Who Saves More, the Naive or the Sophisticated Agent?

58 Pages Posted: 22 Sep 2021

See all articles by Max Groneck

Max Groneck

Stockholm School of Economics, Department of Economics

Alexander Ludwig

Max Planck Society for the Advancement of the Sciences - Munich Center for the Economics of Aging (MEA); Goethe University Frankfurt

Alexander Zimper

University of Pretoria; Kiel Institute for the World Economy

Multiple version iconThere are 2 versions of this paper

Date Written: July 1, 2021

Abstract

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.

Suggested Citation

Groneck, Max and Ludwig, Alexander and Zimper, Alexander, Who Saves More, the Naive or the Sophisticated Agent? (July 1, 2021). CEPR Discussion Paper No. DP16412, Available at SSRN: https://ssrn.com/abstract=3928691

Max Groneck (Contact Author)

Stockholm School of Economics, Department of Economics ( email )

Germany

HOME PAGE: http://https://www.hhs.se/en/Research/Departments/DE/

Alexander Ludwig

Max Planck Society for the Advancement of the Sciences - Munich Center for the Economics of Aging (MEA) ( email )

Amalienstrasse 33
Munich, 80799
Germany

Goethe University Frankfurt ( email )

Grüneburgplatz 1
Frankfurt am Main, 60323
Germany

Alexander Zimper

University of Pretoria ( email )

South Africa

Kiel Institute for the World Economy ( email )

P.O. Box 4309
Kiel, Schleswig-Hosltein D-24100
Germany

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