Double Machine Learning for a Partially Linear Model with Endogenous Treatments and Multivariate Sample Selection

We propose double machine learning (DML) estimators for a partially linear model (PLM) with endogenous treatments and multivariate sample selection. We prove asymptotic normality of the estimators under mild regularity conditions and study finite sample properties on simulated data. The results demonstrate the importance of addressing sample selection in PLMs and the usefulness of the proposed estimators for avoiding selection bias. Moreover, we extend the proposed estimators to the case of endogenous switching.