We estimate a DSGE model where rare large shocks can occur, by replacing the commonly used Gaussian assumption with a Student-t distribution.  We show that the latter is favored by the data in the context of a Smets and Wouters-type model estimated on macro variables, even if we allow for low frequency variation in the shocks' volatility. The evidence is even stronger when we introduce financial frictions as in Bernanke, Gertler and Gilchrist (1999), and correspondingly include a measure of interest rate spreads among the observables. We  provide some evidence that introducing Student-t shocks reduces the importance of low-frequency time-variation in volatility. In particular, we show that the Great Recession of 2008-09 does not result in significant increases in estimated time-varying volatility (i.e., it is not a reversal of the Great Moderation) but is largely the outcome of large shocks.