IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v87y2019i3d10.1007_s11238-019-09710-x.html
   My bibliography  Save this article

Trichotomic discounted utility

Author

Listed:
  • Craig S. Webb

    (The University of Manchester)

Abstract

Recent evidence on intertemporal choice suggests that decision-makers may exhibit both increasing and decreasing impatience simultaneously, called inverse-S discounting. This paper introduces trichotomic discounted utility to model inverse-S discounting. Under trichotomic discounted utility the decision-maker distinguishes between short-term delays, medium-term delays, and long-term delays. Exponential discounting holds within each category, but not necessarily across each category. We provide preference foundations for trichotomic discounted utility in the timed outcomes framework and in the consumption streams framework. The key axiom is a weakening of the time consistency axiom that allows for both increasing and decreasing impatience. We also consider a weak, local version of time consistency, and show that this plausible condition is satisfied only by discount functions with exponential “pieces”.

Suggested Citation

  • Craig S. Webb, 2019. "Trichotomic discounted utility," Theory and Decision, Springer, vol. 87(3), pages 321-339, October.
    • Handle: RePEc:kap:theord:v:87:y:2019:i:3:d:10.1007_s11238-019-09710-x
    DOI: 10.1007/s11238-019-09710-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-019-09710-x
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-019-09710-x?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. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    2. Takeuchi, Kan, 2011. "Non-parametric test of time consistency: Present bias and future bias," Games and Economic Behavior, Elsevier, vol. 71(2), pages 456-478, March.
    3. Geir B. Asheim, 1997. "Individual and Collective Time-Consistency," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 427-443.
    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. Drazen Prelec & George Loewenstein, 1991. "Decision Making Over Time and Under Uncertainty: A Common Approach," Management Science, INFORMS, vol. 37(7), pages 770-786, July.
    6. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    7. Read, Daniel & Airoldi, Mara & Loewe, G, 2005. "Intertemporal tradeoffs priced in interest rates and amounts: a study of method variance," LSE Research Online Documents on Economics 19823, London School of Economics and Political Science, LSE Library.
    8. Charles Harvey, 1995. "Proportional Discounting of Future Costs and Benefits," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 381-399, May.
    9. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
    10. Yoram Halevy, 2015. "Time Consistency: Stationarity and Time Invariance," Econometrica, Econometric Society, vol. 83, pages 335-352, January.
    11. Mohammed Abdellaoui & Han Bleichrodt & Olivier l’Haridon, 2013. "Sign-dependence in intertemporal choice," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 225-253, December.
    12. Yoram Halevy, 2008. "Strotz Meets Allais: Diminishing Impatience and the Certainty Effect," American Economic Review, American Economic Association, vol. 98(3), pages 1145-1162, June.
    13. Erzo G. J. Luttmer & Thomas Mariotti, 2003. "Subjective Discounting in an Exchange Economy," Journal of Political Economy, University of Chicago Press, vol. 111(5), pages 959-989, October.
    14. Diamond, Peter & Koszegi, Botond, 2003. "Quasi-hyperbolic discounting and retirement," Journal of Public Economics, Elsevier, vol. 87(9-10), pages 1839-1872, September.
    15. 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.
    16. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    17. Mohammed Abdellaoui & ArthurE. Attema & Han Bleichrodt, 2010. "Intertemporal Tradeoffs for Gains and Losses: An Experimental Measurement of Discounted Utility," Economic Journal, Royal Economic Society, vol. 120(545), pages 845-866, June.
    18. Jane E. J. Ebert & Drazen Prelec, 2007. "The Fragility of Time: Time-Insensitivity and Valuation of the Near and Far Future," Management Science, INFORMS, vol. 53(9), pages 1423-1438, September.
    19. Arthur E. Attema & Han Bleichrodt & Kirsten I. M. Rohde & Peter P. Wakker, 2010. "Time-Tradeoff Sequences for Analyzing Discounting and Time Inconsistency," Management Science, INFORMS, vol. 56(11), pages 2015-2030, November.
    20. Hayashi, Takashi, 2003. "Quasi-stationary cardinal utility and present bias," Journal of Economic Theory, Elsevier, vol. 112(2), pages 343-352, October.
    21. Drazen Prelec, 2004. "Decreasing Impatience: A Criterion for Non‐stationary Time Preference and “Hyperbolic” Discounting," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 511-532, October.
    22. 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.
    23. Harrell Chesson & W. Viscusi, 2003. "Commonalities in Time and Ambiguity Aversion for Long-Term Risks ," Theory and Decision, Springer, vol. 54(1), pages 57-71, February.
    24. 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.
    25. Arthur E. Attema & Han Bleichrodt & Yu Gao & Zhenxing Huang & Peter P. Wakker, 2016. "Measuring Discounting without Measuring Utility," American Economic Review, American Economic Association, vol. 106(6), pages 1476-1494, June.
    26. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(4), pages 1125-1152.
    27. Dhami, Sanjit, 2016. "The Foundations of Behavioral Economic Analysis," OUP Catalogue, Oxford University Press, number 9780198715535.
    28. 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.
    29. Serdar Sayman & Ayse Öncüler, 2009. "An Investigation of Time Inconsistency," Management Science, INFORMS, vol. 55(3), pages 470-482, March.
    30. Selçuk Onay & Ayse Öncüler, 2007. "Intertemporal choice under timing risk: An experimental approach," Journal of Risk and Uncertainty, Springer, vol. 34(2), pages 99-121, April.
    31. 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.
    Full references (including those not matched with items on IDEAS)

    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. Han Bleichrodt & Yu Gao & Kirsten I. M. Rohde, 2016. "A measurement of decreasing impatience for health and money," Journal of Risk and Uncertainty, Springer, vol. 52(3), pages 213-231, June.
    2. Anke Gerbe & Kirsten I.M. Rohde, 2010. "Risk and Preference Reversals in Intertemporal Choice," Post-Print hal-00911832, HAL.
    3. Arthur E. Attema & Han Bleichrodt & Kirsten I. M. Rohde & Peter P. Wakker, 2010. "Time-Tradeoff Sequences for Analyzing Discounting and Time Inconsistency," Management Science, INFORMS, vol. 56(11), pages 2015-2030, November.
    4. Gerber, Anke & Rohde, Kirsten I.M., 2010. "Risk and preference reversals in intertemporal choice," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 654-668, December.
    5. Mohammed Abdellaoui & Han Bleichrodt & Olivier l’Haridon, 2013. "Sign-dependence in intertemporal choice," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 225-253, December.
    6. Kirsten I. M. Rohde, 2019. "Measuring Decreasing and Increasing Impatience," Management Science, INFORMS, vol. 65(4), pages 1700-1716, April.
    7. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    8. 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.
    9. Sebastian Schweighofer-Kodritsch, 2015. "Time Preferences and Bargaining," STICERD - Theoretical Economics Paper Series /2015/568, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    11. Shotaro Shiba & Kazumi Shimizu, 2018. "Does time inconsistency differ between gain and loss? An intra-personal comparison using a non-parametric elicitation method (A revised version)," Working Papers 1807, Waseda University, Faculty of Political Science and Economics.
    12. Shotaro Shiba & Kazumi Shimizu, 2017. "Does Time Inconsistency Differ between Gain and Loss? An Intra-Personal Comparison Using a Non-Parametric Designed Experimen," Working Papers 1714, Waseda University, Faculty of Political Science and Economics.
    13. Shotaro Shiba & Kazumi Shimizu, 2020. "Does time inconsistency differ between gain and loss? An intra-personal comparison using a non-parametric elicitation method," Theory and Decision, Springer, vol. 88(3), pages 431-452, April.
    14. Daniele Pennesi, 2017. "Uncertain discount and hyperbolic preferences," Theory and Decision, Springer, vol. 83(3), pages 315-336, 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. Pavlo R. Blavatskyy & Hela Maafi, 2020. "A new test of convexity–concavity of discount function," Theory and Decision, Springer, vol. 89(2), pages 121-136, September.
    17. Galizzi, Matteo M. & Miraldo, Marisa & Stavropoulou, Charitini & van der Pol, Marjon, 2016. "Doctor–patient differences in risk and time preferences: A field experiment," Journal of Health Economics, Elsevier, vol. 50(C), pages 171-182.
    18. David J. Freeman & Kevin Laughren, 2024. "Task completion without commitment," Experimental Economics, Springer;Economic Science Association, vol. 27(2), pages 273-298, April.
    19. Ebert, Sebastian & Wei, Wei & Zhou, Xun Yu, 2020. "Weighted discounting—On group diversity, time-inconsistency, and consequences for investment," Journal of Economic Theory, Elsevier, vol. 189(C).
    20. Mohammed Abdellaoui & Olivier l'Haridon & Corina Paraschiv, 2013. "Do Couples Discount Future Consequences Less than Individuals?," Economics Working Paper Archive (University of Rennes & University of Caen) 201320, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.

    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:87:y:2019:i:3:d:10.1007_s11238-019-09710-x. 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.