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Testing the Dismal Theorem

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  • David Anthoff

    (University of California)

  • Richard S. J. Tol

    (University of Sussex)

Abstract

Weitzman's Dismal Theorem has that the expected net present value of a stock problem with a stochastic growth rate with unknown variance is unbounded. Cost-benefit analysis can therefore not be applied to greenhouse gas emission control. We use the Generalized Central Limit Theorem to show that the Dismal Theorem can be tested, in a finite sample, by estimating the tail index. We apply this test to social cost of carbon estimates from three commonly used integrated assessment models, and to previously published estimates. Two of the three models do not support the Dismal Theorem, but the third one does for low discount rates. The meta-analysis cannot reject the Dismal Theorem.

Suggested Citation

  • David Anthoff & Richard S. J. Tol, 2020. "Testing the Dismal Theorem," Working Paper Series 1920, Department of Economics, University of Sussex Business School.
    • Handle: RePEc:sus:susewp:1920
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    1. Horowitz, John & Lange, Andreas, 2014. "Cost–benefit analysis under uncertainty — A note on Weitzman's dismal theorem," Energy Economics, Elsevier, vol. 42(C), pages 201-203.
    2. Wouter Botzen, W.J. & van den Bergh, Jeroen C.J.M., 2012. "How sensitive is Nordhaus to Weitzman? Climate policy in DICE with an alternative damage function," Economics Letters, Elsevier, vol. 117(1), pages 372-374.
    3. John E. Bistline, 2015. "Fat-Tailed Uncertainty, Learning, And Climate Policy," Climate Change Economics (CCE), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-21.
    4. Richard S.J. Tol, 2011. "The Social Cost of Carbon," Annual Review of Resource Economics, Annual Reviews, vol. 3(1), pages 419-443, October.
    5. William Nordhaus, 2018. "Evolution of modeling of the economics of global warming: changes in the DICE model, 1992–2017," Climatic Change, Springer, vol. 148(4), pages 623-640, June.
    6. Samuel Jovan Okullo, 2020. "Determining the Social Cost of Carbon: Under Damage and Climate Sensitivity Uncertainty," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 75(1), pages 79-103, January.
    7. Plambeck, Erica L. & Hope, Chris & Anderson, John, 1997. "The model: Integrating the science and economics of global warming," Energy Economics, Elsevier, vol. 19(1), pages 77-101, March.
    8. Richard S.J. Tol, 2020. "Kernel density decomposition with an application to the social cost of carbon," Working Paper Series 0720, Department of Economics, University of Sussex Business School.
    9. Antony Millner, 2013. "On Welfare Frameworks and Catastrophic Climate Risks," CESifo Working Paper Series 4442, CESifo.
    10. Ikefuji, Masako & Laeven, Roger J.A. & Magnus, Jan R. & Muris, Chris, 2020. "Expected utility and catastrophic risk in a stochastic economy–climate model," Journal of Econometrics, Elsevier, vol. 214(1), pages 110-129.
    11. J. Paul Kelleher & Gernot Wagner, 2019. "Ramsey discounting calls for subtracting climate damages from economic growth rates," Applied Economics Letters, Taylor & Francis Journals, vol. 26(1), pages 79-82, January.
    12. Richard S J Tol, 2018. "The Economic Impacts of Climate Change," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 12(1), pages 4-25.
    13. Cato, Susumu, 2020. "From the St. Petersburg paradox to the dismal theorem," Environment and Development Economics, Cambridge University Press, vol. 25(5), pages 423-432, October.
    14. Frederick Ploeg & Aart Zeeuw, 2019. "Pricing Carbon and Adjusting Capital to Fend Off Climate Catastrophes," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(1), pages 29-50, January.
    15. Ian W. R. Martin & Robert S. Pindyck, 2015. "Averting Catastrophes: The Strange Economics of Scylla and Charybdis," American Economic Review, American Economic Association, vol. 105(10), pages 2947-2985, October.
    16. Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-216, April.
    17. Kenneth J. Arrow & Maureen L. Cropper & Christian Gollier & Ben Groom & Geoffrey M. Heal & Richard G. Newell & William D. Nordhaus & Robert S. Pindyck & William A. Pizer & Paul R. Portney & Thomas Ste, 2014. "Editor's Choice Should Governments Use a Declining Discount Rate in Project Analysis?," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 8(2), pages 145-163.
    18. Nordhaus, William, 1982. "How Fast Should We Graze the Global Commons?," American Economic Review, American Economic Association, vol. 72(2), pages 242-246, May.
    19. Robert S. Pindyck, 2011. "Fat Tails, Thin Tails, and Climate Change Policy," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 5(2), pages 258-274, Summer.
    20. Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
    21. Kelly, David L. & Tan, Zhuo, 2015. "Learning and climate feedbacks: Optimal climate insurance and fat tails," Journal of Environmental Economics and Management, Elsevier, vol. 72(C), pages 98-122.
    22. 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.
    23. David Anthoff & Johannes Emmerling, 2019. "Inequality and the Social Cost of Carbon," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 6(2), pages 243-273.
    24. In Chang Hwang & Richard S. J. Tol & Marjan W. Hofkes, 2019. "Active Learning and Optimal Climate Policy," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 73(4), pages 1237-1264, August.
    25. David Anthoff & Francisco Estrada & Richard S. J. Tol, 2016. "Shutting Down the Thermohaline Circulation," American Economic Review, American Economic Association, vol. 106(5), pages 602-606, May.
    26. 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.
    27. In Hwang & Frédéric Reynès & Richard Tol, 2013. "Climate Policy Under Fat-Tailed Risk: An Application of Dice," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 56(3), pages 415-436, November.
    28. Alexander Golub & Michael Brody, 2017. "Uncertainty, climate change, and irreversible environmental effects: application of real options to environmental benefit-cost analysis," Journal of Environmental Studies and Sciences, Springer;Association of Environmental Studies and Sciences, vol. 7(4), pages 519-526, December.
    29. Lucas Bretschger & Aimilia Pattakou, 2019. "Correction to: As Bad as it Gets: How Climate Damage Functions Affect Growth and the Social Cost of Carbon," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(1), pages 27-27, January.
    30. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    31. Matthew J. Kotchen, 2018. "Which Social Cost of Carbon? A Theoretical Perspective," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 5(3), pages 673-694.
    32. Lucas Bretschger & Aimilia Pattakou, 2019. "As Bad as it Gets: How Climate Damage Functions Affect Growth and the Social Cost of Carbon," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(1), pages 5-26, January.
    33. Katharine Ricke & Laurent Drouet & Ken Caldeira & Massimo Tavoni, 2018. "Country-level social cost of carbon," Nature Climate Change, Nature, vol. 8(10), pages 895-900, October.
    34. David Anthoff & Francisco Estrada & Richard S. J. Tol, 2016. "Shutting Down the Thermohaline Circulation," American Economic Review, American Economic Association, vol. 106(5), pages 602-06, May.
    35. Nordhaus, William D., 1993. "Rolling the 'DICE': an optimal transition path for controlling greenhouse gases," Resource and Energy Economics, Elsevier, vol. 15(1), pages 27-50, March.
    36. Weitzman, Martin L., 2010. "What Is the "Damages Function" for Global Warming — And What Difference Might It Make?," Scholarly Articles 33373343, Harvard University Department of Economics.
    37. William D. Nordhaus, 2012. "Economic Policy in the Face of Severe Tail Events," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(2), pages 197-219, March.
    38. Nicole Glanemann & Sven N. Willner & Anders Levermann, 2020. "Paris Climate Agreement passes the cost-benefit test," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
    39. Brito, Margarida & Moreira Freitas, Ana Cristina, 2003. "Limiting behaviour of a geometric-type estimator for tail indices," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 211-226, October.
    40. Millner, Antony, 2013. "On welfare frameworks and catastrophic climate risks," Journal of Environmental Economics and Management, Elsevier, vol. 65(2), pages 310-325.
    41. Kevin D. Dayaratna & Ross McKitrick & Patrick J. Michaels, 2020. "Climate sensitivity, agricultural productivity and the social cost of carbon in FUND," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 22(3), pages 433-448, July.
    42. Hänsel, Martin C. & Quaas, Martin F., 2018. "Intertemporal Distribution, Sufficiency, and the Social Cost of Carbon," Ecological Economics, Elsevier, vol. 146(C), pages 520-535.
    43. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    44. Samuel Fankhauser & Richard Tol & DAVID Pearce, 1997. "The Aggregation of Climate Change Damages: a Welfare Theoretic Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 10(3), pages 249-266, October.
    45. Richard Tol, 2012. "Leviathan carbon taxes in the short run," Climatic Change, Springer, vol. 114(2), pages 409-415, September.
    46. 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.
    47. Loïc Berger & Johannes Emmerling & Massimo Tavoni, 2017. "Managing Catastrophic Climate Risks Under Model Uncertainty Aversion," Post-Print hal-01744501, HAL.
    48. Frank J. Convery & Gernot Wagner, 2015. "Reflections–Managing Uncertain Climates: Some Guidance for Policy Makers and Researchers," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 9(2), pages 304-320.
    49. Hwang, In Chang & Tol, Richard S.J. & Hofkes, Marjan W., 2016. "Fat-tailed risk about climate change and climate policy," Energy Policy, Elsevier, vol. 89(C), pages 25-35.
    50. Schultze J. & Steinebach J., 1996. "On Least Squares Estimates Of An Exponential Tail Coefficient," Statistics & Risk Modeling, De Gruyter, vol. 14(4), pages 353-372, April.
    51. Grechuk, Bogdan & Zabarankin, Michael, 2014. "Risk averse decision making under catastrophic risk," European Journal of Operational Research, Elsevier, vol. 239(1), pages 166-176.
    52. Kine Josefine Aurland-Bredesen, 2020. "The Benefit-Cost Ratio as a Decision Criteria When Managing Catastrophes," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 77(2), pages 345-363, October.
    53. 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.
    54. Pindyck, Robert S., 2019. "The social cost of carbon revisited," Journal of Environmental Economics and Management, Elsevier, vol. 94(C), pages 140-160.
    55. Richard Tol, 1999. "Spatial and Temporal Efficiency in Climate Policy: Applications of FUND," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 14(1), pages 33-49, July.
    56. Sterner, Thomas & Tol, Richard S. J. & Weitzman, Martin L. & Pizer, William A. & Portney, Paul R. & Arrow, Kenneth J. & Cropper, Maureen L. & Gollier, Christian & Groom, Ben & Heal, Geoffrey M. & Newe, 2014. "Should Governments Use a Declining Discount Rate in Project Analysis?," Scholarly Articles 33373349, Harvard University Department of Economics.
    57. Arrow, K. & Cropper, M. & Gollier, C. & Groom, B. & Heal, G. & Newell, R. & Nordhaus, W. & Pindyck, R. & Pizer, W. & Portney, P. & Sterner, T. & Tol, R. S. J. & Weitzman, Martin L., 2013. "Determining Benefits and Costs for Future Generations," Scholarly Articles 12841963, Harvard University Department of Economics.
    58. Martin L. Weitzman, 2010. "What Is The "Damages Function" For Global Warming — And What Difference Might It Make?," Climate Change Economics (CCE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 57-69.
    59. Martin L. Weitzman, 2011. "Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 5(2), pages 275-292, Summer.
    60. Frances C. Moore & Uris Baldos & Thomas Hertel & Delavane Diaz, 2017. "New science of climate change impacts on agriculture implies higher social cost of carbon," Nature Communications, Nature, vol. 8(1), pages 1-9, December.
    61. William D. Nordhaus, 2011. "The Economics of Tail Events with an Application to Climate Change," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 5(2), pages 240-257, Summer.
    62. In Chang Hwang, 2016. "Active learning and optimal climate policy," EcoMod2016 9611, EcoMod.
    63. Tol, Richard S.J., 2019. "A social cost of carbon for (almost) every country," Energy Economics, Elsevier, vol. 83(C), pages 555-566.
    64. Hwang, In Chang & Reynès, Frédéric & Tol, Richard S.J., 2017. "The effect of learning on climate policy under fat-tailed risk," Resource and Energy Economics, Elsevier, vol. 48(C), pages 1-18.
    65. Ekholm, Tommi, 2018. "Climatic Cost-benefit Analysis Under Uncertainty and Learning on Climate Sensitivity and Damages," Ecological Economics, Elsevier, vol. 154(C), pages 99-106.
    66. Loïc Berger & Johannes Emmerling & Massimo Tavoni, 2017. "Managing Catastrophic Climate Risks Under Model Uncertainty Aversion," Management Science, INFORMS, vol. 63(3), pages 749-765, March.
    67. Chris Hope & Kevin Schaefer, 2016. "Economic impacts of carbon dioxide and methane released from thawing permafrost," Nature Climate Change, Nature, vol. 6(1), pages 56-59, January.
    68. Robert S. Pindyck, 2017. "Coase Lecture—Taxes, Targets and the Social Cost of Carbon," Economica, London School of Economics and Political Science, vol. 84(335), pages 345-364, July.
    69. Mark Budolfson & Francis Dennig & Marc Fleurbaey & Asher Siebert & Robert H. Socolow, 2017. "The comparative importance for optimal climate policy of discounting, inequalities and catastrophes," Climatic Change, Springer, vol. 145(3), pages 481-494, December.
    70. Rob Dellink & Thijs Dekker & Janina Ketterer, 2013. "The Fatter the Tail, the Fatter the Climate Agreement," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 56(2), pages 277-305, October.
    71. William Nordhaus, 2015. "Climate Clubs: Overcoming Free-Riding in International Climate Policy," American Economic Review, American Economic Association, vol. 105(4), pages 1339-1370, April.
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    More about this item

    Keywords

    climate policy; dismal theorem; fat tails; social cost of carbon;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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