In this paper, we derive a semiparametric estimation procedure for the sample selection model when some covariates are endogenous. Our approach is to augment the main equation of interest with a control function which accounts for sample selectivity as well as endogeneity of covariates. In contrast to existing methods proposed in the literature, our approach allows that the same endogenous covariates may enter the main and the selection equation. We show that our proposed estimator is \sqrtn-consistent and derive its asymptotic distribution. We provide Monte Carlo evidence on the small sample behavior of our estimator and present an empirical application. Finally, we brie y consider an extension of our model to quantile regression settings and provide guidelines for estimation.
Sample selection model semiparametric estimation endogenous covariates control function approach quantile regression