IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-03884664.html
   My bibliography  Save this paper

On multiple discount rates and present bias

Author

Listed:
  • Bach Dong Xuan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Bich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Bertrand Wigniolle

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

In this paper, we give axiomatic foundations for a social planner objective function that takes the form of the maxmin of quasi-hyperbolic criteria. The minimum is taken over a set Q of possible pairs of discount rates δ and present bias parameters p0. When there is no present bias, we recover Chambers and Echenique's axiomatization of maxmin exponential preferences, and when Q reduces to a singleton, we get Montiel Olea and Strzalecki's axiomatization of quasi-hyperbolic preferences. To prove our main result, we provide some intertemporal variational representation results of interest for its own sake.

Suggested Citation

  • Bach Dong Xuan & Philippe Bich & Bertrand Wigniolle, 2022. "On multiple discount rates and present bias," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03884664, HAL.
    • Handle: RePEc:hal:cesptp:halshs-03884664
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03884664
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-03884664/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
    2. Thaler, Richard H & Shefrin, H M, 1981. "An Economic Theory of Self-Control," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 392-406, April.
    3. Jean-Pierre Drugeon & Thai Ha Huy, 2022. "A not so myopic axiomatization of discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 349-376, February.
    4. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    5. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
    6. Hayashi, Takashi, 2003. "Quasi-stationary cardinal utility and present bias," Journal of Economic Theory, Elsevier, vol. 112(2), pages 343-352, October.
    7. Stéphane Zuber, 2011. "The aggregation of preferences: can we ignore the past?," Theory and Decision, Springer, vol. 70(3), pages 367-384, March.
    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. 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.
    10. Zou, Ziran & Chen, Shou & Wedge, Lei, 2014. "Finite horizon consumption and portfolio decisions with stochastic hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 70-80.
    11. Matthew O. Jackson & Leeat Yariv, 2015. "Collective Dynamic Choice: The Necessity of Time Inconsistency," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 150-178, November.
    12. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    13. Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
    14. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    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. 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.
    17. 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.
    18. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    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. Lorenzo Bastianello & Jos'e Heleno Faro, 2019. "Time discounting under uncertainty," Papers 1911.00370, arXiv.org, revised Mar 2020.
    2. 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.
    3. 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).
    4. David K. Backus & Bryan R. Routledge & Stanley E. Zin, 2005. "Exotic Preferences for Macroeconomists," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 319-414, National Bureau of Economic Research, Inc.
    5. Chen, Shumin & Zeng, Yan & Hao, Zhifeng, 2017. "Optimal dividend strategies with time-inconsistent preferences and transaction costs in the Cramér–Lundberg model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 31-45.
    6. Antony Millner & Geoffrey Heal, 2015. "Collective intertemporal choice: time consistency vs. time invariance," GRI Working Papers 220, Grantham Research Institute on Climate Change and the Environment.
    7. Shigeta, Yuki, 2022. "Quasi-hyperbolic discounting under recursive utility and consumption–investment decisions," Journal of Economic Theory, Elsevier, vol. 204(C).
    8. Liya Liu & Yingjie Niu & Yuanping Wang & Jinqiang Yang, 2020. "Optimal consumption with time-inconsistent preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 785-815, October.
    9. Koo, Ja Eun & Lim, Byung Hwa, 2021. "Consumption and life insurance decisions under hyperbolic discounting and taxation," Economic Modelling, Elsevier, vol. 94(C), pages 288-295.
    10. Chen Shou & Xiang Shengpeng & He Hongbo, 2019. "Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-13, June.
    11. Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
    12. Vitale, Paolo, 2018. "Robust trading for ambiguity-averse insiders," Journal of Banking & Finance, Elsevier, vol. 90(C), pages 113-130.
    13. Zhao, Qian & Shen, Yang & Wei, Jiaqin, 2014. "Consumption–investment strategies with non-exponential discounting and logarithmic utility," European Journal of Operational Research, Elsevier, vol. 238(3), pages 824-835.
    14. 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.
    15. Bommier, Antoine & Kochov, Asen & Le Grand, François, 2019. "Ambiguity and endogenous discounting," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 48-62.
    16. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, 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. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    19. 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.
    20. Liu, Bo & Niu, Yingjie & Zhang, Yuhua, 2019. "Corporate liquidity and risk management with time-inconsistent preferences," Economic Modelling, Elsevier, vol. 81(C), pages 295-307.

    More about this item

    Keywords

    Discounting; Discount rate; Exponential model; Hyperbolic model; Maxmin expected utility discounting; Maxmin expected utility;
    All these keywords.

    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:hal:cesptp:halshs-03884664. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.