A Comparison of the Accuracy of Design-Based and Model-Based Estimation in the Presence of "All or Nothing" Data

Abstract

Model-based estimation has been used for decades now. It can produce much more accurate estimates than classical design-based approaches in a variety of settings. Of particular interest is tax settings with a goal of estimating a dependent variable, y, such as a qualifying amount or taxable amount, from a model built from an independent variable, x, that typically is some type of cost or expenditure. The independent variable tends to be highly skewed with many low values and fewer larger values; it typically fits a gamma distribution. 

Classical regression assumes model residuals from sampled values are normally distributed around the regression line.  However, this is not a requirement of model-based estimation.

In many tax settings, y=x with probability p, and y=0 with probability 1-p.

This paper reviews the theoretical foundation of applying model-based estimation in this common tax setting and provides simulations demonstrating its efficacy in comparison to common design-based alternatives used in tax — the Mean Per Unit (MPU) or Horvitz-Thompson estimator, and the difference estimator (DIFF). 

Model-based methods were found to be superior to the design approaches in nearly all settings.

KeyWords: Tax, All or Nothing, Model-Based Estimation, Design-Based Estimation, CV, MSE, Confidence Interval Coverage, Simulation