IDEAS home Printed from https://ideas.repec.org/a/kap/enreec/v53y2012i3p309-321.html
   My bibliography  Save this article

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

Author

Listed:
  • Martin 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. Copyright Springer Science+Business Media B.V. 2012

Suggested Citation

  • Martin Weitzman, 2012. "The Ramsey Discounting Formula for a Hidden-State Stochastic Growth Process," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 53(3), pages 309-321, November.
    • Handle: RePEc:kap:enreec:v:53:y:2012:i:3:p:309-321
    DOI: 10.1007/s10640-012-9594-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10640-012-9594-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10640-012-9594-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    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.
    10. Six, M. & Wirl, F., 2015. "Optimal pollution management when discount rates are endogenous," Resource and Energy Economics, Elsevier, vol. 42(C), pages 53-70.
    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.
    13. Knoke, Thomas & Elsasser, Peter & Kindu, Mengistie, 2024. "Considering the land-cover elasticity of ecosystem service value coefficients improves assessments of large land-use changes," Ecosystem Services, Elsevier, vol. 68(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rick van der Ploeg, 2020. "Discounting and Climate Policy," CESifo Working Paper Series 8441, CESifo.
    2. Cropper, Maureen, 2012. "How Should Benefits and Costs Be Discounted in an Intergenerational Context?," RFF Working Paper Series dp-12-42, Resources for the Future.
    3. Freeman, Mark C. & Groom, Ben, 2016. "How certain are we about the certainty-equivalent long term social discount rate?," Journal of Environmental Economics and Management, Elsevier, vol. 79(C), pages 152-168.
    4. Kollenberg, Sascha & Taschini, Luca, 2016. "Emissions trading systems with cap adjustments," Journal of Environmental Economics and Management, Elsevier, vol. 80(C), pages 20-36.
    5. 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.
    6. Weitzman, Martin L., 2010. "Risk-adjusted gamma discounting," Journal of Environmental Economics and Management, Elsevier, vol. 60(1), pages 1-13, July.
    7. 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.
    8. Moritz Drupp & Mark Freeman & Ben Groom & Frikk Nesje, 2015. "Discounting disentangled: an expert survey on the determinants of the long-term social discount rate," GRI Working Papers 196a, Grantham Research Institute on Climate Change and the Environment.
    9. 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 Kiel).
    10. Gollier, Christian, 2016. "Gamma discounters are short-termist," Journal of Public Economics, Elsevier, vol. 142(C), pages 83-90.
    11. 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.
    12. Freeman, Mark C., 2010. "Yes, we should discount the far-distant future at its lowest possible rate: A resolution of the Weitzman-Gollier puzzle," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 4, pages 1-21.
    13. Mark C. Freeman & Ben Groom, 2015. "Positively Gamma Discounting: Combining the Opinions of Experts on the Social Discount Rate," Economic Journal, Royal Economic Society, vol. 125(585), pages 1015-1024, June.
    14. Koen Vermeylen, 2013. "The Consumption Discount Rate for the Distant Future (if we do not die out)," Tinbergen Institute Discussion Papers 13-201/VI, Tinbergen Institute.
    15. Freeman, Mark C. & Groom, Ben, 2016. "How certain are we about the certainty-equivalent longterm social discount rate?," LSE Research Online Documents on Economics 67258, London School of Economics and Political Science, LSE Library.
    16. Rintaro Yamaguchi, 2019. "Intergenerational Discounting with Intragenerational Inequality in Consumption and the Environment," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 73(4), pages 957-972, August.
    17. Fleurbaey, Marc & Zuber, Stéphane, 2015. "Discounting, risk and inequality: A general approach," Journal of Public Economics, Elsevier, vol. 128(C), pages 34-49.
    18. Antonio Nesticò & Gabriella Maselli & Patrizia Ghisellini & Sergio Ulgiati, 2023. "A Dual Probabilistic Discounting Approach to Assess Economic and Environmental Impacts," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 85(1), pages 239-265, May.
    19. Eric Fesselmeyer & Haoming Liu & Alberto Salvo, 2022. "Declining discount rates in Singapore's market for privately developed apartments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 330-350, March.
    20. Johansson-Stenman, Olof & Sterner, Thomas, 2015. "Discounting and relative consumption," Journal of Environmental Economics and Management, Elsevier, vol. 71(C), pages 19-33.

    More about this item

    Keywords

    Discounting; Climate change; Long term; Hidden state;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:enreec:v:53:y:2012:i:3:p:309-321. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.