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Time discounting: Declining impatience and interval effect


  • Yusuke Kinari


  • Fumio Ohtake


  • Yoshiro Tsutsui



Most studies have not distinguished delay from intervals, so that whether the declining impatience really holds has been an open question. We conducted an experiment that explicitly distinguishes them, and confirmed the declining impatience. This implies that people make dynamically inconsistent plans. We also found the interval effect that the per-period time discount rate decreases with prolonged intervals. We show that the interval and the magnitude effects are caused, at least partially, because subjects' choices are influenced by the differential in reward amount, while Weber's law solves neither the delay nor the interval effects.
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Suggested Citation

  • Yusuke Kinari & Fumio Ohtake & Yoshiro Tsutsui, 2009. "Time discounting: Declining impatience and interval effect," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 87-112, August.
  • Handle: RePEc:kap:jrisku:v:39:y:2009:i:1:p:87-112
    DOI: 10.1007/s11166-009-9073-1

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    References listed on IDEAS

    1. Scholten, Marc & Read, Daniel, 2006. "Beyond discounting: the tradeoff model of intertemporal choice," LSE Research Online Documents on Economics 22710, London School of Economics and Political Science, LSE Library.
    2. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    3. van der Pol, Marjon & Cairns, John, 2002. "A comparison of the discounted utility model and hyperbolic discounting models in the case of social and private intertemporal preferences for health," Journal of Economic Behavior & Organization, Elsevier, vol. 49(1), pages 79-96, September.
    4. Read, Daniel, 2001. "Is Time-Discounting Hyperbolic or Subadditive?," Journal of Risk and Uncertainty, Springer, vol. 23(1), pages 5-32, July.
    5. Kirby, Kris N. & Marakovic, Nino N., 1995. "Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting within Subjects and Amounts," Organizational Behavior and Human Decision Processes, Elsevier, vol. 64(1), pages 22-30, October.
    6. Pender, John L., 1996. "Discount rates and credit markets: Theory and evidence from rural india," Journal of Development Economics, Elsevier, vol. 50(2), pages 257-296, August.
    7. 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.
    8. 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.
    9. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
    10. Marc Scholten & Daniel Read, 2006. "Discounting by Intervals: A Generalized Model of Intertemporal Choice," Management Science, INFORMS, vol. 52(9), pages 1424-1436, September.
    11. Read, Daniel & Roelofsma, Peter H. M. P., 2003. "Subadditive versus hyperbolic discounting: A comparison of choice and matching," Organizational Behavior and Human Decision Processes, Elsevier, vol. 91(2), pages 140-153, July.
    12. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
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    Cited by:

    1. Shinsuke Ikeda & Myong-Il Kang, 2015. "Hyperbolic Discounting, Borrowing Aversion and Debt Holding," The Japanese Economic Review, Japanese Economic Association, vol. 66(4), pages 421-446, December.
    2. Yamane, Shoko & Yoneda, Hiroyasu & Takahashi, Taiki & Kamijo, Yoshio & Komori, Yasuhiro & Hiruma, Fumihiko & Tsutsui, Yoshiro, 2013. "Smokers, smoking deprivation, and time discounting," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 45(C), pages 47-56.
    3. Han, Ruokang & Takahashi, Taiki, 2012. "Psychophysics of time perception and valuation in temporal discounting of gain and loss," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6568-6576.
    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. Alessio Biondo, 2012. "What’s up after brain drain? Sometimes, somewhere, someone comes back: a general model of return migration," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 59(3), pages 269-284, September.
    6. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    7. Kirsten Rohde, 2010. "The hyperbolic factor: A measure of time inconsistency," Journal of Risk and Uncertainty, Springer, vol. 41(2), pages 125-140, October.

    More about this item


    Time discount rate; Declining impatience; Interval effect; Subadditivity; Weber’s Law; D81; D90;

    JEL classification:

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


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