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Asymptotic efficiency of semiparametric two-step GMM


  • Xiaohong Chen

    () (Institute for Fiscal Studies and Yale University)

  • Jinyong Hahn

    (Institute for Fiscal Studies)

  • . .

    (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.

Suggested Citation

  • Xiaohong Chen & Jinyong Hahn & . ., 2012. "Asymptotic efficiency of semiparametric two-step GMM," CeMMAP working papers CWP31/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:31/12

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    References listed on IDEAS

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    Cited by:

    1. Xiaohong Chen & Andres Santos, 2015. "Overidentification in Regular Models," Cowles Foundation Discussion Papers 1999, Cowles Foundation for Research in Economics, Yale University.
    2. Michael Jansson & Demian Pouzo, 2017. "Some Large Sample Results for the Method of Regularized Estimators," Papers 1712.07248,
    3. Xiaohong Chen & Yin Jia Qiu, 2016. "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: a Gentle Guide," Cowles Foundation Discussion Papers 2032, Cowles Foundation for Research in Economics, Yale University.
    4. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey, 2016. "Locally robust semiparametric estimation," CeMMAP working papers CWP31/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. repec:gam:jsusta:v:9:y:2017:i:12:p:2260-:d:121850 is not listed on IDEAS
    6. Hidehiko Ichimura & Whitney K. Newey, 2017. "The influence function of semiparametric estimators," CeMMAP working papers CWP06/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Daniel A. Ackerberg & Kevin Caves & Garth Frazer, 2015. "Identification Properties of Recent Production Function Estimators," Econometrica, Econometric Society, vol. 83, pages 2411-2451, November.

    More about this item


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

    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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