Who Saves More, the Naive or the Sophisticated Agent?

43 Pages Posted: 31 Mar 2017 Last revised: 7 Dec 2022

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

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Date Written: July 1, 2022

Abstract

We consider a class of additively time-separable life-cycle consumption-savings models with iso-elastic per period power utility featuring resistance to inter-temporal substitution of θ with linear consumption policy functions. The utility maximization problem is dynamically inconsistent for almost all specifications of effective discount factors. Pollak (1968) shows that the savings behavior of a sophisticated and a naive agent is identical with logarithmic utility (θ = 1). We extend this result by showing that the sophisticated agent saves in any period a greater fraction of her wealth than the naive agent if and only if θ ≥ 1, irrespective of the discount function.

Keywords: Life-Cycle Model; Discount Functions; Dynamic Inconsistency; Epstein-Zin-Weil Preferences

JEL Classification: D15, D91, E21

Suggested Citation

Groneck, Max and Ludwig, Alexander and Zimper, Alexander, Who Saves More, the Naive or the Sophisticated Agent? (July 1, 2022). SAFE Working Paper No. 169, Available at SSRN: https://ssrn.com/abstract=2943885 or http://dx.doi.org/10.2139/ssrn.2943885

Max Groneck

Stockholm School of Economics, Department of Economics ( email )

Germany

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

Alexander Ludwig (Contact Author)

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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