DSGE priors for BVAR models

Similar to Ingram and Whiteman (J Monet Econ 34:497–510, 1994), De Jong et al. (in: Proceedings of the American Statistical Association Bayesian, 1993) and Negro and Schorfheide (Int Econ Rev 45:643–673, 2004) , this study proposes a methodology of constructing dynamic stochastic general equilibrium (DSGE) consistent prior distributions for Bayesian vector autoregressive (BVAR) models. The moments of the assumed Normal–Inverse–Wishart (no conjugate) prior distribution of the VAR parameter vector are derived using the results developed by Fernandez-Villaverde et al. (Am Econ Rev 97(1):21–26, 2007) , Christiano et al. (Assessing structural vars, 2006) and Ravenna (J Monet Econ 54(2):48–64, 2007) regarding structural VAR (SVAR) models and the normal prior density of the DSGE parameter vector. In line with the results from previous studies, BVAR models with theoretical priors seem to achieve forecasting performance that is comparable—if not better—to the one obtained using theory free ‘Minnesota’ priors (Doan, Econ Rev 3(1):1–100, 1984). Additionally, the marginal-likelihood of the time-series model with theory found priors—derived from the output of the Gibbs sampler—can be used to rank competing DSGE theories that aim to explain the same observed data (Geweke, Contemporary Bayesian econometrics and statistics, 2005). Finally, motivated by the work of Christiano et al. (Handbook of monetary economics, 2010a; Involuntary unemployment and the business cycle, 2010b) and Del Negro and Schorfheide (Int Econ Rev 45:643–673, 2004), we use the theoretical results developed by Chernozhukov and Hong (J Econom 115(2):293–346, 2003) and Theodoridis (An efficient minimum distance estimator for DSGE models, 2011) to derive the quasi-Bayesian posterior distribution of the DSGE parameter vector.