Theoretical Priors for BVAR Models & Quasi-Bayesian DSGE Model Estimation

We build upon the work of Ingram and Whiteman (1994), De Jong et al. (1993) and Del Negro and Schorfheide (2004) to propose a methodology of constructing Dynamic Stochastic General Equilibrium (DSGE) consistent prior distributions for Bayesian Vector Autoregressive (BVAR) models. Further, motivated by the studies of Del Negro and Schorfheide (2004), Christiano et al. (2010) and the theoretical results developed by Chernozhukov and Hong (2003) we illustrate how the posterior moments of the BVAR parameter vector can be used to obtain the posterior inference with respect to the DSGE model. The moments of the assumed Normal-Inverse Wishart 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 prior density of the DSGE parameter vector. Two data driven hyper-parameters unwind the "intensity" of these theoretical priors avoiding bimodality problems that could possibly arise from the strong disagreement between "tight" priors and the data (see, De Jong et al., 1993). The combination of the VAR marginal likelihood function - approximated using the "Laplace" transform - with the prior distribution of the DSGE parameter vector delivers the posterior distribution of the latter. In line with the results from previous studies, BVAR models with theoretical priors seem to achieve forecasting performance that is comparable - if not better - with the one obtained using theory free "Minnesota" priors (Doan et al., 1984). Finally, a small monte carlo experiment and an empirical exercise reveals very supportive results for the quasi bayesian estimator proposed in this study relatively to the standard full information bayesian maximum likelihood estimator.