Private Risk Premium and Aggregate Uncertainty in the Model of Uninsurable Investment Risk

This paper studies cyclical properties of the private risk premium in a model where a continuum of heterogeneous entrepreneurs are subject to aggregate as well as idiosyncratic risks, both of which are assumed to be highly persistent. The calibrated model matches highly skewed wealth and income distributions of entrepreneurs found in the Survey of Consumer Finances. We provide an accurate numerical solution to the model even though the model is shown to exhibit serious nonlinear- ities that are absent in incomplete market models with idiosyncratic labor income risk. The model is able to generate the aggregate private risk premium of 2-3 percent and the low risk-free rate. However, it generates very little variation in these variables over the business cy- cle, suggesting that the model lacks the ability to amplify aggregate shocks.