Conditional forecasting with DSGE models - A conditional copula approach

DSGE models may be misspecified in many dimensions, which can affect their forecasting performance. To correct for these misspecifications we can apply conditional information from other models or judgment. Conditional information is not accurate, and can be provided as a probability distribution over different outcomes. These probability distributions are often provided by a set of marginal distributions. To be able to condition on this information in a structural model we must construct the multivariate distribution of the conditional information, i.e. we need to draw multivariate paths from this distribution. One way to do this is to draw from the marginal distributions given a correlation structure between the different marginal distributions. In this paper we use the theoretical correlation structure of the model and a copula to solve this problem. The copula approach makes it possible to take into account more flexible assumption on the conditional information, such as skewness and/or fat tails in the marginal density functions. This method may not only improve density forecasts from the DSGE model, but can also be used to interpret the conditional information in terms of structural shocks/innovations.