On Identication of Bayesian DSGE Models

In recent years there has been increasing concern about the identi…cation of parameters in dynamic stochastic general equilibrium (DSGE) models. Given the structure of DSGE models it may be di¢ cult to determine whether a parameter is identi…ed. For the researcher using Bayesian methods, a lack of identi…cation may not be evident since the posterior of a parameter of interest may di¤er from its prior even if the parameter is unidenti…ed. We show that this can even be the case even if the priors assumed on the structural parameters are independent. We suggest two Bayesian identi…cation indicators that do not su¤er from this di¢ culty and are relatively easy to compute. The …rst applies to DSGE models where the parameters can be partitioned into those that are known to be identi…ed and the rest where it is not known whether they are identi…ed. In such cases the marginal posterior of an unidenti…ed parameter will equal the posterior expectation of the prior for that parameter conditional on the identi…ed parameters. The second indicator is more generally applicable and considers the rate at which the posterior precision gets updated as the sample size (T ) is increased. For identi…ed parameters the posterior precision rises with T , whilst for an unidenti…ed parameter its posterior precision may be updated but its rate of update will be slower than T . This result assumes that the identi…ed parameters are p T -consistent, but similar di¤erential rates of updates for identi…ed and unidenti…ed parameters can be established in the case of super consistent estimators. These results are illustrated by means of simple DSGE models. JEL Classi…cations: C11, C15, E17 Key Words: Bayesian identi…cation, DSGE models, posterior updating, New Keynesian Phillips Curve. We are grateful to Cheng Hsiao, Dale Poirier, and Ivan Jeliazkov for helpful discussions.