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Semiparametric estimation and inference using doubly robust moment conditions

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  • Rothe, Christoph
  • Firpo, Sergio

Abstract

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step. The key difference is that we do not impose any parametric restriction on the nuisance functions that are estimated in a first stage, but retain a fully nonparametric model instead. We call these estimators semiparametric doubly robust estimators (SDREs), and show that they possess superior theoretical and practical properties compared to generic semiparametric two-step estimators. In particular, our estimators have substantially smaller first-order bias, allow for a wider range of nonparametric first-stage estimates, rate-optimal choices of smoothing parameters and data-driven estimates thereof, and their stochastic behavior can be well-approximated by classical first-order asymptotics. SDREs exist for a wide range of parameters of interest, particularly in semiparametric missing data and causal inference models. We illustrate our method with a simulation exercise.

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Bibliographic Info

Paper provided by Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil) in its series Textos para discussão with number 330.

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Date of creation: 05 Dec 2013
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Handle: RePEc:fgv:eesptd:330

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  1. Tan, Zhiqiang, 2006. "Regression and Weighting Methods for Causal Inference Using Instrumental Variables," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1607-1618, December.
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  15. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
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Cited by:
  1. Alexandre Belloni & Victor Chernozhukov & Iván Fernández-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers CWP77/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Sloczynski, Tymon & Wooldridge, Jeffrey M., 2014. "A General Double Robustness Result for Estimating Average Treatment Effects," IZA Discussion Papers 8084, Institute for the Study of Labor (IZA).
  3. Huber, Martin, 2014. "Causal pitfalls in the decomposition of wage gaps," Economics Working Paper Series 1405, University of St. Gallen, School of Economics and Political Science.

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