On Identification of Bayesian DSGE Models

Abstract

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 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.

News Shocks under Financial Frictions

“…Thus, if we hardwire a counterfactual common trend growth rate in the two series, we may distort inference on business cycle implications that is of interest to us. 25 We have examined the identification of the model parameters using various metrics: evidence on prior and posterior densities, marginal likelihood comparisons between the baseline model and a model estimated without news shocks, and the tests of Iskrev (2010) and Koop et al (2013). These results are available upon request.…”

Macroprudential policy and house prices in an estimated Dynamic Stochastic General Equilibrium model for South Africa

“…Another challenge, is the absence of lags identification when using a DSGE model with Bayesian estimation (An & Schorfheide, 2007). As a result, Koop, Pesaran, and Smith (2013) proposed two Bayesian identification indicators. Even though there are drawbacks, DSGE models are mostly used for macroprudential analysis because they have many advantages that make them superior to simple time series models.…”

“…Usually, the parameters are identified by assessing the differences between the parameters' prior and posterior distributions. According to Koop, Pesaran and Smith (2013:313), “identification in forward‐looking models with lags, is dependent on the assumed structure of the model dynamics while in forward‐looking models with no lags, coefficients of the expectational variables are not identified since they do not enter the likelihood function; and in cases of more complicated models that have unobserved variables and no analytical solution, it is difficult to determine whether the models are identified.” This lack of identification in DSGE models that are estimated using Bayesian techniques is unlikely to be evident given that the prior may be different from the posterior even in cases where the parameter is not identified (Koop et al, 2013). In addition, for unidentified parameters, the posterior may also be updated as the sample size increases.…”

Global robust Bayesian analysis in large models

“…In contrast to the subsequent literature on identification in DSGE models (e.g. Iskrev (2010); Komunjer and Ng (2011); Koop et al (2013)) that primarily focuses on asymptotic identification, the framework here takes the Bayesian approach of conditioning on current observed data.…”