There is considerable empirical evidence that both individual consumers and larger entities such as countries bear more idiosyncratic risk than is consistent with complete and frictionless Arrow-Debreu markets. Evidence at the level of the individual consumer is discussed, for example, in Hayashi [1985] and Zeldes [1989], who show that individual consumption is poorly correlated with aggregate consumption. Evidence at the international level is discussed, for example, in Backus, Kehoe, and Kydland [1992], who point out the low correlation between consumption levels across countries.
That individuals bear idiosyncratic risk can be captured by many departures from the Arrow-Debreu framework. Three important examples of such models are incomplete market models, where there are not enough securities to insure against all events; models of liquidity constraints in which individual consumers are assumed unable to borrow as much as they would like in loan markets; and models of adverse selection and moral hazard. Incomplete market models are discussed by Radner [1972], Hart [1975], and Duffie and Shafer [1985], for example. Examples of models of liquidity constraints can be found in Bewley [1980], Dumas [1980], Townsend [1980], Scheinkman and Weiss [1986], Abel [1990], Kehoe, Levine, and Woodford [1992] and Heaton and Lucas [1997]. Models of liquidity constraints typically involve incomplete markets, as not only are there short sales constraints on securities, but securities are limited in number as well. These papers have largely focused on the computation of special types of equilibria in economies where the outside asset is a fiat money of no intrinsic value. In these equilibria shocks have long term consequences. We show that this is also the case in the incomplete market model considered in this paper.