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Weitzman meets Nordhaus: Expected utility and catastrophic risk in a stochastic economy-climate model

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  • Masako Ikefuji
  • Roger J. A. Laeven
  • Jan R. Magnus
  • Chris Muris

Abstract

We specify a stochastic economy-climate model, adapting Nordhaus' deterministic economy-climate model by allowing for Weitzman-type stochasticity. We show that, under expected power utility, the model is fragile to heavy-tailed distributional assumptions and we derive necessary and sufficient conditions on the utility function to avoid fragility. We solve our stochastic economy-climate model for two cases with compatible pairs of utility functions and heavy-tailed distributional assumptions. We further develop and implement a procedure to learn the input parameters of our model and show that the model thus specified produces robust optimal policies. The numerical results indicate that higher levels of uncertainty lead to less abatement and consumption, and to more investment.

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Paper provided by Institute of Social and Economic Research, Osaka University in its series ISER Discussion Paper with number 0825.

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Date of creation: Dec 2011
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Handle: RePEc:dpr:wpaper:0825

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  1. Keller, Klaus & Bolker, Benjamin M. & Bradford, D.F.David F., 2004. "Uncertain climate thresholds and optimal economic growth," Journal of Environmental Economics and Management, Elsevier, vol. 48(1), pages 723-741, July.
  2. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, April.
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  5. 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.
  6. Fishburn, Peter C, 1976. "Unbounded Utility Functions in Expected Utility Theory," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 163-68, February.
  7. Andrew J. Leach, 2004. "The Climate Change Learning Curve," Cahiers de recherche 04-03, HEC Montréal, Institut d'économie appliquée.
  8. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
  9. Kelly, David L. & Kolstad, Charles D., 1999. "Bayesian learning, growth, and pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 491-518, February.
  10. Ryan, Terence M, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Comment," The Quarterly Journal of Economics, MIT Press, vol. 88(1), pages 133-35, February.
  11. Gollier, Christian, 2008. "Discounting with Fat-Tailed Economic Growth," IDEI Working Papers 523, Institut d'Économie Industrielle (IDEI), Toulouse.
  12. Gollier, Christian, 2002. "Time Horizon and the Discount Rate," Journal of Economic Theory, Elsevier, vol. 107(2), pages 463-473, December.
  13. Ackerman, Frank & Stanton, Elizabeth A. & Bueno, Ramón, 2010. "Fat tails, exponents, extreme uncertainty: Simulating catastrophe in DICE," Ecological Economics, Elsevier, vol. 69(8), pages 1657-1665, June.
  14. Roughgarden, Tim & Schneider, Stephen H., 1999. "Climate change policy: quantifying uncertainties for damages and optimal carbon taxes," Energy Policy, Elsevier, vol. 27(7), pages 415-429, July.
  15. Arrow, Kenneth J, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, MIT Press, vol. 88(1), pages 136-38, February.
  16. Robert J. Barro, 2009. "Rare Disasters, Asset Prices, and Welfare Costs," American Economic Review, American Economic Association, vol. 99(1), pages 243-64, March.
  17. Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
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Cited by:
  1. David Comerford (University of Edinburgh), 2013. "A balance of questions: what can we ask of climate change economics?," ESE Discussion Papers 216, Edinburgh School of Economics, University of Edinburgh.
  2. Masako Ikefuji & Roger Laeven & Jan Magnus & Chris Muris, 2013. "Pareto utility," Theory and Decision, Springer, vol. 75(1), pages 43-57, July.

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