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Testing the Dismal Theorem

Author

Listed:
  • 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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    Cited by:

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    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," NBER Working Papers 32544, National Bureau of Economic Research, Inc.
    4. 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.

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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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