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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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    Cited by:

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    2. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    3. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jul 2020.
    4. Lee, Sokbae & Salanié, Bernard, 2020. "Filtered and Unfiltered Treatment Effects with Targeting Instruments," CEPR Discussion Papers 15092, C.E.P.R. Discussion Papers.
    5. 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.
    6. Sung Jae Jun & Sokbae Lee, 2020. "Causal Inference under Outcome-Based Sampling with Monotonicity Assumptions," Papers 2004.08318, arXiv.org, revised Nov 2021.
    7. Vanhems, Anne & Van Keilegom, Ingrid, 2013. "Semiparametric transformation model with endogeneity: a control function approach," LIDAM Discussion Papers ISBA 2013018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Victor Aguirregabiria & Allan Collard-Wexler & Stephen P. Ryan, 2021. "Dynamic Games in Empirical Industrial Organization," Papers 2109.01725, arXiv.org, revised Sep 2021.
    9. Haitian Xie, 2020. "Efficient and Robust Estimation of the Generalized LATE Model," Papers 2001.06746, arXiv.org, revised Feb 2022.
    10. 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.
    11. Hidehiko Ichimura & Whitney K. Newey, 2015. "The Influence Function of Semiparametric Estimators," CIRJE F-Series CIRJE-F-985, CIRJE, Faculty of Economics, University of Tokyo.
    12. Sung Jae Jun & Sokbae Lee, 2018. "Identifying the Effect of Persuasion," Papers 1812.02276, arXiv.org, revised Feb 2022.
    13. 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.
    14. 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.
    15. Sung Jae Jun & Sokbae (Simon) Lee, 2020. "Causal inference in case-control studies," CeMMAP working papers CWP19/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Minji Bang & Wayne Gao & Andrew Postlewaite & Holger Sieg, 2021. "Using Monotonicity Restrictions to Identify Models with Partially Latent Covariates," NBER Working Papers 28436, National Bureau of Economic Research, Inc.
    17. Kai Quan Zhang & Hsing Hung Chen, 2017. "Environmental Performance and Financing Decisions Impact on Sustainable Financial Development of Chinese Environmental Protection Enterprises," Sustainability, MDPI, vol. 9(12), pages 1-14, December.
    18. Daniel A. Ackerberg & Kevin Caves & Garth Frazer, 2015. "Identification Properties of Recent Production Function Estimators," Econometrica, Econometric Society, vol. 83, pages 2411-2451, November.
    19. Liqiong Chen & Antonio F. Galvao & Suyong Song, 2021. "Quantile Regression with Generated Regressors," Econometrics, MDPI, vol. 9(2), pages 1-35, April.

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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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