A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting

TL;DR

This paper develops a straightforward axiomatic framework for exponential and quasi-hyperbolic discounting, enhancing understanding of their normative foundations using adapted utility theory techniques.

Contribution

It offers a new, simple axiomatic foundation for both discounting models, with transparent assumptions and proofs, applicable to finite and infinite horizons.

Findings

Axioms lead to exponential and quasi-hyperbolic discounting models.

Framework applies to finite and infinite horizon settings.

Simplifies previous axiomatizations with transparent assumptions.

Abstract

The main goal of this paper is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting. Exponential discounting has a well-established axiomatic foundation originally developed by Koopmans (1960, 1972) and Koopmans et al. (1964) with subsequent contributions by several other authors, including Bleichrodt et al. (2008). The papers by Hayashi (2003) and Olea and Strzalecki (2014) axiomatize quasi-hyperbolic discounting. The main contribution of this paper is to provide an alternative foundation for exponential and quasi-hyperbolic discounting, with simple, transparent axioms and relatively straightforward proofs. Using techniques by Fishburn (1982) and Harvey (1986), we show that Anscombe and Aumann's (1963) version of Subjective Expected Utility theory can be readily adapted to axiomatize the aforementioned types of discounting, in both finite and infinite horizon settings.