Doubly-Robust Parametric Estimation in Moment Conditions Models with Missing-at-Random Data

Abstract

We consider estimation of finite dimensional parameters defined by a set of moment restrictions when observations on key variables are missing-at-random. We consider the verify-in-sample and verify-out-of-sample cases of Chen, Hong and Tarozzi (2008) and present parametric alternatives to their semiparametric estimators. These alternatives are extension of the Augmented Inverse Probability Weighted (AIPW) estimator of Robins, Rotnitzky and Zhao (1994). We also consider a modification proposed by Cao, Tsiatis and Davidian (2009) and present it as a one-step update of the AIPW estimators. Compared to other parametric estimators, the AIPW estimator and its modification provide additional protection against inconsistency due to parametric misspecification. They are also locally efficient in the absence of misspecification. Simulation results in the context of missing instrumental variables suggest that both estimators are likely to be useful when the researcher is reasonably certain about key components of the parametric specifications.