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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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 18157.

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Date of creation: Jun 2012
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Publication status: published as Martin Weitzman, 2012. "The Ramsey Discounting Formula for a Hidden-State Stochastic Growth Process," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 53(3), pages 309-321, November.
Handle: RePEc:nbr:nberwo:18157

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  1. 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.
  2. 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.
  3. 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.
  4. Pizer, William & Newell, Richard, 2000. "Discounting the Distant Future: How Much Do Uncertain Rates Increase Valuations?," Discussion Papers dp-00-45, Resources For the Future.
  5. Newell, Richard G. & Pizer, William A., 2004. "Uncertain discount rates in climate policy analysis," Energy Policy, Elsevier, vol. 32(4), pages 519-529, March.
  6. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
  7. 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.
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Cited by:
  1. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART - LERECO 14-01, INRA UMR SMART.
  2. Ian Bateman, 2013. "EAERE Award for the Best Paper Published in Environmental and Resource Economics During 2012," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 56(1), pages 1-2, September.

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