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

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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.

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Notes

  1. Note that Hof et al. (2010) do a cost-benefit analysis under worst-case assumptions, incorrectly referring to this as minimax regret.

  2. Just like the mean, any percentile is based on the entire distribution.

  3. The period of 1950–2000 is used for the calibration of the model, which is based on the IMAGE 100-year database (Batjes and Goldewijk 1994). The scenario for the period 2010–2100 is based on the EMF14 Standardised Scenario, which lies somewhere in between IS92a and IS92f (Leggett et al. 1992). The 2000–2010 period is interpolated from the immediate past (http://earthtrends.wri.org), and the period 2100–3000 extrapolated.

  4. See Anthoff and Tol (2010), Tol (2002c, 2010) for a discussion of alternative welfare functions.

  5. Recall that the law of large numbers is independent of the dimensionality or complexity of the data generating process.

  6. The rate of the decline of the carbon tax was set by trial and error; the chosen rate ensures that greenhouse gas concentrations do not increase.

  7. Note that we numerically derive the entire objective function instead of finding its optimum through successive approximations of the objective function; we do this for the four alternative decision criteria considered in this paper.

  8. Recall that the definition of regret requires that the optimum tax be found for each state of the world, that is 10,000 times in our case. We saved the value of the objective function for each state of the world and each tax. This is possible as we defined policy such that it can be characterised by a single number (the initial tax) and as discretised that initial tax.

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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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Authors and Affiliations

  1. School of Natural Resources and Environment, University of Michigan, Ann Arbor, MI, USA

    David Anthoff

  2. Department of Economics, University of Sussex, Falmer, United Kingdom

    Richard S. J. Tol

  3. Institute for Environmental Studies, Vrije Universiteit, Amsterdam, The Netherlands

    Richard S. J. Tol

  4. Department of Spatial Economics, Vrije Universiteit, Amsterdam, The Netherlands

    Richard S. J. Tol

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Correspondence to Richard S. J. Tol.

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Anthoff, D., Tol, R.S.J. Climate policy under fat-tailed risk: an application of FUND . Ann Oper Res 220, 223–237 (2014). https://doi.org/10.1007/s10479-013-1343-2

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