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Asymptotic efficiency of semiparametric two-step GMM

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  • Daniel Ackerberg
  • Xiaohong Chen
  • Jinyong Hahn

Abstract

Many structural economics models are semiparametric ones in which the unknown nuisance functions are identifi ed via nonparametric conditional moment restrictions with possibly non-nested or overlapping conditioning sets, and the finite dimensional parameters of interest are over-identi fied via unconditional moment restrictions involving the nuisance functions. In this paper 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 nonparametric methods in the fi rst 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.

Suggested Citation

  • Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2014. "Asymptotic efficiency of semiparametric two-step GMM," CeMMAP working papers 28/14, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:28/14
    DOI: 10.1920/wp.cem.2014.2814
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    More about this item

    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; State Space Models

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