Posterior Inferences on Incomplete Structural Models : The Minimal Econometric Interpretation

The minimal econometric interpretation (MEI) of DSGE models provides a formal model evaluation and comparison of misspecified nonlinear dynamic stochastic general equilibrium (DSGE) models based on atheoretical reference models. The MEI approach recognizes DSGE models as incomplete econometric tools that provide only prior distributions of targeted population moments but have no implications for actual data and sample moments. This study, based on the MEI approach, develops a Bayesian posterior inference method. Prior distributions of targeted population moments simulated by the DSGE model restrict the hyperparameters of Dirichlet distributions. These are natural conjugate priors for multinomial distributions followed by corresponding posterior distributions estimated by the reference model. The Polya marginal likelihood of the resulting restricted Dirichlet-multinomial model has a tractive approximated log-linear representation of the Jensen-Shannon divergence, which the proposed distribution-matching posterior inference uses as the limited information likelihood function. Monte Carlo experiments indicate that the MEI posterior sampler correctly infers calibrated structural parameters of an equilibrium asset pricing model and detects the true model with posterior odds ratios.