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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. Christian Gollier, 2012. "Pricing the Planet's Future: The Economics of Discounting in an Uncertain World," Economics Books, Princeton University Press, edition 1, number 9894.
    3. 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.
    4. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
    5. 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.
    6. 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.
    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.
    8. repec:hrv:faseco:33373345 is not listed on IDEAS
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    Cited by:

    1. Lee Endress & James Roumasset & Christopher Wada, 2016. "Do Natural Disasters Make Sustainable Growth Impossible?," Working Papers 2016-12, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    2. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART - LERECO 14-01, INRA UMR SMART-LERECO.
    3. 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.
    4. 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.
    5. Six, M. & Wirl, F., 2015. "Optimal pollution management when discount rates are endogenous," Resource and Energy Economics, Elsevier, vol. 42(C), pages 53-70.
    6. repec:eee:forpol:v:83:y:2017:i:c:p:58-69 is not listed on IDEAS

    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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