Multiplicity of separable recursive utilities with non-unit EIS in the Bansal–Yaron model

Determine whether multiplicity of separable recursive utilities can arise in the constant-volatility Bansal–Yaron long-run-risk consumption model when the elasticity of intertemporal substitution is non-unit.

Background

The paper studies recursive utility fixed points in unbounded-consumption environments and distinguishes between uniqueness among all recursive utilities and uniqueness within the class of separable recursive utilities, which have the form of consumption multiplied by a function of the current Markov state. For non-unit elasticity of intertemporal substitution, the paper establishes uniqueness within this separable class in its general Markov framework.

For the constant-volatility specification of the Bansal–Yaron long-run-risk model, the paper establishes multiplicity of separable recursive utilities at unit elasticity of intertemporal substitution, identifying distinct log-linear and log-quadratic solutions. The authors explicitly leave unresolved whether analogous multiplicity can occur when the elasticity of intertemporal substitution differs from one.