Efficient Estimation of Counterfactual Distributions and Testing Distributional Treatment Effects

Abstract

This article considers efficient estimation of and inference on counterfactual distributions in a discrete (binary or multivalued) treatment. The counterfactual distributions are estimated by weighted sample averages and the distributional effects are tested by the Mann-Whitney statistics. The difference between this study and other studies in the literature is the way to estimate the weighting functings. While other studies estimate the weighting functions either parametrically or semiparametrically or nonparametrically without incorporating the restrictions on the weighting functions, we estimate the weighting functions by imposing those restrictions. As a result, our estimated counterfactual distribution functions and the Mann-Whitney statistics are efficient, attaining the semiparametric efficiency bounds which are also derived in the paper. A small scale simulation study and an application to the job training program illustrate the practical value of the proposed approach.