Partial identification and inference for conditional distributions of treatment effects

This paper considers identification and inference for the distribution of treatment effects conditional on observable covariates. Since the conditional distribution of treatment effects is not point identified without strong assumptions, we obtain bounds on the conditional distribution of treatment effects by using the Makarov bounds. We also consider the case where the treatment is endogenous and propose two stochastic dominance assumptions to tighten the bounds. We develop a nonparametric framework to estimate the bounds and establish the asymptotic theory that is uniformly valid over the support of treatment effects. An empirical example illustrates the usefulness of the methods.