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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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    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. Keisuke Hirano & Jack R. Porter, 2023. "Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits," Papers 2302.03117, arXiv.org.
    3. Isaiah Andrews & Anna Mikusheva, 2022. "GMM is Inadmissible Under Weak Identification," Papers 2204.12462, arXiv.org, revised May 2023.
    4. Christoph Breunig & Ruixuan Liu & Zhengfei Yu, 2022. "Double Robust Bayesian Inference on Average Treatment Effects," Papers 2211.16298, arXiv.org, revised Feb 2024.

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