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How Should the Distant Future be Discounted when Discount Rates are Uncertain?


  • Christian Gollier
  • Martin L. Weitzman


It is not immediately clear how to discount distant-future events, like climate change, when the distant-future discount rate itself is uncertain. The so-called "Weitzman-Gollier puzzle" is the fact that two seemingly symmetric and equally plausible ways of dealing with uncertain future discount rates appear to give diametrically opposed results with the opposite policy implications. We explain how the "Weitzman-Gollier puzzle" is resolved. When agents optimize their consumption plans and probabilities are adjusted for risk, the two approaches are identical. What we would wish a reader to take away from this paper is the bottom-line message that the appropriate long run discount rate declines over time toward its lowest possible value.

Suggested Citation

  • Christian Gollier & Martin L. Weitzman, 2009. "How Should the Distant Future be Discounted when Discount Rates are Uncertain?," CESifo Working Paper Series 2863, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_2863

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    References listed on IDEAS

    1. Hepburn, Cameron & Groom, Ben, 2007. "Gamma discounting and expected net future value," Journal of Environmental Economics and Management, Elsevier, vol. 53(1), pages 99-109, January.
    2. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
    3. Freeman, Mark C., 2009. "Yes, we should discount the far-distant future at its lowest possible rate: a resolution of the Weitzman-Gollier puzzle," Economics Discussion Papers 2009-42, Kiel Institute for the World Economy (IfW).
    4. Gollier, Christian, 2004. "Maximizing the expected net future value as an alternative strategy to gamma discounting," Finance Research Letters, Elsevier, vol. 1(2), pages 85-89, June.
    5. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
    6. Gollier, Christian, 2010. "Expected net present value, expected net future value, and the Ramsey rule," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 142-148, March.
    7. Newell, Richard G. & Pizer, William A., 2003. "Discounting the distant future: how much do uncertain rates increase valuations?," Journal of Environmental Economics and Management, Elsevier, vol. 46(1), pages 52-71, July.
    8. Gollier, Christian, 2009. "Should we Discount the Far-Distant Future at its Lowest Possible Rate?," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 3, pages 1-14.
    9. Wolfgang Buchholz & Jan Schumacher, 2008. "Discounting the Long-Distant Future: A Simple Explanation for the Weitzman-Gollier-Puzzle," CESifo Working Paper Series 2357, CESifo Group Munich.
    10. Phoebe Koundouri & Theologos Pantelidis & Ben Groom & Ekaterini Panopoulou, 2007. "Discounting the distant future: How much does model selection affect the certainty equivalent rate?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 641-656.
    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. Newell, Richard G. & Pizer, William A., 2004. "Uncertain discount rates in climate policy analysis," Energy Policy, Elsevier, vol. 32(4), pages 519-529, March.
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    More about this item


    discount rate; term structure; climate change; cost-benefit analysis;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • Q51 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Valuation of Environmental Effects


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