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Testing the Dismal Theorem

Author

Listed:
  • David Anthoff
  • Richard S. J. Tol

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 and most estimators. The meta-analysis does offer qualified support for the dismal theorem.

Suggested Citation

  • David Anthoff & Richard S. J. Tol, 2022. "Testing the Dismal Theorem," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 9(5), pages 885-920.
    • Handle: RePEc:ucp:jaerec:doi:10.1086/720612
    DOI: 10.1086/720612
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    Cited by:

    1. Tol, Richard S.J., 2024. "A meta-analysis of the total economic impact of climate change," Energy Policy, Elsevier, vol. 185(C).
    2. Giacomo Marangoni & Jonathan R. Lamontagne & Julianne D. Quinn & Patrick M. Reed & Klaus Keller, 2021. "Adaptive mitigation strategies hedge against extreme climate futures," Climatic Change, Springer, vol. 166(3), pages 1-17, June.
    3. Frances C. Moore & Moritz A. Drupp & James Rising & Simon Dietz & Ivan Rudik & Gernot Wagner, 2024. "Synthesis of evidence yields high social cost of carbon due to structural model variation and uncertainties," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 121(52), pages 2410733121-, December.
    4. Prieto, F. & García-García, C.B. & Salmerón-Gómez, R., 2025. "Modelling global fossil CO2 emissions with a lognormal distribution," Socio-Economic Planning Sciences, Elsevier, vol. 97(C).
    5. Faustino Prieto & Catalina B. Garc'ia-Garc'ia & Rom'an Salmer'on G'omez, 2024. "Modelling Global Fossil CO2 Emissions with a Lognormal Distribution: A Climate Policy Tool," Papers 2403.00653, arXiv.org.

    More about this item

    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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