Survival and long-run dynamics with heterogeneous beliefs under recursive preferences

I study the long-run behavior of a two-agent economy where agents differ in their beliefs and are endowed with homothetic recursive preferences of the Duffie-Epstein-Zin type. When preferences are separable, the economy is dominated in the long run by the agent whose beliefs are relatively more precise, a result consistent with the market selection hypothesis. However, recursive preference specifications lead to equilibria in which both agents survive, or to ones where either agent can dominate the economy with a strictly positive probability. In this respect, the market selection hypothesis is not robust to deviations from separability. I derive analytical conditions for the existence of nondegenerate long-run equilibria, and show that these equilibria exist for plausible parameterizations when risk aversion is larger than the inverse of the intertemporal elasticity of substitution, providing a justification for models that combine belief heterogeneity and recursive preferences.