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Asymptotic efficiency of semiparametric two-step GMM

Listed author(s):
  • Xiaohong Chen

    ()

    (Institute for Fiscal Studies and Yale University)

  • Jinyong Hahn

    (Institute for Fiscal Studies)

  • Zhipeng Liao

    (Institute for Fiscal Studies)

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: 15 Oct 2012
Handle: RePEc:ifs:cemmap:31/12
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