0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year" Suppose the annual real interest rate r(t) reverts to m according to the Ornstein Uhlenbeck (OU) continuous time process dr(t) = alpha[m - r(t)]dt + kdw(t), where w is a standard Wiener process. Then we prove that the long run rate of interest is r_infinity = m-k^2/2alpha^2. This confirms the Weitzman-Gollier principle that the volatility and the persistence of interest rates lower long run discounting. We fit the OU model to historical data across 14 countries covering 87 to 318 years and estimate the average short rate m and the long run rate r_infinity for each country. The data corroborate that, when doing cost benefit analysis, the long run rate of discount should be taken to be substantially less than the average short run rate observed over a very long history."> 0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year" Suppose the annual real interest rate r(t) reverts to m according to the Ornstein Uhlenbeck (OU) continuous time process dr(t) = alpha[m - r(t)]dt + kdw(t), where w is a standard Wiener process. Then we prove that the long run rate of interest is r_infinity = m-k^2/2alpha^2. This confirms the Weitzman-Gollier principle that the volatility and the persistence of interest rates lower long run discounting. We fit the OU model to historical data across 14 countries covering 87 to 318 years and estimate the average short rate m and the long run rate r_infinity for each country. The data corroborate that, when doing cost benefit analysis, the long run rate of discount should be taken to be substantially less than the average short run rate observed over a very long history."> 0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year" Suppose the annual ">
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Discounting the Distant Future

Author

Listed:
  • J. Doyne Farmer

    (Mathematical Institute and Institute for New Economic Thinking, Oxford & Martin School, University of Oxford)

  • John Geanakoplos

    (Cowles Foundation, Yale University)

  • Jaume Masoliver

    (Departament de Fisica Fonamental, Universitat de Barcelona)

  • Miquel Montero

    (Departament de Fisica Fonamental, Universitat de Barcelona)

  • Josep Perello

    (Departament de Fisica Fonamental, Universitat de Barcelona)

Abstract
If the historical average annual real interest rate is m > 0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year" Suppose the annual real interest rate r(t) reverts to m according to the Ornstein Uhlenbeck (OU) continuous time process dr(t) = alpha[m - r(t)]dt + kdw(t), where w is a standard Wiener process. Then we prove that the long run rate of interest is r_infinity = m-k^2/2alpha^2. This confirms the Weitzman-Gollier principle that the volatility and the persistence of interest rates lower long run discounting. We fit the OU model to historical data across 14 countries covering 87 to 318 years and estimate the average short rate m and the long run rate r_infinity for each country. The data corroborate that, when doing cost benefit analysis, the long run rate of discount should be taken to be substantially less than the average short run rate observed over a very long history.

Suggested Citation

  • J. Doyne Farmer & John Geanakoplos & Jaume Masoliver & Miquel Montero & Josep Perello, 2014. "Discounting the Distant Future," Cowles Foundation Discussion Papers 1951, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1951
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d19/d1951.pdf
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    References listed on IDEAS

    as
    1. Christian Gollier & Phoebe Koundouri & Theologos Pantelidis, 2008. "Declining discount rates: Economic justifications and implications for long-run policy [‘Regime switches in interest rates’]," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 23(56), pages 758-795.
    2. Dasgupta, Partha, 2004. "Human Well-Being and the Natural Environment," OUP Catalogue, Oxford University Press, number 9780199267194.
    3. 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.
    4. Martin L. Weitzman, 2007. "A Review of the Stern Review on the Economics of Climate Change," Journal of Economic Literature, American Economic Association, vol. 45(3), pages 703-724, September.
    5. Freeman, Mark C. & Groom, Ben & Panopoulou, Ekaterini & Pantelidis, Theologos, 2015. "Declining discount rates and the Fisher Effect: Inflated past, discounted future?," Journal of Environmental Economics and Management, Elsevier, vol. 73(C), pages 32-49.
    6. Hepburn, Cameron & Koundouri, Phoebe & Panopoulou, Ekaterini & Pantelidis, Theologos, 2009. "Social discounting under uncertainty: A cross-country comparison," Journal of Environmental Economics and Management, Elsevier, vol. 57(2), pages 140-150, March.
    7. J. Doyne Farmer & John Geanakoplos, 2009. "Hyperbolic Discounting Is Rational: Valuing the Far Future with Uncertain Discount Rates," Cowles Foundation Discussion Papers 1719, Cowles Foundation for Research in Economics, Yale University.
    8. 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.
    9. William D. Nordhaus, 2007. "A Review of the Stern Review on the Economics of Climate Change," Journal of Economic Literature, American Economic Association, vol. 45(3), pages 686-702, September.
    10. 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.
    11. M. F. M. Osborne, 1959. "Brownian Motion in the Stock Market," Operations Research, INFORMS, vol. 7(2), pages 145-173, April.
    12. 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.
    13. Stern,Nicholas, 2007. "The Economics of Climate Change," Cambridge Books, Cambridge University Press, number 9780521700801, September.
    14. Arrow, K. & Cropper, M. & Gollier, C. & Groom, B. & Heal, G. & Newell, R. & Nordhaus, W. & Pindyck, R. & Pizer, W. & Portney, P. & Sterner, T. & Tol, R. S. J. & Weitzman, Martin L., 2013. "Determining Benefits and Costs for Future Generations," Scholarly Articles 12841963, Harvard University Department of Economics.
    Full references (including those not matched with items on IDEAS)

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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. How much is our distant future worth?
      by Steve Cecchetti and Kim Schoenholtz in Money, Banking and Financial Markets on 2014-08-11 17:10:42

    Citations

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    Cited by:

    1. Katz, Yuri A., 2017. "Value of the distant future: Model-independent results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 269-276.
    2. Gollier, Christian, 2016. "Gamma discounters are short-termist," Journal of Public Economics, Elsevier, vol. 142(C), pages 83-90.
    3. Jaume Masoliver & Miquel Montero & Josep Perelló, 2021. "Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations," Mathematics, MDPI, vol. 9(14), pages 1-26, July.

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    More about this item

    Keywords

    Discounting; Environment; Interest rates; Inflation; Ornstein-Uhlenbeck process;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics

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