Fluctuations of representative agent economies are not very costly. So if business cycles matter, it must be because agents face uninsured idiosyncratic risk which is somehow worsened by aggregate fluctuation. Idiosyncratic risk could be counteracted either through aggregate stabilization or public insurance provision. Our framework allows us to ask which of these mechanisms is optimal. We study a real business cycle model with a job matching function which, under non-distortionary full insurance, would decentralize the optimum. However, we assume public insurance can only be financed by distorting labor taxes, and that there is moral hazard in job search behavior. Without insurance, workers save to smooth their consumption. Our dynamic general equilibrium simulation characterizes the asset distribution in terms of a few moments. We interpolate the value function and check accuracy by new methods. We find that aggregate fluctuations have little average effect on unemployment, but they are costly because recessions greatly increase the probability of remaining unemployed long enough to deplete asset buffer stocks. Both public insurance provision and aggregate stabilization by increasing the procyclicality of tax collection imply nontrivial benefits.
