DP16412 Who Saves More, the Naive or the Sophisticated Agent?

Author(s): Max Groneck, Alexander Ludwig, Alexander Zimper
Publication Date: July 2021
Keyword(s): Choquet Expected Utility Preferences, Discount Functions, Dynamic inconsistency, Epstein-Weil-Zin Preferences, Life-Cycle Model, Naive Agent, Savings Behavior, Sophisticated Agent
JEL(s): D15, D91, E21
Programme Areas: Monetary Economics and Fluctuations
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=16412

We consider an additively time-separable life-cycle model for the family of power period utility functions u such that u'(c) = c^(-theta) for resistance to inter-temporal substitution of theta > 0. The utility maximization problem over life-time consumption is dynamically inconsistent for almost all specifications of effective discount factors. Pollak (1968) shows that the savings behavior of a sophisticated agent and her naive counterpart is always identical for a logarithmic utility function (i.e., for theta = 1). As an 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 whenever theta > 1 (theta < 1) irrespective of the specification of discount factors. We further show that this finding extends to an environment with risky returns and dynamically inconsistent Epstein-Zin-Weil preferences.