A tale of fat tails

We document the extent to which major macroeconomic series, used to inform linear DSGE models, can be characterized by power laws whose indices we estimate via maximum likelihood. Assuming data follow a linear recursion with multiplicative noise, low estimated indices suggest fat tails. We then ask whether standard DSGE models under constant gain learning can replicate those fat tails by an appropriate increase in the estimated gain and without much change in the transmission mechanism of shocks. We find that is largely the case via implementation of a minimum distance estimation method that eschews any allegiance to distributional assumptions.