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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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    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. Lawrence Summers & Richard Zeckhauser, 2008. "Policymaking for posterity," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 115-140, December.
    3. Stern,Nicholas, 2007. "The Economics of Climate Change," Cambridge Books, Cambridge University Press, number 9780521700801.
    4. John A. Cairns & Marjon M. Van Der Pol, 1997. "Saving future lives. A comparison of three discounting models," Health Economics, John Wiley & Sons, Ltd., vol. 6(4), pages 341-350, July.
    5. Cropper, Maureen L & Aydede, Sema K & Portney, Paul R, 1994. "Preferences for Life Saving Programs: How the Public Discounts Time and Age," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 243-265, May.
    6. Steffen Andersen & Glenn W. Harrison & Morten I. Lau & E. Elisabet Rutström, 2008. "Eliciting Risk and Time Preferences," Econometrica, Econometric Society, vol. 76(3), pages 583-618, May.
    7. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
    8. 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.
    9. 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.
    10. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
    11. 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.
    12. 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.
    13. Yvan Lengwiler, 2005. "Heterogeneous Patience and the Term Structure of Real Interest Rates," American Economic Review, American Economic Association, vol. 95(3), pages 890-896, June.
    14. Bleichrodt, Han & Gafni, Amiram, 1996. "Time preference, the discounted utility model and health," Journal of Health Economics, Elsevier, vol. 15(1), pages 49-66, February.
    15. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    16. Harvey, Charles M., 1994. "The reasonableness of non-constant discounting," Journal of Public Economics, Elsevier, vol. 53(1), pages 31-51, January.
    17. Ben Groom & Cameron Hepburn & Phoebe Koundouri & David Pearce, 2005. "Declining Discount Rates: The Long and the Short of it," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 32(4), pages 445-493, December.
    18. 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.
    19. Read, Daniel, 2001. "Is Time-Discounting Hyperbolic or Subadditive?," Journal of Risk and Uncertainty, Springer, vol. 23(1), pages 5-32, July.
    20. Christian Gollier & Richard Zeckhauser, 2005. "Aggregation of Heterogeneous Time Preferences," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 878-896, August.
    21. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," The Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January.
    22. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    Cited by:

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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.
    7. Collins, Alan R. & Hansen, Evan & Hendryx, Michael, 2012. "Wind versus coal: Comparing the local economic impacts of energy resource development in Appalachia," Energy Policy, Elsevier, vol. 50(C), pages 551-561.
    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.
    12. Michael A. Kuhn, 2021. "Electronic Benefit Transfer and Food Expenditure Cycles," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 40(3), pages 744-773, June.
    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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