Correlated shocks in estimated DSGE models

In simulating and estimating DSGE models, we typically assume that exogenous shocks exist and that they capture aggregate uncertainty. Further, they are either interpreted as structural or as measurement error. Therefore, we almost always assume orthogonality of those shocks restricting the off-diagonal elements of the variance-covariance matrix. In this paper, we ask the question whether correlated shocks matter when we estimate typical DSGE models and what we can learn from including them. We argue that using correlated shocks is useful as a robustness test: observing correlated shocks implies that the underlying DSGE model is misspecified and we can understand the weaknesses of the underlying model. We find sizable and relevant differences for the three DSGE models estimated when we include correlated shocks. This holds for the estimation of structural parameters, driving forces of fluctuations, and the size and sign of the estimated shocks.