Who Saves More, the Naive or the Sophisticated Agent?
58 Pages Posted: 22 Sep 2021
Date Written: July 1, 2021
We consider an additively time-separable life-cycle model for the family of power period utility functions u such that u 0 (c) = c −θ for resistance to inter-temporal substitution of θ > 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 θ = 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 θ > 1 (θ < 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.
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