Distribution-Matching Posterior Inference for Incomplete Structural Models

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.