Who saves more, the naive or the sophisticated agent? - Max Groneck; Alexander Ludwig; Alexander Zimper (Leibniz Institute for Financial Research SAFE, 2022)
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 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 ( = 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 ≥ 1, irrespective of the discount function.
Keywords: D15; D91; E21; 330; Life-Cycle Model; Discount Functions; Dynamic Inconsistency; Epstein-Zin- Weil Preferences