Idiosyncratic Risk and the Business Cycle: A Likelihood Perspective

This paper asks whether uninsurable idiosyncratic income risk affects aggregate consumption over the business cycle. I explore this question using an incomplete mar-kets business cycle model in which the extent of idiosyncratic risk varies over the business cycle in line with recent empirical findings. I present a method for estimat-ing general equilibrium incomplete markets models with rich household heterogeneity using likelihood-based methods. I use the estimated model to construct a counter-factual series for aggregate consumption under complete markets. The results show that time-varying idiosyncratic risk has substantial effects on the dynamics of aggre-gate consumption. Had markets been complete, the variance of aggregate consumption growth would have been up to 32 % lower and the drop in consumption in the Great Recession up to 1.9 percentage points smaller.