Two-Step Estimation, Optimal Moment Conditions, and Sample Selection Models

Abstract

Two step estimators with a nonparametric first step are important, particularly for sample selection models where the first step is estimation of the propensity score. In this paper we consider the efficiency of such estimators. We characterize the efficient moment condition for a given first step nonparametric estimator. We also show how it is possible to approximately attain efficiency by combining many moment conditions. In addition we find that the efficient moment condition often leads to an estimator that attains the semiparametric efficiency bound. As illustrations we consider models with expectations and semiparametric minimum distance estimation.

Keywords: Efficiency, Two-Step Estimation, Sample Selection Models, Semiparametric Estimation

JEL Classification: C10, C21