Who Saves More, the Naive or the Sophisticated Agent?

Abstract

We consider a class of additively time-separable life-cycle consumption-savings models with iso-elastic per period power utility featuring resistance to inter-temporal substitution of θ with linear consumption policy functions. The utility maximization problem is dynamically inconsistent for almost all specifications of effective discount factors. Pollak (1968) shows that the savings behavior of a sophisticated and a naive agent is identical with logarithmic utility (θ = 1). We extend this result by showing that the sophisticated agent saves in any period a greater fraction of her wealth than the naive agent if and only if θ ≥ 1, irrespective of the discount function.

Keywords: Life-Cycle Model; Discount Functions; Dynamic Inconsistency; Epstein-Zin-Weil Preferences

JEL Classification: D15, D91, E21