Who Saves More, the Naive or the Sophisticated Agent?

Abstract

We construct and solve a dynamically inconsistent Choquet expected utility life-cycle model for naive and sophisticated agents, respectively. Pollak (1968) shows that the realized saving behavior of naive and sophisticated agents be- comes identical for a logarithmic period-utility function. As a generalization of Pollak's analysis, we compare the saving behavior of both types of agents for the family of isoelastic utility functions. We show that a sophisticated agent saves more in every period than her naive counterpart if and only if her period- utility function is more concave than the logarithmic function. This relationship holds for arbitrary survival beliefs and time-discount factors. Quantitatively, the difference in saving behavior across the two types can be large.

Keywords: Survival beliefs; Ambiguity; Choquet expected utility; Dynamic inconsistency

JEL Classification: D91, D83, E21