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Hyperbolic Discounting of the Far-Distant Future

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  • Nina Anchugina
  • Matthew Ryan
  • Arkadii Slinko

Abstract

We prove an analogue of Weitzman's (1998) famous result that an exponential discounter who is uncertain of the appropriate exponential discount rate should discount the far-distant future using the lowest (i.e., most patient) of the possible discount rates. Our analogous result applies to a hyperbolic discounter who is uncertain about the appropriate hyperbolic discount rate. In this case, the far-distant future should be discounted using the probability-weighted harmonic mean of the possible hyperbolic discount rates.

Suggested Citation

  • Nina Anchugina & Matthew Ryan & Arkadii Slinko, 2017. "Hyperbolic Discounting of the Far-Distant Future," Papers 1702.01362, arXiv.org.
    • Handle: RePEc:arx:papers:1702.01362
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    References listed on IDEAS

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    1. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    2. Nina Anchugina & Matthew Ryan & Arkadii Slinko, 2016. "Aggregating time preferences with decreasing impatience," Papers 1604.01819, arXiv.org.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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