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Climate policy under fat-tailed risk: an application of FUND

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  • David Anthoff
  • Richard Tol

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Abstract

We apply four alternative decision criteria, two old ones and two new, to the question of the appropriate level of greenhouse gas emission reduction. In all cases, we consider a uniform carbon tax that is applied to all emissions from all sectors and all countries; and that increases over time with the discount rate. For a one per cent pure rate of the time preference and a rate of risk aversion of one, the tax that maximises expected net present welfare equals $120/tC in 2010. However, we also find evidence that the uncertainty about welfare may well have fat tails so that the sample mean exists only by virtue of the finite number of runs in our Monte Carlo analysis. This is consistent with Weitzman’s Dismal Theorem. We therefore consider minimax regret as a decision criterion. As regret is defined on the positive real line, we in fact consider large percentiles instead of the ill-defined maximum. Depending on the percentile used, the recommended tax lies between $100 and $170/tC. Regret is a measure of the slope of the welfare function, while we are in fact concerned about the level of welfare. We therefore minimise the tail risk, defined as the expected welfare below a percentile of the probability density function without climate policy. Depending on the percentile used, the recommended tax lies between $20 and $330/tC. We also minimise the fatness of the tails, as measured by the p-value of the test of the null hypothesis that recursive mean welfare is non-stationary in the number of Monte Carlo runs. We cannot reject the null hypothesis of non-stationarity at the 5 % confidence level, but come closest for an initial tax of $50/tC. All four alternative decision criteria rapidly improve as modest taxes are introduced, but gradually deteriorate if the tax is too high. That implies that the appropriate tax is an interior solution. In stark contrast to some of the interpretations of the Dismal Theorem, we find that fat tails by no means justify arbitrarily large carbon taxes. Copyright Springer Science+Business Media New York 2014

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  • David Anthoff & Richard Tol, 2014. "Climate policy under fat-tailed risk: an application of FUND," Annals of Operations Research, Springer, vol. 220(1), pages 223-237, September.
  • Handle: RePEc:spr:annopr:v:220:y:2014:i:1:p:223-237:10.1007/s10479-013-1343-2
    DOI: 10.1007/s10479-013-1343-2
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    1. Hennlock, Magnus, 2009. "Robust Control in Global Warming Management: An Analytical Dynamic Integrated Assessment," Discussion Papers dp-09-19, Resources For the Future.
    2. Richard S. J. Tol, 1999. "The Marginal Costs of Greenhouse Gas Emissions," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 61-81.
    3. P. Michael Link & Richard S. J. Tol, 2004. "Possible economic impacts of a shutdown of the thermohaline circulation: an application of FUND," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 3(2), pages 99-114, September.
    4. Tol, Richard S.J. & Ebi, Kristie L. & Yohe, Gary W., 2007. "Infectious disease, development, and climate change: a scenario analysis," Environment and Development Economics, Cambridge University Press, vol. 12(5), pages 687-706, October.
    5. Tol, Richard S.J., 2005. "Emission abatement versus development as strategies to reduce vulnerability to climate change: an application of FUND," Environment and Development Economics, Cambridge University Press, vol. 10(5), pages 615-629, October.
    6. Richard S.J. Tol, 2006. "Multi-Gas Emission Reduction for Climate Change Policy: An Application of Fund," The Energy Journal, International Association for Energy Economics, vol. 0(Special I), pages 235-250.
    7. Richard Tol, 2002. "Estimates of the Damage Costs of Climate Change, Part II. Dynamic Estimates," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 21(2), pages 135-160, February.
    8. Hof, Andries F. & van Vuuren, Detlef P. & den Elzen, Michel G.J., 2010. "A quantitative minimax regret approach to climate change: Does discounting still matter?," Ecological Economics, Elsevier, vol. 70(1), pages 43-51, November.
    9. Tol, Richard S. J., 2002. "Welfare specifications and optimal control of climate change: an application of fund," Energy Economics, Elsevier, vol. 24(4), pages 367-376, July.
    10. Richard S. J. Tol, 2010. "International Inequity Aversion And The Social Cost Of Carbon," Climate Change Economics (CCE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 21-32.
    11. Anthoff, David & Tol, Richard S.J., 2010. "On international equity weights and national decision making on climate change," Journal of Environmental Economics and Management, Elsevier, vol. 60(1), pages 14-20, July.
    12. Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
    13. 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.
    14. Richard Tol, 2002. "Estimates of the Damage Costs of Climate Change. Part 1: Benchmark Estimates," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 21(1), pages 47-73, January.
    15. Tol, Richard S. J., 2001. "Equitable cost-benefit analysis of climate change policies," Ecological Economics, Elsevier, vol. 36(1), pages 71-85, January.
    16. William D. Nordhaus, 2009. "An Analysis of the Dismal Theorem," Cowles Foundation Discussion Papers 1686, Cowles Foundation for Research in Economics, Yale University.
    17. Daiju Narita & Richard Tol & David Anthoff, 2010. "Economic costs of extratropical storms under climate change: an application of FUND," Journal of Environmental Planning and Management, Taylor & Francis Journals, vol. 53(3), pages 371-384.
    18. van den Bergh, Jeroen C. J. M., 2004. "Optimal climate policy is a utopia: from quantitative to qualitative cost-benefit analysis," Ecological Economics, Elsevier, vol. 48(4), pages 385-393, April.
    19. Hennlock, Magnus, 2009. "Robust Control in Global Warming Management: An Analytical Dynamic Integrated Assessment," Working Papers in Economics 354, University of Gothenburg, Department of Economics.
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    As found on the RePEc Biblio, the curated bibliography for Economics:
    1. > Environmental and Natural Resource Economics > Climate economics > Uncertainty

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    1. van den Bergh, J.C.J.M. & Botzen, W.J.W., 2015. "Monetary valuation of the social cost of CO2 emissions: A critical survey," Ecological Economics, Elsevier, vol. 114(C), pages 33-46.
    2. Richard S.J. Tol, 2018. "The impact of climate change and the social cost of carbon," Working Paper Series 1318, Department of Economics, University of Sussex Business School.
    3. David Anthoff & Richard S. J. Tol, 2020. "Testing the Dismal Theorem," Working Paper Series 1920, Department of Economics, University of Sussex Business School.
    4. Foley, Duncan K. & Rezai, Armon & Taylor, Lance, 2013. "The social cost of carbon emissions: Seven propositions," Economics Letters, Elsevier, vol. 121(1), pages 90-97.
    5. Matthew Adler & David Anthoff & Valentina Bosetti & Greg Garner & Klaus Keller & Nicolas Treich, 2016. "Priority for the Worse Off and the Social Cost of Carbon," CESifo Working Paper Series 6032, CESifo.
    6. In Chang Hwang & Richard S.J. Tol & Marjan W. Hofkes, 2013. "Active Learning about Climate Change," Working Paper Series 6513, Department of Economics, University of Sussex Business School.
    7. Thijs Dekker & Rob Dellink & Janina Ketterer, 2013. "The Fatter the Tail, the Fatter the Climate Agreement - Simulating the Influence of Fat Tails in Climate Change Damages on the Success of International Climate Negotiations," CESifo Working Paper Series 4059, CESifo.
    8. Francisco Estrada & Richard S J Tol & Wouter J W Botzen, 2017. "Global economic impacts of climate variability and change during the 20th century," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-16, February.
    9. Crost, Benjamin & Traeger, Christian P., 2011. "Risk and aversion in the integrated assessment of climate change," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt1562s275, Department of Agricultural & Resource Economics, UC Berkeley.
    10. In Chang Hwang & Richard S.J. Tol & Marjan W. Hofkes, 2013. "Tail-effect and the Role of Greenhouse Gas Emissions Control," Working Paper Series 6613, Department of Economics, University of Sussex Business School.

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