Equilibrium Indeterminacy and Extreme Outcomes: A Fat Sunspot Ta(i)l(e)

Competing explanations for the fat-tailed empirical distribution of aggregate time series range from exogenous stochastic volatility, boundedly rational agents reflecting a lot of structural change or that exogenous structural shocks are themselves extreme. We build on this literature and show that sunspots in dynamic models can accumulate as linear recursions with multiplicative noise. Thus, using known results from the large deviations literature allows us to conclude that even small sunspot shocks can lead to large movements in endogenous variables. We apply these results to models that admit indeterminacies to investigate the empirical relevance of sunspots in accounting for observed fat-tails in output.