Estimation of an average causal response function in a high-dimensional sample selection model with application to US Job Corps program

Abstract

Average causal response function (ACRF) is a valuable tool for assessing treatment effects with dose functions, particularly in the presence of endogeneity. Motivated by the US Job Corps program, this paper studies the identification and estimation of an ACRF under sample selection and high-dimensional controls, in which both outcomes and treatment are partially observed. We derive Neyman-orthogonal moments to identify the ACRF, provide a causal decomposition of this parameter, and develop a semiparametric sieve estimator. We establish the asymptotic properties of the estimator and demonstrate its finite-sample performance through Monte Carlo experiments. Empirical analysis shows that there exist significant heterogeneous effects of residential components on risky behavior outcomes but not on earnings, which offers new insights for policy makers.