Semiparametric Instrumental Variable Estimation in an Endogenous Treatment Model1

In this paper we propose an instrumental variables (IV) estimator for a semiparametric outcome model with endogeous discrete treatment variables. The main contribution of our paper is that the identi…cation, consistency and asymptotic normality of our estimator all hold even under misspeci…cation of the treatment model. As expected from Newey and McFadden (1994), the covariance matrix for the parameters and functions of interest does not depend on estimation uncertainty of the instruments for the endogenous treatments. Further, we extend our method to the nonparametrtic case with both continuous and discrete exogenous variables. We prove identi…cation, consistency and asymptotic normality and provide uniform convergence results for estimated functions of interest.