On Modeling Risk Shocks

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 (relatively small second moment for productivity) and high-risk (relatively large second moment for productivity) and the fraction of both types is time-varying. We show that a small change in the fraction of risky types (a change from 1% to 2% of the population) can result in a large quantitative effect or a risk shock relative to standard models. The bankruptcy rate and the risk premium in the economy are very sensitive to a change in the composition of agents and is countercyclical