Semiparametric instrumental variable estimation in an endogenous treatment model

We propose instrumental variable(IV) estimators for quantile marginal effects and the parameters upon which they depend in a semiparametric outcome model with endogenous discrete treatment variables. We prove identification, consistency, and asymptotic normality of the estimators. We also show that they are efficient under correct model specification. Further, we show that they are robust to misspecification of the treatment model in that consistency and asymptotic normality continue to hold in this case. In the Monte Carlo study, the estimators perform well over diverse designs covering both correct and incorrect treatment model specifications.