Heterogeneous risk aversion and the dynamics of the wealth distribution

This paper studies the role played by differences in risk-aversion in a affecting the long-run distribution of wealth across agents in the context of a stochastic growth model with complete markets. The economy is populated by two types of Epstein-Zin agents who differ only in their attitudes toward risk. The paper derives conditions on the parameters of the model under which a type’s wealth converges to zero almost surely in the long-run. As in the expected utility framework, the long-run distribution of wealth in this economy is always degenerate. However, unlike the expected utility framework, according to the parameters of the model, the latter is dominated by either less or more risk-averse agents. By choosing riskier portfolio strategies less risk-averse agents enjoy returns on their investments characterized by a higher mean and a higher variance than the ones enjoyed by more risk-averse agents. The former effect tends to make less risk-averse agents wealthier over time, while the latter tends to make them poorer. When the latter effect prevails the wealth of less risk-averse agents converges to zero almost surely. The separability between attitudes toward intertemporal substitution and attitudes toward risk-aversion allowed by Epstein-Zin preferences plays a key role in this analysis. In the standard expected utility framework, in fact, less risk-averse agents (i.e., agents that are more willing to substitute consumption intertemporally) always dominate the long-run distribution of wealth in a growing economy. Keywords: Wealth distribution, risk aversion, heterogeneous agents. JEL Classification: D31, O40.