An IV estimator for a functional coefficient model with endogenous discrete treatments

We propose instrumental variables (IV) estimators for averaged conditional treatment effects and the parameters upon which they depend in the context of a semiparametric outcome model with endogenous discrete treatment variables. For this model, the treatment impacts are unknown functions of a vector of indices that depend on a finite dimensional parameter vector. We develop the theory for an estimator of these impacts when they are averaged over regions of interest. We prove identification, consistency and N-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 propensity score model. In the Monte Carlo study, the estimators perform well over a wide variety of designs covering both correct and incorrect propensity score model specification.