Catching Up with the Joneses: Heterogeneous Preferences and the Dynamics of Asset Prices
EFA 2001 Barcelona Meetings; The Wharton School, Rodney L. White Center Working Paper No. 014-00
47 Pages Posted: 8 Nov 2000
Date Written: December 19, 2000
Many classical dynamic models of asset pricing, such as Lucas's exchange economy and Cox, Ingersoll and Ross's production economy, use a representative investor framework to study the determination of asset prices. This approach renders the computation of equilibrium elegantly simple and contributes much to our understanding of how underlying economic structures such as preferences, endowments and production technologies, influence asset prices. On the other hand, heterogeneity among investors is a prevailing feature in capital markets. In reconciling with this empirical observation, the contribution of the literature on aggregation is to identify conditions under which individual preferences can be aggregated and thus provide the theoretical justification for such a representative agent framework. Despite these important aggregation results, a representative investor framework assumes away many interesting issues such as the relation between cross-sectional wealth distribution, the behavior of asset prices and trading patterns. To tackle these issues, heterogeneity has to be modeled explicitly. We consider a pure exchange economy populated by a continuum of agents. Agents in our model have "catching up with the Joneses" preferences and differ only in the curvature of their utility functions. Capital markets in our model are complete. We study equilibrium asset prices and individual consumption-portfolio policies both numerically and analytically, using asymptotic analysis. Because of the "catching up with the Joneses" feature of preferences, our economy exhibits stationary long-run behavior, unlike the analogous economy populated by agents with separable preferences. We show that heterogeneity can have a drastic effect on the behavior of asset prices, in particular, on their conditional moments. Dynamic re-distribution of wealth among the agents in heterogeneous economies leads to time-variation in aggregate risk aversion and market price of risk, generating empirically observed negative relation between conditional return volatility and expected returns on one hand and the level of stock prices on the other hand. This stands in contrast with the behavior of homogeneous economies with the same preferences, in which such relation is positive. Moreover, the heterogeneous model is shown to be capable of generating various empirical phenomena of asset prices. Our work is closely related to a recent paper by Campbell and Cochrane (1999), in which a particular representative-agent model with catching up with the Joneses preferences is shown to replicate numerous empirically observed features of stock returns. In their model of preferences, Campbell and Cochrane assume that the local curvature of the utility function of the representative agent is decreasing in the level of consumption, inducing counter-cyclical variation in Sharpe ratio. In addition, they use a carefully crafted nonlinear process for the social standard of living (the distinctive feature of catching up with the Joneses preferences, called exogenous habit level by Campbell and Cochrane) to control the volatility of interest rates. As we demonstrate in this paper, a heterogeneous economy can give rise to similar qualitative and quantitative properties of stock returns through a different economic mechanism and with far simpler assumptions about individual preferences: constant curvature of the utility function and linear process for the standard of living.
JEL Classification: E0, E1, E2, G0, G1
Suggested Citation: Suggested Citation