Estimation and inference for distribution functions and quantile functions in treatment effect models

We propose inverse probability weighted estimators for the distribution functions of the potential outcomes under the unconfoundedness assumption and apply the inverse mapping to obtain the quantile functions. We show that these estimators converge weakly to zero mean Gaussian processes. A simulation method is proposed to approximate these limiting processes. Based on these results, we construct tests for stochastic dominance relations between the potential outcomes. Monte-Carlo simulations are conducted to examine the finite sample properties of our tests. We apply our test in an empirical example and find that a job training program had a positive effect on incomes.