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Annals of Operations Research

, Volume 220, Issue 1, pp 223–237 | Cite as

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

  • David Anthoff
  • Richard S. J. Tol
Article

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.

Keywords

Climate change Integrated assessment Decision making under uncertainty Deep uncertainty Fat-tailed risk Dismal Theorem 

Notes

Acknowledgements

An earlier version of this paper was presented at the ESOP Workshop on Climate and Distribution, Oslo, 22–23 June 2010 and at seminars at the Universities of East Anglia and Sussex; we are grateful to the participants for a useful discussion. An anonymous referee and Martin Weitzman also had useful comments on an earlier version of the paper. Financial support by the ClimateCost project is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Natural Resources and EnvironmentUniversity of MichiganAnn ArborUSA
  2. 2.Department of EconomicsUniversity of SussexFalmerUnited Kingdom
  3. 3.Institute for Environmental StudiesVrije UniversiteitAmsterdamThe Netherlands
  4. 4.Department of Spatial EconomicsVrije UniversiteitAmsterdamThe Netherlands

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