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 technology with her own capital stock. The general equilibrium is characterized by a closed-form recursion in the CARA-normal case. Incomplete markets introduce a risk premium on private equity, which reduces the demand for investment. As compared to complete markets, the steady state can thus have both a lower capital stock due to investment risk, and a lower interest rate due to precautionary savings. Furthermore, the anticipation of high real interest rates in the future feeds back into high risk premia and low investment in the present, thus slowing down convergence to the steady state. Our results highlight the importance of private risk premia for capital accumulation and business cycles.