Plausible GMM: A Quasi-Bayesian Approach

TL;DR

This paper introduces a quasi-Bayesian framework for structural estimation in economics that accounts for potential misspecification of moment conditions, providing robust inference and decision rules.

Contribution

It develops a quasi-Bayesian approach that models belief about misspecification, with theoretical guarantees and empirical illustrations for relaxed moment conditions.

Findings

Quasi-posterior concentrates around true parameters.

Method yields approximately optimal Bayesian decision rules.

Provides frequentist coverage results for inference.

Abstract

Structural estimation in economics often makes use of models formulated in terms of moment conditions. While these moment conditions are generally well-motivated, it is often unknown whether the moment restrictions hold exactly. We consider a framework where researchers model their belief about the potential degree of misspecification via a prior distribution and adopt a quasi-Bayesian approach for performing inference on structural parameters. We provide quasi-posterior concentration results, verify that quasi-posteriors can be used to obtain approximately optimal Bayesian decision rules under the maintained prior structure over misspecification, and provide a form of frequentist coverage results. We illustrate the approach through empirical examples where we obtain informative inference for structural objects allowing for substantial relaxations of the requirement that moment conditions hold exactly.