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On uniform asymptotic risk of averaging GMM estimators

Author

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  • Xu Cheng
  • Zhipeng Liao
  • Ruoyao Shi

Abstract

This paper studies the averaging GMM estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. We establish asymptotic theory on uniform approximation of the upper and lower bounds of the finite‐sample truncated risk difference between any two estimators, which is used to compare the averaging GMM estimator and the conservative GMM estimator. Under some sufficient conditions, we show that the asymptotic lower bound of the truncated risk difference between the averaging estimator and the conservative estimator is strictly less than zero, while the asymptotic upper bound is zero uniformly over any degree of misspecification. The results apply to quadratic loss functions. This uniform asymptotic dominance is established in non‐Gaussian semiparametric nonlinear models.

Suggested Citation

  • Xu Cheng & Zhipeng Liao & Ruoyao Shi, 2019. "On uniform asymptotic risk of averaging GMM estimators," Quantitative Economics, Econometric Society, vol. 10(3), pages 931-979, July.
    • Handle: RePEc:wly:quante:v:10:y:2019:i:3:p:931-979
    DOI: 10.3982/QE711
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    Cited by:

    1. Zhang, Xiaomeng & Zhang, Xinyu, 2023. "Optimal model averaging based on forward-validation," Journal of Econometrics, Elsevier, vol. 237(2).
    2. David M. Kaplan, 2022. "Smoothed instrumental variables quantile regression," Stata Journal, StataCorp LP, vol. 22(2), pages 379-403, June.
    3. Xin Liu, 2024. "Averaging Estimation for Instrumental Variables Quantile Regression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(5), pages 1290-1312, October.
    4. Cheng Chou & Ruoyao Shi, 2020. "Utilizing Two Types of Survey Data to Enhance the Accuracy of Labor Supply Elasticity Estimation," Working Papers 202018, University of California at Riverside, Department of Economics.
    5. Yong Bao & Xiaotian Liu & Lihong Yang, 2020. "Indirect Inference Estimation of Spatial Autoregressions," Econometrics, MDPI, vol. 8(3), pages 1-26, September.
    6. Zhang, Xinyu & Liu, Chu-An, 2023. "Model averaging prediction by K-fold cross-validation," Journal of Econometrics, Elsevier, vol. 235(1), pages 280-301.
    7. Bruce E. Hansen & Seojeong Lee, 2021. "Inference for Iterated GMM Under Misspecification," Econometrica, Econometric Society, vol. 89(3), pages 1419-1447, May.
    8. David M. Kaplan, 2019. "Unbiased Estimation as a Public Good," Working Papers 1911, Department of Economics, University of Missouri.
    9. Ruoyao Shi, 2021. "An Averaging Estimator for Two Step M Estimation in Semiparametric Models," Working Papers 202105, University of California at Riverside, Department of Economics.
    10. Heiler, Phillip & Mareckova, Jana, 2021. "Shrinkage for categorical regressors," Journal of Econometrics, Elsevier, vol. 223(1), pages 161-189.
    11. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    12. Cl'ement de Chaisemartin & Xavier D'Haultf{oe}uille, 2020. "Empirical MSE Minimization to Estimate a Scalar Parameter," Papers 2006.14667, arXiv.org.
    13. Edvard Bakhitov, 2020. "Frequentist Shrinkage under Inequality Constraints," Papers 2001.10586, arXiv.org.
    14. Abadie, Alberto & Gu, Jiaying & Shen, Shu, 2024. "Instrumental variable estimation with first-stage heterogeneity," Journal of Econometrics, Elsevier, vol. 240(2).
    15. Boot, Tom, 2023. "Joint inference based on Stein-type averaging estimators in the linear regression model," Journal of Econometrics, Elsevier, vol. 235(2), pages 1542-1563.

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