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.
Mathematics Subject Classification: 62E15
Distribution, Estimator, Imputation, Treatment, Quantile.