Idiosyncratic Production Risk, Growth, and the Business Cycle

We introduce a neoclassical growth economy with idiosyncratic production risk and incomplete markets. Each agent is an entrepreneur operating her own neoclassical technology with her own capital stock. The general equilibrium is characterized in closed form. Idiosyncratic production shocks introduce a risk premium on private equity and reduce the demand for investment. The steady state is characterized by a lower capital stock due to entrepreneurial risk and a lower interest rate due to precautionary savings as compared to complete markets. The private equity premium is endogenously countercyclical: the anticipation of low savings and high interest rates in the future feed back to high risk premia and low investment in the present. Countercyclicality in risk taking slows down convergence to the steady state and amplifies the magnitude and persistence of the business cycle. These results, which contrast sharply with those obtained in Bewley models, highlight the macroeconomic significance of missing markets in production and investment risk.