Exponential versus Hyperbolic Discounting: A Theoretical Analysis

13 Pages Posted: 3 Nov 2014 Last revised: 28 Aug 2016

See all articles by Michael Osborne

Michael Osborne

University of Sussex Business School

Date Written: August 2016

Abstract

This article casts doubt on the conclusion reached by experimentalists in behavioral economics (and other subjects such as social psychology and political science) that hyperbolic discounting explains their data better than exponential discounting. A dual expression to the exponential discounting equation is derived, the expression containing the full array of interest rates implied by every root solving the equation, including the negative and complex-valued interest rates, thereby employing and giving meaning to interest rates ignored by most economists for centuries. The dual expression has discount factors that are structurally similar to, and quantitatively identical with, those of the simple, hyperbolic discounting equation, making it difficult to distinguish which type of discounting was employed by subjects of past experiments, and implying that further, more detailed experiments are required to determine which type of discounting is most relevant.

Keywords: complex, discounting, exponential, hyperbolic, interest, intertemporal

JEL Classification: B41, C02, D03, D9, G02

Suggested Citation

Osborne, Michael J., Exponential versus Hyperbolic Discounting: A Theoretical Analysis (August 2016). Available at SSRN: https://ssrn.com/abstract=2518162 or http://dx.doi.org/10.2139/ssrn.2518162

Michael J. Osborne (Contact Author)

University of Sussex Business School ( email )

Jubilee Building
University of Sussex, Falmer
Brighton, Sussex BNI 9SL
United Kingdom

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