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PROPERTIES OF DOUBLY ROBUST ESTIMATORS WHEN NUISANCE FUNCTIONS ARE ESTIMATED NONPARAMETRICALLY

Published online by Cambridge University Press:  03 December 2018

Christoph Rothe  and
Sergio Firpo
Christoph Rothe*
Affiliation:
University of Mannheim
Sergio Firpo
Affiliation:
Insper Institute of Education and Research
*
*Address correspondence to Christoph Rothe, Department of Economics, University of Mannheim, D-68131 Mannheim, Germany; e-mail: rothe@vwl.uni-mannheim.de.
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Abstract

An estimator of a finite-dimensional parameter is said to be doubly robust (DR) if it imposes parametric specifications on two unknown nuisance functions, but only requires that one of these two specifications is correct in order for the estimator to be consistent for the object of interest. In this article, we study versions of such estimators that use local polynomial smoothing for estimating the nuisance functions. We show that such semiparametric two-step (STS) versions of DR estimators have favorable theoretical and practical properties relative to other commonly used STS estimators. We also show that these gains are not generated by the DR property alone. Instead, it needs to be combined with an orthogonality condition on the estimation residuals from the nonparametric first stage, which we show to be satisfied in a wide range of models.

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ARTICLES
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Econometric Theory , Volume 35 , Issue 5 , October 2019 , pp. 1048 - 1087
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

An earlier working version of this article was circulated under the title “Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions”. We would like to thank Matias Cattaneo, Michael Jansson, Marcelo Moreira, Ulrich Müller, Whitney Newey, Cristine Pinto, and audiences at numerous seminar and conference presentations for their helpful comments; and Bernardo Modenesi for excellent research assistance. Christoph Rothe gratefully acknowledges financial support from German Scholars Organization & Carl-Zeiss-Stiftung. Sergio Firpo gratefully acknowledges financial support from CNPq-Brazil.

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