DSGE-based priors for BVARs and quasi-Bayesian DSGE estimation

A new method for estimating Bayesian vector autoregression (VAR) models using priors from a dynamic stochastic general equilibrium (DSGE) model is presented. The DSGE model priors are used to determine the moments of an independent Normal-Wishart prior for the VAR parameters. Two hyper-parameters control the tightness of the DSGE-implied priors on the autoregressive coefficients and the residual covariance matrix respectively. Selecting the values of the hyper-parameters that maximize the marginal likelihood of the Bayesian VAR provides a method for isolating subsets of DSGE parameter priors that are at odds with the data. The ability of the new method to correctly detect misspecified DSGE priors is illustrated using a Monte Carlo experiment. The method gives rise to a new ‘quasi-Bayesian’ estimation approach: posterior estimates of the DSGE parameter vector can be recovered from the BVAR posterior estimates. An empirical application on US data reveals economically meaningful differences in posterior parameter estimates when comparing the quasi-Bayesian estimator with Bayesian maximum likelihood. The new method also indicates that the DSGE prior implications for the residual covariance matrix are at odds with the data.