IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v89y2020i2d10.1007_s11238-020-09747-3.html
   My bibliography  Save this article

A new test of convexity–concavity of discount function

Author

Listed:
  • Pavlo R. Blavatskyy

    (Montpellier Business School)

  • Hela Maafi

    (Université Paris 8)

Abstract

Discounted utility theory and its generalizations (e.g., quasihyperbolic discounting, generalized hyperbolic discounting) use discount functions for weighting utilities of outcomes received in different time periods. We propose a new simple test of convexity–concavity of discount function. This test can be used with any utility function (which can be linear or not) and any preferences over risky lotteries (expected utility theory or not). The data from a controlled laboratory experiment show that about one third of experimental subjects reveal a concave discount function and another one third of subjects reveal a convex discount function (for delays up to two month).

Suggested Citation

  • 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.
  • Handle: RePEc:kap:theord:v:89:y:2020:i:2:d:10.1007_s11238-020-09747-3
    DOI: 10.1007/s11238-020-09747-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-020-09747-3
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11238-020-09747-3?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. Kirsten Rohde, 2010. "The hyperbolic factor: A measure of time inconsistency," Journal of Risk and Uncertainty, Springer, vol. 41(2), pages 125-140, October.
    2. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    3. 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.
    4. 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.
    5. Chapman, Gretchen B., 1996. "Expectations and Preferences for Sequences of Health and Money," Organizational Behavior and Human Decision Processes, Elsevier, vol. 67(1), pages 59-75, July.
    6. Pavlo R. Blavatskyy & Hela Maafi, 2018. "Estimating representations of time preferences and models of probabilistic intertemporal choice on experimental data," Journal of Risk and Uncertainty, Springer, vol. 56(3), pages 259-287, June.
    7. Loewenstein, George, 1987. "Anticipation and the Valuation of Delayed Consumption," Economic Journal, Royal Economic Society, vol. 97(387), pages 666-684, September.
    8. 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.
    9. 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.
    10. Maribeth Coller & Melonie Williams, 1999. "Eliciting Individual Discount Rates," Experimental Economics, Springer;Economic Science Association, vol. 2(2), pages 107-127, December.
    11. 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.
    12. 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.
    13. 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.
    14. Bohren, Oyvind & Hansen, Terje, 1980. " Capital Budgeting with Unspecified Discount Rates," Scandinavian Journal of Economics, Wiley Blackwell, vol. 82(1), pages 45-58.
    15. Saul Pleeter & John T. Warner, 2001. "The Personal Discount Rate: Evidence from Military Downsizing Programs," American Economic Review, American Economic Association, vol. 91(1), pages 33-53, March.
    16. Shane Frederick, 2005. "Cognitive Reflection and Decision Making," Journal of Economic Perspectives, American Economic Association, vol. 19(4), pages 25-42, Fall.
    17. 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.
    18. Pavlo R. Blavatskyy, 2016. "A monotone model of intertemporal choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 785-812, October.
    19. Pavlo Blavatskyy, 2018. "Temporal dominance and relative patience in intertemporal choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 361-384, March.
    20. Serdar Sayman & Ayse Öncüler, 2009. "An Investigation of Time Inconsistency," Management Science, INFORMS, vol. 55(3), pages 470-482, March.
    21. 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.
    22. 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.
    23. 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. 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.
    2. 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.
    3. 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.
    4. Mohammed Abdellaoui & Olivier l'Haridon & Corina Paraschiv, 2013. "Do Couples Discount Future Consequences Less than Individuals?," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201320, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    5. Anke Gerbe & Kirsten I.M. Rohde, 2010. "Risk and Preference Reversals in Intertemporal Choice," Post-Print hal-00911832, HAL.
    6. 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.
    7. Craig S. Webb, 2019. "Trichotomic discounted utility," Theory and Decision, Springer, vol. 87(3), pages 321-339, October.
    8. 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.
    9. Kirsten I. M. Rohde, 2019. "Measuring Decreasing and Increasing Impatience," Management Science, INFORMS, vol. 65(4), pages 1700-1716, April.
    10. Blavatskyy, Pavlo, 2019. "Future plans and errors," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 85-92.
    11. 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.
    12. 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.
    13. Abdellaoui, Mohammed & Kemel, Emmanuel & Panin, Amma & Vieider, Ferdinand M., 2019. "Measuring time and risk preferences in an integrated framework," Games and Economic Behavior, Elsevier, vol. 115(C), pages 459-469.
    14. 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.
    15. Jindrich Matousek & Tomas Havranek & Zuzana Irsova, 2022. "Individual discount rates: a meta-analysis of experimental evidence," Experimental Economics, Springer;Economic Science Association, vol. 25(1), pages 318-358, February.
    16. Paola Manzini & Marco Mariotti, 2007. "Choice over Time," Working Papers 605, Queen Mary University of London, School of Economics and Finance.
    17. Venkataraghavan Krishnaswamy & Aseem Pahuja & R. P. Sundarraj, 2016. "Integrating Time-Preferences into E-Negotiation Systems: A Model, Elicitation Approach and Experimental Implications," Group Decision and Negotiation, Springer, vol. 25(6), pages 1137-1167, November.
    18. Pavlo R. Blavatskyy, 2022. "Intertemporal choice as a tradeoff between cumulative payoff and average delay," Journal of Risk and Uncertainty, Springer, vol. 64(1), pages 89-107, February.
    19. Pavlo Blavatskyy, 2020. "Expected discounted utility," Theory and Decision, Springer, vol. 88(2), pages 297-313, March.
    20. Pavlo R. Blavatskyy & Hela Maafi, 2018. "Estimating representations of time preferences and models of probabilistic intertemporal choice on experimental data," Journal of Risk and Uncertainty, Springer, vol. 56(3), pages 259-287, June.

    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:89:y:2020:i:2:d:10.1007_s11238-020-09747-3. 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.