Semiparametric Two-Step Estimation Using Doubly Robust Moment Conditions

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step, but retain a fully nonparametric specification in the first step. Such estimators exist in many economic applications, including a wide range of missing data and treatment effect models, partially linear regression models, models for nonparametric policy analysis, and weighted average derivatives. We show that these estimators are √ n-consistent and asymptotically normal under weaker than usual conditions on the accuracy of the first stage estimates, have smaller first order bias and second order variance, and that their finite-sample distribution can be approximated more accurately by classical first order asymptotics. We argue that because of these refinements our estimators are useful in many settings where semiparametric estimation and inference are traditionally believed to be unreliable. JEL Classification: C14, C21, C31, C51 ∗First version: December 20, 2012. This version: May 23, 2014. Christoph Rothe, Columbia University, Department of Economics, 420 W 118th St, New York, NY 10027, USA. Email: [email protected]. Sergio Firpo, Escola de Economia de Sao Paulo FGV-SP, R. Itapeva, 474/1215, Sao Paulo-SP, 01332-000, Brasil. E-Mail: [email protected]. We would like to thank Matias Cattaneo, Michael Jansson, Marcelo Moreira, Ulrich Müller, Whitney Newey, Cristine Pinto, and seminar audiences at Brown, Columbia, EPGE-FGV, University of Pennsylvania, Princeton, PUC-Rio, the 2012 Greater NY Metropolitan Colloquium and the 2013 North American Summer Meetings for their helpful comments. Sergio Firpo gratefully acknowledges financial support from CNPq-Brazil.