Plausible GMM: A Quasi-Bayesian Approach

2025-07-01

AI Summary

This paper addresses the practical issue in structural estimation that moment conditions may not hold exactly. We propose a quasi-Bayesian inference framework that explicitly incorporates the researcher’s subjective prior beliefs about the degree of model misspecification. Building upon the generalized method of moments (GMM), the approach models moment condition deviations via a prior distribution, yielding a quasi-posterior with desirable frequentist coverage properties. Unlike conventional methods, our framework does not require the strong assumption of exact moment validity, yet still delivers efficient and concentrated inference on structural parameters and supports optimal decision-making. Empirical results demonstrate that the method remains robust and informative—even when moment conditions are only approximately satisfied—exhibiting excellent statistical performance and reliable uncertainty quantification.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Estimating structural parameters with uncertain moment conditions
• Modeling misspecification beliefs via prior distributions
• Providing quasi-Bayesian inference for economic models

Innovation

• Quasi-Bayesian approach for structural estimation
• Prior distribution models misspecification beliefs
• Quasi-posteriors ensure optimal Bayesian decisions