Optimal Decision Rules for Weak GMM

TL;DR

This paper develops optimal decision rules for weakly identified GMM models, introducing a quasi-Bayes approach with robust properties and proposing new tests and confidence sets for such settings.

Contribution

It derives the limit experiment for weak GMM, introduces a quasi-Bayes decision framework, and proposes robust tests and confidence sets for weak identification.

Findings

Quasi-Bayes decision rules have desirable properties under weak identification.

Proposed tests are weighted average power-optimal and robust to weak identification.

Established a Bernstein-von Mises-type result for the quasi-Bayes posterior.

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.