Unconditional quantile partial effects under endogeneity

This paper studies identification, estimation and inference of general unconditional quantile partial effects models 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. We propose a semi-parametric 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. We apply the proposed methods to estimate the unconditional quantile effects of class size on educational performance.