DSGE priors for BVAR models

Similar to Ingram and Whiteman (1994), De Jong et al. (1993) and Del Negro and Schorfheide (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. (2007), Christiano et al. (2006) and Ravenna (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 et al., 1984). Additionally, the marginal-likelihood of the time-series model with theory founded 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, 2005). Finally, motivated by the work of Christiano et al. (2010b,a) and Del Negro and Schorfheide (2004) we use the theoretical results developed by Chernozhukov and Hong (2003) and Theodoridis (2011) to derive the quasi Bayesian posterior distribution of the DSGE parameter vector.