Rapport du ministère du Travaile r sur l'application de la loi des assurances sociales (statistiques du 1 janvier 1935 au 31 décembre 1936) " (Journal officiel, 2 December 1938). 33. Rapports concernant le fonctionnement des services de la Caisse générale de garantie. 34. Rapports de la Commission de surveillance de la Caisse des dépôts et consignations. IV. — Studies 35. L'assurance obligatoire contre l'invalidité en Allemagne. Recueil de documents sur la prévoyance sociale (Direction de l'assurance et de la prévoyance sociales). Berger-Levrault & C le , éditeurs, 5, rue des Beaux-Arts, Paris. 1905. 36. Bulletin de la Statistique générale de la France, t. XVII, 1927-1928, pp. 415441. Librairie Félix Alean, 108, Boulevard S*-Germain, Paris. 37. Bulletin de la Statistique générale de la France, t. XXV, fase. IV, 1936. Librairie Félix Alean, 108, Boulevard S'-Germain, Paris. 38. J. FERDINAND-DREYFUS: Les prévisions statistiques et financières des assurances sociales. Les presses universitaires de France, 49, Boulevard S'-Michel, Paris. 1923. 39. E. FLEURY: Commentaire pratique et critique de la loi du 5 avril 1928 sur les assurances sociales. Librairie du Recueil Sirey, 22, rue Soufflot, Paris. 1929. 40. F. NETTER: " Etude de démographie ouvrière d'après les statistiques d'assurances sociales". Journal de la Société de statistique de Paris, December 1935. Librairie Berger-Levrault, 5, rue Auguste-Comte, Paris. GERMANY Invalidity, Old-Age and Widows' and O r p h a n s ' Insurance for Workers CONTENTS Page Part I 1891-1914 INTRODUCTION • CHAPTER I : Demographic Estimates, Bases and Experience 1. Biometrie Tables Cessation of Old-Age Pensions Mortality and Cessation Rates for Invalid Pensioners . . . Mortality of Healthy Persons and Validity Tables . . . . Probability of becoming Invalid Sickness Probabilities relating to Marital Status and to Survival of Dependants • Distribution of Wives of Insured Men in Categories . . . . Distribution of Widows of Insured Men in Categories . . . Difference in Age of Husband and Wife Data relating to Children 2. Insured Population Estimate of the Initial Insured Population Subsequent Estimates of the Insured Population . . . . Estimates of the Number of Entrants into Insurance Each Year Estimate of the Annual Number of Exits from Insurance . Experience 3. Number of Beneficiaries Table of Symbols introduced in Chapter I CHAPTER I I : Financial Estimates, Bases and Experience 1. Contributions Wage Classes and Rates of Contribution Calculation of the Present Value of Contributions . . . . Experience 2. State Aid Calculation of the Present Values of Individual Supplements and Grants Experience 277 278 278 278 279 285 297 301 301 305 309 312 313 316 317 317 319 321 322 322 324 326 326 326 327 329 329 330 330 272 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Page 3. Benefits Conditions of Award and Amount of Benefit Invalidity Pensions Old-Age Pensions Payments to Survivors Repayment of Contributions Calculation of Present Values of Invalidity Pensions . . . Unit Invalidity Pension in the Course of Payment . . . Invalidity Pension in Course of Acquisition CapitalValuesof thelnvalidity Pensions awarded Each Year Calculation of Present Values of Old-Age Pensions . . . . Unit Old-Age Pension Capital Values of Old-Age Pensions awarded Each Year Calculations in Respect of Repayments of Contributions . Calculation of Present Values of Widows' Pensions and Allowances Calculation of Present Values of Orphans' Pensions and Allowances Experience 4. Other Expenditure Administration Expenses and Cost of Medical Aid . . . . 331 331 331 334 335 336 337 337 339 345 346 346 348 349 Table of Symbols introduced in Chapter II 366 CHAPTER I I I : Financial 1. System Calculation of Average Premiums in the Preparatory Investigations General Average Premiums In respect of the Initial Insured Population In respect of Future Entrants . . . In respect of Present and Future Insured Persons together Average Premiums for a Fixed Period Average Premiums for the Normal Period 2. Average Premiums and Annual Estimates calculated as at Uanuaryl900 Present Value of Cost of Benefits , Invalidity and Old-Age Pensions in Course of Payment . . Invalidity Pensions in Course of Acquisition Old-Age Pensions in Course of Acquisition Repayments of Contributions Average Premiums and Actuarial Balance-Sheet. Comparison of Various Premiums. Annual Estimates . . . . j 352 356 363 364 364 369 370 370 370 371 371 372 374 376 376 376 378 379 380 380 3. General Average Premium as at 1 January 1910 Rate of Contribution in each Wage Class State Charge 383 384 384 4. Actuarial Balance-Sheet as at 1 January 1914 In respect of the Insured Population on 1 January 1914 . . In respect of the Annual Crop of New Entrants In respect of the Total Annual Number of Exits Financial Equilibrium 384 384 385 385 386 273 GERMANY Page 5. Financial Organisation of the Insurance Institutions 6. Experience . . . . 387 . Table of Symbols introduced in Chapter III CHAPTER IV: Financial 389 390 Administration 392 1. Investment of Funds, Statutory Provisions and Regulations 392 2. Statistics of Investments Composition of the Accumulated Funds Interest Yield 393 393 394 3. Actuarial and Financial Control. — Statistics Actuarial and Financial Control Statistics . BIBLIOGRAPHY 395 395 395 396 I. Legislative Texts II. Reichstag Documents III. Administrative Documents IV. Studies 396 396 397 397 I N D E X OF T A B L E S I. II. Rates of Cessation of Old-Age Pensions General Mortality and Mortality of Pensioned Railway Employees III. Cessation of Invalidity (1891-1897 Table, common to Both Sexes) IV. Cessation of Invalidity (1906 Table, common to Both a. «\ OCAC&J 278 280 282 QQc «vv V. Mortality of Invalids 289 VI. Validity Table and Mortality Rates of Healthy Lives (Males) 290 VII. Validity Table and Mortality Rates of Healthy Lives . 293 VIII. Validity Table (Females) 295 IX. Mortality of Healthy Lives 296 X. Rates of becoming Invalid 298 XI. Rates of becoming Invalid (Probabilities in 0.00001). . . 300 XII. Survivorship Factors for Widows and Dependants (Insured Men) 302 XIII. Probabilities relating to Marital Status and Survivorship of Dependants (Insured Women) 304 XIV. Distribution of Wives of Insured Men by Age and Category 308 XV. Probabilities for subdividing Widows of Insured Men in Categories 310 18 274 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Page XVI. XVII. XVIII. XIX. XX. XXI. XXII. XXIII. XXIV. Difference in Age of Husband and Wife Life Table for Children (Both Sexes combined) Age Distribution of Children according to Age of Father Probabilities t\x that an Insured Man aged a; is the Father of a Child under 15 Years of Age Total and Insured Populations (from the Industrial Census of 12 June 1907) Insured Population (as at 1 January 1914) Movement of the Insured Population during 1914 (Estimates in Thousands) Total Number of Pension Beneficiaries: Experience . . . Number of Lump-sum Payments made as Repayments of Contributions Present Value a.x of a Unit Contribution payable Weekly at 3.5 Per Cent. Interest XXVI. Weekly Contributions received Each Year by Regional Institutions XXVII. State Grants — Experience (in thousand Marks) . . . . XXVIII. Present Value of an Invalidity Pension in Course of Payment, payable Monthly, with Interest at 3.5 Per Cent. XXIX. Present Value of an Invalidity Pension in Course of Acquisition, payable Monthly after 4 Years Waiting Period, with Interest at 3.5 Per Cent XXX. Present Value of an Old-Age Pension in Course of Acquisition, payable Monthly, with Interest at 3.5 Per Cent. X X X I . Present Value at Death of Husband of Right to a Widow's Pension and Allowance, with Interest at 3.5 Per Cent. X X X I I . Present Value of the Right to a Widow's Pension and Allowance in respect of an Invalid or Insured Person at Any Age, with Interest at 3.5 Per Cent X X X I I I . (a) Present Value of the Right to an Orphan's Pension ceasing at Age 15, with Interest at 3.5 Per Cent. . X X X I I I . (b) Present Value of the Right to an Orphan's Allowance payable at Age 15, with Interest at 3.5 Per Cent. . XXXIV. Average Annual Amount of Pensions: Experience (in Marks) XXXV. Total Amount paid Each Year in respect of the Various Benefits: Experience XXXVI. Administration Expenses and Cost of Medical Aid: Experience XXXVII. Annual Estimate of Expenditure on the Scheme . . . . XXXVIII. Financial Results from the Inauguration of the Scheme until 1913 XXXIX. Distribution of Total Investments 312 313 314 315 318 319 321 323 323 XXV. 328 329 330 338 343 347 355 357 360 361 363 364 365 382 389 394 275 GERMANY Part II 1924 ONWARDS Page INTRODUCTION 399 CHAPTER I : Demographic Estimates, Bases and Experience . . . . . . 1. Biometrie Tables Invalidity Rates Rates of Cessation of Invalidity and Old-Age Pensions. . . Award of Widows' Pensions Rates of Cessation of Widows' Pensions 2. Insured Population Experience . . . • 3. Number of Beneficiaries 1927 Estimates Investigations Preparatory to the 1933 Reform Experience ' 401 401 401 401 403 404 404 407 408 408 408 410 CHAPTER I I : Financial Estimates, Bases and Experience 413 1. Contributions . . Wage Classes and Rates of Contribution Estimates of Contribution Income Experience 2. State Aid 415 3. Other Receipts Sums credited as Interest Income Grants from the Unemployment Insurance Scheme . . . . 417 417 417 4. Benefits Conditions governing Award of Benefit Amount of Benefit Maintenance of Benefit Rights Preservation of Rights in Course of Acquisition in the Case of Transfers between "the Workers' Insurance Scheme and the Salaried Employees' or the Miners' Insurance Scheme (Wanderversicherung) Estimates of the Annual Cost of Benefits Experience 417 417 418 420 421 422 423 Other Expenditure Administration Expenses Cost of Optional Medical Benefits Contributions to the Miners' Insurance Scheme Repayments to the Salaried Employees' Insurance Scheme 425 425 42& 426 42& 5. . CHAPTER I I I : Financial System 413 413 414 415 427 1. Tables of Annual Estimates Estimates of Receipts and Expenditure from 1927 to 1931 Estimate of Receipts and Expenditure from 1929 to 1938 . 427 427 428 2. Annual Results of the Operation of the Scheme 429 3. Actuarial Balance-Sheets 430 276 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Page 4. Consolidation of the Financial Position (Act of 21 December 1937) Grants from the Unemployment Insurance Scheme . . . . Supplementary Payments made by the Reich Government CHAPTER I V : Financial 1. 2. 3. Administration 432 433 433 434 Investment of Funds. — Statutory Provisions and Regulations Authorised Classes of Investment. Provisions Peculiar to Certain Classes Statistics of Investments Composition of the Fund Interest on Invested Funds Interest Yield 434 436 436 437 438 Statistics. — Actuarial and Financial Control Statistics Actuarial and Financial Control 438 438 439 . BIBLIOGRAPHY 434 439 I. Legislative Texts II. Parliamentary and Administrative Documents III. Articles IV. Books , . . 439 440 440 441 INDEX OF TABLES I. Probability of becoming Invalid II. Rates of Cessation of Invalidity III. Estimated Movement of Insured Population, 1930-1970 . . IV. Estimated Annual Number of Beneficiaries . V. Number of Beneficiaries: Experience VI. Age Distribution of Pensioners : Experience VII. Contributions: Experience VIII. State Aid: Experience I X . Total Annual Amount of Benefit Payments made by Institutions X. (a) Average Monthly Amount of Current Pensions: Experience (b) Average Monthly Amount of Newly Awarded Pensions: Experience XI. Total Amount of Pensions paid Each Year: Experience . . . XII. Probable Financial Progress from 1927 to 1931 XIII. Probable Financial Progress from 1929 to 1938 XIV. Financial Progress: Experience ; XV. Balance-Sheet as at 1 January 1933 XVI. Total Amount and Distribution of Investments : Experience . 401 402 405 409 411 412 415 416 423 424 424 425 427 429 430 431 437 PART I 1891-1914 INTRODUCTION Compulsory social insurance against invalidity and old age was introduced in Germany by the Act of 22 June 1889 [1]. The Imperial Government tabled a draft Bill in 1887 and the final Bill [4] in 1888. The latter was laid before the Reichstag on 22 November 1888 and after a number of amendments became the Act of 22 June 1889, which came into operation on January 1891. The 1888 Bill was accompanied by an explanatory statement [5] and a financial memorandum [6] to which was attached a mathematical appendix [7]. In the course of the debate in the Reichstag various other memoranda and notes were published [8, 9,10]. The 1897 [11] and 1899 [14] Bills and the accompanying memoranda [12, 13, 15, 16] prepared the way for the Act of 13 July 1899 [2], which came into force on 1 January 1900. The 1909 Bill [17] and its appendix [18] led up to the fourth book of the Social Insurance Code [3], by which the benefit of compulsory insurance was'extended to widows and orphans as from 1 January 1912. An actuarial analysis [19] of the financial position on 1 January 1914 showed that the contribution scales in force since 1912 were sufficient and that there was even a surplus, relatively of small importance, of 270 million marks. Thus, up to that date, the financial progress of the scheme had been within the limits laid down in the actuarial basis. The war and the monetary depreciation which followed completely altered this relationship. The accumulated funds disappeared almost entirely: from 2,105.5 million marks at the end of 1913 they decreased to 329.6 million RM. at the end of 1924. From the point of view of actuarial technique, with which this study is concerned, the years 1913 to 1924 must therefore be considered as abnormal and consequently the examination of this period can hardly serve any useful purpose. Part I of this study therefore ends at the end of 1913, leaving for Part II the period beginning with 1924, after the monetary inflation. CHAPTER I DEMOGRAPHIC ESTIMATES, BASES AND EXPERIENCE § 1. — Biometrie Tables The tables to which attention will be drawn in this paragraph are those which have been used directly either in preparatory investigations or in investigations leading up to amendments made during the operation of the scheme. A large number of other tables must be disregarded •which were used for the purpose of making comparisons but were not finally adopted 1 . CESSATION OF OLD-AGE PENSIONS With the help of data obtained during the early years of the operation of the scheme rates of cessation were calculated applicable to old-age pensioners who had attained age 70. The data were derived from 278,631 old-age pensions and 25,984 cases of cessation by death, commutation, suspension or other causes and, after interpolation and graduation, the following table of rates of cessation was obtained [13: p. 3579]: TABLE I. RATES OF CESSATION OF OLD-AGE PENSIONS Age Probabilities in 0.0001 70 years. . . . 71 » 72 > 73 » ? 74 75 . 76 » 77 > 78 » 79 » 80 » 81 > s 82 3 83 84 » 85 . . . . . . 692 728 768 817 880 953 1,033 1,123 1,219 1,321 1,429 1,543 1,663 1,789 1,921 2,059 Age 86 years. . . . 87 » 88 » 89 » 90 » 91 » 92 » • 93 » 94 » 95 » 96 » 97 » 98 » 99 » 100 » Probabilities in 0.0001 2,203 2,353 2,509 2,671 2,839 3,013 3,193 3,379 3,571 3,769 3,973 • 4,183 4,399 4,621 4,849 1 Information regarding some of these tables and in some cases a partial reproduction may be found in Nos. 23 to 26 in the Bibliography at the end of this Part. 279 GERMANY MORTALITY AND CESSATION RATES FOR INVALID. PENSIONERS The mortality of invalid pensioners was first calculated by reference to two tables: a table constructed by Zimmermann 1, based on the mortality of pensioned German railway employees, and the table of general German mortality in the period 1871-1881 2. These two tables are reproduced in table II. Zimmermann's mortality rates are lower than those of similar tables constructed for other industries and from age 69 onwards are even below the general mortality rates. Zimmermann's figures were adopted to. age 69 and thereafter the general mortality rates were used [6: p. 77-81]. An examination of data obtained during the early years of the social insurance scheme indicated the need for adopting select cessation rates for invalid pensioners taking into account the duration of invalidity. Accordingly attention was given to the substitution for the aggregate table of mortality in use until then of a double-entry table giving cessation rates of invalid pensioners according to age and duration of invalidity. The first investigations [13: pp. 3580, 3581 and 16: p. 26-29] dealt with 65,994 cards relating to invalidity pensions which were first awarded in one of the eleven quarters in the period 1 October 1891 to 30 June 1894. The probabilities of cessation were calculated according to the age and the number of the quarter in which cessation occurred (quarter 0 being the quarter during which the pension commenced to be paid), by means of the following formulae: 0EX 4 oI * lEx \&x — 2 l'-x i o*x e^x rEx In these formulae, rlx represents the number of invalids aged x who came under observation (at the date of the decision establishing title to pension) during the quarter r. rEx represents the number of cessations of pension which occurred at age x during the quarter r. 1 Über Dienstunfähigkeits- und Sterbensverhältnisse vom Jahre 1884. 1886. 2 Statistisches Jahrbuch für das Deutsche Reich 1928, p. 40. Berlin, 280 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE II. GENERAL MORTALITY AND MORTALITY OF PENSIONED RAILWAY EMPLOYEES Age 16 years. . . General mortality Zimmerrates: total mann's German invalid population mortality table rates 1871-1881 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 » " » » » » » » » » » » " " » » » » » » 0.00451 0.00531 0.00610 0.00685 0.00750 0.00805 0.00853 0.00852 0.00847 0.00848 0.00855 0.00868 0.00885 0.00905 0.00928 o!o0954 0.00984 0.01019 0.01058 0.01101 0.01148 0.01199 0.01253 0.01308 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 " » » » » » » » » » » » » » » » » » » » 0.01363 0.01418 0.01475 0.01537 0.01605 0.01680 0.01761 0.01848 0.01941 0.02040 0.02145 0.02256 0.02374 0.02501 0.02639 0.02790 0.02956 0.03139 0.03342 0.03568 17 » n »» 0.1182 0.1141 0.1100 0.1060 0.1020 0.0981 0.0943 0.0905 0.0868 0.0831 0.0795 0.0757 0.0720 0.0685 Age 60 years. . . 61 > 62 63 64 65 . 66 67 68 69 70 71 72 73 nr 0.0640 0.0640 • 0.0640 0.0639 0.0639 0.0639 0.0639 0.0639 0.0633 0.0622 0.0599 0.0583 0.0558 0.0546 0.0530 0.0525 0.0520 0.0516 0.0512 0.0510 0.0503 0.0496 0.0486 0.0485 0.0485 0.0487 0.0489 0.0495 0.0501 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 s > ) i 9 Ï i S > » > ) > » 1 ï ! » ï ) » > > ï J ) » î ) » » » y > } ) ) 3 General mortality Zimmerrates: total mann's German invalid population mortality table rates 1871-1881 0.03820 0.04100 0.04409 0.04748 0.05118 0.05520 0.05956 0.06429 0.06942 0.07500 0.08108 0.08770 0.09489 0.10267 0.11105 0.12004 0.12965 0.13989 0.15077 0.16230 0.0512 0.0529 0.0550 0.0573 0.0602 0.0629 0.0653 0.0685 0.0715 0.07500 0.08108 0.08770 0.09489 0.10267 0.11105 0.12004 0.12965 0.13989 0.15077 0.16230 0.17448 0.18731 0.20074 0.21467 0.22900 0.24363 0.25846 0.27344 0.28852 0.30370 0.31902 0.33457 0.35047 0.36689 0.38404 0.40217 0.42158 0.44259 0.46560 0.49102 0.51930 0.17440 0.18731 0.20074 0.21467 0.22900 0.24363 0.25846 0.27344 0.28852 0.30370 0.31902 0.33457 0.35047 0.36689 0.38404 0.40217 0.42158 0.44259 0.46560 0.49102 0.51930 281 GERMANY From these probabilities relating to quarters, annual probabilities were obtained by the use of the formulae: a W = 1 — (1 — ,<7X) (1 — 1> O T H CS CO * * CO CO CO CO CO OiO) O O O O O O TH T « o o o o © © o o i OS + + 00 + t> e2 * «3 S C irt -a" + + o © CS SO 00 CM xri * H (M co co <^ -«^ *# O I O O I COCO*Í *-l «rH *-l O O O o O *í -H O o r^ oo oo os ^t* ••# «^ • # ••# o o CO O0 CTS O ^H HrHrHCqiN IO CS O CTS CTS . O ^H CS CS CO CS CM CM CS CS *H -r* -TH ^ H «r» O O O O O O O O O O O O TH - ^ ^H ^H CS o o o o o o o o o so *r« r^ co CT* O O O O O O o r^ oo ers o O *r< ^ H ^H ^ T H O O O O O O O CO CO IO s * v# es o o o r t l O O W O © CM 00 Oï Os Os O* OS » i « * - * « * ~* O O O O O o intot^cocs o ' o ' o o o O O O O es o o o o o o o © o © CTS CTS CTS CTS CM CM CO * # SO CM CM CM CM CM O O O O O t o t o r^ co ers o o o o es ©" o ' © ©' o l O O W O l ß CO * # ^ I O l O co co co co co o o o o es O »* O O O O ^lOlOiO CS CS CS CS CS CS © O ©_ © © CO CO ^ O o r^ oo ers cO CO CO CO CO © © © © © o ' o ' ©' ©' © SO © CO I > ^H *H -ÇH CM CS CO o o o o o o o o o o o o o o o o o o o o o o o o c-> r^ o o o o o o i> o o o o o o o o o o o o o o o .TH O O O O o o o o o I O ^ CO CM *H o o o o o o o o o o o e i x t > t o TH «r< o es o o o o o o es' o o o o o o o o o o o o o o o r^ i o co -r« os o o o o o o o o o o o o r^ o o o o r% o o o o o o C> I O « H T H *TH T H *TH o o o o o o o o rH -»rl T H T H o o © o o o o o o o o 0> ^« o o © io © o o o o o o o o o o « « ( N I M M * # o o o o © © © © © © © © © © o o r^ o ©' © © © © © © o © © © CTS CTI Cft CTS o i > r^ r^ r> rx © ©_ ©_ ©_ ©_ ©' o ' ©' ©' ©' © © © © © IO » * CO CM ^H Oí CT* CTs C^ï CTï r M O C 0 r - i Oi (N(NMfMrH CO CO CO CO CM O o o o o I O I O SO * í - # o o o o o o o o o o o o o O 0Í H-i ^H *rH T H *r4 *H O O O O O O O •TH * H -TH ^ H * H £ - ^s* K^ »^ »^ ^^ O O O T H *TH o o o o CO co co co co co c o i n » « « © © ORGANISATION 2 3C + 10 Age attained by the invalid when the rate of cessation of invalidity coincides with the mortality rate of the total male population ACTUARIAL Probabilities of cessation of pension during the following years after date of award of pension 282 O O O O o o o o o o i n o i o o <* co co es CM CM CM es es CM o o o o es cq M IM CN ^T* o o o o o IO O IO O lO ^ H T H O O OÍ o o o o o o o o o o o o es o es' o o o o o i o o e* co a> O i o «O r>» co (M ( N (O IO » * C0 CO CO CO CO CO e >> O *H SS CO * # ^H CM CO "# CO CO CO CO CO 283 GERMANY Ctf K Ol fi « " " " © r i C^ CO - # KO KO, LO LO KO KO CO t-N G0 © KO KO KO LO KO Or. O v f Oï CO v f v f O O CS CS CO CO CO O O O O O O O O o d c o O o M v f r-» r i es es n C0 v f cO 00 CO CO CO CO CO o o o o o o o o o o CS * # r » CO CO CO CO CO t N O O O l N ^ CO C0 v f - ^ v f o o © o © o o ©' o o o o o o © © © © © ri - # vf v f v f •*# o o o o o o o o o o moiooifl CO *# v f LO »O kO KO ILO I O I O o o o o o o o o o o o o r^ o o o o r^ o o o o r* o o o o o o i>. r>. o o o o o o o o o o © oo r>- co {Jl 00 0 0 CO 0 0 o o o o o o o o o o » O O W í O í O cO v f r i © CO r i n ^ r t O O rf r ¡ W r i H .O Ö O O O N»Í00( KO © t-» Vf Vf Vf O O © U © lO O N( © Vf O o o o o o © © CO CS r i O ri vf O n vf vf O KO CS IT^ r i v f KO O O o o o o o rMNOr es © © KO O CS LO © ©" kO r l CO i O KO KO © © ©'© 0 0 CO CO CO KO LO ©, © '©'© © r l CS CO v f cO cO Í O cO Í O ©t © © © © © © ' © ' © * © ©* © r l GS vf GO © © oo r-» co Q0tM>r»i> O © © © © © ' © © © * © ' © vo © vf © © o CS © © ©' ri © © ©" © o . © co co © i O © © CO c o © © © © © © " © ' © © © " l O \0 KO O © © es vf r>. © CÛCOCD C D t N © © © © ©# © ' © * © ' © ' ©' l O !>• © i O l O I O © O0 © *H © © © © © © ' © * © ' © * ©* © es © es r^ © r>. o ©' -r-i r-» ©_ ©' CS r-. ©# ©' CO o* © ©* vf c~* © © © © © © &> © © © © © © o © © © © o o o o o 0 > O r i r% © LO KO vf CO CO CO CS CS M í N N - - " - r»00 o CS CO v f KO CO S S S KO © © © © © © © © es co vf KO © CO CS r f © © io © © © ©"©'©"©©* © © " © ' © " ©' es es es es n s £ cD00l>r(CO © 0 0 TH VO 0 0 IM>O0COCO © © © © © © ' © ' © * © © © r~» © © © © o o o o © © © © © , v f r>. ^ H i o © IMMÄCOffi © © © © ©_ © ' © " © * © ©' © iO CS OO © © >-H © © vf •«rH ^H o © © iO O IO CO lr>. -rH © ^-t C-N C-» OO OO © ©_ © ©_ © © t ©" ©" ©" © ©* © © © © *-I © -H ^-f © o o o o © © © © © ©*©*©'©"© IO KO 00 © ©* r% es r-* es oo co co es es ri c o »O KO v f v f ri rHr< ri ri O O O O O ~ "R E E I O © C* 00 © © n CS CO vf vf vf vf vf vf i O KO KO KO KO © co c^ oí r^ vf r-» r-» oo oo © © IO OO © ©' KO © © io © vf co co I O i O IO iOlO vf v i CO CO © ©# © ' ©" O i O O W O ÍO oo c^ r-N © io E £ S S S © CS CS ©' •«H KO © iO OO © ©' o O l O O W O vf -ri CS ©" KO KO © KO KO t O v f CO ^rH © © ^H es co vf © © 00 ©# ©' o o o o © © co © TH ^H ^H TT* es es o © ©* ©* ©* LO © © CO CO 0 0 © © ©* © ' o vf t>. -rt ©* © KO KO © 0 0 e s TH © © © ^H es co co KO r < n r i r < r l © * © " © © ' ©* es © vf es es I O © i O KO I O © © © i > oo T-4 CO © © r~» r-» r-» e-* i>., © r*. co oo co co o o © o © © © © © © © ' © © ' © " ©* o ©'©*©'©' ö o o o C-N © CO CO © © © es es es co vo © r-* co © © vf r~» oo oo © © © © ©# © *H © ©* ©' ©* ©* © © © © o o o o o o o o o o o o © © © © © © ' ©* © ©* ©" IO © © © © KO Vf CO CS r l 0 0 0 0 OO OO 00 es es co co vf co r-* r i co r» © © TH es co vf OO 0 0 0 0 0 0 r i r i r l r i r H ©" © ' ©* © ©" O O C N Í O O CO 0 0 © CS KO v f v f i O KO KO © © © © ©# ©" © ' © ' © * © © © r t CO © © © © o o © © © © © © © ©'©*©"©"© © © o o o o o o o o © © ©# © © ' ©* © ' ©* © © r^ oo © r^ t-» r-* r-» e-* 0 0 KO 0 0 CO © © - © © © © © © c-* LO KO © vf oo es co © loiotocor* o o o o o o o o o o "CS © CO v * © LO © v f © LO © ^ es co vf OODlOOOr* vf vf ^ vf iO © © © © © ©"©*©*©©" © co r-> oo © o o o o o o o o o' o i O KO KO KO ITS © c^ oo © cO cO © cO cO LO © © KO © OO © CO 0 0 © oa © © ©" © ' ©" KO © © © © ^ ^ "^î ^H ^ ©'©*©' © © © co KO co r^ es vf r^ © © r^ oo © © ' ©* ©* ©" © I O KO i O © © r^ KO co es © © -ri CS CO «H r ; r ( r i r t o ©'©*©* © © i O CO KO CO ^H -r-i es vf c^ © © © © © © © es © © LO CO e s TH T H e s C0 Vf KO © T H r - ¡ T-i r H ©*©'©*© © © KO © ' © © r^ co © r» vf T * T-* °. ^ ^î ^ ^ © © © " © * © ' vf io © r>> oo « r ¡ r< r ¡ r ¡ © ' © © © ' © ' KO vf t> ri ©* © ' © ' © * © * ©" © © © © CO KO co es es es KO © ^ r¡ rt r¡ ri © * © " © © ' © © KO KO KO © © ° ^. ^ ^. ^ es co vf O O O ^ H r4 co r*» es r-> co © © © © «e-t O O r i r H ^ ©'©'©*©*© © © ri r¡ ri ri ri © " © © © © " ©" © * © ' © • © KO KO ri ri o KO © © © KO © © © KO KO © © co co © io © © © © © TH © © ^H T-¡ -r¡ © co r^ © vf co © © © © © © © TH ^H -«-H o ©'©'©'© © KO © © vf co es r i es co vf KO KO © © n oo KO CS CS CO r ¡ r* r i © ' ©* © © KO co vf ri ©' © es oo vf © tr^. r i n es co co ri ri r* ri r i © " © ' © * © ' ©' © r> © © © © IO © © K O co © es KO oo © © © © © © © n TH ^ t © © © © © KO © © © © KO i n , KO *H © TH CO es © I O KO © K O © r-* © © KO KO KO KO KO © KO KO co © es ©*©*©'©© ö ©' © ©* ©* KO Vf - # CO CO rH T ^ r i r ¡ r i © ©' ©' ©' © 5 S - S R es es es es es © © ri n ri ri © © © © ri © es r^ es r* co r i -«n es es co es es es es co VH r j r i r i S E S S E iO © !>• 00 © © © © © cO R Í E S E r* 02 w 0 1 ¿3 r H rOi 00 S oo m + ul 100 to CO •* (N o O Oí *-t CO o CS tO t O tO es •*« e s »o 1M 1 1 11111 11111 o Ol CS CS O to i o CO CO -J< LO C i CS O O CO CO CO O l •«* r^OOOrlCO es es co co co d o o d d LO O» O CS t O O tO * * CS TH i o t o co o cs CO CO CO *3* <£ d o d o d t o t o o co es L O T H o i , 'ÌtOOlrH - # <}4 O *# ce c j <-i . o 00 CO 00 CO O l ifJ^OOO-H es es es co co d o ~ d d o" to *3* co co o wo d i O tO i o to co co d o to r i Oi *# d i 1 i' i i to LO co co ^ k f ì es es o o* 0 01 ^M co o tO WO O l O O O CS O trx ** *H CS O LO C0 I>. 1> O * * Cv O <3* d C M Ä O - r i N T - ¡ T H es c i es d o" o * o o CS s^ ITN O -4* CO 1 1 - TH *r¡ TH T-J CS d d d d oi tO tO co o • o ** 00 CO o r>. o t o CO O* < f O *H CO co co CQ d o o io O IO co o" oi to to CO d r-* oo co 0 0 0 es co o" d LO es t o CS T-< O CS *d* «J* d o o •»# oo CO to t o CS WO ^ tO * # •*$• d o es t o t o es ^ cs o es s# "¿H *3* *jj* ó<ó<ó<ó o cs v * CS oo o co < f o* o t o t o o co N i O H f f ï < * tO O l T-i . oo cs es es es o d o d r-v o t o wo o i CO O l <& O tO O T H CO LO tO co co co co co o d o o d 00 O IM - * tO CO *^* "^ *4* * # o o o" o o r v o t o L O •*# * # O l CO CO CO rítN'J'íOr» es es es es es i o r^ o t o wo CO CO O l *H O o o o n c o i o es co co co co o o o o o tO OO 0 < M - * CO CO "¿)* * i l * # d d o d o CS to s* co co <¿ to iH (M vi o' to (M ^ *í o to iO tO ^ o' o ^ Ol ** o' co Ol ^ IO o' IM IM O ^ to TH (M v^ tO IM *# ^ tO IO tO ^ O "ri Ol <í o' o' o' o' o o d oc>ö O l O IM tO IO O O O O O W0 vt< oo ^ es o" O TH *3* * # •>* * # * # © d o d o d LO O O O L O 0 1 I > tO t p t-» co •*# L O O r** r i rH rH T ^ - H d o d o o* ri oi O O O CO I>. CO CO ILO l > O w t û t M » o tO l O Oí O *# O tO,** CO I O CO 00 CO CO CO CO o d d d r* o CO O l O r* co co o d r» o t c w * # •»í O l CO 00 CO T H es . o CO CO O l o O O n CS CO CO LO o wo co <¿ oí to to co <¿ o es * # es oo o co • # d ó co M I O T H O I , JIIÛC1H • ^ * * * # IO 1 o' o o o X > 1 00 Age at award of pension O Probabilities of cessation of pension during the following years after date of award of pension 0a " 0.4910 0.5193 i i o etí ~ 0) * 0.4656 0.4910 0.5193 Mortality rates for the total male population 3C + 10" ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Age attained by the invalid when the rate of cessation of invalidity coincides with the mortality rate of the total male population 284 ni £ s >> t o r^ oo o í r » r^ r^ r » r>» LO I O tO t-N 00 OÍ O l O l O l Ol Oí 285 GERMANY The investigations were further extended [21] to cover 444,654 invalidity pensions (311,540 males and 133,114 females) which began to be paid from 1891 to 1899, that is to say before the amendments to the scheme introduced in 1899. The cessations were observed from 1891 to 1903 and included 210,482 cases. Calculation was made not only of select rates for durations not exceeding eleven years but also of ultimate rates for longer durations of invalidity. Finally, three tables were published in 1906 in respect of males, females and both sexes respectively. The table for both sexes combined is reproduced below (table IV, pp. 287-288); it has become classic in the theory of social insurance. For the calculations relating to supplementary benefits awarded to survivors it was necessary to use a table relating solely to the mortality of invalid pensioners. Reference was made first of all [18: p. 544] to the table of the Prussian railway pension fund (1895-1898 experience) and later [19: p. 32] to the rates—appreciably smaller than these— in the table of the Prussian and Hessian railways, constructed from the experience in 1908-1912 of 76,653 years of exposure and 6,128 cases of death. These two tables are reproduced below (table V, p. 289). MORTALITY OF HEALTHY PERSONS AND VALIDITY TABLES To obtain mortality rates for healthy persons recourse was had, in the first preparatory investigations, to an indirect method in which there was first constructed a " validity table " (Aktivitätsordnung). For each age there was calculated the number of survivors, divided into healthy and invalid lives, out of an initial group of healthy persons at age 16, by means of the formulae Ihi ~ fa — he 1 — — hi Jaa T -L- h\f hi k=C + £ where the values of lx were calculated by a continuous process as follows 1: £ = C¿ 1 6 (i-f) C = C v ( l - y ) 1 l + t (1 - a17) , etc. i6> li7» e*c-> represent the annual rates of becoming invalid. p. 297. See below, 1 1> o o o o o o o o o o o o o o o o o o o o o co ce en CM +• CD + i« 0 s CO Oí ^3* co o o io io co co o o o o v * H I N C0 • * I O •c}* "*3* *•# * ^ *•# © t-N 0 0 © © •># * # »•# •»# I O t H CN CO » * I O vo vo vo vo v o rH © co © ^ H e£) ^ H r-» r-» oo co co c o © © © © -«ri O * # T H 00 © © O ^ co co co » * fcd* © <* 0 0 0 0 I > CTS CN CO « ^ I O * * * * v# < # © © © ©* © ©" © ' © * © ' © © ' © ' © © " © * © © © * VO © < * 0 0 CM © © IO © © 00 © © © O co co.co . ^rH TH CN CO h # * * * * ^ # <ÍH » ^ © tx> © co © © © © © co co co co co o o o o o co co co co co © © © © © © © o © © © ' © * © * o © ' © ' ©* ©* T H ^ 0 0 T-t I O 0 0 0 0 0 0 CT» co co co co co co ^ i o © co (Ti © © © *4 CO > © tM i o CN CN CN CO CO * # * # v^ » ^ v# 00 ^

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Ol > S. « n •< Probabilities of cessation of pension during the following years after date of award of pension «5 Os Í oo t» CO *£> -* O 00 CO vi O vil vil CO O tO «O CO O O O » CO 00 T * CO vi» o o o o o o o o o o 2 ' 1 i I + 1 2 6* Í s O O O» 0 0 «r< - d * iß I ß o ' o ' o o ' o" O O O O O co co co co co o o o ' o' o" o"o o o o o o o o o o * r l CO t O CT» * - t ^ * # v i v i Vß CT» CO CO v i ^ OO f * CO t O CTS o co v i v i v i v i o o o o o o o o o o t O v i l CO CO v i l t O O O O C 1 - # CM CM CO CO CO t O CT» CO 0 0 v i t O 0 0 <^H CO t o CO CO v i v i v i o ' o o ' o' o" o ' o " o ' o ' o" o o o o o o o o o v i to o» co co ^toco^co co co eo_ v i v i o © © o' o o o o o o o o o co o» to vi* co CO «* O 00 O CM SS1 CS¡CM CO o ' o o ' o' o o o o o o o o o o o o o O O o o o o O -í O O o ( O v i l CO CO incoo« co co o o o o o CM CM CM o o o vit ^H 0 » 0 0 t O CT» r i v i ' vit vii I ß » ß o o' o' o o CT3 « j i ( Q u ' I.O CM v i t O 0 0 ^ H CO CO CO CO v i CO t o O » ' T i vift v i v i vit I O i ß o' o o o o © o o o o o o o o o © © © © o CO CO CT» t£> v i r ^ C O - í « C O CM CM CM < N C S CO CO - 3 * t O CT» O CM v i t O CO CO CO CO CO CO CO 0 0 v i l « CT» T ^ K t D O r t vit vit vit v i l Ó o o' o o' o ' © © o ' o" o o o o o o o o o o o o ö o o o o o © ©' © v i CO CO 0 » t o O f t CO v i t O ( M ( M CM CM CM " * C 0 O 5 s # t O OO O CM v i t O CM CO CO CO CO CT» CO 0 0 v i l ^ 4 CO TH CO t O CT» CO vît v i l v i t v i l o o o o o ' o o ' o o O o o o o o to v i co co v i O O O O O t O O» CO 0 0 v i t IO O v O» ^< O í C O CM o O O O O C O O i * i CO v i CM CM CM O O O O t O 0 0 © CM v i CM CM CO CO CO to oo -«H co to o o' o o o o o' o o o' CO CO v i t v i l v i l O O o o o o o o o o o o o o o o O o O O o v i ^H O» 0 0 t O O » ^H v i l vil .vii i ß »O O » t O v i t CO CO v * t o 0 0 O CSI CM CM CM CO CO O O o o o o o o o o o o o o' o i c o m o o to oo o v i oo to rv o» o ^ o o o o o o o o o o o o o o O O O v i l t O CT» CO CO v i l t O 0 0 - r * CO CO CO CO v i t v i l o o o 0 0 O v i 0 0 CO C M J i O ^ C O •*-! ^ CM CM CM o o ^ H ^ « « r l CM CM CO CT» t O v i CO CO v i t O 0 0 O CM CM CM CM CO CO vît t o CT» CO CM v i l t O 0 0 ^ CO CO CO CO v i l 0 0 v i l ^ O» 0 0 CO t O CT» * - l v i t vil vit vît i ß i ß o o' o o © ' © ' © ' © © o ' o o o" o o o o o o o o o o o o o o o o o o o o to to oo o v i »o to rv o» o o o' o ' o' o Age at award of pension O -r* CT» v* co co v i *M er» O I O O I Ü O - O v i tO v i O C O C S ^ t Û C f t O O * »9" t O OO O CO ot O CO O» CO • * CO CO v * t o 00 O C M v i tO CM CO CO CO CO + o CT» CT» CT) CT» o o o o Ì o CT» O ) O ) O ) CT» 0.4910 0.5190 0.5480 0.5190 0.5480 0.5480 ÍÍ - s s s s 0.4910 0.5190 0.5480 0.5190 0.5480 0.5480 288 o o CO CO O » t O v i T * CO v * t O 0 0 CM CM CM CM CM CO CO v i t t O CT» O CS] v i t O 0 0 CO CO CO CO CO o' o' o ' o' o ' o ' o ' o ' o ' o" »o to r>» oo o» O r l M W v « CT» CT» CT» CT» CT» CO 0 0 v i ^H CT» • H CO t O CT» v * • »ii - i t vii «#' » ß o o' o' o' o o 00 - i »ß sL e • • •• O " r l CM CO v i .CO 0 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 I ß t o C-v. 0 0 CT» CT» CT» CT» CT» CT» o 289 GERMANY TABLE V. — Age 1895-1898 Table of the Prussian Railways Pension Fund MORTALITY OF INVALIDS 1895-1898 Table of the Prussian Railways Pension Fund 1908-1912 Table of the Prussian and Hessian Railways Pension Fund 58 years 59 » 60 » 0.082 0.081 0.081 0.0752 0.0749 0.0734 61 62 63 64 65 66 67 68 69 70 » » » » » » » » » » 0.080 0.080 0.080 0.081 0.082 0.083 0.084 0.085 0.087 0.089 0.0712 0.0683 0.0656 0.0637 0.0626 . 0.0628 0.0635 0.0656 0.0682 0.0706 71 72 73 74 75 76 77 78 79 80 » » » » » » » » » » 0.093 0.098 0.103 0.111 0.120 0.130 0.140 0.151 0.162 0.174 0.0733 0.0769 0.0816 0.0875 0.0942 0.1018 0.1101 0.1190 0.1287 0.1390 81 82 83 84 85 86 87 88 89 90 » » » » " » » » » » 0.187 0.201 0.215 0.228 0.242 0.257 • 0.273 0.288 0.303 0.318 0.1500 0.1619 0.1747 0.1886 0.2041 0.2216 0.2415 0.2648 0.2921 0.3237 91 92 93 94 95 96 97 98 " » » » » » » » 0.333 0.348 0.3610 0.4053 0.4572 0.5163 0.5843 0.6486 0.6923 0.7500 1908-1912 Table of the Prussian and Hessian Railways Pension Fund — 16 years 17 » 18 " 19 » 20 » 0.443 0.415 0.386 0.362 0.339 0.1904 21 22 23 24 25 26 27 28 29 30 » » » » » » »' » » » 0.314 0.290 0.270 0.251 0.233 0.220 0.210 0.202 0.194 0.186 0.1895 0.1885 0.1874 0.1862 0.1849 0.1834 0.1817 0.1798 0.1777 0.1754 31 32 33 34 35 36 37 38 39 40 » » " » » » » » » » 0.182 0.179 0.175 0.171 0.166 0.161 0.156 0.151 0.145 0.139 0.1729 0.1699 0.1660 0.1611 0.1551 0.1478 0.1398 0.1315 0.1232 0.1155 41 ' 42 43 44 45 46 47 48 49 50 » » » » » » » » » » 0.133 0.128 0.123 0.118 0.114 0.110 0.105 0.102 0.098 0.095 0.1081 0.1011 0.0943 0.0881 0.0830 0.0793 0.0767 0.0750 0.0740 0.0730 51 52 53 54 55 56 57 » •» » » » » » 0.093 0.090 0.088 0.087 0.085 0.084 0.083 0.0720 0.0712 0.0708 0.0710 0.0720 0.0732 0.0745 — — Age — — — — — — 19 290 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION On the basis of the following data: general rates of mortality from the German table 1871-1881, mortality rates for invalids from Zimmermann's table, rates of becoming invalid from Behm's table, there was calculated [5: p. 80 and 6: p. 95] for males the validity table reproduced in table VI, together with the mortality rates for healthy lives which are directly deduced therefrom: TABLE VI. — VALIDITY TABLE AND MORTALITY RATES OF HEALTHY LIVES (Males) Survivors of an initial group of 60,657 healthy lives at age 16 Age Total Healthy lives Invalids h r I* Probability that a healthy person will die without having become an invalid aa X 16 years 17 » 18 » 19 » 20 » 21 » 22 » 23 » 24 " 25 » 26 » 27 » 28 » 29 » 30 " 31 » 32 » 33 » 34 » 35 » 36 » 37 » 38 » 39 » 40 41 42 43 44 45 46 47 48 49 50 51 52 53 » » » » » » » " » » » » » » . . . . 60,657 60,383 60,063 59.696 59,287 58,843 58,369 57,871 57,378 56,892 56,410 55,927 55,442 54,951 54,454 53,949 53,434 52,908 52,369 51,815 51,244 50,656 50,049 49,422 60,657 60,377 60,051 59.677 59,260 58,808 58,326 57,818 57,314 56,815 56,319 55,819 55,316 54,803 54,281 53,747 53,200 52,637 52,057 51,456 50,832 50,184 49,510 48,806 6 12 19 27 35 43 53 64 77 91 108 126 148 173 202 234 271 312 359 412 472 539 616 0.00451 0.00528 0.00609 0.00682 0.00744 0.00798 0.00846 0.00843 0.00838 0.00835 0.00844 0.00851 0.00869 0.00886 0.00908 0.00931 0.00958 0.00986 0.01022 0.01061 0.01100 0.01142 0.01191 0.01237 48,775 48,110 47,428 46,729 46,010 45,272 44,511 43,728 42,919 42,086 41,228 40,343 39,433 38,497 48,073 47,310 46,515 45,688 44,822 43,918 42,968 41,973 40,927 39,828 38,674 37,460 36,184 34,842 702 800 913 1,041 1,188 1,354 1,543 1,755 1,992 2,258 2,554 2,883 3,249 3,655 0.01282 0.01330 0.01376 0.01433 0.01487 0.01554 0.01616 0.01688 0.01762 0.01836 0.01921 0.02007 0.02101 0.02208 • 291 GERMANY TABLE VI. VALIDITY TABLE AND MORTALITY RATES OF HEALTHY LIVES (continued) (Males) Probability that a healthy person will die without having become an invalid Survivors of an initial group of 60,657 healthy lives at age 16 Age Total h 54 years . . . . 55 » 56 » 57 » 58 " 59 » 60 61 . 62 63 64 65 66 67 68 69 70 71 72 73 74 • 75 76 77 78 79 » » " » » » » » » » » » » » » » » » » » 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 " " » » » " » " » » » » » » » » » » " " " . . . . . . . . Healthy lives Invalids IXa" l "X • aa x q 37,534 36,544 35,524 34,474 33,392 32,276 33,429 31,946 30,390 28,760 27,055 25,279 4,105 4,598 5,134 5,714 6,337 6,997 0.02315 0.02434 0.02557 0.02713 0.02871 0.03064 31,124 29,935 28,708 27,442 26,139 24,802 23,433 22,037 20,620 19,189 17,750 16,310 14,880 13,468 12,085 10,743 9,454 8,228 7,077 6,010 23,432 21,524 19,569 17,582 15,584 13,600 11,651 9,763 7,974 6,312 4,807 3,518 2,456 1,620 1,000 568 292 132 50 15 7,692 8,411 9,139 9,860 10,555 11,202 11,782 12,274 12,646 12,877 12,948 12,792 12,424 11,848 11,085 10,175 . 9,162 8,096 7,027 5,995 0.03270 0.03485 0.03724 0.03977 0.04246 0.04584 0.05009 0.05463 0.06070 0.06873 0.07322 0.07796 0.08318 0.08726 0.09217 0.09561 0.09995 0.10155 0.10275 0.10350 5,032 4,156 3,378 2,700 2,120 1,635 1,236 917 666 474 330 225 150 97 61 38 23 13 7.3 3.9 2.0 0.10400 0.10431 5,035 4,156 3,378 2,700 2,120 1,635 1,236 917 666 474 330 225 150 97 61 38 23 13 7.3 3.9 2.0 3 (3.3) 0 (0.4) — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — 292 . ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The calculations were revised [16: p. 30-32] on the basis of a new table of invalidity and a select table of cessation of invalidity. The principle of the method remained unchanged, but the values of lx were calculated from ix and o^+h by the following formulae: . ë = c i» (i - °f) t = C k, (l - °-f) + « i» (1 - *M) (l - 3fi) , etc. In table VII (p. 293) appear the figures obtained by the second calculation of lx and lx, the sum of which reproduces the column lx, which had also been used in the first calculation; the last column of this table gives the probability ç ,aa that a healthy man will die without becoming invalid, the values Of this probability at each age being derived from the validity table and the rates of invalidity ix by means of the formula l x A new validity table was constructed for females (table VIII, p. 295) [18: pp. 539-540] by the same method but oh the following bases: general mortality rates from the 1871-1881 table for the female population; select mortality rates for invalids (females) from the table published in 1906 *; rates of becoming invalid from a table constructed on the basis of data supplied by the workers' insurance scheme between 1900 and 1905 2. For the calculations relating to benefits awarded to survivors a life table lx for invalids was. introduced [18: p. 544], together with mortality rates for invalids, ql, deduced from data collected from 1895 to 1898 by the Prussian railways pension fund. In a later memorandum [19: pp. 28-30] the indirect method was entirely abandoned in favour of a direct reference to the mortality rates for healthy lives produced between 1908 and 1912 by the Prussian and Hessian railways pension fund. These two series of mortality rates for healthy lives are reproduced in table IX, p. 296. 1 2 See above, p. 285. See below, p. 297, and table X, column 5. ÏOCOCOCOCOCOCOCOCOCO cncncncncncncntncncn wccœcowww W^IÏ> M C3 *•• enff>vJ 00 (O O ^ O>fc3>f>rf>rf>t^v3C0W00 KJtocotp-cnox^'-JOoco ©tDvJCntOOvJtf>>*vJ Ol<£i00^MO(C<»OCn tf"OtC>OOCOc£>4>t04> We£>CTSkf>Cn<£)O0h>t£>#^ (Û CO vJ Oï Üt (t> W t « *^C7TtnOi^>j-J > ^Jj» "tD^'toV'^o'cc'oo^C' h*W«OOWCO^(£) O^tOCOtf^t^CnOivjoO WW«t3H*iû00UlMO sJNJWOWOOlOODW •ft-**CncnOtCnCntncnCrt ODtOOO^l^MWWlP' v j #< ^ v j w «: en HA o» M CD«OCOvJOOOOCnb5v3h^ f » *4 d> tO W « ^ w O &*03O* CObStO fed^djO h* Iso'^'as'tvsXD'^j^'fco'o'co tDCOOtOiûbP-OCnrf^Cn M 00 J> h¡> <£) » «û ^ *»^3 oocococnctffcstocooïço a>Cncntf-rf>Geeocofc9W> C 0 ^ t Û O 0 i v J t Û 0 5 0îrf> ^00CJXCO»-keocobO'to^i-a. wojoœoowccwtocn H ^ H ^ H - O O O O O O O ^OOcOtOcOOOOOGOOO ppoopppp oöööööoo oooooooo ïsDtOCOCOCOCOCOCOCOCO «O^OObSÜTCOO^UlCO cocn^coi^o^cocovj O Ö Ö Ö O O O O O Ö K>U>K>ls5b5l>3^H Ä ^M' v i en i)> N) i^ o o ce va v j WO>H*COO)tnCnvj^iA O O Ö O O Ö O O O O CntncncnCncncncn wcnvjsjûocoo w OiOO^^OOCOO vj v j vj v ] vj v ] *J Oí oo vj ers as Ci vj oo o 294 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE V I I . VALIDITY TABLE AND MORTALITY RATES OF HEALTHY LIVES (continued) Survivors of an initial group of 60,657 healthy lives at age 16 Age 60 y e a r s ' 61 » 62 » 63 » 64 » 65 » 66 » 67 » 68 » 69 » . . . . Total Healthy lives '* raa 31,124 29,935 28,708 27,442 26,139 24,802 23,433 22,037 20,620 19,189 26,464 24,883 23,244 21,565 19,865 18,152 16,421 14,672 12,945 11,272 4,660 5,052 5,464 5,877 6,274 6,650 7,012 7,365 7,675 7,917 0.0292 0.0314 0.0337 0.0363 0.0392 0.0424 0.0455 0.0487 0.0522 0.0562 0.0605 0.0650 0.0704 0.0764 0.0825 0.0889 0.0955 0.1024 0.1098 0.1175 X Invalids aa X 70 71 72 73 74 75 76 77 78 79 "' » » » » » » » " » 17,750 16,310 14.880 13,468 12,085 10,743 9,454 8,228 7,077 6,010 9,680 8,175 6.785 5,527 4,414 3,432 2,595 1,893 1,330 898 8,070 8,135 8095 80 81 82 83 84 85 86 87 88 89 » » » » » » »> » » » 5,035 4,156 3,378 2,700 2,120 1,635 1,236 917 666 474 577 349 196 98 43 16 3 4,458 3,807 3,182 2,602 2,077 1,619 1,233 917 666 474 90 91 92 93 94 95 96 97 98 99 » » » » » » » » » » 330 225 150 97 61 38 23 13 7 4 100 » . . . . Probability that a healthy person will die without having become an invalid 2 — — - 7 - — — 7J94Ï 7,671 7,311 6,859 6,335 5,747 5,112 330 225 150 97 61 38 23 13 7 4 2 0.1271 0.1334 0.1500 0.1642 0.1809 — — — — — — — — —' — — -— — — — - w j y ***H*-mo***-ienoo-*(N *". ®. "i. °- "L1 °°. "*- "1. °°- . (M Or^rH«!HtO(uö»HOQO y Survivors of an initial group of 62,324 healthy lives at age 16 o Healthy Invalids lives IO 1 i>ioc^aiiooift>cscoiíti os" oo" rC iñ «af «f *•<" OT oo" to" m*Hr-.^oo IM m_r-_os ^ m •*."*.•*.»*, \ñ r i ^ r ^ CTíVCaiOiCOOCOtO^CO ^ C ^ " ( N " Co"co" rN OMO N O coNOcoc *#" CN" *-T oT c-T io" co" ^T aT oo" Ci5rlCOrlOCO[>íOOOH ^lOr>OlM OtO'rHtOOC C^-ç-^OO^lO^T-l *"*„**, « û . ^ . , 1 ^ a^c^to^oi co t to" io" co" tri T-T oT oo" to" vo" co" TÍ" O " OO" to" io" c C0C0C0C0C0 w m EH Cu Survivors of an initial group of 62,324 healthy lives at age 16 S o >> ©*H(MCO 00. IO C> -rH r t r i ^ M M O O O C O tOritONCOUOCOrHrHrrt -^H f *#tOtOCNCTiCOtO i ^toooTHCot a i oo o* OÍ M ^ (N lO 00 ¡N tN tN tO T^ ^ tO 00 00 CN tO CO O IO O »# OO M tí? O » í 00 (N Ot>tOlOlOa)OC lOO^flTNOO r t co »* io i> » asûor^toio* *# ^ »># *J* 0 W Oì CO C\ O < nOOO^O)c lO^OiO^^- OniNCOO'ultûrNOOOi COCOCOCOCOCOCOCOCOCO onMcoo> O-rKMCO-^kOtOr-cOai *3* • ^ *•# * ^ ^J* * 296 ACTUARIAL TECHNIQUE AND FINANCIAL TABLE IX. ORGANISATION MORTALITY OF HEALTHY LIVES (Probabilities in 0.00001) 1895-1898 Table of the Prussian Railways Pension Fund Age 1905-1912 Table of the Prussian and Hessian Railways Pension Fund 16 y e a r s . 17 » . 18 " . 19 » . 20 » . . . . . . 372 373 374 375 376 258 21 22 23 24 25 26 27 28 29 30 » " » » " » » » " » . . . . . . . . . . . . . . . . . . . . 377 378 379 380 382 384 388 395 406 423 262 261 257 253 251 251 258 267 279 292 31 32 33 34 35 36 37 38 39 40 » » » » » » » » » » . . . . . . . . . . . . . . . . . . . . 446 475 510 551 595 641 689 739 791 844 307 322 339 359 380 403 430 459 491 525 41 42 43 44 45 46 47 48 49 50 » » " » » » » » » » . . . . . . . . . . . . . . . . . . . . 898 953 1,009 1,070 1,140 1,220 1,300 1,380 1,460 1,540 564 605 648 693 741 792 849 914 987 1,065 51 52 » » . . . . 1,620 1,710 1,150 1,238 Age 1895-1898 Table of the Prussian Railways Pension Fund 1905-1912 Table of the Prussian and Hessian Railways Pension Fund 53 y e a r s . . 54 » 55 » 56 > 57 58 59 60 ' 1,800 1,890 1,990 2,100 2,210 2,320 2,440 2,580 1,323 1,408 1,493 1,578 1,663 1,756 1,860 1,979 61 62 63 64 65 66 67 68 69 70 2,730 2,900 3,100 3,310 3,560 3,860 4,160 4,560 5,110 5,810 2,120 2,289 2,489 2,717 2,968 3,242 3,539 3,870 4,248 4,725 6,750 7,800 8,900 10,000 11,100 •12,200 13,300 14,400 15,600 16,800 5,578 6,466 7,390 8,352 9,356 10,404 11,498 12,643 13,841 15,096 18,400 19,900 21,500 22,900 24,400 25,800 27,300 28,900 16,414 17,797 19,252 20,784 22,399 24,105 25,909 27,819' 29,847 32,002 Î 71 72 73 74 75 76 77 78 . 79 80 81 82 83 84 85 86 87 88 89 90 Ï » j ! » » ) 5 ' 7 1 S ' ) > Í » » > ' ' y > i , > ' » . . — GERMANY 297 PROBABILITY OF BECOMING INVALID The probabilities of becoming invalid which were used in the earliest calculations came from Behm's table relating to workers in various industries 1. The first experience of the scheme, up to 1894, showed appreciable differences from the rates in this table and accordingly these were adjusted by means of factors deduced from the comparison of various data relating to the age distribution of invalids [13: pp. 3584-3585]. A new table was constructed [16: pp. 13-24] which was based on the industrial census as at 14 June 1895 and on the invalidity pensions which began to be paid in the years 1895, 1896 and 1897. The number of cases of invalidity occurring at the mean ages was taken to be the greatest of the figures relating to each of the three years in question. The probabilities of becoming invalid at each age were obtained by a process of graphic interpolation. Subsequently [18: pp. 538, 539 and 544] recourse was had: (1) to the 1895-1898 invalidity table of the Prussian railways pension fund-; (2) for calculations relating to benefits granted to widows, to a table constructed from the experience of the scheme itself in respect of the pensions granted from 1900 to 1905 and from the insured population between these two dates. The latter was estimated on the basis of the 1895 industrial census projected, in each age group, in accordance with the growth observed since the preceding industrial census (1882). The four invalidity tables mentioned above are collated in table X (p. 298). In a subsequent memorandum [19: pp. 21-28] the following were adopted: (1) for males, the rates from the Prussian and Hessian railways pension fund, constructed from the experience during the quinquennium 1908-1912 of 1,518,594 insured persons who had completed their waiting period and 12,716 cases of invalidity; (2) for females, a table constructed by comparing the experience of the scheme itself in the period 1906-1908 with the table adopted for males (see table XI) and with the table previously used for widows' benefits (see table X, column 5). The tables adopted for males and females are reproduced in table X I . 1 A description of the characteristics of this table and in particular of the statistical material on which it was based does not seem to have ever been published. A note attached to a technical memorandum [6: p. 96] indicates merely that the crude figures were graduated on the assumption that the probability of becoming invalid doubled itself every 5 years from age 20, that is to say, by applying the formula ix = ¿20 2 B in which i20 was given an approximate value obtained by the method of least squares 0.00019036. 298 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE X. — Age 16 years. . 17 ) g 18 > . 19 > . 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49' 50 51 52 53 54 55 56 57 ï ï > > . » t » . > . 1 t » . > . ) » t » . » s . Ï I > > g » . ) , ) # » . » > ^ » » » ' • , » » » . » . » m' » . RATES OF BECOMING INVALID Table deduced from the experience of Behm's Table the workers' insurance scheme from 1895 to 1897 1895-1898 Table of the Prussian Railways Pension c Fund Table deduced from the experience of the workers' insurance scheme from 1900 to 1905 (females) — — — 0.00011 0.00012 0.00014 0.00017 0.00019 0.0001 0.0002 0.0003 0.0004 0.0005 0.00002 0.00004 0.00007 0.00010 0.00016 0.00013 0.00022 0.00025 0.00029 0.00033 0.00038 0.00044 0.00050 0.00058 0.00066 0.00076 0.0007 0.0009 0.0011 0.0012 0.0013 0.0014 0.0016 0.0017 0.0018 0.0019 . 0.00023 0.00031 0.00039 0.00048 0.00059 0.00070 0.00081 0.00093 0.00106 0.00120 0.00034 0.00067 0.00108 0.00154 . 0.00216 0.00278 0.00332 0.00378 0.00418 0.00453 0.00087 0.00100 0.00116 0.00133 0.00152 0.00175 0.00201 0.00231 0.00265 0.00305 0.0021 0.0022 0.0023 0.0024 0.0026 0.0028 0.0030 0.0032 0.0035 0.0038 0.00134 0.00148 0.00163 0.00181 0.00203 0.00226 0.00252 0.00280 0.00310 0.00341 0.00484 0.00513 0.00539 0.00566 0.00593 0.00622 0.00654 0.00691 0.00732 0.00780 0.00350 0.00402 0.00462 0.00530 0.00609 0.00700 0.00804 0.00923 0.01061 0.01218 0.0041 0.0045 0.0050 0.0056 0.0062 0.0069 0.0076 0.0083 0.0091 0.0101 0.00374 0.00410 0.00449 0.00495 0.00545 0.00600 0.00665 0.00740 • 0.00830 0.00940 0.00836 0.00901 0.00975 0.01061 0.01159 0.01270 0.01396 0.01538 0.01697 0.01874 0.01399 0.01608 0.01847 0.02121 0.02437 0.02799 0.03215 0.0113 0.0126 0.0141 0.0157 0.0175 0.0195 0.0218 0.01060 0.01190 0.01340 0.01520 0.01730 0.01960 0.02210 0.02069 0.02286 0.02523 0.02784 0.03067 0.03376 0.03711 299 GERMANY TABLE X. RATES OF BECOMING INVALID Table deduced from the experience of Behm's Table tbe workers' insurance scheme from 1895 to 1897 Age 58 years. . . . (continued) 1895-1898 Table of the Prussian Railways Pension Fund Table deduced from the experience of the workers' insurance scheme from 1900 to 1905 (females) 59 60 » », 0.03693 0.04242 0.04873 0.0243 0.0270 0.0305 0.02500 0.02860 0.03260 0.04074 0.04465 0.04885 61 62 63 64 65 66 67 68 69 70 » » » » » » » » » » 0.05598 0.06430 0.07387 0.08485 0.09747 0.11196 0.12861 0.14773 0.16970 0.19493 0.0345 0.0385 . 0.0425 0.0470 0.0530 0.0610 0.0690 0.0770 0.0850 0.0950 0.03700 0.04180 0.04690 0.05300 0.05970 0.06700 0.07500 0.08400 0.09700 0.11200 0.05337 0.05820 0.06336 0.06886 0.07472 0.08096 0.08756 0.09455 0.10194 0.10974 71 72 73 74 75 76 77 78 79 80 » » » » » » » " » » 0.22392 0.25721 0.29546 0.33939 0.38986 0.44783 0.51442 0.59092 0.67878 0.77972 0.1050 0.1150 0.1250 0.1400 0.1550 0.1750 0.1950 0.2150 0.2400 0.2680 0.13100 0.15300 0.17700 0.19400 0.20700 0.21900 0.22800 0.23700 0.24400 0.25000 0.11796 0.12662 0.13572 0.14528 0.15531 0.16578 0.17678 0.18828 0.20030 0.21284 81 82 83 84 85 86 87 88 89 90 » » » » » » » » » » 0.89569 — — — — — 0.3050 0.3500 0.3970 0.4470 0.5000 0.5600 0.6200 0.6800 0.7400 0.8000 0.25600 0.26200 0.26800 0.27300 0.27800 0.28300 0.28700 0.29000 91 92 » » — 0.8600 0.9200 - — — — • — • . — — — — —— .—. — — — —• — — 300 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XI. — RATES OF BECOMING INVALID (Probabilities in 0.00001) Males (Prussian Females and (workers' Hessian Railways insurance scheme Pension 1906-1908) Fund 1908-1912) Age 20 years. . 21 22 23 24 25 26 27 28 29 » » " » » » » » » 30 " . . . . Age 85 96 107 119 131 143 155 168 181 194 80 112 148 191 248 320 390 438 476 497 515 60 61 62 63 64 65 66 KOf\ CT 543 556 573 •595 622 654 691 732 32 33 34 35 36 37 38 39 " » » » » » » » 207 22 r t 233 246 259 272 285 298 314 333 40 41 42 43 44 45 46 47 48 49 » » » » » » » » » » 358 386 428 484 554 640 742 860 994 1,144 780 836 901 975 1,061 1,159 1,270 1,396 1,538 1,697 50 » 51 » 52 • » 53 » 54 » 55 » 1,310 1,492 1,690 1,904 2,134 2,437 1,874 2,069 2,286 2,523 2,784 3,390 ox *JU\J Males (Prussian Females and (workers' Hessian Railways insurance scheme Pension 1906-1908) Fund 1908-1912) 56 y e a r s . . 57 » . 58 » . 59 » . » » » " » » » 2,799 3,215 3,693 4,242 3,997 4,603 5,210 5,817 4,873 5,598 6,430 7,387 8,485 9,747 11,196 6,424 7,580 8,910 10,403 12,104 14,016 16,479 AO OCA A O CiA O 68 69 » » 14,773 16,970 21,319 23,698 70 71 72 73 74 75 76 77 78 79 » » » » » » » » » » 19,493 22,392 25,721 29,546 33,846 37,412 39,609 41,782 43,931 46,057 26,049 28,373 30,671 32,944 35,190 37,412 39,609 41,782 43,931 46,057 80 81 82 83 . 84 85 86 87 88 89 » » » » » » » » » » 48,160 50,240 52,297 54,333 56,347 58,340 60,312 62,264 64,195 66,106 48,160 50,240 52,297 54,333 56,347 58,340 60,312 62,264 64,195 66,106 67,998 67,998 ' 9 0 » . . 10,310 GERMANY 301 SICKNESS The loss of contributions due to sickness was estimated [6: p. 86] from the mean annual numbers Kx of days of sickness at each age. These means were taken from a table constructed by Heym 1 using statistics collected by an insurance company dealing with persons belonging to a wide range of industries. Subsequently [8: p. 300] in the calculation of the income of the scheme account was taken of the assimilation of sickness periods to contribution periods by reducing by one the mean number of weeks of contribution. PROBABILITIES RELATING TO MARITAL STATUS AND TO SURVIVAL OF DEPENDANTS Insured Males At each age the proportion of men married and widowed in the total male population for insured trades, taken from the industrial census at 5 June 1882, was used to represent the probability wx that an insured person would, on decease, leave one or more claimants (widow,,or orphan less than 15 years old) [8: pp. 296, 297 and 13: pp. 3593]. The probability that an insured person on decease would leave a widow was then considered [18: p. 542] and it was deemed to be the same as the proportion Z,x of married men in the total male population in insured trades. This proportion was first deduced at each age from the industrial census of 1895. Later [18: p. 542] effect was given to. the proportions indicated by the 1907 industrial census (which were on the average 10 per cent, less than the former) and later still [19: pp. 36-37] to the corresponding proportions in the general census of 1910 (table XII). Insured Females The probability w'y that an insured woman who died after becoming a widow would leave one or more orphans less than 15 vears old was first deduced [8: p. 297] from data given in the industrial census of 5 June 1882. This probability was deemed to be the same as the proportion of widows in thè total female population in insured trades. It was thus assumed, for simplicity, that every widow on decease would leave one or more children less than 15 years old. Experience showed that this assumption produced figures which were too high, particularly at the older ages. Consequently [13: pp. 3593-3594 and 16: pp. 34-35] it was decided to retain the figures previously obtained up to age 45 and to substitute after that age: up to age 50 a constant figure constituting the maximum rate; from age 50 a series rapidly decreasing to very small figures at age 60 and disappearing at age 70. 1 Anzahl und Dauer der Krankheiten in gemischter Bevölkerung Fünfundzwanzig Jahre Erfahrungen der Versicherungsgesellschaft " Gegenseitigkeit " zu Leipzig. Leipzig, 1884. 302 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XII. SURVIVORSHIP FACTORS FOR WIDOWS AND DEPENDANTS (Insured men) Age Probability v)x that an insured man willdeath leave at his one or more dependants m Probability Ç that an insured man will leave a widow at his death From the 1895 industrial census From the 1910 general census 0.0000 0.0000 0.0005 0.0045 _ — — — — — — 0.034 0.060 0.100 0.148 0.204 0.273 0.340 0.406 0.466 0.520 0.003 0.014 0.040 0.097 0.182 0.283 0.387 0.482 0.562 0.631 17 18 19 » » » 20 21 22 23 24 25 26 27 28 29 » » » » » » » » » 0.0145 0.0285 0.0690 0.1225 0.1964 0.2704 0.3444 0.4182 0.4921 0.5660 30 31 32 33 34 35 36 37 38 39 » » » » » » » » » » 0.6395 0.7076 0.7514 0.7806 0.8064 • 0.8260 0.8438 0.8551 0.8658 0.8758 0.572 0.620 0.660 0.696 0.732 0.765 0.792 0.810 0.822 0.832 0.684 0.731 0.767 0.791 0.812 0.827 0.841 0.854 0.862 0.866 40 41 42 43 44 45 46 47 48 49 » » » 0.8815 0.8860 0.8885 0.8905 0.8920 0.8930 0.8940 0.8950 0.8960 0.8970 0.834 0.838 0.840 0.840 0.840 0.840 0.840 0.838 0.836 0.834 0.870 0.874 0.878 0.881 0.882 0.883 0.883 0.883 0.882 0.880 50 51 52 53 54 55 56 57 58 59 » » 0.8978 0.8986 0.8993 0.9000 0.9007 0.9014 0.9021 0.9028 0.9035 0.9042 0.832 0.830 0.826 0.824 0.818 0.811 0.806 0.794 0.786 0.776 0.876 0.872 0.868 0.864 0.859 0.853 0.847 0.841 0.834 0.824 » . . . . ' . . . . . . . . . . . » » » » » » " . . . . . . . » » » . . . . . . . . » » . . . . . . . . . . 307 GERMANY Healthy wives (of insured men) themselves insured Healthy wives (of insured men) not themselves insured and not liable to enter insurance Healthy wives (of insured men) jaa Fv 2- I c Healthy wives (of insured men) not themselves insured jaa F -2 F All wives of insured men Healthy wives (of insured men) not themselves insured but liable to enter insurance F„ (1 - a) - F°y Pensioned invalid wives (of insured men) Invalid wives (of insured men) lH F v -Ü- L Not pensioned invalid wives (of insured men) F, /:; taaV The results obtained at individual ages for these various categories of wives (of insured men) are reproduced in table X I V . 308 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XIV. DISTRIBUTION OF WIVES OF INSURED MEN BY AGE AND CATEGORY Numbers of wives of insured men Healthy lives Age Not themselves insured Total Total 20 years Invalids Themselves insured Total Not Likely to likely enter into to enter insurance into insurance Not pensioned Total Pensioned 22,500 22,500 9,000 13,500 7,717 5,783 0 0 0 21 22 23 24 25 26 27 28 29 30 » » » » » » » " " " 54,000 85,000 109,100 125,000 135,000 142,500 148,200 152,500 154,500 155,000 53,995 84,974 109,013 124,837 134,703 142,015 147,459 151,432 153,079 153,202 13,400 16,100 18,100 19,400 20,400 21,200 22,000 22,500 23,000 23,500 40,595 68,874 90,913 105,437 114,303 120,815 125,459 128,932 130,079 129,702 27,100 48,160 65,034 76,725 84,360 90,377 94,930 98,890 100,754 101,585 13,495 20,714 25,879 28,712 29,943 30,438 30,529 30,042 29,325 28^117 5 26 87 163 297 485 741 1,068 1.421 1,798 4 21 73 138 252 413 630 909 1,208 1,522 1 5 14 25 45 72 111 159 213 276 31 32 33 34 35 36 37 38 39 40 » » » » » » » " » " 154,000 152,500 148,000 144,000 138,100 132,300 125,000 118,000 112,000 106,000 151,798 149,892 145,025 140,645 134,413 128,305 120,750 113,504 107,262 101,029 24,000 24,500 25,000 25,400 25,600 25,800 25,900 26,000 25,700 25,100 127,798 125,392 120,025 115,245 108,813 102,505 94,850 87,504 81,562 75,929 101,048 99,940 96,360 92,968 88,056 83,083 76,850 70,760 65,804 61,184 26,750 25,452 23,665 22,277 20,757 19,422 18,000 16,744 15,758 14,745 2,202 2,608 2,975 3,355 3,687 3,995 4,250 4,496 4,738 4,971 1,854 2,182 2,462 2,749 2,985 3,192 3,338 3,466 3,603 3,736 348 426 513 606 702 803 912 1,030 1,135 1,235 41 42 43 44 45 46 47 48 49 50 » » " " » » » » » " 101,500 96,300 92,000 87,000 83,000 79,000 75,500 71,500 67,500 63,300 96,242 90,801 86,222 80,997 76,700 72,411 68,577 64,286 59,994 55,546 24,000 22,900 21,800 20,800 19,900 19,100 18,500 17,900 17,200 16,700 72,242 67,901 64,422 60,197 56,800 53,311 50,077 46,386 42,794 38,846 58,316 54,814 52,076 48,626 45,919 43,073 40,239 36,869 33,492 29,825 13,926 13,087 12,346 11,571 10,881 10,238 9,838 9,517 9,302 9,021 5,258 5,499 5,778 6,003 6,300 6,589 6,923 7,214 7,506 7,754 3,947 4,112 4,317 4,461 4,665 4,851 5,055 5,206 5,354 5,422 1,311 1,387 1,461 1,542 1,635 1,738 1,868 2,008 2,152 2,332 51 52 53 54 55 56 57 58 59 60 » » » » » » » » » » 59,500 57,000 54,700 52,700 49,400 46,500 43,000 39,500 36,500 32,600 51,462 48,513 45,729 43,182 39,579 36,335 32,671 29,084 25,944 22,276 16,200 15,600 15,000 14,300 13,600 12,900 12,200 11,300 10,400 9,500 35,262 32,913 30,729 28,882 25,979 23,435 20,471 17,784 15,544 12,776 26,521 24,300 22,196 20,429 17,818 15,697 13,299 11,254 9,638 7,648 8,741 8,613 8,533 8,453 8,161 7,738 7,172 6,530 5,906 5,128 8,038 8,487 8,971 9,518 9,821 10,165 10,329 10,416 10,556 10,324 5,508 5,758 6,029 6,366 6,447 6,556 6,472 6,369 6,324 5,921 2,530 2,729 2,942 3,152 3,374 3,609 3,857 4,047 4,232 4,403 309 GERMANY TABLE XIV. DISTRIBUTION OF WIVES OF INSURED BY AGE AND CATEGORY (continued) MEN Numbers of wives of insured men Invalids Healthy lives Not themselves insured Age Total Total 61 years 62 » 63 » 64 » 65 » 66 » 67 » 68 » 69 » 70 » Not pensioned Pensioned 8,500 7,400 6,400 5,500 4,700 4,100 3,000 2,000 1,600 1,400 11,566 10,386 9,185 8,034 6,885 5,658 4,405 3,126 1,922 1,203 6,911 6,299 5,684 5,059 4,435 3,608 2,865 2,082 1,240 725 4,655 4,087 3,501 2,975 2,450 2,050 1,540 1,044 682 478 10,634 10,814 10,915 10,966 10,915 10,742 9,595 7,874 6,478 5,797 6,129 6,314 6,432 6,509 6,549 6,445 5,757 4,724 3,887 3,478 4,505 4,500 4,483 4,457 4,366 4,297 3,838 3,150 2,591 2,319 1,875 1,311 906 576 321 166 55 1,100 700 600 300 100 80 50 775 611 306 276 221 86 5 447 408 184 216 201 71 3 328 203 122 60 20 15 2 5,125 4,489 3,994 3,424 2,779 2,234 1,845 1,500 1,200 1,000 3,075 2,693 2,396 2,054 1,667 1,340 1,107 900 720 600 2,050 1,796 1,598 1,370 1,112 894 738 600 480 400 800 600 400 300 200 150 100 50 30 10 480 360 240 180 120 90 60 30 18 6 320 240 160 120 80 60 40 20 12 4 7,000 5,800 4,900 4,000 3,100 2,400 1,900 1,500 1,200 1,000 81 82 83 84 » » » » 800 600 400 300 200 150 100 50 30 10 » » » » » Total 20,066 17,786 15,585 13,534 11,585 9,758 7,405 5,126 3,522 2,603 » » » » » » » » » » 86 87 88 89 90 Total Not Likely to likely enter into to enter insurance into insurance 30,700 28,600 26,500 24,500 22,500 20,500 17,000 13,000 10,000 8,400 71 72 73 74 75 76 77 78 79 80 OK Themselves insured — — — — — — — — .— — — — — — — — — — — — 4,138,340 8,308,563 838,930 2,969,633 2,284,172 685,461 329,777 218,237 111,540 DISTRIBUTION OF WIDOWS OF INSURED MEN IN CATEGORIES In a later memorandum [19: pp. 36-52] recourse was had to three series of probabilities—reproduced in table XV—relating to widows of insured men. The following probabilities were calculated for each of the age groups shown in the industrial census of 14 June 1907, from the data of that census, and then probabilities for individual ages were obtained by interpolation: 310 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION (1) on the assumption that the number of wives of insured men who are themselves insured is the same as the number of insured married women, the probability £iy that the widow of an insured man is herself insured; (2) with the help of the proportion of wives of insured men who are not occupied, the probability Qy that the widow of an insured man will never enter into insurance; (3) with the help of the proportion of occupied widows and divorced women who.are insured, the probability QlyP that the invalid widow of an insured man will be in receipt of a pension. X V . — P R O B A B I L I T I E S FOR S U B D I V I D I N G OF I N S U B E D MEN I N CATEGORIES TABLE that the widow of an insured man is herself insured (for a total of 10,000) Probability n" s that the widow of an insured man will never enter into insurance (for a total of 10,000) Probability iljf that the invalid widow of an Insured man will be pensioned (for a total of 1,000) 2,293 2,273 2,254 2,224 2,193 2,105 2,015 1,906 1,787 1,688 3,770 3,756 3,664 3,294 2,992 2,750 2,564 2,418 2,289 2,172 730 650 611 596 585 577 569 561 553 545 Probability a" y Age 20 years 21 » 22 » 23 »> 24 » 25 " 26 » 27 » 28 " 29 » . . . WIDOWS 30 31 32 33 34 35 36 37 38 39 " » ». » ». ». ». « » « 1,668 1,688 1,717 1,767 1,807 1,837 1,857 1,876 1,886 1,896 2,063 1,970 1,880 1,793 1,709 1,629 1,555 1,535 1,545 1,608 537 529 521 513 505 497 489 481 474 468 40 41 42 43 .44 45 46 47 48 49 » » ». ». ». >» » » .» » 1,906 1,896 1,886 1,876 1,866 1,857 1,847 1,827 1,807 1,768 1,697 1,900 2,104 2,309 2,515 2,723 2,930 3,135 3,337 3,535 462 456 450 444 438 432 426 420 414 408 • 311 GERMANY TABLE XV. PROBABILITIES FOB SUBDIVIDING W I D O W S OF INSURED MEN IN CATEGORIES (continued) Age 50 years . . . Probability CJ„ y that the widow of an insured man is herself insured (for a total of 10,000) Probability n"* that the widow of an insured man will never enter into insurance (for a total of 10,000) Probability Q ^ that the invalid widow of an insured man will be pensioned (for a total of 1,000) 51 52 53 54 55 56 57 58 59 » » » » » » " » » 1,728 1,688 1,648 1,608 1,569 1,529 1,479 1,430 1,370 1,310 3,728 3,916 4,098 4,274 4,445 4,610 4,770 4,934 5,104 5,283 402 396 390 384 377 369 361 353 345 337 60 61 62 63 64 65 66 67 68 69 » » » » .» » » » » » 1,251 1,191 1,132 1,072 1,013 933 834 715 596 476 5,475 5,685 5,920 6,188 6,498 6,861 7,214 7,566 7,917 8,267 328 319 309 298 286 273 259 244 228 211 70 71 72 73 74 75 76 77 78 79 » » » » » » » » 397 338 298 278 259 207 122 68 34 18 8,616 8,964 9,278 9,533 9,721 9,848 9,930 9,976 193 174 154 133 111 89 67 45 23 » O QOC . / , •JtfXJ • 10,000 With the help of these probabilities and of some of the biometrie data mentioned above, a table was constructed showing at each age the distribution of 10,000 widows of insured men, at the date of husband's death, according to whether they are healthy or invalid and insured or uninsured. The number of invalid widows who have not been insured and who consequently cannot be entitled to an invalidity pension 1 is w ; n p = 10,000 lf (i - Q;P) . 1 The numbers lü and lv, together with Z"a, formed the validity table for females which had been constructed directly from the mortality rates of healthy persons and probabilities of becoming invalid. See above, pp. 292 and 297, and tables IX and X. 312 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The number of healthy widows who will not enter into insurance is obtained by deducting from the number 10,000 Q.y of widows not r liable to enter insurance the number 10,000 -~ of invalid widows, that is (cr;-lj\. w 7 = 10,000 The number of widows who are themselves insured is represented by Wy = 10,000 Q.y, and the number of invalid widows who had been insured and who consequently may be entitled to an invalidity pension is given by w? = io;ooo lf o; p . DIFFERENCE IN AGE OF HUSBAND AND W I F E The average age of wife in relation to the age of husband [18: p. 543} was based on a double-entry table which represented the distribution, TABLE XVI. DIFFERENCE IN AGE OF HUSBAND AND WIFE Age of husband Age or wife 20 years 21 years 21 22 23 24 25 » " » » » 22 23 24 25 26 » " " » » 26 27 28 29 30 » » » » » 26 26 27 28 28 » » » " » 31 32 33 34 35 » » » » » 29 30 31 32 32 » » » » » 36 37 38 39 40 » » « » » 33 34 35 36 3? » » » »• » / Age of husband Age of wife Age of husband Age of wife 41 years 42 » 43 » 44 » 45 » 38 years 39 » 40 » 41 » 42 » 61 years 62 » 63 » 64 » 65 » 55 years 56 » 57 » 58 " 59 » 46 47 48 49 50 » » '» » » 43 43 44 45 46 » » >» » » 66 67 68 69 70 60' 60 » 61 » 61 » 62 » 51 52 53 54 55 » » » » » 47 48 49 50 50 » » » » » 71 » 72 » 73' » 74 » 75 » 62 63 64 65 66 » » » » » 56 57 58 59 60 » » » » » 51 52 53 54 54 » 76 77 78 79 80 » » » » » 67 68 68 69 69 » » » » » 81 82 83 » » » 70 70 71 » » » » » » » » » » » 313 GERMANY according to both age of wife and age of husband, of the female population of Thuringia 1 at the 1880 census. These results—reproduced in table XVI—were compared with others, from a different source, but it was decided [19: p. 51] that the substitution of other figures was not necessary. DATA RELATING TO CHILDREN Mortality In order to estimate the mortality of children of insured men recourse was had to the following: (1) a life table lz—reproduced below—in respect of the total German population between 1871 and 1881, for children of both sexes [18: p. 546]; TABLE X V I I . LIFE TABLE FOR CHILDREN (Both sexes combined) Age German life table 1871-1881 0 200,000 1 year 152,987 143,156 138,449 135,292 132,997 3 4 5 6 7 8 9 10 » » » » " » » » 11 12 13 14 15 » » » » 131,277 129,941 128,884 128,030 127,326 126,726 lÌé'Ì96 125,710 125,244 124,770 (2) a table deduced from the results of the general census 2 for the years 1891-1900, which included monthly rates for the first year of life and quarterly rates for the second year [19: p. 52]. Age Distribution of Children, according to Age of Father Reference was made to the following [18: p. 546, and 19: pp. 51, 52]: (1) a double-entry table giving kx the number of children at each age from 0 to 14, according to age of father; this table, which 1 2 See p. 305. Statistik des Deutschen Reichs, Band 200. cN Wf | | r i i i co | i i i i i i i i | i 1 1 1 COTJ ^ t " H c o sj» e o •*- C4coos*a i i i i CO I I 1 I IO 1 1 o to 1 -v—t i | ] 00 GO CO CO -P< O ••HT-OOOO iftm<<*#CO co•*- .COTHC»f01> «H-«i CN vtf tv^-tf^-OS COOJOTOÍ ©-3"*OtOtUOCOCNCOCN COCOíNíNOO -H O 00 00 ï > CO-r-: CO t-CO COtfî-CCNCO CNO cN T- iDiOCOWCO T H ^ - r - ^ m CDOOmCMO) r - * - ^ cours co CN CN CN CD cDwTMncNco © CO *tf lO -tf **©oor~co cJW-rUfiO Os - t ^ OS C O n O l O O CNCDCDO*^ O CO Os 00 OS O i O CO CO OS t - î O •*-OS T H - r i OS 0 0 CO CD -4" O ií5 O l OS ( N N »CS *3* CN T - " ^ I - T r-^HCOO-tf ifSGOCOOst— r - < N i - O l » OlcD^CUt- CNOSCSf-CO CN->-<00CJiO «ft»co-iHin cooocNic-3* ©»tfcOCOOS ißCNt-r-co OSOOOOOS -ri LO co co t QOOCOOO mc-iooocn OOr-# -r-CNOsOO CNCN-^tCNCN i n as co •*-i« COCDCN-r-O T H •*-• ^ t ^ - r i co co •*-< oo -rOI>iO«ïvJ -w ooco-^crico COCOCN-H-TH OOO -H OCOCO ( i ^ i ^ , ^ , 1 1 -r-COOOOS-f c N C O - ^ C7S t í 3 TH eOCOii5cD Os t ^ - v T i r t CO OSOCNCOCN CO ( N T - •*-" T H trtt^ I£500>-HCO(N CiCOOSCOr*r*-r4 C O O W f C O CN CN * * * * CO íNíNíNCÍíN t ^ ^ - C - O O T-COCOOÏÍ N CN -r* ( N •»H cOCDGOcOCO COLOCÓOS ^ * - ' n - r t l~-CDiiîO--a' OOCOCDv-pco CDOOiOC* ( N O i f i •*-" iftliî oscN-vícoas COO^nOSCO ^ ^ H ^ C N cNi>incoco COCOifiCOcO CNCNCNCNCN mcomm-H CO-¡f(NO(D CN CN CN C N - ^ OSO-^OSCN mcDCNOOOS - ^— •« r-osm-t-nfs |>**-*s*C0 ococo-#iO COCN^- lOin r~cN-»-iocOCDOCOCO ^ • n í N f N l N l— Í > C O * 3 * C D ííSCDiríCO-* iA-*<<(N in«íooo03 r-cococN o ^ o i o c n (NíN-rHCN-*H CO tí5 OS «S* - ^ CNCN COtNCD i 1 COT-COOO ^ «r--*n{Nco m-nocs-i T"ri(NP;(D CDO © O C^OO •*-! co t i l j | j CN ooobifl | ( N ^ n > í j IJ 5 I ocooo 1 T H -tf !>. > m o •J to T - -«-< -rH Os OS CD CNCO v f L f i t O OS CO 0 0 CO CO íNcor-aooo OO-i-fOSOSO tr~ t~~ i£5 CO - ^ OOOsO osos CDO* OS-<í O cocOLniftiA §§§ss 00t"*-OCN CO CN OS CO CO CN CN -TH * - -r* 315 GERMANY is based on statistics compiled by the Ministry for Internal Affairs in respect of IVL,. fathers belonging to the staff of the Prussian railways, is reproduced opposite (table XVIII). (2) the results of an enquiry l made by organisations of private employees on the economic position of their members during the month of October 1903 [19: p. 52]. Probability r\x that an Insured Man aged x is the Father of a Child aged less than 15 These probabilities were derived from the experience of the staff of a section of the Prussian railways (Berg-Markische Eisenbahn) ; they are reproduced in table XIX. TABLE Probabilities r¡x that an insured man is the father of a child under 15 years of age Age of insured man 19 y e a r s . . . 20 » . . . 0.0010 0.0057 21 22 23 24 25 " » » » » . . . . . . . . . . . . . . . 0.0125 0.0225 • 0.0375 0.0575 0.1244 26 27 28 29 30 » » " » » . . . . . . . . . . . . . . . 0.2450 0.3740 0.4915 0.5990 0.6850 31 32 33 34 35 » » » » » . . . . . . . . . . . . . . . 0.7560 0.7930 0.8183 0.8370 0.8505 36 37 38 39 40 » » » » » . . . . . . . . . . . . . . . 0.8602 0.8650 0.8680 0.8710 0.8715 41 42 43 44 45 » » » » » . . . . . . . . . . . . . . . 0.8705 0.8640 0.8537 0.8415 0.8315 | 1 1 1 XIX Age of insured man Probabilities nx that an insured man is the father of a child under 15 y ears of age 46 y e a r s . . . 47 » . . . 48 " . . . 49 " . . . 50 » . . . 0.8225 0.8145 0.8055 0.7910 0.7710 51 52 53 54 55 » » » » » . . . . . . . . . . . . . . . 0.7450 0.7130 0.6705 0.6210 0.5600 56 57 58 59 60 » » » » " . . . . . . . . . . . . . . . 0.4950 0.4333 0.3850 0.3400 0.3050 61 62 63 64 65 » » " » » . . . . . . . . . . . . . . . 0.2880 0.2710 0.2540 0.2349 0.2215 66 67 -68 69 70 » » » » » . . . . . . . . . . . . . . . 0.2120 0.2010 0.1880 0.1730 0.1530 71 72 73 » » " . . . . . . . . . 0.1225 0.0710 0.0050 | See Reichstag, 12. Legislaturperiode, I. Session, 1907, No. 226. 316 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION §2. — Insured Population Under the 1889 Act the following were compulsorily insured as from age 18: (1) workmen, assistants, journeymen, apprentices or domestic servants, who receive a salary or emolument; (2) salaried employees whose annual salary does not exceed 2,000 RM. The 1899 Act extended the field of compulsory insurance to include foremen, technical employees, teachers and tutors, whose salary does not exceed 2,000 RM. In addition both these Acts provided that the liability to insure could be applied to small tradesmen by a decision of the Federal Council. Under the Act of 1911 compulsory social insurance covered, as from 1 January 1912, all workers belonging to one or other of the following classes: (1) workmen, assistants, journeymen, apprentices, domestic servants; (2) works officials, foremen and other salaried employees in a similar position, provided that in each case this employment is their principal occupation; (3) commercial clerks and apprentices, assistants and apprentices in pharmacies; (4) members of the theatrical profession and musicians ; (5) teachers and tutors; (6) crews of seagoing vessels and of vessels engaged in inland navigation, who fulfil the following conditions: (a) they must have attained age 16; (b) they must be in receipt of a remuneration other than free maintenance; (c) if they belong to one of the classes enumerated under (2) to (5) inclusive, their regular annual salary must not exceed 2,000 RM. It was also provided that the Federal Council could extend the liability to insurance to the following persons either throughout the Federation or only in particular districts: (1) persons carrying on industry and other owners of businesses who employ regularly not more than one insured workman; (2) persons engaged in home industry whatever the number of workers they employ. 317 GERMANY ESTIMATE OF THE INITIAL INSURED POPULATION In order to estimate the initial insured population, reference was made to the industrial census of 5 June 1882. Taking into account the various classes of workers covered by the insurance scheme, figures were obtained for their total, and for its distribution in quinquennial or decennial age groups. The distribution at individual ages was thence deduced directly by graphic interpolation. Account was taken of the growth of the insured population between 1882 and 1889 on the basis of the known increase in the total population between 1880 and 1885. Two further adjustments were made to allow for, on the one hand, insured relatives of an agricultural employer living with him and working for him in return for remuneration and, on the other hand, salaried employees who are not insurable by reason of the variety of their employments [6: pp. 81-83]. The figure finally arrived at for the insured population in the middle of 1889 was 11,018,000, including 7,322,000 men and 3,696,000 women. SUBSEQUENT ESTIMATES OF THE INSURED POPULATION The industrial census of 14 June 1895 brought out a total of 11,813,000 workers engaged in insurable employment, distributed in the following manner: Males Females Age group Total (in thousands) 18-20 20-30 30-40 40-50 . . . . 750 754 2,417 1,618 1,035 67» 345 110 542 561 1,488 547 405 326 179 58 1,292 1,315 3,905 2,165 1,440 1,004 524 168 . . . 7,707 4,106 11,813 » » " » 60-70 » . 70 years and over Total 331,271 were added to the males to take into account workers completing their military service, and the estimate was projected to the beginning of the year 1900 by means of an annual coefficient of increase 1 / fixed at 1.013942, on the basis of the increase shown by a comparison of the two industrial censuses of 1882 and 1895 [16: pp. 11-13]. 1 The annual coefficient oí increase of a population is simply the ratio of the population at the end of the year to that at the beginning of the year, on the assumption that this ratio remains constant. 318 ACTUARIAL T E C H N I Q U E A N D F I N A N C I A L ORGANISATION The same procedure and the same coefficient of increase were adopted until the results of the 1907 industrial census became known. This census—by the inclusion of a question for that purpose—enabled a direct enumeration to be made of the male and female insured populations. In each age group the figure for the insured population was divided by that for the total population to produce an " insurance ratio ". The results are reproduced below (table XX). TABLE X X . — TOTAL A N D I N S U R E D POPULATIONS (From the industrial census of 12 June 1907) Females Males Age group Total population (1) (2) 16-18 years . 18-20 » 20-25 » 25-30 » 30-40 " 40-50 » 50-60 » 60-70 » 70 and over . Unknown . . 1,191,927 1,162,590 2,654,736 2,467,146 4,220,293 3,177,104 2,167,715 1,386,701 719,451 3,120 Total . . 19,150,783 Proportion Total Insured insured population ( 4 ) = | y X 1,000 population Proportion Insured insured population (7)4^X1,000 (5) (6) (7) (4) (5) 1,600,482 2,382,126 1,524,351 865,159 358,479 44,018 659.7 716.2 589.7 648.7 564.4 479.8 399.1 258.5 61.2 673,869 644,638 1,135,418 564,567 652,419 475,429 306,970 137,349 17,166 563.0 549.5 429.7 230.9 154.8 145.7 126.0 82.1 18.8 — — 1,196,941 1,173,156 2 6 " 9i¿ 2,445,124 4,213,857 3,263,413 2,437,183 1,672,056 913,176 1,884 — — 9,959,145 — 19,959,134 4,607,825 — (3) 786,405 832,620 In order to obtain the insured population as at 1 January 1914, the following procedure was adopted [19: pp. 11-14]. Recourse was had to the distribution of the total population, as at 1 January 1911, according to year of birth and year of age, drawn up by the Imperial Statistical Office 1. This distribution was projected to 1 January 1914, by applying to each group an appropriate survivorship factor in accordance with the German mortality table 1901-1910 a. Applying to the figures obtained in this way the insurance ratios in table XX above, the insured population as at 1 January 1914 was obtained and its distribution according to year of birth. This produced a total of 11,420,600 men and 4,980,600 women, distributed as follows: 1 2 Statistik des Deutschen Reichs, Band 240 (2), p. 254. This method was justified by a check calculation which reproduced with • sufficient accuracy the figures of the 1907 census from those of the 1911 census. 319 GERMANY TABLE X X I . INSURED POPULATION (As at January 1914) Males Males Females Year of birth (in thousands) (in thousands) 1897 1896 1895 1894 1893 1892 1891 1890 1889 1888 1887 1886 1885 1884 1883 1882 1881 1880 1879 1878 1877 1876 1875 1874 1873 1872 1871 1870 1869 1868 1867 1866 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Females Year of birth 446.2 468.8 461.0 465.3 458.3 438.2 430.0 412.7 390.5 382.8 367.1 348.5 338.8 320.6 295.3 291.5 272.4 271.1 263.8 258.7 252.5 246.0 235.6 222.5 211.2 206.0 165.7 184.6 175.4 162.1 153.0 151.0 376.9 374.5 352.9 339.3 311.1 271.9 240.8 204.6 172.4 149.3 128.8 113.8 101.5 90.2 80.1 76.8 72.0 72.8 72.8 71.9 70.8 70.4 67.8 64.3 61.0 61.0 48.7 56.1 54.5 51.4 49.4 51.2 1865 1864 1863 1862 1861 1860 1859 1858 1857 1856 1855 1854 1853 1852 1851 1850 1849 1848 1847 1846 1845 1844 1843 1842 1841 1840 1839 1838 1837 1836 1835 1834 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136.9 132.9 125.0 115.6 107.4 109.8 104.8 96.8 89.9 81.5 74.3 74.1 68.1 61.1 53.0 48.4 39.8 30.9 24.1 20.1 17.5 13.7 10.8 9.7 7.2 6.4 4.5 3.5 2.4 \.l 1.0 0.5 47.4 47 5 44"8 41'5 37'6 39'2 37-0 33-5 301 27'3 23-7 24-2 21-4 20-6 17-9 18-5 15-8 14-0 11-2 10-4 9-7 8-1 6-4 5'6 3-2 2-1 0-6 0-2 0-1 — — ~ The same method also enabled an estimate to be made of the insured population at the end of the year 1914 and its age distribution. ESTIMATES OF THE NUMBER OF ENTRANTS INTO INSURANCE EACH YEAR In the preparatory investigations it was assumed [7: p. 101] that all entries would take place at the three youngest ages, 16, 17 and 18, and, moreover, that their number (^dtx and fdly) at each age and for 320 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION each sex would remain constant from year to year and could be deduced from the age distribution (JTLX and êFy) of the initial population by means of the formulae For females For males m 9lw = JRw' £>l 17 ^ #17 et ¿17 - # 1 6 »aa ¿16 ¿18 JYL — l t = t/C18 = #18 " jaa ¿17 # n jaa I'll In a subsequent calculation [16: p. 43-44] it was assumed that all entries would take place at ages 16, 17 or 18 and that the numbers m 9Lx and f9ly could still be calculated by means of the above formulae but that the basic age distribution would be that shown for each sex by the 1895 industrial census. The following results were thus obtained for male and female entrants: ^ ^ = 370,500 m = 10,800 = 6,600 9Hu m dlla 1 ¡ftu = 265,400 f 9l» = 12,300 JLjg = 5,400 Instead of supposing, as hitherto, that these numbers would remain constant, it was assumed that they would increase in conformity with the annual coefficient of increase of the active population, whose value / = 1.013942 was obtained from a comparison of the industrial censuses of 1882 and 1895 \ Consequently, in order to estimate the number of entrants in the year 1900, the numerical values of mdZx and ffTLv obtained from the industrial census were multiplied by the factor fiJ>. In order to obtain a closer estimate the following procedure was adopted in a later memorandum [19: pp. 14-18]. The number of entrants at age 16 was deduced, for males and females separately, Age at entry 17 18 19 30-39 » » » Males . » 1,000 250 100 55 200 100 75 Females .1,000 225 90 50 210 110 90 1 In a previous investigation [13: p. 3617] the annual coefficient of increase was taken to be 1.00935, which corresponded to the increase in the total population between 1816 and 1900. 321 GERMANY from t h e insured populations at the beginning and end of the year 1914. Applying to these numbers the proportions given in t h e table on page 320, which were obtained from statistical data based on contribution cards, the numbers of entrants at ages greater t h a n 16 were obtained. When the number of entrants at each age bad been calculated in this manner for t h e year 1914, table X X I I was constructed [ 1 9 : p p . 18-19] by reference t o figures obtained in t h e manner indicated above 1 for the insured population at the beginning and end of t h e year. This table gives a complete picture of t h e movement of insured persons during the year in question; in particular t h e total n u m b e r of exits from insurance and their age distribution are shown. TABLE X X I I . — MOVEMENT OF THE INSURED POPULATION DURING 1 9 1 4 (Estimates in thousands) Males Year of birth 1898 1897 1896 1895 1894-1885 . . . 1884-1875 . . . 1874 and earlier. Total . . . Females Population at beginning of 1914 at end of 1914 446.2 468.8 461.0 4,032.2 2,707.5 3,304.9 456.9 468.2 482.4 465.3 3,960.6 2,633.0 3,148.2 11,420.6 11,614.6 Population Entrants Exits at at end beginning of 1914 of 1914 Entrants Exits 1.1 458.0 92.0 114.0 46.0 t 32.4 20.7 25.0 92.0 163.6 46.0 120.5 34.0 190.7 376.9 374.5 352.9 2,033.5 745.6 1,097.2 387.0 .388.0 87.0 371.9 35.0 367.8 19.0 340.6 81.0 1,815.5 727.3 43.0 1,051.7 35.0 1.0 92.0 41.7 31.3 299.0 61.3 80.5 815.0 4,980.6 5,061.8 688.0 606.8 621.0 The number of entrants in later years was deduced from t h e figures obtained for 1914 b y means of t b e annual coefficient of increase / , for which t h e v a l u e o f 1.02 was adopted for males and 1.014 for females. ESTIMATE OF THE A N N U A L N U M B E R OF E X I T S FROM INSURANCE The t o t a l number of exits from the field of insurance during 1914, shown in table X X I I , when compared with t h e exits due t o d e a t h a n d invalidity, produced [19: p p . 19-20] figures which related t o exits from 1 See p. 320. 21 322 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION insurance due to other miscellaneous causes. The latter are shown below: Exits from insurance top cause» other than death or invalidity Age 18 19 30-39 » >» » Total Males Females 90,600 30,900 19,000 146,400 101,700 , 55,800 91,000 40,600 30,100 188,900 53,400 18,000 444,400 422,000 For later years the numbers of exits were deduced from the figures relating to 1914 by means of the annual coefficient of increase / already used for entrants, that is, 1.02 for males and 1.014 for females. EXPERIENCE The annual returns of the Federal Insurance Office produced the following figures: Year 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 Insured population in thousands 11,490 11,650 11,813 11,978 12,145 12,314 12,486 12,660 12,836 13,015 13,197 13,381 Year 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 Insured population in thousands 13,600 13,756 13,948 14,143 14,958 15,226 15,444 15,660 15,878 16,099 16,324 § 3. — Number of Beneficiaries From the statistical returns published each year are extracted the numbers of pensions due to invalidity l , temporary invalidity (sickness} and old age, which were current on 1 January in each year. 1 The conditions of award and the method of calculation, in respect of the various classes of benefit, are described in Chapter II, pp. 331-337. 323 GERMANY TABLE X X U I . TOTAL NUMBER OF PENSION BENEFICIARIES: EXPERIENCE Pensions In force in year Invalidity 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 11,999 37,815 71,755 110,377 161,670 210,859 264,899 324,319 405,337 486,945 574,833 663,140 734,985 780,762 814,575 841,992 868,086 893,585 918,760 940,875 965,624 998,339 I Sickness — — — — — ' — — — 5,118 8,700 12,146 14,186 16,977 20,141 22,099 20,081 19087 18,502 16,965 15,768 15,905 16,555 Old Age Total 118,997 150,403 166,976 183,168 195,723 203,955 203,644 201,329 195,133 188,472 179,450 168,550 156,618 145,466 134,080 125,603 116,887 108,637 102,362 98,335 93,369 90,071 87,261 118,997 162,402 204,791 254,923 306,100 365,625 414,503 466,228 519,452 598,927 675,095 755,529 833,944 897,428 934,983 962,277 978,960 995,810 1,014,449 1,034,060 1,050,012 1,071,600 1,102,155 TABLE XXIV. — NUMBER OF LUMP SUM PAYMENTS MADE AS REPAYMENTS OF CONTRIBUTIONS Year 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 . . . ; On death On marriage 2,271 16,766 22,537 25,811 30,367 34,142 32,342 32,028 32,603 32,526 33,951 32,829 35,464 36,779 37,560 34,936 38,297 5,411 8,245 63,444 99,805 121,977 135,097 156,122 158,184 153,282 154,468 154,368 151,856 153,226 152,478 151,347 148,441 147,292 154,901 18,094 On grant of pension under workmen's compensation insurance — — — 234 355 575 778 855 767 710 616 586 549 494 446 279 324 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Further, at the end of 1913, 12,066 widows' or widowers' pensions and 94,435 orphans' pensions were in course of payment. The repayment of contributions 1 in the event of death or marriage and, as from 1900, to holders of a workmen's compensation pension, was made in one lump sum: the number of such payments in respect of each year is given in table XXIV (p. 323). Repayments of contributions were abolished as from 1 January 1912, when the benefit of insurance was extended to survivors; however, a certain number of them were made, with retrospective effect, after that date. TABLE OF SYMBOLS INTRODUCED IN CHAPTER I / = Life table (healthy lives and invalids together). jaa jìi l x lx = Number of healthy lives and invalids respectively from the validity table. GX = Aggregate or ultimate probabilities of cessation of invalidity. O'w+ft = i = Rates of becoming invalid. ~aa "* = Probabilities of death of a healthy life without previously having become invalid. I1 = Life table for invalids. Select probabilities of cessation of invalidity. \x (jl = Mortality rates of invalids. ¡KJJ = Average annual number of days of sickness. L. r* = Probabilities t h a t an insured man will on decease leave one or m o r e claimants t o benefit; = Probabilities t h a t an insured woman who dies after becoming a-widow will leave one or more orphans aged less than 15. W,y = Probabilities t h a t an insured.man will on decease leave a widow. Y = Probabilities t h a t an insured woman is single. ¡i = Probabilities of marriage in respect of females. Fy = N u m b e r of wives of insured men. •po v = N u m b e r of healthy wives (of insured men) who are themselves insured. GERMANY 325 A = Proportion of widows of workers in insured trades who are themselves employed. Q = Probabilities that the widow of an insured man is herself insured. ryis 'v = Probabilities that the widow of an insured man will never enter into insurance. Qtp v = Probabilities that the widow of an insured man who is invalid will be in receipt of a pension. W?" P = Number of invalid widows (of insured men) who are not pensioned. Y^tms v = Number of healthy widows (of insured men) who will not enter into insurance. W = Number of widows (of insured men) who are themselves insured. W,p = Number of invalid widows (of insured men) who are pensioned. lz = Life table for children. f}Z = Number of children aged z according to the age x of father. = Number of fathers corresponding to the kx children. Y) '* = Probabilities that an insured man aged x is the father of a child aged less than 15. / = Annual coefficient of increase. jfî * = Initial male insured population or the male insured population at a given date. es " = Initial female insured population or the female insured population at a given date. m — Annual number of male entrants into insurance. ^dX-a = Annual number of female entrants into insurance. fTi CHAPTER II FINANCIAL ESTIMATES, BASES AND EXPERIENCE § 1. — Contributions WAGE CLASSES AND RATES OF CONTRIBUTION Insured persons are divided iiito classes according to their wages and for each class a rate of contribution is fixed which is apportioned equally between the insured person and his employer. The 1889 Act instituted four wage classes which were defined, together with the corresponding rates of contribution, as follows 1M. Wage class I II Ill IV Annual wages in marks up 350 550 more t o 350 t o 550 t o 850 t h a n 850 Weekly rate of total contribution in marks 0.14 0.20 0.24 0.30 Without altering the first three classes, the 1899 Act limited class IV to wages between 850 and 1150 marks and created a new class V for wages in excess of 1150 marks, to which was assigned a weekly rate of 0.36 marks K On 1 January 1912, when the benefit of insurance was extended to survivors, the wage classes remained unaltered but the rates of contribution were increased to the following figures: Wage class I II Ill IV V Annual wages in marks up t o 350 t o 550 t o 850 t o more t h a n 350 550 850 1,150 1,150 Weekly rate of total contribution in marks 0.16 0.24 0.32 0.40 0.48 These rates of contribution were fixed by the Act for a period of ten years. 327 GERMANY CALCULATION OF THE PRESENT VALUE OF CONTRIBUTIONS 1 The present value of a unit contribution payable as long as the insured person is a healthy life is \ = —•„ where D* = L• v , N . = > , D* and V „aa "x -x ~ < -x ¿¿¿"x x 1+ Í As the contributions are payable weekly, the present value was taken as aa(52) aa 3.x — ax Q.x a2 where a^ = 1 and a, =0.5154, these being approximate values for a rate of interest of 3.5 per cent. The normal annual number of weekly contributions was taken as 47, .-since the pensions were to be reduced if the annual number of weekly »contributions was less than this figure. Account was taken of the loss of contributions during periods of sickness [7: p. 100] by reference to a sickness table which gave for each age the average number K^ of days of sickness per annum per insured person 2 . The number of weekly contributions not paid on account of sickness was taken as K equal to —- and the corresponding present value was calculated by the iormula * 2 D ;" K . ? D:° Finally, the present value of the expected contributions for an insured erson aged x was calculated, on the basis of a unit weekly payment, y the formula E n .„ aa(«2) Cx = 47 ax 0*2°* x —— 5 7 Dx Subsequently [8: p. 300] the adjusting factor for periods of sickness was abolished and the number of weeks of contribution was diminished by one. If payment of contributions ceases in all cases at a fixed age, say for example 70, temporary expressions are used a.'x,70-x| rC - iC oa 1 More modern symbols have been substituted for those used in the original memoranda. 2 See Chapter I, p. 301. 328 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION and „atusa) „aa«2) aa<62) 3-Jc, 70-x\ As an illustration are reproduced from a later memorandum [19: p. 64], the numerical results obtained at a rate of interest of 3.5 per cent, for the present value of future contributions in respect of an insured person of a given age, when (a) payments are made weekly, (b) the annual amount of the contribution is a unit and (c) the payments are continued until the insured person becomes invalid or dies. P R E S E N T V A L U E a ° a < 6 2 ) O F A U N I T CONTRIBUTION P A Y A B L E TABLE X X V . x W E E K L Y AT 3 . 5 P E R CENT. I N T E R E S T Age of insured person at date of calculation of present valu« Maies Females 16 y 2 years 17 y 2 » 18 % " 19% " 21.150 20.927 20.703 20.475 20.350 20.090 19.828 19.562 20 y 2 2i y 2 22 y 2 23 y 2 24 y 2 25 y 2 26 y 2 27 y 2 28 y 2 29 y 2 » » » » » » » » » » 20.244 20.007 19.764 19.513 19.254 18.987 18.711 18.428 18.137 17.840 19.293 19.021 18.745 18.466 18.183 17.901 17.621 17.340 17.056 16.767 30 y 2 3i y 2 32 y 2 33 y 2 34 y 2 35 y 2 36 % 37 y 2 38 y 2 » » » » » » » " » 39 y 2 » 17.535 17.222 16.902 16.574 16.238 15.893 15.540 15.178 14.807 14.428 16.472 16.168 15.856 15.535 15.206 14.867 14.521 14.167 13.806 13.437 40 y 2 41 y 2 42% 43 y 2 44 y 2 45 y 2 46 y 2 47 y 2 48 y 2 • 49% » » .. » » » » » ». » 14.040 13.644 13.240 12.831 12.416 11.998 11.577 11.154 10.731 ' 10.307 13.062 12.680 12.293 11.901 11.503 11.100 10.694 10.283 9.870 9.454 . Age of insured person at date of calculation of present value 50% years . Males Females 9.036 8.616 8.194 7.769 7.339 6.915 6.506 6.108 5.716 5.326 51 % 52% 53% 54% 55% 56% 57 % 58% 59% " » » » » » » » . . . 9.885 9.464 9.044 8.624 8.203 7.783 7.365 6.950 6.539 6.134 60% 61 % 62% 63% 64% 65 % 66% 67 % 68 % 69% » » » » » » » » » » . . . . . . . . . . 5.735 5.344 4.963 4.592 4.234 3.889 3.558 3.241 2.937 2.648 4.933 4.545 4.176 3.826 3.497 3.190 2.912 2.665 2.445 2.245 70% 71 % 72% 73% 74% 75 % 76% 77% 78% 79% » » » » » » » » » » . . . . . . . . . . 2.374 2.119 1.890 1.690 1.526 1.402 1.303 1.213 1.128 1.045 2.061 1.894 1.745 1.611 1.490 1.381 1.279 1.181 1.076 0.975 80% " 0.957 0.805 . . . . 329 GERMANY EXPERIENCE Detailed figures are published annually in respect of thecontributions received by the territorial insurance institutions. Below are reproduced: (1) the total annual number of weekly contributions; (2) the distribution of 1,000 contributions between the different wage classes; (3) the average amount of the weekly contribution. TABLE XXVI. — 427,183 424,418 428,584 441,859 453,202 479,512 490,680 507,630 544,232 523,154 541,613 551,220 575,338 596,464 619,054 639,875 655,980 b65,932 674,195 698,382 733,816 730,848 752,118 l-t . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . Distribution it 1,000 contributions into classes Number of weekly contributions in thousands Year 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 W E E K L Y CONTRIBUTIONS RECEIVED EACH Y E A R BY REGIONAL INSTITUTIONS . 253 235 229 230 227 221 214 206 199 189 179 157 146 138 133 127 119 114 105 91 84 77 78 II III IV 384 404 397 394 392 385 379 370 361 342 336 329 324 313 305 290 274 263 250 241 227 207 209 217 223 232 233 235 241 243 244 244 238 239 254 259 255 250 244 242 243 254 259 262 256 257 146 138 142 143 146 153 164 180 196 158 162 169 174 175 178 183 183 179 178 177 174 176 164 V — — — — • — • — — — 73 84 91 97 119 134 156 182 201 213 232 253 284 292 Average amount of a weekly contribution in marks 0.2081 0.2086 0.2097 0.2099 0.2104 0.2117 0.2133 0.2155 0.2174 0.2255 0.2280 0.2318 0.2340 0.2379 0.2406 0.2446 0.2492 0.2520 0.2549 0.2586 0.2623 0.3498 0.3491 The annual contribution income appears in the last column of table XXXVIII (p. 389). § 2. — State Aid Financial aid from the State included, from the date of inauguration of the scheme until 1 January 1912, the individual supplement (Reichszuschuss) of 50 marks, which was added to each invalidity and old-age pension, and also the repayment to the insurance institutions of the increments in respect of periods of military service, based on the scale :330 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION of the second wage class. On 1 January 1912 the individual supplement was extended to widows' and widowers' pensions and, to the amount of 25 marks, to orphans' pensions; at the same time a grant-in-aid was introduced for the purpose of increasing the amount of each widow's allowance by 50 marks and each orphan's allowance by 16.66 marks; •on the other hand, the repayment of the increments in respect of periods of military service was abolished on that date. •CALCULATION OF THE PRESENT VALUES OF INDIVIDUAL SUPPLEMENTS AND GRANTS Since the individual supplements and grants were fixed in amount for each class of pension, the present value may be deduced directly from the present value of the fixed portion of the corresponding benefit. The method of calculation of the latter is described in § 3 below 1 . EXPERIENCE The total amount of the yearly financial grants from the State is ¡shown in thousands of marks in table XXVII. TABLE XXVII. — STATE GRANTS—EXPERIENCE (in thousands of marks) Individual supplements Year 1891 1892 1893 1894 1695 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 ' 1 ,. . . . . . . . . . . . . . . . . . . . . . . . . See pp. 337 et seq. . 6,050 9,041 11,337 13,922 16,930 19,225 21,824 24,380 27,080 30,714 33,803 37,756 41,732 45,126 47,174 48,553 49,392 50,266 51,214 52,219 52,933 55,069 58,526 Eepayment of increments in respect of periods of military service 1 3 7 13 21 28 48 68 93 122 150 177 204 228 256 287 319 350 Total 6,050 9,041 11,337 13,923 16,933 19,232 21,837 24,401 27,108 30,762 33,871 37,849 41,854 45,276 47,351 48,757 49,620 50,522 51,501 52,538 53,283 55,069 58,526 GERMANY 331 In this table the second column includes, up to 1911, only the individual supplements added to invalidity and old-age pensions, while from 1912 onwards it includes also the individual supplements added to widows' and orphans' pensions and the individual grants added to widows' and orphans' allowances. § 3. — Benefits The 1889 Act from the outset provided for invalidity and old-age pensions and for repayments of contributions to survivors of deceased insured men and to insured women on marriage. . These classes of benefit continued to be granted until 1 January 1912, but the 1899 Act introduced appreciable amendments to the conditions of award, the method of calculation and, consequently, the amount of the payments. The 1911 Act introduced pensions and allowances to widows and orphans and at the same time abolished the repayments of contributions; the invalidity and old-age pensions were also subjected to various amendments. In addition, the insurance institutions were empowered from the commencement of the scheme to grant to insured persons or invalids medical benefit (called " optional " benefit) for the purpose of the prevention or cure of invalidity. A brief description will be given of the conditions of award—especially the provisions relating to waiting period and maintenance of benefit rights—and the rules for the calculation of benefits which have been successively applied. The various classes of benefit will be considered in turn. In the preceding paragraph it was seen that all classes of pension and also widows' and orphans' allowances included a portion whose cost is borne by the State and the amount was mentioned at which this portion was successively fixed. Hence it is only necessary here to consider the amount of the benefits which are borne by the insurance institutions. CONDITIONS OF AWARD AND AMOUNT OF BENEFIT Invalidity Pensions In the Event of Permanent Invalidity Since the coming into force of the scheme the invalidity pension has, in principle, been awarded to all insured persons who become permanently incapable of remunerative work (excluding incapacity covered by workmen's compensation insurance). Under the 1889 Act an insured person was deemed to be an invalid when by reason of his bodily or mental condition he was no longer able to earn a wage at least equivalent to the sum of (1) one-sixth of the average annual wage on the basis of which contributions had been paid on his behalf during the last five years and (2) one-sixth of 300 times the average daily wage of workmen in the locality where he last worked otherwise than in a purely , temporary capacity. 332 A C T U A R I A L T E C H N I Q U E AND FINANCIAL ORGANISATION The 1899 Act simplified the definition of invalidity. As from 1 January 1900, an insured person was deemed to be an invalid when his earning capacity was permanently reduced by one-third, that is to say when he was no longer capable of earning, in any employment suited to his strength and ability which could reasonably be assigned to him in view of his training and former employment, one-third of the wage usually earned in the same district by a physically and mentally sound worker of the same kind with similar training. This definition was essentially retained by the 1911 Act. In the Event of Temporary Invalidity The 1889 Act provided in addition that an insured person who was not permanently incapable of remunerative work, but who had been disabled continuously for a year, should receive an invalidity pension for the further duration of his incapacity. As from 1 January 1900, under the 1899 Act the continuous period of disablement entitling to pension was reduced to 26 weeks. Temporary invalidity pensions were continued under the 1911 Act under the heading of " sickness pensions " (Krankenrenten). Waiting Period The award of an invalidity pension has always been subject to the completion of a waiting period. In the beginning this comprised five years each containing 47 weekly contributions. As from 1 January 190O it was sufficient for 200 weekly contributions to have been paid, provided that not less than 100 contributions had been paid under the provisions of the compulsory insurance scheme x. From the inauguration of the scheme until 1 January 1912 the periods reckoned towards completion of the waiting period included, in addition to weeks covered by contributions, weeks of sickness up to a maximum of one year and weeks of military service. As from 1 January 1912 only contributions actually paid were taken into account. A transitional provision of the 1889 Act allowed periods of salaried employment, military service and sickness before the date of coming into force of the Act to be taken into account for the completion of the waiting period, if they were not separated from the occurrence of the event insured against by more than five years and provided that one year's compulsory contributions had been paid. The 1899 and 1911 Acts introduced analogous transitional arrangements applicable to the classes of insured persons to which they extended the liability to insurance. Maintenance of Benefit Rights In the early years of the scheme's operation the right to benefit was suspended when 47 weekly contributions had not been paid either compulsorily or voluntarily during four successive years, taking into account the weeks of sickness, up to a maximum of one year, and the weeks of military service which were deemed to be equivalent to weeks actually covered by the payment of contributions. The right to benefit was restored after a new waiting period of five years. 1 If this proviso was not complied with, the waiting period could not be completed until a total of 500 contributions had been paid. 333 GERMANY Under the 1899 Act the right to benefit was suspended when the stamps appearing on an insurance card two years after the date ofissue did not represent at least 20 weekly contributions; the right to benefit was restored after a new waiting period of 200 weekly contributions. The 1911 Act introduced the following two modifications to the provisions in force: (1) an insured person aged not less than 40 nor more than 60 could revive his right to benefit only if he had paid 500 weekly contributions before the'lapse of his right and in that case he was subjected to a new waiting period of 500 weekly contributions; (2) an insured person aged more than 60 could revive his right to benefit only if he had paid 1,000 weekly contributions before the lapse of his right and in that case he was subjected to a new waiting period of 200 weekly contributions. For the maintenance of benefit rights the following periods were taken into account in addition to weeks covered by the payment of contributions: under the 1889 Act, weeks of sickness up to a maximum of one year and periods of military service; under the 1899 Act, which on this point was reproduced by the 1911 Act, periods of sickness and military service, as before, and in addition periods during which benefit is received under the workmen's compensation or other insurance schemes. Amounts of the Pension borne by the Insurance Scheme The invalidity pension charged to the insurance scheme has been from the beginning composed of two portions, (1) a basic sum (Grundbetrag) and (2) increments (Steigerungsbetrag) which depended on the number and amount of the contributions paid. As from 1 January 1912 it could include in addition a bonus (Kinderzuschuss) for each child under 15 years of age. An indication will be given below of the scales which have been successively applieu to eacu oi tuese portions of pension. The 1889 Act fixed the basic sum at 60 marks per annum for all insured persons. Under the 1899 Act the basic sum comprised: 0.12 marks for each contribution paid in wage class I "•i^i jj ,, H ii ii )» ii ii *• "•1Ö U.lo ,, ,, ,, ,, ,, ,, ,, . ,, ,, ,, ,, ,, ,, ,, ,, ,, HA A » 0.20 „ „ „ „ „ „ „ „ V With the help of this scale the amount of the basic sum was obtained by taking the sum of the amounts corresponding to the 500 contributions paid in the highest wage classes; if the number of contributions was less than 500, it was made up to this total on the assumption that the missing contributions had been paid in wage class I. The 1911 Act did no. more than reproduce the provisions relating to the calculation of the basic sum. 334 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The increments were calculated in accordance with the following scales : Annual Increment, in marks, corresponding to a weekly contribution Wage class I II Ill IV V Before 1 January 1900 On and after 1 January 1900 0.02 0.06 0.09 0.13 0.03 0.06 0.08 0.10 0.12 . . Under the 1911 Act, if the recipient of an invalidity pension maintained one or more children under 15 years of age, he received for each child a bonus equal to one-tenth of the amount of his pension, including the State supplement. SII J A 7> .* An insured person aged 70 or more who was not an invalid received an old-age pension. If he subsequently became an invalid the invalidity pension was substituted for the old-age pension. Waiting Period The waiting period prescribed for entitlement to the old-age pension was fixed by the 1889 Act at 30 contribution years, that is to say, 30 times 47, or 1,410 weekly contributions. It was reduced by the 1899 Act to 1,200 weekly contributions. The weeks reckoning towards the completion of the waiting period were determined according to the same rules as for invalidity pensions. As a transitional provision a reduction of the waiting period was allowed under the following conditions. Under the 1899 Act the waiting period was reduced by x — 40 years for every insured person whose age x was greater than 40 at the date of coming into force of the scheme, if he had completed during the three years preceding that date at least 141 weeks of military service, sickness or employment in àn occupation which was compulsorily insurable under the Act. As from 1 January 1900, this transitional provision was modified as follows. The waiting period was reduced by 40 (x — 40) \seeks of contribution for every insured person whose age x was greater than 40 at the date when the insurance scheme was applied to his occupational group, if he proved that during the three years preceding that date he had been employed at that trade—even if during that period his employment had been interrupted by military service, sickness or by other circumstances specified in that Act. No such proof was required of an insured person if 200 weekly contributions or more had been paid during the first five years of the application of the scheme to his occupational group. 335. GERMANY Maintenance of Benefit Rights The statutory provisions relating to invalidity pensions have alwaysbeen applicable to old-age pensions. Amount of the Pension borne by the Insurance Scheme The old-age pension has since the origin of the scheme consisted of' only one element, for the calculation of which the two following scales.were applied in turn: Annual amount, in marks, corresponding to one weekly contribution Wage class Before 1 January 1900 On and after 1 January 1900 0.04 0.06 0.08 0.10 0.05 0.075 0.10 0.125 0.15 I II Ill IV V — Before 1 January 1900 the amount of the old-age pension was" assessed, on the basis of the first of the above scales-, by calculating; the total sum corresponding to the number of weekly contributions. required for the waiting period, that is, 1,410. In cases where periods of prior service were reckoned as weeks of contribution, they were: made to correspond, in calculating the amount of the old-age pension, with the average wage earned during the 141 weeks of employment. prescribed for the application of the reduction in the waiting period. On and after 1 January 1900 the method of calculation was the same but the scale was altered (see above) and the number of weekly contributions required'for the waiting period was reduced to 1,200. In* cases where the number of weekly contributions actually paid' was less'il riAA //AA _- J A T AnAt}\ I ^-J- -*' - ' tumi ¿\)\j ¡ i w as íruin i January l a i z ; aim perluu» oi priur service were reckoned as contribution weeks, these periods were taken into account, in the calculation of the amount of pension, on the basis of the average wage earned during the three years of employment prescribed for the application,of the reduction in the waiting period. In. cases where the number of weekly contributions actually paid was at' least 200 (400 as from 1 January 1912) and periods of. prior service; were reckoned as contribution weeks, these were divided, between thewage classes, in the calculation of the amount of, pension^.proportionatelyr to the number of contributions paid in each of these classesPayments io Survivors' The 1911 Act instituted, as from- 1 January 1912, pensions and« allowances for the benefit of widows, and onphans to.be-granted under the same conditions as to waiting period and; maintenance of benefit! rights as invalidity pensions. Payment», to survivors were defined int the following manner. 336 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Widows'1 (or Widowers') Pensions A pension is granted to the widow of an insured man if she is permanently disabled *; a widow who is temporarily disabled receives, after 26 consecutive weeks of invalidity, a widow's pension for the further duration of her invalidity. The payment of a widower's pension is subject to two supplementary conditions: that the insured wife defrayed the whole or the greater part of the cost of maintenance of her family and that the widower is in need. The amount of the widow's (or widower's) pension which is borne by the insurance scheme is fixed at 3/10 of the amount of the invalidity pension, borne by the insurance scheme, which the invalid received or which the insured person would have received if instead of dying he had become disabled. Widow's Allowance (Witwengeld) An allowance equal to 12 monthly payments of the widow's pension is paid on the death of the husband, if the widow herself fulfils the conditions regarding the waiting period and maintenance of benefit rights required for the invalidity pension or if the widow is in receipt of an invalidity pension because she had been herself insured. Orphan's Pension The orphan's pension is granted, on the death of an insured father, to his legitimate children aged less than 15 and, on the death of an insured mother, to her fatherless children aged less than 15. The amount of the orphan's pension which is borne by the insurance scheme is fixed, for the first orphan, at 3/20 and, for each further orphan, at V40 of the amount of the invalidity pension, borne by the insurance scheme, which the invalid received or which the insured person would have received if instead of dying he had become disabled. Orphan's Allowance (Waisenaussteuer) An allowance equal to eight monthly payments of the orphan's pension is paid to each orphan on attaining the age of 15, if the mother herself fulfils the conditions regarding the waiting period and maintenance of benefit rights required for the invalidity pension or if she is in receipt of an invalidity pension because she had been herself insured. Repayment of Contributions Under the 1889 Act half of the contributions paid on behalf of the insured person were repayable in the three following cases: • (1) if an insured man dies before becoming entitled to a pension: the repayment inures to the benefit of his widow and, in the absence of a widow, of his legitimate children under 15 years of age; (2) if an insured woman dies before becoming entitled to a pension: the repayment inures to the benefit of her legitimate children under 15 years of age if they are already fatherless; 1 It cannot be received at the same time as an invalidity pension granted to the widow by virtue of her own personal insurance; in cases where the widow is entitled to both classes of pension at the same time she receives the one which is the greater in amount. 337 GERMANY (3) if an insured woman marries and ceases to be insured before becoming entitled to a pension: she herself receives the benefit of the repayment. The 1899 Act extended the benefit of the repayment of contributions to the following: children whose father has never supported them; a widower whose wife was the support of the family; injured workmen rendered permanently incapable of work. The 1899 Act stipulated that the repayments could not be made if at least five years had not been covered by the actual payment of contributions. The 1899 Act reduced to 200 the number of weekly contributions which must have been paid. The 1911 Act repealed all provisions relating to the repayment of contributions. CALCULATION OF PRESENT VALUES OF INVALIDITY PENSIONS 1 Unit Invalidity Pension in the Course of Payment First Calculation [7: p. 96] The present value of a unit invalidity pension in the course of payment was calculated by means of a continuous process using the formula a* = 1 + v (1 — (7X) a*+1 commencing with aM which has been taken equal to unity (ox represents the probability of cessation of invalidity) 2 . For monthly payments the formula is o ¿(12) = ex i (> /> —3C "•X "1* and 0.463 was taken as an approximate value for S12. Second Calculation [16: p. 30] When the probabilities of cessation of invalidity were defined by a select table 3—for durations of invalidity not greater than 11 years— select annuity values a ^ . ^ were calculated instead of a x , commencing with the identity a i [x]+u = a i x+u and applying a continuous.process using the formula a M+fc = 1 + î> (1 <*[x]+h) a[x]+ft+i • 1 More usual symbols have been substituted for those employed in the original memoranda. a3 See pp. 279-281. See pp. 281-289. 22 338 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION As an illustration are reproduced from a later memorandum [19: p. 53] the numerical results obtained, at 3.5 per cent, interest, for the present value of an invalidity pension in the course of payment, according to the age and sex of pensioner. TABLE X X V I I I . — P R E S E N T VALUE OF AN I N V A L I D I T Y P E N S I O N IN COURSE OF P A Y M E N T , PAYABLE MONTHLY, W I T H I N T E R E S T AT 3 . 5 P E R C E N T . Age of pensioner at date of calculation of the present value 20 years 21 » 22 » 23 » 24 » 25 » 26 » 27 » 28 » 29 » . For a unit amount of pension Males Females 3.951 4.079 4.204 4.326 4.444 4.560 •4.678 4.795 4.912 5.029 6.434 6.830 7.234 7.619 8.007 8.400 8.786 9.133 9.430 9.711 Age of pensioner at date of calculation of the present value 60 years 61 » 62 » 63 » 64 » 65 » 66 » 67 » 68 » 69 » . For a unit amount of pension Males Females 7.086 7.021 6.942 6.854 6.751 6.639 6.515 6.381 6.238 6.087 9.605 9.401 9.188 8.961 8.724 8.479 8.229 7.968 7.706 7.438 30 31 32 33 34 35 36 37 38 39 » » » » » » " » » » 5.144 5.253 5.362 5.472 5.581 5.688 5.796 5.899 6.002 6.103 9.969 10.199 10.401 10.587 10.752 10.902 11.028 11.119 11.194 11.262 70 71 72 73 74 75 76 77 78 79 » » » » » » » » » » 5.923 5.756 5.587 5.408 5.229 5.048 4.863 4.677 4.488 4.295 7.163 6.885 6.609 6.333 6.057 5.785 5.513 5.248 4.990 4.741 40 41 42 43 44 45 46 47 48 49 » » » » » " » » » » 6.196 6.285 6.374 6.462 6.548 6.631 6.709 6.785 6.853 6.918 11.303 11.335 11.343 11.339 11.323 11.297 11.256 11.204 11.148 11.079 80 81 82 83 84 85 86 87 88 89 » » » » » » » » » » 4.105 3.916 3.731 3.550 3.375 3.205 3.041 2.884 2.734 2.589 4.501 4.267 4.042 3.827 3.622 3.428 3.244 3.068 2.901 2.741 50 51 52 53 54 55 56 57 58 59 » » 6.974 7.026 7.075 7.119 7.154 7.178 7.194 7.189 7.163 7.133 11.002 10.914 10.816 10.704 10.578 10.444 10.291 10.135 9.970 9.794 90 91 92 93 94 95 96 97 98 99 » » » » » » » » » 2.452 2.320 2.194 2.074 1.956 1.839 1.717 1.578 1.395 1.103 2.589 2.445 2.307 2.175 2.046 1.918 1.784 1.631 1.431 1.119 100 » 0.629 0.629 » » » » » » » » . . • . . » . 339 GERMANY Invalidity Pension in course of Acquisition First Calculation [7: pp. 96-99] The present value of a unit invalidity pension in the course of acquisition was calculated approximately for an insured person aged x in the following manner. Take a group of lx healthy lives at the time tv at which the present value of the invalidity pensions in course of acquisition is to be calculated. In the year following t0 there will be lx ix cases of invalidity, giving rise a year later, at the time t0 + 1, to a crop of C ix (i - f invalidity pensions. If each of these pensions is of unit amount, the present value of this first crop of pensions calculated at the time t0 is CK^-fj.v.^Z In addition, account is taken of the pensions paid between t0 and t0 -+- 1 7 aa • 1 / on the assumption that ——- pensions are awarded in the middle of each month, and proceeding as follows. At the end of the first month, there are to be taken into account: (1) the payments made during half of the month, whose present value is expressed by * CK 12 ' 24 ' and (2) the monthly instalments of pension in the course of payment, Cx i "x 12 \ 24 whose present value is V 12 7aa l . * ** ( 1 _ ffx 12 12 Y 24 At thé end of the second month, there are similarly: (1) the present value 3 naa • lx *x 12 rr ^ ' 24 of the payments made during half the month; and 340 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION (2) the monthly instalments of pension in the course of payment, whose total number consists of (a) the survivors of the first monthly crop of new pensions, viz. C i* (, _ 3 12 \ CT., x 24 and (b) the survivors of a new crop of invalids arising in the middle of the second month, viz. iaa ' / ¡•x lx ( i 12 \ CT, 24/ ' making a total of 12 • V 24 * The present value of these monthly instalments of pension is consequently ida ia • l / , î!_ *-h (2 - — 12 ' 12 24 °x \ Proceeding in the same manner for each month in succession a total is obtained of — 24 23 JL ' 12 i /„ ^ 4 \ . 12 . ' 12 L £ /.. V 24/ + 121 or, at the rate of interest of 3.5 per cent., approximately Ç ix (0.4893 — 0.1428 a x ) . Finally, the present value of the pensions commencing during the first year, from t0 to t0 + 1, is expressed by the formula * ai D* 7 aa = ix • ,-, x ix ex v where ex = v ( i — ^ \ Si™! + 0.4893 - 0.1428 exclude invalidity due to industrial accidents, the factor i* was replaced by ix—ux; and on the assumption that ux = kix it was only necessary to adjust the result calculated with ix by multiplying by 1 — k. On the basis of invalidity statistics relating to railway staff the factor 1 — k was taken as 0.87. In the original Bill the invalidity pension was granted only after a waiting period of one year and during the first four years it was calculated at a reduced rate which increased year by year, without however exceeding half the fixed portion of the normal pension. In order to * di(12 make allowance for these provisions there was substituted for a x a new present value b^2.x which was calculated, for the sake of 1 simplicity, by taking the amount of the pension to be — for the first A four years during which the reduced pension is payable and one unit for the fifth year and onwards, thus: , *.»-ai ^OC+ 6 2 i »-..ai U2> 2D a a X A calculation was then made of the present value of the invalidity pension provided for in the original Bill, that is to say, taking into account a pension which as from the fifth year of invalidity was composed of: (1) a fixed portion amounting to 24 per cent, of the annual wage *; (2) increments dependent on the number of years of insurance completed since the end of the waiting period, in the following manner: 4 per mille of the annual wage for each of the first 15 years of insurance completed since the end of the waiting period; 6 per mille of the annual wage from the 16th to the 35th year of insurance completed since the end of the waiting period; 8 per mille of the annual wage from the 36th to the 45th year of insurance completed since the end of the waiting period. For males the calculations were made on the assumption of an average annual wage of 500 marks, that is to say, on the basis that the fixed portion of the pension would be 120 marks, that the maximum pension would be 250 marks and that the increments would be fixed at 2, 3 and 4 marks respectively. For females all these figures were reduced in the proportion of % which, according to the Bill, was to be the ratio between the amounts of the pensions to females and males. 1 Under the original Bill there would have been five wage classes with annual basic wages rising by intervals of 100 marks, from 300 to 700 marks. 342 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION To sum up, the present value of the pension provided for in the 1888 Bill was expressed, in the case of an insured man aged x, by the formula ! _ k (120 / *. = ^ r ^X ^ . 2> x+r + *Nf * "* + +1 +5 2 3C + 20 2 ^ • 'Nf 1 2 ) + 3C + 6 3C + 40 3C+50 at(i2> + 3 2 'NT + 4 2 *N 3C+21 x + 41 or r ¿ öx+6 -+- Í3 X + 2 1 + &x+il , *0aiU2>I putting CO *~ai02) - ^ »»,01(12) x Second Calculation [13: pp. 3610, 3611 and 16: pp. 50-52] The présent value of a unit invalidity pension in course of acquisition is obtained, for an insured person aged x, and taking into account a waiting period of 4 years, by the formula „ai(12) ™x+i oo *-^x ai(i2) 4|ax where - v x+i jaa • ''x *x a ina) M , and lvT at(i2) Nœ 2D; X For an insured person aged x, the present value of the right to increments of invalidity pension of which the amount increases by unity for every year completed since the end of the waiting period is obtained by the formula P „ai &X + 5 a¿(12) 4 a — l s ~Z~ää where (Ú „ai(i2) _ ^ ^ ^«(12) X • Under the provisions of the Bill, to which the actuarial investigations made from 1895 to 1899 related, the waiting period was reduced to 200 contribution weeks and the invalidity pension was composed of a fixed portion g and of increments whose total increased by a constant amount m for each contribution vear. 343 GERMANY Invalidity pensions awarded during the fifth year of insurance must then, on the average, have equalled g + 4.5 m; invalidity pensions awarded during the sixth year of insurance must on the average have equalled g + 5.5 m, and so on. As a result of this method of assessing the amount of the invalidity pension, its present value, for an insured person aged x, could be expressed thus ^,i, , at(i2) <%x (g,m) = g . MSLX , _ + 4.5 m ai(i2) 4[a.x . p + m 4 ,a a oi(i2) . As an illustration are reproduced, from a later memorandum [19: pp. 54, 551, the numerical results of a calculation of the present value, at the rate of interest of 3 % per cent., of an invalidity pension in course of acquisition, according to the age of the insured person, and for men and women separately, on the two alternative assumptions, (1) that the amount of the pension is constant and equal to unity and (2) that the amount increases by unity for each contribution year. TABLE XXIX. — PRESENT VALUE OF AN INVALIDITY PENSION IN COURSE OF ACQUISITION, PAYABLE MONTHLY AFTER 4 YEARS WAITING P E R I O D , WITH INTEREST AT 3 . 5 PER CENT. For a unit amount of pension Age of insured person at date of calculation of the present value 1 6 % years 17 % » 18% » 19% » 20 % » ¿L y2 " . . For an amount which increases annually for every year of contribution Males Females Males Females 1.015 1.054 1.094 1.135 1.926 1.998 2.073 " 2.151 35.262 36.587 37.975 39.427 55.309 57.371 59.529 61.789 1.179 2.234 40.943 64.157 A l . X ¿Z, ci ctA n Ü.D1U / A f\it e •íl.X/LU CC f.Qt. Uci.-±0** C\C\C\ 22 % 23 % 24% 25 % 26 % 27 % 28 % 29 % » » » » » « » » 1.265 1.309 1.354 1.401 1.448 1.497 1.547 1.599 2.397 2.478 2.559 2.638 2.715 2.790 2.864 2.938 42.275 42.609 42.914 43.189 43.432 43.643 43.821 43.966 65.645 65.757 65.823 65.856 65.860 65.834 65.769 65.654 30 % 31 % 32% 33 % 34% 35 % 36 % 37 % 38 % 39 % » » » » » » » » » » 1.652 1.707 1.764 1.822 1.883 1.946 2.010 2.078 2.148 2.220 3.012 3.090 3.166 3.246 3.328 3.411 3.497 3.584 3.674 3.765 44.075 44.146 44.175 44.161 44.100 43.989 43.825 43.604 43.324 42.981 65.482 65.244 64.943 64.566 64.113 63.585 62.977 62.292 61.525 60.678 344 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TAHLE X X I X . PRESENT VALUE OF AN INVALIDITY PENSION IN COURSE OF ACQUISITION, PAYABLE MONTHLY AFTER 4 YEARS WAITING PERIOD, WITH INTEREST AT 3 . 5 PER CENT (continued). Age of insured person at date of calculation of the present value Males 40 % years 41% » 42% » 43% » 44% •» 45% » 46% > 47% . » 48% » 49% » » 50% si % 52% » 53% » . . ï 54% 55% 56% 57 % 58% 59% 60% 61% 62% 63% 64% 65% 66% 67% 68% 69% S » » Î » » , » > 1 » 9 » » > ' »» 70% 71% 72% • 73% 74% 75% 76% 77% 78% 79% » 80% » Sí " 5» )ï » ï» î» î) . . For an amount which increases annually for every year of contribution Por a unit amount of pension Females Males Females 2.295 2.373 2.454 , 2.537 2.622 2.708 2.796 2.884 2.973 3.063 3.858 3.952 4.048 4.146 4.244 4.344 4.443 4.544 4.644 4.744 42.573 42.097 41.552 40.940 40.261 39.516 38.708 37.838 36.909 35.924 59.747 58.734 57.637 56.455 55.190 53.839 52.406 50.888 49.291 47.615 3.153 3.243 3.334 3.424 3.514 3.602 3.688 3.768 3.844 3.913 4.845 4.946 5.048 5.151 5.254 5.350 5.432 5.501 5.559 5.610 34.884 33.789 32.639 31.428 30.152 28.814 27.424 25.990 24.517 23.013 45.860 44.030 42.104 40.091 37.976 35.818 33.679 31.544 29.396 27.212 3.975 4.029 4.075 4.112 4.140 4.158 4.166 ' 4.161 4.144 4.111 5.658 5.696 5.715 5.715 5.696 5.657 5.593 5.497 5.372 5.222 21.488 19.953 18.418 16.897 15.399 13.933 12.506 11.125 9.797 8.529 ' 24.961 22.697 20.503 18.395 16.383 14.481 12.730 11.163 9.756 8.488 . 4.061 4.000 3.932 3.852 3.753 3.628 3.486 3.343 3.203 3.073 5.047 4.857 4.663 4.468 4.271 4.073 3.882 3.693 3.505 3.353 7.331 6.227 5.236 4.367 3.648 3.094 2.659 2.277 1.946 1.654 7.345 6.330 5.445 4.673 4.001 3.417 2.906 2.454 2.048 1.693 2.970 3.267 1.389 1.310 . 345 GERMANY Capital Values of the Invalidity Pensions awarded Each Year [8: pp. 292-294] On the assumption that the insured population remained " stationary ", that is to say, that it would remain unchanged in total and in age distribution, the following method of procedure was adopted. Let the number of insured males at age # at any given time be JHX, and let Cx be the present value of the unit invalidity pensions commencing during a year in which the beneficiaries are aged from x to x + 1, or, in other words, let Cx be the capital value of the invalidity pensions awarded to insured males who become invalid between age x and x + 1 during the year under consideration 1 . The capital value of all the unit pensions awarded during a year to beneficiaries aged at least e is expressed JC S — ^ i J\lx lx <2X The Bill that was under consideration provided for a waiting period of five years and contained transitional provisions under which the weeks during which the insured person had been employed in an insurable occupation during the five years preceding his incapacity could be taken into account for the purpose of completing four years of waiting period. In order to give effect to these provisions the following were taken as the present value of the crop of invalidity pensions which would be awarded each year from the date of coming into force of the scheme (for males): 0 X "V for the first year Î) )? second year 15 H third year >! I) fourth year îî 1Ï fifth year î) Î! sixth and subsequent years 1 "Kl ¿»V2i Under the provisions of the same Bill the invalidity pension was to consist of. a fixed portion equal to 12.5 per cent, of the annual wage together with increments calculated on the following scale: 0.25 per cent, of the annual wage for each of the 20 years following the completion of the waiting period; 0.5 per cent, of the annual wage for each of the completed years between the 21st and the 45th following the completion of the waiting period. Consequently, the capital values of the invalidity pensions which would be awarded in each year following the coming into force of the 1 For the calculation of <3X see above, p. 340. 346 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION scheme, were estimated for an average annual wage of 100 by the following formulae (for males): m äcl = 0 m 3CÌ = 12.5 m jci 7 m 1 àC3 = 12.5 ití>i = 12.5 m i = 12.5 m i m m „A mMA n XÎ = 12.5 m j 4 + 0.25 mJCL "«L = 12.5 mjcl + 0.25 ( 2 \ ttso m 22 42 12.5 m j d + 0.25 ^ . \ m < - 2 jcl) / m JCÍ - ' S m /í€^ + 2a 42 + 0.5 / 2m^-2m< Analogous expressions d£n for females were obtained in the same manner. CALCULATION OF PRESENT VALUES OF OLD-AGE PENSIONS X Unit Old-Age Pension [7: pp. 99-100] Under the provisions of the 1888 Bill, the old-age pension was payable to every insured person who attained age 70, and who had not previously become an invalid, for so long as he remained a healthy life; if he became an invalid the invalidity pension was substituted for the old-age pension. The amount of the old-age pension was to be fixed at 24 per cent, of the annual wage. The present value, at age x, of the right to a unit pension awarded under these conditions is given by the formula Naa •to-xfi-x — aa x or, giving effect to the payment in monthly instalments aa(i2) 70-x|äjc ao == 70-x¡^'X ^ ^12 where 0.463 is an approximate value for 812. 1 More modern symbols have been substituted for those used in the original memoranda. 347 GERMANY The present value of a pension granted at the commencement of the scheme to an insured person who had already attained or passed the age of 70 is given, for a unit amount, by = 0.463 a. (x > 70). The present value of an old-age pension of 120 marks per annum (calculated on the basis of a mean annual wage of 500 marks) may then be represented by í£ which is obtained by the formulae aa(i2) if x < 70 and if X > 70 lx — 120 7o_x|a. 120 a! As an illustration are reproduced from a later memorandum [19: p. 57] the numerical results obtained, with interest at 3.5 per cent., according to age and sex, for the present value of a unit old-age pension in course of acquisition, on the assumptions that the pension age is fixed at 65 and at 70. TABLE X X X . — P R E S E N T VALUE OF AN OLD-AGE P E N S I O N IN COURSE OF ACQUISITION PAYABLE MONTHLY, W I T H I N T E R E S T AT 3 . 5 P E R C E N T . Age of insured person at date of calculation of the present value 1 6 % years 1?% " 18% » 19% " . . For a pension of unit amount payable from age 65 For a pension of unit amount payable from age 70 Males Females Males Females 0.251 0.260 0.270 0.281 0.147 0.153 0.159 0.165 0.052 0.054 0.056 0.059 0.022 0.023 0.024 0.025 0.291 0.303 0.061 0.063 0.066 0.068 0.071 0.074 0.076 0.079 0.083 0.086 0.026 0.027 0.028 0.029 0.030 0.032 0.033 0.034 0.036 0.037 0.089 0.093 0.097 0.101 0.105 0.109 0.114 0.119 0.124 0.129 0.039 0.041 0.042 0.044 0.046 0.048 0.051 0.053 0.055 0.058 20% » 9-1 l/_ „ 22% 23% 24% 25% 26% 27% 28% 29% » » » » » « " » 0.327 0.339 0.353 0.366 0.381 0.396 0.412 0.171 0.178 0.185 0.192 0.200 0.208 0.216 0.225 0.235 0.245 30% 31% 32% 33% 34% 35% 36% 37% 38% 39% » " » » " » » » " » 0.428 0.445 0.463 0.482 0.502 0.523 0.545 0.568 0.593 0.618 0.256 0.267 0.278 0.291 0.304 0.317 0.332 0.347 0.363 0.380 Ô.3Î4 348 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE X X X . PRESENT VALUE OF AN OLD-AGE PENSION IN COURSE OF ACQUISITION PAYABLE MONTHLY, WITH ÍNTEREST AT 3 . 5 PER CENT. (continued) Age of insured person at date of calculation of the present value 40 V2 years 41% " 42% " 43% " 44% » 45% » 46% » 47% » 48% » 49% " 50% 51% 52% » " » S3V. 54% 55% 56% 57% 58% 59% » » » » " » 60% 61% 62% 63% 64% 65% 66% 67% 68% 69% » » » " .. » » » » " . . For a pension of unit, amount payable from age 65 For a pension of unit amount payable .from age 70 Males Females Males Females 0.645 0.674 0.705 0.737 0.772 0.810 0.851 0.895 0.943 0.996 0.399 0.418 0.439 0.462 0.486 0.513 '0.541 0.573 0.607 0.645 0.135 0.141 0.147 0.154 0.161 0.169 0.178 0.187 0.197 0.208 0.061 0.064 0.067 0.070 0.074 0.078 0.082 0.087 0.092 0.098 1.055 1.120 1.192 1.273 Ü364 1.466 1.583 1.718 1.875 2.059 0.687 0.733 0.785 0.844 0.910 0.986 1.077 1.185 0.961 0.762 0.220 0.234 0.249 0.266 0.285 0.306 0.331 . 0.359 0.391 0.430 0.105 0.112 0.120 0.128 0.139 0.150 0.164 0.180 0.200 0.223 2.278 1.966 1.674 1.402 1.621 0.590 0.446 0.330 0.388 0.466 — — — __ — .— — — 0.476 0.531 0.599 0.683 0.789 0.927 1.110 1.356 1.699 2.193 0.251 0.286 0.330 0.388 0.466 0.572 0.724 0.948 1.284 1.805 T— — Capital Values of Old-Age Pensions awarded Each Year [8: p. 294] In the course of the debate on the 1888 Bill a number of amendments were considered. This is the reason why the calculation of the capital values was made on the assumptions that the pension age would be 65 and that its amount would be fixed at 12.5 per cent, of the annual wage. It was assumed first that at the inception of the scheme there would be an exceptional number of pensions awarded, the total number of which would be given, for example for males, by ^ 3YLX and secondly 65 that the normal number of pensions awarded to males in each of the GERMANY 349 following years would be equal to the constant figure of 3Tt65. Consequently the capital values of old-age pensions which would be awarded during each year following the coming into force of the scheme were calculated for an average annual wage of 100, by the following formulée (formales): m s£= 12.5 2 J î l x a r 2 ) and 65 m 3t\ = 12.5 ;m 66 a r i 2 > (where t > 1) . The figures for females were calculated in a similar manner. CALCULATIONS IN RESPECT OF REPAYMENTS OF CONTRIBUTIONS * The Reichstag Committee which examined the 1888 Bill introduced a clause which provided for the compulsory repayment of contributions in three distinct cases: this clause was embodied in the Act and has already been referred to above 2. First Calculation The total amount of the repayments to be made on the death of insured males aged x was calculated in the following manner [-8: pp. 295-297]: The number of repayments in the case of insured males aged between x and x + 1 is 3ilx qaa Wx where qaa represents the probability that an insured male aged x will die in the year without having become an invalid 3 , and where wx represents the probability 4 that an insured man aged x will on his death leave one or more benefit claimants, that is to say, cither a widow or one or more orphans aged less than 15. For insured males of all ages the probable number of repayments during the first year of operation is then given by 6 64 2 ^ & Wx • 16 On the assumptions that the deaths all occur in the middle of the year and that the annual amount of the contribution is fixed at 1, the total amount of the expected repayments for the first year of operation of the scheme is J 64 1 More modern symbols have been substituted for those used in the original memoranda. 2 See p. 336. 3 See above, p. 292. 4 See Chap. I, § 1, p. 301. 6 It was assumed that the old-age pension would be granted at age 65 and that the repayment of contributions would not be subject to any waiting period (the condition that five contribution years should have been completed did not appear in the Bill to which this calculation related). 350 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION The calculation of the repayments for each successive subsequent year is made on the. assumption that the insured population is stationary. For the second year of operation of the scheme there are 2 OKx € Wx repayments in respect of the initial insured persons, who have paid on the average one and a half years of contribution, and m-_ aa ,™, aa 9tu ?i. wlt = 3VL1 J\lx qx wx + - JTt16 q * 64 1 64 aa = - 2, Wx qx wx + ^ ^ . 3TI» qx ze>v In general, for the repayments made during the (t + 1) the year of operation of the scheme, on the basis of an annual contribution fixed at 1, there is , 6 4 t+1 = r2¿m-xqx , 6 4 wx + - 2¡ 3KX qx wx+ 2 1T ..... + ~ 2 ^ where o* = i vx. By the same reasoning as under the first hypothesis we then pass to the present value at any age x and obtain — " 5 D aa * .aa ¿^ "x 2 D* ¿ v ''x Finally, the present value of the rights to a widow's pension and allowance is calculated, for an insured person aged x and for a unit annual amount, by the formula N d X(U> ^£> = _ L ^ „aa 1 ^aa .^J D aa faaa V x Six v + i l Ñ D ¡ o1 V "\ jc(y) ~ j /\ "x \lx v x(y) J The invalid life table t and the invalid mortality rates q* have been borrowed from the Prussian railways pension fund. See above, p. 285. 355 GERMANY In order to take account of amounts which increase by a unit each year, instead of remaining constant at one unit, it is sufficient to replace (Ú ^*x 27 ) 28 » 29 . . . . λ »Ï 5 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 , » J » Î > j j j ' , > > » ) > .» >» .» .» . . When pension and allowance are each of unit amount Age of widow at death of husband 50 years . . . . When pension and allowance are each of unit amount 1.058 1.083 1.091 1.029 0.979 0.934 0.900 0.874 0.849 0.828 51 52 53 54 55 56 57 58 59 » » » » » » » » » 2.177 2.316 2.456 2.594 2.735 2.874 3.008 3.144 3.278 3.412 0.816 0.811 0.806 0.805 0.801 0.797 0.794 0.808 0.833 0.878 60 61 62 63 64 65 66 67 68 69 » » » » » » » » » » 3.551 3.693 3.846 4.009 4.189 4.388 4.571 4.736 4.890 5.029 0.936 1.038 1.147 1.260 1.379 1.504 1.634 1.765 1.902 2.039 70 71 72 73 74 75 76 77 78 79 » » » » » » » » » » - 5.154 5.262 5.338 5.371 5.352 5.285 5.176 5.044 4.895 4.740 356 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION becomes a widow at age y, is expressed by the following formula, using ÎÏÏ.TÏ 7ÏT1A CL IT) the numbers Wv , W y , W y and W y , which have been defined above 1 , and also the present values a of a unit invalidity pension in course of payment and in course of acquisition: W inp i(i2) . TTTi>ns v aids) . TIT« . TTT'P 10,000 The numerical values obtained for W y ' at different ages y of the widow at date of death of insured husband, with interest at 3.5 per cent., appear in table XXXI. The present value of the same benefit rights acquired by an insured man aged x is calculated with the aid of fy?y by taking in turn, as in the first calculation, the two cases where the insured first becomes an invalid and where he dies without having become an invalid. Below are reproduced (table XXXII) the numerical results obtained, with interest at 3.5 per cent., to represent. (1) the present value of the widow's pension and allowance together, each of unit amount, in respect of an invalid at any given age; (2) the present value of the widow's pension and allowance together i n •pacmo/>f n f QTÍ í n a n r o r í n o p o n n a t o m r m v o T ï aero r\n t . h a a c o i i m n . tions (a) that the amount of each benefit is constant and equal to a unit and (li) that the amount of each benefit increases by one unit for each contribution year. CALCULATION OF PRESENT VALUES OF ORPHANS' PENSIONS AND ALLOWANCES 3 [18: pp. 546-547] The present value of a unit orphan's pension in the course of payment, ceasing at age 15, is calculated on the basis of the children's life-table lz by means of the commutation functions D z = lz vz and • Nz = 2 D;z z and \vs-z&z — p. z or, taking into accountthe-payment in-monthly-instalments,-by,|ie-zaz 1 2 3 — |i»-zaz — 0.463 See pp. 311-312. See above, pp. 337 and 342. More modern symbols have been substituted for those used in the original memoranda. 357 GERMANY TABLE XXXII. PRESENT VALUE OF THE RIGHT TO A WIDOW'S PENSION AND ALLOWANCE IN RESPECT OF AN INVALID OR INSURED PERSON AT . ANY AGE, WITH INTEREST AT 3 . 5 PER CENT. Age of invalid or insured person at date of calculation of the present value In respect of when pension and allowance are each of unit amount In respect of an insured persor when pension and pension and allowance allowance increase by are each of one unit for unit amount each year of contribution 17% 18% 19% » » " — — — 0.349 0.362 0.376 0.390 12.628 13.103 13.600 14.119 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% » » » « » " » » » " 0.080 0.117 0.162 0.214 0.267 0.316 0.358 0.392 0.421 0.447 0.405 0.421 0.437 0.453 0.470 0.488 0.505 0.523 0.542 0.561 14.662 15.019 15.164 15.300 15.425 15.540 15.643 15.735 15.815 15.883 30% 31% 32% 33% 34% 35% 36% 37% 38% 39% » " » » » » » » » » 0.468 0.488 0.507 0.527 0.547 0.569 0.595 0.625 0.662 0.706 0.581 0.602 0.623 0.645 0.668 0.692 0.716 0.742 0.769 0.796 15.938 15.979 16.006 16.016 16.008 15.983 15.937 15.871 15.782 15.669 40% 41% 42% 43% 44% 45% 46% 47% 48% 49% » » » » » » » » » » 0.755 15.532 0.867 0.926 0.984 1.040 1.095 1.151 1.207 1.261 0.825 u.oo* 0.885 0.916 0.948 0.980 1.013 1.047 1.081 1.115 15.182 14.969 14.732 14.470 14.184 13.875 13.544 13.191 50% 51% 52% 53% 54% 55% 56% 57% 58% 59% » » » » » » » » » » 1.311 1.358 1.400 1.436 1.470 1.502 1.530 1.553 1.570 1.584 1.149 1.183 1.215 1.248 1.280 1.311 1.342 1.371 1.399 1.425 12.817 12.424 12.010 11.577 11.121 10.646 10.153 9.646 9.128 8.600 . . . . . . . . . , . . . U.ÖU» . . . . . . . • . . . . . . ÍO.O/V 358 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION TABLE X X X I I . — P R E S E N T VALUE OF T H E RIGHT TO A W I D O W ' S P E N S I O N AND ALLOWANCE IN RESPECT OF AN INVALID OR I N S U R E D P E R S O N AT ANY A G E , W I T H I N T E R E S T AT 3 . 5 P E R CENT, (continued) at date of calculation of the present value In respect of an invalid when pension and allowance are each of unit amount , In respect of an insured person when pension and pension and allowance increase by allowance are each of one unit for unit amount each year of contribution » » » » » » » " 1.598 1.611 1.620 1.626 1.628 1.626 1.623 1.620 1.617 1.612 1.452 1.477 1.500 1.520 1.538 1.553 1.566 1.577 1.587 1.596 8.064 7.523 6.981 6.443 5.912 5.392 4.887 4.396 3.922 3.464 70% 71% 72% 73% 74% 75% 76% 77% 78% 79% » " » » » » " » » » 1.606 1.600 1.591 1.577 1.555 1.526 1.488 1.442 1.391 1.335 1.604 1.610 I.bi3 1.608 1.595 1.573 1.541 1.501 1.454 1.400 3.024 2.607 2.226 1.887 1.602 1.379 1.198 1.031 0.877 0.730 80% 81% 82% 83% » » » » 1.273 1.205 1.133 1.058 1.340 0.584 — — — — — — 60% years ei % " 62% 63% 64% 65% 66% 67% 68% 69% . . . . . . . . The present value, at the date of death of an insured man aged x, of the right to unit orphans' pensions is given b y ' 15 R x ^(12) 115-zaz z=t> "XX •where, at each age x the symbols kx represent, for a number of fathers ~M-X— the-number-of~children"living alrages~z~from~0~to~14~and where ~~ y¡x is the probability that an insured man is the father of a child under age 15 x. The calculation of the present value of the right to unit orphans' pensions at any given point in the lifetime of the insured man is analogous to that •which has been made for widows' pensions. 1 See above, pp. 313 and 315, and tables XVIII and XIX. 359 GERMANY Two alternative assumptions are made: (1) The insured man dies without having become an invalid. p.aa aa *^X 9x (12) IS^JCIZ) ', (2) the insured man dies after having become an invalid: • ^ p. i or ix -s Representing by vO(12) 1 B D^'' i (12) Di 'X the sum of these two results and taking iy.a(i2) " ^ -p.a(i2) X the present value required is given by the formula Na is11*«) a(i2) aa If instead of being a fixed unit amount the pension is assumed to grow by a unit for each contribution year the formula becomes •^b A /T \a(12) ìxm Na(12) _ ^ ^ 15 i, 3C(Z) _x ~ Dr -OU2) 16^XI.Z) ~ Dr ' The calculations in respect of orphans' allowances are made with the help of the same formulae, but substituting for i16_zaz the ratio -p—, which represents the present value, for a child aged z, of a unit allowance payable on his attaining age 15. As an illustration are reproduced from a later memorandum [19: pp. 41-42] the numerical results giving, at 3.5 per cent, interest, the present value of the right to an orphan's pension ceasing at age 15 and the present value of the right to an orphan's allowance payable at age 15, when the calculation of each of these values is made: (1) in respect of an invalid at any given age, for a benefit of unit amount ; (2) in respect of an insured man at any given age, for a benefit of unit amount; (3) in respect of an insured man at any given age, for a benefit whose amount increases by one unit for each contribution year. 360 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XXXIII (a). PRESENT VALUE OF THE RIGHT TO AN ORPHAN'S PENSION CEASING AT AGE 1 5 , WITH INTEREST AT 3.5 PER CENT. Age of invalid or insured person at date of calculation of the present value 17% " is% » 19% " 20% 21% 22 % 23 % 24% 25% » » » » " " In respect of an invalid when pension is of unit amount In respect of an insured person when pension is of unit amount pension increases by one unit for each year of contribution _ — — — 0.854 0.886 0.920 0.955 16.753 17.383 18.043 18.732 0.992 1.030 1.068 1.107 1.146 1.183 1.218 1.249 1.274 1.294 19.453 19.690 19.385 19.031 18.627 18.171 17.665 17.111 16.514 15.876 261/2 » 27% 28% 29% » » » 0.621 0.940 1.384 1.980 2.734 3.601 4.553 5.533 6.453 7.283 30% 31% 32% 33% 34% 35% 36% 37% 38% 39% » » » » » » » » » » 7.956 8.430 8.728 8.834 8.766 8.535 8.121 7.590 7.015 6.420 1.307 1.312 1.310 1.302 1.287 1.265 1.237 1.203 1.166 1.125 15.205 14.506 13.785 13.048 12.300 11.546 10.794 10.048 9.313 8.592 40% 41% 42% 43% 44% 45% 46% 47% 48% 49% » » » » » » » » >• » 5.825 5.225 4.652 4.146 3.695 3.283 2.893 2.522 2.197 1.919 1.081 1.033 0.983 0.933 0.881 0.827 0.771 0.713 0.657 0.603 7.888 7.206 6.555 5.921 5.321 4.753 4.221 3.728 3.273 2.854 50% 51% » " 1.660 1.424 0.548 0.495 2.474 2.131 5-¿% " 1.048 0.895 0.763 0.645 0.536 0.437 0.352 0.398 0.354 0.313 0.276 0.240 0.207 0.178 1.550 1.307 1.015 0.836 0.682 0.550 0.438 53% 54% 55% 56% 57% 58% 59% » » » » » » » • • . . . . . . . . . ' . . . . . . . . . . .' • 361 GERMANY TABLE XXXIII (a). PRESENT VALUE OF THE RIGHT TO AN ORPHAN'S PENSION CEASING AT AGE 1 5 , WITH INTEREST AT 3.5 PER CENT. (continued) In respect of an insured person when In respect of an invalid when allowance Is of unit amount allowance is of unit amount allowance increases by one unit each year of contribution 6 0 % years 61% » 62% » 63% 64% 65% ' 66% J 67% 68% 69% ' 0.283 0.227 0.180 0.143 0.112 0.085 0.062 0.042 0.025 0.012 0.152 0.130 0.109 0.091 0.075 0.059 0.044 0.031 0.019 0.009 0.343 0.263 0.197 0.142 0.097 0.062 0.036 0.018 0.007 0.002 70% 0.003 0.003 Age of invalid or insured person at date of calculation of the present value Ï Ï Ì Ì TABLE XXXIII (b). PRESENT VALUE OF THE RIGHT TO AN ORPHAN'S ALLOWANCE PAYABLE AT AGE 1 5 , WITH INTEREST AT 3.5 PER CENT. Age of invalid or insured person at date of calculation of the present value In respect of an invalid when allowance is of unit amount 1 6 % years 17% » 18% " 19% » 20% 21% 22% 23% 24% 25% 26% 27% 28% .29% .... » » » » » » » » » » 0.082 0.120 0.172 0.236 0.313 0.400 0.493 0.590 0.689 In respect of an insured person when allowance is oi unit amount allowance increases by one unit for each year of contribution 0.117 0.122 0.126 0.131 2.549. 2.646 2.746 2.851 0.136 0.141 0.147 0.152 0.158 0.163 0.169 0.174 0.179 0.183 2.961 3.004 2.974 2.938 2.895 2.844 2.787 2.723 2.652 2.574 362 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION TABLE X X X I I I (£>)• P R E S E N T VALUE OF THE RIGHT TO AN O R P H A N ' S ALLOWANCE P A Y A B L E AT AGE 1 5 , W I T H I N T E R E S T AT 3 . 5 P E R CENT. (continued) Age of invalid or insured person at date of calculation of the present value In respect of an invalid allowance is of unit amount In respect of an insured person when allowance is of unit amount allowance increases by one unit each year of contribution 0.782 0.866 0.940 1.000 1.042 1.061 1.056 1.032 0.991 0.940 0.187 0.191 0.193 0.195 0.196 0.196 0.195 0.193 0.190 0.187 2.490 2.400 2.304 2.203 2.098 1.989 1.877 1.764 1.649 1.533 31% 32 % 33% 34% 35% 36% 37% 38% 39% " 40 V» 41% 42% 43% 44% 45% 46% 47% 48% 49% » » » » » » » » » 0.879 0.813 0.747 0.684 0.623 0.564 0.507 0.455 0.409 0.365 0.182 0.177 0.171 0.164 0.157 0.149 0.141 0.132 0.123 0.114 1.418 1.306 1.193 1.084 0.978 0.876 0.780 0.688 0.602 0.521 50% 51% 52 % 53% 54% 55% 56% 57% 58% 59% » » » » » » » » » » 0.322 0.279 0.240 0.207 0.178 0.152 0.127 0.104 0.083 0.064 0.105 0.095 0.085 0.076 0.067 0.058 0.050 0.043 0.036 0.029 0.447 0.380 0.320 0.266 0.218 0.176 0.140 0.109 0.083 0.062 60% 61% 62% 63% 64% » " » » » 66% 67% 68% 69% » » » » 0.048 0.035 0.025 0.018 0.013 0.UU8 0.005 0.003 0.002 0.001 0.023 0.018 0.014 0.011 0.008 07005 0.004 0.002 0.001 0.001 0.045 0.032 0.022 0.014 0.009 0.005 0.003 0.001 » » » » » » » . . . . . . . . . . . . — — GERMANY 363 EXPERIENCE Average Amounts of Benefits The average annual amounts for invalidity and for old-age pensions respectively are given by the following figures. TABLE X X X I V . — AVERAGE ANNUAL AMOUNT OF PENSIONS'. E X P E R I E N C E (in marks) Year 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 . . . . . . . . . . . . . . Invalidity pensions Old-age pensions 113 115 118 122 125 127 130 132 132 142 146 150 124 128 130 126 133 134 137 139 143 146 150 153 Year 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 Invalidity pensions Old-age pensions 152 155 159 163 166 170 175 177 180 187 195 155 157 159 161 162 163 164 164 165 166 167 . . . . . . . . . . . . . During the years 1912 and 1913 the average annual amount of widows' pensions was 77 and 78 marks respectively, and that of orphans' pensions was 32 marks in each year. The average amount of repayments of contributions has been continually increasing in each category; the figures given below indicate the extent of these increases: Average payment in marks Repayment of contributions on death . . . Repayment of contributions on marriage . . Repayment of contributions on the granting of a pension under the workmen's compensation scheme year 1900 49 32 year 1909 95 39 47 95 Total Amount paid Each Year for Each Category of Benefit The sums paid out each year for invalidity and old-age pensions and for all repayments of contributions appear in table XXXV. Further, the following total amounts were paid during the years 1912 and 1913 respectively: (1) widows' pensions: 167 and 801 thousand marks; (2) orphans' pensions: 629 and 2,573 thousand marks. 364 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XXXV. TOTAL AMOUNT PAID EACH YEAR IN RESPECT OF THE VARIOUS BENEFITS: EXPERIENCE (in thousands marks) Year 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 Invalidity pensions (including sickness pensions) _ . . . . . 1,339 5,207 10,032 15,333 20,845 27,061 34,363 42,368 54,224 66,322 80,377 95,035 107,981 117,427 124,618 130,281 136,338 142,716 148,977 154,505 161,811 170,750 Repayments of Contributions 15,299 21,025 22,706 . 24,420 26,497 27,327 27,556 27,450 26,826 26,224 24,656 23,507 22,113 20,868 19,476 18,355 17,312 16,353 15,550 15,011 14,468 14,053 13,738, _ — — — 219 1,975 3,391 4,497 5,446 6,617 6,925 7,134 7,556 7,858 8,172 8,436 8,855 9,237 9,420 9,430 10,246 1,970 1 6201 Total 15,299 22,364 27,913 34,452 42,049 50,147 58,008 66,310 74,640 87,065 97,903 111,018 124,704 136,707 145,075 151,409 156,448 161,928 167,686 173,418 179,219 177,834 185,108 i Although the repayment of contributions was abolished as from 1 January 1912, the above sums were paid retrospectively during the years 1912 and 1913. § 4 . — Other Expenditure ADMINISTRATION EXPENSES AND COST OF MEDICAL AID Estimates adopted in the Actuarial Investigations —In- the--actuaria]-investigations-undert.aken-Avhile-the-i899-Act-was being formulated [16: pp. 61, 62] the total cost of administration expenses and medical aid was estimated at 6.94 per cent, of the contribution income, according to the actual experience of the year 1897. In a later memorandum [18: pp. 554-556] administration expenses and the cost of medical aid were A^alued separately, on the basis of the experience in the years 1904 to 1907. The average annual cost per insured person was estimated to be 1.3449 for administration expenses and 1.1467 for the cost of medical aid. 365 GERMANY Finally, in a 1914 memorandum [19: pp. 71, 72] on the basis of the 1909-1913 experience, the percentage of the contribution income taken for administration expenses was 8.5 and for the cost of medical aid 10. Experience The sums expended annually for administration and medical aid appear in table XXXVI, which also allows a comparison to be made between administration expenses and the total receipts or the total expenditure. TABLE XXXVI. ADMINISTRATION EXPENSES AND COST OF MEDICAL A I D : EXPERIENCE Administration expenses ' Year Cost of medical aid Annual amount (in thousand marks) , 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 . . . . . . 32 108 365 632 1,176 1,886 2,630 4,016 5,664 7,369 9,396 10,450 11 649 13,144 14,630 16,443 19,548 21,344 23,408 24,646 26,562 29,851 3,838 4,776 4,952 5,267 5,889 6,420 6,879 7,672 8,580 10,029 10,676 11,694 12,552 13.745 14,700 15,864 16,901 18,254 19,661 21,367 21,854 23,481 24,408 Percentage of total annual expenditure Percentage of total annual receipts % % 29.2 26.3 22.8 20.0 18.5 16.5 15.2 14.6 14.2 13.7 13.0 12.4 11.8 4.0 4.8 4.8 4.8 5.1 5.1 5.2 5.5 5.7 6.4 6.4 '6.8 6.9 11.7 7.1 11.7 11.9 12.0 12.2 12.5 12.8 12.6 13.4 13.2 7.2 7.4 7.5 7.8 8.1 8.4 8.1 6.8 6.8 366 ACTUARIAL T E C H N I Q U E ANP FINANCIAL ORGANISATION TABLE OF SYMBOLS INTRODUCED IN CHAPTER II CO = Limiting age of the life table. i = Annual interest on a monetary unit. = Discounting factor, l + i — Commutation functions corresponding to lx • D : N; v = Present value of the invalidity pension. C D at(i2) 1 -.aida) „aida) * ' x «a, <%x (g,m) = Commutation functions used in calculating the present value of an invalidity pension in the course of being acquired. ^^"Present"vaíue^of a u n i t invalidity pension~in course^ of acquisition (payment by monthly instalments, 4 years' waiting period). = Another present value of the invalidity pension (g represents the amount of the basic sum and m the amount of the increment corresponding to a contribution year). GERMANY 367 Present value of the right to a unit old-age pension granted at age 70 (payment by monthly instalments). 70 -xfi-X í£ = Present value of the old-age pension. m fCi m tu>i ' ' '• ~ C a Prtal value of invalidity pensions granted, during the ith year of operation, to insured men (for a fixed unit amount and for the amount provided in the Bill). f nrx fnpiv ' ' ' = Capital value of invalidity pensions granted during the ith year of operation to insured women (for a fixed unit amount and for the amount provided in the Bill). m = Capital value of old-age pensions granted during the ith year of operation to insured men (for the amount provided in the Bill). Mna ' fftpi ' = Capital value of old-age pensions granted during the ith year of operation to insured women (for the amount provided in the Bill). 2f = Amount of repayments to be made during the ith year of operation on the death of insured men. T\r j\jr Sr * ' *' * — Commutation functions used in calculating the present value of. the right to repayments of contributions made on the death of an insured man. r * = Present value of the right to repayments of contributions made on the death of an insured man, for a unit amount. P„T = Present value of the right to repayments of contributions made on the death of an insured man, for an amount which increases by one unit for each contribution year. x T = Present value of the right to repayments of contributions in respect of the male insured population at 1 January 1900. f = Present value of the right to repayments of contributions in respect of insured men who enter during the year. V 'v = Present value calculated as at the date of death of the insured man, according to the age y of the widow, of the right to a widow's unit pension and unit allowance. 368 ACTUARIAL TECHNIQUE AND FINANCIAL ' x(y) DÌ Ky> > ^xiy) '•»(y) ORGANISATION Present value calculated as at the date of death of the insured- man, according to his age x, of the right to a widow's unit pension and unit allowance. Commutation function corresponding to the invalid life-table t . Commutation functions used in calculating the present value of the right to a widow's pension and allowance. Present value of the right to a widow's pension and allowance of unit amount. W„ Present value calculated as at the death of an insured man in respect of his widow aged y, of the right to a widow's unit pension and unit allowance. D,,N2 Commutation functions, corresponding to the children's life-table lz. \¡s-z&z Present value of a unit orphan's pension in course of payment, ceasing at age 15 and payable in monthly instalments. Present value, as at the death of an insured man aged x, of the right to unit orphans' pensions ceasing at age 15 and payable in monthly instalments. w'-'xiz) Commutation function used in calculating the present value of the right to unit orphans' pensions, ceasing at age 15, at any given point in the lifetime of an insured man (payable in monthly instalments). Present value of the right to unit orphans' pensions, ceasing at age 15, at any given point in the lifetime of an insured man (payable in monthly instalments). .(la) 15\* "-IXU) Present value of the right to orphans' pensions, ceasing at age 15, calculated at any given point in the lifetime of an insured man, when the amount of the pension increases by one unit for each contribution year (payable iñTliioñthly^ instalments). CHAPTER III FINANCIAL SYSTEM At the time of the preparatory investigations and during the operation of the scheme, the financial system was the subject of important actuarial researches to which reference has already been many times made and which, indeed, form the fundamental basis of the present survey. The principal purpose of these researches was to choose the appropriate rates of contribution that would ensure financial equilibrium. The essential problem has always been to value the items composing the Assets and Liabilities in the actuarial balance-sheet: from this calculation could be deduced the amount of the average premiums required to balance assets and liabilities or alternatively the actuarial balance-sheet could be completed by taking into account the rates of contribution actually in force. Under the provisions of the Government Bill of 1888, the rates of contribution had to be fixed on the basis of general average premiums required to secure financial equilibrium provided that the initial insured population is taken together with the new entrants into insurance during each of the years of operation of the scheme [7, 8]. During the investigations of the Reichstag committee this principle was abandoned and it was decided that the contributions should be fixed for a certain period so that it would be possible to set up the capital values of the pensions emerging in the period, and, at the same time, cover all other expenditure. The rates were first calculated for a period of ten years and, later, they were to be revised every five years. In other words, average premiums for a fixed period were substituted for the general average premiums. The average premiums calculated for a period of ten years served as a guide in choosing the rates of contribution put into force in 1891, which were fixed for the various wage classes so as to guarantee financial equilibrium for each class taken separately [8, 9, 10]. In the actuarial memoranda on which the 1897 and 1899 Bills were based, different average premiums were brought out, but in the end, on the basis of the figure obtained by the overall average premium, it was decided to introduce a new wage class * and to retain the rates in force in the other classes for a period of ten years from 1 January 1900 [13, 16]. When insurance benefits to survivors were introduced the general average premiums were re-calculated and this led to an increase in the rates of contribution * [18]. 1 See p. 326. 24 370 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Finally, an actuarial balance-sheet was constructed as at 1 January 1914 and this indicated that the rates of contribution put into force on 1 January 1912 should be retained [19]. In the following pages a brief analysis will be made in chronological order of the calculations of average premiums and the actuarial balancesheets which were drawn up in the course of the various actuarial . investigations. It will be seen that certain of these investigations provided material for solving not only the problem of financial equilibrium but also other important questions : in particular they led to an estimate of the annual emerging costs, of the sums provided by the State (year by year and present value) and of the growth of the accumulated funds. § 1. — Calculation of Average Premiums in the Preparatory Investigations* GENERAL AVERAGE PREMIUMS [7: pp. 100-103] In respect of the Initial Insured Population Taking the initial male insured population, at each age x the number of insured persons was represented by Jtt x . For this group, the present value of a uniform annual contribution of 7tj was 2 CO ^Ì-2J 2ft* r* • 18 The present value of benefit payments in respect of the same group was 3 2 2H* I** + <) • 16 Hence financial equilibrium in respect of this group necessitated an average premium for the initial population: CO 2 ^ft, {< + O •'» co 2™*r« 16 A similar procedure was adopted for the initial female insured population. 1 In all these calculations the basic rate of interest is taken as 3.5 per cent. Yx is calculated for a unit annual contribution in the same way as Cx for3 a unit weekly contribution. For the calculation of Cx see p. 327. See Chapter II. The formulae reproduced correspond with the original form of the 1888 Bill, under which no provision was made for repayment of contributions. 2 371 GERMANY It was then observed that the adoption of TC¿ as the amount of the average premium would imply that insured persons entering after the first year, that is to say, future entrants, would have the same age distribution as the initial entrants. It appeared more reasonable, however, in view of the compulsory nature of the scheme, to assume that future entrants would be mainly young people. In respect of Future Entrants It was assumed that the total number of male entrants each year would have the following constant composition: m at a 9Us ge 16 m at age 17 m r at age 18 dl17 3 Lls The numbers ¿ft^, ¿ft17 and £)t18 were derived from the distribution of the initial insured population at •the ages in question 1. The present value of unit contributions in respect of male insured persons who enter during the first year is represented by 18 v^m3lxTx 16 and the present value of benefit payments in respect of the same persons *>y 18 16 on the assumption that they all enter in the middle of the year. Actuarial equilibrium in respect of these persons would have necessitated the following average premium, which has been taken as the average premium applicable to the new entrants in future year (for males) : 18 ,w ; is 16 The same procedure was adopted for future female entrants. In respect of Present and Future Insured Persons together The average premium applicable to future entrants, TZf, was less than the average premium in respect of the initial insured population, 1 See p. 320. 372 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION 7tj, since the age distribution of the latter was less favourable than that of the former. In a compulsory social insurance scheme, which is assumed to continue in perpetuity, it is certain that each year a number of new entrants will be added to the insured population and that this number will be almost entirely composed of young persons. Accordingly, the initial insured population and future entrants were considered together for the purpose of calculating a general average premium which would be applicable to all insured persons. .The resulting'premium ng so defined evidently lay between TZ¿ and 7t¿ and it was obtained, on the assumption that the number and age distribution of new entrants each year would remain unchanged, by the formula 6) 18 . 16 JR. vx 18 3 + v* 2 "X r, + w- 2 > . r, + 16 10 or 2 on, « + o +.—— 2 m ^ « + <) In it» J- v p* lfi 18 2 ¿m* rx + - — 2 "^ r* 16 .x ^ 16 The same procedure was adopted for calculating the general average premium applicable to females. AVERAGE PREMIUMS FOR A FIXED PERIOD [8: pp. 299-300] After much discussion, the adoption of a general average premium, which had at first been considered, was rejected, mainly owing to the fear that it might lead to too great an accumulation of funds. The following system was substituted for that originally envisaged. The period of operation of the scheme is divided into quinquennial periods, except for the first which is decennial, and in each period the income is equated to the outgo in respect of (1) the setting-up of the capital values of pensions awarded in the period and (2) the repayments of contributions and miscellaneous expenditure. At the beginning of a period let & = 2 &* » the total male and female insured population 1, which is assumed to be constant, and let ß be the average annual premium, expressed as a percentage of wages, which is to be calculated for this period. Then 1 On the assumption that Sx = JKX + 9X. 373 GERMANY the present value of contributions at the beginning of the period will be, for an average annual wage of 100, 1 — V10 fig vi 1 — V r ' 1 — Vs Vi r8 & 1 —v if the period is one of ten years, and if the period is one of five years. In Chapter II * a broad description was given of the calculation of the capital values, for an average annual wage of 100, 3Ct, 9tt in respect of invalidity pensions awarded in each year of the operation of the scheme, and 3it, 3ti in respect of old-age pensions awarded in each year of the operation of the scheme. The present value, at the commencement of the period concerned, of the cost of setting up these capital values, for an average annual wage of 100, is obtained by taking 2 vt+i Cae\ + 'xi + m3e% + '¿O 0 for the first period and 2 ^t+i (m3ci + W + m< +1<) 0 o for each of the other periods. A similar procedure is adopted for the repayments of contributions. Let ^¡ be the total amount of the three categories of repayments of contributions made during the rth year of operation, calculated on the basis of an anaual contribution fixed at 1. The present value of these repayments, on the basis of an average annual wage of 100, is given by the formula 9 ß 2vt+i % for the first p e r i o d ' a n d 0 4 ß ^ y Vt+i % for each of the other periods. 1 See pp. 345-346 and 348-349. 374 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION • Finally, the average premium in respect of the period considered, expressed as a percentage of wages, is 2 »' (M + f^t +. m< + '<) ßo = 1 — V" ¿J 1_ & v -á ^ for the first period and 2 »' ex* + x* + *xa + 'o 1 - Ü6 « - — & - 2 »' 't for each of the other periods. It is possible t o give effect to changes in the insured population by giving to & different values in the calculation relating to each period. In this way the following figures applicable to the first decennial period were obtained: 4.453 6.625 7.919 9.715 for „ „ „ the first wage class ,, second „ „ „ third „ fourth ,, „ From these figures the average premiums applicable to the first decennial period were obtained by increasing them by 20 per cent. in order to build up a reserve fund and by adding 1 mark to each in order to cover the cost of administration. The following premiums were thus obtained: 6.344 marks in 8.950 „ „ 10.503 „ „ 12.658 „ „ the first wage class ,, second „ ,, „ third „ „ fourth „ ., AVERAGE PREMIUMS FOR THE NORMAL PERIOD [10: pp. 3-7] The normal period is assumed to be attained when each insured person may be deemed to have entered at age 16 and when the insured population may be deemed to be stationary, that is to say, constant as regards both numbers and age distribution. Consequently, when the insurance scheme has attained its normal position each insured 1 person at age x will have paid about x + K — 16 yearly contributions. On the basis of an annual invalidity pension consisting of (1) a fixed portion of 60 marks and (2) increments equal to m for each contribution week (assuming 47 weekly contributions are paid each year), the capital 375' GERMANY value of invalidity pensions granted during a year to insured males is expressed l by <0 tú A / 60 2 ^ K ex + 47 m 2 (* + o " \ 16 ) ^ ** e* • On the basis of an old-age pension of constant amount r commencing' at age 70, the capital value of old-age pensions awarded during a year to insured males is given by ' ~n oa(i2) C/1C70 3*70 The calculation of the present value of all pensions awarded during a year for each wage class separately is made by giving to m and r their respective numerical values. The same procedure is adopted for females and finally a total H„ is obtained which represents the capitalised value of invalidity and old-age pensions awarded to men and women in all wage classes. The total amount of repayments of contributions, in respect of an annual contribution fixed at 1, is given by the following expression which is deduced from the formulae reproduced above 2 , since every repayment at age x, in the norma] period, covers the same number of 1 contributions, x -f- K — 16. 3» = 2 (* + ¿-16) + 2 (y + \ -16)9* m *?" a w*+ Ï™ w'y + 2 (y + \ -16) *» 4 H» • The present value of the contributions paid during a year, on the basis of an annual contribution fixed at ß n paid in the middle of the year, is given by the formula ^"12^ + 2 ^ . where 3KLX and &>y represent the numbers of male and female insured persons at age x ànd y respectively, which are assumed to remain constant in the normal period. 1 <3X represents the present value of a unit invalidity pension at age x, at which it was awarded. See above, p. 340. 2 See pp. 349-350. It should be observed, however, that in the expression used here account is taken of the period offiveyears during which contributions must have been regularly paid in order that the repayment may be granted. S76 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Finally, for any year in the normal period, the equation of the contribution income to the capitalised value of the pensions awarded, account being taken of the repayments of contributions, produces the average premium for the normal period: ft.- »•(2 ^ + 2 * . ) - j 3. In this way the following annual figures were obtained: 9.0621 marks for the first wage class 16.2729 „ „ „ second „ „ 21.8683 „ „ „ third „ 29.2367 „ „ „ fourth „ to which one mark was added to cover administration expenses. § 2. — Average Premiums and Annual Estimates calculated as at 1 January 1900 PRESENT VALUE OF COST OF BENEFITS In order to construct the actuarial balance-sheet and at the same time to determine the average premiums it was necessary to calculate: (1) the present value of invalidity and old-age pensions in course of payment on 1 January 1900; (2) the present value of invalidity pensions in course of acquisition in respect of (a) the insured population on 1 January 1900; and (b) entrants into insurance in the year 1900 and subsequently; (3) the present value of old-age pensions in course of acquisition in respect of (a) the insured population on 1 January 1900; and (b) entrants into insurance in the year 1900 and subsequently; (4) the present value of repayments of contributions in respect of (a) the insured population on 1 January 1900 and (¿>) entrants into insurance in the year 1900 and subsequently. Invalidity and Old-Age Pensions in Course of Payment [16: pp. 44-50] The present value of invalidity pensions in course of payment on 1 January 1900 has been calculated with the aid of the distribution of these pensions according to year of award and also of a capitalising factor representing the average present value of invalidity pensions awarded during a given year. . 377 GERMANY In a previous calculation the following average present values 1 had been applied to the invalidity pensions in force on 1 January 1897: 1 for pensions which had been in force for y year on the average, r ' i ~2 LaM + a* "i M+iJ 3 for pensions which had been in force for — years on the average, "2" L a M+i + a M+2j 9 and so on up to pensions which had been in force for ^ years on the average. In this way capitalisation factors i ¿}m were obtained representing the average present value of a unit invalidity pension in force, on January 1897, which had been awarded -^ years previously. In order to obtain factors applicable to pensions in force on 1 January 1900, graphic extrapolation was used to extend the series of factors which had been calculated when t = 1, 3, ... 9, to cover values of I it1m equal to 11, 13 ... 17. It was sufficient to apply these factors to the numbers ¿J1900_i_n of pensions in force on 1 January 1900, which had 1 t been awarded during the year 1900 — ^ — — and to sum 17 2 i it'm • -y*1 9 0 0 - i —t- in order to obtain the present value of invalidity pensions in force on 1 January 1900, on the basis of a fixed unit amount. As regards increments, each of the preceding values was multiplied by the average amount of the increment according to year of award, obtained from experience, and then these results were added together to produce m X 3 ' -idm- 3 1900-J• —' it'Til ' 1900-i-— The total result was therefore represented by the formula 17 17 Qlo = s • 2 iL • ¿L-ì-±+ 2 m i™-ì-±.ìtjm • "»-* 1«3 The present value Q1900 of the old-age pensions in force on 1 January 1900 was obtained in a similar manner. 1 The expression a1 has been defined in Chapter II : see p. 337. 378 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Invalidity Pensions in Course of Acquisition [16: pp. 50-54] The calculation has been made on the basis of a waiting period of four years by means of the formulae reproduced in Chapter II K As regards the insured population on 1 January 1900, the calculation rests on the following two fundamental present values: Present Value of a Fixed Portion of Unit Amount (a) in respect of an insured person, whose age x is less than 20, and who has not completed the waiting period, ai(i2) N on D°a (b) in respect of an insured person, whose age x is equal to or greater than 20 and who has normally completed the waiting period, N;1""' 1c or, in total, for the total number 16 of males and females, forming the insured population on 1 January 1900, c 19 ^(»(12) ) in respect of an insured person, whose age a: is such that 20 < x < 25 and who has normally completed the waiting period but who was not 16 years old on 1 January 1891, the date of coming into force of the scheme, * + i _ l 6 ) Nf2)+S^f D! a 1 Seecpp. 341-343. 379 GERMANY (c) in respect of an insured person, whose age x > 25, who normally was included in the initial insured population, 12> 9.5 Nf 12 ' + Sf X +1 J aa or, in total, for the total number 16 of males and females, forming.the insured population on 1 January 1900, 19 ia pf\ V¿i9oo — — ^"V| e If & K l\Tai(12) * ' aa 16 »raids) 20 I + oai02)\ Sai '-'x ^ai(i2) " £• & i _u T ' ^S ! * \ 1/ K. M a i < 1 2 > 20 T^aias) üi aa *-'21 U22 ^ai(i2) U23 • x+1 oaia2)\ ' 4--r ^X +^ ^ • +3 ^ ^ +4 4 , ^ + +^ I + ^24 w ^,ai which has been expressed above 1. The present value of the cost of invalidity pensions applicable to these persons is given by the result of the summation 18 /V° "NT* cw i(12; ST> ¿(12) .») where the numbers 3>tx = m3rix + 3tx represent, for the year concerned, the number of male and female entrants, who are all assumed to enter at ages 16, 17 or 18. Old-Age Pensions in Course of Acquisition [16: p. 55]. The present value of old-age pensions in course of acquisition was obtained directly, on the basis of a unit amount, by means of the formulae 69 f\va — "SÎ /? aaa V1900 ^ ^ *2>x w-x^x 16 for the insured population on 1 January 1900, and 18 16 for the new entrants into insurance in a given year. 1 See p. 343. 380 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Repayments of Contributions The calculation of the present value of the repayments of contributions in respect of (a) t h e insured population at 1 J a n u a r y 1900, and (b) the new entrants into insurance during 1900 and the following years have been seen above 1 . AVERAGE P R E M I U M S AND ACTUARIAL B A L A N C E - S H E E T . — COMPARISON O F V A R I O U S P R E M I U M S . — A N N U A L ESTIMATES The actuarial balance-sheet as at 1 J a n u a r y 1900, which coincides with the calculation of new average premiums, is based on a rate of interest of 3 per cent. On the liabilities side appear the following present values: Present value of invalidity and old-age pensions in force Present value of invalidity pensions in course of acquisition . In respect of the insured population on 1 January 1900 In respect of future entrants Present value of old-age pensions in course of acquisition . In respect of the insured population on 1 January 1900 In respect of future entrants.. y Qisoo »3 1900 .... r _^( 1.0315 [g . (¿v 1.0315 + m • PQL] i* fi V*f Vf f^oa S ' Viuoo fi vi i—vf g-Ql Present value of repayments of contributions 1.038 Present value of administration expenses and cost of medical aid . . . . . . . n^r\t ~ 0.0694. C^ 1 ft V*/i + i—vf The method of calculation of these present values, with the exception of t h e last, has j u s t been described. As regards t h e cost of administration and medical aid, this is based on t h e actual experience of the year 1897, for which t h e cost was equal t o 6.94 per cent, of the contribution income. This proportion was assumed t o hold for each year from 1 J a n u a r y 1900 onwards, and hence the present value of the cost was obtained b y applying the factor 0.0694 to the figure €LX appearing as the first item on t h e assets side 2 . As regards t h e calculations in respect Of new entrants into insurance each year, for each benefit component the present value as at 1 J a n u a r y 1900 was considered: (1) in respect of entrants in t h e year 1900, i.e. w* /» Q ; 1 2 See pp. 351-352. See below. 381 GERMANY (2) in respect of entrants in the year 1901, i.e. and so on. The sum of the results thus obtained, with the discount factor v, and the annual coefficient of increase /, produces the present value of the benefit component considered: 1 — Vf V The expression for the present value of invalidity pensions in course of acquisition is multiplied by the factor 1.0315 in order to take into account temporary invalidity pensions. For the numerical calculations the values of g and m were taken to be g == 101.94 m = and 1.61 which were based on statistical returns for the period 1891-1895. On the assets side appear (1) the present value of contributions in respect of the insured population on 1 January 1900: 16 and in respect of new entrants into insurance each year: is vi fi "Kg ~. 7 2 i ^x *• x j 1 — »/ M or, in total, \ir i — v fi? 1 (2) the value of the accumulated funds. The calculation of the average premiums is deduced directly from the figures appearing under the various items of the actuarial balancesheet and produces the following results: 15.47 marks a year for the average premium 7t¡ in respect of the insured population on 1 January 1900; 9.31 marks a year for the general average premium 7t9 in respect of present and future contributors taken together. In order to apportion the general average premium among the wage classes the method of direct calculation was applied to one of the wage classes and the premium applicable to each of the others was deduced from this result on the assumption that the contributions in the various classes should be in the same proportions as the benefits, that is to say, in proportion to the numbers 1; 1.5; 2; 2.5; and 3. 382 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Comparison of the Various Premiums The actuarial memorandum of 1899 contained certain other observations of a particular interest with regard to the choice of the technical structure of the financial organisation. The system which had been in operation since the beginning was based on the setting-up of capital values, and if this system were maintained the annual premium would increase up to a maximum amount of 11.80 marks. The fixed premium, in respect of an entrant into insurance at age 16, required to cover the cost of his benefits, including State grants, was calculated to be 11.11 marks 1. This premium which was " equitable " for entrants at age 16 and, a fortiori, for all other entrants, would be exceeded : from 1922 onwards if receipts and expenditure were balanced annually 2 and from 1930 onwards if, in accordance with the system then in force, capital values were set up in respect of pensions awarded each "" year. Annual Estimates With the aid of the data used in calculating the average premiums the following estimated annual costs of the insurance scheme from 1900 onwards were calculated first in total and then per insured person. TABLE X X X V I I . — ANNUAL ESTIMATE OF EXPENDITURE ON THE SCHEME Y ' 1900 • 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1920 1930 1940 1950 1960 1970 1980 2020 . . . . . . . Total in million marks Per insured person in marks 62.8 68.8 74.4 79.7 84.8 89.7 94.4 ' 98.9 103.2 107.3 111.2 114.9 118.4 138.7 155.5 167.0 174.0 177.1 178.0 178.3 4.96 5.43 5.88 6.30 6.70 7.09 7.46 7.81 8.15 8.48 8.78 9.08 9.35 10.96 12.28 13.19 13.74 13.99 14.06 14.09 178.4 14.10 1 To cover only expenditure charged to the institutions, excluding State grants, the fixed premium for an entrant at age 16 was calculated to be 9.29 marks. 2 The premium which would have been necessary to establish this balance year by year appears in the last column of table XXXVII. 383 GERMANY The annual cost per insured person defined the contribution which would have been necessary each year in order that receipts and expenditure should balance. From the figures in table XXXVII it was possible to check the result obtained for the present value of the cost of the insurance scheme as at 1 January 1900. Moreover an estimate was obtained of the total funds which would have been accumulated at the time when the annual cost attained its maximum of 14.10 marks per annum—on the hypothesis that a general average premium of 9.31 marks per annum was immediately adopted and assuming that the State would pay 0.40 mark per annum for each insured person on account of the assimilation of periods of military service with contribution periods. On these assumptions the interest on the invested funds ought, at that time, to compensate for the difference 14.10—9.31—0.40 = 4.39 : at the rate of 3 per cent, the accumulated funds would then amount to 147 marks multiplied by the number of insured persons. § 3. — General Average Premium as at 1 January 1910 [18: pp. 548-574] As a preparation for the introduction of insurance benefits for survivors, numerical values were obtained as at 1 January 1910, for all the items which should appear in an actuarial balance-sheet, excluding, however, the present value of contributions, since the rate of contributions had to be calculated. All the present values were calculated with interest at the rate of 3 per cent, and in respect of the total number of insured persons, that is to say, in respect of the insured population as at the date of the balance-sheet and in respect of those who would subsequently enter into insurance. On the liabilities side appear: Millions of marks Present acquired rights resent value vaiue of oi ace Present resent value of 11 I n v a l i d i t y a n d o l d . a g e benefits rights in course [ Survivors' benefits of acquisition . J Cost of medical aid Administration expenses Total 735 14,824 2,294 1,517 1,780 21,150 The figure in respect of survivors' benefits includes, as a safety margin, an addition of 10 per cent, to the calculated figure. In order to calculate the cost of medical aid and administration expenses, the average annual costs per insured person were first obtained from statistics collected from 1903 to 1907, viz. 1.1467 and 1.3449 respectively. The present values were obtained by multiplying these two figures by the present value of unit contributions (see below). On the assets side appear: (1) the accumulated funds, the amount of which as at 31 December 1909 was obtained by linear extrapolation from the known amounts as at 31 December 1905, 1906 and 1907, viz. 1,577 million marks; 384 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION (2) the product of the present value of unit contributions calculated by the general average premium ng, or, taking into account the loss of contributions during military service, 1.323 ng million marks. Equating assets and liabilities produces a linear equation the solution of which gives to Tzg the value of 14.79. RATE OF CONTRIBUTION IN EACH WAGE CLASS Statistics collected from 1903 to 1907 produced an average number of weekly contributions per annum of 48.26 and an average amount of weekly contribution equal to 0.24631, or an average annual contribution of 0.24631 x 48.26 = 11.89. The ratio of the calculated general average premium izg to this 14.79 average annual contribution, viz. . .\Q = 1-24, gave the factor by which the contributions then in force in each class had to be multiplied. The figures thus obtained were rounded off to the even integer below, for the first two classes, and the even integer above for the others. The rates of contribution finally adopted corresponded to an average annual premium of 14.86 marks. STATE CHARGE The annual charge falling on the State under the heading of survivors' insurance was estimated for a period of ten. years. The premium corresponding to the total charge falling on the State—for all classes of benefit—was calculated with the aid of the present values used in calculating the average premium, and, taking into account the safety margin of 10 per cent, added in respect of survivors' benefits, an annual premium of 6.531 marks was obtained. § 4. — Actuarial Balance-Sheet as at 1 January 1914 [19: pp. 73-80] IN RESPECT OF THE INSURED POPULATION ON 1 JANUARY 1914 The assets and liabilities were first calculated in respect of the insured population on 1 January 1914, with a rate of interest of 3.5 per cent. ASSETS Accumulated funds Present value of future contributions . Deficiency LIABILITIES Million marks 2,105.5 3,915.4 4,907.5 10,928.4 Million marks Present value of pensions in course of payment . . . . Present value of benefits in course of acquisition . . . Present value of cost of medical aid Present value of administra- 972.5 9,236.8 388.7 330.4 10,928.4 385 GERMANY The figure representing the value of the accumulated funds was obtained by taking the cost price for stocks and shares and the book value for real property. The present value of pensions in course of payment and also that of benefits in course of acquisition is the sum of the results obtained for each class of pension: invalidity, old-age, widows' and orphans'; for benefits in course of acquisition separate consideration was given to basic sums and increments. As regards medical aid and administration expenses, it was assumed that the annual expenditure would represent a constant 10 per cent, and 8.5 per cent, of the contribution income *. IN RESPECT OF THE ANNUAL CROP OF NEW ENTRANTS An actuarial balance-sheet was then constructed limited to the persons who entered into insurance each year, who were assumed to have a constant age distribution, as shown by the coefficients3 deduced from statistics compiled on the basis of contribution cards . With interest at 3.5 per cent., this balance-sheet was constructed as follows for each sex separately: ASSETS LIABILITIES Million marks Present value of future contributions . . . Deficiency Males Females 130.0 268.7 63.6 118.5 332.3 248.5 Million marks Present value of: Invalidity pensions . Old-age pensions to age 70 Widows' pensions and allowances . Orphans' pensions . Orphans' allowances Cost of medical aid . Administration expenses . . . . Males Females 240.8 222.9 1.6 23.9 9.7 1.4 26.9 13.0 22.8 11.0 332.3 248.5 IN RESPECT OF THE TOTAL ANNUAL NUMBER OF EXITS Account was taken of persons who left the field of insurance for causes other than 8death or invalidity, by reference to figures calculated for the year 1914 . Considering each sex separately and maintaining the rate of interest at 3.5 per cent., a third actuarial balance-sheet, reproduced below, was constructed in respect of the group of persons who were expected to cease to be insured each year. 1 2 3 See p p . 364-365. See p p . 319-321. See p p . 321-322. 25 386 ACTUARIAL TECHNIQUE AND FÍNANCIALORGANISATION ASSETS LIABILITIES Million marks Present value of future contributions . . . Deficiency Million maris Males Females 79.2 130.0 135.0 124.4 265.0 Present valué of: Invalidity pensions . Old-age pensions to age 70 Widows' pensions and allowances . Orphans' pensions . Orphans' allowances Cost of medical aid . Administration expenses . . . . 203.1 FINANCIAL Males Females 206.0 187.5 6.2 1.5 20.8 7.0 1.0 13.0 7.9 11.0 6.7 265.0 203.6 EQUILIBRIUM The comparison of these three balance-sheets led to the following conclusions: As regards males, new entrants each year will bring with them a deficiency of 63.6 millions, while exits will extinguish a deficiency of 135.0 millions. The combined result of these two movements, then, will be to increase the assets as compared with the liabilities by 71.4 millions. Similarly, as regards females, each year the assets will be increased as compared with the liabilities by 124.4 — 118.5 = 5.9 millions. If it be assumed that the' annual coefficient of increase / applies equally to entrants as to exits, the improvement in the assets as compared with the liabilities resulting from the double movement of entry and exit in all future years is given in millions by the formula? 71.4 (v* /* + v* / 2 + ) = 71.4 ? „ for males and 5.9 (»* /* + v* / 2 + ) = 5.9 yf for females. On the basis of an annual coefficient of increase / equal to 1.02 for males and 1.01 i for females, and taking interest at 3.5 per cent., there is obtained ™ ti = Total amount of repayments of contributions, of all kinds during the ith year of operation of the scheme. = Total amount of repayments of contributions of all kinds during a year in the normal period. = Capital value of invalidity and old-age pensions awarded during a year of the normal period to insured males and females. ij = Average present value of invalidity pensions in force on 71 1 J a n u a r y 1900, which were awarded - years previously. ¡V- , 1900-i-i Q'i = Present value of invalidity pensions in payment on l *w Q"i l8 »° 1 = N u m b e r of invalidity pensions in force on 1 J a n u a r y 1900, l which were awarded during the year 19PQ-J--. 1 J a n u a r y 1900. = Present value of old-age pensions in payment on 1 J a n uary 1900. See table X X X V I . GERMANY io Q1900 p Oia Visoo Oc" Qtx» 1900 Qtx* c Y * 391 = Present value of a unit invalidity pension in course of acquisition, calculated in respect of the insured population as at 1 January 1900. = Present value of the right to an invalidity pension increment which increases by one unit for each contribution year, calculated in respect of the insured population as at 1 January 1900. = Present value of invalidity pensions in course of acquisition calculated in respect of the group of new entrants into insurance in the year. = Present value of old-age pensions in course of acquisition, calculated in respect of the insured population as at 1 January 1900. = P r e s e n t value of old-age pensions in course of acquisition, - calculated in respect of the group of new entrants into insurance in the year. = Present value of the contributions expected from an insured person aged x, on the basis of an annual payment equal to a unit. CHAPTER IV FINANCIAL ADMINISTRATION § 1. — Investment of Funds. — Statutory Provisions and Regulations Each institution itself invests the funds which it has put to reserve, in accordance with the statutory provisions and regulations and under the control of the Insurance Office. The 1889 Act merely stipulated that the insurance funds should be invested in accordance with the rules which were applied to the investment of the workmen's compensation insurance funds. The latter could be either entrusted to a public savings bank or invested in accordance with the provisions in each of the Federated States relating to trust funds. In States where there were no such provisions, funds could be invested (1) in loans issued or guaranteed by the Reich or by a State; (2) in loans issued by communes, associations of communes or provinces; (3) in loans issued by credit institutions of one or other of these bodies, provided that the loan could be called in by the creditor or that provision was made for its regular amortisation. Funds could also be placed at interest with the Reichsbank. Insurance institutions could be empowered by an association of communes or by a Federated State, to invest, subject to revocation, part of their accumulated funds, not exceeding one quarter, in other remunerative investments than those prescribed by the Act or in real estate. The 1899 Act authorised the investment of insurance funds under the conditions laid down in the Civil Code for investing trust funds, or in accordance with the rules governing the investment of trust funds in force in the Federated State in which the institution operated. The various types of investment so prescribed correspond closely with those enumerated under (1), (2), (3), (4), (8) and (9), in the second part of this survey 1 . Further, the institution could be authorised: by the Federated State in which it operates, to make loans to communes and to associations of communes; by the Insurance Office, up to a maximum of half its accumulated funds, for the purpose of avoiding loss of capital or for the purpose of helping undertakings intended mainly or exclusively for the benefit, of insured persons, to make other investments than those prescribed for the investment of trust funds and in particular to acquire real estate; however, as soon as.the total of these investments exceeded a quarter of the funds the institution had also to obtain the consent of the association of communes or of the Federated State, as the case might be. 1 Chapter IV, § l,.see below, pp. 434-435. 393 GERMANY The Federated State could enact regulations limiting the total amount which institutions were allowed to allocate to this or that category of investments. The 1911 Act reproduced to a large extent the provisions of the 1899 Act. The consent of the Insurance Office became necessary in all cases, whether it was a question of authorising the various types of investment or of limiting the total amount which could bs allocated to a particular category. The Act itself authorised the purchase of bearer bonds of joint-stock mortgage banks, when they were entered as first class in the list drawn up by the Reichsbank. It further stipulated that at least a quarter of the total funds must be invested in bonds of the Reich or of the Federated States. 2. — Statistics of Investments COMPOSITION OF THE ACCUMULATEÜ FUNDS The apportionment of the accumulated funds among the main classes of investment, for the regional institutions alone up to 1899, and for the whole of the insurance scheme as from 1900, is given in absolute figures and in percentages in table XXXIX. A proportion of the accumulated funds has been employed in " social" investments, that is to say in financing enterprises or undertakings of benefit to insured persons or even to the whole of the general public. These, investments had as their object: (1) the building of working-class houses; in respect of a total amount which increased from 12 millions in 1896 to 483 millions in 1913; (2) the granting of rural credits : in respect of a total amount which increased from 13 millions in 1896 to 120 millions in 1913; (3) the building of hospitals, curative institutions, public health and other establishments for public utility purposes: in respect of a total amount which increased from 6 millions in 1896 to 562 millions in 1913; (4) the building by the Regional Insurance Offices of hospitals, sanatoria, convalescent homes and homes for the aged; in respect of a total amount which increased from 12 millions in 1900 to 80 millions in 1913. The proportion of social investments in the total invested funds reached the following figures each year: Year Percentage 1896 1897 1898 1899 1900 1901 1902 1903 . . . . . . . 1904 . . . . . . . 6.7 8.9 13.8 19.0 23.5 30.0 32.0 33.8 35.9 Year 1905 1906 1907 1908 1909 1910 1911 1912 1913 . . . . . . : Percentage 38.3 40.9 44.6 43.2 45.8 48.9 50.1 49.6 50.6 394 A C T U A R I A L T E C H N I Q U E AND F I N A N C I A L ORGANISATION TABLE XXXIX. D I S T R I B U T I O N - O F TOTAL INVESTMENTS Securities Year Loans State F u n d s or Railway Funds Empire F u n d s of ComFunds g u a r a n - munes teed by t h e State To Communes On mortgages 3 5 6 4 Cash in hand Furniture and Fittings 8 9 10 1,976 5,266 7,667 8,588 9,224 9,436 10,577 11,234 14,802 22,287 31,394 38,331 44,067 49,424 55,083 61,098 68,573 76,736 81,937 85,014 89,083 92,306 96,676 1,044 4,562 5,618 9,280 8,169 7,115 5,495 6,895 12,948 13,593 13,851 13,186 15,393 20,563 26,291 24,080 21,189 21,270 23,195 27,931 30,565 40,623 30,729 26 34 38 41 43 44 46 49 51 52 51 51 Í8 46 16 15 13 14 18 21 18 15 14 15 17 17 21 15 To Real Savings E s t a t e Banks 7 (in thousand marks) 5,364 13,562 21,920 25,276 26,033 24,841 25,484 24,935 25,128 28,964 32,284 32,015 34.132 34,253 35,627 36,222 34,504 36,223 37,701 41,669 52,219 66,584 76,564 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 21,788 35,163 47,433 54,788 64,060 70,938 73,298 71,799 76,977 109,313 111,059 119,806 126,283 130,525 134,121 137,311 138,758 143,891 148,452 156,729 174,178 224,865 285,608 28,532 14,489 3,166 49,446 37,426 5,833 71,328 60,370 12,100 99,080 83,606 22,642 129,022 102,369 41,678 167,361 118,862 61,037 197,716 146,104 79,180 216.507 185,854 99,667 231,298 218,619 120,310 279,678 237,700 151,982 298,060 264,348 175,125 316,165 288,475 195,665 335,608 306,316 217,700 354,198 326,143 239,914 366,946 351,284 262,096 379,226 385,908 287,313 383,599 435,440 313,709 384,159 473,338 344,063 383,718 505,238 382,460 382,211 540.298 416,083 380,843 564,154 455,045 380,389 603,917 499,140 381,911 650,833 559,963 107 107 151 311 231 151 168 151 ' 221 2,243 3,042 3,833 4,781 5,385 6,090 7,366 8,293 9,931 H.4Ì1 12,223 13,275 14,472 15,804 — — — — —. — — — — — — — — — -— —— — — • — 7,006 7,609 Proportions (per thousand) 1900 . 1901 . 1902 . 1903 . 1904 . 1905 . 1906 . 1907 . 1S08 . 1909 . 1910 . 1911 . 1912 . 1913 . 34 35 32 31 29 29 27 25 24 24 25 30 34 36 129 120 119 116 112 108 104 99 97 94 94 99 117 136 331 321 314 310 305 297 288 273 258 244 230 216 197 181 281 284 286 283 281 284 293 310 318 321 325 321 313 309 180 188 .194 201 207 212 218 223 231 243 250 259 259 266 3 3 4 4 5 5 6 6 7 7 8 7 7 7 — — — — — — — — —. — 4 • — 4 INTEREST YIELD The rate of interest yielded by securities on the basis of the purchase price, was calculated to be as follows, in respect of regional institutions 395 GERMANY only up to 1899, and in respect of the whole of the insurance scheme from 1900 onwards: Year 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 §3. Percentage 3.67 3.67 3.66 3.65 3.58 3.53 3.49 3.49 3.50 3.53 3.56 3.55 Year " Percentage 1903 1904 1905 1906 190.7 1908 1909 1910 1911 1912 . . . . : . . 1913 Actuarial and Financial Control. 3.54 3.54 3.53 3.53 3.55 3.57 3.57 3.57 3.59 3.61 3.65 Statistics ACTUARIAL AND FINANCIAL CONTROL From the very beginning insurance institutions were subjected to the supervision of a central body, the Reich Insurance Office, which could at any time examine their financial administration. All the information relating to the administration of the scheme and all the accounts had to be furnished to that Office in accordance with its instructions and within the time limits which it had itself prescribed. It laid down the rules which the institutions had to follow in compiling their accounts. The 1889 Act formed within the Insurance Office a Calculation Bureau which had the following particular duties: (1) to apportion the cost of benefits between the Reich and the various institutions; (2) to help in statistical investigations. These provisions have not been amended in any essential particulars by subsequent Acts. The 1899 Act specified that a copy of the draft budget should be submitted to the Insurance Office and that the latter should formulate its objections if the draft was not in conformity with the legal or statutory regulations (" or if the draft was likely to imperil the solvency of the institution ", added the 1911 Act.) It has been seen above that the rates of contribution were fixed by law for decennial periods: it followed that at the expiration of each of these periods the average premiums had to be revised and consequently that an actuarial balance-sheet had to be constructed at least once in ten years. STATISTICS The Insurance Office collected the returns of the various institutions and with the help of its Calculation Bureau analysed them for the purpose of compiling each year statistics relating to the whole of the insurance scheme and publishing them in its monthly review [22]. 396 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION BIBLIOGRAPHY I. — Legislative Texts 1. " Gesetz betreffend die Invaliditäts- und Altersversicherung, vom 22. Juni 1899 ". Reichsgesetzblatt 1899, S. 97. 2. " Invalidenversicherungsgesetz vom 13. Juli 1899 ". Reichsgesetzblatt 1899, S. 393. 3. " Die Reichsversicherungsordnung vom 19. Juli 1911 ". Reichsgesetzblatt 1911, S. 509. II.—Reichstag Documents 7. Legislaturperiode, IV. Session 1888/89 4.- Entwurf eines Gesetzes betreffend die Alters- und Invaliditätsversicherung (S. 1-19). 5. Begründung (S. 19-71). 6. Denkschrift über die Höhe der finanziellen Belastung, welche durch den Gesetzentwurf betreffend die Alters- und Invaliditätsversicherung voraussichtlich hervorgerufen werden wird (S. 72-94). 7. Mathematische Anlage zu der Denkschrift betreffend die aus der Alters- und Invaliditätsversicherung zu erwartende finanzielle Belastung (S. 95-126). 8. Denkschrift über die Höhe der wöchentlichen Beiträge, welche infolge der Kommissionsbeschlüsse erster Lesung für jeden Versicherten zu entrichten sind (S. 292-320). , 9. Finanzielle Folgerungen aus den Kommissionsbeschlüssen zweiter Lesung (S. 321-330). 10. Denkschrift über die Höhe der wöchentlichen Beiträge, welche im Beharrungszustande nach den Reichstagsbeschlüssen zweiter Lesung im Durchschnitt für das Reich in jeder Lohnklasse voraussichtlich zu erheben sind (15 S.). 8. Legislaturperiode, IV. Session 1895/97 11. Entwurf eines Invalidenversicherungsgesetzes (55 S.). 12. Begründung (59 S.). 13. Denkschrift betreffend die finanzielle Entwicklung der Invaliditäts- und Altersversicherungsanstalten und der zugelassenen besonderen Kasseneinrichtungen (92 S.). 10. Legislaturperiode, I. Session 1898/99 14. Entwurf eines Invalidenversicherungsgesetzes (S. 1-162). 15. Begründung (S. 163-370). 16. Denkschrift betreffend die Höhe und Verteilung der finanziellen Belastung aus der Invalidenversicherung (135 S.). 12. Legislaturperiode, IL Session 1909/10 17. Entwurf einer Reichsversicherungsordnung (299 S.). 18. Anlagen zum Entwurf einer Reichsversicherungsordnung (784 S.). 13. Legislaturperiode, IL Session 1914/15 19. Denkschrift über die Vermögenslage der Invaliden- und Hinterbliebenenversicherungsträger am 1. Januar 1914 (82 S.). GERMANY 397 III. — Administrative Documents 20. Amtliche Nachrichten des Reichsversicherungsamts, 1901. 2. Beiheft. 21. Amtliche Nachrichten des Reichsversicherungsamts, 1906. 1. Beiheft. (Das Ausscheiden der Invalidenrentenempfänger der Jahre 1891 bis 1899 aus dem Rentengenuss). 22. " Finanzieller und statistischer Jahresbericht ". Amtliche Nachrichten des Reichsversicherungsamts. IV. — Studies 23. L. WEBER: "Etude sur les tables de mortalité d'invalides et sur les tables d'invalidité au point de vue des calculs d'assurance ". Institut des actuaires français. Bulletin trimestriel, No. 30, October 1897, pp. 144-201. 24. M. BELLOM : Les lois d'assurance ouvrière à l'étranger. Tome 3 (1) : " Assurance contre l'invalidité ". Paris, 1905. 25. Recueil de documents sur la prévoyance sociale réunis par le Ministère du Commerce: " L'assurance obligatoire contre l'invalidité en Allemagne ". Berger-Levrault & C le , Paris, 1905. 26. M. CASTELLANI: Sulla frequenza della invalidità. Cassa nazionale per le assicurazioni sociali. Rome, 1925. 27. E. WITTE and M. SAKMANN: Financial History of the Workers' Invalidity, Old-Age and Survivors' Insurance of Germany. Social Security in America Social Security Board. Washington, 1937. PART II 1924 ONWARDS INTRODUCTION The position of invalidity, old-age and widows' and orphans' insurance for workers 1 was, in 1924, very different from that which might have been expected, judging from the valuation balance-sheet as at 1 January 1914. As a result of the war and the depreciation of the mark the accumulated funds had almost entirely disappeared; their total at the end of 1924 was only 329.6 million RM., as compared with 2,105.5 million marks at the end of 1913. Taking into account the growth of reserves which should normally have taken place between 1913 and 1924, the workers' insurance assets may be estimated to have suffered a loss of about 4,000 million marks. At the end of the period of inflation, when once again attention was directed to the financial equilibrium of the insurance scheme, it was decided to abandon the accumulation system based on average premiums, on which the financial organisation had hitherto rested, and to adopt the assessment system. It will be seen that the rates of contribution were no longer dependent on the calculation of average premiums and that no attempt was made to build up-again the actuarial reserves. It is not the object of the following study to set forth in their chronological order the numerous legislative amendments made since 1924. A detailed analysis will first be made of two tables of annual estimates which were constructed for a quinquennial and for a decennial period respectively. The estimates in these tables were in fact exceeded, in the first place by reason of increases in and extensions to the benefit payments and secondly as a result of the economic crisis. In 1930 the position proved to be critical and it continued to become more and more dangerous with the increase in unemployment and the reduction in hours of labour entailing lower wages. Accordingly steps had to be taken through the Emergency Decrees to make a considerable reduction in the level of most benefits. These restrictive measures were not sufficient for the purpose and an effort was made through the Act of 7 December 1933 to secure the solvency of the workers' insurance scheme at the same time as that of the salaried employees' and miners' insurance schemes. The technical memorandum attached to the text of this Act sets forth, by means of three actuarial balance-sheets based on different assumptions, the estimated financial position and future progress of the workers' insurance scheme. The 1933 Act stipulates that " the value of future contributions and other assets—including Reich grants—must adequately 1 Hereinafter called " workers' insurance scheme ". 400 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION cover all future expenditure ". The explanatory statement makes it clear that it is intended to organise the finances of the scheme on the basis of an accumulation system with average premiums, that is to say, to return to the pre-1914 system. However, the increase of the resources by the amount required to permit this change was deferred until such time as the expenditure on unemployment insurance had decreased by a similar amount. The object of the Act of 21 December 1937 was to transfer to the workers' insurance scheme part of the unemployment insurance income released by the almost total disappearance of unemployment and also to charge the Reich Government- with the cost of the uncovered liabilities. In this way the 1937 Act made it possible to establish the finances of the workers' insurance scheme on the basis of an accumulation system with average premiums. CHAPTER I DEMOGRAPHIC ESTIMATES, BASES AND EXPERIENCE § 1. — Biometrie Tables INVALIDITY RATES 1 Investigations Preparatory to the 1933 Reform [20] The probability of becoming invalid was deduced from data obtained from the workers' insurance scheme during the period 1925-1930, which gave for quinquennial age groups from age 20 to 65 the ratio of the number of persons becoming invalid to the total number of insured persons. The results are given in table I for each sex separately and also for both sexes combined. TABLE I. — PROBABILITY OF BECOMING INVALID Age group (years) 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 Males Females All insured persons 0.00099 0.00315 0.00537 0.00581 0.00738 0.00997 0.01757 0.03472 0.08670 0.00122 0.00407 0.00650 0.00783 0.01340 0.01824 0.03624 0.06636 0.14168 0.00050 0.00321 0.00547 0.00610 0.00867 0.01189 0.02168 0.04268 0.10325 RATES OF CESSATION OF INVALIDITY AND OLD-AGE PENSIONS Investigations Preparatory to the 1933 Reform The rates of cessation of invalidity and old-age pensions for all insured persons, irrespective of sex, were obtained from the experience of the workers' insurance scheme itself during the period 1924-1927 2. They appear in a double-entry table according to age and duration of 1 Invalidity has the same definition as in the pre-1914 scheme (see Part I, p p . 331-332). 2 Amtliche Nachrichten für Reichsversicherung, 1931, No. 10, p . 456. 26 402 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION TAHLE I I . — RATES OF CESSATION OF I N V A L I D I T Y (both sexes together) Select cessation rates when the following number of years has elapsed since grant of pension Age at becoming invalid 0 2 1 4 3 5 6 7 8 Ultim- 9 10 Age ate attained cessation after 11 rates years 33 22 • 0.2609 0.3013 0.2196 0.1760 0.1318 0.0965 0.0745 0.0590 0.0475 0.0395 0.0340 0.0320 23 322 34 24 324 35 25 326 36 26 328 37 27 0.2100 0.2100 0.1553 0.1294 0.1050 0.0840 0.0670 0.0551 0.0465 0.0390 0.0350 330 38 28 332 39 29 334 40 30 336 41 31 338 42 32 0.1590 0.1550 0.1189 0.0920 0.0765 0.0641 0.0560 0.0481 0.0420 0.0373 0.0350 340 43 33 343 44 34 346 45 35 349 46 36 352 47 37 0.1416 0.1400 0.1067 0.0865 0.0725 0.0620 0.0515 0.0440 0.0390 0.0370 0.0360 355 48 38 358 49 39 361 50 40 364 51 41 367 52 42 0.1386 0.1300 0.1024 0.0840 0.0701 0.0594 0.0510 0.0470 0.0430 0.0395 0.0375 370 53 1 43 373 54 44 376 55 45 379 56 46 382 57 58 • 47 0.1291 0.1170 0.0915 0.0735 0.0646 0.0565 0.0505 0.0463 0.0428 0.0405 0.0382 385 48 388 59 49 391 60 50 394 61 51 397 62 52 0.1095 0.0962 0.0776 0.0651 0.0580 0.0515 0.0473 0.0440 0.0410 0.0394 0.0397 400 63 53 405 64 54 412 65 55 422 66 56 440 67 57 0.0817 .0.0754 0.0607 0.O507 0.0463 0.0442 0.0425 0.0405 0.0412 0.0422 0.0440 470 68 58 510 69 59 547 70 60 605 71 61 660 • 72 62 0.0592 0.0582 0.0499 0.0469 0.0442 0.0440 0.0470 0.0510 0.0547 0.0605 0,0660 727 73 63 806 74 64 890 75 65 972 76 66 1056 77 67 0.O259 0.0470 0.0510 0.0547 0.0605 0.0660 0.0727 0.0806 0.0890 0.0972 0.1056 1154 78 68 1264 79 69 1371 80 70 1478 81 71 1602 82 72 0.O373 0.0727 0.0806 0.0890 0.0972 0.1056 0.1154 0.1264 0.1371 0.1478 0.1602 1746 83 73 1896 84 74 2042 85 75 2183 86 76 2319 87 77 0.0528 0.1154 0.1264 0.1371 0.1478 0.1602 0.1746 0.1896 0.2042 0.2183 0.2319 2443 88 78 2545 89 79 2739 90 80 2881 91 81 3024 92 82 0.O801 0.1746 0.1896 0.2042 0.2183 0.2319 0.2443 0.2545 0.2739 0.2881 0.30,24 3168 93 83 3313 94 84 3458 95 85 3604 96 86 3750 97 87 3897 98 88 4044 99 89 4191 100 . • • _ ' 403 GERMANY invalidity for the first ten years of invalidity and in an ultimate table for durations of ten years and over. Both tables follow fairly closely the classic tables of 1906 1 . 2The ultimate table is run into the general mortality table of 1924-1926 from age 65. AWARD OF W I D O W ' S PENSIONS Investigations Preparatory to the 1933 Reform The probability that on the death of a healthy insured person or an invalid pensioner a pension will be payable to his widow is obtained from the formula W * = A a , T i K qx + ix ix where: ZÄ = the number of pensions awarded to the widows of insured men or invalid pensioners who died within a year at age x. Ax = the number of healthy insured men aged x. <¡x = the mortality rate of a healthy male at age x. 3X = the number of male invalids aged x. Qx = the mortality rate of a male invalid at age x. In the calculation of Wx the numbers Zx, Ax and J^. are taken from statistics for the years 1925-4930 and the mortality rates of healthy males are deduced from the general mortality table for 1924-1926. To obtain the invalid mortality rates a combined table was constructed by adopting the figures in previous returns 3 down to age 64 and by having recourse after that age to the general mortality table for 1924-1926. The probability that the death of a healthy insured male, aged x, will give rise to the payment of a widow's pension is obtained from the product ?* W* • The probability that the death of an invalid insured male, aged x, will give rise to the payment of a widow's pension is obtained from the product ?x wx • 1 2 See Part I, p. 286. Cf. Statistik des Deutschen Reichs, Bd. 401, or Statistisches Jahrbuch für das Deutsche Reich, 1929, pp. 36, 38. 3 See Drucksachen des Reichstags, 12. Legislaturperiode, 1. Session, 1907, No. 226, p. 33. 404 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION RATES OF CESSATION OF WIDOWS' PENSIONS Investigations .Preparatory to the 1933 Reform After an examination of the experience of the years 1925-1929, the female mortality table for 1891-1900 x was adopted for the rates of cessation of widows' pensions. §2. — Insured Population The workers' insurance scheme includes compulsorily, with a few exceptions, all wage-earning manual workers, whatever their wages, age, sex and nationality. Investigations Preparatory to the 1933 Reform The insured population was estimated in quinquennial age groups for each year from 1930 to 1940 and at five-yearly intervals from 1940 to 1970. Since the data collected by the insurance institutions were neither sufficiently reliable nor complete enough for the purpose, recourse had to be had to information obtained from the general censuses and in particular to two tables of estimates relating to the progress of the total population and the employed population respectively. The first gives the estimated progress of the total population in quinquennial age groups for males and females separately from 1928 to 2,000, based on the general German mortality for 1924-1926 and on the assumption that the birth rate would decrease by 25 per cent, in a parabolic curve from 1927 to 1955 and would then remain constant at that level 2 . The second table gives the age distributions, for males and females separately, of the employed population between the years 1925 and 1940, based on data from the industrial census of 1925 3. The employed population is obtained from the total population in each age group by means of an " employment ratio " which is assumed to be constant. On the further assumption that the ratio of the insured population to the employed population remains constant in each age group table III was constructed. This table forms the fundamental basis underlying all the estimates in the 1933 technical memorandum. 1 2 3 Statistik des Deutschen Reichs, Bd. 200. Ibid., Bd. 401, II, pp. 652-653. Ibid., Bd. 408, pp. 318-319. TABLE III. Age group (years) 1930 ESTIMATED MOVEMENT OF INSURED POPULATION 1931 1932 1933 1934 193 (a) Males 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 2,371,515 2,169,939 1,838,974 1,238,922 1,038,666 929,330 861,175 811,936 638,987 429,548 2,170,506 2,187,509 1,850,655 1,314,775 1,052,887 928,844 865,991 804,601 661,339 441,346 1,970,806 2,166,560 1,870,945 1,382,726 1,075,536 932,732 871,289 794,515 • 695,962 438,028 1,758,666 2,159,126 1,873,404 1,462,792 1,110,298 928,358 878,032 789,472 706,480 454,251 1,666,346 2,125,337 1,910,909 1,505,459 1,154,015 928,844 887,183 782,136 715,683 467,893 1,687 2,088 1,931 1,543 1,212 933 888 779 719 478 12,328,992 12,278,453 12,199,099 12,120,879 12,143,805 12,263 (i>) Females Under 20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 1,637,282 1,424,199 784,827 478,542 402,708 289,088 259,758 222,961 171,779 118,293 1,497,929 1,429,538 788,721 485,467 411,179 292,436 264,350 222,843 177,962 121,307 1,357,656 1,411,741 797,289 490,661 419,487 297,458 269,466 220,963 189,092 119,611 1,210,945 1,404,178 797,029 502,608 427,144 300,420 274,452 222,138 192,577 124,226 1,142,878 1,381,487 809,491 505,897 434,149 305,056 280,880 221,550 197,299 127,617 1,153 1,356 815 512 440 31 28 22 20 130 5,789,437 5,691,732 5,573,424 5,455,717 5,406,304 5,42 TABLE III. — ESTIMATED MOVEMENT OF INSURED POPULATIO (continued) Age group (years) 1939 1940 1945 1950 19 (a) Males Under 20 . . . . 20-25 25-30 30-35 35-40 40-45 . . ' 45-50 50-55 55-60 60-65 . Total 2,217,648 1,366,433 1,891,849 1,603,962 1,473,199 1,037,233 888,147 803,226 692,894 536,105 2,270,028 1,282,636 1,858,033 1,620,818 1,510,596 1,089,727 892,963 804,601 . 690,702 539,055 2,045,448 1,923,954 1,141,750 1,559,715 1,585,915 1,357,541 1,042,272 808,269 713,054 517,669 2,004,199 1,729,328 1,712,317 958,163 1,526,397 1,425,588 1,298,024 943,973 716,560 534,261 1,88 1,69 1,53 1,43 93 1,37 1,36 1,17 83 53 12,510,696 12,559,159 12,695,587 12,848,810 12,77 (f>) Females m Under 20 20-25 25-30 30-35 50-55 55-60 60-65 Total . . . . . . . . . . . 1,510,807 884,952 790,798 528,751 465,427 334,286 301,083 240,943 199,097 150,220 1,547,140 825,332 776,260 532,387 471,455 339,051 306,069 Ï 244,704 200,222' 152,481 1,394,449 1,235,107 472,246 507,109 489,863 363,131 334 537 262,569 219,895 152,387 1,372,833 1,108,304 706,941 308,525 466,405 377,167 358,283 287,016 235,971 167,362 1,28 1,09 63 46 28 35 37 30 25 17 5,406,364 5,395,101 5,431,293 5,388,807 5,23 407 GERMANY EXPERIENCE From the data collected by the insurance institutions themselves it was possible to estimate the total number of insured persons and their distribution according to age and sex. The first results of investigations x made in 1934 were published in 1935 separately for the territorial insurance institutions and for the institutions connected with the special schemes (the Reich Railways pension funds, the miners' fund and the seamen's fund). They refer to the year 1933 for the territorial institutions, to 1 January 1934 for the Reich Railways pension funds and the miners' fund and to 1 July 1934 for the seamen's fund. Below is reproduced the age distribution of 10,000 insured persons, applicable to the total insured population, for males, females and both sexes respectively. The absolute figures for the total insured population have been estimated to be 11,490,000 males and 5,836,000 females. DISTRIBUTION OF 1 0 , 0 0 0 INSURED PERSONS BY YEAR OF BIRTH FOR THE TOTAL INSURED Year of birth 1867 1868 1869 1870 1871 1872 1873 1874 1875 1880 1885 1890 1895 1900 1905 1910 1915 1920 a n d earlier . . . . . t o 1879 t o 1884 t o 1889 t o 1894 t o 1899 to 1904 to 1909 t o 1914 to 1919 and later Total POPULATION Males Females Total 2 36 46 59 58 78 88 99 590 652 765 831 1,097 1,535 1,694 1,661 707 2 3 26 34 47 43 60 70 74 474 583 755 867 985 1,137 1,533 2,192 1,115 2 3 32 42 55 53 72 82 91 551 628 762 844 1,059 1,401 1,639 1,840 844 2 10,000 10,000 10,000 The approximate estimates made each year show that the number of insured persons remained round about the figure 17-18 millions during the whole period 1924-1934. The total insured population and its age distribution were determined more exactly as at 1 January in each of the years 1933, 1934 and 1935 [22: year 1937]. 1 See Chapter IV, § 3, p. 438, where a brief analysis is made of the methods used. 408 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION § 3. — Number of Beneficiaries 1927 ESTIMATES When the table of annual estimates for the period 1927-1931 was constructed, a calculation was also made of the estimated annual number of pensions in force from 1925 to 1975 [17: pp. 289-291]. The figures at quinquennial intervals are reproduced below. Year Invalidity and old-age pensions Widows' (or widowers') pensions (in thousands) 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1,465 1,955 2,251 2,427 2,526 2,579 2,608 2,624 2,632 2,637 2,639 228 396 518 593 635 656 666 670 672 673 673 In this calculation it was assumed that the annual crop of insured persons or survivors who became entitled each year to an invalidity, old-age or widows' pension would remain invariable as regards both numbers and age distribution. For the rates of cessation of invalidity pensions recourse was had to the 1908 data obtained from the experience up to the end of 1906 of the cessation of pensions granted in the period 1896 to 1905. The results indicated (see the table above) that as from about 1960 the number of invalidity and old-age pensions and of widows' and widowers' pensions would remain practically stationary. INVESTIGATIONS PREPARATORY TO THE 1933 REFORM The estimates of the annual numbers of beneficiaries in receipt of the various benefits were obtained by applying the biometrie factors described in § 1 of this chapter to the annual numbers of the insured GERMANY 409 populations appearing in table III. Distinction was made between the pensions in force on 1 January 1931, the annual number of which was obtained merely by applying the cessation rates to the initial figures, and pensions granted after 1 January 1931, for which account had to be taken of both the probabilities of award and of cessation. As regards invalidity and old-age pensions the figures relating to cessation were obtained directly up to 1950, after which date extrapolation was used by means of a curve of the second degree. For widows' pensions the number of pensions in force on 1 January 1931 was taken from the statistical data of the insurance scheme and was then projected by means of the cessation rates mentioned above (1891-1900 table of female mortality). For widows' pensions granted after 1 January 1931, there are three distinct classes: (a) those which follow invalidity and old-age pensions which were in force on 1 January 1931; • (b) those which follow invalidity and old-age pensions granted after 1 January 1931; and (c) those which are granted on the death of a healthy insured person. For all these classes the annual crops of new pensions are obtained by using the probabilities defined above. Direct calculation up to 1980 can be made only for class (c). For the remaining two classes the available data did not allow direct calculation beyond 1950, after which date figures were obtained by extrapolation. For class (a) a straight-line decrease was assumed between 1950 and 1980, while for class (¿>) practically the same result was obtained either by direct extrapolation, using the method of least squares, or by assuming from 1950 a constant ratio between the number of widows' pensions and the number of invalidity and old-age pensions. The annual numbers of cessations of pensions are obtained up to 1950 by means of the cessation rates mentioned above, after which date figures are obtained by extrapolation by a curve of the third degree. As regards orphans' pensions, in the absence of appropriate data and because of their secondary importance compared wif.h the invalidity, old-age and widows' pensions, the annual numbers were estimated summarily. Taking into account the war orphans and the fall in the birth-rate it was assumed that the total number of orphans' pensions would decrease year by year until 1935. The decrease actually experienced between 1928 and 1931 was assumed to be prolonged until 1935, at which date the number of pensions was taken as 500,000. From 1935 the calculations were based on the hypotheses already mentioned: viz. a parabolic decrease in the birth-rate from 1927 to 1955, entailing a total decrease of one-quarter of the initial figure, and a constant birth-rate after 1955. These estimates were then revised in order to take into account the legislative amendments made by the crisis decrees, in particular the extension of the waiting period. The following figures were thus obtained, which are appreciably below the results of the first calculations. 410 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION TABLE IV. ESTIMATED ANNUAL NUMBER OF B E N E F I C I A R I E S (in thousands) I n t h e m i d d l e of t h e year 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1955 1960 1965 1970 1975 1980 Number of invalidity and old-age pensions in payment Number of widows' pensions in p a y m e n t Number of o r p h a n s ' pensions in p a y m e n t 2,481 2,503 2,575 2,642 2,705 2,771 2,836 2,906 2,977 3,040 3,092 3,133 3,178 3,227 3,266 3,298 3,322 3,353 3,491 3,584 3,647 3,693 3,650 3,419 592 610 629 648 666 684 701 718 735 752 769 785 800 815 829 842 855 867 899 885 822 756 707 663 359 355 351 348 344 341 337 334 316 299 281 266 256 246 239 232 EXPERIENCE The annual report of the Reich Insurance Office [22] includes a very complete series of statistical data relating to beneficiaries. In particular there are a general table showing the annual movement in the number of pensions in each category, an analysis of the year's crop of new pensions (age and sex distribution of invalidity and old-age pensions and of widows' pensions; marital status of invalidity and old-age pensioners; distribution of widows according to husband's age at death; age distribution of orphans; distribution of orphans according to age of father—or mother—at death; etc.) an analysis of the cessations of pensions (age distribution for invalidity and old-age pensions and for widows' pensions, average duration of pensions, etc.) and finally an analysis of the pensions in payment at the beginning of the year. Only the principal data are here reproduced relating to the pensions in payment at the beginning of each year, i.e.: 411 GERMAN'S (1) the number of pensioners in each class: TABLE V. —• NUMBER OF B E N E F I C I A R I E S : EXPERIENCE Pensions Current on 1 January in the year 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 . . . . . . . . . . Invalidity and old-age Widows' Orphans" 1,230,347 1,372,174 1,529,070 1,660,652 1,766,881 1,888,717 2,014,418 2,163,538 2,285,712 2,296,920 2,393,566 2,422,088 2,443,954 2,459,201 2,478,950 157,312 187,805 233,401 277,619 334,280 389,329 490,764 640,183 651,732 559.592 580,479 594,854 612,343 630,389 649,935 828,619 779,384 735,884 695,613 649,486 545,411 349,030 350,112 334,754 311,762 294,746 283,651 (2) the sex distribution of the total number of invalidity and old-age pensioners, published from 1930 onwards as percentages, viz: On 1 January 1930 1931 1932 1933 1934 1935 1936 1937 1938 . Males Females Total 64.1 64.8 65.4 65.3 66.5 66.8 67.1 67.3 67.5 35.9 35.3 34.6 34.7 33.5 33.2 32.9 32.7 32.5 100 100 100 100 100 100 100 100 100 (3) the age distribution of invalidity and old-age pensioners and of pensioned widows: co^iocooìcof-t-cDco© . o * © r - - o lísoiocococoeo j o i-* TH o í o í eo »ri t-* o i I H o í i-eoco oKDiDMinoicDiHcoœm . o* o CD o - * eo o i of CD r* »ft 'I o i-* i-I o í o í eo * * i>" o í —* o í i-coco u -o 3, O " ^^CO _OÍO)COeO^- ooc-it-r^coooiftiftcor¿oodi*ciiíí003¿T¡ oioiiHOOOi-ij'coeoiHOocD O'H-J'OOiflWO'fl'OìO OOOi^oiedcDoio»#o' iHOÌOiOi iHoi^HOieooicocDl>»ftco O i - «# I H O CD CO Oi CD CD l > | - O O o " I H o í CO CD OÍ O -** 00 iHOÍOiOi I H I H Oí CO u « 100.00 100.00 100.00 100.00 -rHt-CDCOlftiHOÍCOiHCOO 1 OOOicOiftCCCOOiOO«*^ o * o o " o - ^ o i i d o od co* co 100.00 1-.COCO iHCOO^PCTsCCI^-COCT'CDCi . ©©oiiftoicoo-.-í'-a'-^eo i O O O O I H o i iL« O* C-* CD t ^ i-OÍCO 100.00 «^coocot—cooeocococo . oíoo-^r-oioivpoor-i^-co | o o T . -H oi eo* -* CD" I-" i-* o 0-*eOi-«i-<»flti-»i-iiHoooo . OOiH-*OO-*00iftt^00 1 O O O C5 I H Oi -3* CO CD* »ft* O ^HOi-3" . 1S : : : ; : : : : :. :s o 'J-d¿HiOiftCDCD 0 öooooo.oooooS co+3+J-+-S+J+J+J *a-M+a+J ra C00ift0»ft0»ft0if50»ft0 i-ioitNeoeo**-*ift»ftcDCDt> Total . . . T-COCO •rtOi-* 100.00 ooooor^'fl'cocoi-icor-1-' . OÍ CO »Í3 CO CO Oi »ft i-" O Oi C| o o -ri -ri o í eo **' r-" o i o í co" C>«a*-3 100.00 OÍ o r-* l-í m OÍ i-" CD «•- ¡n ** 1 o i-« i - oí OÍ" co io t-" eo o oí 100.00 100.00 100.00 100.00 100.00 100.00 100.00 (OMiHtûoOt*-C"iOOfO»# . CNCT>t-> I H m o i I H 00 P- O0 if) j © O I M Oí o í CO »ft C-CO CO* Oi -r^OiCO Widows' and widowers' pensions cnoiotûcoodcooforo< era CD i - i n eo i * eo • * oo co 1 O O I H OÍ o í cd »ft 00 ^ CO 0 ¡ -nOiCO (b) Invalidity and old-age pensions T H I N eo ©OÍIHOO-3 CO O o o o o o i - co* co i n »o co 1.1.1929 CU i-< »ft co I H eo »ft »ft co »ft o , o © i i * * i - 1 ^ t - co • * eo ddooTH'cíios'v'cí OOIH'OÏOÎCO-*OÔ-*OOI e o " l > in»«»« i-.OÍ^ O O «*-» ^H o í ed «#" r-» -#* OO* »ft* 1-.O4C0 1.1.1927 0. I»! 1.1.1925 1.1.1926 2 Age group W U ¡25 W ' .©OiHCOOïlOCOiftCOCO o o " o o o " o i CD" - * <¿ o ^-OiiO 100.00 100.00 ^ N T K N O O W C O S Í ' Í O J I H CD Oi CO • * O Oí OS I H OO «* i-^p-äpr-oocoot-oics . 100.00 100.00 -f-i-íPOt-CTicDaooír-eoco -r* ift - n t - Oí OO O • * OO -tf »ft «o o -«-i i-* o» o í * * t-" ed co CD iHOiCO IHOÍCO 100.00 C0C000e0iHifiOl>iHißCO O VPCT)CD Oí t - CS OO OO Ol Oí I O O O I H c i o í CO CD CO 00 OO J i-tOíCO | 100.00 1.1.1937 1.1.1938 OOOiOOCOmOi-^OCOOÎiH | O »3* OO «äf I H CD t— • * Cí t - Ci 1 O O O i-i > )> ÎI !> >) >! 1 5 Under the Act of 24 December 1937 periods of compulsory military service and of labour service and periods of war service are taken into account for pension increments as well as weeks of contributions, provided that the insured person had previously paid at least one contribution to the workers' insurance scheme or to the salaried employees' or miners' schemes. 420 ACTUARIAL T E C H N I Q U E AND FINANCIAL The Order conditions of three periods of the charge ORGANISATION of 1 September 1938 lays down the amounts and the award of the increments due in respect of each of these of service and at the same time it fixes the proportion under this head which is to be borne by the Reich 1. Widows' Pensions An account has been given above of the Reich supplement to widows' pensions and the modifications which it has undergone. From 1 January 1924 to 30 June 1932 the basic sum remained fixed at 6/10 of the basic sum applicable to the invalidity and old-age pension. From 1 July 1932 to 31 December 1933 the ratio between the two basic sums was reduced to 5/10. The basic sum was abolished on 1 January 1934, as from which date the Federal supplement takes its place. From 1 January 1924 to 30 June 1932 the increment remained fixed at 6/10 of the invalidity pension increment which the husband was receiving or which he would have received in the event of becoming invalid; this coefficient was reduced from 6/10 to 5/io as from 1 July 1932. Orphans' Pensions An account has been given above of the Reich supplement to orphans' pensions and the modifications which it has experienced. From 1 January 1924 to 30 June 1932 the basic sum remained fixed at 5/10 of the basic sum applicable to the invalidity and old-age pension. From 1 July 1932 to 31 December 1933 the ratio between the two basic sums was reduced to */10. The basic sum was abolished on 1 January 1934, as from which date the Reich supplement takes its place. From 1 January 1924 to 30 June 1932 the increment remained fixed at 8 / 10 of the invalidity pension increment which the father (or mother) was receiving or which he (or she) would have received 6 in the4 event of becoming invalid; this coefficient was reduced from /10 to /io as from 1 July 1932. MAINTENANCE OF BENEFIT RIGHTS In accordance with the provisions in force in 1924, the right to benefit expired when the stamps appearing on an insurance card two years after the date of issue did not represent at least 20 weekly contributions. Nevertheless, pensions were granted in cases where the period between the date of entry into insurance and the occurrence of the event insured against was covered by contributions actually paid to the extent of at least three-quarters. For the purpose of maintenance of benefit rights the following were counted as weekly contributions in addition to insurance stamps affixed to insurance cards: (1) contributions to the salaried employees' insurance scheme; (2) periods during which the insured person was in receipt of an invalidity pension under the workers', miners', salaried employees' or industrial accident scheme; (3) periods served in the German or allied army during the 19141918 War. 1 See above, pp. 415-417. GERMANY 421 These provisions suffered many amendments. On 1 January 1938 the following regulations came into force. Maintenance of benefit rights is made conditional on the payment each civil year of at least 26 weekly contributions. This condition is not required to be fulfilled for the first year of insurance or in cases where the insured person was invalid in the course of the year. Nevertheless, pensions are granted in cases where the period between the date of entry into insurance and the occurrence of the event insured against is covered by contributions to the extent of at least one-half. For the purpose of maintenance of pension rights the following are reckoned as contributions: weeks of (1) military service; (2) labour service; (3) attendance at a course of industrial training or ideological instruction recognised by the Reich Insurance Office; (4) sickness, and maternity involving incapacity for work; (5) unemployment during which the insured person is in receipt of unemployment benefit or public assistance. PRESERVATION OF RIGHTS IN COURSE OF ACQUISITION IN THE CASE OF TRANSFERS BETWEEN THE WORKERS' INSURANCE SCHEME AND THE SALARIED EMPLOYEES' OR THE MINERS' INSURANCE SCHEME (•Wanderversicherung) The methods by which the three insurance schemes for workers, salaried employees and miners are co-ordinated are rather complex; the present description is confined to the general principles on which the provisions concerning transfers between the workers' and the salaried employees' schemes are based. The establishment and maintenance of pension rights are determined with reference to the total of the contribution periods, including periods assimilated with contribution periods, completed in all the insurance institutions to which the person in question has belonged. For the calculation of the pension, a distinction must be made between the basic pension on the one hand and the increments on the other. Although the qualifying period is roughly the same in both schemes (five years), the basic pension for workers (72 RM. a year) is lower than that for salaried employees (360 RM. a year); each institution must pay the fixed pension component prescribed by its regulations if the contribution periods completed with it are not less than the qualifying period. If this condition is not satisfied, it pays the said fixed component multiplied by a reduction coefficient. The coefficient is obtained from the ratio of the total contribution periods completed with the institution in question to the qualifying period fixed by its regulations. Supplementing these rules is a clause setting a maximum to the fixed pension component that the insured person may receive, which may not exceed the highest such component, namely, 360 RM. a year. When this last clause applies, the amount by which it reduces the result obtained from the application of the general rule is deducted from the liability of the institution where the level of pensions is lowest, namely, the workers' insurance institution. 422 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION The increments to which the insured'person has acquired a right from one of the institutions are.normally paid in full by that institution. When, however, he receives all or part of the basic pension from the ò salaried employees' insurance institution, i.e. — x 360 RM., the increments due from the workers' insurance institution are reduced by á i> sum equal to — X 144 RM. (If the increments due from the latter q scheme do not exceed this figure they are withdrawn altogether.) The application for pension may be submitted to either of the institutions to which the insured person has belonged, and the institution in question must then pay the whole of the pension, being entitled to reimbursement for any component paid on behalf of any other institution 1 . • ESTIMATES OF THE ANNUAL COST OF BENEFITS Investigations Preparatory to the 1933 Reform The average annual amount of pension in the three categories was calculated from an examination of pensions granted before 1 January 1931 and pensions granted after that date. These average amounts multiplied by the number of beneficiaries for each category gave the total emerging costs. The sum of these emerging costs added to the cost of administration gave the estimated total expenditure under the scheme. In order to calculate the average amount of pension, each constituent element was examined in turn. For thé basic sum and Reich supplement recourse was had to the experience of the scheme itself. As regards the increments proportioned to the number and amount of contributions paid, the method adopted was, in the case of invalidity and old-age pensions, to follow out a theoretical " average insurance life", separately for each sex. Increments due to contributions paid before the inflation were calculated and then increments due to those paid after, the inflation. In the case of widows' pensions it was found that, on the basis of the actual experience of the scheme, the number of contributions to be taken into account in calculating increments in respect of a widows' pension could bë obtained from the number of contributions to be taken into account in calculating increments in respect of an invalidity and old-age pension on the assumption that the payment of the latter had taken place five years earlier. This relationship applies to all contributions, whether paid before or after the inflation. It follows, therefore, that in order to obtain the number" of contributions which govern pension increments in these two casés it is sufficient to use the figures obtained for invalidity and old-age ensions and tó make therefrom a deduction equivalent to five years. he calculation of the average amount of orphans' pensions was made in a similar manner to that adopted in the case of invalidity and old-agè pensions. These methods were applied, with variations, to benefit payment's in force in 1931, to the payments reduced by the Emergency Decrees P 1 See below, p. 426. 423 GERMANY and finally to the payments consequent upon the legislation which came into force on 1 January 1934. As in the case of the estimate of the contribution income, account was taken in turn of three hypotheses regarding the progress of economic conditions, namely: (a) the economic conditions prevailing in 1929 would remain unaltered; (b) the rate of unemployment and the.wages level would remain the same as at the beginning of 1933; (c) unemployment would return to the 1929 figures but wages would remain at the 1933 level. In table IX are reproduced the estimates made on each of these three hypotheses for the annual emerging cost of benefits payable by the insurance institutions under the legislation which came into force on 1 January 1934. TABLE IX. TOTAL ANNUAL AMOUNT OF B E N E F I T MADE BY INSTITUTIONS PAYMENTS (estimated in thousands of RM.) Hypothesis 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 (a) (ft) (c) 536,254 897,956 1,050,398 1,169,905 1,265,748 1,333,159 1,377,632 1,416,815 1,425,684 1,352,254 734,065 878,914 949,762 1,060,725 1,082,167 1,067,203 1,017,660 955.710 863,664 718,013 735,055 889,586 1,027,305 1,126,412 1,194,637 1,234,475 1,246,053 1,252,705 1,226,923 1,131,721 EXPERIENCE Average Amount of Monthly Pensions The average amount of current pensions calculated for each calendar quarter is published every year [22]. Figures are reproduced below (table X (a)) for the first quarter of each year -, which show clearly the effect of the increase in pension scales which took place in 1927 and the subsequent reductions in 1932. 424 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The second part of the same table (X (b)) refers to the annual crops of newly awarded pensions, in respect of which the average amounts are appreciably higher. TABLE x (a). AVERAGE MONTHLY AMOUNT OF CURRENT P E N S I O N S : EXPERIENCE (in RM.) Period . Y e a r 1926 F i r s t q u a r t e r 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1 Invalidity and old-age pensions Widows' pensions Orphans' pensions 24.92 25.32 29.34 33.31 35.55 36.25 35.83 30.10 30.15 30.59 30.74 30.79 30.78 14.27 14.26 19.18 21.63 21.03 21.69 10.02 10.20 13.17 14.28 14.95 14.98 . . . . . . . . . . . . i i 18.59 18.85 19.09 19.27 19.32 19.11 11.16 11.08 10.98 10.80 10.53 10.10 Not calculated. TABLE X (¿>). AVERAGE MONTHLY AMOUNT OF N E W L Y PENSIONS: EXPERIENCE AWARDED (in RM.) Invalidity and old-age pensions 1930 1931 1932 1933 1934 1935 1936 (whole y e a r ) 1937 » i Not calculated. . . . . . ' Males IFemales Total 45.88 47.25 47.76 40.17 38.16 37.38 37.98 37.57 28.29 28.83 29.32 22.56 19.63 19.66 19.96 19.48 40.60 42.03 42.99 35.52 32.53 32.08 32.31 i Widows' Orphans' pensions pensions 20.37 22.42 24.70 20.54 19.35 19.55 19.86 18.31 . . . 16.68 17.10 16.74 12.04 10.31 10.59 10.62 10.09 . . . . . . . . . . . Total Amount paid each Year for each Class of Pension The total annual cost of invalidity and old-age, widows' and orphans' pensions, including State aid, is shown in table XI, which demonstrates the results of the increase in pension scales in 1926 and 1927 and also the effect of the general reductions applied in 1932. 425 GERMANY TABLE X I . — TOTAL AMOUNT OF PENSIONS PAID EACH Y E A R : E X P E R I E N C E (in thousands of RM.) Year 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 . . . . . . Invalidity and old-age pensions Widows' pensions Orphans' pensions Total 245,748 404,484 533,158 617,107 753,331 863,632 973,052 1,043,277 938,153 879,503 905,626 922,730 929,573 933,592 20,323 33,817 48,248 67,998 97,727 121,627 171,104 183,500 141,788 130,759 136,109 141,787 146,566 151,457 81,697 109,331 128,542 118,073 131,428 131,539 127,125 117,429 58,502 48,214 47,429 44,435 40,940 38,284 347,768 547,632 709,948 803,178 982,486 1,116,798 1,271,281 1,344,206 1,138,443 1,058,476 1,089,164 1,108,952 1,117,079 1,123,333 § 5. — Other Expenditure ADMINISTRATION EXPENSES To the administration expenses of the insurance institutions themselves and of the Reich Insurance Office must be added the payments made to the Post Office for services rendered in the sale of social insurance stamps and the payment of benefits. In the investigations preparatory to the 1933 reform [20] the total cost of administration was estimated at the constant figure of 70 million RM. . The actual cost of administration is given below in thousands of RM. Year 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 Payments to the Post Office i Total cost 6,471 14,134 13,233 12,130 13,630 15,227 15,260 15,853 24,171 32,974 37,599 43,413 52,203 55,029 61,884 65,116 57,266 53,802 58,553 61,237 61,349 62,601 . . i Before 1930 these p a y m e n t s were made b y t h e Reich. 426 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION COST OF OPTIONAL MEDICAL BENEFITS In the course of t h e investigations preparatory t o the 1933 reform, it was necessary t o estimate t h e cost of optional medical benefits in ¡order t o include it i n t h e actuarial balance-sheets. The figures recorded for 1931 and 1932 were t h o u g h t to be on t h e low side and the probable ¡expenditure under this head was assumed t o remain constant at 50 million RM. per annum. The t o t a l sum applied to medical benefit is settled each year by agreement between the insurance institutions; it amounted to the following figures in thousands of. RM. : 1924 1925 1926 1927 1928 1929 1930 . . . . . . 23,336 41,287 50,496 60,106 78,188 97,622 99,315 1931 1932 1933 1934 1935 1936 1937 69,018 40,969 35,139 40,436 46,313 47,438 53,452 C O N T R I B U T I O N S TO THE M I N E R S ' INSURANCE SCHEME As from 1938, under t h e Act of 21 December 1937, the workers' insurance scheme h a s to p a y to the miners' scheme an annual contribution of 50 million RM. R E P A Y M E N T S TO THE SALARIED E M P L O Y E E S ' INSURANCE S C H E M E I t has been seen above t h a t , under t h e provisions made to preserve the benefit rights of insured persons who transfer from the workers' t o t h e salaried employees' scheme or vice versa, each insurance scheme repays t o the other t h e benefit components paid on its account. Since transfers from t h e workers' to the salaried employees' scheme are much more numerous than transfers in the other direction the balance of repayments is always to the benefit of the salaried employees' scheme. The following amounts, in thousands of RM., were credited to the salaried employees' scheme and debited to the workers' scheme: 1926 1927 1928 . . . : . . 1929 1930 1931 325 9,774 9,356 12,728 21,024 26,247 1932 1933 . . . . . . 1934 1935 1936 1937 25,150 unknown 28,980 30,120 31,036 31,922 CHAPTER III FINANCIAL SYSTEM § 1. — Tables of Annual Estimates ESTIMATES OF RECEIPTS AND EXPENDITURE FROM 1927 TO 1931 [17] On the basis of the provisions of the Act of 28 July 1925, and making allowance for the amendments made by the Acts of 25 June and 10 December 1926, a series of annual estimates was drawn up for five consecutive years, showing the probable financial progress of the insurance scheme during a quinquennium. TABLE XII. — PROBABLE FINANCIAL PROGRESS FROM 1927 TO 1 9 3 1 (in millions of RM.) a *C ao O •4-i CQ CD a "to "ai "53 C3 4 5 5 6 7 11 11 11 11 11 tfl CD o -*> a» a •a Surplus (+) deflclency (—) 3 to Ö O Repayment of benefit components to salaried employees' scheme Repayments to Reich in respect of payments for revalorisation of increments +j m SS O Optional medical beneflts and cost of administration Year a o Expenditure Invalidity and old-age pensions Receipts 679 + 29 0.6 737 — 18 800 — 74 4 867 — 134 11 939 — 199 23 On account of the improvement in employment and the increase in wages the contribution income for 1927 was estimated to be 5 per cent. in excess of that for 1926; the figure for each subsequent year being obtained from the preceding year by adding 1 per cent. The expected interest income was estimated on the basis of the experience of the year 1925, having regard to the amount and probable yield of the invested funds. Other items of income, consisting of fines and various miscellaneous credits, were estimated on the basis of the corresponding amounts received in 1925. 428 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The estimated expenditure on invalidity, widows' and orphans' pensions was calculated on the basis of the actual experience of the period 1 October 1925 to 30 September 1926, during which the Act of 28 July 1925 was in force. Adjustments were made to allow for the amendments introduced by the Acts of 25 June and 10 December 1926. The cost of the optional benefits and administration expenses were estimated at 15 per cent, of the contribution income, this fraction being adopted after a consideration of the actual fractions 13.1 per cent. and 13.5 per cent, which were obtained in 1924 and 1925. Miscellaneous expenditure included, in addition to interest due on the deficit at the rate of 7 per cent, (as from 1928), the repayment of pension increments to the salaried employees' scheme and the repayments to the Reich which it was thought could be charged to the insurance institutions in respect of the expenditure incurred by the Reich for the revalorisation of the increments. Table XII led to the conclusion that contributions should be increased by 11 to 12 per cent, in order to guarantee the equality of receipts and expenditure in the period 1927-1931. It was observed also that a stationary condition had not been arrived at, that is to say, that the scheme was still in the period where the number of pensions in force was increasing year by year. ESTIMATE OF RECEIPTS AND EXPENDITURE FROM 1929 TO 1938 [18] The estimates analysed above very quickly became out of date in consequence principally of the Act of 8 April 1927, which increased the contributions and improved the benefits, and also as a result of the Act of 29 March 1928. A new table of annual estimates was constructed for the period 1929-1938 giving effect to the provisions of these two Acts. The contribution income, which had risen to 875.2 million RM. in 1927 and to 1,080 million RM. in 1928, was estimated to be 1,140 million RM. in 1929, taking into account the introduction of a new wage class as from 1 January 1928. The figure adopted for 1929 was maintained for each of the subsequent years. The sums received as interest increase or decrease according as surpluses or deficiencies augment or diminish the fund. Other items of receipts include the grant of 40 million RM. obtained out of the Customs revenue under the Act of 7 August 1925, until 31 March 1935 (consequently only 10 million RM. for the year 1935), and an annual amount of 10 million RM. in respect of appreciation, miscellaneous profits and receipts. In order to obtain a figure for the emerging costs of benefits, the estimated numbers of pensions in force (according to the figures obtained in the course of calculations made for the first table of annual estimates * were multiplied by the average amounts of benefit. For the invalidity and old-age and widows' and widowers' pensions the' emerging cost increases rapidly because both the nunúor of beneficiaries and the average amount of pension increase at the same time. It was assumed that the number of beneficiaries of orphans' pensions would remain practically stationary. For, the cost of administration expenses the estimate 1 See above, p. 408. 429 GERMANY showed an increase every second year in order to give effect to the expected increase in the number of beneficiaries. Finally, table XIII was constructed, which shows the probable financial progress of the insurance scheme. TABLE XIII. PROBABLE FINANCIAL PROGRESS FROM 1 9 2 9 TO 1 9 3 8 (in millions of RM.) Receipts Expenditure Con- Inter- Mistribu- est cella- Total neous tions Op- Cost of Bene- tional admi- Total fits medical nistrabenefits tion 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 Surplus (+) Year i 2 3 4 5 6 7 8 9 . . . . . . . . . . 1,140 1,140 1,140 1,140 1,140 1,140 1,140 1,140 1,140 1,140 45 55 60 65 70 70 70 65 60 50 50 50 50 50 50 50 20 10 10 10 1,235 1,245 1,250 1,255 1,260 1,260 1.230 1,215 1,210 1,200 740 810 885 960 1,035 1,110 1,185 1,260 1,340 1,420 85 90 90 90 90 90 90 90 90 90 55 55 60 60 65 65 70 70 75 75 880 • 955 1,035 1,110 1,190 1,265 1,345 1,420 1,505 1,585 or deficiency (—) 10 + + + + + — — — — — 355 290 215 145 70 5 115 205 295 385 § 2 . — Annual Results of the Operation of the Scheme The summary of the annual Profit and Loss Accounts reproduced in table XIV sets forth the actual progress of the finances of the insurance scheme, that is to say, the actual figures for the principal items of receipt, exclusive of State aid, and expenditure and consequently the increase or decrease of the accumulated funds. Part I of this monograph x contained an analysis of the system by which the cost of benefits was divided since 1900 among the different insurance institutions. This system was abolished by an Act of 23 June 1921 and since that Act came into operation the whole cost of benefits (after deduction of the State aid) has been divided by the Reich Insurance Office between the insurance institutions in proportion to the contributions collected by each during the financial year in question. 1 See p p . 387-388. 430 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XIV. — FINANCIAL PROGRESS: EXPERIENCE (in millions of RM) Expenditure Receipts Surplus Year 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 MiscellContributions Interest aneous Total Pensions 375.9 252.2 5.8 7.5 362.6 4.9 568.2. 386.1 550.0 13.3 775.5 525.0 659.6 19.9 96.0 875.2 29.6 95.7 1,000.5 601.8 1,075.9 54'.7 71.2 1,201.8 671.7 1,092.1 78.2 65.1 1,235.4 769.9 986.4 87.8 51.5 1,125.7 905.8 924.1 969.9 819.2 88.8 16.1 725.7 794.2 642.1 70.8 12.8 744.6 690.1 8.2 678.6 57.8 843.8 60.5 57.0 ! 961.3 674.4 945.4 66.0 8 35.9 1! 1,047.3 705.6 1,044.0 98.3 s 71.7 1,214.0 712.2 1,160.4 103.2 15.1 1,278.7 718.3 Op- Cost of tional admi- Miscellmedical nistra- aneous benefits tion 23.3 41.3 50.5 60.1 78.2 97.6 99.3 69.0 41.0 35.1 40.4 46.3 47.4 53.5 24.2 33.0 37.6 43.4 52.2 55.0 61.9 65.1 57.3 53.8 58.6 61.2 61.3 62.6 (+) Total or deficiency ' (—) 300.2 + 75.7 0.5 465.8 +' 101.4 5.4 617.9 + 157.6 4.8 707.3 + 293.2 2.0 805.9 + 395.9 i 3.8 930.9 + 304.5 8.4 4.1 1,071.1 + 54.6 5.5 1,109.5 — 185.4 910.4 — 184.7 17.9 782.1 — 37.5 3.1 776.1 + 185.2 2.7 1.8 2 814.9 + 232.4 885.3 + 328.7 64.4 837.3 + 441.4 2.9 2 i Under this heading are included the payments from the unemployment insurance scheme to maintain the benefit rights of unemployed persons, viz. a total of 52.9 in 1934, 18.0 in 1935, 15.2 in 1936 and 10.4 in 1937 (in-millions of RM.). s In these figures are included depreciation of the assets as a result of the revaluation of properties and furniture and fittings (50.9 million RM. in 1936; 0.7 million RM. in 1937). s Including sums received from unemployment insurance to compensate the loss of interest' due to the postponement of the transfer to the workers' insurance scheme of part of the unemployment insurance contribution (25 million RM. In 1936; 13 million RM. in 1937). § 3. — Actuarial Balance-Sheets The essential purpose of the investigations preparatory to the 1933 reform, to which reference has already been frequently made, was the construction of an actuarial balance-sheet. With a view to justifying the reform, which was then only in the form of draft proposals, it was found necessary to construct several balance-sheets. The first referred to the operation of the scheme under the legislation in force in 1931, the second took account of the restrictions imposed by the emergency decrees and, finally, the third dealt with the scheme as amended by the provisions of t h e 1933 Bill, as they were applied as from 1 January 1934. Only the third balance-sheet, which relates to 1 January 1933J will be considered here. This includes in fact three investigations ofthe financial position, corresponding with the three hypotheses, already mentioned above, regarding the future permanent state of the economic situation. 431 GERMANY Under hypothesis (a), which takes the optimistic view, the rate of Unemployment and the wages level experienced in 1929 were taken as the standard, that is to say, a period of prosperity was assumed: Under hypothesis (6), which takes the pessimistic view, recourse is had to figures relating to the beginning of 1933, that is to say, to a period of economic crisis. Hypothesis (e), a compromise between these extremes, is based on the 1929 unemployment rate, as in hypothesis (a), and the 1933 wages level—as in hypothesis (b). Moreover, under each hypothesis, calculations have in turn been made at two rates ,of interest: 4 and 5 per cent. Table XV sets forth the results obtained under each of the three hypotheses and at the two rates of interest. TABLE XV. BALANCE-SHEET AS AT 1 JANUARY 1 9 3 3 (Interest at 5 and 4,per cent.) LIABILITIES ASSETS Hypoth esis (a) I. Contributions ¿ . . II. Reich supplements . III. Reich subsidies . . IV. Thousand million RM. 5% 4% 24.4 29.8 5.7 7.2 4,0 5.0 1.2 1.2 Total . . . 35.3 0.6 I. Contributions . . . II. Reich supplements . III. Reich subsidies : . 13.4 '5.7 4.0 1.2 16.5 7.2 5.0 1.2 . Total . . . Deficit . . . . . . 24.3 7.7 29.9 10.1 Contributions . . . Reich supplements . Reich subsidies . . Reserves 20.2 5.7 4.0 1.2 Deficit 43.2 2.7 Thousand million RM. 5% 4%. I. Invalidity and oldage pensions . . . Widows' pensions . Orphans' pensions . Other pensions i .ex-. Administrative penses and cost oí voluntary insurance Total . . . II. III. IV. V. 27.1 3.9 1.1 1.4 34.7 5.0 1.4 1.8 2.4 35.9 3.4 45.9 23.9 3.5 0.9 1.3 29.7 4.4 1.2 1.7 2.4 32.0 3.0 40.O 25.9 3.8 1.0 1.4 32.8 4.7 1.3 1.8 2.4 3.0 34.5 43.6 Hypoth esis (b) ?v. i 1 I. Invalidity and oldage pensions . . . II. Widows' pensions . I I I . Orphans' pensions . IV. Other pensions i . . V. Administrative expenses and cost of voluntary insurance Total . . . Hypoth esis (c) I. II. III. IV. Total . . . Deficit 31.1 3.4 24.8 7.2 5.0 1.2 38.2 5.4 I. Invalidity and oldage pensions . . II. Widows' pensions . I I I . Orphans' pensions . IV. Other pensions i . . V. Administrative expenses and cost of voluntary insurance Total . . . i This item includes the fractions of pensions paid in arrears, payments in respect of migrants and payments to insured persons in the Saar Territory. 432 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION These estimates led to the following conclusions. If the cost of benefits borne by the insurance institutions were covered each year by the contribution income (assessment system) the ratio of the total contribution to the upper wage limit of each class, which was 5 per cent, in 1933, should be gradually increased until it reached: Under hypothesis (a) Under hypothesis (b) Under hypothesis (c) 5.1 in 1950, 7.5 in 1975 when the emerging cost of benefits would be at its maximum. 8.6 in 1950, 8.8 in 1955, when the emerging cost of benefits would be at its maximum. 6.0 in 1950, 7.5 in 1970, when the emerging cost of benefits would be at its maximum. If, on the other hand, it is assumed that as from the date of the balance-sheet all insured persons are subject to the payment of a general average premium, this should be determined as follows (as a percentage of the upper limit in each wage class), according to the hypothesis and rate of interest: Hypothesis (a) (b) (c) Rate of interest 4 per cent. 5 per cent. 5.45 8.06 6.09 5.12 7.87 5.84 § 4. — Consolidation of the Financial Position (Act of 21 December 1937) On the basis of the conclusions drawn from the actuarial balancesheets constructed as at 1 January 1933, and taking into account the uncertainty regarding the possibility of obtaining an interest yield of 4 per cent, and the fact that the new Act did not come into force until one year after the date of the balance-sheet, and finally making provision for a safety margin, the investigations preparatory to the 1933 Act allow for a rate of contribution permanently fixed at 6.5 per cent, of the upper limit of each wage class. The immediate adoption of this rate would, on the most probable estimates, obviate the necessity for any later increase in the contributions and would enable financial stability to be maintained on the basis not of an assessment system, as was the case from 1924 onwards, but of an accumulation system with general average premiums. The explanatory statement which preceded the Act lays down that the necessary increase in contributions shall take place only when the cost of unemployment insurance shall have decreased by an equivalent amount. Consequently, the reform undertaken in 1933 could not be carried out before it became possible, in consequence of an improvement in the position of the unemployment insurance scheme, to obtain from the financial resources of thè latter scheme contributions for the benefit of the workers' insurance scheme. In 1937 this condition was found GERMANY 433 to be satisfied: the number of unemployed persons was greatly reduced and, on the other hand, the resources of the unemployment insurance scheme, which continued to receive 6.5 per cent, of wages, had increased with the number of contributors and the level of wages. The time had thus arrived for redistributing in a different manner the resources of the various insurance schemes. However, the allocation of the total deduction made from employees' wages among the different insurance schemes was not altered; but it was laid down that the resources which were available in the unemployment insurance scheme should be used to make grants to the other schemes, and in particular to the workers' insurance scheme. Apart from minor amendments—already mentioned above—relating to the Reich subsidies, the extension of the waiting period and the introduction of a new wage class, the Act of 21 December 1937 includes the two following clauses, which were essential for the consolidation of the financial position. GRANTS FROM THK UNEMPLOYMENT INSURANCE SCHEME 1 The unemployment insurance scheme must each year transfer to the workers' insurance scheme an amount equal to 18 per cent, of the total contributions received.by the latter. It has been estimated [46] that this will produce a supplementary income of the order of 190 millions, equivalent to an increase in the rate of contributions of 0.9 per cent. of the upper limit of each wage class. SUPPLEMENTARY PAYMENTS MADE BY THE REICH GOVERNMENT It has already been mentioned that the supplementary income required to establish financial solvency on the basis of an accumulation system with general average premiums was estimated to correspond to an increase in the rate of contributions of 1.5 per cent, of the upper limit of each wage class. Since the transfer from the unemployment insurance scheme is equivalent to only 0.9 per cent., there had still to be found an item of income corresponding to about 0.6 per cent. of wages 2. The liabilities thus remaining uncovered were made chargeable to the Reich, which must pay the interest on the amount concerned and eventually undertake its gradual redemption, in accordance with regulations to be made by the Minister of Labour in agreement with the Minister of Finance. 1 These grants have been referred to in Chapter II, § 3, under the heading of 2" Other Receipts ", p. 417. In addition, the workers' insurance scheme is compelled to make to the miners' insurance scheme an annual grant of 50 million RM. (see p. 426) which decreases the grant which it receives from the unemployment insurance scheme and increases pro tanto the burden falling on the Reich. 28 CHAPTER IV FINANCIAL ADMINISTRATION § 1. — Investment of Funds. — Statutory Provisions and Regulations The Social Insurance Code lays down first that the fund shall be invested at interest and as far as possible in such a way as to maintain a stable value. It then gives a restrictive list of the authorised classes of investment for social insurance funds, with the proviso that the Minister of Labour may authorise other investments, subject to revocation. Certain investments are placed under special regulations to which reference will be made as and when they occur in the course of the list given below. AUTHORISED CLASSES OF INVESTMENT. — PROVISIONS PECULIAR TO CERTAIN CLASSES (1) Bonds issued by the Reich or a State or by a Reich or State credit institution, and loans entered in the public debt register of the Reich or of a State. The Reich Government fixes the amount up to which this class must be included among the investments. This amount may not be fixed at such a figure that it exceeds one-quarter of the total fund: in fact this maximum proportion was the figure adopted in 1923. Until this proportion is attained the insurance institution must each year invest in this class an amount equal to at least 10 per cent, of the increase in the value of its fund. As from 1 January 1938, under the Order of 14 April 1938-1, the securities which must compulsorily appear among the investments of insurance institutions include only bonds issued by the Reich and loans entered in the public debt register of the Reich. Until these securities account for at least one-half of the fund, there must be allocated to them each year at least three-quarters of the increase in the value of the fund. • (2) Bonds, the interest on which is guaranteed by the Reich or a State or by a Reich or State credit institution. (3) Loans, the security for which is a safe mortgage on a parcel of land in Germany; safe trusts on real estate or annuity bonds on parcels of land in Germany. 1 See ReichsGesetzblatt I, No. 58, 21 April 1938, or Industrial and Labour Information, Vol. LXVI, No. 13, 27 June 1938. GERMANY 435 The legislative text makes the following provisions: (i) a mortgage, a trust on real estate, or an annuity bond may be deemed to be safe if the loan does not exceed two-thirds of the value of the parcel of land; (ii) as a rule the loan must be made on a first mortgage; (iii) the value of the parcel of land assumed for the purpose of the loan shall not exceed the ordinary value ascertained by careful investigation; in determining this value there shall be taken into account only the permanent qualities of the parcel of land and the income which it can yield permanently to any owner under suitable administration; (iv) loans shall not be made on building plots or on new buildings which are not completed and not yet capable of yielding income, nor. on parcels of lands which are not capable of yielding a permanent income, such as pits, quarries and mines,; the Minister of Labour may authorise exceptions in particular cases. (4) Securities, especially mortgage deeds, and bonds of all kinds issued by German public bodies or by credit institutions belonging to such bodies, provided that the said securities or bonds have been approved by the Government as suitable for the investment of trust funds. (5) Securities by the State laws (appropriate to the institution to which the fund belongs) for the investment of trust funds. (6) Bearer mortgage deeds issued by the German mortgage banks, on which the Reichsbank makes loans in class I. These mortgage deeds are specified each year by the Reichsbank. (7) In bonds on securities or mortgages in which investment is permitted under Nos. (1) to (5) above in accordance with the rules of the Reich Loan Fund or the Reichsbank. (8) Deposits in a public savings bank which is declared by the competent authority of the State in which its head office is situated to be suitable for the investment of trust funds. (9) Deposits in the Reichsbank, a State bank or any other German bank declared by law to be suitable for the purpose. (10) Bonds of German public bodies, and of school districts and ecclesiastical parishes, provided that these bonds can be called in by the creditor or that provision is made for their regular amortisation. (11) Bonds for which a public body covered by No. (4) above or a credit institution belonging to such a body, or a public savings' bank of the kind mentioned under No. (8), or a bank mentioned under No. (9), is security on its own account. . (12) Short-term loans under bond for which sufficient security is given. Investments in the last two classes must be approved by the Reich Insurance Office. The Reich Minister of Labour may make general regulations concerning these investments and in particular may fix a maximum amount for their total aggregate. Available funds may also be used to purchase land in Germany, in loans for public utility purposes or in shares in undertakings for such purposes. Public utility undertakings are deemed to include cooperative societies and their federations, the operations of which 436 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION according to their rules are carried on exclusively or mainly for the benefit of persons insured under the invalidity insurance and the salaried employees1 insurance schemes. Purchase of land at a price higher than that fixed by the Minister of Labour and the construction of buildings at a cost in excess of that fixed by the Minister of Labour require special approval. § 2. — Statistics of Investments • COMPOSITION OF THE FUND Every year a detailed description of the fund is published [22]: the analysis given below shows the amounts in each of the principal classes of investment as at 31 December 1937. COMPOSITION OF THE FUND AS AT 3 1 DECEMBER 1 9 3 7 * (in thousands of RM.) Cash in hand (including balances at the bank and in post office cheque accounts) . . . Securities (at purchase price): I. Public loans: To the Reich / To States To communes and provinces . . . . II. Other securities: Loans to a Reich or State credit instiMortgage deeds Communal mortgage bank bonds . . Other miscellaneous securities . . . Loans (amounts actually advanced) : I. Secured loans: To the States To provinces and communes . . . . To other public bodies To public utility undertakings or cooperative societies for building houses To private persons . II. Mortgages, loans and annuity bonds on real estate: Mortgages on Land for working-class dwellings . Miscellaneous real estate III. Balances in savings banks. IV. Shares in public utility undertakings, 170,438 841,358 82,698 42,263 98,630 636 268,842 84,205 79,523 27,088 103,854 60,278 7,032 8,149 1,236 4,536 284,761 46,575 82,940 5,770 5,346 Real estate (hnnlc vaìiieì F urnit Total 1,498,155 637,565 123,899 14,210 2,444,267 i At the same date the debts of the insurance institutions, amounting to 4,957 thousand RM., reduced the total value of the fund to 2,439,310 thousand RM. •<* CD S H n ET" CO CO cO cO CO cO CO CO CO CO cO CO cO cO CO COCOCOCOCOCOCOCOCOfcOfcOtOtOtOtO 00v4O)Cnrf>05b0HkOc000vjaJCnrf> CD (O CO CO CO CO cO *£> 00 bu bO bS bp tO bO ooaivjoiOT^ cO cO CO cO co CO cO COCOCOCOGOCOCO oovjoicntí>oobO M. S <î CD c+ CD e. e » e. GG vJCnvj^co^^h^- H* • h * i-kh*b0bï>b0h* vjvJO(ÛO00CJt0tn^CJJO O O k*> * » ^ n W b S oonOif'Ovjo O as.i-* rf>bocoo (-* 2 *ä a vj as 00 ** o «o to CO ••* 00 bO cOrf>bO>-*oooo OOOi>cnOtnb5 "*h2 V "*•* V l "tO "Ln"co" asCnrf>C0tObSC0COG0b0fcOtOl-*^>-* ^ C J t w o i, w r f >, H A ^ o v o a ï H * t o c o * * W O I O O ) J H * J V J V J C O V J O I ^ ^ W ©CObOCOCOOOfcO ©rf>cototoasrf> O a Cr CD i-te O «û Î Û (D ( ¿ ( û t û CD K^ W W CO W W W W rt> vjff>Ol*rWK»^ g tri o 3 B CM N-i. a CD a <¡ M te "ä bOWCO^Cncn#*ti^rf>tC^COCOCOCOCO oiomoo^oiüiwrf>tnwi>w^ ^osooobsoooobacn^oocouivj Ö *1 tí a o 5 k* to H* >-^ k* H* 1-^ >-* t-^ H* H» bS CO hP> t>J C n g s O t O ^ i t - M O O O W C O C O r A O ^ O tO Cn 4> bS O Or 00 cO «-J t n tir* co CO co * aitTiOiaiOicTivj c o ^ o o w t o ^ víMW'^WtDNX as " ^ b i © ^ "vj "co OCnobOGococo boboooooooooco COrf>i-* ¡OO* CD O ^Tsolobr^ © © ooocoti^oococo ocooco^icovj >-*H*H*bSb5tOb0 i C « O O ^ C O Ü 1 1s5 *co "as " ^ "tf^ a* "vj O^CnO^bObS ooobObocoaïcn a 00 O l O) Ü1 V I O) OO o £+ ">-*"cnVo>'üi"cn'o í d e 05 c» h» * * *> oo v j g » t a hs t s *•• >-» ^ en P E o o CD » •-S er o o o o o o o o o o o o o o © © o o o o o o o o o o o o o o o o o o o o o o o o o o o o o V"to*cOb5vjocnbo rf^jo co #"•_<» o co "co "to "rf> "to "Î* i o "*o oasastí>oo>-^bo OOb5oocoh^to 438 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION INTEREST YIELD The following figures show year by year the rate of interest yielded in total by the invested funds: Year 1927 1928 1929 1930 1931 1932 Rate per cent. 4.2 5.5 5.9 5.8 6.1 5.4 Year Rate per cent. 1933 . . . . . . . 4.9 1934 4.8 1935 4.4 1936 4.2 1937 4.2 § 3. — Statistics. — Actuarial and Financial Control STATISTICS The insurance institutions draw up statistical schedules relating to their experience and send them each year to the Reich Insurance Office, in accordance with instructions sent to them. This central,Office collates the statistics and publishes each year in its report [22] data referring to the preceding financial year. 3 Apart from these statistics drawn up periodically, special enquiries are occasionally made. This study will be confined to a brief summary } of the methods used since 1934 by the territorial institutions and by the special schemes for determining the total insured population and its age distribution 2. In the territorial institutions the collection of Contributions is made by means of stamps affixed to insurance cards supplied to insured persons. Each of these cards, on which 52 stamps may be fixed, must be exchanged within two years of the date of issue. To keep an account of all the cards returned to the institutions after exchange would have entailed lengthy and costly administrative operations which, moreover, would not have provided very accurate data, since no account could be taken of (i) insured persons who left the insurance scheme since the date of exchange of cards and before the date of the enquiry and (ii) insured persons who had not yet exchanged the card given to them on their entry into insurance. It seemed preferable, therefore, to adopt an indirect method based on the following principle: Each institution submits a return of the number of contributionstamps sold in its district during the specified, period of observation. This number, which is known to be exact within a relatively small margin of error, is taken to be the same as that of the stamps affixed to the cards during the same period; From an analysis of a sample of about one-third of the cards returned to the institutions the mean 1 For a more detailed study of this, see the original document [21] or an analysis of it which appeared in the International Labour Review, Vol. XXXII, No.2 4, October 1935 [44]. The first results of these enquiries, published in 1935, are referred to and reproduced in part in Chapter I, § 2, p. 407. GERMANY 439 number of weekly contributions per insured person during the period of observation is calculated. The number, of insured persons is obtained by dividing the figure representing the total of weekly stamps by the calculated average number of weekly contributions per insured person. The insured population obtained in this manner cannot be related to a fixed date but only to the whole of the period of observation, which in the early investigations was limited to the year 1933. The number calculated by this method may also be defined as the probable .number of insured persons who purchased the contribution-stamps sold in the district covered by the territorial institution, on the assumption that each person buys a number of stamps equal to the average number of weekly contributions calculated per insured person. The special institutions usually issue a perforated card in the name of each of their insured members. Consequently the number of insured persons and their distribution by sex and year of birth have been ascertained directly; each institution had only to compute the perforated cards made out. ACTUARIAL AND FINANCIAL CONTROL Workers' insurance institutions are placed under the control of the Reich Insurance Office. The latter may at any time inspect the accounts of any one of the institutions. The institutions must produce to the Office on demand all books, vouchers, documents, records and certificates in their custody, and in general give all information required for the purpose of exercising control. The draft of the annual budget must be submitted to the central Office at least two weeks before the date of its coming into operation. The Office may make amendments to this draft when it is inconsistent with statutory provisions or when it is likely to threaten the solvency of the institution. In addition, in order to exercise control over the financial progress and in particular to verify that the scale of contributions is fixed at its appropriate level, the Minister of Labour must have an actuarial balance-sheet drawn up every four years; the first of these balancesheets relates to 31 December 1936. BIBLIOGRAPHY 1. 2. 3. 4. 5. 6. I. — Legislative Texts Notification of the new text of the Federal Insurance Code. Dated 15 December 1924. — Legislative Series, 1924, Ger. 10. Act to amend the calculation of pensions under the invalidity insurance system. Dated 23 March 1924. — Legislative Series, 1925, Ger. 4. Act respecting the development of the salaried employees' and invalidity insurance systems and respecting health measures under the Reich insurance system. Dated 28 July 1925. — Legislative Series, 1935, Ger. 6. Act to amend the Reich Insurance Code and the Salaried Employees' Insurance Act. Dated 25 June 1926. — Legislative Series, 1926, Ger. 4. Act respecting benefits and contributions under the invalidity insurance system. Dated 8 April 1927. — Legislative Series, 1927, Ger. 3. Act respecting benefits under the invalidity and salaried employees' insurance systems. Dated 29 March 1928. — Legislative Series, 1928, Ger. 3. 440 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION 7. Act respecting benefits under the invalidity insurance system. Dated 12 July 1929. — Legislative Series, 1929, Ger. 4. 8. Fourth Order of the President of the Reich to make provision for ensuring economic and financial stability and the maintenance of internal order. Dated 8 December 1931. — Legislative Series, 1931, Ger. 9. 9. Order of the President of the Reich respecting measures for the maintenance of unemployment relief and social insurance and for the lightening of the burden of public welfare expenses of the communes. Dated 14 June 1932. — Legislative Series, 1932, Ger. 4. 10. Order to supplement public benefits. Dated 19 October 1932. — Legislative Series, 1932, Ger. 9. 11. Act to maintain the solvency of the invalidity insurance, salaried employees' insurance and miners' insurance systems. Dated 7 December 1933. — Legislative Series, 1933, Ger. 12. 12. Order respecting the amendment, re-issue and administration of certain provisions of the Reich Insurance Code, the Salaried Employees' Insurance Act and the Federal Miners' Benefit Societies Act. Dated 17 May 1934. — Legislative Series, 1934, Ger. 9. 13. Act respecting the development of the social insurance system. Dated 5 July 1934. — Legislative Series, 1936, Ger. 10. 14. Verordnungen (1 bis IS) zum Aufbau der Sozialversicherung (see source quoted below under 47). 15. Ninth Order for the development of the social insurance system. Dated 6 August 1935. — Legislative Series, 1935, Ger. 9 (D). 16. " Gesetz über den Ausbau der Rentenversicherung vom 21. Dezember 1937." Amtliche Nachrichten für Reichsversicherung, 1937, No. 12. II. — Parliamentary and Administrative Documents 17. 18. 19. 20. 21. 22. " Eine versicherungstechnische Bilanz behufs Nachprüfung der Beiträge zur Invalidenversicherung." Amtliche Nachrichten des Reichsversicherungsamts, 1927, No. 4. " Denkschrift über Leistungen und Beiträge in der Invaliden- und Angestelltenversicherung." Drucksachen des Reichstags, IV. Wahlperiode, No. 741, 1928. " Gesetz zur Erhaltung der Leistungsfähigkeit der Invaliden-, der Angestellten- und der knappschaftlichen Versicherung vom 7. Dezember 1933. Begründung." Anlage zum Reichsarbeitsblatt, 1933, No. 36, Partie IV. " Versicherungsmathematische Denkschrift für die finanzielle Lage und künftige Entwicklung der Invalidenversicherung und die geldlichen Auswirkungen des Gesetzes." Anlage zum Reichsarbeitsblatt, 1933, No. 36, Partie IV. " Die Versicherten der Invalidenversicherung, Anzahl, Geschlechts- und Altersgliederung." Amtliche Nachrichten für Reichsversicherung, 1935, No. 4. " Jahresbericht des Reichsversicherungsamts." Amtliche Nachrichten des Reichsversicherungsamts, 1924-1927; Amtliche Nachrichten für Reichsversicherung, 1928 and following years. III. — Articles 23. 24. 25. DOBBERNACK: " Der finanzielle Stand der deutschen Sozialversicherung vor und nach dem Weltkriege." Zeitschrift für die gesamte Versicherungswissenschaft, Band 28, 1928, p. 58. AURIN : " Wandlungen in der sozialen Rentenversicherung." Zeitschrift für die gesamte Versicherungstvissenschajt, Band 28, 1928, p. 233. HEINZE: " D i e schwierige Lage der Invalidenversicherung und ihre Gründe." Die Reichsversicherung, 1931, p. 4. GERMANY 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 441 DOBBERNACK und SATJERBORN: " Entwicklung und Stand der deutschen Sozialversicherung," Die Reichsversicherung, 1932, p. 33. FROMMHOLD: " D e r Leidensweg der Invalidenversicherung." Deutsche Invalidenversicherung, 1932, p. 116. ——: " Ein Rückblick und ein Ausblick, Aufbau oder Umbruch der Sozialversicherung." Deutsche Invalidenversicherung, 1932, p. 146. HEINZE: " Die Sozialversicherung 1924 bis 1931 in Zahlen." Die Reichsversicherung, 1932, p. 139. DOBBERNACK: " Die finanzielle Lage der Invaliden-, der Angestelltenund der knappschaftlichen Pensionsversicherung unter Berücksichtigung der Notverordnung." Die Reichsversicherung, 1932, H. 6, p. 160. ——: " Die Finanzlage der deutschen sozialen Rentenversicherungen." Zeitschrift für die gesamte Versicherungswissenschaft, 1933, p. 275. und SAUERBORN: " Entwicklung und Stand der deutschen Sozialversicherung." Die Reichsversicherung, 1933, H. 2/3, p. 33. : " Entwicklung und Stand der Sozialversicherungsfinanzen unter besonderer Berücksichtigung der Rentenversicherungen." Reichsarbeitsblatt, Teil IV, 1933, p. 254. HEINZE: "Drei Grundforderungen zum Neuaufbau der Invalidenversicherung." Die Reichsversicherung, 1933, p. 81. '-: " Grundsätzliches zur Neuordnung der Invalidenversicherung." Deutsche Invalidenversicherung, 1933, No. 6, p. 87. : " Bilanzen in der Rentenversicherung der deutschen Arbeiter." Zentralblatt für Reichsversicherung und Reichsversorgung, 1933, No. 23, p. 358. und STREBEL: "Ausbau der Statistik in der deutschen Invalidenversicherung." Die Reichsversicherung, 1933, p. 341. DOBBERNACK: "Die deutschen Sozialversicherungsfinanzen." Annales d'Economie Commerciale, 1934, H. 2, p. 141. : " Die Sanierung der deutschen sozialen Rentenversicherungen." Zeitschrift für die gesamte Versicherungswissenschaft, 1934, p. 1. HEINZE : " Ausbau der statistischen Grundlagen in der deutschen Invalidenversicherung." Reichsarbeitsblatt, Part IV, 1934, p. 388, and 1935, p. 235. : " Grundsätzliches zur Anlagepolitik der neuen Invalidenversicherung." Die Reichsversicherung, 1935, H. Î, p. 23. " The Reform of Workers' Compulsory Pension Insurance in Germany." International Labour Review, Vol. XXXI, Nos. 3-4: March 1935, pp. 398-418; April 1935, pp. 539-554. HEINZE : " Der versicherungstechnische Neubau der deutschen Invalidenversicherung." Die Reichsversicherung, 1935, p. 117. " Statistics of Persons insured under Workers' Compulsory Pension Insurance in Germany." International Labour Review, Vol. XXXII, No. 4, October 1935, pp. 515-522. DOBBERNACK: " Überblick über Inhalt und Bedeutung des Gesetzes über den Ausbau der Rentenversicherung." Deutsche Invalidenversicherung, 1938, No. 1, p. 3. IV. — Rooks 46. 47. DOBBERNACK: Die Rettung der Rentenversicherung. Kohlhammer, Stuttgart-Berlin, 1934. Reichsversicherungsordnung nebst Einführungsgesetz, Ergänzungsbestimmungen und Ausführungsvorschriften. Herausgegeben von Dr. Franz Eichelsbacher. C. H. Beck'sche Verlagsbuchhandlung. Munich and Berlin, 1938. GREAT RRITAIN AND NORTHERN IRELAND National Health Insurance and Contributory Pensions Scheme CONTENTS Page INTRODUCTION 447 Part I NATIONAL HEALTH INSURANCE CHAPTER I: Demographic Estimates, Bases, and Experience 1. Biometrie Tables Mortality Rates 'Sickness and Disablement Rates . Marriage and Widowhood Rates Issue Rates 2. Insured Population Preparatory Estimates Experience of Operation of Scheme 449 449 451 452 454 457 457 458 • • • CHAPTER I I : Financial Estimates, Bases, and Experience 1. 2. 3. 4. 449 . . . . . ,Contributions State Grants Total Income Benefits and Administration Expenses Qualifying Conditions Maintenance of Rights of Persons who are in Arrears Arrears due to Unemployment Medical Benefit Administration Expenses CHAPTER I I I : Financial System 1. Financial System Basic Premium Reserve Values and Transfer Values Initial Liability , Redemption of Outstanding Reserve Values . . . 461 461 462 462 463 464 464 465 465 465 467 467 467 468 468 • 469 444 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Page CHAPTER I I I : Financial Scheme (continued) 2. Financial Organisation . . • Reserve Values (Apportionment) Account Reserve Suspense Fund Contingencies Funds Central Fund . Unemployment Arrears Fund Apportionment of Contributions 3. Actuarial Balance-Sheets . . CHAPTER IV: Financial Administration 1. Investment of Funds Investment of Funds standing in the Investment Account . Investment of Sums paid over to Societies and Investments by the Minister of Health on behalf of Societies . . . . . 2. Valuation of Investments 3. Interest Rates 4. Actuarial Valuations BIBLIOGRAPHY 469 470 470 471 471 472 473 473 476 476 476 477 478 479 480 483 I. Legislative and Administrative Texts II. Reports and Memoranda III. Books and Articles IV. Reports on Operation of Scheme 483 484 485 486 INDEX OF TABLES L II. III. Life Table 1920-1921 (England and Wales) Morbidity and Invalidity Tables . . . Probabilities of Marriage for Women and Probabilities of becoming a Widow IV. Probability of Issue to a Member during One Year V. (a) Age-Distribution of Entrants into and Exitants from National Health Insurance. (¿>) Age-Distribution of the Insured Population of Great Britain and Northern Ireland (exclusive of Deposit Contributors) at 1922-1923 . . ' VI. Age Distribution per Thousand Members of Approved Societies as at 31 December 1931 VII. Number of Insured Persons: Experience VIII. Receipts IX. Expenditure X. Central Fund . . . XI. Apportionment of Weekly Contribution XII. Summaries of Valuations Balance-Sheets . .. XIII. Investments of Approved Societies at the Valuation Dates. XIV. Total Accumulated Funds at 31 December each Year . . . . 450 453 455 456 458 459 459 463 466 472 473 474 478 479 GREAT BRITAIN AND NORTHERN IRELAND 445 Part II WIDOWS', ORPHANS', AND OLD-AGE CONTRIBUTORY PENSIONS Page CHAPTER I: Demographic Estimates, Bases, and Experience . . . . 487 1. Biometrie Tables Mortality Tables Tables showing Marital Condition Tables showing Composition of Family 2. Insured Population Original Estimates Estimates of 1935 Experience 487 487 488 491 . 3. Annual Numbers of Beneficiaries 496 CHAPTER I I : Financial Estimates, Bases, and Experience 1. 2. 3. 4. 5. Contributions State Grants Total Income Benefits Sundry and Total Expenditure 497 . •CHAPTER I I I : Financial System 1. Preparatory Studies Theoretical Premiums and Gradual Rise in Rates Table of Annual Estimates State Charges Preliminary Estimate of Assets and Liabilities 2. Subsequent Estimates and Review 1929 Estimates First Decennial Review 3. Experience CHAPTER IV: Financial Administration 1. Temporary Balance 2. Investment of Funds 3. Accounting, Actuarial Reports, Statistics 493 493 494 495 497 499 500 500 502 504 504 Contribution 504 505 506 507 508 508 508 511 512. 512 512 512 BIBLIOGRAPHY 514 I. II. III. 514 515 515 Legislation Reports and Memoranda Experience 446 ACTUARIAL TECHNIQUE AND INDEX FINANCIAL ORGANISATION OF T A B L E S Page I. II. III. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. XIX. XX. XXI. XXII. Rates of Mortality 488 Proportions of Persons Single, Married and Widowed used in the Calculations for the First Decennial Review, 1935 . . 489 "Percentage Age Distributions of Wives under Age 70 for Various Ages of Husbands 489 Rates of Remarriage of Widows 490 Number of Children under Age 14 left by 1,000 Married Men • and Widowers dying at the Ages shown 491 Number and Ages of Children left by Insured Males . . . . 492 Estimated Number of Insured Persons aged 16-65 in Certain Future Years 494 Percentage of Population in National Health and (latterly) Pensions Insurance 495 Number of Insured Persons : Experience 495 Numbers of Beneficiaries at 31 December in each Year from 1926 to 1936 , . 496 Estimated Cost of Old-Age Pensions to Persons over Age 70 499 Income for the Period 4 January 1926 to 31 March 1937 . . . 501 Expenditure for the Period 4 January 1926 to 31 March 1937. 503 Estimate of the Exchequer Charge under the Widows', Orphans' and Old-Age Contributory Pensions Act, 1925 505 Aggregation of Exchequer Charges in Respect of Pensions 506 Aggregation of .State Grants actually Paid in respect of Pensions 507 Present Values at Beginning of 1926 of Assets and Liabilities 508 Receipts and Payments, and Balances in the Treasury Pensions Account during the Period from 1 April 1929 to 31 March 1946 as Estimated for the Bill of 1929 509 Estimate of Expenditure on Benefits and Income from'Contributions and Exchequer Grants in each Financial Year from 1934-35 to 1965-66 510 Actuarial Balance-Sheet: Present Values of Assets and Liabilities at 3y 3 per cent, per annum 511 Actual Balances in Pensions Accounts 511 Investment of Funds in Treasury Pensions Account . . . 513 INTRODUCTION Compulsory insurance in the United Kingdom of Great Britain and Northern Ireland is dealt with below in two separate studies. The first studies the financial organisation of the scheme of insurance against sickness and disablement (National Health Insurance) 1 , a distinction between these two risks being unnecessary on account of the definition adopted for disablement, which is regarded as a continuance of sickness. The second deals with the financial organisation of the scheme combining widows' and orphans' insurance and old-age insurance (Contributory Pensions). The national health insurance scheme and the widows', orphans' and old-age contributory pensions scheme are very much the same in scope, and the contributions are collected jointly. In all other respects the two schemes are clearly distinct. National Health Insurance is administered chiefly by (1) approved societies, i.e. insurance institutions which satisfy the conditions laid down by the Act for health insurance carriers and have been approved as such by the administrative authorities, and (2)' insurance committees2 for administering medical benefit to members of approved societies and all benefits to insured persons who are not members of such societies. Approved societies and insurance committees are both subject to the supervision and authority of a Central Government department, as will be shown later. The contributory pensions scheme, on the other hand, is administered directly, as described in the second study, by central departments. From the financial point of view, too, it is essential to distinguish between the two schemes, which in this respect are completely independent and are based upon different technical principles. The National Insurance Act of 1911 introduced a compulsory scheme of insurance against sickness and disablement in Great Britain and Ireland on the same date — 15 July 1912. The scheme was divided into two separate parts in 1922, after the promulgation of the measures establishing the Irish Free State. The scheme discussed below is that in force in Great Britain (England, Wales, and Scotland) and the whole of Ireland up to 1922, and in the United Kingdom of Great Britain and Northern Ireland from 1923 onwards. Any provisions special to Northern Ireland are left out of account, and in many cases the statistics given refer to Great Britain alone. The principal events in the development of the health insurance scheme may be briefly recapitulated. On 15 July 1912 the existing 1 Maternity benefit is also provided under the health insurance scheme, but is left out of account here whenever possible, since it does not belong to,the scope of the present volume. 2 Except in Northern Ireland, where the Ministry of Labour performs the work entrusted in Great Britain to the insurance committees. 448 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION companies and societies, such as the friendly societies which administered insurance privately, were brought into the compulsory insurance scheme, which met with few difficulties in application. Following the abnormal period 1914-1918, contributions and benefits were found to be no longer in line with the level to which the cost of living had risen. The rates of both were accordingly raised, from 5 July 1920, by the National Health Insurance Act, 1920. The introduction of widows', orphans' and oid-age pensions lightened the burden on the health insurance scheme by substituting an old-age pension between the ages of 65 and 70 for the sickness and disablement benefit previously payable between these ages; contributions in respect of the latter scheme were consequently reduced, from 4 January 1926, by the Widows', Orphans' and Old-Age Contributory Pensions Act, 1925, and were made to terminate at the age of 65 instead of 70. Finally, since 1930 a series of measures have been adopted to deal with the special circumstances arising out of the economic depression, and, in particular, to protect the rights of unemployed insured persons. All previous legislation has been consolidated under the National Health Insurance Act of 1936 1. The widows', orphans' and old-age insurance scheme introduced in Great Britain by the 1925 Act supplemented rather than replaced the non-contributory old-age pension system in force under the Acts of 1908 and 1924. Legislation to provide simular benefits was also passed by Northern Ireland. Since the scheme at present in operation in Northern Ireland is completely independent, and since the principal technical studies on the subject were made solely with reference to Great Britain, the present study of the contributory pensions scheme is limited to the latter country. Leaving out of account minor changes, three principal stages may be distinguished in the evolution of widows', orphans' and old-age insurance. During the first of these stages the 1925 Act came into operation ; this was effected in several steps: on 4 January 1926 the collection of contributions and the payment of widows' and orphans' pensions began; on 2 July 1926, the payment of old-age pensions to persons over 70 years; and finally on 2 January 1928, the payment of old-age pensions to persons between 65 and 70 years of age. The second stage was marked by the Act of 1929, which extended the scope of non-contributory pensions to widows (in particular, the age for the grant of such pensions was lowered to 55) as from 1 January 1931, in some cases, 1 July 1930. In the third stage, beginning in 1930, special measures have been introduced with a view to mitigating the effects of the economic depression. All previous legislation has been consolidated under the Widows', Orphans, and Old-Age Contributory Pensions Act of 1936 2. 1 2 See Bibliography, Part I, No. 13. See Bibliography, Part II, No. 6. PART I NATIONAL HEALTH INSURANCE CHAPTER I DEMOGRAPHIC ESTIMATES, BASES AND EXPERIENCE § 1. — Biometrie Tables MORTALITY RATES The mortality rates of the English Life Table No. 6 (1891-1901) were used in connection with the preparatory work when the National Health Insurance scheme was being formulated, but soon after the Actuarial Advisory Committee appointed in 1912 observed in its first report [22] that these rates were obsolete and should be altered to allow for recent and continual fall in the death rate. The number of deaths for decennial age-groups was obtained from the registration returns for England and Wales for the three years 1908-1910. The population at the central date of this period, i.e. 30 June 1909, was estimated, use being made of the 1901 census figures. Since the results of the 1911 census were not yet known, the population on 31 March 1911 was calculated on the assumption that the net migration and mortality rates between'1901 and 1911 were the same as those experienced between 1891 and 1901, i.e. that: Population aged x to x + 10 in 1911 Population aged x — 10 to a; in 1901 Population aged x to x + 10 in 1901 Population aged x — 10 to a; in 1891 The population at 30 June 1909 was then obtained by arithmetical interpolation [20, 22]. The Royal Commission on National Health Insurance of 1924, and in particular the Departmental Actuarial Committee which was instructed to assist it in technical matters, noted that the death rate had fallen substantially since the period 1908-1910: It concluded [33] that the mortality rates prepared by the 1912 Actuarial Committee must be replaced by those which had been compiled for the preparatory work [32] on the contributory pensions scheme, which had the advantage of being based on the most recent statistics available (for England and Wales), namely the 1921 census returns and the registered deaths in 29 450 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION the two years 1920 and 1921. This table, which has been used ever since, is reproduced below: TABLE I. LIFE TABLE 1 9 2 0 - 1 9 2 1 (ENGLAND AND WALES) Probability that a person of an exact age will survive one year Age Men Women Age Men Women 16 years. . 17 » . . 18 » . . 19 » . . 0.99749 0.99728 0.99706 0.99685 0.99744 0.99730 0.99718 0.99708 60 years. . 61 » . . 62 » . . 63 » . . 64 » . . 0.97447 0.97238 0.97009 0.96757 0.96478 0.98133 0.97979 0.97808 0.97617 0.97403 20 21 22 23 24 » » » » » .. .. .. .. .. 0.99666 0.99650 0.99637 0.99626 0.99616 0.99699 0.99690 0.99680 0.99669 0.99657 65 66 67 68 69 • » » » " » 0.96168 0.95824 0.95443 0.95023 0.94562 0.97162 0.96889 0.96578 0.96228 0.95840 25 26 27 28 29 » » » » » .. .. .. .. .. 0.99605 0.99593 0.99581 0.99569 0.99556 0.99646 0.99636 0.99627 0.99619 0.99612 70 71 72 73 74 » .. » .. " .. » .. »• .. 0.94058 0.93509 0.92912 0.92261 0.91545 0.95416 0.94958 0.94466 0.93933 0.93349 30 31 32 33 34 >» » " » » .. .. .. .. .. 0.99543 0.99528 0.99511 0.99491 0.99469 0.99605 75 0.99597 76 0.99587 77 0.99575 78 0.99562 . 7 9 » » » » » .. .. .. .. .. 0.90751 0.89900 0.89010 0.88080 0.87120 0.92700 0.91974 0.91165 0.90285 0.89340 35 36 37 38 39 » » » » » .. .. .. .. .. 0.99445 0.99420 0.99395 0.99369 0.99343 0.99549 0.99535 0.99520 0.99504 0.99487 80 81 82 83 84 » " » » » .. .. .. .. .. 0.86130 0.85110 0.84050 0.82930 0.81730 0.88330 0.87280 0.86210 0.85130 0.84040 40 41 42 43 44 » » » » " .. .. .. .. .. 0.99316 0.99286 0.99253 0.99216 0.99174 0.99468 0.99446 0.99421 0.99393 0.99362 85 86 87 88 89 » " » » » .. .. .. .. .. 0.80430 0.79040 0.77570 0.76050 0.74570 0.82930 0.81790 0.80610 0.79380 0.78080 45 46 47 48 49 » » » » » .. .. .. .. .. 0.99127 0.99075 0.99018 0.98955 0.98885 0.99328 0.99291 0.99251 0.99207 0.99158 90 91 92 93 94 " » » » » .. .. .. .. .. •0.73100 0.71800 0.70700 0.69800 0.69100 0.76700 0.75200 0.73600 0.71900 0.70400 50 51 52 53 54 " » » » » .. .. .. .. 0.98808 0.98723 0.98628 0.98522 0.98405 0.99103 0.99042 0.98975 0.98901 0.98819 95 96 97 98 99 » .. » .. » .. » .. » .. 0.68600 0.67700 0.66200 0.64100 0.61100 0.69100 0.68000 0.67100 0.65900 0.64100 55 56 57 58 59 » » » » » .. .. .. .. .. 0.98276 0.98135 0.97982 0.97817 0.97639 0.98728 0.98628 0.98519 0.98401 0.98273 100 101 102 103 » " » » 0.56000 0.50000 0.40000 0.61400 0.57500 0.52000 0.43200 .. .. .. .. .. .. .. .. .. — GREAT BRITAIN AND NORTHERN IRELAND 451 SICKNESS AND DISABLEMENT RATES The Act defines sickness and disablement as incapacity for work caused " by some specific disease or bodily or mental disablement ". Sickness benefit is granted from the fourth day of incapacity and continues for a period or periods not exceeding 26 weeks in all. For the purpose of calculating this period of 26 weeks, detached periods of incapacity separated by intervals of less than 12 months are linked together and treated as if they formed a single illness. Benefit granted after the expiry of 26 weeks is termed disablement benefit 1 . It follows from the linking together just mentioned that in any twelve months an insured person who has once received disablement benefit cannot, in the case of repeated incapacity, receive sickness benefit, but only further disablement benefit. In order to obtain data on sickness and disablement for the purposes of compulsory social insurance, reference was made to the returns of a friendly society—the Independent Order of Oddfellows, Manchester Unity Friendly Society—which had made an investigation covering the years 1893-1897. Figures were taken from the results of the investigation, showing for each occupational group the average number of weeks of sickness per member and per annum, classified by age and the length of the period of sickness (under or over 26 weeks). The figures relating to periods of sickness up to 26 weeks were taken as sickness rates, and those relating to periods after the first 26 weeks as disablement rates 2. Before these rates were adopted for the purpose of compulsory insurance they were critically examined on the following grounds. The occupational distribution of the members of the Manchester Unity was not representative of that of the persons to be insured under the proposed compulsory system, a larger proportion of whom would belong to occupations involving greater risks. By weighting the special rates of sickness for the respective occupational classes in accordance with the distribution of persons under the insurance scheme, average rates of sickness for the whole population were obtained, which were found to be about 10 per cent, above the general Manchester Unity standard. On the other hand, the compulsory scheme, unlike the friendly societies, would not have to provide for sickness due to industrial accidents. It was considered that these two factors would neutralise each other, and therefore the table referring to the whole membership of the Manchester Unity (Manchester Unity Sickness Table [19]) was adopted in the preliminary calculations [20, 21]. Although it referred to men only, it was decided to apply it, in the absence of sufficiently reliable special data for women, to the whole insured population. The Actuarial Committee of 1912 made a number of adjustments in the Manchester Unity table, the most important being that intended to allow for the waiting period of three days in the case of insured persons applying for sickness benefit for the first time within a year. Since the friendly societies have no such provision, the benefit periods to which the 1 To complete the summary account given here reference may be made to another publication of the INTERNATIONAL LABOUR OFFICE—Studies and Reports, Series M (Social Insurance), No. 14, Geneva, 1937, The Evaluation of Permanent Incapacity for Work in Social Insurance—which contains a detailed study, based on legislation and legal decisions, of the British conception of 2incapacity. These definitions of sickness and disablement rates will be used throughout the present study. 452 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Manchester Unity tables refer begin with the first day of sickness. The various adjustments made in the Manchester Unity table, and the arithmetical methods by which they were effected, are described and discussed in the appendices to the first annual report [22] on the administration of the health insurance scheme, which include also a sickness table for both sexes and separate disablement tables for men and women. The same Committee recommended for computing the initial reserves a loading of 12a/4 per cent, on the Manchester Unity rates in order to provide a safety margin. The practical working of the scheme soon showed that sickness was more frequent among women than among men, and that the use of a common table ought to be abandoned. In 1919, therefore, at the same time as the publication [14J of the bases of the first actuarial valuation 1 , special sickness rates were published for women, higher than those for men, and at the same time the disablement rates for women were raised. The bases used for the second actuarial valuation were the same except for a special liability added in the case of married women. The studies made by the Royal Commission of 1924 led to the conclusion that the Manchester Unity table should be retained as a basis for men but rejected for women. For men, however, a small redistribution of the rates was made between sickness and disablement and also the previous loading of 12 s / 4 per cent, was dropped. For women were introduced the rates which had just been calculated from a study of a group of approved societies so chosen as to constitute a microcosm of the whole insured population. This selected societies' experience covered about 500,000 men and 400,000 women during the years 1921, 1922 and 1923. The figures for 1923, which were higher than the average for the three years, were chosen and loaded by 10 per cent. The change meant that the technical bases of the scheme were brought into closer relation with the results obtained from the operation of the Act 2 and that sickness tables putting married women in a separate category could be used. These tables [14: 1929] served as the basis for the third actuarial valuation. As regards women, the rates drawn from the selected societies' experience were iñ turn found no longer to reflect current experience. On the basis of the figures in the returns of a group of representative societies relating t o the years 1928-1930, which were reduced by 10 per cent., the sickness rates applicable to spinsters and widows and those applicable to married women aged 39 or over were lowered, while those applicable to married women aged under 39 were raised. Separate disablement rates were established for spinsters and widows, on the one hand, and married women on the other. The rates which were finally used as the basis of the fourth actuarial valuation are reproduced in table II. MARRIAGE AND WIDOWHOOD RATES The practical application of certain clauses governing the payment of .contributions or the granting of benefit depends on the marital condition of the insured person. l " Chapter III will return to the subject of the four actuarial valuations that have been made in the health insurance scheme. 2 For a thorough statistical study of sickness and disablement as observed in the operation of the Act, cf. the articles by Sir A. W. Watson [46, 47]. GREAT BRITAIN AND NORTHERN TABLE II. 453 IRELAND MORBIDITY AND INVALIDITY TABLES Average number of weeks of sickness and disablement benefits payable to 100 members within one year 1 Age 16 years 17 » 18 " ±9 » 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 » » » » » " » » » » » » » » " » " » " » ». " » » » » » » » » » » » » » » » " » » » » » » » Men .... 84 81 76 71 67 64 63 62 61 61 61 61 61 62 63 64 65 67 68 70 72 74 77 80 83 86 ' 89 92 95 99 103 108 113 118 123 128 134 139 145 152 159 167 176 184 193 203 214 224 235 Sickness Spinsters Married and widows women 80 82 84 85 86 87 87 87 87 86 86 85 84 83 82 81 80 80 80 81 82 83 85 87 89 92 95 98 101 104 107 110 114 117 121 124 128 132 137 142 147 152 158 164 171 179 188 199 212 320 319 318 316 314 311 307 301 291 277 262 248 236 226 218 211 205 200 196 193 190 187 185 183 182 181 181 180 180 180 180 181 182 183 185 186 188 190 193 196 199 202 206 210 215 221 228 237 248 Disablement Spinsters Married Men and widows women —— 10 13 16 19 21 24 26 28 30 32 33 34 36 37 39 41 43 45 47 49 52 55 58 61 65 68 71 74 78 82 87 95 105 116 130 145 162 180 201 223 249 279 315 359 411 472 540 — — 15 23 31 39 47 55 63 70 77 84 90 96 102 108 . 113 118 122 126 130 134 138 142 ' 147 152 158 164 171 179 187 196 206 217 229 241 254 269 286 305 326 350 377 408 443 483 528 579 637 • — — 55 63 71 79 87 95 103 110 117 124 130 136 142 148 153 158 163 168 174 • 181 188 196 > 205 215 226 238 251 265 281 298 316 336 357 380 405 432 461 493 528 567 610 657 708 763 822 885 952 i The above are " central rates ", i.e. the total number of weeks of sickness or disablement benefit payable during the year of age following the exact age given in the table per hundred of persons alive in the middle of that year of age. 454 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Data Used for the Preparatory Studies [20] In making the preliminary estimates, use had to be made of the following data: (1) rates of marriage, at each age, of spinsters and widows respectively; (2) the proportion of married women at any given age who become widows in the course of the year (widowhood rate) ; (3) the probabilities in regard to marital, condition of insured persons (men and women) at a given age. The rates of marriage of spinsters and widows were deduced from the. registered marriages for the ten years 31 March 1896 to 31 March 1906, compared with the female population at various ages enumerated at the census of 1901, that is to say the middle point of the ten years referred to. With regard to the proportion of married women at any given age who become widows in the course of the year, there were no statistics immediately bearing upon this point. The proportion was accordingly calculated directly. For England and Wales the 1901 census figures were used to obtain the distribution of husbands and wives for various combinations of ages. The mortality rates of the husbands were assumed to be those shown by the English life table No. 6 (males). For Scotland and Ireland, the distribution of husbands and wives for various combinations of ages was obtained, in the absence of any table, by adjusting the results derived from the English table in order to allow for the fact that there is a slightly greater difference of age between husbands and wives in Scotland and Ireland than in England and Wales. The probability that an insured man will at a given age be a bachelor, a married man or a widower was calculated from the 1901 census returns, the rates of mortality for married men and bachelors being taken to be the same. The same probabilities were next calculated for women. These data were also used for the 1st and 2nd valuations. Data used Subsequently The adoption of the 1920-21 (England and Wales) life table as the general mortality basis involved consequential changes in the widowhood rates employed in the third and fourth valuations. No change was made in the original marriage rates used in the first and second valuations. Table III gives the marriage rates (for spinsters and widows) and the widowhood rates used as a basis for the fourth actuarial valuation. ISSUE RATES In the preparatory work [20] the probability of issue to a married man was calculated—in the absence of statistics for the United Kingdom —from statistics relating to New Zealand suitably modified to allow for the lower birth rates prevalent in the United Kingdom. The rates of issue to married women were calculated from: (1) the rates of issue to married men; (2) the table mentioned above showing the distribution of husbands and wives according to various combinations of ages. GREAT BRITAIN AND NORTHERN IRELAND 455 TABLE I I I . — P R O B A B I L I T I E S OF MARRIAGE FOR WOMEN AND P R O B A B I L I T I E S OF BECOMING A W I D O W Probability of marriage Probability (spinsters of becoming and a widow widows) Age 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.0071 0.0164 0.0309 0.0494 0.0689 0.0866 0.1005 0.1085 0.1112 0.1091 0.1035 0.0955 0.0862 0.0766 0.0672 0.0586 0.0509 0.0443 0.0386 0.0338 0.0298 0.0264 0.0234 0.0208 0.0038 0.0038 0.0039 0.0040 0.0040 0.0041 0.0042 0.0043 0.0044 0.0045 0.0046 0.0048 0.0050 0.0052 0.0054 0.0056 0.0058 0.0061 0.0064 0.0067 0.0070 0.0073 0.0076 0.0080 1 Age 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64. . . . . Probability of marriage Probability (spinsters of becoming and a widow widows) 0.0186 0.0167 0.0150 0.0135 0.0121 0.0109 0.0098 0.0088 0.0079 0.0071 0.0063 0.0056 0.0049 0.0043 0.0037 0.0033 0.0028 0.0024 0.0021 0.0018 0.0016 0.0014 0.0012 0.0010 0.0009 0.0084 0.0089 0.0094 0.0100 0.0106 0.0113 0.0120 0.0127 0.0135 0.0144 0.0154 0.0165 0.0178 0.0192 0.0207 0.0223 0.0240 0.0258 0.0277 0.0298 0.0321 0.0345 0.0371 0.0400 0.0432 i The above are "central rates", e.g. the probability of marriage of a spinster or a widow is the ratio of the number of marriages in a year of age following the exact age given in the table to the number of spinsters and widows alive in the middle of that year of age. The work of the 1912 Actuarial Committee [22] made it possible to put the New Zealand results aside and to make use instead of the statistics derived from an analysis of the returns of the general 1911 census relating to the Metropolitan Borough of Camberwell, which was selected as being on the whole representative of the general population. These statistics showed, by quinquennial age groups: (1) the numbers of husbands and of wives (excluding widows and widowers) ; (2) the numbers of husbands and of wives with one or more children under one year of age (twin births being counted as single births). From these figures issue rates were calculated in respect of: (1) married men; (2) all men; (3) married women, irrespective of age at marriage (" aggregate " values) ; (4) married women according to age at marriage (" select " values). 456 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Judging from the results obtained from the working of the health insurance scheme itself, the Actuarial Committee appointed in connection with the Royal Commission of 1924 concluded [33]: (1) that the rates in relation to the age of the fathers must be subjected to a proportionate reduction to 85 per cent, of their original values ; (2) that the rates in relation to the age of the mothers should be taken from the ' results of the Selected Societies' experience, subject to a fixed loading of 10 per cent. • The issue rates computed on the basis of these recommendations were used in the case of men for the third actuarial valuation. In the case of women a further reduction of 15 per cent, was made in the issue rates as part of the revision of the women's basis as from 1 January 1933 made in the light of the experience of 1928-30 K The issue rates used for the fourth valuation were thus obtained; they are reproduced in table IV. TABLE IV. PROBABILITY OF ISSUE TO A MEMBER DURING ONE YEAR Age 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 . . . . . . . . . . . . . . . . . . . . . . . . . . Men . — — 0.001 0.008 0.023 0.045 O.068 0.089 0.107 0.122 0.135 0.145 0.152 0.157 0.160 0.160 0.158 0.154 0.148 0.141 0.132 0.123 0.112 0.102 Married women 2 Spinsters and widows 2 0.340 0.510 0.590 0.530 0.440 0.355 0.285 0.240 0.210 0.189 0.171 0.156 0.143 0.131 0.120 0.110 0.100 0.091 0.082 0.073 0.065 0.057 0.049 0.041 — 0.002 0.003 0.004 0.005 0.006 0.006 0.006 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 Age 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . Men . 0.091 0.081 0.071 0.062 0.054 0.046 0.039 0.033 0.028 0.024 0.020 0.016 0.014 0.011 0.009 0.007 0.006 0.005 0.004 0.003 0.002 0.002 0.002 0.001 0.001 Married women 2 Spinsters and widows2 0.033 0.026 0.019 0.013 0.008 0.005 0.003 0.002 0.001 0.001 0.001 0.001 0.001 0.001 — — — — — — _ — — .— — — — — —' — 1 — — — — — .—. — — • — — — — — — — — — — — — i The above are " central rates ", i.e. the ratios of the number of maternity benefits payable in the year of age following the exact age given in the table per thousand of persons alive in the middle of that year of age. s Provision for posthumous births is made in the rates applicable to married women. 1 See above, p. 452. GREAT BRITAIN AND NORTHERN IRELAND 457 § 2. — Insured Population Insurance is compulsory for all persons of the age of 16 1 and upwards who are employed within the meaning of the Act 2 . Persons liable to be insured are entitled to apply for admission to approved societies and if they are not a member of one within a certain time after entry into insurance, are treated as deposit contributors, in which case they are entitled to benefits only 3up to the amount of the contributions made by or in respect of them . If, however, within two years of entry into insurance a deposit contributor is able to prove that the state of his health is such that he cannot obtain admission to an approved society he is admitted to a special " insurance section " of the Deposit Contributors Fund and is entitled to the normal benefits of the scheme. Besides 4members of approved societies and deposit contributors the scheme covers members of the forces of the Crown who do not join approved societies. These persons are grouped in a special fund—-the Navy, Army and Air Force Insurance Fund. PREPARATORY ESTIMATES When the preparatory work on the scheme was in progress, use had to be made of the most recent census statistics available, namely those for 1901. The proportion of the occupied population that would become liable to insurance was estimated separately for England, Wales, Scotland, and Ireland. Even for a given occupation there was considerable difficulty in calculating the ratio of the insured population to the occupied population. In most cases a more or less arbitrary approximation had to be accepted, namely that the whole of the occupation would be liable to insurance or else that it would be excluded. Persons working for an employer were distinguished from persons working on their own account. Finally, a table of the distribution of the insured population by quinquennial age-groups and by sex, derived from the 1901 census figures, was constructed for the whole of the United Kingdom. This preliminary estimate was next related to the date chosen for the application of the proposed scheme, namely 1 May 1912 6. For this purpose, the population was assumed to have increased between 1901 and 1912 on the basis of the same net migration and mortality rates as were experienced between 1891 and 1901. 1 As from 4 April 1938, all boys and girls leaving school and taking up insurable employment before reaching the age of 16 have been brought within the scope of the scheme by the Juvenile Contributors Act [18] of 1937 for the purpose of medical benefit only. 2 For the definition of " employed persons " and for the persons or classes of persons not liable to insurance, cf. INTERNATIONAL LABOUR OFFICE: Studies and Reports, Series M, No. 10, Compulsory Pension Insurance, Geneva, 1933, pp.3 101-103. These contributions are credited to a special fund, the Deposit Contributors Fund, and entered in a personal account. 4 The group of " exempt persons " is not considered here. Until 30 April 1921 (in Scotland, 31 December 1920) they were entitled to medical benefit and sanatorium benefit, after that date to medical benefit only. Exempt persons are, however, not entitled to medical benefit in Northern Ireland. 6 The scheme actually came into operation on 15 July 1912. 458 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION EXPERIENCE OF OPERATION OF SCHEME In an article [46] published in 1927 Sir A. W. Watson gave the tables reproduced below, showing the age distribution of the insured population on the one hand and of the persons entering into and passing out of insurance on the other. The figures for the insured population of Great Britain and Northern Ireland include the members of the approved societies and of the Navy, Army and Air Force Insurance Fund, but not the deposit contributors. They are derived from returns one-fifth of which relate to the end of 1922 and the rest to the end of 1923. The number of entrants and exitants was calculated on the basis of a sample enquiry relating to the years 1921-1923. TABLE V. (a) A G E - D I S T R I B U T I O N OF ENTRANTS INTO E X I T A N T S FROM NATIONAL HEALTH INSURANCE AND (Sample experience, 1921-1923) Women Spinsters Married and widows Entrants | Exitants Entrants | Exitants Entrants | Exitants Men Agei 61 12 6 5 4 6 4 2 * 17 16 13 21 14 12 59 19 8 4 3 4 2 1 100 100 100 16 years . 17-19 years 20-24 » 25-29 » 30-34 » 35-44 " 45-54 » 55 years a n d 0 v e r 1 «I 28 20 12 14 8 6 1 14 23 20 27 12 3 7 21 22 30 14 6 100 .100 100 i " Age " in this table is the difference between the year in which the event occurred and the year of birth. (b) A G E - D I S T R I B U T I O N OF THE I N S U R E D P O P U L A T I O N OF GREAT BRITAIN AND N O R T H E R N IRELAND (EXCLUSIVE OF DEPOSIT CONTRIBUTORS) AT 1922-1923 (In thousands) Age (last birthday) 16-19 years 20-24 ' 25-29 ' 30-34 ' 35-39 ' 40-44 ' 45-49 ' 50-54 ' 55-59 ' 60-64 ' 65-69 ' O v e r 70 years Total Men Women Spinsters Married and widows women 1,303 1,588 1,250 1,122 1,047 973 901 763 603 446 288 235 1,103 1,100 548 310 220 171 143 116 94 69 42 30 8 102 158 145 134 121 99 72 47 29 13 10 10,519 3,946 938 GREAT BRITAIN AND NORTHERN IRELAND • 459 More recent figures giving the age distribution of members of approved societies were recorded [43] as at 31 December 1931 and are reproduced in table VI below. TABLE V I . AGE DISTRIBUTION P E R THOUSAND MEMBERS OF A P P R O V E D SOCIETIES AS AT 3 1 D E C E M B E R 1 9 3 1 Age 25-35 35-45 45-55 55-65 Women Men » » » » 268 257 190 164 121 457 246 138 98 61 1,000 1,000 The number of persons insured under the scheme is published annually for each country, sex, and category. The following table shows the aggregate results: TABLE V I I . NUMBER OF I N S U R E D P E R S O N S : EXPERIENCE (United Kingdom) Women Men ' Years Members of approved societies Deposit contributors Navy, Army and Air Force Members of approved societies Deposit contributors 1912-13 . . . 1914 . 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 ! 1935 1 1936 1 . . . . 8,959,200 9,173,900 9,269,700 9,486,600 9,481,100 9,599,100 9,633,200 9,662,900 9,770,600 9,945,100 10,069,000' 10,319,700 10,467,600 10,757,600 10,932,800 10,848,200 10,980,900 11,206,700 11,314,200 11,379,900 11,246,700 11,277,100 11,408,900 11,765,550 242,700 225,800 224,900 216,800 230,700 223,100 290,900 256,900 184,600 188,500 180,500 177,400 177,300 182,800 172,000 160,800 156,400 154,200 152,700 147,300 140,600 133,400 132,550 136,850 106,000 245,000 430,000 590,000 780,000 860,000 360,000 260,000 255,000 233,000 176,000 167,500 165,400 156,400 152,400 145,400 135,300 129,300 124,300 121,300 118,300 114,300 120,300 125,300 3,847,500 3,909,900 4,036,900 4,390,900 4,685,200 4,998,700 4,972,600 4,936,900 4,808,400 4,933,800 5,073,400 5,266,000 5,356,000 5,467,700 5,571,300 5,713,900 5,804,500 5,882,100 5,904,000 5,904,100 5,855,150 5,879,000 5,936,700 6,032,050 103,700 96,800 98,600 130,000 155,600 170,600 171,000 131,900 99,800 92,900 91,800 95,100 98,700 104,800 102,800 102,300 107,900 114,700 116,100 121,050 125,800 133,300 135,550 140,200 i Approximate figures subject to adjustment. 460 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION It should be noted that the figures contained in this table are not always comparable. The number of insured men could only be estimated approximately in the years 1915-1919. Until 1921 the figures for the various categories referred to Great Britain only, whereas from 1922 onwards they refer to the whole of the United Kingdom. Again, since 1920 the membership of the approved societies has represented the number of members on the books of the societies at the end of the year (including those temporarily remaining insured persons after ceasing to be employed), whereas before that date it was based on the number of contribution cards surrendered, increased by the approximate number of members serving with the forces. Finally, the upper age limit remained at 70 years until 1927, but was lowered in 1938 to 65 years. Below is given a table showing the membership of the approved societies as calculated at the different actuarial valuations [30, 35, 38, 43]: TemporMen Spinsters Married and widows women «y insured married women (class K) (In thousands) 1st actuarial valuation: 31 Dec. 1938. Figures revised so as to take account of the exclusion of the Irish Free State 9,956 •5,430 36 1 2nd actuarial valuation: 31 Dec. 1922, 31 Dec. 1923 Figures revised so as to take account of the lowering of the upper age limit from 70 to 65 10,094 9,807 3,916 928 261 4,789 3rd actuarial valuation: 31 Dec. 1927, 31 Dec. 1928, 31 Dec. 1929 . . . . 10,816 4,295 1,132 136 4th actuarial valuation: 31 Dec. 1931, 31 Dec. 1932, 31 Dec. 1933, 31 Dec. 1934 11,260 4,396 1,128 169 CHAPTER II FINANCIAL ESTIMATES, BASES, AND EXPERIENCE § 1. — Contributions Contributions are normally the same for all compulsorily insured persons of the same sex. The rate is fixed irrespective of wages 1unless the insured person belongs to one of certain special categories . The normal weekly contribution was at first fixed at the following rates : Men Insured person's contribution Employer's contribution Total d. d. d. 4 3 3 3 1 6 The need of increasing benefits in order to bring them into line with the higher cost of living led to the raising of these rates in 1920 to the following figures : • Men Insured person's contribution Employer's contribution Total d. d. d. 5 4 5 5 10 9 The introduction of widows', orphans' and old-age insurance lowered the upper age-limit under the health insurance scheme from 70 to 65 years 1 For the rates of contribution for these categories, cf. Bibliography, No. 13. 462 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION for purposes of sickness and disablement benefit and of contributions, and in consequence the contributions could be reduced to the following rates, which came into operation on 1 January 1926 and are still in force : Women Insured person's contribution Employer's contribution Total d. d. d. 4% 4 4% 4% 9 The technical data upon which the financial organisation of the scheme is based, and which are used for the actuarial valuations, take account of the non-payment of contributions by members during sickness, and also during periods of unemployment up to an average of 2.6 weeks per insured person per annum (i.e. up to an unemployment rate of 5 per cent.). The present probable value of the future contributions has been calculated for the total insured population at each actuarial valuation. The figure thus obtained is placed on the assets side of the actuarial balance-sheet K The total annual contributions actually paid appear in the first column of table VIII. § 2. — State Grants The original Act of 1911 fixed the principal State grant at twoninths of the expenditure on benefits and administration in respect of men and one-fourth in respect of women. The Act of 1920 fixed a flat rate of two-ninths, which was reduced by the Act of 1926 to one-seventh for men and one-fifth for women. The present probable value of future State grants is included on the assets side of each of the actuarial balance-sheets 2. The total amount of State grants actually paid in each year is shown in table VIII. § 3. — Total Income The table below shows the total sums which in each year have been credited under the head of contributions, State grants, and interest on accumulated funds. The figures relate to Great Britain up to 1 March 1922 and to the United Kingdom after that date. 1 An actuarial balance-sheet is included in each of the four actuarial valuations already referred to. The four balance-sheets are brought together in table XII. 2 See table XII below. 463 GREAT BRITAIN AND NORTHERN IRELAND TABLE VIII. RECEIPTS (Thousand £) • Year! 1912-13 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 2 1935 2 1936 2 butions 26,572 16,797 18,284 17,784 18,166 18,245 18,205 22,688 25,190 25,314 26,580 27,799 28,119 24,819 26,746 26,389 26,386 26,473 26,233 26,813 26,497 27,399 27,805 29,050 Interest 453 618 899 1,199 1,628 2,265 2,721 3,271 3,695 4,173 4,929 5,411 5,733 6,039 5,633 5,812 5,767 6,396 6,256 6,260 6,186 6,272 6,343 6,439 Parliamentary votes and grants . Total 33,419 23,152 25,640 24,142 25,559 27,965 29,560 36,165 40,644 38,027 38,513 40,447 42,109 38,018 40,143 39,521 39,973 40,389 39,740 39,407 38,824 39,983 40,962 43,105 6,395 5,737 6,457 5,159 5,764 7,455 8,634 10,206 11,759 8,540 7,104 7,237 8,257 7,160 7,764 7,320 7,820 7,520 7,251 6,334 6,141 6,312 6,814 7,616 i The 1912-13 ligures relate to tbe period 15 July 1912 to 11 January 1914, and tne 1914 figures relate to 12 January to 31 December 1914. Tbe later figures relate to calendar years. s Approximate figures subject to adjustment. § 4. — Benefits and Administration Expenses Health insurance benefits, like contributions, are fixed at a flat rate for men, unmarried and married women respectively. They comprise cash benefits in respect of sickness, disablement, or maternity, and medical benefit *. In addition, an approved society which on valuation is found to have a sufficiently large surplus for the purpose may apply a part of that surplus to the provision of additional benefits for its members. These additional benefits generally consist of additions to the normal rates of cash benefits and/or payments toward the cost of various forms of special treatment, such as dental and ophthalmic treatment. The normal rates of cash benefits were fixed by the 1911 Act as follows : Men s. Cash benefits: Weekly sickness benefit Weekly disablement benefit . . . . Maternity benefit d. 10 0 5 0 30 0 Women s. d. 7 6 5 0 30 0 1 S a n a t o r i u m benefit used also t o be g r a n t e d , b u t was discontinued ih G r e a t Britain in 1921 a n d in N o r t h e r n I r e l a n d in 1930. 464 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION They were increased in 1920 to the following figures : Men Cash s. d. s. d 15 7 40 0 6 0 12 7 40 0 6 0 benefits: Weekly sickness benefit . . Weekly disablement benefit Maternity benefit The normal rates of sickness and disablement benefit payable to women were reduced by the Act of 1932, being fixed as follows from 1 January 1933: Unmarried women s. d. Cash Married women s. <1. benefits: Weekly sickness benefit . . Weekly disablement benefit 12 6 0 0 10 5 0 0 QUALIFYING CONDITIONS In order to be able to claim sickness and disablement benefits at the above rates the insured person must have been continuously in insurance for 104 weeks and have actually paid 104 contributions. A period of 26 weeks in insurance and the actual payment of 26 contributions, however, gives a right to sickness benefit at a specified reduced rate of 9s. for men and 7s. 6d. for women. The payment of maternity benefit requires a period of 42 weeks in insurance and the actual payment of 42 contributions. MAINTENANCE OF RIGHTS OF PERSONS WHO ARE IN ARREARS If there are arrears in the payment of contributions, sickness and disablement benefits may be reduced or suspended, but for this purpose arrears due to proved incapacity or unemployment are not taken into account. Maternity benefit may also be suspended (other than maternity benefit granted to women who marry and cease work). The reduction or suspension during a benefit year (which approximates to the calendar year) depends on the total number of weeks of contributions (including weeks of sickness and credits in respect of unemployment) during the preceding contribution year (i.e. the year ending in the previous July), as follows: Total contributions paid 50 or over 36-49 . . . . . . . . Effect on benefits No reduction or suspension. Sickness and disablement benefits reduced according to scale 1. Maternity benefit not affected. 26-35 Sickness and disablement benefits suspended. Maternity benefit not affected. 25 or under Sickness, disablement and maternity benefits suspended. 1 This scale is reproduced in INTERNATIONAL LABOUR OFFICE, Studies and Reports, Series M., No. 10, already cited. ' GREAT BRITAIN AND NORTHERN IRELAND 465 ARREARS DUE TO UNEMPLOYMENT The continuation of insuran.ee in the event of unemployment has been one of the principal subjects of British insurance legislation since the first step was taken in this direction by the Act of 1921. A special study would be necessary to describe the successive measures that have been taken on behalf of the unemployed. It may merely be recalled that under the system recently introduced by the 1935 Act the rights of unemployed insured persons are maintained: (1) in full during a period of free insurance, varying from 18 to 24 months; (2) after this period of free insurance, from year to year in regard to medical and maternity benefit if the insured person had been insured for ten years when his free period of insurance began. The same Act set up a special Unemployment Arrears Fund to finance the new expenditure involved and to equalise over approved societies as a whole some part of the. losses arising from unemployment. The working of this Fund is briefly summarised in the next chapter 1. MEDICAL BENEFIT All insured persons are continuously insured for medical benefit: (1) (2) (3) (4) as long as they are insurably employed; during incapacity for work; for life after attaining the age of 65 ; during 18 to 24 months after cessation of insurable employment or after recovery from incapacity which commenced during such employment ; (5) during the period of extended insurance allowed in the manner indicated above, if they prove inability to obtain employment. The cost of medical benefit was not placed on a self-supporting basis until the beginning of 1927. From that date the maximum amount to be applied for the provision of the benefit and for its administration has remained at 13s. per insured person. The total sums granted each year under the head of the various benefits are indicated in table IX, which refers to Great Britain up to 1 March 1922 and to the United Kingdom after that date. ADMINISTRATION EXPENSES The amounts allocated for the purposes of administration have been varied from time to time and the present position is as follows. Each approved society may appropriate each year for the purposes of its administration an amount equal to 4s. 6d. per member, but this amount is raised to 4s. 63/4d. if the society grants additional benefits in cash, and may also be increased by 5 per cent, of the expenditure of 1 See below, p. 472. 30 466 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION the society on additional benefits in kind. The maximum annual amount allowed for the administration of insurance committees is fixed at 6d. per insured person who is entitled to medical benefit.' The State contributes to the administration expenses in the same proportion as to the cost of benefits and in addition pays the whole cost of the administration of the central departments. The actual annual amounts expended on administration are shown in table IX below. TABLE IX. EXPENDITURE (Thousand £) Benefits Yeari 1912-13 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934l 1935 « 1936 4 Sickness 6,038 6,458 5,119 4,370 4,102 4,887 5,081 6,163 8,096 9.354 8,813 10,065 10,564 12,832 13,409 11,572 13,513 11,386 11,320 11,282 11,554 10,021 10,287 10,909 Disab- Materlement2 nity 184 832 1,108 1,232 1,309 1,396 2,002 3,063 3,877 4,397 4,820 5,253 6,364 7,424 6,397 6,691 6,596 6,306 6,497 6,306 6,545 6,643 6,727 1,223 1,368 1,270 1,221 1,045 1,009 1,188 1,924 1,994 1,881 1,793 1,747 1,751 1,807 1,787 1,798 1,784 1,850 1,808 1,754 1,621 1,634 1,644 1,717 Cost of administration Medical Other benefits s Total benefits 3,755 5,620 4,571 5,011 4,728 5,561 6,507 10,017 10,710 9,628 9,227 9,203 9,458 9,586 9,822 10,137 10,381 10,313 10,938 10,156 10,363 10,277 10,609 11,086 711 817 772 692 790 859 1,233 1,084 605 419 688 742 978 2,011 4,062 3,105 2,852 3,409 3,366 2,915 2,651 2,608 2,584 2,927 11,727 14,447 12,563 12,401 11,897 13,625 15,405 21,190 24,468 '25,159 24,918 26,577 28,004 32,600 36,504 33,009 35,221 33,554 33,738 32,604 32,495 31,085 31,767 33,366 Approved socie- Central ties and departinsurance ments committees Total 3,157 2,316 2,475 2,442 2,391 2,515 2,946 3,666 3,900 3,810 3,869 3,861 3,940 4,125 4,248 4,358 4,423 4,678 4,728 4,665 4,749 4,643 4,639 4,712 4,075 3,002 3,177 3,135 3,156 3,367 4,062 4,979 5,389 4,970 4,960 4,923 5,011 5,167 5,299 5,374 5,508 5,791 5,826 5,725 5,811 5,720 5,732 5,834 918 686 702 693 765 852 1,116 1,313 1,489 1,160 1,091 1,062 1,071 1,042 1,051 1,016 1,085 1,113 1,098 1,060 1,062 1,077 1,093 1,122 i The 1912-13 flgures relate to the period 15 July 1912 to 11 January 1914, and the 1914 flgures relate to 12 January to 31 December 1914. The later figures relate to calendar years. 2 Disablement benefit began in July 1914. s Including Sanatorium Benefit, which was discontinued in Great Britain in 1921, and in Northern Ireland on 30 September 1930. * Approximate,flgures subject to adjustment. CHAPTER III FINANCIAL SYSTEM § 1. — Financial Equilibrium The principle of the financial organisation of the health insurance scheme has not undergone any important change since the scheme was brought into operation in 1912. The structure of the financial scheme has already been indicated to some extent in the previous chapter in the reference made there to the flat rates of contribution and benefit, irrespective of age at entry and wages, and to the fixed ratios which the State grants bear to actual expenditure (for men, unmarried and married women respectively). BASIC PREMIUM The fundamental technical basis of the scheme is the constant premium relative to an insured person who normally completes his full insurance career, that is to say, joins the scheme at the age of 16. This theoretical basic premium is determined by balancing the present values of the society's obligations and expectations in respect of the insured person at the time he joins on the assumption that this takes place at age 16. It satisfies what may be called the principle of " individual equity " for insured persons joining at the minimum age. In the course of the preparatory work the basic premium for age 16 was calculated separately for each class of benefit from the biometrie and financial data mentioned in the previous chapters, account being taken not only of the cost of benefits but also of the costs of administration. The first figures arrived at were [20]: 6.58d. a week for men ; 5.47d. a week for women. The theoretical premiums so calculated were used as a basis for determining the rates of contributions to be prescribed by the Act. These were fixed slightly higher than the basic premiums, being 7d. for men and 6d. for women. It was thus expected that there would be a surplus of receipts which would provide a safety margin. This safety margin subsequently disappeared when, as a result of the adjustments made to the sickness and disablement rates t y the Actuarial Committee of 1912 the theoretical premiums came to coincide with the statutory rates of contribution [22]. By fixing the rates of contribution at the level of the theoretical basic premiums, insured persons were secured, in every case, at least as advantageous conditions as they would have found outside the health insurance scheme. This guarantee was particularly necessary in Great 468 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Britain, where the technical system introduced for the social insurance scheme was similar to that of the friendly societies already in existence. The rates of contribution have since been twice amended, but, on both occasions, they have been kept close to the basic premiums as calculated for persons of each sex entering insurance at the age of 16. RESERVE VALUES AND TRANSFER 'VALUES The financial structure of the health insurance scheme rests on the notion of an individual actuarial reserve which is simply the difference between the present values and expectations (part of the benefits and cost of administration not paid by the State) and liabilities (part of contributions credited to the institution) of each insured person with regard to the institution to which he belongs. The terminology in use in Great Britain distinguishes between the actuarial reserve at the time of entry into insurance (the reserve value) and the actuarial reserve at the time of exit by transfer to another society or otherwise (the transfer value), these two values being calculated on the assumption that the insured person at the time in question belongs to a select healthy group of persons 1. The reserve values differ from the transfer values and are always smaller because the conditions of the qualifying period reduce the expectations of the insured person during the first two years of his membership of the insurance scheme, whereas there are no similar conditions in the case of transfer from one society to another. The calculation of the actuarial reserves is based on the data mentioned in the two previous chapters. As the insured person is neither ill nor disabled at the moment of becoming insured or of transferring from one society to another, and as he therefore belongs to a specially selected group, the disablement rates mentioned above are lowered before being used for calculating the reserve values and transfer values. The tables used from 1 January 1933 [15] onwards comprise schedules of: (1) reserve values for three categories: men, spinsters and widows, married women ; (2) special reserve values for women who continue to be employed for a year after marriage; (3) transfer values applicable to persons transferring from one society to another, established separately for the above three categories, account being taken of the period of membership (under 6 months, from 6 to 12 months, one year or over) ; (4) transfer values applicable to persons ceasing to be insured, established separately for the three categories. INITIAL LIABILITY The total reserve values calculated for all insured persons affiliated to approved societies during the first 15 months of application of the Act was £69,500,000, The State subsidy (originally fixed at 2/„ of the 1 Each of these reserves differs from the general average reserve in respect of members in all states of health, such as would be required at an actuarial valuation of the Society. See below, p. 479. GREAT BRITAIN AND NORTHERN IRELAND 469 expenditure on benefits and administration in respect of men, and 1/i in respect of women) enabled provisions to be made for a proportion of the basic contribution to be retained by the central authorities in order to liquidate this initial deficiency. The sum so retained was paid into a sinking fund, which it was estimated at the outset would provide for the payment of interest at 3 per cent., and the gradual redemption of this capital sum in about 20 years, thereafter becoming available for an extension of the statutory benefits. Subsequently, the proportion of contributions retained for reserve value purposes has been varied from time to time (see table XI) and in consequence the probable date of redemption has been materially deferred \ REDEMPTION OF OUTSTANDING RESERVE VALUES The first actuarial valuation [30] showed a liability of £64,000,000 in respect of outstanding reserve values at 31 December 1918. The extension of contributions and benefits under the Act of 1920 was estimated to bring the liability up to £110,000,000, and the period needed for its redemption to 35 years. At the second actuarial valuation [35] (1922-1923) the outstanding reserve values were estimated at £97,400,000. The introduction of widows', orphans' and old-age insurance diminished the obligations of the health insurance institutions by lowering the age limit from 70 to 65 years; on the other hand, the fraction of contributions allocated to the redemption of reserve values was reduced from 1 January 1926. In consequence of these new provisions it was calculated that the liability would be completely redeemed by 1955. The third actuarial valuation [38] (1927-1929) showed a liability of £49,600,000 in respect of outstanding reserve values, and the fourth [43] (1931-1934) showed a total liability of £47,800,000. During the period between the third and fourth valuations redemption had been delayed by the admission under the Contributory Pensions Act of 1929 to voluntary insurance of a considerable number (about 60,000 men and 10,000 women) of persons in excepted employments. Since the interest on outstanding reserve values (fixed a t 3 percent.) is the first charge on the sinking fund contributions, the sum available for redemption being the balance is' peculiarly susceptible to changing conditions. During the last 15 years, when unemployment has been so prevalent, the resulting retardation of the redemption of the reserve values has been of material importance. § 2. — Financial Organisation The finances of the health insurance scheme are administered separately from the general State finances. There are four distinct National Health Insurance Funds for England, Wales, Scotland and Northern Ireland respectively, which are under the management and supervision of the Ministry of Health 1 for England and Wales, the Department of Health 2 for Scotland, and the Ministry of Labour for Northern Ireland. 1 2 See pp. 470-473. These authorities publish annual reports on the administration of health insurance. [50, 51.] 470 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION They are subject to audit by the supreme accounting authority (the Comptroller and Auditor General) who reports direct to Parliament on the results of his investigations. Within each of these four funds separate special funds are kept for insured persons belonging to particular categories: navy, army and air force, exempt persons, deposit contributors. Contributions, which constitute the main resources of the insurance scheme, are collected through the Post Office by the sale of stamps, the entire proceeds being paid to the Ministry of Health 1. They are allocated in the first instance to the four National Health Insurance Funds and then, after making the statutory deductions for reserve values, contingencies fund, the Central Fund and the Unemployment Arrears Fund are credited to the various approved societies, the Deposit Contributors' Fund, the Deposit Contributors Insurance Section, the Navy, Army and Air Force Insurance Fund, and the Exempt Persons' Fund within the four National Health Insurance Funds, according to the number of contributions claimed in respect of the different categories of insured persons or of the members of different societies. Before studying the apportionment of contributions within each National Health Insurance Fund, a brief account may be given of the principal funds on which the financial organisation of the insurance scheme essentially depends 2. RESERVE VALUES (APPORTIONMENT) ACCOUNT The fractions of contributions allocated to the service of reserve values are deducted by the Ministry of Health and paid into a sinking fund, the Reserve Values (Apportionment) Account". From 1 January 1926 this Account receives out of every normal contribution 17/ao d. in the case of men and 11/?0 d. in the case of women. Its purpose is in the first instance to pay interest at 3 per cent, per annum on outstanding reserve values and then to redeem these values. The sums not used for the payment of interest are distributed among the approved societies in proportion to the amount of their outstanding reserve values. The sums deducted from contributions within each society for the service of reserve values obviously cannot correspond to the sums finally allocated to the crediting of interest on outstanding reserve values and to their redemption. The former can be fixed as soon as the number of contributions is known, whereas the latter depend, in particular, on the age distribution of the insured population and the marita! condition of insured women. RESERVE SUSPENSE FUND The Reserve Suspense Fund is in essence a central fund within the national funds. It is created for the purpose of facilitating credits and debits in respect of reserve values and transfer values. It provides the reserve value in respect of every insured person of the age of 17 years or over becoming affiliated after 13 October 1913. It receives the transfer 1 For the sake of simplicity the supervising authority will be referred to throughout as the Ministry of Health. This term is correct only for England and Wales and should be interpreted as meaning the Department of Health for Scotland and the Ministry of Labour for Northern Ireland. 2 The position of each of these funds at the end of the year and a survey of their operations are published in an annual statement of accounts; [54], GREAT BRITAIN AND NORTHERN IRELAND 471 values in respect of persons ceasing to be insured for reasons other than death. In the event of a transier it receives the transfer value from the insured person's old society and pays it to the society to which he is transferred. The Reserve Suspense Fund provides medical benefit for persons of 65 years or over and in order that the necessary funds may be available for this purpose, it receives from approved societies on members attaining the age of 65 the appropriate sums in order to provide for the liability in respect of medical benefit for the remainder of life. It acts as a reinsurance fund in respect of marriage among insured women, receiving a fixed sum for marriage and paying out in respect of such women as remain in insurance (about one-fifth) the > reserve appropriate to a married woman of that age. It is also liable to supply the special deficiency grants made in the case of " apprehended deficiency " (i.e. where it appeared to the valuer that a deficiency would be disclosed on valuation) to cover: (a) total worsening due to the introduction of the 1926 Act ; (b) losses due to arrears of contributions arising under the 1932 and 1935 Acts. If the Reserve Suspense Fund is unable to meet these deficiency grants, the burden falls on the Central Fund' 1 . CONTINGENCIES FUNDS Attached to each society is a fund known as the contingencies fund, which serves as a primary relief fund to meet any deficiency revealed by the actuarial valuation. When there is no deficiency, the contingencies fund is added to the benefit fund after the actuarial valuation and will contribute to the amount of surplus at the following actuarial valuation. In the case of a Society with registered branches a separate valuation is made of each branch but there is a common Contingencies Fund for the whole Society against which all deficiencies in the individual branches are primarily chargeable. The income of the Contingencies Fund is drawn from a levy on contributions fixed by law at between 3 /16d. and 4/16d. Since 1 January 1936 the maximum of 4/i8d. has been levied. CENTRAL FUND The Central Fund is a joint Fund for the whole of the United Kingdom, which is administered by a joint committee of representatives of the four countries. Its essential purpose is to meet any deficiency in a society not covered by the Contingencies Funds so far as this excess deficiency is attributable to causes beyond the control of the Society, i.e. to abnormal rates of sickness due to occupation or unhealthy environment. Its chief sources of income are: 1. A levy of one-fourth of the portion of the contribution allocated for the purposes of the Contingencies Fund. This levy is only made when the position of the Central Fund renders it necessary and has in fact been discontinued since 1 January 1936; i See below p. 472. 472 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION 2. 3. 4. Annual State subsidy of £150,000 (only payable before 1921) ; Nine-tenths of sums received from unclaimed insurance stamps; Health insurance portion of contributions paid by employers in respect of persons who continue in employment after the age of 65 ; 5. Any amounts of benefits in excess of £50 when an insured person is being treated in hospital. 6. The interest of the Fund itself. Table X shows the growth of the Central Fund. TAHLE X. CENTRAL FUND Expenditure Receipts A t 31 December Contri- S t a t e butions g r a n t s Interest Miscellaneous * £ £ £ £ £ 1918-1919 1920. . . 1921. 1922. 1923. 1924. 1925. 1926. 1927. 1928. 1929. 1930. 1931. 1932. 1933. 1934. 1935. 1936. . . Unclaimed stamps Grants t o so- Other Higher cieties grants cost of in aid to so- medical of defi- cieties i benefit ciencies £ _ 157,131 986,181 450,000 276,680 150,000 100,788 943 — — 8,870 106,227 — — .— — 10,561 109,415 10,164 — — — 3,312 82,027 —- 2,661,5122 — — — 1,823 193,877 4,350 — 55 59,987 138,346 895 2,000 — 29 60,750 94,504 42 21,258 — 8 69,637 85,377 61,155 —— 10 77,192 8,457 — — — 2 81,793 — — — — 2 44,446 . 908 18,742 — — 84,000 6,544 446,242 — — — 180,605 107,421 1,453,329 6,385 — 173,118 200,000 107,386 278,418 2,185 — 192,741 347,250 127,684 286,518 30,563 — 201,165 283,625 154,858 286,128 433,191 — 225,878 268,775 150,889 276,866 51,860 — • — • £ £ • — — — • • — • 371,508 506,428 1,014,855 1,034,710 — 1,159,893 81,397 — 24.878 —'763 — 406,671 295 169,244 — 617 — 25,739 —125,547 — 789,157 — 26,340 — — — • — • Miscell- Balance aneous» at end of year £ £ 1,593,312 — 2,119,838 3,916 2,231,018 55,922 1,913,399 2,443 1,489,869 —_ 3,336,577 — 2,499,151 12,219 1,461,104 — 1,595,885 1,656,666 — 1,737,698 — 1,357,446 101,702 730,802 1,297 2,463,858 2,316 3,192,540 11,568 3,979,055 80,959 3,601,524 7,753 4,437,979 — • i Payable from the Central Fund when the Reserve Suspense Funds are unable to meet the deficit. 2 Including £100,000 as special grant under section 2 of N.H.I. (Cost of Medical Benefit) Act, 1924. 3 From 1931 onwards interest credited to National Health Insurance funds on grants paid in arrear. * From 1932 onwards the greatest part of these receipts came from the Health Insurance portion of contributions paid by employers in respect of persons who continue In employment after the age of 65. UNEMPLOYMENT ARREARS FUND This fund was set up under the 1935 Act and commenced to operate as from July 1934. In addition to meeting expenditure arising out of the extension of insurance and excusai of arrears in the event of unemployment it serves to equalise some part of the contribution losses experienced by individual societies. It is financed as to one half out of a levy on each contribution, and as to the other half out of moneys provided by the State. The levy on contributions which is retained out of the approved societies' benefit funds was fixed for the period July 1934 to December 1935 at 1 / 4 d. per contribution for men and 1/10d. per contribution for women. As from January 1936, owing to the improvement in employment, the levy has been reduced to 1/td. for men and 1/12d. for GREAT BRITAIN AND NORTHERN IRELAND 473 women. A further reduction in the levy to 1/12d. for men and 1/2id. for women came into operation from the beginning of 1937. Out of this Fund there is credited to the approved societies S1/^. for each week of proved unemployment per member. APPORTIONMENT OF CONTRIBUTIONS The essential machinery of the financial organisation of the scheme and the changes that have taken place since its inception are brought out by the following table, which shows the main figures successively adopted for the apportionment of contributions. TABLE XI. — APPORTIONMENT OF WEEKLY CONTRIBUTION From 15/7/1912 (revised in 1918 A c t retrospectively) Men | W o m e n For the benefit funds . For protective reserves. . For service of reserve values . Total . . Prom 15/7/1912 to 4/7/1920 (according t o 1918 Act) Men |Women From 5/7/1920 to 31/12/1920 From 1/1/1921 t o 31/12/1925 From 1/1/1926 Men | Women Men ¡Women Men d. d. d. d. d. d. d. |Women d. 5«/. 4V, 5*/. 4V. 7V. 7V« 7'/. -71/. 'Vio V. Va V. V. V. V. V« 17/ ISO 11 IV. IV, IV. 7 6 7 6 Va. IVa 10 V. IV» 9 IVa 10 d. d. 1 7Vl0 X 1 '20 9 9 »vT i As from 2 July 1934 these figures include the levies for the benefit of the Unemployment Arrears Fund. § 3 . — Actuarial Balance-Sheets An analysis was given in the preceding paragraph of the basis of financial equilibrium and the essential features of the financial organisation of the insurance scheme. The documents showing the financial situation, i.e. the actuarial balance-sheets drawn up as a result of each of the actuarial valuations, will now be reproduced. The principal items in those balance-sheets are: 1. On the liabilities side the total present probable value of benefits and administration expenses; 2. In the assets side the total present probable value of contributions, the total present probable value of State subsidies and the amount of accumulated funds. The present values are calculated for the insured population existing at the date of the valuation in each society on the basis set up in the Valuation Regulations in force. The amount of accumulated funds is estimated in accordance with definite rules to which reference will be made later 1 . The funds of the societies shown in the valuations include 1 See p. 479. 474 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION the amount of unredeemed reserve values. The difference between the present probable value of benefits including cost of administration, and the present probable value of the part of the contributions credited to the societies, increased by the present probable value of State grants, represents the general average reserve, which can also be computed directly. Special grants to prevent deficiencies from appearing 1 operated from 1 June 1926 and are included as assets in both the third and fourth actuarial balance-sheets. In the former instance, however, they were included under the heading of " other assets " and in the latter they were shown as a separate item. TABLE XII. — SUMMARIES OF VALUATIONS BALANCE-SHEETS 1st Valuation (31 December 1918) (rate of interest 3 % p.a.) LIABILITIES £ Present Value of Benefits, and Cost of Administration 451,307,197 Contingencies Funds 6,569,449 Other Liabilities 1,154,347 Administration Balances, etc 2,378,075 Surpluses . . 17,273,887 less Deficiencies 80,919 Net Surplus . ASSETS £ Present Value of Future Contributions 253,995,536 Present Value of State Grants 103,599,634 Total Funds . 119,479,279 Other Assets 1,527,587 17,192,968 478,602,036 478,602,036 2nd Valuation (1922-1923) (rate of interest: 3 % P-a-) LIABILITIES ASSETS £ Present Value of Benefits, and Cost of Administration 610,475,666 Other Liabilities 32,158 Surpluses . . 42,413,319 less Deficiencies 91,675 Net Surplus Present Value of Contributions 333,013,790 Present Value of State Grants 135 584,752 Total Benefit Funds . . . 180,973,104 Appreciation in the Value of Securities 1,651,285 Other Assets 1,606,537 42,321,644 652,829,468 652,829,468 3rd Valuation (1927-28-29) (rate of interest: 4% p.a.) LIABILITIES £ Present Value of Benefits, and Cost of Administration - . 541,745,721 Surpluses . . 36,638,344 less Deficiencies 847,667 Net Surplus 1 See above, p. 471. ASSETS £ 35,790,677 Present Value of Contributions 330,703,314 Present Value of State Grants 86,788,868 Total Benefit Funds . . . 156,023,648 Appreciation in the Value of Securities 2,198,060 Other Assets 1,822,508 577,536,398 577,536,398 475 GREAT BRITAIN AND NORTHERN IRELAND 4th Valuation (1931-32-33-34) (rate of interest: 4% p.a.) ASSETS LIABILITIES £ Present Value of Benefits, and Cost of Administration 550,905,913 Surpluses . . 37,484,686 less Deflcien• cies . . . . 740,983 Net Surplus 36,743,703 587,649,616 Present Value of Contributions Present Value of State Grants Total Benefit Funds . . . Special Grants made in the case of " apprehended deficiency " under Section 3 of the National Health Insurance Act, 1926 Other Assets £ 340,500,696 87,602,106 157,495,239 946,661 1,104,914 587,649,616 CHAPTER IV FINANCIAL ADMINISTRATION § 1. — Investment of Funds The Minister ascertains periodically the sums standing in the National Health Insurance Fund to the credit of each approved society, the Navy, Army and Air Force Insurance Fund, the Deposit Contributors Fund, the Deposit Contributors Insurance Section, and the Reserve Suspense Fund, which are available for investment. One half of the sums so ascertained in respect of a society is carried to a separate account called the " Investment Account " and the remaining half is, at the option of the society, (a) paid over to. the society for investment, or (b) invested by the Minister on behalf of the society in securities selected by the society, or (c) carried to the credit of the society with the other half in the Investment Account. INVESTMENT OF FUNDS STANDING IN THE INVESTMENT ACCOUNT Sums carried to the credit of societies in the Investment Account (together with other balances in the National Health Insurance Fund, the Central Fund and the Unemployment Arrears Fund not required to meet current liabilities) must be paid over to the National Debt Commissioners, and by them invested in accordance with regulations made by the Treasury in any securities which are for the time being authorised by Parliament as investments for Savings Banks funds 1. The Commissioners must, in making the investment, give preference to stocks or bonds issued under the provisions of the Acts relating to borrowing for raising capital for the purposes of the Local Loans Fund where the purpose for which the capital is required is the making of advances for the purposes of the Housing Act, 1936. The Commissioners must present to Parliament annually an account of the securities held by them in which moneys forming part of the National Health Insurance Fund, the Central Fund, and the Unemployment Arrears Fund are for the time being invested. Selection by the National Debt Commissioners from among the authorised investments is the responsibility of the Commissioners themselves, although they may ascertain the views from time to time 1 The investments authorised for Savings Banks Funds are securities issued by the authority of Parliament, the interest on which is a charge on the Consolidated Fund of the United Kingdom. GREAT BRITAIN AND NORTHERN IRELAND 477 of the Financial Advisers to the National Health Insurance Joint Committee. The financial advisers are the Government Actuary and the ccountant-General of the Ministry of Health. The holdings of the National Debt Commissioners at 31 December 1937 on behalf of the National Health Insurance Funds were as follows: 1. Investments on behalf of approved Societies, the Deposit Contributors Fund, the Navy, Army and Air Force Insurance Fund, and the Reserve Suspense Fund (for Great Britain) : £ 2y2 percent. Consolidated Stock Local Loans 3 per cent. Stock Guaranteed 2% per cent. Stock Guaranteed 3 per cent. Stock 3y2 per cent. War Stock 4 per cent. Funding Stock, 1960-1990 . . . 3% per cent. Conversion Stock 4 per cent. Consolidated Stock 3 per cent. Funding Stock, 1959-1969 . . . 2. 190,000 72,572,256 2,466,176 4,167,997 20,438,305 712,549 10,524,259 5,748,100 686,816 Investments on behalf of the Central Fund: £ Local Loans 33 per cent. Stock . . . . . . Guaranteed 2 /4 per cent. Stock Guaranteed 3 per cent. Stock 3y2 per cent. War Stock 4 per cent. Funding Stock, 1960-1990 . . . 3Í4 per cent. Conversion Stock 4 per cent. Consolidated Stock 3 per cent. Funding Stock, 1959-1969 . . . 3. 2,293,088 62,179 99,298 1,791,262 34,039 1,922,316 348,330 14,193 Investments on behalf of the Unemployment Arrears Fund: £ Local Loans 3 per cent. Stock 3% per cent. War Stock 3% per cent. Conversion Stock 414,718 318,176 16,445 INVESTMENT OF SUMS PAID OVER TO SOCIETIES AND INVESTMENTS BY THE MINISTER OF HEALTH ON BEHALF OF SOCIETIES Every approved society must invest any sums paid to the society for investment, and must for the purpose have power to invest in any investments in which trustees are for the time being by law empowered to invest trust funds \ or in any stocks, mortgages or other securities issued by any local authority within the meaning of the Local Loans Act, 1875, and charged on any rates levied by or on the order or precept 1 Investments open to trustees under the Trustee Act, 1925, and the Trusts (Scotland) Act, 1921, in addition to those open to the National Debt Commissioners as mentioned above, include stocks issued by the Indian, Dominion and Colonial Governments, mortgages on real property and in certain circumstances debentures and. guaranteed or preference stocks of railway companies. 478 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION of that authority, or in any other securities * for the time being approved by the Minister. Where a Society has to realise funds to meet current expenditure it must draw proportionately from the Investment Account and its own investments. The investments held by Societies themselves and by the Minister on their behalf at 31 December 1937 are approximately summarised as follows: British Government securities Indian and Colonial securities Local Authorities' securities Railways Other securities 38,758,000 8,324,000 8,070,000 3,322,000 1,125,000 A detailed statement of the investments held by the Ministry of Health on behalf of approved societies in securities selected by them was published annually up to and including 1930 [54]. Each of the actuarial valuations briefly indicates how the securities of the approved societies are distributed over the main types of investment. This information is reproduced in the following table. TABLE XIII. ' INVESTMENTS OF APPROVED SOCIETIES AT THE VALUATION DATES (in thousands of £) At the second valuation At the first valuation Mortgages and loans . . . . British G o v e r n m e n t securities British Local A u t h o r i t i e s ' securities Other investments 262 14,682 1,693 1 3,100 33,656 At the fourth valuation At the third valuation 2 1,271 1,600 5,418 42,524 2,511 5,488 2 6,692 43,435 2 2,636 4,991 i This figure represents 8,673 thousands of £ invested in War Loans and 6,009 thousands of £ in War Bonds, other British Government securities being included under the figure 1,693 shown below. 2 Including Dominion, Indian and Colonial Government securities. Table XIV opposite shows the total accumulated funds at the end of each year. § 2. — Valuation of Investments The value of the investments forming part of the Benefit Funds shown on the assets side of the actuarial balance-sheet is calculated in each case in accordance with the rules laid down in administrative regulations. The various methods employed in the four actuarial valuations that have so far been made will now be described. 1 The Minister has not approved any other securities beyond allowing certain Societies to use money available for. investment for the purchase of property for use as their own offices. GREAT BRITAIN AND NORTHERN IRELAND 479 TABLE XIV. — TOTAL ACCUMULATED FUNDS AT 31 DECEMBER EACH YEAR (thousands of £) Total at 31 December Great Britain | United Kingdom 22,983 — 32,749 — 41,224 — 51,446 — 62,119 — 71,882 — 81,443 — 92,231 — 101,879 — 111,023 —. 118,284 — 128,369 — 128,187 • 126,519 — 127,684 — 126,925 127,991 — 129,319 — 128,906 — 128,767 — 131,272 134,736 137,823 — Year - 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1 1935 1 1936 x — • i Approximate figures subject to adjustment. In the first actuarial valuation, securities were taken at the purchase price less the accrued interest. In the second and third valuations investments in securities quoted on the Stock Exchange were valued at the middle market prices (less accrued interest) on the valuation date. The adoption of this second method showed an appreciation in the investments due to differences between the purchase price and the market quotation. The amount of the appreciation of securities was shown as a separate item on the assets side of the second and third actuarial balance-sheets. In the fourth valuation the fixed-yield securities quoted on the Stock Exchange were valued at an actuarial amount, namely at such an amount that the interest income would be equivalent to a yield of 4% per cent., appropriate provision being made in the case of redeemable securities. In this way the appreciation in investments was estimated at about £1,800,000, and in addition net profits of nearly £500,000 had accrued between the third and fourth valuations from the realisation of securities. § 3. — Interest Rates The rate of interest used for actuarial purposes remained fixed at 3 per cent, until 1 January 1926, since when it has been 4 per cent. The sum credited to the societies, however, as interest on their outstanding reserve values are still calculated at 3 per cent. The flat rate of interest payable.from time to time on the sums standing to the credit of societies in the Investment Account is dependent upon the interest received and is prescribed by the Joint Committee by Regu- 480 ACTUARIAL T E C H N I Q U E AND F I N A N C I A L ORGANISATION lations on the advice of their financial advisers. Profits on realisation of investments are set off against any losses on realisation and any balance together with any undistributed interest acts as a reserve against depreciation and tends to ensure stability in rate of interest. The income from the sums placed to the credit of the societies in the Investment Account was calculated on the basis of a rate of interest of 3V4 per cent, up to 31 December 1917; this rate was subsequently raised to 4 per cent., 41/¡¡, and finally to 5 per cent. The prescribed rate of interest payable on sums invested in the Investment Account is, since the beginning of 1936,5 per cent, for moneys placed in the account before 1 January 1936 and 3 per cent, for othef moneys. The yield on the whole assets of the societies, including the outstanding reserve values which carry 3 per cent, interest only, is estimated to have been about 4 x / 4 per cent, for the period between the third and fourth valuations. § 4. — Actuarial Valuations An actuarial valuation relating to all the approved societies in the United Kingdom is usually made every five years under the supervision of the Government Actuary l . In the first valuation the position of all the approved societies in Great Britain and Ireland as at 31 December 1918 was considered. The second valuation was made as at 31 December 1922 for about half of the societies covering about one-fifth of the total numbers insured and as at 31 December 1923 for the remainder. In the third valuation the approved societies were divided into three groups and the valuations related to the end of 1927,1928 and 1929 respectivelv1. The fourth actuarial valuation was carried out in four stages, as àt the end of 1931," 1932, 1933 and 1934. For administrative efficiency and economy the work of valuing the societies is spread out so as to be carried on almost without interruption. A special report was made by the Government Actuary on the results of each of the actuarial valuations [30, 35, 38, 43]. Only a brief account 2 can be given here of the principles on which the actuarial valuations are based and the methods by which they are carried out 3 . The first step is to make an estimate year by year of the number óf insured persons and of their distribution according to age. The results of these estimates depend on the biometrie laws adopted and are based on the hypothesis that these laws will continue to apply in the future. In the light of the provisions of the legislation and the financial basis laid down therein, the probable income and expenditure for any given year in the future may then be calculated. By assuming an invariable rate of interest it is thus immediately possible to obtain the probable present value of the liabilities and expectations of each insurance institution. Before each actuarial valuation is carried out administrative regulations are issued, defining the bases to be followed in the course of the operations [14], As a result of the actuarial valuation of a society or section, an ac1 A separate valuation is made for each centralised society and for each branch in the case of a society with registered branches. 2 For a fuller account cf. Bibliography,.No. 43, pp. 4 and 5. 3 Figures taken from the reports on the actuarial valuations have frequently been quoted in these pages. GREAT BRITAIN AND NORTHERN IRELAND 481 tuarial balance-sheet is drawn up which may show either a surplus or a deficiency. The actuarial balance sheet of all approved societies and their branches taken together constitutes the general actuarial balancesheet which was reproduced above 1. The results' of the actuarial valuations also include detailed information concerning the societies showing a surplus and those showing a deficiency. The table below gives the principal statistics of surpluses for the four actuarial valuations. 2nd 3rd 4th Societies with a surplus Total amount of surplus (Membership) (£) Average surplus per member (£) 15,928,428 14,970,275 15,222,143 15,473,186 17,273,887 42,413,319 36,638,344 37,484,686 1.08 2.83 2.41 2.42 ,, „ The purpose of the valuation is not only to calculate the total surplus, but also to determine what part of it is to be regarded as disposable. The valuer is required, in the exercise of his professional judgment to certify what part (if any) of the surplus may appropriately be applied in additional benefits during the ensuing quinquennium, having regard to the circumstances and prospects of the society. In the four valuations the estimated disposable surplus was as follows : Amount of surplus Membership of societies with surplus of societies with disposable surplus (a) (« 1st valuation 15,928,428 14,370,148 14,970,275 14,726,636 2nd 15,222,143 11,588,144 3rd 15,473,186 14,733,621 4th Fraction Total Disposable surplus Fraction (6) (a) (c) £ (d) £ (d) (c) 0.90 0.98 0.76 0.95 9.184,087 17,273,887 42,413,319 26,619,161 36,638,344 19,811,266 37,484,686 20,105,033 0.53 0.63 0.54 0.54 The amount of the disposable surplus having been calculated, it remains to decide how to distribute it. If a society is certified to have a disposable surplus, it may use it for granting additional benefits, which are spread, as a rule, over a five-year interval beginning two years after the valuation date. The additional benefits are granted in accordance with rules laid down in a scheme which is drawn up by the managing body of the society, with the help of estimates regarding the anticipated i Table XII. 3i 482 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION costs which are included in an appendix to the valuation report. The scheme must be referred to the Central Department for approval. T h e table below gives the total results of the four actuarial valuations for societies with deficiencies. 1st valuation 2nd 3rd 4th Societies with a deficiency (Membership) Total amount of deficiency 322,350 228,110 722,131 667,752 80,919 91,675 847.667 740,983 (£) Average deficiency per member (£) 0.25 0.40 1.17 1.11 If t h e valuation shows t h a t there is a deficiency, this automatically brings into play t h e mechanism of relief, which works in two stages: • (1) recourse t o the primary relief afforded within each society by its contingencies fund; (2) recourse t o the secondary relief afforded by the Central F u n d . The statistics of these operations are as follows: 1st valuation 2nd 3rd „ 4th ,, Number of societies with a deficiency Number of societies covering deficiency out of contingency fund 407 134 418 292 403 126 310 244 Number of claims to the Central Fund 4 8 24 ! 34 2 i One from a branch society which had 85 branches in deficiency. 2 One from a branch society with 15 branches in deficiency. The position of the contingencies funds of all the societies together was as follows: £ 1st valuation 2nd „ 3rd „ 4th „ 6,569,000 5,825,000 5,225,000 3,254,000 T h e a m o u n t of the deficiencies in regard to which the question of grants from the Central F u n d arose w a s : £ 1st valuation 2nd „ 3rd „ 4th „ ' . . 11,107 23,258 502,969 505,107 GREAT BRITAIN AND NORTHERN IRELAND 483 Before recourse was had to the Contingencies Funds or to the Central Fund, special deficiency grants 1 were, in the third and fourth valuations, credited to the societies in all cases of apprehended deficiency. At the third and fourth valuations equality of assets and liabilities was produced in 177 and 228 units by grants of £83,445 and £250,670 respectively, while deficiencies were reduced in 399 and 292 units by grants of £436,962 and £695,991 respectively. The report of the Government Actuary on the results of each valuation also includes: (1) an analysis and review of the sources of profit and loss; (2) suggestions for ensuring the financial equilibrium of the scheme. In actual fact, the considerations and recommendations contained in the four reports [30, 35, 38, 43] published in 1922, 1927, 1931 and 1937 have had the greatest influence, and are the origin of most of the amendments made in the legislation. BIBLIOGRAPHY I. — Legislative and Administrative Texts 1. National Health Insurance Act, 1920. L. S. 2, 1920, G.B. 2. 2. National Health Insurance (Prolongation of Insurance) Act, 1921. L. S., 1921, G.B. 1. 3. National Health Insurance Act, 1922. L. S., 1922, G.B. 4. 4. National Health Insurance (Cost of Medical Benefit) Act, 1924, L. S., 1924, G.B. 2. 5. National Health Insurance Act, 1924. L. S., 1924, G.B. 6. 6. Economy (Miscellaneous Provisions) Act, 1926. L. S., 1926, G.B. 7. 7. National Health Insurance Act, 1928. L. S., 1928, G.B. 2. 8. National Health Insurance (Prolongation of Insurance) Act, 1930. L. S., 1930, G.B. 11. 9. National Economy Act, 1931. L. S., 1931, G.B. 9. 10. National Health Insurance (Prolongation of Insurance) Act, 1931. L. S., 1931, G.B. 11. 11. National Health Insurance and Contributory Pensions Act, 1932. L. S., 1932, G.B. 8. 12. National Insurance and Contributory Pensions Act, 1935. L. S., 1935, G.B. 2. 1 2 See above, p. 474. The Legislative Series of the International Labour Office. / 484 13. 14. 15. 16. 17. 18. ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION National Health Insurance Act (Consolidation), 1936. G.B. 8. National Health Insurance (Valuation) Regulations. S. R. and O., 1919, No. 1119 1. S. R. and O., 1924, No. 1316. S. R. and O., 1929, No. 415. S. R. and O., 1933, No. 552. S. R. and O., 1938, No. 281. L. S., 1936, National Health Insurance (Reserve and Transfer Values) Regulations. S. R. and O., 1924, No. 1468. S. R. and O., 1928, No. 403. S. R. and O., 1935, No. 465. S. R. and O., 1936, No. 1314. National Health Insurance (Investment Account) Regulations. S. R. and O., 1924, No. 1459. National Health Insurance (Investment Account Rate of Interest) Regulations. S. R. and O., 1932. No. 155. S. R. and O., 1936, No. 664. National Health Insurance (Juvenile Contributors and Young Persons) Act, 1937. L. S., 1937, G.B. 4. II. — Reports and Memoranda a 19. An Account of an Investigation of the Sickness and Mortality Experience of the Independent Order of Oddfelloivs (Manchester Unity) during the five years 1893-1897. Manchester, 1903. 20. Report of the Actuaries in relation to the Scheme of Insurance against Sickness, Disablement, etc., embodied in the National Insurance Bill, 1911. Cd. 5681 of 1911. 21. Report of the Actuaries in relation to the National Insurance Bill as amended in Committee. Cd. 5983 of 1911. 22. Report for 1912-13 on the Administration in England of the National Insurance Act. Part I (Health Insurance). Cd. 6907 of 1914. 23. Report for 1913-14 on the Administration in England of the National Insurance Act. Cd. 7469 of 1914. 24. Interim Report of the Departmental Committee on Approved Society Finance and Administration. Cd. 8251 of 1916. 25. Further Report of the Departmental Committee on Approved Society Finance arid Administration. Cd. 8396 of 1916. 26. Final Report of the Departmental Committee on Approved Society Finance and Administration. Cd. 8451 of 1917. 27. Memorandum explanatory of the Provisions of the National Health Insurance Bill, 1917. Cd. 8816 of 1917. 28. Report on the Administration of National Health Insurance during the years 1914-17. Cd. 8890 of 1917. 29. National Health Insurance Bill, 1920. Report by the Government Actuary upon the Financial Provisions of the Bill. Cmd. 612 of 1920. 1 S. R. and O. is the abbreviation used for the collection of orders and rules published under the title " Statutory Rules and Orders ". a All these documents, with the exception of the first, are published by H.M. Stationery Onice. GREAT BRITAIN AND NORTHERN IRELAND 485 30. Report by the Government Actuary on the Valuations of the Assets and Liabilities of Approved Societies as at 31st December 1918. Cmd. 1662 of 1922. 31. Memorandum on the National Health Insurance Bill (cost of medical benefit). Cmd. 2102 of 1924. 32. Widows', Orphans' and Old-Age Contributory Pensions Bill. Report by the Government Actuary on the Financial Provisions of the Bill. Cmd. 2406 of 1925. 33. Report of the Royal Commission on National Health Insurance. Cmd. 2596 of 1926. 34. Economy (Miscellaneous Provisions) Bill. Report of the Government Actuary on the Clauses of the Bill relating to National Health Insurance. Cmd. 2603 of 1926. 35. Report by the Government Actuary on the Second Valuation of the Assets and Liabilities of Approved Societies. Cmd. 2785 of 1927. 36. Report by the Government Actuary on an Examination of the Sickness and Disablement Experience of a Group of Approved Societies in the period 1921-27. Cmd. 3548 of 1930. 37. Prolongation of Insurance. Memorandum by the Minister of Health and the Secretary of State for Scotland explaining the Proposed Financial Resolutions. Cmd. 3966 of 1931. 38. Report by the Government Actuary on the Third Valuation of the Assets and Liabilities of Approved Societies. Cmd. 3978 of 1931. 39. National Health Insurance and Contributory Pensions Bill. Memorandum explanatory of the Bill by the Minister of Health and the Secretary of State for Scotland. Cmd. 4072 of 1932. 40. National Health Insurance and Contributory Pensions Bill, 1932. Report by the Government Actuary on the Financial Provisions of the Bill. Cmd. 4073 of 1932. 41. National Health Insurance and Contributory Pensions Bill, 1935. Memorandum explanatory of the Bill by the Minister of Health and the Secretary of Stat« for Scotland. Cmd. 4905 of 1935. 42. National Health Insurance and Contributory Pensions Bill, 1935. Report by the Government Actuary on the Financial Provisions of the Bill. Cmd. 4906 of 1935. 43. Report by the Government Actuary on the Fourth Valuation of the Assets and Liabilities of Approved Societies. Cmd. 5496 of 1937. III. — Books and Articles 44. P. N. HARVEY: "The Scheme of National Health Insurance considered in Relation to the Valuations of Approved Societies as at 31 December 1918" (Journal of the Institute of Actuaries, Vol. LIV, Part I I , July 1923). 45. M. B. KNOWLES: "Social Insurance in Great Britain. The System of National Health Insurance" (Transactions of the Eighth International . Congress of Actuaries, June 1927). 46. Sir A. W. WATSON: "National Health Insurance: A Statistical Review" (Journal of the Royal Statistwal Society, Vol. XC, Part I I I , 1927). 47. I D . : "The Analysis of a Sickness Experience" (Journal of the Institute of Actuaries, Vol. LXI1, Part I, July 1931). 48. W. J. FOSTER and F. G. TAYLOR : National Health Insurance. London, 1937. 49. Approved Societies Handbook. H.M. Stationery Office. 486 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION IV. —'• Reports on Operation of Scheme 50. 51. 52. 53. 54. Annual Report of the Ministry of Health. London. Annual Report of the Department of Health for Scotland. Edinburgh. Abstract of Labour Statistics of the United Kingdom. Statistical Abstract for the United Kingdom. National Health Insurance Fund Accounts (Annual Accounts with Appendix). 55. Account showing the nature and amount of the securities held by the Commissioners for the Reduction of the National Debt as investments for moneys forming part of the National Health Insurance Funds. PART II WIDOWS', ORPHANS', AND OLD-AGE CONTRIBUTORY PENSIONS CHAPTER I DEMOGRAPHIC ESTIMATES, BASES, AND EXPERIENCE § 1. — Biometrie Tables MORTALITY TABLES In 1925, during the preparatory work '[9] which preceded the introduction of the widows', orphans' and old-age contributory pensions scheme, it was observed in the first place that death rates showed a general and continuous tendency to fall. The conclusion was drawn that none of the existing mortality tables could be used, and it was therefore decided to construct a new table on the basis of the 1921 population census data relating to England and Wales1 and. the registered deaths in the two years 1920 and 1921. This table was adopted both for National Health Insurance and for the Contributory Pensions scheme. It showed, for the middle period of life, mortality rates substantially below those contained in the English Life Table, No. 8,1910-12. Further, it was assumed that the mortality rates of the insured population would be materially above those for the whole population of England and Wales; to some extent a margin was thus provided to meet the contingency, considered probable, of a continued fall in death rates. For England and Wales no information was available on the influence of marital condition on the male death rate. The statistics for Scotland showed a lighter death rate for married men than for the whole male population; it was decided that the difference should be retained as a possible margin in the value of the liability and that the rates relating to the whole male population should be uniformly applied. Mortality tables compiled previously on the basis of population censuses and registered deaths had shown higher death rates for widows than for the female population as a whole. On the other hand, it was expected that the comparatively high rates of remarriage would fall in consequence of the operation of the Act. The selective influence was 1 See Part I, Chapter I, section 1, p. 449; and table I, p. 450. 488 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION therefore held to be small, and it was assumed that the mortality rates for widows would tend to approach those for the whole female population. In addition, the pensions granted to widows and orphans would improve the conditions of widows and would thus directly tend to reduce their death rate. After consideration of these various arguments, it was decided that the mortality tables which had been constructed for each sex should be applied uniformly to all insured persons and beneficiaries in Great Britain whatever their marital condition. In calculating the value of allowances to orphans, the rate of mortality for the first year of life was taken at 0.075 and that for the following year of life at 0.025; above that age it was deemed to be negligible. The estimates, included in the Actuarial Report which appeared in 1935 [16], are based on: (1) mortality rates for the whole population of Great Britain, shown separately for each sex; (2) special mortality rates for married men and for widows. The first of these rates were deduced from the census population of 1931 and the deaths registered in the three years 1930-1932. The rates for married men were determined on the basis of the general death rate for men in Great Britain and of the statistics for Scotland, where the marital condition at death is recorded. The rates for widows were derived from experience of the contributory pensions scheme. These various mortality rates are shown in the table below: TABLE I. RATES OF MORTALITY All men Married m e n Age W (2) 16... ; .. 20 25 . . . . . . . 30 35 40 . . . . . . 45 50 55 60 65 70 75 80 85 90 0.0023 0.0032 0.0033 0.0034 0.0043 0.0057 0.0081 0.0113 0.0162 0.0243 0.0381 0.0606 0.0956 0.1456 0.2106 0.2872 0.0014 0.0021 0.0023 0.0028 0.0038 0.0050 0.0072 0.0101 0.0146 0.0220 0.0347 ' 0.0551 0.0870 0.1325 0.1916 0.2614 1 All women 1 (3). 0.0022 0.0027 0.0030 0.0033 0.0037 0.0045 0.0060 0.0083 0.0119 0.0180 0.0278 0.0450 0:0748 0.1193 0.1806 0.2531 Widows2 (4) 0.0050 0.0050 0.0050 0.0050 0.0053 0.0059 0.0071 0.0095 0.0135 0.0191 0.0299 0.0465 — — — — 1 These rates of mortality represent the probabilities of dying within one year of the age stated. . .. 2 For ages over 70, rates for " all women " were used. TABLES SHOWING MARITAL CONDITION The proportion of married, single, and widowed insured persons of each sex was calculated in 1925 [9] from the 1921 census statistics for England and Wales, leaving the category of war-widows out of account. GREAT BRITAIN AND NORTHERN 489 IRELAND In estimates subsequently made [16], the following figures, based on the 1931 census returns for Great Britain, were substituted: TABLE I I . PROPORTIONS OF P E R S O N S S I N G L E , MARRIED AND W I D O W E D USED IN THE CALCULATIONS FOR T H E FIRST D E C E N N I A L R E V I E W , 1 9 3 5 (per thousand in each age group) Men Age group Bachelors Married Widowers Spinsters Married 996 863 480 227 143 119 115 112 109 105 100 89 79 .67 59 4 136 515 762 840 856 849 833 807 765 702 616 504 389 266 — 977 745 416 257 212 186 173 164 162 161 164 163 156 151 149 23 254 577 725 749 745 728 702 651 568 456 337 219 125 60 » 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 "Women s ï > î » » » J > > ) ï 85 and o 1 5 11 17 25 36 55 84 130 198 295 417 544 675 Widows 1 7 18 39 69 99 134 187 271 380 500 625 724 791 As regards the relative ages of husband and wife, the probabilities of the different combinations were at first [9] taken from a combined table based on the 1911 census returns for England and Wales. Subsequently, estimates were based on the combined table below, derived from the actual working of the scheme: TABLE I I I . PERCENTAGE AGE D I S T R I B U T I O N S OF W I V E S U N D E R AGE 7 0 FOR VARIOUS AGES OF HUSBANDS Ages of husbands Age of wives Under 20 yrs. 20-25 » 25-30 >• 30-35 » 35-40 " 40-45 » 45-50 » 50-55 " 55-60 » 60-65 » 65-70 » AH ages u n d e r 70 Un- I 85 der 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 and 20 1 over 52.0 44.0 3.4 0.5 0.1 8,7 69.5 19.6 1.8 0.3 0.1 0.8 27.1 57.8 12.2 1.7 0.3 0.1 0.1 4.2 31.3 51.0 11.3 1.7 0.3 0.1 0.8 7.2 32.0 46.6 11.2 1.8 0.3 0.1 0.2 1.8 9.0 30.9 44.5 11.2 1.9 0.4 0.1 0.1 0.6 2.5 9.4 29.9 43.7 11.2 2.1 0.4 0.1 0.1 0.3 1.1 3.1 9.7 29.0 42.8 11.3 2.1 0.5 0.1 0.5 1.4 3.5 10.0 29.9 41.5 11.2 1.9 0.1 0.3 0.7 1.8 4.1 10.5 31.9 40.6 10.0 0.1 0.1 0.5 0.9 2.4 5.4 14.6 36.0 40.0 0.1 0.1 0.4 1.1 2.3 5.5 10.7 22.3 57.5 0.1 0.3 0.9 1.9 4.0 7.4 13.1 23.5 48.8 0.2 0.4 0.9 1.9 4.7 8.6 14.1 25.1 44.1 0.4 0.7 1.3 2.2 4.3 10.6 17.2 24.3 39.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 For the rate of remarriage of widows recourse was had in the original estimates, in the absence of more recent and suitable statistics, to the figures previously compiled [9] on the basis of the experience during 490 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION the period 1854-1900.of the Patriotic (Russian War) Fund. These rates, classified according to the number of years completed since widowhood were applied to the numbers of new widows arising in the general population for a series of years prior to 1911: the aggregation of the survivors of these widows reproduced very closely the numbers of widows enumerated at various ages at the 1911 census. It was therefore decided to adopt these rates of remarriage, but to allow for the effect of the cessation of pension on remarriage by reducing them by one-third. The experience gained from the working of the contributory pensions scheme made it possible to establish new rates of remarriage of widows, reproduced below: TABLE IV. Age of widow at death of husband RATES OF REMARRIAGE OF WIDOWS' Probabilities per 1,000 Probabilities per 1,000 of remarriage during the undermentioned of remarperiods (in years) after widowhood riage during the year following the io%- n%4%ey attained 8%13%»%14%%IV,tv,Wr?%? 0-% 1% t% 3% iy2 % 6% '1% 8% »% »y. uy2 «% 13% u% 1% agei m- w- 22yrs. 15 93 153 154 147 136 120 100 82 67 56 48 42 37 32 28 27 >• 15 78 106 102 95 85 72 59 48 40 34 29 25 21 18 15 32 12 58 71 66 60 52 43 34 27 22 18 15 12 10 8 7 37 10 41 48 43 37 30 24 18 14 11 9 7 5 4 3 3 42 » 27 30 25 21 17 14 11 8 6 4 3 2 2 2 1 47 16 19 15 12 9 7 5 4 3 2 1 1 1 1 •1 52 » 9 11 8 6 4 3 2 1 1 ' 1 1 1 1 1 1 57 5 6 4 2 1 1 1 1 1 0 0 0 3 3 2 1 1 0 0 0 62 -• i 1 — 24 21 18 16 14 12 10 9 8 7 6 5 4 3 3 2 2 2 2 0 0 0 — * These rates are applicable only to women who at the attained age have been widowed for more than 15 years. GREAT BRITAIN AND NORTHERN 491 IRELAND TABLES SHOWING COMPOSITION OF FAMILY In the original estimates [9] the payments to children of widows and to orphans were calculated by means of a combined table giving the distribution of children by age and by the age at death of the father. This table, which is reproduced below, is based essentially on the probabilities of survival and the probabilities of issue for men. The latter probabilities were obtained from the figures which had been calculated for purposes of the National Health Insurance scheme by the Actuarial Committee of 1912 *: a reduction of 15 per cent, was introduced to allow for the fall in the birth rate between the pre-war and immediate post-war years. The figures obtained were checked and found after some adjustment to be compatible with the information on the composition of the family obtained from a special question which was included in the 1921 census schedule. TABLE V. — NUMBER OF CHILDREN UNDER AGE 1 4 LEFT BY 1 , 0 0 0 MARRIED MEN AND WIDOWERS DYING AT THE AGES SHOWN Age of father Ages oí children 22 ti 27*4 01 0-1 year 1-2 years 2-3 » 3-4 » 4-5 » 5-6 » 6-7 » 7-8 » 8-9 " 9-10 » 10-11 » 11-12 » 12-13 » 13-14 » Totals 182 363 191 85 24 5 — — — —. — — —^ — — 138 275 229 196 166 130 94 55 26 7 2 — —— — 32 54 37 ti 42 H 108 217 201 187 187 176 167 156 138 117 93 67 40 18 5 11 154 145 150 156 162 164 170 163 165 156 149 139 123 105 43 86 87 94 104 113 124 131 139 146 153 155 162 155 156 47% 52>/2 57 H 62 ti 67 yt 20 40 42 47 54 62 71 80 89 100 108 119 126 134 142 8 15 17 20 23 28 33 38 45 53 60 69 77 87 96 2 5 6 7 8 11 13 15 19 22 26 31 37 43 51 1 2 2 3 3 3 4 6 7 8 10 13 15 19 22 850 1,318 1,877 2,178 1,848 1,234 669 296 118 — — 1 1 1 2 2 3 3 4 5 6 8 10 46 i The numbers shown against age 0 represent the allowance made for posthumous births. Statistical data were collected from the experience of the scheme showing the number and age of children in respect of insured married men and widowers who died in 1931 ; they resulted in the proportions shown in table VI. For the actuarial report of 1935 [16] a new estimate was made by a process similar to that used in the first investigations save that the size of families was adjusted to allow.for the continued fall in the birthrate; it was assumed that the number of births per thousand married women aged 16 to 45 would gradually fall from 118 to 110 between 1934 and 1941, and would thereafter remain constant. 1 Cf. Part I, Chapter I, section 1. 492 ACTUARIAL T E C H N I Q U E AND F I N A N C I A L TABLE V I . ORGANISATION N U M B E R AND AGES OF CHILDREN LEFT BY I N S U R E D MALES (Great Britain: 1931) Number and ages of children (including step-children) under age 14 left by 1,000 insured married men (with children under age 14) dying at the ages shown : Age oí father Ages of children 20-25 Posthumous births . . . 0-1 y e a r 1-2 y e a r s 2-3 . . >. ? 3-4 4-5 > 5-6 6-7 ^ 7-8 » 8-9 ' ì 9-10 10-11 11-12 > 12-13 » 13-14 " 25-30 238 . 135 412 276 221 • 237 221 171 77 198 47 165 5 119 3 92 3 65 29 — 23 — 10 — 3. 3 •— ' 1 • 2 — Î Ì T Dtals 1,180 1,576 35-40 40-45 45-50 50-55 55-60 60-65 74 57 168 100 161 122 170 137 198 154 164 191 213 183 192 191 188 205. 161 198 139 - 215 109 221 73 208 26 121 20 94 42 75 89 103 117 135 158 185 186 208 224 254 252 184 160 19 44 55 65 83 104 127 141 177 191 228 246 274 197 200 11 22 25 27 43 65 88 99 123 154 172 242 286 240 232 5 17 25 28 33 47 66 77 92 125 154 201 268 271 274 12 17 17 25 40 43 57 67 84 131 150 192 243 273 318 30-35 2,083 2,370 2,372 2,151 1,829 1,683 1,669 Number and, ages of children (including step-children) under age 14 left by 100 insured widowers (with children under age 14) dying at the ages shown: Age of father Ages of children 0-1 y e ar 1-2 y e 2-3 3-4 " 4-5 5-6 6-7 7-8 8-9 9-10 • 10-11 ' 11-12 ' i 12-13 13-14 25-30 30-35 35-40 40-45 19 3 8 11 16 16 16 28 16 13 16 16 8 2 3 6 2 3 10 10 14 7 28 19 29 28 1814 10 5 2 3 12 6 12 11 20 20 18 29 32 15 22 26 19 13 16 20 16 . . . . ' . . . . . . 3 . . . Totals . . . . — — 145 162 198 207 45-50 2 3 0 5 7 10 18 14. 20 21 30 17 19 .171 50-55 2 1 1 2 4 6' 6 9 14 17 20 30 22 24 158 55-60 60-65 1 — — — — 2 4 2 4 8. 7 -. 10 21 25 33 28 145 1 3 4 8 11 16 14 28 37 29 151 GREAT BRITAIN AND NORTHERN IRELAND 493 § 2. — Insured Population The scope of the contributory pensions scheme coincides very nearly with that of the National Health Insurance scheme, but it is somewhat wider in that it includes " excepted employments " and " exempt persons ". Workers in excepted employment are not compulsorily insured under the National Health Insurance Acts; as a rule they 1 contribute only for widows' and orphans' pensions , and such persons pay a lower contribution 2. " Exempt persons " are employed persons who have obtained certificates of exemption from health insurance, chiefly on the grounds of not being mainly dependent for their livelihood on insurable employment; as a rule they do not contribuate 3to the oldage pension scheme, and therefore pay a lower contribution . ORIGINAL ESTIMATES [9] The number and age distribution of compulsorily insured persons were at first derived from the valuation returns of approved societies under the National Health Insurance scheme 4. The corresponding figures for deposit contributors, members of the armed forces, persons in excepted employments, and exempt persons were added to those obtained from these estimates. The resulting tables were found to be comparable with the figures for occupied persons recorded in the 1911 Census. This statistical material was first of all used to calculate the proportions reproduced below, showing for each age group the ratio in 1923 of the compulsory insured (National Health Insurance figures adjusted to include excepted persons) to the total population. The composition of the total population in July 1925 and at the end of the following years was obtained by applying the mortality rates adopted as bases to the results of the 1921 population census for Great Britain and taking account of the factors described in the next paragraph. From the movement of the total population and the proportions just mentioned (given in columns 2 and 3 of table Vili), a table was constructed showing the movement of the compulsorily insured population. In the calculations use was made of the following hypotheses. The net loss by emigration was assumed to remain constant, it being noted that an increase in emigration would probably result from a decline in the death rate and that it would tend to counterbalance any .additional cost of pensions under the scheme which might arise by reason of the said decline. A fixed annual figure of 40,000 men and 17,000 women was adopted for the net loss of emigration. The Census returns suggested that the number of persons attaining the age of 16 would remain fairly constant, although subject to various influences working in opposite directions: increase in population, fall in the infantile mortality rate, fall in the birth rate. It was therefore assumed that the number of persons of each sex attaining the age of 16 would remain at 410,000 in each year until 1950, after which it was expected that the figure would fall. The shortage in contributions due to sickness or 1 2 3 4 In general they are covered by a special old-age scheme. See below, p. 497. See below, p. 498. Cf. Part I. 494 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION unemployment was estimated on the basis already used for this purpose for the National Health Insurance scheme. For unemployment taken separately, an average of 2 % weeks per insured person per annum was adopted, corresponding to an unemployment rate of five per cent, for the insured population as a whole. For the estimates relating to women, it was assumed that the proportion of women continuing in insurance on marriage would remain constant at one-seventh. ESTIMATES OF 1935 The actuarial report of 1935 [16] contains an estimate of the insured population and its distribution by quinquennial age groups for each sex at the middle of 1935 and of every tenth subsequent year, compared with the figures for 31 December 1931 (see table VII below). This estimate was based on the results of the 1931 Census, the death rates and birth rates indicated in § 1, and the hypothesis that on an average immigrants and emigrants would balance each other. To the total populations so arrived at proportions insured based on those set out in the last two columns of table VIII below were applied to obtain future insured populations. The numbers of persons who would be excluded from insurance on account of prolonged unemployment were estimated on the basis of the legislation in force previous to the 1935 Act and were deducted from these insured populations. It was further assumed that the unemployment rate for the insured population would remain at 14% per cent., i.e. the average rate for the five years ending 31 March 1934. TABLE VII. ESTIMATED NUMBER OF INSURED PERSONS AGED 16-65 IN CERTAIN FUTURE YEARS (Figures in thousands) Age group Insured population at 31 December 1931 Men 16-20 years . 5 20-25 25-30 » J 30-35 35-40 > 40-45 » 45-50 » 50-55 55-60 60-65 » Î Î Women 1,332 1,215 1,768 1,372 1,630 861 1,355 549 1,143 435 • 1,058 360 991 309 898 256 808 211 579 148 Estimated insured population in middle if year * 1945 . 1935 Men Women 1,271 1,148 1,676 1,296 1,665 868 1,472 571 449 1,227 1,074 370 994 313 918 262 222 814 652 171 Men Women 1,162 1,046 1,646 1,251 1,558 789 1,485 553 1,439 483 1,291 405 1,078 335 925 274 816 236 706 211 1955 Men Women 906 1,015 1,378 1,042 1,425 718 1,462 534 1,363 441 1,324 395 1,287 364 1,132 304 903 256 726 223 1965 Men Women 986 1,284 1,244 1,223 1,246 1,303 1,218 1,161 '1,077 887 884 972 623 445 402 382 333 296 277 246 Total (16-65 ) 11,562 5,716 11,763 5,670 12,106 5,583 12,015 5,183 11,629 4,860 1 The figures for years later than 1935 make no allowance for the reinstatement in insurance, under the Act of 1935, of certain persons whose insurance was to have terminated, on account of protracted unemployment, under the terms of the National Health Insurance and Contributory Pensions Act of 1932. 495 GREAT BRITAIN AND NORTHERN IRELAND The proportion of the total population which is subject to the widows', orphans' and old-age contributory pensions scheme, according to the 1931 returns, is given below, side by side with the corresponding proportions (relating to health insurance) used in the original calculations. TABLE VIII. — PERCENTAGE OF POPULATION IN NATIONAL HEALTH AND (LATTERLY) PENSIONS INSURANCE ' Year 1931 Year 1923 16-20 years 20-25 » 25-30 » 30-35 » 35-40 » 40-45 » 45-50 » . . ; 50-55 » 55-60 » 60-65 » Men Women Men Women 85 84 82 79 76 73 70 66.5 62 57 66 57 34.5 27 22 19 16 14 12 10 85.5 89 86.5 81.5 78.5 76.5 75 73 70 67 78 68.5 44 30 25.5 22.5 20.5 18 17 15 EXPERIENCE The number of insured persons recorded for each country and each sex is published annually. The general results for Great Britain arereproduced below. TABLE IX. NUMBER OF INSURED PERSONS: EXPERIENCE x (Figures in thousands) On 31 December 1926 1927 1928 1929 1930 1931 1932 1933 19342 19352 19362 ' ". . . . Men Women Total 11,484 11,648 11,918 12,066 12,258 12,371 12,460 12,473 12,585 12,798 13,019 5,605 5,705 5,935 6,036 6,127 6,143 6,159 6,158 6,204 6,294 6,398 17,089 17,353 17,853 18,102 18,385 18,514 18,619 18,631 18,789 19,092 19,417 i Including persons temporarily remaining insured alter payment of contributions has. ceased. 2 Approximate figures subject to adjustment. 496 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION § 3. — Annual Numbers of Beneficiaries As will be shown in Chapter III, the financial organisation of the scheme is based, among other things, on an estimate of the annual cost of benefits. For the original estimates the probable number of pensions in payment in each year was calculated on the basis of the data analysed above in the preceding sections. Further, the abolition for insured persons of the means test and other conditions on which the award of an old-age pension at 70 had hitherto depended was estimated to involve the granting of pensions to 75,000 men over the age of 70 and to the wives over 70 of 12,000 of these men. The total numbers of beneficiaries, according to the annual statistics compiled for each country, by sex and by category, are reproduced below. TABLE X. —• NUMBERS OF BENEFICIARIES AT 3 1 DECEMBER IN EACH YEAR FROM 1926 TO 1936 (Figures in thousands) Year 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 . . . . . . . . . . . . . Non-contributory Contributory b'eneflts benefits Under Under the Act the Act Age 65-70 •of 1925 pensions of 1929 Wid- Orphans ows Wid- Orphans WidMen Women ows ows 113 96 81 68 70 59 48 40 32 24 17 222 188 159 133 116 • 98 80 63 46 32 20 — — — 213 286 274 262 249 235 219 50 107 161 222 275 327 372 . 423 457 494 550 40 82 113 153 198 228 254 277 283 287 285 — 360 373 395 415 430 446 461 476 492 — 177 198 238 249 257 264 280 294 291 Total beneficiaries 425 473 1,051 1,147 1,505 1,662 1,715 1,775 1,808 1,842 1,874 CHAPTER II FINANCIAL ESTIMATES, BASES, AND EXPERIENCE § 1. Contributions As in the National Health Insurance scheme, compulsorily insured persons are as a rule required to pay contributions at a flat rate irrespective of sex and age, but special lower rates apply to certain categories of insured persons. A brief account will be given in Chapter III of the technical considerations which led to the fixing of contributions at a rate rising successively with each ten-year period of operation of the Act. The rates which applied during the first period (1926-1935) and those which came into force on 1 January 1936 are reproduced below. ' NORMAL W E E K L Y CONTRIBUTIONS First period: 1926-1935 Men ' Second period: 1936-1945 Insured person's share Employer's share Total Insured person's share Employer's share Total d. d. d. d. d. d. 4y 2 2 4% 2% 9 4y 2 5% 3 5y 2 2% 11 5y 2 For persons in excepted employments and not contributing to insurance for old-age pensions, the following lower weekly rates of contribution have applied since the scheme came into force: Men Women Insured person's share Employer's share Total d. d. d. 3% iy2 3y 2 2 7 3y 2 From the beginning of 1938 all women in excepted employment ceased to be insurable. 32 498 ACTUARIAL T E C H N I Q U E ' AND FINANCIAL ORGANISATION For persons holding certificates of exemption under National Health Insurance, the following weekly rates have applied since 1926: Insured person's share Employer's share Total d. d. d. 2% 4% • 2J4 ' 1 2>/2 The Contributory Pensions Scheme has included voluntary contributors since its introduction. These contributors were almost entirely persons who had been previously compulsorily insured; t h e y had to be insured both for National Health Insurance and for Contributory Pensions, and t h e same conditions applied to t h e m as to compulsory contributors. From the beginning of 1938 b y virtue of the Voluntary Contributors Act of 1937 [7], t h e conditions of voluntary insurance were materially altered. Persons who h a d already become voluntary contributors had the option of remaining under the old conditions or of separating their National Health Insurance and their Compulsory Pensions Insurance. In the latter case t h e y could continue in insurance for Contributory Pensions alone or, in the case of men, for Widows' and Orphans' Pensions alone. F r o m 1 J a n u a r y 1938 persons m a y on ceasing t o be compulsorily insured become voluntary contributors for Contributory Pensions or only for Widows' and Orphans' benefits, whether or not they choose to remain as v o l u n t a r y contributors in the National Health Insurance Scheme. All of these v o l u n t a r y contributors who come under the conditions of t h e Act of 1937 p a y t h e normal contributions (including t h e employer's share) corresponding t o t h e benefits for which they are insured, and they are entitled t o t h e normal benefits, provided t h a t they pay on the average 50 weekly contributions each year. In cases where they pay on the average less t h a n 50 contributions a year b u t not less t h a n 26, their benefits are proportionately reduced. Persons who h a v e never been compulsorily insured m a y enter voluntary insurance under t h e Contributory Pensions scheme (but not under the National H e a l t h Insurance scheme) as " Special Voluntary Contributors " subject to t h e following conditions. They must be aged under 40 a t e n t r y and, in t h e case of a m a n , t h e total income at t h e date of entry into insurance m u s t not exceed £400 a year, of which £200 m a y be unearned. I n the case of a woman, the respective figures are £250 and £125. Men can elect to be insured either for Widows' and Orphans' benefits only or for both Old-Age and Widows' and Orphans' benefits. The contributions of special voluntary contributors are equivalent, for each age a t e n t r y , to t h e value of t h e benefits payable up towage 70 (not including t h e cost'of administration) to the average married man. The full benefits to which t h e y are entitled are the same as for compulsorily insured persons (including old-age pensions after 70), but in cases where the average n u m b e r of contributions paid each year is less than 50 b u t not less t h a n 26, t h e benefits are proportionately reduced. For t h e special voluntary contributors entering during 1938 the age limit at entry is increased to 55 and t h e lowest rates in the scales of contributions are applied t o t h e m whatever t h e age at entry. GREAT BRITAIN AND NORTHERN 499 IRELAND Estimates of the annual income from contributions were made during the preparatory work ; the results are included in the table showing the original yearly estimates (see below, table XIV). The figures published in 1925 were repeated, only slightly modified, in the estimates accompanying the Act of 1929 (see table XVIII). A more recent estimate, taken from the actuarial report of 1935, is included in table XIX, forecasting the financial working of the contributory pensions scheme from 1934-35 to 1965-66. The present probable value of contributions is given in the actuarial estimates of 1assets and liabilities as at 1 January 1926 and 31 March 1934 respectively . The total annual 2 contributions actually paid appear from the results of the working of the scheme, which are assembled below (in table XII). § 2. — State Grants The State grants in respect of pensions to persons over the age of 70 may be said to be outside the financial organisation of the contributory pensions scheme. Before the introduction of the scheme these persons were already in many cases receiving non-contributory pensions under the 1908-1924 Acts; the Í925 Act granted pensions without limitation on account of means, etc., to insured persons, their wives, and their widows on the attainment of the age of 70. In the preparatory work, the annual cost to the State of pensions granted under the earlier scheme and the proposed additional charges were estimated separately. The results are given below: TABLE XI. —ESTIMATED COST OF OLD-AGE PENSIONS TO PERSONS OVER AGE 7 0 (Figures in £ millions) Financial year < 1 2 1925-26 1926-27 1927-28 1928-29 1929-30 1930-31 1931-32 1932-33 1933-34 1934-35 1935-36 1940-41 1945-46 1950-51 1955-56 1960-61 1965-66 .• Cost under 1908-24 Acts Additional charge proposed 27.0 29.0 29.7 30.4 31.1 31.8 32.6 33.4 34.2 35.0 35.9 40.9 46.4 51.1 54.4 55.8 56.8 1.7 2.7 3.2 3.3 3.6 3.8 4.0 4.3 4.6 4.7 5.4 6.2 6.9 7.2 7.4 7.6 — Total 27.0 30.7 32.4 33.6 34.4 35.4 36.4 37.438.5 39.6 40.6 46.3 52.6 58.0 61.6 63.2 64.4 See below, tables XVII and XX. The financial year ends on 31 March. The first financial period included 15 months: 1 January 1926-31 March 1927. 500 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The present value of the enlarged rights accorded by the 1925 Act was estimated, as at 1 January 1926 and on a 4 per cent, basis, at £126,000,000 [9]. In fact the cost of the pensions to persons over 70 years of age which became payable through the introduction of the contributory pensions scheme cannot be exactly determined; but it has been possible to estimate [16] that the part not paid off on 31 March 1934 had a present value, at that date and on a 3 !/3 per cent, basis, of £187,000,000. The sums actually paid each year to persons over 70 since the coming into force of the contributory pensions scheme are given — under separate headings for contributory and non-contributory pensions — in table XVI below. The other part of the State grant is incorporated in the financial structure of the contributory pensions scheme. An account will be given in. Chapter III of the estimates by means of which the amount to be credited each year was decided 1. Here it will merely be noted that the variations in this amount are determined by the technical structure of the scheme and that they appear in each of the tables constructed to estimate the financial progress of the scheme 2. On the bases described in Chapter I it was also possible to deduce the probable present value of the liability assumed by the State in undertaking to pay the above-mentioned grants (other than the grants in respect of insured persons over 70). This liability, estimated at £650,000,000 for 1 January 1926, was recalculated on somewhat different bases for 31 March 1934 and was found to have risen to £935,000,000. The actuarial report of 1935 justifies, this increase by a consideration of the causes giving rise to it, which will be discussed in the next chapter. The amount of the annual grants actually made by the State, which did not differ from the figures adopted in the Acts, is included below in the table showing the results of the working of the scheme 3. § 3. — Total Income Table XII opposite brings together the sums which in each financial year were credited to the principal items of income. § 4. — Benefits The old-age pensions granted to insured persons and their wives over age 70 do not enter directly into the financial structure of the contributory pensions scheme and, as has been stated above, their cost is borne entirely by the State. The old-age pensions actually included in the contributory scheme may thus be regarded as temporary annuities payable between ages 65 and 70. The old-age pension is, with unimportant exceptions, fixed at a flat rate of 10s. a week. An allowance equal to the pension is granted to a pensioner's wife when she reaches age 65. 1 These amounts are fixed by the Act up to the financial year 1945-46 inclusive; see table XIX below, column 10. 2 See tables XIV, XVIII and XIX. 3 See table XII. 501 GREAT BRITAIN AND NORTHERN IRELAND TABLE XII. — INCOME FOR THE PERIOD 4 JANUARY 1 9 2 6 TO 3 1 MARCH 1937 (Figures in £ millions) 1926-27 (15 months) . . . 1927-28 . . . • 1928-29 1929-30 1930-31 1931-32 1932-33 1933-34 1934-35 1935-36 1936-37 Receipts from contributions 25.9 23.2 23.3 24.1 23.5 21.8 22.3 22.9 23.6 25.4 30.9 Totals 266.9 Financial year Interest 0.3 1.1 1.8 2.0 2.2 2.1 1.7 0.9 0.9 0.8 0.4 14.2 Exchequer contributions 4.0 4.0 4.0 4.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 Total income 100.0 381.1 30.2 28.3 29.1 30.1 34.7 33.9 35.0 35.8 37.5 40.2 46.3 The conditions to be fulfilled for obtaining an old-age pension are normally 1 the following: (a) the payment of 104 weekly contributions; (b) five years in insurance immediately preceding attainment of age 65; (c) an average of contributions paid or deemed to have been paid during the last three years in insurance fixed at 39 weeks a year. A widow's pension, equal to the old-age pension but withdrawn in the event of remarriage, is granted if the insured person married before reaching the age of 60 2. The benefits granted in respect of orphans consist of: (a) Orphans' pensions properly so called, granted to children having lost both parents, up to age 14 3. (b) Widows' allowances in respect of each dependent child under age 14 3. The orphan's pension is fixed at 7s. 6d. a week and the widow's allowance at 5s. a week for the eldest child and 3s. for each younger child. The granting of widows' and orphans' pensions requires normally 4 : (a) the payment of 104 weekly contributions; (b) two years in insurance immediately preceding the death; 1 Subject to special provisions applicable to certain cases and subject to certain exceptions. 2 Otherwise the granting of the widow's pension is subject to certain conditions. Cf. for instance, INTERNATIONAL LABOUR OFFICE: Compulsory Pension Insurance (Studies and Reports, Series M, No. 10, 1933, p. 306). 3 In case of continued school attendance, up to 31 July of the year following the4 sixteenth birthday. Subject to special provisions applicable to certain cases and subject to certain exceptions. 502 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION (c) an average of contributions paid or deemed to have been paid during the last three years in insurance fixed at 26 weeks a year. As a transitional measure, non-contributory pensions were introduced by the 1925 and 1929 Acts for the surviving dependants of persons normally employed in an insurable occupation who died before 4 Januaryd926. Under the 1925 Act, the widows of such persons were entitled to the following benefits: (a) temporary pensions lapsing when the youngest child reaches age I41/2; • (b) Allowances in respect of each dependent child under age 14 x. Pensions were also granted to orphans (of both parents) of such persons. The 1929 Act extended the benefit of these non-contributory pensions: (a) by raising the age to be reached by thè youngest child before the temporary widow's pension lapses from 14% to 16; (b) by granting annuities from age 55 to widows of the above-mentioned persons, (these annuities are withdrawn in the event of remarriage). Non-contributory pensions are granted at the same rates as normal contributory pensions. The estimates and results in regard to old-age pensions for persons over 70 are reproduced in tables XI (above) and XVI (below) respectively. As regards the other benefits for the aged, widows and orphans, whether contributory or non-contributory,.detailed estimates were made, the results of which appear below in tables XIV, XVIII and XIX. The present value at 1 January 1926 of contributory pensions to persons under age 70 was estimated on a 4 per cent, basis at £950,000,000 in 1925. It was calculated in 1935 that the additions resulting from the 1929 Act corresponded to a present value, on a 4 per cent, basis, of £93,000,000. Finally, the present value of the benefits, whether contributory or non-contributory, guaranteed by the legislation in force at 31 March 1934, including the benefits in respect of voluntary contributors but excluding pensions to persons over age 70, was estimated, on a 3 y¡¡ per cent, basis, at a total of £1,411,000,000. § 5. — Sundry and Total Expenditure The cost of administration was originally estimated at £500,000 per annum, that is to say, at 2 per cent, of the contributions (for the first ten years). This sum was found to be insufficient, and the estimates made for the 1929 Act raised the annual amount to over £1,000,000. In the 1934 balance-sheet the present value of administration expenses in future years is represented by a liability of £15,000,000. 1 In case of continued school attendance, up to 31 July of the year following the sixteenth birthday. GREAT BRITAIN AND NORTHERN 503 IRELAND The table below shows the amounts actually allotted to the principal items of expenditure in each financial year: TABLE XIII. — EXPENDITURE FOR THE PERIOD 4 JANUARY 1926 TO 31 MARCH 1937 (Figures in £ millions) Pensions and allowances Financial year 1926-27 (15 months) 1927-28 . . . . 1928-29 1929-30 1930-31 1931-32 1932-33 1933-34 1934-35 1935-36 1936-37 Tot lis NonContributory contributory Age widows' Widows' pensions and and (from orphans' orphans' 65 to 70 benefits benefits years) Total 6.9 4.8 4.1 3.6 7.9 10.5 9.7 - 8.8 8.0 7.4 6.6 1.3 3.2 5.1 7.1 9.0 10.6 12.1 13.8 15.0 16.4 17.3 3.0 13.6 14.7 16.4 -17.4 17.8 18.3 18.9 19.5 20.1 8.2 11.0 22.8 25.4 33.3 38.5 39.6 40.9 41.9 43.3 44.0 78.3 110.9 159.7 348.9 Expenses Total or admin- expenditure istration • 1.0 0.9 1.0 1.1 1.3 1.3 1.3 1.2 1.3 1.3 1.4 9.2 11.9 23.8 26.5 34.6 39.8 40.9 42.1 43.2 44.6 45.4 13.1 362.0 CHAPTER III FINANCIAL SYSTEM The financial system of the contributory pensions scheme is completely centralised. The equilibrium between income (contributions and State grants) and expenditure is established in the aggregate inside a single fund, the Treasury Pensions Account, the management of which will be considered in Chapter IV. § 1. — Preparatory Studies [9] THEORETICAL PREMIUMS AND GRADUAL RISE IN CONTRIBUTION RATES In the preparatory work on the scheme, a calculation was made of the theoretical premiums that from the actuarial point of view corresponded to the rights granted to insured persons (up to age 70) provided they entered insurance at the minimum age, i.e. 16. The bases used were those described in the preceding chapters, 4 per cent, being taken as the basic rate of interest, and the weekly rates obtained, rounded to the nearest penny, were lOd. for men and 5d. for women. The premiums so calculated constitute the essential theoretical basis of the financial system and serve as the starting-point for the determination of the rising scale of rates of contribution, which was fixed as follows: Period Up to 1935 1936 to 1945 1946 to 1955 1956 onwards . . : Men d. 9 11 13 15 Women d. 4y2 5% 6% 7% A comparison of these rates with the theoretical premiums shows that during the first period (up to 1935) the contribution of a person entering insurance at age 16 is insufficient to balance the benefits guaranteed up to age 70. After 1935, on the contrary, his contribution will cover the benefits guaranteed up to age 70 and also a fraction of any benefits he may receive after that age. From 1956 onwards, it was calculated that, for persons then entering insurance at age 16, the normal rate of contribution would be sufficient on average, if accumulated at interest, to meet the cost of all benefits before and after age 70. It follows that the principle of " individual equity " is satisfied in every case, that is to say, that the present probable value of contributions in respect of any one person never exceeds the present probable value of the benefits guaranteed to him. 505 GREAT BRITAIN AND NORTHERN IRELAND T A B L E OF A N N U A L ESTIMATES The decision to increase the weekly rates of contribution by successive stages followed not only from the values obtained for the theoretical premiums but also from the annual amounts over which it was considered advisable, for reasons to be indicated later, to spread the State grants. A table may first be given showing the annual estimates prepared in 1925. TABLE XIV.— ESTIMATE OF THE EXCHEQUER CHARGE UNDER THE WIDOWS', ORPHANS' AND OLD-AGE CONTRIBUTORY PENSIONS ACT, 1 9 2 5 (Figures in £ millions) Pensions and allowances Year To To widows persons and aged Total chil65-70 dren (1) (2) Total expenditure Expenses (other than to penadmi- sions nistra- to pertion sons over 70) (3) (4) (3) + W (5) Contributions (6) 1925-26 2.4 2.4 0.3 2.7 4.5 1926-27 10.9 10.9 0.5 11.4 22.3 1927-28 11.6 2.9 14.5 0.5 15.0 22.7 1928-29 1929-30 1930-31 1931-32 1932-33 1933-34 1934-35 1935-36 1936-37 1940-41 1945-46 1946-47 1950-51 1955-56 1956-57 1960-61 1965-66 12.7 14.1 15.3 16.5 17.7 18.7 19.5 20.6 21.7 26.0 30.7 31.4 34.1 36.1 36.4 37.5 38.8 12.4 13.2 13.8 14.3 15.0 15.7 16.4 17.3 18.0 20.1 21.1 21.2 21.4 21.1 21.1 21.1 21.5 25.1 27.3 29.1 30.8 32.7 34.4 35.9 37.9 39.7 46.1 51.8 52.6 55.5 57.2 57.5 58.6 60.3 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 25.6 27.8 29.6 31.3 33.2 34.9 36.4 38.4 40.2 46.6 52.3 53.1 56.0 57.7 58.0 59.1 60.8 22.9 23.3 23.5 23.7 23.9 24,0 24.1 25,5 29.6 30.1 32.0 36.2 36.6 38.4 42.7 42.8 42.7 Net estimated expenditure under the Bill other than expenditure in respect of old-age pensions to persons over 70 (5) —(6) (7) (Surplus, 1.8) (Surplus, 10.9) (Surplus, 7.7) 2.7 4.5 6.1 7.6 9.3 10.9 12.3 12.9 10.6 16.5 20.3 16.9 19.4 19.3 15.3 16.3 18.1 " Additional cost of old-age pensions to persons over 70 (8) Relief to the Net. Exche- estimated quer in expenditure respect under the of Bill health and (7)+ (8) unem— (9) ployment (9) 1.7 2.7 ' 0.5 3.2 3.3 3.6 3.8 4.0 4.3 4.6 4.7 4.8 5.4 6.2 6.4 6.9 7.2 7.2 7.4 7.6 2.2 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.4 2.4 2.4 2.4 2.5 2.5 2.5 2.5 (10) (Surplus, 1.8) (Surplus, 9.2) (Surplus, 5.5) 3.7 5.5 7.4 9.1 11.0 12.9 14.6 15.3 13.1 19.5 24.1 20.9 23.9 24.0 20.0 21.2 23.2 Column 7 shows the net difference between the total expenditure on pensions (other than pensions to persons over 70 but including expenses of administration) and contributions. Column 8 gives an estimate of the additional cost of old-age pensions to persons over 70 under the 1925 Act. Since the granting of an old-age pension from age 65 lightens 506 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION the burden of the National Health Insurance and of the Unemployment Insurance schemes, the rates of contribution in the two latter could be reduced. In addition to the reduction in the contributions of insured persons and their employers, a reduction in the State grant to National Health Insurance and to Unemployment Insurance was occasioned by the exclusion of persons age 65 to 70 from benefit under those systems. This relief to the Exchequer was estimated at the amounts shown in column 9. Column 10 thus gives the net charge falling upon thè Exchequer as a result of the introduction of contributory pensions under the 1925 Act, due account being taken of the rising rates of contribution indicated above. STATE CHARGES The annual figures contained in column 10 were compared with the net charge to the State in respect of non-contributory old-age pensions under the 1908-1924 Acts and war pensions. It was estimated that the former of these charges would gradually increase, while the latter would fall fairly rapidly. In the preparation of the financial system for the contributory pensions scheme, it was held desirable to keep the aggregate State charge in respect of pensions (those of the scheme itself, non-contributory old-age pensions, and war pensions) at a practically constant figure from year to year. The table below, showing that the figures of column 10 (in table XIV) approximately satisfy this condition, justifies their adoption, and therefore the prescribed rise in the rates of contribution. TABLE XV. AGGREGATION OF EXCHEQUER CHARGES IN OF PENSIONS RESPECT (As estimated in 1925. — Figures in £ millions) Year 1925-26 1926-27 1927-28 1928-29 1929-30 1930-31 1931-32 1932-33 1933-34 1934-35 1935-36 1936-37 1940-41 1945-46 1946-47 1950-51 1955-56 1956-57 1960-61 1965-66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Non-contributory old-age pensions 27.0 29.0 29.7 30.4 31.1 31.8 32.6 33.4 34.2 35.0 35.9 36.9 40.9 46.4 47.4 51.1 54.4 54.7 55.8 56.8 War pensions 67.0 63.5 59.3 56.6 54.1 51.6 49.2 47.0 45.3 44.0 42.7 41.5 37.2 32.0 30.9 26.8 21.4 20.3 15.7 10.1 Widows', orphans' and old-age contributory pensions 5.7 6.2 5.0 5.0 5.3 5.5 5.7 6.0 6.3 6.4 13.1 19.5 24.1 20.9 23.9 24.0 20.0 21.2 23.2 Total 94.0 98.2 95.2 92.0 90.2 88.7 87.3 86.1 85.5 85.3 85.0 91.5 97.6 102.5 99.2 101.8 99.8 95.0 92.7 90.1 GREAT BRITAIN AND NORTHERN 507 IRELAND It should be observed that the last column but one of this table reproduces the figures of column 10 in table XIV only from the year 1936-1937 onwards. For each of the preceding years the State charges on account of contributory pensions are represented, not by the sum necessary to make up the difference between income and expenditure, but by the amount resulting from the Act. This latter amount is calculated by adding to the additional charge in respect of pensions to persons over age 70 (table. XIV, column 8) an annual grant of £4,000,000 and deducting from this total the estimated figure (table XIV, column 9) of the relief to the Exchequer in respect of health and unemployment insurance. Thus for the first decennial period, use was made of a process of equalisation which substituted a constant annual sum for a gradually rising charge. It has been thought interesting to combine in the table below the returns of the actual grants made by the State in respect of the various charges imposed on it. It will be seen that in agreement with the estimates the total annual charge has remained practically constant. TABLE XVI. AGGREGATION OF STATE GRANTS ACTUALLY PAID IN R E S P E C T OF P E N S I O N S (Thousand £) Old-age pensions to persons over 70 Year 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1 . . . . . . Exchequer payments Under 1908-1924 Acts Under 1925-1929 Acts Pensions Account 27,390 26,808 25,474 24,377 23,632 22,197 21,122 19,643 18,595 17,615 16,560 2,594 6,022 8,578 10,541 13,044 15,631 18,556 20,705 23,139 25,501 27,594 4,000 4,000 4,000 4,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000 War pensions Total 63,192 59,792 56,733 54,100 51,765 49,467 46,825 45,052 43,297 42,461 41,411 97,176 96,622 94,785 93,018 97,441 97,295 97,503 97,400 98,031 99,577 100,565 i Provisional figures. PRELIMINARY ESTIMATE OF ASSETS AND LIABILITIES Table XIII shows that the Exchequer contribution of £4,000,000 for each year up to 1935-36 guarantees to the contributory pensions scheme the sums required to meet its charges. A comparison was also made, during the preparatory work on the 1925 Act, between the present capital values of the assets and liabilities of the scheme. The result is exhibited in the following table : 508 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION ' TABLE XVII. PRESENT VALUES AT BEGINNING OF 1926 OF ASSETS AND LIABILITIES (In £ millions at 4 per cent, per annum) LIABILITIES ASSETS Contributory pensions to persons under 70 Non-contributory pensions 950 . . 32 Increase in pensions to persons over 70 Benefits to voluntary contributors Total 126 13 Statutory contributions (employer and worker) Contributions of voluntary contributors State grants to cover: Contributory pensions to persons under 70 Voluntary insurance . . . . Non-contributory pensions . Increase in pensions to persons over 70 Total 1,131 354 1 596 12 42 126 1,131 It is important to note that this table was based on calculations relating only to the population which, according to the estimates, would become insured at the date when the scheme came into operation. The table of annual estimates (table XIV), on the contrary, relates for each financial year to the total insured population, that is to say, besides the persons becoming insured at the date when the scheme came into force, also those entering insurance later. § 2. — Subsequent Estimates and Review 1929 ESTIMATES [11] During the preparation of the 1929 Act, new estimates were made. The table below shows that they do not differ much from the first ; it also gives an estimate'(column 6) of the additional charge introduced by this Act. Column 3 shows the annual Exchequer contribution as fixed by the 1929 Act for each year up to 1945-46. From 1930-31 this sum took the place of the £4,000,000 a year which were to be granted up to 1935-36 under the 1925 Act. The adoption of this new schedule for the annual grant was intended in the first place to increase the State participation in the cost of the scheme in order to meet the additional expenditure entailed by the 1929 Act. At the same time it avoided the sudden increase that would otherwise have had to be made in the total State grant in 1936-37, while providing for the complete absorption of the temporary balance in the Treasury Pensions Account during the period in question, i.e., up to 1945-46. FIRST DECENNIAL REVIEW The actuarial report for 1935 [16] includes a third table of estimates (see table XIX) calculated on the basis of new data, which have already been mentioned 1. The State grant is shown in column 10, the figures 1 See Chapters I and II. GREAT BRITAIN AND NORTHERN 509 IRELAND up to 1945-46 being those fixed by law and the figures for subsequent years being the amounts required to balance the account. IN THE T R E A S U R T P E N S I O N S ACCOUNT DURING T H E P E R I O D FROM 1 A P R I L TABLE XVIII. •— RECEIPTS AND PAYMENTS, AND BALANCES 1929 TO 3 1 MARCH 1 9 4 6 AS ESTIMATED FOR THE BILL OF 1929 (Figures in £ millions) Expenditure Receipts Financial. year 1929-30 1930-31 1931-32 1932-33 1933-34 1934-35 1935-36 1936-37 1937-38 1938-39 1939-40 1940-41 1941-42 1942-43 1943-44 1944-45 1945-46 Contributions Exchequer Interest contribution Total income under present scheme under new proposals Total Balance in Treasury Pensions Account a t end of year (1) (2) (3) (4) (5) (6) (7) (8) 23.4 23.7 23.8 23.9 24.0 24.1 25.6 29.7 29.8 30.0 30.0 30.1 30.1 30.2 30.3 30.3 31.7 1.9 1.9 1.8 1.5 1.2 1.0 0.8 0.7 0.6 0.6 0.5 0.4 0.3 0.2 0.2 0.1 4.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0 21.0 21.0 21.0 21.0 29.3 34.6 35.6 36.4 37.2 38.1 40.4 45.4 46.4 47.6 48.5 49.5 50.4 51.4 51.5 51.4 52.7 26.7 28.9 30.7 32.4 34.4 36.3 38.0 40.1 41.8 43.2 44.7 46.1 47.3 48.5 49.5 50.3 51.2 0.6 6.5 9.0 8.6 8.0 7.5 7.1 6.6 6.2 5.9 5.6 5.3 4.9 4.6 4.3 4.1 3.7 27.3 35.4 39.7 41.0 42.4 43.8 45.1 46.7 48.0 49.1 50.3 51.4 52.2 53.1 53.8 54.4 54.9 44.8 44.0 39.9 35.3 30.1 24.4 19.7 18.4 16.8 15.3 13.5 11.6 9.8 8.1 5.8 2.8 0.6 The same report also contains an actuarial balance-sheet as at 31 March 1934 for the population insured at that date, on the basis of interest at 3 % per cent. It is reproduced below. This balance-sheet includes both contributory and non-contributory pensions, but the pensions to persons over age 70 are excluded. It indicates a State liability of £935,000,000. As stated above % this liability increased by £285,000,000 between 1925 and 1935, an increase justified by an examination of its causes, which were principally as follows: (1) the excess of interest on the initial liability over the grants actually made by the State; (2) the supplementary charge introduced by the 1929 Act; (3) the shortage of contributions due to unemployment; (4) the fall in the death rate ; (5) loss due to entrants into insurance after the youngest age, less relief due to the failure of large numbers of persons to become voluntary contributors on ceasing compulsory insurance; (6) the substitution of interest at the rate of 3V3 per cent, for the 4 per cent, originally adopted, and other changes in the bases. 1 See p. 500. 510 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XIX. ESTIMATE OF EXPENDITURE ON BENEFITS AND INCOME FROM CONTRIBUTIONS AND EXCHEQUER GRANTS IN EACH FINANCIAL YEAR FROM 1934-35 TO 1965-66 On the basis of (i) future average rate of unemployment, 24% per cent, per annum of the population under the scheme; (ii) decennial increases of contributions 1936, 1946 and 1956; and (iii) termination of insurance in cases of protracted unemployment as provided by the National Health Insurance and Contributory Pensions Act, 1932 (Figures in £ millions) Excess of total ExexpenContributory Rediture Total ceipts Total penses of Inover expenfrom cost admin- diture contri- terest receipts Wi- Old-age of dows' pen- benefits istrafrom butions and or- sions tion contriphans' (from butions pen- 65 to 70 and sions years) interest (3) (4) (6) (7) (8) (9) (2) (5) 18.8 43.2 42.0 1.2 23.1 0.8 15.1 19.3 16.4 19.3 44.4 43.1 1.3 24.6 0.6 19.2 Cost of benefits NoncontriFinancial butory widows' year and orphans' pensions Exchequer contribution i (10) 1934-35 1935-36 (1) 8.1 7.4 1936-37 1937-38 1938-39 1939-40 1940-41 1941-42 1942-43 1943-44 1944-45 1945-46 6.7 6.1 5.5 4.9 4.5 4.1 3.8 3.5 3.2 2.9 17.7 18.7 19.8 20.7 -21.6 22.5 23.3 24.0 24.7 25.3 19.7 20.1 20.5 21.0 21.5 22.1 22.6 23.2 23.7 24.0 44.1 44.9 45.8 46.6 47.6 48.7 49.7 50.7 51.6 52.2 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.5 1.5 1.5 45.4 46.2 47.1 47.9 49.0 50.1 51.1 52.2 53.1 53.7 28.6 28.8 28.9 29.0 29.1 29.2 29.2 29.3 29.4 30.6 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.4 0.3 0.2 16.3 16.9 17.7 18.5 19.5 20.5 21.5 22.5 23.4 22.9 15.0 16.0 17.0 18.0 19.0 20.0 21.0 21.0 21.0 21.0 1946-47 1947-48 1948-49 1949-50 1950-51 1951-52 1952-53 1953-54 1954-55 1955-56 2.6 2.4 2.2 1.9 1.7 1.5 1.4 1.2 1.1 0.9 26.0 26.5 27.0 27.6 28.0 28.5 28.9 29.4 29.7 30.1 24.2 24.4 24.6 24.7 24.8 24.9 24.9 25.0 25.1 25.2 52.8 53.3 53.8 54.2 54.5 54.9 55.2 55.6 55.9 56.2 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 54.3 54.8 55.3 55.7 56.0 56.4 56.7 57.1 57.4 57.7 34.5 34.5 34.4 34.3 34.2 34.1 34.0 33.9 33.8 35.0 — — — — — — — — — 19.8 20.3 20.9 21.4 21.8 22.3 22.7 23.2 23.6 22.7 13.7 20.3 20.9 21.4 21.8 22.3 22.7 23.2 23.6 22.7 1956-57 1957-58 1958-59 1959-60 1960-61 1961-62 1962-63 1963-64 1964-65 1965-66 0.8 0.7 0.6 0.5 0.4 0.3 0.3 0.2 0.2 0.1 30.4 30.8 31.1 31.4 31.7 32.0 32.3 32.6 32.8 33.0 25.3 25.3 25.5 25.7 25.9 26.2 26.4 26,8 27.2 27.8 56.5 56.8 57.2 57.6 58.0 58.5 59.0 59.6 60.2 60.9 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 58.0 58.3 58.7 59.1 59.5 60.0 60.5 61.1 61.7 62.4 38.6 38.5 38.4 38.3 38.1 38.0 37.8 37.7 37.5 37.3 19.4 19.8 20.3 20.8 21.4 22.0 22.7 23.4 24.2 25.1 19.4 19.8 20.3 20.8 21.4 22.0 22.7 23.4 24.2 '25.1 — — — • — — — — — — 13.0 14.0 i Up to 31 March 1946, as fixed under Ì929 Act; from 1 April 1946, as required to balance account for each year. 2 It is understood that certain profits amounting to £2.8 millions have been made by changes of investments. As all investments have to be realised by 1946, when the balance at the credit of the account will disappear, it is deemed advisable to regard this small sum as a margin for loss on realisation. GREAT BRITAIN AND NORTHERN 511 IRELAND TABLE X X . — ACTUARIAL B A L A N C E - S H E E T : P R E S E N T VALUES OF AND L I A B I L I T I E S AT 3 % P E R CENT. P E R ANNUM ASSETS (In £ millions) ASSETS LIABILITIES Present value of: Widows' and orphans' pensions: Now in force Claimable in future . . . Pensions between 65 and 70 : Now in force Claimable in future . . . F u t u r e cost of administration Total 181 534 42 654 15 Balance in hand Present value of: Statutory contributions (employer and worker): At the present rates . . . Decennial increases . . . Exchequer contributions, as defined by statute, till 1945-46 Balance of Exchequer contributions, to be met in such manner as Parliament may hereafter determine . . . . 1,426 28 344 119 171 764 1,426 Total § 3. — Experience The main lines on which the financial system has functioned during the first ten years appears from a joint examination of tables XII and XIII in Chapter II. Comparison of the annual income and expenditure totals shows that the temporary balance in the Pensions Accounts was as follows at the end of each year: TABLE XXI. — ACTUAL BALANCES IN P E N S I O N S ACCOUNTS (Figures in £ millions) Financial year 1926-27 (15 months) 1927-28 1928-29 1929-30 1930-31 1931-32 1932-33 1933-34 1934-35 1935-36 1936-37 Balance in pensions accounts at end of year 21.0 37.4 42.7 46.3 46.4 40.5 34.6 28.3 22.6 18.2 19.1 CHAPTER IV FINANCIAL ADMINISTRATION § 1. — Temporary Balance The financial system adopted for the contributory pensions scheme does not provide for the accumulation of actuarial reserves; but a temporary balance may arise, and did so, principally in the first two years of the scheme, when contributions were collected but no contributory old-age pensions at 65 were paid. This balance reached its maximum in 1931 and has since been decreasing rapidly. The date at which it will completely disappear depends on several factors, the most important of which is the degree of unemployment. It has been seen * that the estimates of the first decennial review, proceeding from a number of hypotheses, placed the date on which the temporary balance would have been completely absorbed at 1946. The temporary balance at the end of each year, i.e. the total balance in the Pensions Accounts, in given in table XXI above. § 2. — Investment of Funds The sums standing to the credit of the Treasury Pensions Account 2 may from time to time be invested in such manner as the Treasury may direct. In actual fact the selection of the investments is left to the National Debt Commissioners 3. The securities in which the money is invested are indicated in the accounts published each year [22]. The figures for 1935, 1936 and 1937 are reproduced below in table XXII. § 3. — Accounting, Actuarial Reports, Statistics There are two Pensions Accounts, one for England and Wales, and one for Scotland, administered by the Minister of Health and the Department of Health for Scotland respectively. They are audited every year by the Comptroller and Auditor-General, who submits the audited accounts 1 2 See table XIX. To which are credited from time to time those sums standing to the credit of 3the Pensions Accounts which are not required to meet expenditure. See Part I, p. 476. GREAT BRITAIN AND NORTHERN 513 IRELAND to Parliament together with the results of his investigations. The report of the Comptroller and Auditor-General is appended to the Accounts [22] in which are published at the end of each financial year the sums credited with and debited to the Treasury Pensions Account, the Pensions Account, and the Pensions (Scotland) Account. TABLE XXII. — INVESTMENT OF FUNDS IN TREASURY PENSIONS ACCOUNTS At 31 March 1935 At 31 March 1936 Nominal amount Market value Nominal amount Market value Nominal amount Market value £ £ £ £ £ £ 5 per cent. Conversion Loan, 1944-64 3 per cent. Treasury Bonds, 1933-42 . 2,423,900 2,514,829 2 % per cent. Treas u r y Bonds, 1937 745,600 773,284 745,600 758,865 2 per cent. Treasury Bonds, 1935-38 . 8,936,700 9,068,971 2 per cent. Treasury Bonds, 1939-41 . 5,001,300 4,886,493 3 per cent. Conversion Loan, 1948-53 1,409,713 1,479,317 1,409,713 1,479,317 4 % per cent. Conversion Loan, 1940-44 10,046,554 11,308,652 10,586,028 11,796,805 Guaranteed Loans u n d e r t h e Trade Facilities Acts, 1921-26, and the Finance Act, 1934 305,283 108,000 108,000 305,283 Treasury Bills . . 1,435,000 1,433,708 Totals . . At 31 March 1937 — 25,253,054 — 20,660,471 9,424,911 10,845,520 3,001,300 2,972,304 1,409,712 1,415,880 4,587,905 4,914,793 302,497 435,000 302,497 434,605 — 20,885,602 The following items are credited to the Treasury Pensions Account: (1) its own interest; (2) the annual statutory grant of the State in respect of contributory pensions to persons under age 70; (3) any surpluses on the Pensions Accounts; (4) any sums not immediately re-employed on the occasion' of the sale or redemption of securities. The following items are charged against this Fund: (1) the sums handed over to the National Debt Commissioners for investment; (2) any payments made to meet deficiencies on the Pensions Accounts. 33 514 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION A section of the 1925 Act provides that the Government Actuary shall report on the financial working of the scheme for the first time in 1935 and subsequently every ten years. The first actuarial report compiled in accordance with this provision was published in 1935. It contains an analysis of the experience for the first eight years of the working of the scheme and an estimate of the probable working of the scheme up to 1965, accompanied by an actuarial balance-sheet as at 31 March 1934. In the course of the preceding chapters, frequent use has been made of this report and its most important data and estimates have been reproduced. Finally mention may be made of two subjects with which it terminates. The first relates to a suggestion occasionally made for extending compulsory insurance by raising the limit of remuneration (£250 a year) above which non-manual workers are not liable. As has already been mentioned, from the beginning of 1938, in virtue of the Voluntary Contributors Act of 1937, men earning between £250 and £400 a year may become voluntary contributors under the Contributory Pensions scheme. The actuarial report states that an extension of the .contributory pensions scheme must be accompanied by a corresponding extension of health insurance, and would consequently mean an increase in the amount of the reserve values. The additional burden thus created would seriously disturb the financial equilibrium of the National Health Insurance scheme. The second point relates to the maintenance of pension insurance for unemployed insured persons. The report was published a few weeks before the introduction of the 1935 Act, and the discussion of the proposal may be considered as an introduction to the actuarial report [15] prepared in connection with that Act. A summary of the results of the working of the scheme appears in the annual reports of the Ministry of Health [18] and the Department of Health for Scotland [19]. BIBLIOGRAPHY I. — Legislation 1. Widows', Orphans' and Old-Age Contributory Pensions Act, 1925. L. S.,1 1925, G.B. 7. 2. Widows', Orphans' and Old-Age Contributory Pensions Act, 1929. L. S., 1929, G.B. 6. 3. Widows', Orphans' and Old-Age Contributory Pensions Act, 1931. L. S., 1931, G.B. 5. 4. National Health Insurance and Contributory Pensions Act, 1932. L. S.r 1932, G.B. 8. 5. National Health Insurance and Contributory Pensions Act, 1935. L..S.t G.B. 2. 6. Widows', Orphans' and Old-Age Contributory Pensions Act (Consolidation), 1936. L. S., 1936, G.B. 5. 7. Widows', Orphans' and Old-Age Contributory Pensions (Voluntary Contributors) Act, 1937. L. S., 1937. G.B. 1. 1 L. S. =. Legislative Series of the International Labour Onice. GREAT BRITAIN AND NORTHERN II. — Reports and IRELAND 515 Memoranda1 8. Widows', Orphans' and Old-Age Contributory Pensions Bill. Memorandum explanatory of the Bill. Cmd. 2,405 of 1925. 9. Widows', Orphans' and Old-Age Contributory Pensions Bill. Report by the Government Actuary on the financial provisions of the Bill. Cmd. 2,406 of 1925. 10. Widows', Orphans' and Old-Age Contributory Pensions Bill, 1929. Memorandum explanatory of the Bill. Cmd. 3,412 of 1929. 11. Widows', Orphans' and Old-Age Contributory Pensions Bill. Financial Memorandum, 1929. 12. National Health Insurance and Contributory Pensions Bill. Memorandum explanatory of the Bill by the Minister of Health and the Secretary of State for Scotland. Cmd. 4,072 of 1932. 13. National Health Insurance and Contributory Pensions Bill, 1932. Report by the Government Actuary on the financial provisions of the Bill. Cmd. 4,073 of 1932. 14. National Health Insurance and Contributory Pensions Bill, 1935. Memorandum explanatory of the Bill by the Minister of Health and the Secretary of State for Scotland. Cmd. 4,905 of 1935. 15. National Health Insurance and Contributory Pensions BUI, 1935. Report by the Government Actuary on the financial provisions of the Bill. Cmd. 4,906, 1935. 16. Widows', Orphans' and Old-Age Contributory Pensions Acts, 1925-1932. Report by the Government Actuary. H.C. 82, 1935. 17. Widows', Orphans' and Old-Age Contributory Pensions (Voluntary Contributors) Bill, 1937. Report by the Government Actuary on the financial provisions of the Bill. Cmd. 5,415, 1937. III. — Experience 18.. Annual Report of the Ministry of Health, London. 19. Annual Report of the Department of Health for Scotland, Edinburgh. 20. Statistical Abstract for the United Kingdom. 21. Abstract of Labour Statistics of the United Kingdom. 22. Accounts of the Treasury Pensions Account, the Pensions Account and the Pensions (Scotland) Account (annual accounts). 1 All these documents are published by H.M. Stationery Office. ITALY General Scheme of Compulsory Insurance against Invalidity, Old Age and Death CONTENTS Page INTRODUCTION CHAPTER I: Demographic Estimates, Bases and Expérience . . . . . 1. Biometrie Tables. Invalidity Rates Mortality of Invalids Mortality of the General Population . Décrémentai Rates of Healthy Lives Family Statistics 2. Initial Insured Population 3. Movement of the Insured Population 4. Annual Number of Beneficiaries Invalidity Pensions Old-Age Pensions Death Benefits. CHAPTER I I : Financial Estimates, Bases and Experience 1. Contributions Ratio of Contributions to Wages Present Value of Unit Contribution payable by the Insured Population 2. State Grants 3. Other Receipts 4. Benefits Present Values of some Essential Annuities Total Annual Amounts of Benefits 5. Other Expenditure Cost of Administration Benefits in Kind CHAPTER I I I : Financial System . 1. Calculation of the Theoretical Average Premiums 2. Financial Equilibrium Liabilities of the Scheme in respect of Insured Persons . . Expected Income of the Scheme in respect of Insured Persons Comparison of the Expected Income and Liabilities of the Scheme in respect of Insured Persons 3. Actuarial Reserves 4. Safety Reserves 519 520 520 520 521 521 524 525 526 527 528 528 530 532 534 534 535 535 536 538 539 539 550 551 551 551 552 552 555 556 567 567 560 561 518 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION CHAPTER IV: Financial Administration 1. Investments Statutory Provisions Statistics of Investments 2. Actuarial and Financial Control 3. Accounts and Statistics BIBLIOGRAPHY I. II. III. Page 562 562 562 562 563 564 564 Legislative Texts . .' Administrative Publications Articles APPENDIX 564 564 565 565 INDEX OF TABLES I. II. III. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. XIX. XX. XXI. XXII. XXIII. Invalidity Rates Aggregate Mortality Rates of Invalids . Mortality Rates of the General Population (1901-1910) . . . Mortality Rates of the General Population (1921-1922). . . Life Table of Healthy Lives Marital Status of Insured Males Number of Children aged less than 15 Number of Dependent Children aged less than 18 Age Distribution of Insured Population Estimate of Number of Invalidity Pensions Estimate of Number of Old-Age Pensions Number of Pensions in Payment: Experience Contribution Income: Experience Estimated Total Sums to be provided each Year to cover the addition of 100 lire to each Invalidity and Old-Age Pension granted by the State Revenues of the Invested Funds Value of an Invalidity Annuity to an Invalid . . . . . . Portion of the Invalidity Pension which depends on the Duration of the Contribution Period Amount of Pensions in Payment at End of each Year . . Average Premium for each Constituent Part of Pension . . Balance-Sheet as at 31 December 1936 Compulsory Insurance Fund Fund for Pensions in Payment Safety Reserves 520 521 522 523 524 525 525 526 528 529 531 532 535 537 538 541 546 550 553 559 560 561 561 INTRODUCTION The insurance of employed persons against invalidity, old age and death was introduced in Italy on 1 July 1920, by the Act of 21 April 1919 [1], which was replaced later bv the Royal Decree of 30 December 1923 [2]. The general principles of the financial system on which the scheme was first established have been preserved. Investigations made after several years of working, the results of which were published in 19241925, led to the maintenance of the technical basis hitherto in use. The method of calculating pensions which was introduced by the Act of 13 December 1928 [3] involved an increase in their cost, without however necessitating an alteration in the technical basis. The other Acts have had only a slight effect on the financial system. The entire legislation was codified by Legislative Decree of 4 October 1935 [4]. In Italy the scheme of insurance for employed persons against invalidity, old age and death is, in effect, a general compulsory scheme covering all employed persons including agricultural workers but excluding certain persons insured under special schemes. Its principal object is the payment of invalidity and old-age pensions, and temporary pensions for six months to survivors. It is administered by a central body, the National Fascist Institute of Social Insurance (Istituto Nazionale Fascista della Previdenza Sociale) 1, which has control over most of the social insurance schemes in the country: unemployment insurance, insurance against tuberculosis, maternity insurance, special schemes, etc. The Legislative Decree of 14 April 1939 effected in the pension insurance scheme important amendments which could not be embodied in this study; the new provisions, whose coming into force is spread over the years 1939-1949, are given in an appendix. 1 New title given by the Decree oí 27 March 1933 to the National Social Insurance Fund (Cassa Nazionale per le assicurazione sociali). CHAPTER I DEMOGRAPHIC ESTIMATES, BASES AND EXPERIENCE § 1. — Biometrie Tables Invalidity connotes inability to earn. Invalidity is defined as the permanent (or presumedly permanent) reduction of the earning capacity to less than one-third (i.e. a reduction of at least two-thirds) of the normal earnings of persons who carry on in the same district an occupation compatible with the occupational class and with the previous standard of living of the insured 1 . INVALIDITY RATES From the outset the probabilities of becoming invalid which were adopted were those of Zimmermann's table relating to the non-train staff of the German Railways. Statistics collected during the working of the scheme give some preliminary indication of the actual incidence of invalidity in the Italian social insurance scheme; they will be amplified by new data and by investigations now being made [10, 14]. TABLE I. INVALIDITY RATES Number becoming invalid per 1,000 insured persons according to experience Age 25-29 30-34 35-39 40-44 50-54 55-59 group .' . for years 1921-31 lor years 1929-32 lor year 1932 1.42 1.79 2.14 2.25 3.46 5.50 9.62 0.98 1.35 1.70 2.24 3.00 4.78 8.33 0.86 1.49 2.35 3.47 5.17 8.29 15.16 ; 1 Definition amended by the Legislative Decree of 14 April 1939. See Appendix, p. 565. 521 ITALY MORTALITY OF INVALIDS The décrémentai table of invalids by age and duration of invalidity 1 published in 1906 relating to German social insurance experience has been adopted as basis. The figures in this table have been decreased by one-tenth 2, in order, on the one hand, to allow for decrement by death alone and, on the other hand, to leave a margin of safety. A statistical enquiry, carried out during application of the scheme, into the 125,821 pensions granted between 1920 and 1932, and the deaths occurring among the pensioners in question (of which there were 27,949) has provided the Italian scheme with its own statistics of invalid mortality [17]. Its main result was the compilation of six tables, relating respectively to: the " central " average duration of invalidity (for all durations of invalidity and for invalidity exceeding five years); the crude invalidity rates selected according to age and duration of invalidity; the " truncated ", " compact " and aggregate mortality rates; the selected rates after adjustment; and lastly the selected rates which, for durations of invalidity exceeding 14 years, merge with the ' general Italian mortality rates. The crude rates of the aggregate table are reproduced below. TABLE II. AGGREGATE MORTALITY RATES OF INVALIDS Crude rate per 1,000 Age 0.2372 0.1392 0.1102 0.0901 0.0827 0.0800 0.0723 0.0697 0.0625 0.0597 0.0659 0.0801 20 years 25 » 30 » 35 " 40 » 45 » 50" » 55 » 60 » 65 » 70 » 75 " All ages 0.0703 MORTALITY OF THE GENERAL POPULATION For the drafting of the Legislative Decree of 1919 recourse was had to the mortality table constructed for the whole of the Italian population using the census data of 1901 and 1910 and the records of deaths occurring in the decennium 1901-1910. 1 2 See pp. 286-288. For table as thus modified see Bibliography, 5: tables VIII, IX, X. 522* TABLE III. MORTALITY RATES OF THE GENERAL POPULATION (1901-1910) Age Mortality rates (per thousand) Males and Males Females females 0 y e a r 167.71 70.40 1 » 2 y e a r s 30.80 17.43 3 » 11.72 4 » 7.68 5 » 4.98 6 » 3.33 7 » 2.47 8 » 2.18 9 » 2.26 10 » 2.56 11 » 12 " 2.97 3.39 13 " 3.78 14 » 4.12 15 » 16 » 4.43 4.76 17 " 18 » 5.20 5.70 19 » 20 » 6.19 21 » 6.61 22 " 6.89 23 » 6.99 24 » 6.96 25 » 6.85 26 » 6.73 27 " 6.67 28 " 6.66 29 » 6.65 30 " 6.67 31 " 6.70 32 » 6.76 33 » 6.84 34 » • 6.94 35 » 7.06 36 » 7.23 7.45 37 " 38 " 7.74 39 » 8.09 40 " 8.48 41 » 8.88 42 » 9.27 43 " 9.62 44 » 9.96 45 » 10.31 46 » 10.72 47' » 11.25 48 " 11.90 49 » 12.64 152.11 160.12 71.36 70.87 31.85 31.32 17.89 17.66 12.43 12.08 8.50 8.07 5.83 5.40 4.14 3.72 3.22 2.84 2.87 2.53 2.90 2.57 3.19 2.87 3.60 3.28 4.06 3.71 4.50 4.14 4.89 4.48 5.22 4.81 5.53 5.15 5.86 5.52 6.18 5.93 6.48 6.33 6.74 6.68 6.96 6.91 7.12 7.07 7.24 7.09 7.33 7.09 7.39 7.05 7.46 7.04 7.52 7.09 7.55 7.08 7.58 7.13 7.61 7.15 7.66 7.18 7.73 7.28 7.81 7.35 7.89 7.47 7.99 7.61 8.10 7.75 8.23 7.98 8.38 8.24 8.54 8.51 8.68 8.79 8.80 9.04 8.84 9.24 8.82 • 9.40 8.80 9.59 9.81 8.87 9.10 10.21 9.50 10.73 10.03 11.36 Age Mortality rates (P 3r thousand) Males and Males Females females 50 years 13.45 10.66 51 » 14.32 11.37 52 » 15.21 12.13 53 » 16.05 12.87 54 » 16.85 13.60 55 » 17.73 14.44 18.83 15.52 56 » 20.28 16.95 57 » 58 » 22.11 18.77 24.25 59 » 20.88 26.62 60 » 23.26 61 29.17 25.87 62 " 31.84 28.67 34.44 31.50 63 » 64 " 37.01 . 34.37 65 » 39.83 37.54 66 » 43.19 41.28 47.38 45.82 67 " 68 » 52.43 51.23 69 " 58.15 57.34 64.49 70 » 64.07 71.38 71 " 71.32 72 " 78.78 79.02 86.35 73 » 86.89 74 » 94.13 95.00 102.62 103.74 75 » 76 » 112.31 113.52 123.69 124.72 77 » 78 » 137.38 137.87 153.05 152.69 79 » 80 » 169.78 168.42 186.64 184.29 81 82 " 202.71 199.52 218.56 214.76 83 " 84 » 234.71 230.53 251.60 247.27 85 » 86 » 269.62 265.37 289.10 285.16 87 " 310.32 306.89 88 » 89 " 333.49 330.77 90 » 358.74 356.92 386.18 385.41 91 » 415.82 416.25 92 » 447.65 449.38 93 » 94 » 481.56 484.69 517.41 521.98 95 » 96 » 554.99 561.01 594.01 601.47 97 » 634.16 642.98 98 » 675.03 685.10 99 » 12.11 12.87 13.71 14.49 , 15.25 16.13 17.20 18.63 20.45 22.58 24.96 27.53 30.25 33.00 35.70 38.67 42.25 46.57 51.84 57.77 64.27 71.36 78.90 86.63 94.54 103.18 112.91 124.20 137.65 152.84 169.13 185.44 201.28 216.67 232.40 249.33 267.69 287.26 308.33 331.87 357.38 385.20 419.09 450.00 480.52 525.00 578.95 625.00 666.67 679.93 Annali di S atistica, S eries V, V ol. 10, 191 9,. pp. 282-2 87. In more recent investigations, however, reference was made to the mortality table for the general population based on the census data of 1921 and records of deaths during the year 1921 and 1922. TABLE IV. MORTALITY RATES OF THE G E N E R A L 523 POPULATION (1921-1922) Age Mortality rates (r er thousand) Males and Males Females females 0 year 135.63 1 » 51.54 2 years 22.88 3 » 11.61 4 ,, 8.11 5 » 5.50 6 " 4.61 7 " 3.65 8 » 3.12 9 " 2.83 10 " 2.58 11 " 2.38 12 " 2.34 13 » 2.51 14 » 2.84 15 » 3.18 16 . » 3.59 17 " 4.09 18 » 4.61 19 » 5.11 20 " 5.64 21 » 6.28 22 " 6.69 23 » 6.68 24 » 6.37. 25 6.10 26 » 5.70 27 " 5.38 28 » 5.33 29 » 5.46 30 » 5.54 31 » 5.60 32 " 5.67 33 » 5.74 34 " 5.81 35 » 5.90 36 » 6.03 37 » 6.19 38 " 6.35 39 " 6.52 40 » 6.75 41 » 6.98 42 » 7.26 43 " 7.61 44 » 8.00 45 " 8.44 46 » 8.92 47 " 9.43 48 " 9.95 49 » 10.53 Annali di Statistica, 121.28 49.34 21.75 11.51 7.92 5.65 4.71 3.75 3.19 2.87 2.77 2.56 2.54 2.77 3.16 3.56 4.07 4.55 4.84 5.00 5.21 5.44 5.61 5.72 5.78 5.83 5.86 5.87 5.89 5.90 5.90 5.89 5.90 5.98 6.11 6.24 6.39 6.52 6.59 6.65 6.73 6.83 6.94 7.06 7.21 7.39 7.59 7.88 8.31 8.85 128.66 50.46 22.33 11.56 8.02 5.58 ' 4.66 3.70 3.15 2.85 2.67 2.46 2.44 2.64 3.00 3.37 3.83 4.32 4.73 5.06 5.42 5.85 6.13 6.18 6.06 5.96 5.79 5.65 5.63 5.70 5.73 5.75 5.795.87 5.97 6.08 6.22 6.36 6.48 6.59 6.74 6.90 7.10 7.33 7.60 7.91 8.25 8.65 9.12 9.68 Mortality rates (per thousand) Age Males 50 years 11.18 51 » 11.92 52 » 12.72 53 » 13.63 54 » 14.43 55 » 15.40 56 » 16.41 57 » 17.63 58 » 19.18 59 » 20.98 60 " 22.86 61 » 24.92 62 » 27.08 63 » 29.37 64 » 31.95 65 » 34.84 66 » 38.05 67 » 42.14 68 » 47.20 69 " 52.80 70 » 58.57 71 » 64.73 72 » 71.36 73 » 78.73 74 » 87.13 75 " 96.61 76 » 108.22 77 » 120.61 78 » 134.30 79 » 147.38 80 " 161.27 81 » 175.94 82 » 191.33 83 » 207.40 84 » 224.07 85 » 241.25 86 » 258.86 87 " 276.78 88 » 294.93 89 » 313.19 90 » 331.47 91 » 349.67 92 » 367.69 93 » 385.47 94 » 402.93 95 » 420.02 96 » 436.68 97 » 452.79 98 » 468.47 99 " 483.78 100 " 498.45 101. » 512.60 102 » 526.22 103 » 539.33 104 " — 105 » — Series V I , Vol. V I I I , 1931, p p . 325-327. Females Males and females 9.46 10.31 10.19 11.04 10.89 11.79 11.47 12.53 12.05 13.23 12.76 14.07 13.49 14.95 14.55 16.09 16.10 17.64 17.96 19.46 19.88 ' 21.35 21.96 23.42 24.12 25.57 26.41 27.86 29.04 30.47 32.07 33.44 35.47 36.76 39.95 41.04 45.49 46.34 51.47 52.12 57.54 58.05 63.97 64.34 70.64 70.99 78.02 78.37 86.60 86.86 96.48 96.54 108.65 108.64 120.81 121.65 132.98 133.12 145.11 146.19 157.71 159.37 170.74 173.12 184.13 187.39 197.82 202.10 211.75 217.18 225.86 232.56 240.09 248.16 254.33 263.91 268.60 279.73 282.80 295.55 296.91 311.30 310.88 326.93 324.66 342.37 338.24 357.59 351.59 372.54 364.68 387.19 377.50 401.52 390.03 415.50 402.28 429.11 414.22 442.36 425.85 455.22 437.18 467.69 448.20 479.80 458.91 491.50 469.33 502.84 479.45 — 524 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION DECREMENTAL RATES OF HEALTHY LIVES Décrémentai rates of healthy lives have not been derived from direct data, but have been calculated [5: pp. 25-28] from a combination of rates of becoming invalid with mortality rates of invalid lives and. of the general population. • The method of calculation consists of the progressive determination of figures relating to successive years of age by means of inductive formulae. The numbers lax of healthy lives of each age drawn from 10,000 healthy lives aged 20 are reproduced, for each sex, in table V. TABLE V. LIFE TABLE OF HEALTHY LIVES Males Age Number of healthy lives 20 years 10,000 21 " 9,937 22 » . 9,870 23 » 9,800 24 » 9,730 Females Age Number of healthy lives 50 years 51 » 52 » 53 » 54 » 7,476 7,316 7,142 6,956 6,757 Age 20 'years 10,000 21 " 9,934 • 22 i » 9,865 23 it 9,795 24 " 9,723 L9 9,661 9,593 9,526 9,460 9,394 55 56 57 58 59 " » » » » 6,545 6,320 6,080 5,820 5,536 25 26 27 28 29 30 31 32 33 34 " " » » » 9.328 9,262 9,196 9,129 9,061 60 61 62 63 64 » » » » » 5,229 4,896 4,545 4,178 3,803 30 31 32 33 34 35 36 37 38 39 » " » ' " » 8,990 8,918 8,844 8,766 8,686 65 66 67 68 69 » " » » » 3,429 3,062 2,700 2,349 2,013 35 36 37 38 39 40 41 42 43 44 » » » » » 8,603 8,515 8,421 8,323 8,221 70 71 72 73 74 » » » " » 1,694 1,384 1,121 886 688 40 41 42 43 44 45 46 47 48 49 » » » » " 8,113 8,001 7,884 7,758 7,623 75 76 77 78 79 » » » " " 524 390 281 191 115 45 46 47 48 49 80 » 51 îï )S ») » i* .. )» » J» )» 1) 11 )» Ï» 1» 11 ») » 1» 1* « )» " λ 1» Number of healthy lives Age 50 y e a r s 51 » 52 " 53 » 54 " 7,319 7,162 6,990 6,803 6,603 9,650 9,576 9,502 9.428 9,352 55 56 57 58 59 » » " » " 6,387 6,157 5,909 5,639 5,343 9,277 9,202 9,125 9,047 8,968 60 61 62 63 64 » » » » » 5,021 4,672 4,302 3,915 3,520 8,886 8,802 8,717 8,629 8,539 65 66 67 68 '69 » " » » » 3,123 2,734 2,352 1,982 1,630 70 8,448 8,353 71 8,254 72 8,153 73 8,047 ' 7 4 » » » » 'V 1,300 1,000 736 510 327 7,939 7,828 7,715 7,593 7,461 » » j» » » » » " 25 26 27 28 Number of healthy lives 75 76 183 75 525 ITALY FAMILY STATISTICS In the preliminary investigations [5] recourse was had to two tables relating to family statistics, viz. the marital status of male insured persons and the number of children of married male insured persons. The proportion of the total male insured persons who are married was obtained by adding one-tenth to the corresponding proportion for the whole population derived from the 1911 Census data, intermediate values being obtained by graphic interpolation. TABLE VI. — MARITAL STATUS OF INSURED MALES Proportion of insured who are married (1911 Census figures increased by 1 / l 0 ) ge group 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 65-70 . . . . . . . . 0.147 0.583 0.815 0.891 0.913 0.920 0.910 0.888 0.843 0.774 In order to obtain the average number of children aged less than 15 per insured male the following data were considered: (1) the Austrian table of 1896 for private employees; (2) statements concerning invalidity pensions paid under the German scheme of workers' insurance during 1912. The two series of figures derived from these sources showed a satisfactory agreement, and it was decided to use as a basis for the estimates the Austrian table increased by one-fifth and graduated graphically. TABLE VII. Age 22 27 32 37 42 47 52 57 62 NUMBER OF CHILDREN AGED LESS THAN 1 5 Average number per insured male (Austrian table 1896, increased by i/ 6 ) 0.024 0.0312 1.123 1.891 2.189 1.864 1.300 0.761 0.388 Further data were derived from the operation of the Italian insurance scheme itself during the years 1929 to 1932, showing separately information relating to old-age pensioners and invalidity pensioners [10]. 526 ACTUARIAL T E C H N I Q U E AND FINANCIAL TABLE V I I I . N U M B E R OF D E P E N D E N T AGED LESS THAN Central age of group 20 y ears 25 30 35 40 45 50 55 60 65 70 » iy Mean number of children per Invalidity pensioner 0.04 0.27 0.77 1.21 1.40 1.11 0.76 0.49 0.26 0.12 0.02 i ag es ORGANISATION 0.42 Mean age of children 1 year 2.4 years 3.7 » 5.7 » 8.2 » 9.6 » 10.7 » 11.8 " 12.4 » 12.9 » 11.6 » 9.6 CHILDREN 18 » Mean number of children per old-age pensioner Mean age of children — . — — — ' — — — —. — — .—. — 0.18 0.11 0.02 10.8 12.7 11.5 0.08 12.5 § 2. — Initial Insured Population Insurance against invalidity, old age and death in Italy takes the form of a general scheme for employed persons. It includes as compulsory contributors all employed persons of both sexes aged 15 to 65, whether they are workers or salaried employees, with certain exceptions, the most important being that of salaried employees in receipt of a monthly salary exceeding 800 lire 1 . However, in the preliminary technical investigations the salary limit was 350 lire a month for salaried employees and 3,600 lire a year for agricultural workers. Successive estimates were made on the assumption that the age at which title to old-age pension commenced was first 60 and then 65. The initial number of persons insured was estimated from the census of 10 June 1911, and more particularly from the statements in it showing the distribution of employed persons (within each class, viz. workers, salaried employees, and persons working on their own account) classified according to occupation, sex, and in the following age-groups: 15-21, 21-30, 30-45, 45-65 [5: pp. 11-18 and 98-101]. Subsequently [6: p. 44] the figures deduced for 1911 were brought down to 1920 by the addition of 18 per cent., which exceeds the rate of increase of the total population, viz. from 34.5 millions in 1911 to 40 millions in 1920 (including the new provinces). The figures arrived at for 1920 were (in millions): Age Males 15-60 15-65 6.5 6.7 Females 3.2 3.3 • Total 9.7 10.0 1 Provisions amended by Legislative Decree of 14 April 1939. See Appendix, p. 565. ITALY 527 The distribution of the number insured according to individual ages was arrived at sometimes by means of graphic interpolation and sometimes by applying a correction formula *. § 3. — Movement of the Insured Population It was considered reasonable to assume that both the total number of insured persons and their age distribution would remain constant. It was also assumed that entry into insurance would always take place at age 15. On these assumptions the age distribution follows a law which must be consistent with the décrémentai law of healthy lives already adopted. In fact the annual decrease in a body of people aged x must be at least equal to the decrease corresponding with the rate of decrement of healthy lives. The age distribution, then, can only be consistent with the décrémentai table of healthy lives if the following inequality always holds good a +1 where C^ represents the mean 2 c;-c; >c;(i-^ )' 2 and (1 — px) represents the rate of decrement of healthy lives corresponding with the table referred to above (table V). In order to satisfy this condition, the individual age distribution of males has been deduced from the distribution in age-groups by making the following adjustments: (1) up to age 40 by graphic interpolation; (2) between 40 and 56 by straight-line interpolation; (3) between 56 and 70 by applying the formula c* — c*+i = c , (i — i>axa). A similar procedure was followed for females: (1) by graphic interpolation for the ages 15-35, 51-59; (2) by straight-line interpolation for the ages 35-50; (3) after 50 years by the same formula c;-c x + 1 = cx(i-pia). The calculations have been carried out [5] so as to give two series of numbers Cx—reproduced in table IX—representing the age distribution of a million male and female insured persons respectively. 1 2 See § 3 below. C.x-1, x denotes, for either sex, the number of insured persons whose age comes between x — 1 and x. 528 ACTUARIAL TECHNIQUE AND FINANCIAL TABLE IX. ORGANISATION AGE DISTRIBUTION OF INSURED POPULATION (per 1 million insured of each sex) Females Males- Age Age Males Females 15 years . 16 » . . 17 » . . 18 » . . 19 » . . 47,800 44,800 42,600 40,300 36,300 58,000 55,000 50,200 44,900 40,900 40 years . 41 » . . 42 » . . 43 » . . 44 » . . 17,500 . 15,300 17,100 15,100 16,700 14,800 16,300 14,600 15,900 14,300 20 21 22 23 24 » » " " » . . . . . . . . . . 31,900 29,600 28,700 28,100 27,600 37,800 35,200 33,400 31,100 29,000 45 46 47 48 49 " " » " » . . . . . . . . . . 15,500 15,100 14,700 14,300 13,900 14,100 13,800 13,600 13,300 13,100 25 26 27 28 29 » " " " " . . . . . . . . . . 27,100 26,600 25,900 25,000 23,900 27,600 26,700 25,700 24,300 22,700 50 51 52 53 54 " " » " » . . . . • . . . . • 13,500 13,100 12,700 12,300 11,900 12,800 12,500 12,100 11,800 11,300 30 31 32 33 34 » " " " " . . . . . . . . . . 22,500 21,600 21,000 20,500 20,000 20,800 19,100 18,000 17,400 16,900 55 56 57 58 59 " " » " » . . . . . . . . . . 11,500 11,100 10,700 10,300 9,800 10,800 10,300 9,600 9,100 8,500 35 36 37 38 39 " » " » " . . . . . . . . . . 19,700 19,400 19,000 18,500 17,800 16,600 16,300 16,000 15,800 15,500 60 61 62 63 64 " » " " » . . . . . . . . . . 9,200 8,600 8,000 7,400 6,700 8,000 7,500 6,900 6,300 5,600 1,000,000 1,000,000 Subsequently, taking into account the various methods of payment of contributions, it was estimated that the total number of compulsorily insured persons was between 6 and 7 million—a total which was appreciably less than that assumed in the preparatory work 1. § 4 . — Annual Number of Beneficiaries INVALIDITY PENSIONS The estimates of the emerging cost of invalidity pensions were based partly on the biometrie tables already described .in § 1 and partly on the data and assumptions relating to the numbers of insured persons (see § § 2 and 3 above). 1 An attempt has been made to compute, from the results of the general census, the total number of compulsorily insured persons and their distribution by^age [16]. 529 ITALY The number of pensions in payment at the end of a year is obtained [5] by summing the following numbers: (1) The number of new invalids accruing during the year under review; (2) the invalids deriving from the number who became invalid in all the preceding years. The calculation is simplified by the assumption already mentioned that the insured population remains constant, both in total number and in age distribution. TABLE X. Number of years since inauguration of scheme 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 • 37 38 39 40 41 42 43 44 45 . . . . . ESTIMATE OF NUMBER OF INVALIDITY PENSIONS Males Females Number of pensioners derived Number of pensioners derived from an insured population of from an insured population of 960,000 aged 1 million aged 965,700 aged 1 million aged less than 60 less than 65 less than 60 less than 65 4,053 6,704 6,347 4,131 7,507 12,352 7,750 12,201 10,500 17,416 11,240 17,738 13,238 22,064 14,580 23,032 15,776 26,371 17,797 28,111 20,900 18,147 30,378 32,989 20,373 34,111 23,896 37,668 22,466 37,586 26,788 42,151 24,435 40,817 29,576 46,437 26,284 43,813 32,261 50,525 34,841 28,018 54,413 46,583 29,639 49,136 37,317 58,100 31,151 51,481 39,686 61,586 32,556 53,626 41,949 64,869 33,858 55,580 44,105 67,951 35,061 57,354 46,151 70,833 36,168 58,956 48,089 73,516 37,183 60,397 49,916 76,003 38,111 61,688 51,634 78,299 38,955 62,838 53,243 80,408 54,742 39,720 63,858 82,337 40,410 • 64,758 56,134 84,091 41,029 65,548 57,421 85,679 41,582 66,238 58,604 87,109 42,074 66,838 59,687 88,391 42,510 60,673 67,357 89,535 42,893 67,803 61,566 90,551. 43,229 68,186 62,371 91,450 43,522 68,513 63,093 92,242 43,776 68,791 63,736 92,936 43,995 64,307 93,544 69,027 44,183 69,226 64,811 94,073 44,344 69,394 65,255 94,534 44,481 69,536 65,643 94,933 44,597 69,655 65,982 95,279 66,276 44,695 69,755 95,578 44,778 69,839 66,532 95,836 44,848 69,909 66,752 96,058 44,907 69,968 66,943 96,249 44,956 70,017 67,106 96,413 34 530 ACTUARIAL TECHNIQUE AND FINANCIAL TABLE X. ORGANISATION ESTIMATE OF NUMBER OF INVALIDITY PENSIONS (concluded) Number of years since inauguration of scheme 46 47 48 . . . 49 50 51 52 53 . . . . 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 . . . . 73 74 75 76 77 78 79 80 . . Males Females Number of pensioners derived Number of pensioners derived from an insured population of from an insured population of 960,000 aged 1 million aged 965,700 aged 1 million aged less than 60 less than 65 less than 60 less than 65 44,997 45,031 45,060 45,084 45,104 45,120 45,134 45,145 45,154 ' 45,162 45,168 45,173 45,177' 45,180 45,183 45,185 45,187 45,188 45,189 45,190 45,191 45,191 45,191 45,191 45,191 45,191 45,191 45,191 45,191 45,191 45,191 45,191 45,191 45,191 45,191 70,058 . 70,092 70,121 70,145 70,165 70,181 70,195 70,206 70,215 70,223 70,229 70,234 70,238 70,241 70,244 70,246 70,248 70,249 70,250 70,251 70,252 70,252 70,252 70,252 70,252 70,252 70,252 70,252 70,252 70,252 70,252 70,252 70,252 70,252, 70,252 67,247 67,368 67,471 67,559 67,634 67,698 67,752 67,798 67,837 67,869 67,897 67,920 67,939 67,955 67,968 67,978 67,987 67,994 68,000 68,004 68,008 68,010 68,013 68,014 68,016 68,016 68,017 68,018 68,018 68,018 68,018 68,018 68,018 68,018 68,018 96,553 96,674 96,777 96,865 96,940 97,004 97,058 97,104 97,143 97,176 97,203 97,226 97,245 97,261 97,274 97,285 97,293 97,300 97,306 97,310 97,314 97,317 97,319 97,321 97,322 97,323 97,323 97,324 97,324 97,324 97,325 97,325 97,325 97,325 97,325 The numbers of invalidity pensions current at the end of each year, resulting from the operation of the scheme, are shown in the second column of table XII below. OLD-AGE PENSIONS The method of estimating the emerging cost of old-age pensions is similar to that used for invalidity pensions [5]. 531 ITALY TABLE XI. ESTIMATE OF NUMBER OF OLD-AGE PENSIONS Males award of first normal pensions, of year at the beginning of which estimate is made Females Number of pensioners derived Number of pensioners derived from an insured population of from an insured population of 960,000 aged less than 60 1 million aged less than 65 965,700 aged less than 60 i million aged less than 65 9,200 18,276 27,170 35,846 44,276 6,000 11,904 17,660 23,232 28,588 8,000 15,863 23,555 31,050 38,327 5,000 9,848 14,516 18,979 23,210 6 7 8 9 10 52,443 60,329 67,916 75,181 82,100 . 33,699 38,535 43,070 47,283 51,158 45,368 52,157 58,674 64,896 70,798 27,186 30,887 34,295 37,399 40,195 11 12 13 14 15 88,645 94,793. 100,521 105,814 110,661 54,688 57,869 60,701 63,183 65,318 76,355 81,545 " 86,350 90,757 94,761 42,683 44,868 46,768 48,480 50,009 115,061 119,015 122,529 125,608 128,262 67,115 68,589 69,833 70,869 71,722 98,362 101,566 104,392 106,938 109,213 51,363 52,548 53,574 • 54,452 55,192 130,504 132,358 133,921 135,225 136,297 72,413 72,965 73,398 73,732 73,984 111,226 112,989 114,515 115,820 116,921 55,807 56,309 56,713 57,032 57,279 137,166 137,860 138,405 138,825 139,141 74,171 74,305 74,400 74,465 74,508 117,836 118,583 119,184 119,658 120,025 57,466 57,605 57,705 57,775 57,824 139,376 139,545 139,665 139,746 139,801 74,536 74,553 74,563 74,570 74,573 120,304 120,510 120,659 120,764 120,836 57,856 57,876 57,889 57,897 57,901 139,835 139,857 139,870 139,878 139,882 74,575 120,883 120,914 120,933 120,944 120,950 57,903 139,884 — 120,954 — 1 2 3 4 5 16 17 18 19 • 20 21 22 23 24 25 26 27 28 29 30 . . . . . . . . . . . . . . . . . . . ; . . . . . . 31 32 33 34 35 36 37 38 39 40 41 . . . . . . 532 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION Figures of the number of old-age pensions current at the end of each year as a result of the operation of the scheme are shown in column 3 of the following table. TAHLE XII. NUMBER OF PENSIONS IN PAYMENT: EXPERIENCE Invalidity Number of pensions current at end of year Year 1920 1921 1922 1923 1924 1925 1926 1927 1928 . 1929 1930 1931 1932 1933 1934 1935 1936 722 1,618 5,362 10,885 16,903 21,654 25,741 38,027 44,546 54,225 66,961 84,244 109,761 137,204 164,094 187,065 210,279 . 1 Old age Number of pensions current at end of year 120 700 2,365 13,314 29,238 81,314 i 100,320 120,363 143,806 157,647 168,852 179,027 191,157 200,861 210,594 Including voluntary insurance from 1927. DEATH BENEFITS The number of deaths of insured males which give rise to the payment of widows' allowances was calculated [5] for C^ insured persons in each age group by multiplying the number of deaths Cx(i-pla-ix) by the marital coefficient P-3C H~ H-S + l 2 where ix represents the probability of becoming an invalid, from Zimmermann's table, and where yLx represents for each age x the proportion of total insured males who are married 1 . The total number, for an insured population of 1 million, obtained by the summation: 2 C * Í1 ~ fi* ~ **) r*i ¡C=20 (where X is the age at which the old-age pension is first payable) 1 See table VI, p. 525. ITALY 533 is 3,514 or 3,847, according as the old-age pension is payable at age 60 or 65. The number of deaths of insured males giving rise to the payments of orphans' allowances is derived in a similar manner by multiplying Cx (1 — f)x — ix) by the coefficient . _ ?x + 9x+i ?«2 where ÎÎ 3 , ÏJ See Appendix, p. 568. See. Chapter I, § 4, pp. 528-532. 21.69 million lire 59.89 71.66 74.52 11 !> 75.00 Î) >» 537 ITALY TABLE XIV. — ESTIMATED TOTAL SUMS TO BE P R O V I D E D EACH YEAR TO COVER THE ADDITION OF 1 0 0 LIRE TO EACH I N V A L I D I T Y AND OLD-AGE P E N S I O N GRANTED BY T H E STATE (In million lire) Females Males For 3,300,000 insured aged less t h a n 65 Addition of Addition of Addition of Addition oí 100 lire to Addition of Addition of 100 lire t o 100 lire t o 100 lire to invalidity 100 lire to 100 lire to invalidity invalidity old-age old-age and old-age and old-age invalidity pension pension pension pension pensions pensions For 1 million insured aged less t h a n 65 Year oí operation ol t h e scheme 1 2 3 4 5 . ! ! ' ; . . . . ! ! . . . 0.3 1.0 1.5 2.0 2.4 For 6,700,000 insured aged less t h a n 65 F o r 1 million insured aged less t h a n 65 Total lor 10,000,000 insured aged less t h a n 65 — 2.01 6.70 10.05 13.40 16.08 0.3 0.9 1.5 2.0 2.6 _ — .— — — 0.99 2.97 4.95 6.60 8.58 3.00 9.G7 15.00 20.00 24.66 3.6 4.1 4.5 4.9 5.3 • 42.88 48.91 54.27 58.96 63.65 3.1 3.5 4.0 4.4 4.8 2.9 3.3 3.6 3.9 4.1 19.80 22.44 25.08 27.39 29.37 62.68 71.35 79.35 86.35 93.02 4.4 4.6 4.8 4.9 5.1 31.68 33.66 35.64 36.96 38.61 99.35 105.35 110.68 115.35 119.68 10 I . . . 2.8 3.2 3.6 3.9 4.2 11 12 13 14 i5 . . . . ! ! ! ! '. . • 4.5 4.8 5.0 5.3 5.5 5.6 5.9 6.2 6.4 6.6 67.67 71.69 75.04 78.39 81.07 5.2 5.6 6.0 6.3 6.6 16 17 18 19 20 . . . . ! . . ! . . . 5.6 5.8 6.0 6.1 6.2 6.8 6.9 7.0 7.1 7.2 83.08 85.09 87.10 88.44 90.45 6.9 7.2 7.5 7.7 7.9 5.2 5.3 5.4 5.5 5.6 39.93 41.25 42.57 43.56 4-4.55 123.01 126.34 129.67 132.00 135.00 21 22 23 24 25 . . . . . . . . ! 6.3 6.4 6.5 6.6 6.7 7.3 7.3 7.4 7.4 7.4 91.12 91.79 93.13 93.80 94.47 8.1 8.3 8.5 8.6 8.8 5.6 5.7 5.7 5.7 5.7 45.21 46.20 46.86 47.19 47.85 136.33 137.99 139.99 140.99 142.32 26 27 28 29 30 . . . . ! . . . ! . . . 6.7 6.8 6.8 6.8 6.9 7.4 7.4 7.4 7.4 7.5 94.47 95.14 95.14 95.14 96.48 8.9 9.0 9.1 9.2 9.3 5.8 5.8 5.8 5.8 5.8 48.51 48.84 49.17 49.50 49.83 142.98 143.98 144.31 144.64 146.31 31 32 33 34 35 . . . . ! . . . . 6.9 6.9 6.9 6.9 7.0 7.5 7.5 7.5 7.5 7.5 96.48 96.48 96.48 96.48 97.15 9.3 9.4 9.4 9.5 9.5 5.8 5.8 5.8 5.8 5.8 49.83 50.16 50.16 50.49 50.49 146.31 146.64 146.64 146.97 147.64 36 ' 37 38 39 40 . . . . . . ! . . ' ! . . . 7.0 7.0 7.0 7.0 7.0 7.5 7.5 7.5 7.5 7.5 97.15 97.15 " 97.15 97.15 97.15 9.5 9.6 9.6 9.6 9.6 5.8 5.8 5.8 5.8 5.8 50.49 50.82 50.82 50.82 50.82 147.64 147.97 147.97 147.97 147.97 41 42 43 44 45 . . . . . . . . ! . . 7.0 7.0 7.0 7.0 7.0 7.5 7.5 7.5 7.5 7.5 97.15 97.15 97.15 97.15 97.15 9.6 9.7 9.7 9.7 9.7 5.8 5.8 5.8 5.8 5,8 50.82 51.15 51.15 51.15 51.15 147.97 148.30 148.30 148.30 148.30 7.0 7.0 7.0 7.0 7.0 7.5 7.5 7.5 7.5 7.5 97.15 97.15 97.15 97.15 97.15 9.7 9.7 9.7 9.7 9.7 5.8 5.8 5.8 5.8 5.8 51.15 51.15 51.15 .51.15 51.15 148.30 148.30 148.30 148.30 148.30 6 . . . . 7! . . . 8 ! 9 ; : . . ! . . . . . . . ! . . . ' ! . . . . . . 46 . . . . 47 . . . . 48 . . . . 49 50 . . . . • 538 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The calculation of the State charge in respect of death benefits based on the probable number of benefits paid each year was estimated [6: pp. 68, 93] to be 3 million lire every six months, ' Having regard to these estimates, the amount of the constant annual charge falling on the State as from 1 July 1924 and for the next six years was fixed at the round figure of 50 million lire a year, payable in two equal sums at the end of each half-year. Actually, the following sums were credited to the Fund: Million lire 50 50 25 1920 1921 1922 1923 1924 1925 1926 1927 25 50 50 25 § 3. — Other Receipts The most important item of income, after the contributions, is the interest revenue of the invested funds: TABLE XV. REVENUES OF THE INVESTED FUNDS (in thousands of lire) Revenue of insurance funds Year 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 > . • . . ' . . . . . : . . . . 3,266 13,143 26,589 40,859 57,478 77,935 104,338 123,047 151,794 157,299 183,191 203,022 217,936 226,082 .230,989 230,003 250,966 Revenue of State Grants Fund 305 2,970 6,004 7,026 7,348 9,651 13,239 13,509 14,486 12,825 11,720 10,012 8,446 5,951 3,325 • 1,796 1,373 ITALY 539 § 4. — Benefits The invalidity pension, like the old-age pension, consists of two portions: (1) a portion provided by the fixed annual State grant of 100 lire; (2) a portion based on the contributions of the insured person and employer which comprises: (a) a basic sum equal to five times the average annual compulsory contribution paid during the insurance period; (¿>) a supplementary sum equal to three-tenths of the total of all the compulsory contributions paid. The pension is increased by one-tenth for each child under the age of 18 supported by the insured. The death benefit consists of a monthly allowance of 50 lire paid during the six months following death in cases where death occurred before receipt of pension. The persons entitled to these allowances are (in order of priority) widows, invalid widowers, children under age 15. The award of a pension is conditional upon the payment of contributions during a qualifying period of 240 weeks for invalidity pensions and 480 weeks for old-age pensions. The title of survivors to benefit on the death of an insured person is not dependent upon a qualifying period. The rules for assessing the pensions specified above are those which were put into force by the Act of 13 December 1928 x. The rates of pension originally fixed by the Legislative Decree of 1919, upon which the preliminary estimates were based, were as follows: the portion of the cost borne by the State was already fixed at 100 lire per pension, but the part due to the contributions of the insured and the employer consisted of: (1) 66 per cent, of the total of the first 120 fortnightly contributions; (2) 50 per cent, of the total of the next 120 fortnightly contributions; (3) 25 per cent, of all later contributions. No provision was made for pension increase in respect of children. PRESENT VALUES OF SOME ESSENTIAL ANNUITIES [5: pp. 33, 35] The present value of the " invalidity annuity to an invalid " is the present value of the immediate annual payment of a unit during the life of an invalid. It is calculated by means of the probabilities of 1 The Legislative Decree of 14 April 1939 considerably modified the conditions of award and the rules for calculating invalidity and old-age pensions. For benefit on death it substituted widows' and orphans' pensions, or, failing them, the repayment of the contributions paid. See Appendix, pp. 567-568. 540 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION survival of invalids l taken from a select table in cases where the duration of invalidity is not greater than 10 years and from an ultimate table for durations exceeding 10 years. The value aj. is first calculated for age x attained after a duration of 11 or more years. For this purpose a reduction formula is used involving only the ultimate probabilities of survival, px, viz., a* = 1 + V PI a< + 1 where and al = 1 (v = (1 + ¿D pi = o . The select values a ¡ , ] + i for age [x] at becoming invalid and duration of invalidity (k < 11) are then obtained by means of the identity a i M+u — a t M+u and using the formula a i . . . .i i M+fe — i ~r v p[x]+k Q-ixi+k+i' Finally a.lxi is obtained, which represents the present value of unit pension at the moment of its being granted. The value of the annuity payable monthly is derived from the value of the immediate annuity by means of the formula (12) i i - ,rri a M = a M — 0.458. The numerical values of a M calculated for males and females respectively and at the two rates of interest 4 per cent, and 5 per cent, are given in table XVI. The present value of the " annuity to a healthy life " is the present value of the immediate annual payment of a unit during the healthy life of a person, ceasing on his becoming invalid. ' It is calculated by the classic formula aa NT or where D^. and N° are the commutation functions corresponding to the healthy life table * C. 1 2 See above, p. 524. See table V p. 524. 541 ITALY TABLE XVI. — VALUE OF AN INVALIDITY A N N U I T Y TO AN Males INVALID Females Age 20 years . . . 21 ' 22 ' 23 24 • 25 ' 26 ' 27 ' 28 ' 29 ' 30 ' 31 ' 32 ' 33 ' 34 ' 35 • 36 ' 37 ' 38 ' 39 ' 40 41 ' 42 ' 43 ' • 44 ' 45 ' 46 ' 47 ' 48 < 49 ' 50 51 ' 52 > 53 > 54 ' 55 ' 56 ' 57 ' 58 ' 59 ' 60 ' 61 ' 62 ' 63 ' 64 > 65 ' 66 ' 67 • 68 ' 69 ' 4 per cent. 5 per cent. 4 per cent. 5 per cent. 4.188 4.319 4.447 4.573 4.694 4.815 4.936 5.058 5.178 5.298 5.416 5.530 5.644 5.757 5.871 5.983 6.094 6.204 6.311 6.418 6.516 6.613 6.708 6.801 6.894 6.982 7.067 7.149 7.223 7.295 7.357 7.417 7.474 7.524 7.568 7.601 7.625 7.629 7.614 7.595 7.559 7.504 7.435 7.356 7.261 7.158 7.042 6.915 6.777 6.635 3.881 3.998 4.116 4.230 4.341 4.452 4.564 4.675 4.786 4.'896 5.005 5.110 5.216 5.322 5.428 5.535 5.638 5.741 5.842 5.945 6.039 6.132 6.222 6.313 6.401 6.488 6.572 6.655 6.728 6.802 6.866 6.927 6.987 7.042 7.089 7.128 7.158 7.169 7.164 7.156 7.130 7.088 7.032 6.967 6.887 6.798 6.698 6.586 6.466 6.338 6.377 6.785 7.201 7.598 7.998 8.407 8.806 9.161 9.464 9.749 10.007 10.239 10.442 10.628 10.794 10.947 11.075 11.174 11.259 11.334 11.385 11.428 11.450 11.458 11.458 11.444 11.419 11.383 11.339 11.289 11.229 11.156 11.073 10.979 10.869 10.754 10.620 10.479 10.332 10.174 5.750 6.112 6.479 6.832 7.188 7.550 7.907 8.223 8.495 8.749 8.987 9.198 9.383 9.555 9.709 9.853 9.979 10.078 10.161 10.241 10.299 10.348 10.380 10.400 10.413 10.416 10.410 10.390 10.364 10.332 10.296 10.243 10.186 10.114 10.030 9.941 9.836 9.720 9.603 9.473 9.332 9.176 9.011 8.830 8.641 8.441 8.234 8.016 7.796 7.570 io!oo4 9.817 9.621 9.411 9.191 8.960 8.723 8.476 8.226 7.971 542 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XVI. VALUE OF AN INVALIDITY ANNUITY TO AN INVALID (concluded) 1 Males Females . Age 70 years . . . 4 per cent. 5 per cent. 4 per cent. 5 per cent. 71 72 73 74 •» » » » . . . . . . . . . . . . 6.476 6.314 6.148 5.975 5.799 6.196 6.050 5.901 5.743 5.581 7.706 7.440 7.171 . 6.901 6.630 7.332 7.091 6.848 6.603 6.355 75 76 77 78 79 » ». » » » . . . . . . . . . . . . . . . 5.621 5.436 5.250 5.060 , 4.863 5.418 5.248 5.077 4.900 4.716 6.360 6.088 5.824 5.565 5.314 6.109 5.858 5.614 5.374 5.140 80 81 82 83 84 » » » " » . . . . . . . . . . . . . . . 4.669 4.476 4.286 4.100 3.918 4.534 4.353 4.174 3.998 3.826 ' 5.070 4.833 4.604 4.383 4.172 4.913 4.691 4.475 4.267 4.068 85 86 87 88 89 » » » » " . . . . . . . . . . . . . . . 3.742 3.572 3.408 3.250 3.098 3.659 3.497 3.341 3.190 3.045 3.971 3.781 3.598 3.423 3.256 3.878 3.697 3.523 3.356 3.196 90 91 92 93 ' 94 " " » » » . . . . . . . . . . . . . . . 2.952 2.812 2.678 2.547 2'.419 2.905 2.771 2.641 2.515 2.391 3.096 2.943 2.796 2.653 2.513 3.043 2.896 2.754 2.617 2.482 95 96 97 98 99 » » » » » . . . . . . . . . . . . . . . 2.290 2.154 1.999 1.801 1.507 2.266 2.134 1.984 1.791 1.502 .2.372 2.223 2.053 .1.838 1.525 2.345 2.201 2.037 1.827 1.520 100 » . . . 1.000 1.000 1.000 1.000 ' The present value of the " invalidity annuity to a healthy life " is the present value to an insured person, at present healthy, of an immediate annual payment of a unit commencing on his becoming invalid and payable during invalidity. It is obtained from the " invalidity annuity to an invalid " by means of the formula 543 ITALY where Nœ represents the commutation function corresponding to •p.ai U x ~ jaa ''x x+i v • / . x I! •* i \ i "ô" 1\x\ J a[x+i]+i i where 1 The present value of the " total annuity to a healthy life " is the sum of the values obtained for the " annuity to a healthy life " and the " invalidity annuity to a healthy life ", viz. a a x —' a act . at x i &x ' If the pension is payable monthly, the correction formula is (12) a a rra n a.x == a.x — 0.458 . Present Value of Benefits I. Present value for the insured population of an invalidity pension of fixed amount a [5: p. 36]. The present value of the pensions which will be granted during the rth year of application of the scheme is given by the formula X-l a V r+i ^ J p . J¿¿ ^x 'lx (12) i à-lx+ìì » = 20 which is written a vr+i K20, introducing the symbols H and K defined by the following formulae: X—1 H* = Cx ix ™a.¡x+¥¡ , H K5 = 2 * > i Thè total present value for all generations (a) = — : — K.20 % is obtained from the equality + 00 > irr 4 VT = -r- . i (20 < ç < X - i) 544 II. ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION Present value for the insured population of an old-age pension of fixed amount a [5: p. 37]. For the r t h year after the inauguration of the scheme the present value is r „ v Cx (12) a ax and the total [a J = a — L x III. ax Present value for the insured population of an invalidity pension whose amount ß depends upon the duration of insurance. First Method [5: pp. 38-40 and 50] It is assumed that in the calculation of the amount of invalidity pension the periods of insurance have a varying effect according to their position in relation to the fifth and the tenth year since the commencement of insurance. In order to take this assumption into account the original estimates based the method of calculation upon the following formulae: Duration of insurance n < 5 5 < n < 10 re > 10 Amount of invalidity pension ß = 0 ß = rcßx + reßa + 5ß s ß = nßi + 10ß 2 + 5ß 3 These formulae were designed in a general form so that they could be adapted to any rule for assessing pensions that could be fixed by the law. The present value (ß) of the invalidity pension can be considered as the sum of three portions corresponding respectively to the coefficients ßx, ß2 and ß3. The first portion depends on all the years of invalidity : (ßO = ßx Î - (5.5 K20 + v K21 + z;2 K32 + . . . + V™1 Kx_x) . 1/ The second portion refers to the first ten years of invalidity: (ß.) = ß2 ^ (5.5 K30 + v K» + v* K22 + vs K23 + + v" K24 + 0.5 v5 K25) ITALY 545 The third portion refers to the first five years of invalidity : (ß3) = % Í . 5 K,0 . In this way the following formulae are obtained, assuming the old-age pension to be granted at age 65: For males: at 4 per cent, (P) = at 5 per cent, (ß) = interest: 25,483,837 ßx + 10,186,624 ß2 + 5,342,331 ß3 interest: 16,533,686 ßx + 7,224,302 ß2 + 3,830,090 ß3 For females: at 4 per cent, (ß) = at 5 per cent, (ß) = interest: 32,382,369 ß t + 13,124,179 ß2- + 6,885,624 ß3 interest: 20,758,016 ßi + 9,171,495 ßa + 4,864,113 ß3 These results do not cover invalidity pensions granted, by virtue of transitional arrangements, under the following conditions: Persons compulsorily insured who become totally incapacitated during the five years from 1 July 1920 are entitled to their pension even if they have not paid 120 fortnightly contributions, provided that they have paid at least 24 and can prove that they have worked regularly during the five years preceding 1 July 1920. Members of the National Provident Fund (predecessor of the compulsory insurance institution) are excused from providing that proof in respect of the years, within the period of five years in question, during which they have paid the minimum contribution. The present value of the total of the invalidity pensions payable under the transitional arrangements was obtained by the formula (ßi + ß= + M 2 (r + i ) „*+» K20 . Second Method [6: pp. 58-61 and 67] By another method a table (table XVII) is first of all constructed which gives the amount of the pension according to the length of the period during which contributions were, or were deemed to have been, paid, on the basis of a maximum pension of 100 lire granted after 50 years of membership. 35 546 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION TABLE XVII. PORTION OF THE INVALIDITY PENSION WHICH DEPENDS ON THE DURATION OF THE CONTRIRUTION PERIOD (on the basis of a maximum pension of 100 lire) Duration of contribution period (years) Amount of invalidity pension (excluding the portion provided by State Grant) Duration of contribution period (years) (Lire) Amount of invalidity pension (excluding the portion provided by State Grant) (Lire) 0 1 2 3 4 0 4.000 8.000 12.000 16.000 25 26 27 28 29 59.370 61.000 62.625 64.250 65.875 5 6 7 8 9 20.000 23.000 26.000 29.000 32.000 30 31 32 33 34 67.500 69.125 70.750 72.375 74.000 10 11 12 13 14 35.000 36.625 38.250 39.875 41.500 35 . . . . . . 36 37 38 39 . . . . . . 15 16 17 18 19 43.125 44.750 46.375 48.000 49.625 40 41 42 43 44 83.750 85,375 87.000 88.625 90.250 20 21 22 23 24 . . . . . . 51.250 52.875 54.500 56.125 57.750 45 46 47 48 49 91.875 93.500 95.125 96.750 98.375 50 100.000 . . . 75.625 77.250 78.875 80.500 82.125 It is immediately apparent that by this method the pensions granted under the transitional arrangements are themselves incorporated in the calculation. Unlike the first method, this second method does not distinguish between the different components of benefit, but on the other hand it divides the pensions into two groups, comprising respectively pensions granted to members of the initial generation and those granted to members of later generations. The calculation of the present values is made by means of the formulae set out below, in which ß r represents the part of the invalidity pension due to the contributions of the insured and the employer after a contri1 bution period of r years and ß represents the mean — (ß -\- ß \ : 547 ITALY (1) Initial generation: For pensions granted after the completion of the qualifying period: 2 K15+r ßr^ tT» ; r=e For pensions granted under the transitional arrangements: K„2rW* ; (2) Future generations: x 1 13 - - vr-i ^¿1 ^15+r ßr+i ~J- >' (3) State grants (including transitional arrangements): (100) = 100 K»v* It + 4-) . These formulae are applied on the basis of: (1) interest at 4 per cent.; (2) old-age pension payable from age 65; (3) one million insured persons of each sex; (4) a maximum of 100 lire for the portion of the pension which depends upon contribution periods; (5) pensions to be assessed by using the coefficients ßx = 1.625 , % = 1.375 , ß, = 1 . The following are the numerical results for the total present values of invalidity pensions (in lire): Initial generation x . . . . F u t u r e generations . . . . Total Males 40,330,872 22,672,417 Females 50,655,803 29,786,416 63,003,289 80,442,219 i Including the present value of " transitional " pensions, namely, 2,241,986 lire for males and 2,889,620 for females. IV. Present value for the insured population of an old-age pension whose amount ß depends upon the duration of insurance. First Method [5: pp. 40-41 and 50] It is assumed that the method of calculating the amount of the old-age pension is defined by the formulae already referred to for invalidity pen- 548 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION sions *. The total present value of old-age pensions is again calculated as the sum of three portions [M, [M...-[M corresponding respectively to the three coefficients ßx , ß. and ßs . The calculation is made by means of the following formulae: IM = ftC8ma;£(l+.5»--t>«) ; [ßj = ß, Cx a V x ^ (1 +5i-v°) ; v [ßJ = ß, C l ( 1 V x 5i. The results produced by these formulae do not cover old-age pensions granted, under transitional arrangements, in accordance with the following clause: " Persons compulsorily insured, whose age at 1 July 1920 was between 60 and 65, will not receive an old-age pension until the expiry of at least five years from that date, and after the payment of 120 fortnightly contributions. " Persons who, at the same date, were more than 55 years old, but not more than 60, will receive a pension after their 65th birthday even if they have not paid 240 fortnightly contributions, provided that they have paid at least 120 and can prove that they have since their 55th birthday worked for a total of 480 weeks at least. " Members of the National Provident Fund are excused from supplying this proof for the years after their 55th birthday during which they have paid the minimum contribution." The present value of the old-age pensions awarded under the transitional arrangements was calculated in a similar manner to that adopted for invalidity pensions by applying the formula 5 vs (ßx + ß2 + ß3) — [lel¡ a66 + . . . + Z70 ~r Qe a [66] + with Qe+r — J ¿ j 8+iP'65+r 1 See above, p. 544. a70 + • • . + Qio %70iJ 549 ITALY where ¡ ^ P , ^ , . represent, relatively to the number of healthy lives attaining age 65, in accordance with the life-table* (namely, males, 3,429; females 3,123) the number of invalids surviving to age 65 + r after 1 * + K- years of invalidity. JL Second Method [6: pp. 61-62 and 67] There is also a second method which might be followed, corresponding to the alternative method indicated in the calculations for invalidity pensions. In this case the following formula would be used: (1) Initial generation; For pensions granted after completion of the waiting-period, X-l-tt r = io For " transitional " pensions, (a) Gompulsorily insured persons aged 55 to 60 at 1 July 1920, (b) Compulsorily insured persons aged 60 to 65 at 1 July 1920, G lää Re 6 v Iz J ¿ j {IjL+r a x + r + Q.T a [x+r]) 5 (2) Future generations; C x Px-i5 „X-l-15 «2) a a V .x (3) State grants; It is sufficient to substitute in the above formulae for ß r the fixed amount of 100 lire, thus [100] = 100 Cx [ £ 2 ( C , a2,aI+r + Qr ,12'aix+r]) + t 1 See table V, p. 524. a Vxl. 550 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION This second method is applied on the basis of (1) (2) (3) (4) interest at 4 per cent.; payment of old-age pension as from age 65; one million insured persons of each sex; a maximum of 100 lire for the part of the pension which depends on contribution periods; (5) pensions to be assessed by using the following coefficients ßx = 1.625, ß2 = 1.375, ß» = 1. The following are the numerical results for the total present values of old-age pensions (in lire): Initial g e n e r a t i o n * . . . . F u t u r e generations . . . . Total Males Females 53,089,726 19,903,124 41,224,946 15,471,915 72,992,850 56,696,861 i Including tlie present value of transitional pensions: viz. 8,814,914 lire, males; and 6,807,428, females. TOTAL ANNUAL AMOUNTS OF BENEFITS According to the records of the operation of the scheme, the totals of the invalidity pensions and old-age pensions in payment at end of each year are shown in the following table. TABLE X V I I I . AMOUNT OF P E N S I O N S IN AT END O F EACH YEAR PAYMENT (in thousands of lire) Year 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 . •. . . . . . . . . . Invalidity pensions Old-age pensions 114 273 1,079 2,550 4,538 6,377 8,397 12,663 16,897 34,946 47,119 64,011 88,693 114,697 139,696 159,833 179,365 46 303 1,107 6,319 14,154 28,381 38,988 74,685 92,324 104,361 114,640 123,922 134,043 142,598 151,635 1 Including pensions paid under voluntary insurance from 1927 onwards. 1 551 ITALY § 5. — Other Expenditure COST OF ADMINISTRATION All the actuarial estimates retained a margin for the purpose of covering the sums required for cost of administration. This margin has been successively estimated at the following percentage of the total contribution income: 13 per cent.; 8.6 per cent.; 7.2 per cent.; 12 per cent. The administration expenses which actually emerged have always been appreciably less than the margin, namely: Actual Administration Expenses (in thousands of lire) Year 1920 1921 1922 1923 1924 1925 1926 1927 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Actual Administration Expenses (in thousands of lire) Year 4,600 6,904 9,259 10,501 10,056 15,293 16,899 17,420 1928 1929 1930 1931 1932 1933 1934 1935 1936 B E N E F I T S IN KIND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . 18,875 19,709 22,472 22,506 23,756 26,184 28,567 31,464 36,041 The following table gives data concerning payments in kind during the operation of the scheme: Year 1926 1927 1928 1929 1930 1931 1932 1933 Average cost per insured person Average cost per beneficiary Number of beneficiaries Total cost Lires Lires Lires 266 1,207 4,656 5,134 17,139 21,822 27,622 33,600 38,413 625,184 874,364 1,934,505 1,549,465 3,207,502 3,557,584 3,935,501 5,967,691 6,506,474 0.1786 0.2186 0.4299 0.3099 0.5832 0.5929 0.6382 0.9422 1.0010 2,350.32 724.41 415.49 301.80 187.15 163.03 142.48 177.61 169.38 In 1934, 1935 and 1936 the total cost of benefits in kind amounted to 6,645,909, 9,056,372 and 9,729,393 lire respectively. CHAPTER III FINANCIAL SYSTEM The financial system of the scheme of insurance for employed persons against invalidity, old age and death is based on the principle of collective accumulation, with as essential technical basis a theoretical average premium calculated by taking into consideration all the generations of insured persons and all the payments falling to be paid out of the funds. In the course of these calculations it was found expedient in certain cases to consider a component part of a benefit or a generation of insured persons separately. However, none of these differentiations was followed through and in the end it was the general average premiums which were used for the purpose of fixing the rates of contribution laid down in the Act. For the purposes of financial equilibrium invalidity, old age and death were considered together. The actuarial estimates were made in most cases on the basis of alternative rates of interest, 4 per cent, and 5 per cent. § 1. — Calculation of the Theoretical Average Premiums Several calculations have been made of the theoretical average premiums, which are the fundamental technical elements upon which the financial system depends. The preliminary calculations were based on the provisions of the 1919 Bill. They were adjusted first to conform with the provisions of the legislation which had come into force, and a second time to give effect to the actual results of the first few years' operation of the scheme. First Calculation [5] The first method was to calculate separately an average premium for each constituent part of the pension. For this it was sufficient to divide the present value of the pension element in question by the present value of a unit contribution—these two values being calculated for the whole insured population. The calculations were based on the following data: (1) the fixed portion of each .pension to be 100 lire; (2) the part of the pension which depends upon the duration of the contribution period to rise to a maximum of 100 lire (after 50 years); (3) the values of the coefficients to be 1: ß t ='1.625, ß, = 1.375, ß s = l 1 With these coefficients the formulae reproduced above (pp. 544-545) conform with the rules for assessing pensions laid down by the 1919 Decree, i.e. with the factors of 66 per cent., 50 per cent, and 25 per cent, (the rate of contribution being fixed at 4 per cent, and the maximum pension at two-thirds of wage). 553 ITALY Assuming the age for the award of the old-age pension to he 65 years, the following results are obtained: TABLE XIX. AVERAGE PREMIUM FOR EACH CONSTITUENT PART OF PENSION Invalidity pension Rate of interest fixed (per cent.) amount of 100 lire Sex Males • Females depending on contribution periods, on basis of maximum of 100 lire After end of qualifying period " Transitional " Old-age pension fixed amount of 100 lire depending on contribution periods, on basis of maximum of 100 lire After end of qualifying period " Transitional " 4 5 4.11 3.65 2.3369 1.9348 0.0864 0.0968 4.47 4.01 2.6736 2.1995 0.1184 0.1324 4 5 5.30 4.63 2.9828 2.4384 0.1112 0.1228 3.48 3.12 2.0783 1.7116 0.0840 0.0940 Since the cost of the fixed portions of pension is borne by the State, the rates of contribution are fixed by reference to thé average premiums which take into consideration only those parts of the pension dependent upon the duration of contribution periods. , The total average premiums are obtained by adding together the average premiums for those pensions granted after completion of the qualifying period and for those granted under transitional arrangements. Since the latter were calculated on the basis of a maximum pension of 100 lire, the corresponding result 2s • must be multiplied by ;r— so as to apply to a maximum pension of two-thirds of the insured wages. j The average annual premiums' were calculated in this manner for the insured persons in each wage class. To the result was added, in the case of males, an additional premium of 0.58 to cover the cost of. allowances to widows and orphans. In each wage class the average premium is expressed as a percentage of the maximum salary (assuming 300 contribution days in the year); The following are the resulting rates of contribution: Ratio of contributions to wages (per cent.) Rate of interest 5 „ ,, . . . . Males (according to wage class) Females F r o m 3.50 t o 3.58 „ 2.93 „ 3.01 3.50 2.91 554 ACTUARIAL T E C H N I Q U E A N D FINANCIAL ORGANISATION These theoretical rates are in all cases less than statutory rates, namely, 4 per cent, of the maximum wage in each class. There is thus a margin of safety which, according to the preliminary estimates,, should be sufficient to cover: (1) expenses of administration; (2) the right to reckon periods of sickness and of military service as contribution periods; (3) the cost of medical treatment of invalids; (4) unfavourable fluctuations which might occur in the frequency of benefit claims. Second Calculation [6] The second method consisted of calculating directly an average premium which would be intermediate between the premium for future generations and the premium for the initial generation of insured persons. This general average premium is first calculated on the basis of a maximum 2s pension of 100 lire, the result then being multiplied by ^ - so as to relate it to a maximum pension of two-thirds of the insured wage *. In the case of males the average annual premium is increased by 0.97 to cover the cost of allowances to widows and orphans. This new additional premium conforms with the amount of 300 lire which was finally adopted for the total allowance on death in place of 180 lire assumed in the first estimates. This method gives the following rates of contribution: Ratio of contributions to wages (per cent.) Rate of interest Males (according to wage class) Females F r o m 3.49 t o 3.65 3.52 This second estimate of the theoretical rates is not appreciably different from the first: in fact it gives additional support to and justification of, the statutory rate (namely 4 per cent, of the maximum wage in each class) and confirms the existence of a margin of safety. * Third Calculation [7] The calculation of the theoretical average premiums was carried out again taking into account the following considerations: The insured population adopted as the basis of the calculations is a stationary one defined in table IX. On this basis the mean number of insured persons existing at any given date should be taken, not as ITALY 555 one million, but at the appreciably lower figure of 979,100 given by the formula 2(2 C - + 2 C «)Since the payment of contributions is made in 24 fortnightly payments it seems preferable, for the calculation of the present value of a unit contribution payable by the insured population, to replace the present value of the immediate annuity certain — + 1 by the present value of 1 1 the continuous annuity certain — + 77 • On the basis of the data underlying the second calculation, but with these adjustments, the theoretical average premium for males, expressed as a percentage of wages is increased from 3.49 to 3.63. The additional premium to be added to cover the cost of allowances to widows and orphans is estimated at the average figure of 0.08 per cent, of salary on the basis of a mean wage of 1,200 lire (instead of the mean of 600 lire previously adopted). The difference between the rate of 3.71 per cent, and the statutory rate of 4 per cent, defines the margin of safety: it represents 7.82 per cent, of the average net premium and 7.25 per cent, of the average gross premium. The premium for future generations can be considered as the individual premium of an insured person entering into insurance at the age of 15. This individual premium, calculated on the bases just described, amounts to 2.26 per cent, of wages, including the additional premium (0.08 per cent.) to cover the cost of widows' and orphans' allowances and the loading (7.82 of the average net premium) corresponding to the safety margin. It is apparent, therefore, that insured persons entering at young ages are subject to a rate of contribution (4 per cent.) which exceeds the individual premium corresponding to their entry-age. The calculations show that the individual premium rises to 3.94 per cent. for entry at age 25 and exceeds 4 per cent, for entry at age 26. Another calculation of the same, individual premiums has been made by adding 10 per cent, to the probabilities of becoming invalid at all ages less than 65, all other factors remaining unchanged. The total individual premium becomes 2.37 per cent, for an insured person who enters at the age of 15 and it exceeds 4 per cent, if entry is after the age of 24. § 2. — Financial Equilibrium Investigations of the financial equilibrium. of the system consist essentially in comparing the expected income and liabilities in respect of all insured persons, present and future; the present value of income and liabilities as they stood at 1 July 1920 are reckoned as at that date. I,-The first years of the operation of the scheme have yielded the following figures for the total contributions paid under the compulsory provisions : Year Millions of lire 1920 (last 6 months) 106 1921 1922 194 239 556 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION In view of these data the 1924 actuarial valuation [7] was based on a total insured population of 3 million and a mean annual contribution of 90 lire, i.e. a total annual contribution income amounting to 270 million lire. LIABILITIES OF THE SCHEME IN RESPECT OF INSURED PERSONS The present values of invalidity and old-age pensions reproduced above 1, relate to a maximum pension of 100 lire, which differs from the real maximum (namely two-thirds of. wage). Consequently they correspond to an annual contribution per insured person c — 6 lire, which differs from the real contribution (fixed at 4 per cent, of wage), and which is arrived at by the following equation 4 s ,™ 2 s 100 *"" *: - — 3 100 The present value of invalidity and old-age pensions for the male insured population 2 amounts to 93.42 million lire for the initial generation (i.e. insured persons aged 16 to 64 on 1 July 1920) and to 42.58 million lire for. all future generations. The latter total represents the sum of the present values corresponding to each crop of entrants, i.e. a (i + v + v* + ...) = a í i + -i) . where ÖL is the present value relating to a single crop of entrants, for example those who were in their fifteenth year on 1 July 1920. This value (6L) is obtained, then, by dividing the total 42.58 by 1 -f —, (i.e. J by 26 if i is taken as 0.04), and becomes 1.64 million-lire. Thus for the total insured population who were aged more than 15 and less than 65 on 1 July 1920 the total is 93.42 + 1.64 == 95.06 million lire. This result relates, as has been seen, to a million insured persons and a contribution of 6 lire, i.e. a total annual contribution of 6 million lire. For a total annual contribution of 270 million lire it would therefore be 95.06 X 270 ,' . .„. ' . " — = 4,277.6 million lire. a , 1 2 See pp. 544 and 548. See pp. 547 and 550. 557 ITALY EXPECTED INCOME OF THE SCHEME IN RESPECT OF INSURED PERSONS By weighting with the numbers C,. in table IX, the weighted average is calculated of the present value of thè continuous temporary annuity to a —aa healthy life \a-xßx • For all ages 15 to 64 this average is 11.44. This figure, which relates to a unit annual contribution, is multiplied by the total annual amount of contributions, viz. 270 million lire. The product must be reduced in the ratio of the " net " premium calculated for old-age and invalidity pensions, viz. 3.63 per cent., to the " gross " premium (statutory rate, viz. 4 per cent.). The final result thus produced is 11.44 X 270 X ^ — = 2,803.1 million lire. COMPARISON OF THE EXPECTED INCOME AND LIABILITIES OF THE SCHEME IN RESPECT OF INSURED PERSONS [ 8 ] The present values of invalidity and old-age pensions shown above x and the results of the second calculation of theoretical premiums provided material for an actuarial valuation. Bringing all the present values into scale with the total annual contributions, assumed to be fixed at C, the valuation balance-sheet may be constructed in the following manner: ASSETS Present value of contributions 26 C LIABILITIES Present value of invalidity and old-age pensions Present value of widows' and orphans' allowances •. Present value of the margin left to cover administration and other expenses . . Total liability 22.721 C 1.04 C 2.239 G 26 C By referring to the results reproduced above 2 relating to the liabilities and expected income of the scheme in respect of insured persons—and consequently to the theoretical average premiums produced by the third calculation—an actuarial valuation giving slightly different figures is arrived at, namely: 1 2 See pp. 544 and 548. See pp. 552-556. 558 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION ASSETS Present value of contributions 25.5 C LIABILITIES Present value of invalidity and old-age pensions Present value of widows' and orphans' allowances Present value of the margin left to cover administration and other expenses . . 23.153 G 0.51 G 1.837 C Total liability 25.5 G In order to construct a third valuation balance-sheet, based on a more precise estimate of the various items, the following procedure was adopted: (1) for the coefficients 0.6666, 0.50 and 0.2708, which for the convenience of calculation had been used in the assessment of pensions, the statutory coefficients were substituted, namely 0.66, 0.50 and 0.25. (2) In view of the results of the first few years' operation of the scheme, the annual cost of allowances to survivors was taken as 0.005 of the total annual amount of contributions. The following results were thus obtained: ASSETS Present value of contributions 25.5 C LIABILITIES Present value of invalidity and old-age pensions Present value of widows' and orphans' allowances Present value of margin left to cover administration and other expenses . . 22.289 C 0.1275 C 3.084 C Total liability 25.5 G i Insurance for employed persons against invalidity, old age and death is administered by the National Fascist Institute of Social Insurance, together with certain special schemes, the chief of which are indicated in the balance-sheet established at the end of each year. Consequently it will not always be possible to distinguish that part which relates specifically to the compulsory insurance of employed persons against invalidity, old age and death. The balance-sheet showing at 31 December 1936 the situation of the different schemes administered by the Institute is reproduced opposite. 559 ITALY TABLE X X . B A L A N C E - S H E E T AS AT 3 1 D E C E M B E R 1936 (in thousands of lire) LIABILITIES ASSETS Bonds State annuities Loans : (1) t o provinces and communes . . . . (2) for building workers' dwellings . . (3) for land improvement (4) t o h y d r o - and thermo-electric undertakings (5) t o agricultural establishments . . . . (6) mortgages and sundry loans . . . . 1,917,022 3,951,073 1,185,994 559,386 217,537 7,732 Shares in sundry institutions of national utility Advances to t h e State for w a r pensions Real estate Credit balance in t h e current account for special schemes: Compulsory insurance against t u berculosis Current accounts and cash in h a n d . Sundry debtors Furniture 2,269,776 for pensions in p a y m e n t : Old-age pensions . 964,514 Invalidity pensions 1,430,478 Widows' and orp h a n s ' pensions . 10,537 (4) I n d u s t r i a l accident pensions 17,732 (5) Pensions for public transport employees 376,432 123,922 42,269 338,916 374,227 507,716 350,820 — Commuted communal pensions fund F u n d for special schemes: transport (1) Public employees' insurance 286,187 (2) I n s u r a n c e of employees of t h e p u blic telephone services administered by p r i v a t e industry 65,446 (3) Insurance of staff of tax-collecting offices 59,231 (4) Insurance of staff of offices for collecting t a x e s on consumption . . . 41,211 (5) Insurance of staff of register and mortgage o f f i c e s . . . . 1,768 19,132 (6) S u n d r y schemes . Debit balance in t h e current account for special schemes: (1) U n e m p l o y m e n t insurance 245,440 246,966 (2) Seamen's insurance (3) Compulsory m a t e r n i t y insurance . . 27,190 (4) I n s u r a n c e of staff of subsidised s h i p ping u n d e r t a k i n g s . 40,468 (5) Salaried employees pensions fund . . 18,502 (6) National family allowances' fund for industrial w o r k e r s . 43,884 (7) F u n d for allowances to salaried employees recalled t o t h e Forces . . . . ,491 Provident fund for central office staff Current accounts and cash in h a n d . Sundry creditors Total öS.Oöfc 315,72817,649 63,968 4,676,119 418,928- Fund (1) (2) (3) 20,044 279,083 Guarantee and Reserve F u n d . . . F u n d to meet fluctuations in investment values S t a t e additions fund F u n d for supplementary invalidity pensions to voluntarily insured persons Compulsory insurance fund . . . . Voluntary insurance fund Total 2,799,693 62,735. 472,975. 624,941 56,227 47a 311,248 9,875,741 560 ACTUARIAL TECHNIQUE AN» FINANCIAL ORGANISATION § 3. — Actuarial Reserves The sums accumulated as actuarial reserves are distributed among several funds according to their object, namely: (a) (b) (c) (d) (e) compulsory insurance fund, voluntary insurance fund, fund for pensions in payment, fund for communal commuted pensions, fund for supplementary invalidity pensions to voluntarily insured persons, (/) fund for State additions, (g) fund for special schemes. The .position of each of these funds as at 31 December appears on the liability side of the general balance-sheet published each year [11]. The compulsory insurance fund deals, in principle, with insured persons who are still active contributors, and consequently includes the reserve needed to cover benefit rights which are still in the process of being acquired. It is fed by the joint contributions of employer and employed and by its own interest income. It has to supply: (1) to the fund for pensions in payment a capital sum sufficient to cover the old-age and invalidity pensions granted during each year (not including State grants); (2) half the expenditure on death benefit (the other half is borne by the State); (3) expenses incurred for the medical care of invalids an'd for measures taken to prevent invalidity. TABLE XXI. COMPULSORY INSURANCE FUNn (in thousands of lire) Year 1920 1921 1922 1923 1924 1925 1926 1927 1928 Position on 31 December . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163,635 387,853 668,820 945,098 1,270,464 1,656,024 2,096,616 2,376,379 2,764,290 Position on 31 December Year 1929 1930 1931 1932 1933 1934 1935 1936 . . . . . . . . . . . . . . . . . . . . . . . . . . . 2,844,095 . 3,129,994 . 3,421,130 . 3,668,176 . 3,860,223 . 4,076,842 . 4,336,310 . 4,676,119 The fund for pensions in payment contains the reserve to cover current pensions. The essential function of this fund is the payment of pensions, and it receives for that purpose from the other reserve funds the present value of the pensions (not including State grants) which are awarded each year. Since the balance-sheet does not distinguish the present values according to the reserve funds from which they come but only according to the nature of the benefits to which they refer, namely, old age, invalidity, survivors, the figures of the table below refer not only to persons insured in the general compulsory scheme but also to those insured voluntarily and those insured in the various special schemes. 561 ITALY TABLE XXII. — FUND FOR PENSIONS IN PAYMENT (in t h o u s a n d s of lire) On 31 December Old -age Invalidity 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 13,591 16,040 20,465 23,672 30,680 36,037 38,737 202,903 279,333 533,103 645,186 718,251 788,737 846,793 899,857 928,693 964,514 9,687 10,463 11,635 12,739 13,644 14,920 19,953 121,673 162,651 338,996 477,070 618,698 778,650 988,831 1,185,509 1,308,902 1,430,478 . . . . . . . . . . § 4. — Safety Reserves Besides the actuarial reserves already mentioned, the National Fascist Institute of Social Insurance possesses safety contingency reserves common to all the funds relating to insurance against invalidity, old age and death. The greater part of these reserves is contained in two funds which appear in the balance-sheet: one is called " Guarantee and Reserve Fund ", while the other is intended to meet fluctuations in the values of investments in securities and, since 1933, in real estate as well. The movement of each of these funds is shown in the following table. TABLE XXIII. SAFETY RESERVES (in thousands of lire) On 3i December 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1 Guarantee and Beserve Fund 51,835 52,474 52,989 53,554 54,153 54,163 54,170 54,182 54,186 54,188 54,189 54,210 54,408 54,503 54,863 54,958 55,052 Fund to meet fluctuations » in investment values Total — — — — — — — — — — — — — — — — 21,381 48,867 70,085 102,362 137,275 193,464 236,917 294,821 315,728 75,567 103,055 124,274 156,572 191,683 247,967 291,780 349,779 370,780 Up to 1932 relating to securities only; thereafter including real estate as well. 36 CHAPTER IV FINANCIAL ADMINISTRATION § 1. — Investments As has been indicated above, the reserves of the scheme of insurance for employed persons against invalidity, old age and death constitute only a part—the most important part, it is true—of the funds administered by the National Fascist Institute of Social Insurance. This section refers to the total of these funds. STATUTORY PROVISIONS The following are the authorised classes of investment: (1) Government securities or those guaranteed by the State; (2) Bonds issued by a credit institution authorised to make loans on the security of real estate (or bonds legally assimilated thereto) ; (3) Purchase of annuities payable by the State to undertakings for the improvement and irrigation of land or for the execution of other public works; (4) Loans at interest to provinces and communes and to their undertakings, and to undertakings for land improvement and land irrigation. (5) Deposits at interest with the " Government Deposit and Loan Fund ", with the Bank of Italy, and with other credit establishments of recognised stability; (6) Mortgage loans at interest for the building of working-class houses or to health establishments engaged in the prevention and cure of disease; (7) Purchase of real estate, urban and rural; (8) Shares in the capital funds of public utility institutions or establishments, subject to a legal authorisation. STATISTICS OF INVESTMENTS The National Fascist Institute of Social Insurance administers jointly the funds accumulated as reserves for the following: Compulsory insurance against invalidity, old age and death; Voluntary insurance against invalidity, old age and death; Special insurance schemes; 563 ITALY Unemployment insurance; Maternity insurance; Tuberculosis insurance ; Special scheme for seamen. It is not always possible to distinguish those results of the National Institute's administration which concern compulsory insurance against invalidity, old age and death; the reader is therefore simply referred to a thorough study, which appeared in 1937, of the Institute's administration of all its property [18]. An idea of how the funds accumulated for the insurance against invalidity, old age and death are divided between the different types of investment may be obtained from the description of the property on the assets side of the balance-sheet annually published [11]. The relevant figures for 31 December 1936 are reproduced in table XX above. The accumulation of funds under the employed persons' insurance scheme has allowed of the granting of long-term loans and of the adoption of an investment policy aiming at carrying out works of public utility. In this way sums paid into the insurance funds, while enabling the institution to carry out its social function, have at the same time played an active part in the sphere of national economics. They have contributed mainly towards the development of railways and roads, land improvement and land drainage, and schemes for improving the living conditions and housing of town workers, and in this way a large p art of the reserves has been used for the benefit of future generations. The following summary shows the total extent to which the National Fascist Institute of Social Insurance participated in works of public interest in the period 1922 to 1934, and at the same time subdivides this class of investments according to the kind of works financed [12]. Purpose of the investments Million lire Improvement and fertilisation of agricultural land . . . . 2,029 Construction of railways 1,111 Construction of workers' dwellings 606 Public works undertaken by Communes and Provinces . . 1,181 Hydro-electric and thermo-electric installations 140 Sea transport 122 Sundry works of public utility—aqueducts, roads, etc. . . 873 Undertakings deemed to be of public utility (share in capital) 63 Organisations deemed to be of public utility (purchase of bonds) 862 Total 6,987 § 2. — Actuarial and Financial Control The finances are supervised by a body composed of: a Councillor of the Court of Accounts nominated by the President of that Court, an official of the Ministry of Corporations and an official of the Ministry of Finance nominated by the respective Ministers, 564 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION a representative of t h e employers and a representative of the insured persons nominated b y the principal organisations respectively. In accordance with t h e regulations drawn up in 1924 b y its governing body t h e National Social Insurance Fund (since 1933 the National Fascist I n s t i t u t e of Social Insurance) is required t o collect demographic, economic and financial statistics which might contribute towards a review of the technical bases underlying t h e general scheme of insurance against invalidity, old age and death. § 3. — Accounts and Statistics The central organisation (namely the National Social Insurance Fund, the National Fascist Institute of Social Insurance) publishes each year a general report [11] of its proceedings, with an introduction bv its Director. BIBLIOGRAPHY I. Legislative Texts 1. Legislative Decree dealing with provision for compulsory insurance against invalidity and old age. Bulletin of the International Labour Office (Basle), 1919, Vol. XIV, p. 127. 2. Decree No. 3814 respecting compulsory insurance against invalidity and old age for persons of both sexes. L. S. l , 1923, It. 12. 3. Act No. 2900, to amend section 8 of Legislative Decree No. 3814. L. S., 1928, It. 5. 4. Legislative Decree No. 1827 to amend and consolidate the laws relating to social insurance. L. S., 1935, It. 5. II. Administrative Publications 5. • L'Assicurazione obbligatoria contro l'Invalidità e la Vecchiaia (Studio Matematico del Prof. Tullio BAGNI). — Pubblicazioni della Divisione Previdenza Sociale, N. 1, Rome, 1919. 6. L'Assicurazione obbligatoria contro l'Invalidità e la Vecchiaia (Prima relazione sull'applicazione al 31/XII/22). — Pubblicazioni della Direzione Generale del Lavoro e della Previdenza Sociale, N. 7, Rome, 1924. 7. Relazioni sopra varie forme di Assicurazioni sociali (Invalidità e Vecchiaia). Cf. Allegato tecnico sulle basi finanziarie dell'Assicurazione obbligatoria contro l'invalidità e la vecchiaia, pp. 71-105. Ministero delle Finanze. Gomitato per le Assicurazioni Sociali. Rome, Libreria dello Stato, 1924. L. S. = Legislative Series of the International Labour Office. ITALY 565 8. Basi finanziarie e prime esperienze dell'assicurazione obbligatoria per la invalidità e la vecchiaia. Relazione del Direttore Generale al Consiglio di Amministrazione. Cassa Nazionale per le Assicurazioni Sociali, Rome, 1925. 9. " L'attività della Cassa Nazionale per le Assicurazioni Sociali nel Primo decennio del Regime Fascista." Le Assicurazioni Sociali, NovemberDecember, 1932. 10. L'Istituto Nazionale Fascista della Previdenza Sociale. Pubblicazione dedicata ai partecipanti al X congresso internazionale degli attuari. Rome, 1934. 11. Rendiconti: " Cassa nazionale per le Assicurazioni Sociali, 1919-1932." " Istituto Nazionale Fascista della Previdenza Sociale 1933, 1934, 1935, etc." 12. L'activité de l'Institut National Fasciste de Prévoyance sociale. Rome, 1935. III. 13. 14. 15. 16. 17. 18. Articles P. MEDOLAGHI. " Il sistema finanziario dell'assicurazione obbligatoria per la invalidità e vecchiaia." Le Assicurazioni Sociali, 1925, p. 19. Gt. MIKELLI. " La frequenza della invalidità nell'assicurazione obbligatoria." Giornale dell'Istituto Italiano degli Attuari, Aprii 1935. Ricerche sulla mortalità degli invalidi. Metodi di raccordo con la tavola di mortalità della popolazione generale. Confronti. Società italiana per il progresso delle scienze. Rome, 1936. " I l numero degli assicurati obbligatori desunto dai censimenti della popolazione generale. Notizie statistiche " (supplement to the review Le Assicurazioni Sociali), May-June 1937. "Mortalità dei pensionati per invalidità nell'assicurazione obbligatoria. Notizie statistiche " (supplement to the review Le Assicurazioni Sociali), September-October 1937. " Le riserve per tutte le gestioni dell'Istituto ed il loro impiego. Notizie statistiche " (supplement to the review Le Assicurazioni Sociali), November-December 1937. APPENDIX While this volume was in the press a Legislative Decree 1 , dated 14 April 1939, was issued which amended the various branches of compulsory social insurance. As regards pension insurance, it should be noted in the first place that insured persons have been divided into four groups : salaried employees, nonagricultural workers, permanent agricultural workers and agricultural day labourers, and that most of the new provisions differ for these classes. The Legislative Decree came into operation on 1 May 1939, but the following account will show that several of its clauses will come into force at a later date. The minimum age for admission to insurance is lowered from 15 to 14 years. For salaried employees the maximum income limit for admission to insurance is raised from 800 to 1,500 lire a month, but the obligation to insure continues for an employee who exceeds this limit after his admission to insurance. 1 Reggio Decreto-Legge No. 636, Gazetta Ufficiale del Regno d'Italia, 3 May 1939, No. 105. 566 ACTUARIAL TECHNIQUE AND FINANCIAL ORGANISATION The wage classes and the rates of contribution corresponding to them are modified. The scales- for the four groups of insured persons are shown below. A. Wage class 1 2 3 4 5 6 7 8 9 B. Wage class 1 2 3 4 5 6 7 8 9 10 Salaried employees Monthly wage (lire) Monthly contribution (lire) Up to 150 150-250 250-400 400-600 600-800 800-1,000 1,000-1,200 1,200-1,400 Over 1,400 11.30 18.80 30.10 45.20 60.20 75.20 90.20 105.20 120.20 Non-agricultural workers Weekly wage (lire) Weekly contribution (lire) U p to 12 12-24 24-36 36-48 48-66 66-84 84-108 108-132 132-156 Over 156 0.90 1.80 2.70 3.60 4.90 6.30 8.20 10.00 11.90 13.60 G. Permanent agricultural labourers Annual contribution (lire) 108 54 Males . . Females. D. Agricultural day labourers Daily contribution (lire) For each man over 18 years For each woman and for young persons between 15 and 18 years 0.36 0.18 567 ITALY The pensionable age is to be lowered gradually year by year to 60 years for men and 55 years for women, as shown below. Pensionable age Year 1940 1941 1942 1943 Men Women 65 64 63 62 61 60 65 59 58 57 56 55 For salaried employees, from 1 January 1940 onwards an insured person will be deemed to be invalid if his loss of earning capacity is one-half, instead of the former ratio of two-thirds. The conditions for the grant of old-age pensions will be as follows from 1 January 1940 onwards: / 1. Completion of a 15-year qualifying period; 2. Payment of a minimum sum in contributions, as follows: Minimum payment (lire) 1,950 750 1 200 Salaried employees Non-agricultural workers Agricultural day labourers { males j m females ' ' ' ' ^ e g ; ; ; ; '600 §j¡¡¡ The conditions for the grant of invalidity pensions will be as follows from 1 January 1940 onwards: 1. Completion of a 5-year qualifying period; 2. Payment of contributions during not less than one year in the 5-year period preceding the application for pension; 3. Payment of a minimum sum in contributions, as follows: Minimum payment (lire) Salaried employees Non-agricultural workers Permanent agricultural labourers I females Agricultural day labourers J j ^ 650 250 200 ; ; ; ; ; f00 Invalidity and old-age pensions will continue to be calculated according to a uniform formula. From 1 January 1940 onwards their amount will be fixed as follows : For male salaried employees, at 54 per cent, of the first 1,500 lire of contributions, at 39 per cent, of the following 1,500 lire and at 24 per cent. of all subsequent contributions; 568 ACTUARIAL T E C H N I Q U E AND FINANCIAL ORGANISATION For female salaried employees, at 43 per cent, of the first 1,500 lire of contributions, at 31 per cent, of thé following 1,500 lire and at 19 per cent. of all subsequent contributions; For male workers and labourers, at 54 per cent, of the first 700 lire of contributions, at 39 per cent, of the following 700 lire and at 24 per cent. of all subsequent contributions ; For women workers and labourers, at 43 per cent, of the first 700 lire of contributions, at 31 per cent, of the following 700 lire and at 19 per cent. of all subsequent contributions. For workers and labourers the children's bonus will in future (from 1 January 1940 onwards) be paid only until the age of 15 years, instead of 18 years as hitherto. Pensions will be payable to survivors from 1 January 1945 onwards. The widow (widower if invalid) and orphans of under 15 years in the case of workers (all classés) and under 18 years in the case of salaried employees will be entitled to a pension on the death of a pensioner or of an insured person who has acquired the right to a pension. The amount of the widow's and orphans' pensions is fixed at a fraction of the amount of the invalidity or old-age pension to which the deceased person was or would have been entitled (including the State subsidy), as follows: 50 per cent, for the widow; 10 per cent, for orphans having lost one parent; 20 per cent, for orphans having lost both parents. The aggregate amount of the widow's and orphans' pensions may not be less than half or more than the whole of the pension to which the deceased person was or would have been entitled. If the insured person dies before acquiring the right to a pension, but has completed at least one contribution year during the five years preceding his death, his widow is entitled to a lump sum equal to the total amount of contributions paid, but not less than 300 lire or more than 1,000 lire. If the deceased leaves no widow, this sum is paid to the orphans. As a transitional measure, if an insured person dies between 1 January 1940 and 1 January 1945, the survivors will receive a lump sum equal to the total amount of contributions paid, but not less than 500 lire or more than 1,000 lire; and if a pensioner dies between 1 January 1940 and 1 January 1945, the survivors will be entitled to one annuity of the pension (excluding children's bonuses). Until 31 December 1949 the State will continue to defray the cost of a fixed part of each invalidity and old-age pension, amounting to 100 lire a year per pension. In addition, it will grant a subsidy from 1 January 1945 and until 31 December 1949 as follows: 50 lire for each widow's pension ; 10 lire for each orphan's pension for orphans having lost one parent; 20 lire for each orphan's pension for orphans having lost both parents. From 1 January 1950 onwards the amount of these subsidies will be reduced by 10 per cent, each year.