IDEAS home Printed from https://ideas.repec.org/p/ema/worpap/2015-02.html
   My bibliography  Save this paper

Uncertain discount and hyperbolic preferences

Author

Listed:
  • Daniele Pennesi

    (Université de Cergy-Pontoise, THEMA)

Abstract

When the discount rate is uncertain, individuals whose preferences are consistent with discounted expected utility, exhibit diminishing impatience. This paper introduces and characterizes a variation of discounted expected utility in which the discount rate depends on the state of the nature that will occur. Quasi-hyperbolic discounting and the model of Dasgupta and Maskin (2005) are particular cases. The present bias disappears when the immediate payoff becomes uncertain. Commitment may be detrimental unless the discount rate is constant.

Suggested Citation

  • Daniele Pennesi, 2015. "Uncertain discount and hyperbolic preferences," THEMA Working Papers 2015-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2015-02
    as

    Download full text from publisher

    File URL: http://thema.u-cergy.fr/IMG/documents/2015-02.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Manel Baucells & Franz H. Heukamp, 2012. "Probability and Time Trade-Off," Management Science, INFORMS, vol. 58(4), pages 831-842, April.
    2. Matthew O. Jackson & Leeat Yariv, 2014. "Present Bias and Collective Dynamic Choice in the Lab," American Economic Review, American Economic Association, vol. 104(12), pages 4184-4204, December.
    3. 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.
    4. Edi Karni & Itzhak Zilcha, 2000. "Saving behavior in stationary equilibrium with random discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 551-564.
    5. Keren, Gideon & Roelofsma, Peter, 1995. "Immediacy and Certainty in Intertemporal Choice," Organizational Behavior and Human Decision Processes, Elsevier, vol. 63(3), pages 287-297, September.
    6. Mathias Dewatripont & Isabelle Brocas & Juan Carrillo, 2004. "Commitment devices under self-control problems: an overview," ULB Institutional Repository 2013/9665, ULB -- Universite Libre de Bruxelles.
    7. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    8. Kota Saito, 2011. "Strotz Meets Allais: Diminishing Impatience and the Certainty Effect: Comment," American Economic Review, American Economic Association, vol. 101(5), pages 2271-2275, August.
    9. Chakraborty, Anujit & Halevy, Yoram, 2015. "Allais meets Strotz: Remarks on the relation between Present Bias and the Certainty Effect," Microeconomics.ca working papers yoram_halevy-2015-7, Vancouver School of Economics, revised 03 Nov 2016.
    10. Higashi, Youichiro & Hyogo, Kazuya & Takeoka, Norio, 2009. "Subjective random discounting and intertemporal choice," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1015-1053, May.
    11. Karni, Edi, 2007. "Foundations of Bayesian theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 167-188, January.
    12. Yoram Halevy, 2015. "Time Consistency: Stationarity and Time Invariance," Econometrica, Econometric Society, vol. 83, pages 335-352, January.
    13. 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.
    14. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
    15. 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.
    16. James Andreoni & Charles Sprenger, 2012. "Estimating Time Preferences from Convex Budgets," American Economic Review, American Economic Association, vol. 102(7), pages 3333-3356, December.
    17. Weber, Bethany J. & Chapman, Gretchen B., 2005. "The combined effects of risk and time on choice: Does uncertainty eliminate the immediacy effect? Does delay eliminate the certainty effect?," Organizational Behavior and Human Decision Processes, Elsevier, vol. 96(2), pages 104-118, March.
    18. Manel Baucells & Franz Heukamp, 2010. "Common ratio using delay," Theory and Decision, Springer, vol. 68(1), pages 149-158, February.
    19. Partha Dasgupta & Eric Maskin, 2005. "Uncertainty and Hyperbolic Discounting," American Economic Review, American Economic Association, vol. 95(4), pages 1290-1299, September.
    20. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    21. Yoram Halevy, 2004. "Diminishing Impatience: Disentangling Time Preference from Uncertain Lifetime," Levine's Bibliography 122247000000000185, UCLA Department of Economics.
    22. Uri Benzion & Amnon Rapoport & Joseph Yagil, 1989. "Discount Rates Inferred from Decisions: An Experimental Study," Management Science, INFORMS, vol. 35(3), pages 270-284, March.
    23. J. Doyne Farmer & John Geanakoplos, 2009. "Hyperbolic Discounting Is Rational: Valuing the Far Future with Uncertain Discount Rates," Cowles Foundation Discussion Papers 1719, Cowles Foundation for Research in Economics, Yale University.
    24. Gollier, Christian & Weitzman, Martin L., 2010. "How should the distant future be discounted when discount rates are uncertain?," Economics Letters, Elsevier, vol. 107(3), pages 350-353, June.
    25. Weitzman, Martin L., 1998. "Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate," Journal of Environmental Economics and Management, Elsevier, vol. 36(3), pages 201-208, November.
    26. 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.
    27. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    28. Gollier, Christian, 2004. "Maximizing the expected net future value as an alternative strategy to gamma discounting," Finance Research Letters, Elsevier, vol. 1(2), pages 85-89, June.
    29. Christopher Harris & David Laibson, 2013. "Instantaneous Gratification," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 205-248.
    30. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    31. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    32. Hayashi, Takashi, 2003. "Quasi-stationary cardinal utility and present bias," Journal of Economic Theory, Elsevier, vol. 112(2), pages 343-352, October.
    33. 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.
    34. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    35. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    36. Thomas Epper & Helga Fehr-Duda & Adrian Bruhin, 2011. "Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting," Journal of Risk and Uncertainty, Springer, vol. 43(3), pages 169-203, December.
    37. Azfar, Omar, 1999. "Rationalizing hyperbolic discounting," Journal of Economic Behavior & Organization, Elsevier, vol. 38(2), pages 245-252, February.
    38. 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.
    39. Myerson, Joel & Green, Leonard & Scott Hanson, J. & Holt, Daniel D. & Estle, Sara J., 2003. "Discounting delayed and probabilistic rewards: Processes and traits," Journal of Economic Psychology, Elsevier, vol. 24(5), pages 619-635, October.
    40. Antony Millner & Geoffrey Heal, 2016. "Collective Intertemporal Choice: the Possibility of Time Consistency," NBER Working Papers 22524, National Bureau of Economic Research, Inc.
    41. 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.
    42. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    43. Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
    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. Salvador Cruz Rambaud & Ana María Sánchez Pérez, 2020. "Discounted and Expected Utility from the Probability and Time Trade-Off Model," Mathematics, MDPI, vol. 8(4), pages 1-17, April.
    2. Anchugina, Nina & Ryan, Matthew & Slinko, Arkadii, 2019. "Mixing discount functions: Implications for collective time preferences," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 1-14.
    3. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.
    4. Thomas Epper & Helga Fehr-Duda, 2012. "The missing link: unifying risk taking and time discounting," ECON - Working Papers 096, Department of Economics - University of Zurich, revised Oct 2018.
    5. 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.
    6. Shou Chen & Richard Fu & Lei Wedge & Ziran Zou, 2019. "Non-hyperbolic discounting and dynamic preference reversal," Theory and Decision, Springer, vol. 86(2), pages 283-302, March.
    7. 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.

    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. Laurent Denant-Boemont & Enrico Diecidue & Olivier l’Haridon, 2017. "Patience and time consistency in collective decisions," Experimental Economics, Springer;Economic Science Association, vol. 20(1), pages 181-208, March.
    2. 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.
    3. 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.
    4. Anke Gerbe & Kirsten I.M. Rohde, 2010. "Risk and Preference Reversals in Intertemporal Choice," Post-Print hal-00911832, HAL.
    5. 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.
    6. 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).
    7. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    8. Lemoine, Derek, 2018. "Age-induced acceleration of time: Implications for intertemporal choice," Journal of Economic Behavior & Organization, Elsevier, vol. 153(C), pages 143-152.
    9. 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.
    10. Ali al-Nowaihi & Sanjit Dhami, 2021. "Preferences over Time and under Uncertainty: Theoretical Foundations," CESifo Working Paper Series 9215, CESifo.
    11. Christopher P. Chambers & Federico Echenique & Alan D. Miller, 2023. "Decreasing Impatience," American Economic Journal: Microeconomics, American Economic Association, vol. 15(3), pages 527-551, August.
    12. Thomas Epper & Helga Fehr-Duda, 2012. "The missing link: unifying risk taking and time discounting," ECON - Working Papers 096, Department of Economics - University of Zurich, revised Oct 2018.
    13. Kirsten I. M. Rohde, 2019. "Measuring Decreasing and Increasing Impatience," Management Science, INFORMS, vol. 65(4), pages 1700-1716, April.
    14. 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.
    15. Jinrui Pan & Craig S. Webb & Horst Zank, 2019. "Delayed probabilistic risk attitude: a parametric approach," Theory and Decision, Springer, vol. 87(2), pages 201-232, September.
    16. 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.
    17. Craig S. Webb, 2019. "Trichotomic discounted utility," Theory and Decision, Springer, vol. 87(3), pages 321-339, October.
    18. Holden, Stein T. & Tilahun, Mesfin, 2019. "How related are risk preferences and time preferences?," CLTS Working Papers 4/19, Norwegian University of Life Sciences, Centre for Land Tenure Studies, revised 16 Oct 2019.
    19. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    20. 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.

    More about this item

    Keywords

    Diminishing Impatience; Uncertainty; Hyperbolic Discounting; Time Inconsistency;
    All these keywords.

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ema:worpap:2015-02. 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: Stefania Marcassa (email available below). General contact details of provider: https://edirc.repec.org/data/themafr.html .

    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.