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A Doubly Corrected Robust Variance Estimator for Linear GMM

Author

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  • Jungbin Hwang

    (Department of Economics, The University of Connecticut)

  • Byunghoon Kang

    (Department of Economics, Lancaster University)

  • Seojeong Lee

    (School of Economics, The University of New South Wales)

Abstract

We propose a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. Our formula additionally corrects for the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005) which corrects for the bias from estimating the efficient weight matrix, so is doubly corrected. Formal stochastic expansions are derived to show the proposed double correction estimates the variance of some higher-order terms in the expansion. In addition, the proposed double correction provides robustness to misspecification of the moment condition. In contrast, the conventional variance estimator and the Windmeijer correction are inconsistent under misspecification. That is, the proposed double correction formula provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time.

Suggested Citation

  • Jungbin Hwang & Byunghoon Kang & Seojeong Lee, 2019. "A Doubly Corrected Robust Variance Estimator for Linear GMM," Discussion Papers 2019-08, School of Economics, The University of New South Wales.
    • Handle: RePEc:swe:wpaper:2019-08
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    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2019-08.pdf
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    2. Hwang, Jungbin & Kang, Byunghoon & Lee, Seojeong, 2022. "A doubly corrected robust variance estimator for linear GMM," Journal of Econometrics, Elsevier, vol. 229(2), pages 276-298.
    3. Bruce E. Hansen & Seojeong Lee, 2021. "Inference for Iterated GMM Under Misspecification," Econometrica, Econometric Society, vol. 89(3), pages 1419-1447, May.
    4. Hwang, Jungbin, 2021. "Simple and trustworthy cluster-robust GMM inference," Journal of Econometrics, Elsevier, vol. 222(2), pages 993-1023.
    5. Rostand Arland Yebetchou Tchounkeu, 2023. "Public Health Efficiency and well-being in Italian province," Working Papers 479, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    6. Bernard Fingleton, 2022. "Modifying the linear two-step Windmeijer correction for the presence of spatial error dependence," Journal of Spatial Econometrics, Springer, vol. 3(1), pages 1-18, December.
    7. Jungbin Hwang & Gonzalo Valdés, 2020. "Finite-sample Corrected Inference for Two-step GMM in Time Series," Working papers 2020-02, University of Connecticut, Department of Economics.
    8. Bernard Fingleton, 2023. "Estimating dynamic spatial panel data models with endogenous regressors using synthetic instruments," Journal of Geographical Systems, Springer, vol. 25(1), pages 121-152, January.
    9. Hwang, Jungbin & Valdés, Gonzalo, 2023. "Finite-sample corrected inference for two-step GMM in time series," Journal of Econometrics, Elsevier, vol. 234(1), pages 327-352.

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    More about this item

    Keywords

    generalized method of moments; finite-sample correction; standard error; misspecification;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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