Who saves more, the naive or the sophisticated agent?

Abstract

This paper studies discrete time finite horizon life-cycle models with arbitrary discount functions and iso-elastic per period power utility with concavity parameter. We distinguish between the savings behavior of a sophisticated versus a naive agent. Although both agent types have identical preferences, they solve different utility maximization problems whenever the model is dynamically inconsistent. Pollak (1968) shows that the savings behavior of both agent types is nevertheless identical for logarithmic utility ( = 1). We generalize this result by showing that the sophisticated agent saves in every period a greater fraction of her wealth than the naive agent if and only if ≥ 1. While this result goes through for model extensions that preserve linearity of the consumption policy function, it breaks down for non-linear model extensions.