Working Paper: CEPR ID: DP16412
Authors: Max Groneck; Alexander Ludwig; Alexander Zimper
Abstract: We consider an additively time-separable life-cycle model for the family of powerperiod utility functions u such that u'(c) = c^(-theta) for resistance to inter-temporalsubstitution of theta > 0. The utility maximization problem over life-time consumptionis dynamically inconsistent for almost all specifications of effective discount factors.Pollak (1968) shows that the savings behavior of a sophisticated agent and her naivecounterpart is always identical for a logarithmic utility function (i.e., for theta = 1). Asan extension of Pollak's result we show that the sophisticated agent saves a greater(smaller) fraction of her wealth in every period than her naive counterpart whenevertheta > 1 (theta < 1) irrespective of the specification of discount factors. We further showthat this finding extends to an environment with risky returns and dynamicallyinconsistent Epstein-Zin-Weil preferences.
Keywords: lifecycle model; discount functions; dynamic inconsistency; savings behavior; naive agent; sophisticated agent; Choquet expected utility preferences; Epstein-Zin preferences
JEL Codes: D15; D91; E21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| sophisticated agent (L85) | savings behavior (D14) |
| theta < 1 (C29) | savings behavior of sophisticated agent (D14) |
| theta > 1 (C29) | savings behavior of sophisticated agent (D14) |
| logarithmic utility function (theta = 1) (D11) | savings behavior of naive and sophisticated agents (E21) |
| concavity parameter (theta) (C61) | savings behavior (D14) |