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Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions

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  • Rothe, Christoph

    ()
    (Columbia University)

  • Firpo, Sergio

    ()
    (Sao Paulo School of Economics)

Abstract

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. 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. We also illustrate the practical relevance of our approach through simulations and an empirical application.

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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 7564.

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Length: 44 pages
Date of creation: Aug 2013
Date of revision:
Handle: RePEc:iza:izadps:dp7564

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Keywords: semiparametric model; missing data; treatment effects; doubly robust estimation; higher order asymptotics;

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  1. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 1053-1079.
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  15. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, 05.
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Cited by:
  1. 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).
  2. 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.
  3. 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.

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