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Risk-Adjusted Gamma Discounting

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  • Martin L. Weitzman

Abstract

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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Handle: RePEc:nbr:nberwo:15588

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  1. 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.
  2. Weitzman, Martin L., 2009. "Additive Damages, Fat-Tailed Climate Dynamics, and Uncertain Discounting," Economics Discussion Papers 2009-26, Kiel Institute for the World Economy.
  3. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
  4. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
  5. 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.
  6. Weitzman, Martin L., 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," Scholarly Articles 3693423, Harvard University Department of Economics.
  7. 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.
  8. Gollier, Christian, 2009. "Should We Discount the Far-Distant Future at Its Lowest Possible Rate?," Economics Discussion Papers 2009-7, Kiel Institute for the World Economy.
  9. Newell, Richard G. & Pizer, William A., 2004. "Uncertain discount rates in climate policy analysis," Energy Policy, Elsevier, vol. 32(4), pages 519-529, March.
  10. 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.
  11. 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.
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Cited by:
  1. Johansson-Stenman, Olof & Sterner, Thomas, 2013. "Discounting and Relative Consumption," Working Papers in Economics 559, University of Gothenburg, Department of Economics.
  2. Geoffrey Heal & Antony Millner, 2013. "Discounting under disagreement," Grantham Research Institute on Climate Change and the Environment Working Papers 112, Grantham Research Institute on Climate Change and the Environment.
  3. Gollier, Christian, 2012. "Asset pricing with uncertain betas: A long-term perspective," TSE Working Papers 12-354, Toulouse School of Economics (TSE).
  4. Gollier, Christian, 2012. "Evaluation of long-dated investments under uncertain growth trend, volatility and catastrophes," IDEI Working Papers 754, Institut d'Économie Industrielle (IDEI), Toulouse.
  5. Gollier, Christian, 2013. "A theory of rational short-termism with uncertain betas," IDEI Working Papers 771, Institut d'Économie Industrielle (IDEI), Toulouse.
  6. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Discounting when income is stochastic and climate change policies," MPRA Paper 27998, University Library of Munich, Germany.
  7. Munnich Vass, Miriam & Elofsson, Katarina, 2013. "Is forest sequestration at the expense of bioenergy and forest products cost-effective in EU climate policy to 2050?," Working Paper Series 2013:9, Department Economics, Swedish University of Agricultural Sciences.
  8. Morgenroth, Edgar, 2011. "How Can We Improve Evaluation Methods for Public Infrastructure?," Papers EC2, Economic and Social Research Institute (ESRI).

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