Who Saves More, the Naive or the Sophisticated Agent?
43 Pages Posted: 31 Mar 2017 Last revised: 7 Dec 2022
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Who Saves More, the Naive or the Sophisticated Agent?
Who Saves More, the Naive or the Sophisticated Agent?
Date Written: July 1, 2022
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
Suggested Citation: Suggested Citation