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Risk-Adjusted Gamma Discounting

  • Martin L. Weitzman

It is widely recognized that the economics of distant-future events, like climate change, is critically dependent upon the choice of a discount rate. Unfortunately, it is unclear how to discount distant-future events when the future discount rate itself is unknown. In previous work, an analytically-tractable approach called "gamma discounting" was proposed, which gave a declining discount rate schedule as a simple closed-form function of time. This paper extends the previous gamma approach by using a Ramsey optimal growth model, combined with uncertainty about future productivity, in order to "risk adjust" all probabilities by marginal utility weights. Some basic numerical examples are given, which suggest that the overall effect of risk-adjusted gamma discounting on lowering distant-future discount rates may be significant. The driving force is a "fear factor" from risk aversion to permanent productivity shocks representing catastrophic future states of the world.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15588.

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Date of creation: Dec 2009
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Publication status: published as Weitzman, Martin L., 2010. "Risk-adjusted gamma discounting," Journal of Environmental Economics and Management, Elsevier, vol. 60(1), pages 1-13, July.
Handle: RePEc:nbr:nberwo:15588
Note: EEE
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  1. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
  2. Gollier, Christian & Weitzman, Martin, 2009. "How Should the Distant Future be Discounted When Discount Rates are Uncertain?," IDEI Working Papers 588, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. GOLLIER Christian, 2008. "Should we discount the far-distant future at its lowest possible rate?," LERNA Working Papers 08.30.274, LERNA, University of Toulouse.
  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. Weitzman, Martin L., 2009. "Additive damages, fat-tailed climate dynamics, and uncertain discounting," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 3, pages 1-29.
  6. Martin L. Weitzman, 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 1-19, February.
  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.
  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. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
  10. 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.
  11. 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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