Efficient Semiparametric Estimation of Quantile Treatment Effects

This paper presents calculations of semiparametric efficiency bounds for quantile treatment effects parameters when selection to treatment is based on observable characteristics. The paper also presents three estimation procedures for these parameters, all of which have two steps: a nonparametric estimation and a computation of the difference between the solutions of two distinct minimization problems. Root-$N$ consistency, asymptotic normality, and the achievement of the semiparametric efficiency bound is shown for one of the three estimators. In the final part of the paper, an empirical application to a job training program reveals the importance of heterogeneous treatment effects, showing that for this program the effects are concentrated in the upper quantiles of the earnings distribution.