Estimating and Identifying Empirical BVAR-DSGE Models for Small Open Economies

Different approaches to modelling the macroeconomy vary in the emphasis they place on coherence with theory relative to their ability to match the data. Dynamic stochastic general equilibrium (DSGE) models place greater emphasis on theory, while vector autoregression (VAR) models tend to provide a better fit of the data. Del Negro and Schorfheide (2004) develop a method of using a DSGE model to inform the priors of a Bayesian VAR. The resulting BVAR-DSGE model partially relaxes the relationships in the DSGE so as to fit the data better. However, their approach does not accommodate the typical restriction of small open economy models which ensures that developments in the small economy cannot affect the large economy. I develop a method that allows this restriction to be imposed and introduce a simple way, suitable for small open economies, of identifying the empirical BVAR-DSGE using information from the DSGE model. These methods are demonstrated using the Justiniano and Preston (2010a) DSGE model. Compared to the DSGE model, the empirical BVAR-DSGE model estimates that there is a larger role for foreign shocks in the small economy's business cycle.