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Asymptotic efficiency of semiparametric two-step GMM

  • Xiaohong Chen

    (Institute for Fiscal Studies and Yale University)

  • Jinyong Hahn
  • Zhipeng Liao
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    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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    File URL: http://www.cemmap.ac.uk/wps/cwp311212.pdf
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    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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    1. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of semiparametric models when the criterion function is not smooth," LSE Research Online Documents on Economics 2167, London School of Economics and Political Science, LSE Library.
    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. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
    5. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2011. "A practical asymptotic variance estimator for two-step semiparametric estimators," CeMMAP working papers CWP22/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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