Recent empirical findings suggest that macroeconomic variables are seldom normally distributed. For example, the distributions of aggregate output growth-rate time series of many OECD countries are well approximated by symmetric exponential-power (EP) densities, with Laplace fat tails. In this work, we assess whether Real Business Cycle (RBC) and standard medium-scale New-Keynesian (NK) models are able to replicate this statistical regularity. We simulate both models drawing Gaussian- vs Laplace-distributed shocks and we explore the statistical properties of simulated time series. Our results cast doubts on whether RBC and NK models are able to provide a satisfactory representation of the transmission mechanisms linking exogenous shocks to macroeconomic dynamics.