Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework

Abstract

This paper develops a class of recursive, but not necessarily expected utility, preferences over intertemporal consumption lotteries. An important feature of these general preferences is that they permit risk attitudes to be disentangled from the degree of intertemporal substitutability. Moreover, in an infinite horizon, representative agent context these preference specifications lead to a model of asset returns in which appropriate versions of both the atemporal CAPM and the intertemporal consumption-CAPM are nested as special cases. In our general model, systematic risk of an asset is determined by covariance with both the return to the market portfolio and consumption growth, while in each of the existing models only one of these factors plays a role. This result is achieved despite the homotheticity of preferences and the separability of consumption and portfolio decisions. Two other auxiliary analytical contributions which are of independent interest are the proofs of (i) the existence of recursive intertemporal utility functions, and (ii) the existence of optima to corresponding optimization problems. In proving (i), it is necessary to define a suitable domain for utility functions. This is achieved by extending the formulation of the space of temporal lotteries in Kreps and Porteus (1978) to an infinite horizon framework. A final contribution is the integration into a temporal setting of a broad class of atemporal non-expected utility theories. For homogeneous members of the class due to Chew (1985) and Dekel (1986), the corresponding intertemporal asset pricing model is derived.

On the Timing and Pricing of Dividends

“…15 This model departs from the Lucas model in two important ways. First, the CRRA preferences are generalized to Epstein and Zin (1989) preferences to separate the coefficient of relative risk aversion from the elasticity of intertemporal substitution. Second, the dynamics of consumption and dividend growth are modified in two ways.…”

Survival and Long-Run Dynamics with Heterogeneous Beliefs Under Recursive Preferences

“…The relatively more pessimistic agent survives (and thus a nondegenerate long-run equilibrium exists) when risk aversion is sufficiently small. In order to shed more light on the results, it is useful to consider the discrete-time version of the recursive preferences, featured by Epstein and Zin (1989): The risk aversion parameter γ drives the risk adjustment of the next-period continuation valueṼ t+1 ; and as risk aversion increases, the lower tail of the distribution ofṼ t+1 will contribute with an increasingly larger penalty to the expected value. When two agents differ in their beliefs, the more pessimistic agent assigns a higher probability to the tail events.…”

Time-Varying Preferences and SAD: Evidence from an Asset-Pricing Model

“…The model differs from the standard Lucas model in two respects. First the representative agent has recursive utility as in Epstein and Zin (1989) and second the parameters of the utility function of the agent are time-varying. The introduction of time-varying preference in a Lucas model is a simple way of capturing the SAD effect on the agent's behavior.…”

“…We turn now to Epstein and Zin (1989) preferences, modified to allow for a representative agent with time-varying risk aversion.…”

“…As a result, equity premia are higher at business cycle troughs than they are at peaks. Basal and Yaron (2004) employ a model where the representative agent has recursive preferences (Epstein and Zin (1989) and show that when consumption growth has a small time-varying, but persistent and predictable component, the model can generate an equity premium close to what is observed in the US data. A second strand of the literature focuses on the observation that the equity premium seems to have declined in recent years, up until recently.…”