Who Saves More, the Naive or the Sophisticated Agent?

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 becomes 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 periodutility 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.