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