Risk shocks with time-varying higher moments

Within the context of a financial accelerator model, we model time-varying uncertainty (i.e. risk shocks) through the use of a mixture normal model with time variation in the weights applied to the underlying distributions characterizing entrepreneur productivity. Specifically, we model capital producers (i.e. the entrepreneurs) as either low-risk (a relatively small second moment of productivity) or high-risk (a relatively large second moment of productivity) and the fraction of both types is time-varying. We show that this modeling feature implies that the aggregate distribution of productivity shocks is non-normal and has time varying kurtosis and skewness; both of these features have important effects on equilibrium characteristics. In particular, after estimating the steady-state share and the change in the fraction of risky entrepreneurs, we show that a small change in the fraction of risky types can result in a large quantitative effect of a risk shock relative to standard models for both financial and real variables. Moreover, the bankruptcy rate and the risk premium in the economy are very sensitive to a change in the composition of entrepreneurs.