When is Market Incompleteness Irrelevant for the Price of Aggregate Risk ? ∗

We construct a model with a large number of agents who have constant relative risk aversion (CRRA) preferences and face potentially tight solvency constraints. 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. 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, as long as they are not permanent, and arise even when households face very tight solvency constraints. ∗We would like to thank Andy Atkeson, John Campbell, Nicolae Garleanu, John Heaton, Francis Longstaff, Narayana Kocherlakota, Per Krusell, Victor Rios-Rull, Kjetil Storesletten, Dimitry Vayanos, the Wharton and UCLA macro lunch participants and seminar participants at UCLA Anderson, UC Irvine, NYU Stern, Princeton, the University of Wisconsin, SUNY Stonybrook, the UC Santa Barbara Conference on Risk Sharing and the AP sessions of the NBER Summer Institute for comments and the NSF for financial support. Dave Backus, Hal Cole, Stijn Van Nieuwerburgh, Pierre-Olivier Weill and Stan Zin provided exceptionally detailed and helpful comments. All remaining errors are our own. †email address: [email protected]. Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104. ‡email address: [email protected], Dept. of Economics, UCLA, Bunche Hall 8357, Box 951477, LA, CA 90095. 1 USC FBE DEPT. MACROECONOMICS presented by Dirk Krueger FRIDAY, October 12, 2007 3:30 pm – 5:00 pm, Room: HOH-706 & INTERNATIONAL FINANCE WORKSHOP