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

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  • Nina Anchugina

    (The University of Auckland)

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 (Econometrica 28(2):287–309, 1960, 1972) and Koopmans et al. (Econometrica 32(1/2):82–100, 1964) with subsequent contributions by several other authors, including Bleichrodt et al. (J Math Psychol 52(6):341–347, 2008). The papers by Hayashi (J Econ Theory 112(2):343–352, 2003) and Olea and Strzalecki (Q J Econ 129(3):1449–1499, 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 (The foundations of expected utility. Reidel Publishing Co, Dordrecht, 1982) and Harvey (Manag Sci 32(9):1123–1139, 1986), we show that Anscombe and Aumann’s (Ann Math Stat 34(1):199–205, 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.

Suggested Citation

  • Nina Anchugina, 2017. "A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting," Theory and Decision, Springer, vol. 82(2), pages 185-210, February.
    • Handle: RePEc:kap:theord:v:82:y:2017:i:2:d:10.1007_s11238-016-9566-8
    DOI: 10.1007/s11238-016-9566-8
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    References listed on IDEAS

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    1. Fishburn, Peter C & Rubinstein, Ariel, 1982. "Time Preference," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 677-694, October.
    2. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    3. Katsutoshi Wakai, 2008. "A Model of Utility Smoothing," Econometrica, Econometric Society, vol. 76(1), pages 137-153, January.
    4. José Luis Montiel Olea & Tomasz Strzalecki, 2014. "Axiomatization and Measurement of Quasi-Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1449-1499.
    5. Young, Eric R., 2007. "Generalized quasi-geometric discounting," Economics Letters, Elsevier, vol. 96(3), pages 343-350, September.
    6. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    7. Pan, Jinrui & Webb, Craig S. & Zank, Horst, 2015. "An extension of quasi-hyperbolic discounting to continuous time," Games and Economic Behavior, Elsevier, vol. 89(C), pages 43-55.
    8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    9. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    10. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    11. W. M. Gorman, 1968. "The Structure of Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(4), pages 367-390.
    12. Hayashi, Takashi, 2003. "Quasi-stationary cardinal utility and present bias," Journal of Economic Theory, Elsevier, vol. 112(2), pages 343-352, October.
    13. Matthew J. Ryan, 2009. "Generalizations of SEU: a geometric tour of some non-standard models," Oxford Economic Papers, Oxford University Press, vol. 61(2), pages 327-354, April.
    14. Grandmont, Jean-Michel, 1972. "Continuity properties of a von Neumann-Morgenstern utility," Journal of Economic Theory, Elsevier, vol. 4(1), pages 45-57, February.
    15. Robin Chark & Soo Chew & Songfa Zhong, 2015. "Extended present bias: a direct experimental test," Theory and Decision, Springer, vol. 79(1), pages 151-165, July.
    16. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
    17. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
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    Cited by:

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    3. Craig S. Webb, 2019. "Trichotomic discounted utility," Theory and Decision, Springer, vol. 87(3), pages 321-339, October.
    4. Craig S. Webb, 2023. "Dynamic Preference Foundations of Expected Exponentially-Discounted Utility," Economics Discussion Paper Series 2303, Economics, The University of Manchester.

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    Keywords

    Axiomatization; Exponential discounting; Quasi-hyperbolic discounting; Anscombe–Aumann model;
    All these keywords.

    JEL classification:

    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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