A model of aggregate economic activity is formulated which enmphasizes the effects of borrowing constraints in the presence of uninsurable risk. An important determinant of current income level is shown to be the cross-sectional distribution of wealth. As this distribution evolves endogenously, the model is capable of producing rich dynamics from a simple specification of exogenous shocks. The model shows that this phenomena can contribute to observed price volatility. IT IS COMMONLY THOUGHT that individuals have only limited opportunities to borrow against future labor income and cannot totally insure all types of risk. It has also been suggested that such departures from the presumptive norm of frictionless, complete information capital markets may have implications for aggregate economic activity. AlthLough there has been some work analyzing the implications of borrowing constraints for individual savings behavior (18, 2, 8), there has been no systematic analysis of how such borrowing constraints will affect the time series properties of output, prices, and interest rates. In this paper, we present a completely specified infinitely lived two agent equilibrium model which emphasizes the roles of borrowing constraint and uninsured risk for affecting aggregate outcomes. Specifically we assume that agents are prohibited from ever having negative nonhuman wealth. The model has the central feature that there is no aggregate uncertainty, but each agent's own productive opportunities are stochastic. If there were a full set of Arrow- Debreu contingent claim markets each agent could attain a certain consumption stream and the resulting allocation and (implicit) relative prices would be constant through time. However, we assume that such markets do not exist. Rather, we assume that at each point in time agents may trade only the single durable asset for the single perishable consumption good. This may be interpreted either as fiat mon ay with a fixed own nominal return of zero, or as claims to productive capital which emits a fixed exogenous flow of the consumption good. We assume also that output may be produced by labor. However, only one of the two agents is productive at any instant in time. The duration of time over which a single agent is productive is assumed to be random, and, for analytical simplicity, is assumed to be generated by a Poisson counting process. The resulting allocation has the property that the agent who is not productive exchanges some of his

We create an analytical structure that reveals the long-run risk-return relationship for nonlinear continuous-time Markov environments. We do so by studying an eigenvalue problem associated with a positive eigenfunction for a conveniently chosen family of valuation operators. The members of this family are indexed by the elapsed time between payoff and valuation dates, and they are necessarily related via a mathematical structure called a semigroup. We represent the semigroup using a positive process with three components: an exponential term constructed from the eigenvalue, a martingale, and a transient eigenfunction term. The eigenvalue encodes the risk adjustment, the martingale alters the probability measure to capture long-run approximation, and the eigenfunction gives the long-run dependence on the Markov state. We discuss sufficient conditions for the existence and uniqueness of the relevant eigenvalue and eigenfunction. By showing how changes in the stochastic growth components of cash flows induce changes in the corresponding eigenvalues and eigenfunctions, we reveal a long-run risk-return trade-off.

Continuous-time Markov processes can be characterized conveniently by their infinitesimal generators. For such processes there exist forward and reverse-time generators. We show how to use these generators to construct moment conditions implied by stationary Markov processes. Generalized method of moments estimators and tests can be constructed using these moment conditions. The resulting econometric methods are designed to be applied to discrete-time data obtained by sampling continuous-time Markov processes.