On Identification of Bayesian DSGE Models

Abstract

This article is concerned with local identification of individual parameters of dynamic stochastic general equilibrium (DSGE) models estimated by Bayesian methods. Identification is often judged by a comparison of the posterior distribution of a parameter with its prior. However, these can differ even when the parameter is not identified. Instead, we propose two Bayesian indicators of identification. The first follows a suggestion by Poirier of comparing the posterior density of the parameter of interest with the posterior expectation of its prior conditional on the remaining parameters. The second examines the rate at which the posterior precision of the parameter gets updated with the sample size, using data simulated at the parameter point of interest for an increasing sequence of sample sizes (<italic>T</italic>). For identified parameters, the posterior precision increases at rate <italic>T</italic>. For parameters that are either unidentified or are weakly identified, the posterior precision may get updated but its rate of update will be slower than <italic>T</italic>. We use empirical examples to demonstrate that these methods are useful in practice. This article has online supplementary material.