Distribution-Matching Posterior Inference for Incomplete Structural Models

TL;DR

This paper presents a Bayesian inference method called distribution-matching posterior inference (DMPI) for incomplete structural models, which improves robustness and distribution matching by using divergence-based quasi-likelihood and advanced Monte Carlo sampling.

Contribution

The paper introduces DMPI, a novel Bayesian inference framework that extends existing methods to handle model misspecification and stochastic singularity in structural models.

Findings

DMPI provides robust inference under misspecification.

DMPI improves distribution matching in Monte Carlo experiments.

Empirical application shows a parsimonious NK model fits business-cycle moments better.

Abstract

This paper introduces a Bayesian inference framework for incomplete structural models, termed distribution-matching posterior inference (DMPI). Extending the minimal econometric interpretation (MEI), DMPI constructs a divergence-based quasi-likelihood using the Jensen-Shannon divergence between theoretical and empirical population-moment distributions, based on a Dirichlet-multinomial structure with additive smoothing. The framework accommodates model misspecification and stochastic singularity. Posterior inference is implemented via a sequential Monte Carlo algorithm with Metropolis-Hastings mutation that jointly samples structural parameters and theoretical moment distributions. Monte Carlo experiments using misspecified New Keynesian (NK) models demonstrate that DMPI yields robust inference and improves distribution-matching coherence by probabilistically down-weighting moment distributions inconsistent with the structural model. An empirical application to U.S. data shows that a parsimonious stochastic singular NK model provides a better fit to business-cycle moments than an overparameterized full-rank counterpart.