Dynamic Equilibrium with Rare Disasters and Heterogeneous Epstein-Zin Investors

Abstract

We consider a general equilibrium Lucas (1978) economy with one consumption good and two heterogeneous Epstein-Zin investors. The output is subject to rare disasters or, more generally, can have non-lognormal distribution with higher cumulants. We demonstrate that the heterogeneity in preferences generates excess stock return volatilities, procyclical price-dividend ratios and interest rates, and countercyclical market prices of risk when the elasticity of intertemporal substitution (EIS) is greater than one. We show that the latter results cannot be jointly replicated in a model where investors have EIS <= 1. Our model produces endogenous time-variation in equilibrium processes without assuming time-varying probabilities of disasters, as in the recent literature with homogeneous investors. We propose new approach for finding general equilibrium, and characterize optimal portfolios and consumptions in terms of tractable backward equations. Finally, we extend analysis to the case of heterogeneous beliefs about disaster probabilities.