Abstract

We construct a model with a large number of agents who have constant relative risk aversion (CRRA) preferences. We show that the absence of insurance markets for idiosyncratic labor income risk has no effect on the premium for aggregate risk if the distribution of idiosyncratic risk is independent of aggregate shocks and aggregate consumption growth is independent over time. In the equilibrium, which features trade and binding solvency constraints, as opposed to Constantinides and Duffie (1996), households only use the stock market to smooth consumption; the bond market is inoperative. Furthermore we show that the cross-sectional wealth and consumption distributions are not affected by aggregate shocks. Equilibrium consumption allocations can be obtained by solving for an equilibrium in a version of the model without aggregate shocks, as in Bewley (1986), and then re-scaling the allocation by aggregate income. These results hold regardless of the persistence of idiosyncratic shocks, and arise even when households face tight solvency constraints, but only a weaker irrelevance result survives when we allow for predictability in aggregate consumption growth.

Citations