Asymptotic Efficiency of Semiparametric Two-step GMM
AbstractIn this note, we characterize the semiparametric efficiency bound for a class of semiparametric models in which the unknown nuisance functions are identified via nonparametric conditional moment restrictions with possibly non-nested or over-lapping conditioning sets, and the finite dimensional parameters are potentially over-identified via unconditional moment restrictions involving the nuisance functions. We discover a surprising result that semiparametric two-step optimally weighted GMM estimators achieve the efficiency bound, where the nuisance functions could be estimated via any consistent nonparametric procedures in the first step. Regardless of whether the efficiency bound has a closed form expression or not, we provide easy-to-compute sieve based optimal weight matrices that lead to asymptotically efficient two-step GMM estimators.
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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1880.
Length: 24 pages
Date of creation: Oct 2012
Date of revision:
Publication status: Published in Review of Economic Studies (July 2014), 81(3): 919-943
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Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Pakes, Ariel & Olley, Steven, 1995.
"A limit theorem for a smooth class of semiparametric estimators,"
Journal of Econometrics,
Elsevier, vol. 65(1), pages 295-332, January.
- Ariel Pakes & Steven Olley, 1994. "A Limit Theorem for a Smooth Class of Semiparametric Estimators," Cowles Foundation Discussion Papers 1066, Cowles Foundation for Research in Economics, Yale University.
- Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
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