Growth, Uncertainty and Business Cycles in an Overlapping Generations Economy

We explore business cycles in overlapping generations economies driven by shocks to total factor productivity growth. Households have uncertain lifetimes and face both uninsurable earnings and employment risk. Unemployment risk is countercyclical and we allow for time-varying volatility of aggregate shocks. Households, with non-separable preferences, save using capital and the relative price of capital varies over time. This setting--with both idiosyncratic and aggregate uncertainty shocks--drives large, countercyclical risk premium and generates high levels of precautionary savings. We find that changes in precautionary savings have important implications for aggregate consumption. Persistent negative shocks to TFP growth, and increases in their uncertainty, drive large declines in consumption. This helps explain the slowdown observed since the onset of the Great Recession. An empirically consistent, moderate shock to TFP growth rates implies a large and persistent fall, against trend, in aggregate consumption. Moreover, a rise in aggregate uncertainty reconciles the recovery in TFP growth rates with a more protracted decline in consumption. Uninsurable income risk helps shape the aggregate response of the economy over the business cycle. Changes in households' precautionary savings motives not only affect the distribution of wealth, it also changes the volatility of aggregate consumption and investment.