Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Optimal CO2 mitigation under damage risk valuation


The current generation has to set mitigation policy under uncertainty about the economic consequences of climate change. This uncertainty governs both the level of damages for a given level of warming, and the steepness of the increase in damage per warming degree. Our model of climate and the economy is a stochastic version of a model employed in assessing the US Social Cost of Carbon (DICE). We compute the optimal carbon taxes and CO2 abatement levels that maximize welfare from economic consumption over time under different risk states. In accordance with recent developments in finance, we separate preferences about time and risk to improve the model’s calibration of welfare to observed market interest. We show that introducing the modern asset pricing framework doubles optimal abatement and carbon taxation. Uncertainty over the level of damages at a given temperature increase can result in a slight increase of optimal emissions as compared to using expected damages. In contrast, uncertainty governing the steepness of the damage increase in temperature results in a substantially higher level of optimal mitigation.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

Figure 1: The optimal carbon tax in US$ per tonne of carbon and the abatement rate as a percentage of business-as-usual emissions (top, 100 years), as well as the CO2 emissions from fossil fuel use and the temperature trajectories (bottom, 200 years), for different uncertainty specifications and evaluation frameworks.


  1. Nordhaus, W. D. Managing the Global Commons: The Economics of the Greenhouse Effect (MIT Press, 1994).

    Google Scholar 

  2. Nordhaus, W. D. A Question of Balance: Economic Modeling of Global Warming (Yale Univ. Press, 2008).

    Google Scholar 

  3. Richels, R. G., Manne, A. S. & Wigley, T. M. Moving beyond concentrations: The challenge of limiting temperature change AEI-Brookings Joint Center for Regulatory Studies 04-11 (2004)

  4. Hope, C. The marginal impact of CO2 from PAGE2002: An integrated assessment model incorporating the IPCC’s five reasons for concern. Integr. Assess. J. 6, 19–56 (2006).

    Google Scholar 

  5. Dietz, S. High impact, low probability? An empirical analysis of risk in the economics of climate change. Climatic Change 108, 519–541 (2009).

    Article  Google Scholar 

  6. Anthoff, D., Tol, R. S. J. & Yohe, G. W. Risk aversion, time preference, and the social cost of carbon. Environ. Res. Lett. 4, 1–7 (2009).

    Article  Google Scholar 

  7. Anthoff, D. & Tol, R. S. J. The impact of climate change on the balanced growth equivalent: An application of FUND. Environ. Res. Econom. 43, 351–367 (2009).

    Article  Google Scholar 

  8. Interagency Working Group on Social Cost of Carbon, U. S. G. Technical Support Document: Social Cost of Carbon for Regulatory Impact Analysis Under Executive Order 12866 (Department of Energy, 2010)

  9. Pycroft, J., Vergano, L., Hope, C. W., Paci, D. & Ciscar, J. C. A tale of tails: Uncertainty and the social cost of carbon dioxide. Econom. E-J. 5, 1–29 (2011).

    Article  Google Scholar 

  10. Kopp, R. E., Golub, A., Keohane, N. O. & Onda, C. The influence of the specification of climate change damages on the social cost of carbon. Econom. E-J. 6, 1–40 (2012).

    Google Scholar 

  11. Kelly, D. L. & Kolstad, C. D. Bayesian learning, growth, and pollution. J. Econom. Dynam. Control 23, 491–518 (1999).

    Article  Google Scholar 

  12. Keller, K., Bolker, B. M. & Bradford, D. F. Uncertain climate thresholds and optimal economic growth. J. Environ. Econom. Manage. 48, 723–741 (2004).

    Article  Google Scholar 

  13. Leach, A. J. The climate change learning curve. J. Econom. Dynam. Control 31, 1728–1752 (2007).

    Article  Google Scholar 

  14. Hanemann, M. in Climate Change Science and Policy (eds Schneider, S. H., Rosencranz, A., Mastrandrea, M. & Kuntz-Duriseti, K.) Ch. 17, 185–193 (Island Press, 2009).

    Google Scholar 

  15. Tol, R. S. The economic effects of climate change. J. Econom. Perspect. 23, 29–51 (2009).

    Article  Google Scholar 

  16. Vissing-Joergensen, A. & Attanasio, O. P. Stock-market participation, intertemporal substitution, and risk-aversion. Am. Econom. Rev. 93, 383–391 (2003).

    Article  Google Scholar 

  17. Bansal, R. & Yaron, A. Risks for the long run: A potential resolution of asset pricing puzzles. J. Finan. 59, 1481–509 (2004).

    Article  Google Scholar 

  18. Bansal, R., Kiku, D. & Yaron, A. Long run risks, the macroeconomy, and asset prices. Am. Econom. Rev.: Papers Proc. 100, 542–546 (2010).

    Article  Google Scholar 

  19. Chen, X., Favilukis, J. & Ludvigson, S. C. An estimation of economic models with recursive preferences. Quant. Econom. 4, 39–83 (2013).

    Article  CAS  Google Scholar 

  20. Bansal, R., Kiku, D. & Yaron, A. An empirical evaluation of the long-run risks model for asset prices. Crit. Finance Rev. 1, 183–221 (2012).

    Article  Google Scholar 

  21. Nakamura, E., Steinsson, J., Barro, R. & Ursua, J. Crises and recoveries in an empirical model of consumption disasters. Am. Econom. J.: Macroeconom. 5, 35–74 (2013).

    Google Scholar 

  22. Kreps, D. M. & Porteus, E. L. Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46, 185–200 (1978).

    Article  Google Scholar 

  23. Epstein, L. G. & Zin, S. E. Substitution, risk aversion, and the temporal behavior of consumption and asset returns: A theoretical framework. Econometrica 57, 937–969 (1989).

    Article  Google Scholar 

  24. Traeger, C. P. Recent developments in the intertemporal modeling of uncertainty. ARRE 1, 261–285 (2009).

    Google Scholar 

  25. Gollier, C. Discounting an uncertain future. J. Public Econom. 85, 149–166 (2002).

    Article  Google Scholar 

  26. Ha-Duong, M. & Treich, N. Risk aversion, intergenerational equity and climate change. Environ. Res. Econom. 28, 195–207 (2004).

    Article  Google Scholar 

  27. Traeger, C. P. Why uncertainty matters—Discounting under intertemporal risk aversion and ambiguity. Econom. Theory (in the press, 2014)

  28. Weil, P. Nonexpected utility in macroeconomics. Quart. J. Econom. 105, 29–42 (1990).

    Article  Google Scholar 

  29. Epstein, L. G. & Zin, S. E. Substitution, risk aversion, and the temporal behavior of consumption and asset returns: An empirical analysis. J. Polit. Economy 99, 263–286 (1991).

    Article  Google Scholar 

  30. Crost, B. & Traeger, C. P. Optimal climate policy: Uncertainty versus Monte-Carlo. Econom. Lett. 120, 552–558 (2013).

    Article  Google Scholar 

  31. Nordhaus, W. D. A review of the Stern review on the economics of climate change. J. Econom. Literat. 45, 686–702 (2007).

    Article  Google Scholar 

  32. Stern, N. (ed.) The Economics of Climate Change: The Stern Review (Cambridge Univ. Press, 2007).

    Book  Google Scholar 

  33. Jensen, S. & Traeger, C. Growth uncertainty in the integrated assessment of climate change. Eur. Econom. Rev. (in the press, 2014)

  34. Nordhaus, W. D. & Yang, Z. A regional dynamic general-equilibrium model of alternative climate-change strategies. Am. Econom. Rev. 86, 741–765 (1996).

    Google Scholar 

  35. Bosetti, V., Carraro, C., Galeotti, M., Massetti, E. & Tavoni, M. Witch: A world induced technical change hybrid model. Energy J. 27, 13–38 (2006).

    Google Scholar 

  36. Bauer, N., Baumstark, L. & Leimbach, M. The ReMIND-R model: The role of renewables in the low-carbon transformation—First best vs second-best worlds. Climatic Change 114, 145–168 (2012).

    Article  Google Scholar 

  37. Broome, J. Counting the Cost of Global Warming (White Horse Press, 1992).

    Google Scholar 

  38. Asheim, G. Intergenerational equity. Annu. Rev. Econom. 2, 197–222 (2010).

    Article  Google Scholar 

  39. Traeger, C. P. A 4-stated DICE: Quantitatively addressing uncertainty effects in climate change. Environ. Res. Econom. (in the press, 2014)

  40. Meinshausen, M., Raper, S. & Wigley, T. Emulating coupled atmosphere–ocean and carbon cycle models with a simpler model, MAGICC6—part 1: Model description and calibration. Atmos. Chem. Phys. 11, 1417–1456 (2011).

    Article  CAS  Google Scholar 

  41. Traeger, C. P. Intertemporal risk aversion. CUDARE Working Paper No. 1102 (2010)

  42. Croce, M. M., Kung, H., Nguyen, T. T. & Schmid, L. Fiscal policies and asset prices. Rev. Financ. Stud. 25, 2635–2672 (2012).

    Article  Google Scholar 

  43. McGrattan, E. R. & Prescott, E. C. Taxes, regulations, and the value of US and UK corporations. Rev. Econom. Stud. 72, 767–796 (2005).

    Article  Google Scholar 

Download references


We are grateful to L. Karp, S. Jensen, A. Butz, M. Hanemann, K. Smith, D. Lemoine, D. Farber and J. Harte, and for financial support by the Giannini Foundation.

Author information

Authors and Affiliations



C.P.T. developed the research question and model and wrote the paper. Both authors together designed the algorithms and the graphical output; C.P.T. assisted and B.C. took the lead in programming and running the model.

Corresponding author

Correspondence to Christian P. Traeger.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Crost, B., Traeger, C. Optimal CO2 mitigation under damage risk valuation. Nature Clim Change 4, 631–636 (2014).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing