Sungbae An and Frank Schorfheide have provided an excellent review of the main elements of Bayesian inference in Dynamic Stochastic General Equilibrium (DSGE) models. Bayesian methods have, for reasons clearly outlined in the paper, a very natural role to play in DSGE analysis, and the appeal of the Bayesian paradigm is indeed strongly evidenced by the flood of empirical applications in the area over the last couple of years. We expect their paper to be the natural starting point for applied economists interested in learning about Bayesian techniques for analyzing DSGE models, and as such the paper is likely to have a strong influence on what will be considered best practice for estimating DSGE models.

The authors have, for good reasons, chosen a stylized six-equation model to present the methodology. We shall use here the large-scale model in Adolfson et al. (2005), henceforth ALLV, to illustrate a few econometric problems which we have found to be especially important as the size of the model increases. The model in ALLV is an open economy extension of the closed economy model in Christiano et al. (2005). It consists of 25 log-linearized equations, which can be written as a state space representation with 60 state variables, many of them unobserved. Fifteen observed unfiltered time series are used to estimate 51 structural parameters. An additional complication compared to the model in An and Schorfheide's paper is that some of the coefficients in the measurement equation are non-linear functions of the structural parameters. The model is currently the main vehicle for policy analysis at Sveriges Riksbank (Central Bank of Sweden) and similar models are being developed in many other policy institutions, which testifies to the model's practical relevance. The version considered here is estimated on Euro area data over the period 1980Q1-2002Q4. We refer to ALLV for details.