Ingram and Whiteman (1994) have shown that priors from DSGE models can be helpful in forecasting. We generalize their approach so that it can be easily applied to any DSGE model and to any VAR. A hierarchical prior is used that consists of a marginal distribution for DSGE model parameters and a distribution for the VAR parameters conditional on the DSGE model parameters. MCMC methods are used to compute a joint posterior distribution. The posterior updating of the DSGE model parameters appears to be crucial for accurate forecasting and use the DSGE model also to achieve identification, thereby making the approach exploitable for policy analysis. We apply this framework to a bivariate VAR in inflation and output and find that the VAR with DSGE priors forecasts better in several dimensions than an array of competitors.