By Georgy Chabakauri
We consider a general equilibrium Lucas (1978) economy with one consumption good and two heterogeneous Epstein-Zin investors. The output is subject to rare large drops or, more generally, can have non-lognormal distribution with higher cumulants. 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. Moreover, the latter results cannot be jointly replicated in a model where investors have EIS ≤ 1 or CRRA preferences. We propose new approach for deriving equilibrium, and extend the analysis to the case of heterogeneous beliefs about probabilities of rare events.
The Lucas tree is still capable of new and important insights, and rare disasters also have a lot of potential in explaining behavior even when they do not happen. The Great Recession has revived this literature that got forgotten. Markets, however, seem not to have forgotten that such events are possible.