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Discounting the Distant Future: How Much Do Uncertain Rates Increase Valuations?

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Pizer, William () (Resources for the Future)
Newell, Richard () (Resources for the Future)

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Abstract

Costs and benefits in the distant future—such as those associated with global warming, long-lived infrastructure, hazardous and radioactive waste, and biodiversity—often have little value today when measured with conventional discount rates. We demonstrate that when the future path of this conventional rate is uncertain and persistent (i.e., highly correlated over time), the distant future should be discounted at lower rates than suggested by the current rate. We then use two centuries of data on U.S. interest rates to quantify this effect. Using both random walk and mean-reverting models (which are indistinguishable based on historical data), we compute the certainty-equivalent rate—that is, the single discount rate that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future. Using the random walk model, which we consider more compelling, we find that the certainty-equivalent rate falls from 3% now to 2% after 100 years, to 1% after 200 years, and down to 0.5% after 300 years. The mean-reverting model leads to a certainty-equivalent rate that remains above 3% for the next 200 years, then falls to 2% after 300 years and to 1% after 400 years. If we use these rates to value consequences at horizons of 400 years, the discounted value increases by a factor of 7,000 based on the random walk model and by a factor of 30 based on the mean-reverting model — both relative to conventional discounting. These results are relevant for a wide range of policy questions involving the distant future. Applying the random walk model to the consequences of climate change, for example, we find that inclusion of discount rate uncertainty doubles the expected present value of mitigation benefits. Other applications and alternative beliefs about the random walk–mean-reverting distinction are easily explored with our table of discount factors over time.

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Paper provided by Resources For the Future in its series Discussion Papers with number dp-00-45.

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Date of creation: 01 Oct 2000
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Handle: RePEc:rff:dpaper:dp-00-45

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  1. Lawrence H. Goulder & William A. Pizer, 2006. "The Economics of Climate Change," NBER Working Papers 11923, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  2. Lassila , Jukka & Valkonen, Tarmo, 2008. "Population ageing and fiscal sustainability in Finland: a stochastic analysis," Research Discussion Papers 28/2008, Bank of Finland. [Downloadable!]
  3. Cameron Hepburn & Phoebe Koundouri & Ekaterini Panopoulou & Theologos Pantelidis, 2006. "Social Discounting Under Uncertainty: A cross-country comparison," The Institute for International Integration Studies Discussion Paper Series iiisdp177, IIIS. [Downloadable!]
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  4. G. Cornelis van Kooten, 2003. "Smoke and Mirrors: The Kyoto Protocol and Beyond," Canadian Public Policy, University of Toronto Press, vol. 29(4), pages 397-415, December. [Downloadable!] (restricted)
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  5. Joseph E. Aldy & Alan J. Krupnick & Richard G. Newell & Ian W.H. Parry & William A. Pizer, 2009. "Designing Climate Mitigation Policy," NBER Working Papers 15022, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  6. J. Doyne Farmer & John Geanakoplos, 2009. "Hyperbolic discounting is rational: Valuing the far future with uncertain discount rates," Levine's Working Paper Archive 814577000000000356, David K. Levine. [Downloadable!]
  7. Parry, Ian & Pizer, William & Fischer, Carolyn, 2002. "How Large Are the Welfare Gains from Technological Innovation Induced by Environmental Policies?," Discussion Papers dp-02-57, Resources For the Future. [Downloadable!]
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  8. J. Doyne Farmer & John Geanakoplos, 2009. "Hyperbolic Discounting Is Rational: Valuing the Far Future with Uncertain Discount Rates," Cowles Foundation Discussion Papers 1719, Cowles Foundation, Yale University. [Downloadable!]
  9. Gonzalo Edwards, 2002. "La Tasa de Descuento en Proyectos de Largo Plazo," Documentos de Trabajo 231, Instituto de Economía. Pontificia Universidad Católica de Chile.. [Downloadable!]
  10. VAN STEENBERGHE, Vincent, 2004. "Core-stable and equitable allocations of greenhouse gas emission permits," CORE Discussion Papers 2004075, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  11. Parry, Ian W.H. & Goulder, Lawrence H., 2008. "Instrument Choice in Environmental Policy," Discussion Papers dp-08-07, Resources For the Future. [Downloadable!]
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  12. Colin Hunt & Seth Baum, 2009. "The ‘hidden’ social costs of forestry offsets," Mitigation and Adaptation Strategies for Global Change, Springer, vol. 14(2), pages 107-120, February. [Downloadable!] (restricted)
  13. Sun, Lili & van Kooten, G. Cornelis & Voss, Graham, 2006. "Quality of Life as an Explanation of the Divergence between Ranchers’' WTA and WTP for Public Forage," 2006 Annual meeting, July 23-26, Long Beach, CA 21162, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
  14. Tol, Richard S. J., 2008. "The Social Cost of Carbon: Trends, Outliers and Catastrophes," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 2(25), pages 1-22. [Downloadable!]
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  15. Gonzalo Edwards, 2003. "The effect of a constant or a declining discount rate on optimal investment timing," Applied Economics Letters, Taylor and Francis Journals, vol. 10(10), pages 657-659, August. [Downloadable!] (restricted)
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  16. David Anthoff & Richard Tol, 2009. "The Impact of Climate Change on the Balanced Growth Equivalent: An Application of FUND," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 43(3), pages 351-367, July. [Downloadable!] (restricted)
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  17. Diwakara, H. & Chandrakanth, M.G., 2007. "Beating negative externality through groundwater recharge in India: resource economic analysis," Conference Papers 43614, University of Agricultural Sciences, Bangalore, Department of Agricultural Economics. [Downloadable!]
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  18. García Fernández, Cristina, 2006. "Cost-benefit Analysis and the Difficulty of Applying it to Climate Change/El análisis coste-beneficio y la dificultad de su aplicación al cambio climático," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 24, pages 639 (12 p, Agosto. [Downloadable!] (restricted)
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