Semiparametric estimation of binary response models with endogenous regressors

In this paper, we propose a two-step semiparametric maximum likelihood (SML) estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach. The first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals. In the second step, the latter are added as control variates to the outcome equation, which is in turn estimated by SML. We establish the estimator's n-consistency and asymptotic normality. In a simulation study, we compare the properties of our estimator with those of existing alternatives, highlighting the advantages of our approach.