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The Ramsey Discounting Formula for a Hidden-State Stochastic Growth Process

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  • Martin L. Weitzman

Abstract

The long term discount rate is critically dependent upon projections of future growth rates that are fuzzier in proportion to the remoteness of the time horizon. This paper models such increasing fuzziness as an evolving hidden-state stochastic process. The underlying trend growth rate is an unobservable random walk hidden by noisy transitory shocks and recoverable only as a probability distribution via Bayesian updating. A simple expression is derived for the time-declining Ramsey discount rate. The components of this hidden-state Ramsey discounting formula are then analyzed, followed by a few remarks about possible implications and applications.

Suggested Citation

  • Martin L. Weitzman, 2012. "The Ramsey Discounting Formula for a Hidden-State Stochastic Growth Process," NBER Working Papers 18157, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:18157
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    5. Christian Gollier, 2012. "Pricing the Planet's Future: The Economics of Discounting in an Uncertain World," Economics Books, Princeton University Press, edition 1, volume 1, number 9894.
    6. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
    7. 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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    Cited by:

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    2. Rick Van der Ploeg, 2020. "Discounting And Climate Policy," OxCarre Working Papers 244, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
    3. Klaus Desmet & Robert E. Kopp & Scott A. Kulp & Dávid Krisztián Nagy & Michael Oppenheimer & Esteban Rossi-Hansberg & Benjamin H. Strauss, 2021. "Evaluating the Economic Cost of Coastal Flooding," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(2), pages 444-486, April.
    4. Knoke, Thomas & Gosling, Elizabeth & Paul, Carola, 2020. "Use and misuse of the net present value in environmental studies," Ecological Economics, Elsevier, vol. 174(C).
    5. Newbery, David M., 2016. "Towards a green energy economy? The EU Energy Union’s transition to a low-carbon zero subsidy electricity system – Lessons from the UK’s Electricity Market Reform," Applied Energy, Elsevier, vol. 179(C), pages 1321-1330.
    6. Ian Bateman, 2013. "EAERE Award for the Best Paper Published in Environmental and Resource Economics During 2012," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 56(1), pages 1-2, September.
    7. Márta Somogyvári, 2018. "Ethical Aspects of Intertemporal Discounting and the Social Discount Rate," Financial and Economic Review, Magyar Nemzeti Bank (Central Bank of Hungary), vol. 17(3), pages 109-132.
    8. Luo, Lanlan & Zou, Ziran & Chen, Shou, 2021. "Discounting for public-private partnership projects in China," Economic Modelling, Elsevier, vol. 98(C), pages 218-226.
    9. Lee H. Endress & James A. Roumasset & Christopher A. Wada, 2020. "Do Natural Disasters Make Sustainable Growth Impossible?," Economics of Disasters and Climate Change, Springer, vol. 4(2), pages 319-345, July.
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    11. Knoke, Thomas & Paul, Carola & Härtl, Fabian, 2017. "A critical view on benefit-cost analyses of silvicultural management options with declining discount rates," Forest Policy and Economics, Elsevier, vol. 83(C), pages 58-69.
    12. Lanlan Luo & Shou Chen & Ziran Zou, 2020. "Determining the Generalized Discount Rate for Risky Projects," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 77(1), pages 143-158, September.

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    More about this item

    JEL classification:

    • Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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