Distributive and Quantile Treatment Effects: Imputation Based Estimators Approach

Abstract

This paper develops two new classes of estimators measuring the distributive effects of a treatment on a population. Using imputation methods, empirical quantile and bootstrap simulations, we managed to define and study the properties of the two classes. The first class is Imputation Based Treatment Effect on distribution based on rank preservation assumption, basically the effect of treatment on the distribution of potential outcome. The second class is Imputation Based Quantile Treatment Effect which, according to this work is supposed to be the true Quantile Treatment Effect since no rank preservation assumption is made. The second class is based on the fact that each quantile before the treatment is tracked after the treatment and the estimator compares the same group before and after. The first class of estimators (for example the one generated by k-Nearest Neighbors imputation method) performs well as classic Quantile Treatment Effect given the simulation result. When applied to Lalonde real data set, it performs better than classic Quantile Treatment Effect and Firpo’s semi parametric estimator especially for middle quantiles. Also, we found that there is a significant difference between the two classes of estimators meaning that the bias caused by rank preservation assumption is quite significant.