Asymptotic Efficiency of Semiparametric Two-step GMM
In 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.
|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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- 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.
- 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.
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