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Asymptotic efficiency of semiparametric two-step GMM

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  • Xiaohong Chen

    (Institute for Fiscal Studies and Yale University)

  • Jinyong Hahn
  • Zhipeng Liao
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    Abstract

    In this note, we characterise 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 non-parametric 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 Info

    Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP31/12.

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    Date of creation: Oct 2012
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    Handle: RePEc:ifs:cemmap:31/12

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    Related research

    Keywords: Overlapping information sets; semiparametric efficiency; two-step GMM;

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    1. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2012. "A Practical Asymptotic Variance Estimator for Two-Step Semiparametric Estimators," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 481-498, May.
    2. 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.
    3. Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
    4. Xiaohong Chen & Oliver Linton & Ingred Van Keilegom, 2002. "Estimation of semiparametric models when the criterion function is not smooth," CeMMAP working papers CWP02/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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