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Characterizing the Amount and Speed of Discounting Procedures

Author

Listed:
  • Jamison Dean T.

    (University of Washington)

  • Jamison Julian

    (Federal Reserve Bank of Boston)

Abstract

This paper introduces the concepts of amount and speed of a discounting procedure in order to generate well-characterized families of procedures for use in social project evaluation. Exponential discounting sequesters the concepts of amount and speed into a single parameter that needs to be disaggregated in order to characterize nonconstant rate procedures. The inverse of the present value of a unit stream of benefits provides a natural measure of the amount a procedure discounts the future. We propose geometrical and time horizon based measures of how rapidly a discounting procedure acquires its ultimate present value, and we prove these to be the same. This provides an unambiguous measure of the speed of discounting, a measure whose values lie between 0 (slow) and 2 (fast). Exponential discounting has a speed of 1. A commonly proposed approach to aggregating individual discounting procedures into a social one for project evaluation averages the individual discount functions. We point to serious shortcoming with this approach and propose an alternative for which the amount and time horizon of the social procedure are the averages of the amounts and time horizons of the individual procedures. We further show that the social procedure will in general be slower than the average of the speeds of the individual procedures. For potential applications in social project evaluation we characterize three families of two-parameter discounting procedures - hyperbolic, gamma, and Weibull - in terms of their discount functions, their discount rate functions, their amounts, their speeds and their time horizons. (The appendix characterizes additional families, including the quasi-hyperbolic one.) A one parameter version of hyperbolic discounting, d(t) = (1+rt)-2, has amount r and speed 0, and this procedure is our candidate for use in social project evaluation, although additional empirical work will be needed to fully justify a one-parameter simplification of more general procedures.

Suggested Citation

  • Jamison Dean T. & Jamison Julian, 2011. "Characterizing the Amount and Speed of Discounting Procedures," Journal of Benefit-Cost Analysis, De Gruyter, vol. 2(2), pages 1-56, April.
    • Handle: RePEc:bpj:jbcacn:v:2:y:2011:i:2:n:1
    DOI: 10.2202/2152-2812.1031
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    4. Lloyd-Smith, Patrick & Adamowicz, Wiktor & Entem, Alicia & Fenichel, Eli P. & Rouhi Rad, Mani, 2021. "The decade after tomorrow: Estimation of discount rates from realistic temporal decisions over long time horizons," Journal of Economic Behavior & Organization, Elsevier, vol. 183(C), pages 158-174.
    5. Fan, Victoria Y & Jamison, Dean T & Summers, Lawrence H, 2018. "Pandemic risk: how large are the expected losses?," Scholarly Articles 35014363, Harvard Kennedy School of Government.
    6. 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.
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    8. Jinrui Pan & Craig Webb & Horst Zank, 2013. "Discounting the Subjective Present and Future," Economics Discussion Paper Series 1305, Economics, The University of Manchester.
    9. Scott Farrow & W. Kip Viscusi, 2013. "Towards principles and standards for the benefit–cost analysis of safety," Chapters, in: Scott O. Farrow & Richard Zerbe, Jr. (ed.), Principles and Standards for Benefit–Cost Analysis, chapter 5, pages 172-193, Edward Elgar Publishing.
    10. Nina Anchugina & Matthew Ryan & Arkadii Slinko, 2016. "Aggregating time preferences with decreasing impatience," Papers 1604.01819, arXiv.org.
    11. W. David Bradford & Paul Dolan & Matteo M. Galizzi, 2019. "Looking ahead: Subjective time perception and individual discounting," Journal of Risk and Uncertainty, Springer, vol. 58(1), pages 43-69, February.
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    13. 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.

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