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Optimal Decision Rules for Weak GMM

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  • Isaiah Andrews
  • Anna Mikusheva

Abstract

This paper studies optimal decision rules, including estimators and tests, for weakly identified GMM models. We derive the limit experiment for weakly identified GMM, and propose a theoretically‐motivated class of priors which give rise to quasi‐Bayes decision rules as a limiting case. Together with results in the previous literature, this establishes desirable properties for the quasi‐Bayes approach regardless of model identification status, and we recommend quasi‐Bayes for settings where identification is a concern. We further propose weighted average power‐optimal identification‐robust frequentist tests and confidence sets, and prove a Bernstein‐von Mises‐type result for the quasi‐Bayes posterior under weak identification.

Suggested Citation

  • Isaiah Andrews & Anna Mikusheva, 2022. "Optimal Decision Rules for Weak GMM," Econometrica, Econometric Society, vol. 90(2), pages 715-748, March.
  • Handle: RePEc:wly:emetrp:v:90:y:2022:i:2:p:715-748
    DOI: 10.3982/ECTA18678
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    References listed on IDEAS

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    1. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    2. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    3. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    4. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(4), pages 667-709, August.
    5. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    6. Chamberlain, Gary & Imbens, Guido W, 2003. "Nonparametric Applications of Bayesian Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 12-18, January.
    7. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    8. Frank Kleibergen & Sophocles Mavroeidis, 2014. "Identification Issues In Limited‐Information Bayesian Analysis Of Structural Macroeconomic Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1183-1209, November.
    9. Kim, Jae-Young, 2002. "Limited information likelihood and Bayesian analysis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 175-193, March.
    10. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    11. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
    12. Hyungsik Roger Moon & Frank Schorfheide, 2012. "Bayesian and Frequentist Inference in Partially Identified Models," Econometrica, Econometric Society, vol. 80(2), pages 755-782, March.
    13. Jean-Pierre Florens & Anna Simoni, 2021. "Gaussian Processes and Bayesian Moment Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 482-492, March.
    14. Luke Bornn & Neil Shephard & Reza Solgi, 2019. "Moment conditions and Bayesian non‐parametrics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(1), pages 5-43, February.
    15. Tetsuya Kaji, 2021. "Theory of Weak Identification in Semiparametric Models," Econometrica, Econometric Society, vol. 89(2), pages 733-763, March.
    16. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84(4), pages 1571-1612, July.
    17. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    18. A. Ronald Gallant, 2016. "Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 229-247.
    19. Kathryn Graddy, 1995. "Testing for Imperfect Competition at the Fulton Fish Market," RAND Journal of Economics, The RAND Corporation, vol. 26(1), pages 75-92, Spring.
    20. Sukjin Han & Adam McCloskey, 2019. "Estimation and inference with a (nearly) singular Jacobian," Quantitative Economics, Econometric Society, vol. 10(3), pages 1019-1068, July.
    21. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    22. A. Ronald Gallant, 2016. "Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference — Author Response to Comments," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 284-294.
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    Cited by:

    1. Li, Jia & Phillips, Peter C. B. & Shi, Shuping & Yu, Jun, 2022. "Weak Identification of Long Memory with Implications for Inference," Economics and Statistics Working Papers 8-2022, Singapore Management University, School of Economics.
    2. Lee, Adam & Mesters, Geert, 2024. "Locally robust inference for non-Gaussian linear simultaneous equations models," Journal of Econometrics, Elsevier, vol. 240(1).
    3. Keisuke Hirano & Jack R. Porter, 2023. "Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits," Papers 2302.03117, arXiv.org.
    4. Isaiah Andrews & Anna Mikusheva, 2022. "GMM is Inadmissible Under Weak Identification," Papers 2204.12462, arXiv.org, revised May 2023.
    5. Christoph Breunig & Ruixuan Liu & Zhengfei Yu, 2022. "Double Robust Bayesian Inference on Average Treatment Effects," Papers 2211.16298, arXiv.org, revised Oct 2024.

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