Unconditional quantile partial effects under endogeneity

This paper studies identification, estimation, and inference of general unconditional quantile partial effects (UQPE) under endogeneity. When a valid instrument is available, we show that using a control-function approach, the UQPE can be identified through the conditional average of the conditional quantile partial effects, given the unconditional quantile of the dependent variable of interest. Based on this identification result, we propose a semiparametric two-step estimator. The first step is based on a control-function quantile regression method, and the second step uses a nonparametric estimator to compute the conditional average. This general formulation includes nonparametric regressions and sieve estimators. The asymptotic properties of the estimator are derived, namely, consistency and asymptotic normality. We also develop practical statistical inference procedures and establish the validity of a bootstrap approach. Monte Carlo simulations show that the proposed methods have good finite-sample properties. Finally, we apply the proposed methods to estimate unconditional quantile effects of class size on educational performance.