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Optimal Decision Rules for Weak GMM
Author(s) -
Andrews Isaiah,
Mikusheva Anna
Publication year - 2022
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta18678
Subject(s) - frequentist inference , bayes' rule , bayes' theorem , estimator , identification (biology) , bayes factor , prior probability , mathematics , decision rule , limit (mathematics) , bayesian probability , class (philosophy) , decision theory , econometrics , computer science , artificial intelligence , statistics , bayesian inference , mathematical analysis , botany , biology
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.