Journal Article

Asymptotic Efficiency of Semiparametric Two-step GMM

Daniel Ackerberg, Xiaohong Chen, Jinyong Hahn and Zhipeng Liao

in The Review of Economic Studies

Volume 81, issue 3, pages 919-943
Published in print July 2014 | ISSN: 0034-6527
Published online April 2014 | e-ISSN: 1467-937X | DOI: https://dx.doi.org/10.1093/restud/rdu011
Asymptotic Efficiency of Semiparametric Two-step GMM

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  • Econometric and Statistical Methods and Methodology: General
  • Multiple or Simultaneous Equation Models; Multiple Variables

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Many structural economics models are semiparametric ones in which the unknown nuisance functions are identified via non-parametric conditional moment restrictions with possibly non-nested or overlapping conditioning sets, and the finite dimensional parameters of interest are over-identified via unconditional moment restrictions involving the nuisance functions. In this article we characterize the semiparametric efficiency bound for this class of models. We show that semiparametric two-step optimally weighted GMM estimators achieve the efficiency bound, where the nuisance functions could be estimated via any consistent non-parametric methods 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.

Keywords: Overlapping information sets; Semiparametric efficiency; Two-step GMM; C14; C31; C32

Journal Article.  8281 words.  Illustrated.

Subjects: Econometric and Statistical Methods and Methodology: General ; Multiple or Simultaneous Equation Models; Multiple Variables

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