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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

    (Institute for Fiscal Studies)

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.

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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    Citations

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    Cited by:

    1. Karun Adusumilli & Dita Eckardt, 2019. "Temporal-Difference estimation of dynamic discrete choice models," Papers 1912.09509, arXiv.org.
    2. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    3. 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.
    4. Chen, Xiaohong & Pouzo, Demian & Powell, James L., 2019. "Penalized sieve GEL for weighted average derivatives of nonparametric quantile IV regressions," Journal of Econometrics, Elsevier, vol. 213(1), pages 30-53.
    5. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jul 2020.
    6. Sung Jae Jun & Sokbae (Simon) Lee, 2018. "Identifying the effect of persuasion," CeMMAP working papers CWP19/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Yusuke Narita & Shota Yasui & Kohei Yata, 2018. "Efficient Counterfactual Learning from Bandit Feedback," Cowles Foundation Discussion Papers 2155, Cowles Foundation for Research in Economics, Yale University.
    8. Minji Bang & Wayne Yuan Gao & Andrew Postlewaite & Holger Sieg, 2021. "Using Monotonicity Restrictions to Identify Models with Partially Latent Covariates," Papers 2101.05847, arXiv.org.
    9. Xiaohong Chen & Yin Jia Jeff Qiu, 2016. "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: A Gentle Guide," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 259-290, October.
    10. Sung Jae Jun & Sokbae Lee, 2020. "Causal Inference in Case-Control Studies," Papers 2004.08318, arXiv.org, revised Oct 2020.
    11. Haitian Xie, 2020. "Generalized Local IV with Unordered Multiple Treatment Levels: Identification, Efficient Estimation, and Testable Implication," Papers 2001.06746, arXiv.org.
    12. Kai Quan Zhang & Hsing Hung Chen, 2017. "Environmental Performance and Financing Decisions Impact on Sustainable Financial Development of Chinese Environmental Protection Enterprises," Sustainability, MDPI, Open Access Journal, vol. 9(12), pages 1-14, December.
    13. Xiaohong Chen & Demian Pouzo & James L. Powell, 2019. "Penalized Sieve GEL for Weighted Average Derivatives of Nonparametric Quantile IV Regressions," Papers 1902.10100, arXiv.org.
    14. 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.
    15. Daniel A. Ackerberg & Kevin Caves & Garth Frazer, 2015. "Identification Properties of Recent Production Function Estimators," Econometrica, Econometric Society, vol. 83, pages 2411-2451, November.

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    More about this item

    Keywords

    Overlapping information sets; semiparametric efficiency; two-step GMM;
    All these keywords.

    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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