Inflation persistence in BRICS countries : A quantile autoregressive ( QAR ) approach

Using the quantile autoregression methodology (QAR), this study contributes to the everexpanding empirical literature by investigating the persistence in inflation for BRICS countries using quarterly time series data collected between 1996 to 2016. Our empirical analysis reveals two crucial findings. Firstly, for all estimated regressions, inflation persistence in the higher percentiles of the QAR regression exhibits unit root tendencies. Secondly, we note that the global financial crisis did alter the levels of inflation persistence at all quantiles for all BRICS countries. Collectively, we advise monetary authorities in BRICS countries to focus on keeping inflation at low and stable rates. JEL Classifications: C21; C31


Introduction
Following the turn of the millennium, much emphasis has been placed on the concept of price stability as the core mandate of monetary policy practice by a vast majority of Central banks worldwide.Since then, there has been a multitude of empirical literature which has considered whether monetary policy has been effective at controlling inflation rates or not (Amano, 2007;Gaffeo & Canzian, 2011;Cioran, 2014;Moore, 2014;Colucci & Valori, 2015;Cukierman, 2017 amongst others).From an academic perspective, the centre of this debate primarily revolves around the issue of whether an observed series of inflation rates behaves as a persistent process over time or exhibits mean-reverting tendencies.At a policy level, a highly persistent inflation process is undesirable since a number of macroeconomic policy models, such as Fisher hypothesis, the expectationsaugmented Phillips curve, the traditional capital asset pricing model (CAPM) and the purchasing power parity (PPP) relationship, depend on the assumption of a stationary inflation process.In particular, the forecastability of inflation by monetary authorities and academics alike is highly distorted if inflation is found to contain unit root characteristics and is believed to have been the underlying factor behind the failure of a number of stabilization programmes (Phiri, 2017).
From an econometric perspective, the most straight-forward method of measuring the persistence in an inflation series is to estimate an autoregressive (AR) process of the inflation rate, and determine whether the sum of the AR coefficients (i.e.SARC) of the lag length p, exceeds unity.The rationale underlying this approach is that the SARC of an AR process of an inflation series is equal to or greater than unity, then inflation is deemed to be highly persistence.Conversely, as the SARC approaches zero, then inflation becomes less persistent and increasing stationary hence rendering the time series more controllable by monetary authorities.Up-to-date, there have been a dearth of empirical studies which have estimated SARC of the inflation process for industrialised countries (Gadzinski & Orlandi, 2004;Batini, 2006;Cuestas & Harrison, 2010;Gerlach & Tillman, 2012;Wolters & Tillman, 2015), developing countries (Khadaroo, 2005;Rangasamy, 2009;Mourelle et al., 2011;Gil-Alana, 2011;Phiri (2012;2016;2017); Balcilar et al., 2016;Gil-Alana et al., 2016;Gupta et al., 2017) and mixed economies (Antonakakis et al., 2016) with these studies providing a variety of conflicting empirical evidences for the differing economies under investigation.
In this current study, we investigate the inflation persistence for BRICS countries, and to the best of our knowledge, this becomes the first study to do so for this group of emerging economies.Besides the lack of availability of empirical literature surrounding the issue for BRCIS countries, we consider the BRICS countries as an interesting case study since a majority of these emerging economies use inflation targeting policy frameworks as official monetary policy mandates.Hence, the ability of Central Banks in BRICS countries to control the inflation rate can be thought of as a benchmark measure of the success of monetary policy conduct in these countries.Moreover, the BRICS countries are representative of emerging economies which are uniquely characterized by highly developed financial markets and open economies, on one end, and high levels of unemployment and widespread income inequality as well as poverty, one the other end.Consequentially, high levels of inflation persistence in the BRICS countries may prove to be more detrimental to the proper functioning of these economies since BRICS countries rely on stable financial environments in order to implement macroeconomic policies aimed at improving their social statuses.
Of recent, a couple of studies have deviated from the conventional use of the autoregressive (AR) framework in favour of quantile regression framework in capturing the persistence within an inflation process (Tsong & Lee, 2011;Manzan & Zerom, 2015;Wolters & Tillman, 2015;Gupta et al., 2017).As critical discussed in Koenker & Hallock (2001), quantile regression provide a number of advantages over other conventional estimation techniques.For instance, the regression coefficients from quantile regression estimates do not vary by concealing on the target variable for most of the percentiles and presents a more complete picture of the relationship between the target variables and the covariates.Moreover, unlike OLS estimates which can be inefficient if the errors are highly non-normal, quantile regression are more robust to non-normal errors and outliers (Koenker & Bassett, 1978).Therefore, quantile regression investigate the impact of the dependent variable at many points of the conditional distribution, not only at the centre but also in the tails (Benoit & Van der Poel, 2009).Thus, in light of the aforementioned advantages, we consider the quantile autoregression (QAR) as an excellent choice for modelling the inflation persistence via SARC estimates for the BRICS countries since the QAR model generally allows for certain asymmetric behaviour within a time series, yet retains the computational simplicity of OLS estimates.
Having provided this brief background to the study, we structure the rest of the manuscript s follows.The next section of the paper presents the QAR model, the third section of the paper presented the empirical data and empirical QAR regression estimates.The paper is concluded in the fourth section of the paper in the form of policy conclusions.

Baseline AR model of inflation
As previously mentioned, we use the SARC estimates as a means of measuring the persistence in an AR process of an inflation series.This methodology assumes that inflation persistence can be captured as the positive serial correlation in a univariate process of the inflation variable Rangasamy (2009).Denoting  as the inflation process, we specify our AR process of inflation as: From regression (1), inflation persistence () is measured as the SARC which is computed as: (2) And the decision rule for evaluating the persistence in the inflation process is that inflation is deemed as being persistent if   1, thus implying that inflation exhibits unit root tendencies.On the other hand, if  < 1, then inflation is assumed to be a stationary, mean reverting process.

Specification of QAR model of inflation
Quantile regression is a method of fitting a regression line through the conditional quantiles of a distribution (Benoit & Van der Poel, 2009).The QAR model by the -th order AR process with random coefficients can thus be specified as follows: Where   's are unknown functions [0,1]  and {  } is a sequence of iid standard uniform random variables.Provided that  0 (  ) +  1 (  ) −1 + ⋯ +   (  ) − are monotone increasing in   , then the -th conditional quantile function of   can be expressed as: Where   ( −1 ) is the conditional distribution function and equation ( 4) is now our baseline representative QAR(p) model of inflation.In creating a vector   = (1,   − 1, … ,  − )', the QAR model can be written as : Whereby   , known as the AR quantiles, can be estimated as: Where the function   (.) is the quantile loss function defined as   () = [ -.( < 0)].Since, the minimization problem represented in equation ( 6) is formed as a linear function of parameters, can be solved very efficiently by linear programming methods (Koenker & Bassett, 1978).In the special case  = 0.5, the quantile regression delivers the least absolute deviation (LAD) estimation of the OLS model (Koenker & Bassett, 1978).
The conditional density of  t on   can be estimated by the difference quotients: For some appropriately chosen sequence of 's i.e. ( −1 ,   ).

Empirical data
All empirical data used in our study consists of annual time series of inflation in consumer prices for Brazil, Russia, India, China and South Africa and all data has been collected for a 20 year period between 1996 and 2016 in quarterly intervals.All time series data has been collected from the International Monetary Fund (IMF) International Financial Statistics database and the summary statistics for the time series are reported in  The SARC estimates are based on estimates of an AR(p) process of inflation with the optimal lag being selected using the AIC information criterion.The AR estimates are based on heteroscedasticity-robust standard errors.

QAR regression estimates results
The estimates of the QAR regressions are reported in Table 2, and have been executed for nine quantiles (i.e. 10 th quantile, 20 th quantile, 30 th quantile, 40 th quantile, 50 th quantile, 60 th quantile, 70 th quantile, 80 th quantile and 90 th quantile).Our empirical results unravel a number of interesting phenomena.For starters, we observe low levels of inflation persistence, defined as SARC estimates below unity, at observations below the 40 th quantile and these gradually begin to increase as one moves up the quantile ranks.We particularly note that the SARC estimates begin to exceed unity after crossing beyond certain quantiles and these limits differ amongst the BRICS countries i.e.50 th quantile for South Africa, 60 th quantile for India, 70 th quantile for Brazil and 80 th quantile for both Russia and China.It is also interesting to note that the range of inflation persistence across the quantiles varies amongst the BRICS ranging from 0.44 to 1.45 for Brazil, 0.24 to 1.87 for Russia, 0.61 to 1.31 for India, -0.11 to 1.23 for China and 0.62 to 1.61 for South Africa.

Sensitivity analysis
In order to ensure that our preliminary QAR estimates are not biased, we perform sensitivity analysis by incorporating a structural break corresponding to the global financial crisis.We consider the sub-prime crisis as an import structural event since the crisis had a significant effect on inflation rates in most countries worldwide, more prominently so around the 2008 period.Indeed, the previous works of Phiri (2017) demonstrate on how the financial crisis altered the degree of inflation persistence in South Africa.Nevertheless the aforementioned study employs traditional OLS estimates which are founded on the realistic assumption that persistence in the inflation process remains uniform across all levels of inflation.We overcome this shortcoming by re-estimating our QAR regressions of inflation for the BRICS countries which involves splitting our observations into tow sub-samples, one corresponding to the pre-crisis period and the other to the post-crisis period.The results of this empirical exercise are recorded in Tables 3 and 4, respectively.Indeed, our results indicate changing dynamics in the inflation series as moves from the pre-crisis to the post-crisis period.For the case of Brazil, we observe that high persistence in the inflation series begin to emerge at the 80 th quantile in the pre-crisis period which reduces to the 50 th quantile in the post-crisis period.For high inflation persistence emerges in the 80 th quantile and 60 th quantile for the pre-crisis and post-crisis periods, respectively.Concerning India, non-stationary trends in the inflation process emerge in the 70 th quantile for the pre-crisis periods and 40 th quantile for the post-crisis period.For the Chinese data the SARC estimates fall we below unity in all quantiles in the pre-crisis periods whereas inflation turns highly persistence in the post-crisis period.Lastly, inflation persistence in South Africa emerges in the 60 th quantile in the pre-crisis which is slightly lowered to the 50 th quantile in the post-crisis periods.Collectively, our results indicate that inflation has been less controllable by Central Banks in BRICS countries in periods subsequent to the financial crisis, more prominently so for Russia and South Africa.

Conclusion
Concerned by the lack of empirical evidence, documenting levels of inflation persistence amongst BRICS countries, our study sought to fill in this gap by applying quantile regression analysis on a univariate series of the CPI inflation for the BRICS economies using time series collected between 1996 and 2016.In being aware of a possible structural break caused by the sub-prime crisis, we also undertook a sensitivity analysis which involved estimate quantile regression for two-sub sample periods corresponding to the pre and post financial crisis periods.Our obtained empirical results certainly have important policy implications for Central Banks in BRICS economies as well as for academics worldwide.From a policy point of view, monetary authorities on BRICS countries should aim at keeping inflation as low as possible.This holds more prominently so for South Africa and Russia in post-crisis periods.From an academic perspective, we encourage future researchers to investigate inflation dynamics across different quantiles for various economies, and in particular, inflation targeting countries.Such an empirical exercise can be undertaken via other univariate quantile regressions like the quantile regression unit root tests or the quantile regression GARCH (QR-GARCH) models.
Table1below.The reported mean statistics show that inflation averages are highest in Russia and lowest in China.Similarly, the reported standard deviations indicate that inflation is most volatile in Russia and least volatile in South Africa.The skewness, kurtosis and normality tests (i.e.Jarque-Bera) statistics all demonstrate that some of the observed time series are not normally distributed, an observation which strengthens the case for quantile regression over OLS estimates.Moreover, the SARC estimates displayed in the last row of Table1 inflation rates in all five BRICS countries behave as stationary process over the full sample period, with South Africa having the highest rates of persistence and China have least persistent levels.

TABLE 1 .
SUMMARY STATISTICS OF THE TIME SERIES Note:

TABLE 2 .
FULL SAMPLE SARC ESTIMATES