When is Recursive Utility Well-Founded?

Abstract

In this note we ask when Epstein-Zin-Weil (EZW) recursive utility over the infinite horizon is well-founded. EZW recursive utility has a parameter $\gamma > 0$ representing risk aversion and a parameter $\psi > 0$ representing intertemporal elasticity of substitution, and is an extension of time-additive isoelastic utility (which corresponds to the special case $\gamma = 1/\psi$). We show that if both $\gamma>1$ and $\psi>1$ (or $\gamma<1$ and $\psi<1$), then the utility process is a `utility bubble'. The only way to assign a value to current utility is to assign ever larger values to future utility. This is an important finding because the case $\gamma,\psi>1$ has been used widely in the literature to explain many financial puzzles. These explanations are unsatisfactory since they rely on ill-founded valuations of consumption streams.

Keywords: Recursive utility, utility bubble, Euler equation.

JEL Classification: G11, D12, D53