IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v82y2017i2d10.1007_s11238-016-9566-8.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-016-9566-8
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-016-9566-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    3. 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.
    4. 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.
    5. 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.
    6. Young, Eric R., 2007. "Generalized quasi-geometric discounting," Economics Letters, Elsevier, vol. 96(3), pages 343-350, September.
    7. 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.
    8. Hayashi, Takashi, 2003. "Quasi-stationary cardinal utility and present bias," Journal of Economic Theory, Elsevier, vol. 112(2), pages 343-352, October.
    9. 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.
    10. 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.
    11. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
    12. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    13. 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.
    14. 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.
    15. 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.
    16. Grandmont, Jean-Michel, 1972. "Continuity properties of a von Neumann-Morgenstern utility," Journal of Economic Theory, Elsevier, vol. 4(1), pages 45-57, February.
    17. Katsutoshi Wakai, 2008. "A Model of Utility Smoothing," Econometrica, Econometric Society, vol. 76(1), pages 137-153, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pavlo Blavatskyy, 2020. "Expected discounted utility," Theory and Decision, Springer, vol. 88(2), pages 297-313, March.
    2. Berenice Anne Neumann & Marc Oliver Rieger, 2023. "A new axiomatization of discounted expected utility," Theory and Decision, Springer, vol. 95(4), pages 515-537, November.
    3. Craig S. Webb, 2019. "Trichotomic discounted utility," Theory and Decision, Springer, vol. 87(3), pages 321-339, October.
    4. Craig S. Webb, 2024. "Dynamic preference foundations of expected exponentially-discounted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(4), pages 921-940, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nina Anchugina, 2015. "A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting," Papers 1511.06454, arXiv.org.
    2. Pavlo Blavatskyy, 2020. "Expected discounted utility," Theory and Decision, Springer, vol. 88(2), pages 297-313, March.
    3. Obara, Ichiro & Park, Jaeok, 2017. "Repeated games with general discounting," Journal of Economic Theory, Elsevier, vol. 172(C), pages 348-375.
    4. Lorenzo Bastianello & José Heleno Faro, 2023. "Choquet expected discounted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1071-1098, May.
    5. Lorenzo Bastianello & Jos'e Heleno Faro, 2019. "Time discounting under uncertainty," Papers 1911.00370, arXiv.org, revised Mar 2020.
    6. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    7. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2022. "Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting," Journal of Economic Theory, Elsevier, vol. 204(C).
    8. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    9. Dorian Jullien, 2018. "Under Risk, Over Time, Regarding Other People: Language and Rationality Within Three Dimensions [Face au risque, dans le temps, par rapport aux autres : langage et rationalité dans trois dimensions," Post-Print halshs-01651042, HAL.
    10. Nicolas Drouhin, 2016. "Non stationary additive utility and time consistency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01238584, HAL.
    11. Kirsten I. M. Rohde, 2019. "Measuring Decreasing and Increasing Impatience," Management Science, INFORMS, vol. 65(4), pages 1700-1716, April.
    12. Dorian Jullien, 2016. "Under Uncertainty, Over Time and Regarding Other People: Rationality in 3D," GREDEG Working Papers 2016-20, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    13. Dorian Jullien, 2018. "Under Risk, Over Time, Regarding Other People: Language and Rationality within Three Dimensions," Research in the History of Economic Thought and Methodology, in: Including a Symposium on Latin American Monetary Thought: Two Centuries in Search of Originality, volume 36, pages 119-155, Emerald Group Publishing Limited.
    14. Stefan A. Lipman & Arthur E. Attema, 2024. "A systematic review of unique methods for measuring discount rates," Journal of Risk and Uncertainty, Springer, vol. 69(2), pages 145-189, October.
    15. Bleichrodt, Han & Rohde, Kirsten I.M. & Wakker, Peter P., 2009. "Non-hyperbolic time inconsistency," Games and Economic Behavior, Elsevier, vol. 66(1), pages 27-38, May.
    16. Kirsten Rohde, 2010. "The hyperbolic factor: A measure of time inconsistency," Journal of Risk and Uncertainty, Springer, vol. 41(2), pages 125-140, October.
    17. Craig S. Webb, 2019. "Trichotomic discounted utility," Theory and Decision, Springer, vol. 87(3), pages 321-339, October.
    18. Andrew Meyer, 2013. "Estimating discount factors for public and private goods and testing competing discounting hypotheses," Journal of Risk and Uncertainty, Springer, vol. 46(2), pages 133-173, April.
    19. Bach Dong Xuan & Philippe Bich & Bertrand Wigniolle, 2022. "On multiple discount rates and present bias," PSE Working Papers halshs-03884664, HAL.
    20. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.

    More about this item

    Keywords

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

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:82:y:2017:i:2:d:10.1007_s11238-016-9566-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.