Computational Economics

, Volume 46, Issue 2, pp 287–303 | Cite as

Bootstraps for Meta-Analysis with an Application to the Impact of Climate Change

  • Richard S. J. Tol


Bootstrap and smoothed bootstrap methods are used to estimate the uncertainty about the total impact of climate change, and to assess the performance of commonly used impact functions. Kernel regression is extended to include restrictions on the functional form. Impact functions do not describe the primary estimates of the economic impacts very well, and monotonic functions do particularly badly. The impacts of climate change do not significantly deviate from zero until 2.5–3.5 \(^{\circ }\hbox {C}\) warming. The uncertainty is large, and so is the risk premium. The ambiguity premium is small, however. The certainty equivalent impact is a negative 1.5 % of income for \(2.5\,^{\circ }\hbox {C}\), rising to 15 % (50 %) for \(5.0\,^{\circ }\hbox {C}\) for a rate of risk aversion of 1 (2).


Impacts of climate change Kernel regression Bootstrap  Risk aversion Ambiguity aversion 

JEL Classification

C14 Q54 



A previous version of this paper was presented at workshops in Munich (9 July 2013), Maynooth (6 September 2013) and Birmingham (7 November 2013). The audience had excellent comments, particularly Donal O’Neill. David Anthoff, Doug Arent, Mike Mastandrea and Bob Ward helped check the input data. Comments by an anonymous referee held to improve the paper. The research leading to these results has received funding from the European Union Seventh Framework Programme FP7/2007–2013 under Grant agreement No. 308601.


  1. Abramson, I. S. (1982). On bandwidth variation in kernel estimates: A square root law. Annals of Statistics, 10(4), 1217–1223.CrossRefGoogle Scholar
  2. Annan, J. D., & Hargreaves, J. C. (2011). On the generation and interpretation of probabilistic estimates of climate sensitivity. Climatic Change, 104(3–4), 423–436.CrossRefGoogle Scholar
  3. Anthoff, D., & Tol, R. S. J. (2009). The impact of climate change on the balanced growth equivalent: An application of FUND. Environmental and Resource Economics, 43(3), 351–367.CrossRefGoogle Scholar
  4. Bosello, F., Eboli, F., & Pierfederici, R. (2012). Assessing the economic impacts of climate change. Review of Environment Energy and Economics, 1–9.Google Scholar
  5. Efron, B., & Tibshirani, R. (1994). An introduction to the bootstrap. London: Chapman & Hall.Google Scholar
  6. Fankhauser, S. (1994). The economic costs of global warming damage: A survey. Global Environmental Change, 4(4), 301–309.CrossRefGoogle Scholar
  7. Fankhauser, S. (1995). Valuing climate change: The economics of the greenhouse (1st ed.). London: EarthScan.Google Scholar
  8. Hope, C. W. (2006). The marginal impact of CO2 from PAGE2002: An integrated assessment model incorporating the IPCC’s five reasons for concern. Integrated Assessment Journal, 6(1), 19–56.Google Scholar
  9. Hope, C. W. (2008). Discount rates, equity weights and the social cost of carbon. Energy Economics, 30(3), 1011–1019.CrossRefGoogle Scholar
  10. Karp, L. (2003). Global warming and hyperbolic discounting. Berkeley: Department of Economics, University of California.Google Scholar
  11. Lange, A., & Treich, N. (2008). Uncertainty, learning and ambiguity in economic models on climate policy: Some classical results and new directions. Climatic Change, 89(1), 7–21.Google Scholar
  12. Maddison, D., & Rehdanz, K. (2011). The impact of climate on life satisfaction. Ecological Economics, 70(12), 2437–2445.CrossRefGoogle Scholar
  13. Maddison, D. J. (2003). The amenity value of the climate: the household production function approach. Resource and Energy Economics, 25(2), 155–175.CrossRefGoogle Scholar
  14. Mendelsohn, R. O., Morrison, W. N., Schlesinger, M. E., & Andronova, N. G. (2000a). Country-specific market impacts of climate change. Climatic Change, 45(3–4), 553–569.CrossRefGoogle Scholar
  15. Mendelsohn, R. O., Schlesinger, M. E., & Williams, L. J. (2000b). Comparing Impacts across Climate Models. Integrated Assessment, 1(1), 37–48.CrossRefGoogle Scholar
  16. Millner, A., Dietz, S., & Heal, G. M. (2013). Scientific ambiguity and climate policy. Environmental and Resource Economics, 55, 21–46.CrossRefGoogle Scholar
  17. Nordhaus, W. D. (1992). An optimal transition path for controlling greenhouse gases. Science, 258, 1315–1319.CrossRefGoogle Scholar
  18. Nordhaus, W. D. (1994a). Expert opinion on climate change. American Scientist, 82(1), 45–51.Google Scholar
  19. Nordhaus, W. D. (1994b). Managing the global commons: The economics of climate change. Cambridge: The MIT Press.Google Scholar
  20. Nordhaus, W. D. (2006). Geography and macroeconomics: New data and new findings. Proceedings of the National Academy of Science, 103(10), 3510–3517.CrossRefGoogle Scholar
  21. Nordhaus, W. D. (2008). A question of balance: Weighing the options on global warming policies. New Haven: Yale University Press.Google Scholar
  22. Nordhaus, W. D. (2013). The Climate Casino: Risk, Uncertainty and Economics for a Warming World. New Haven: Yale University Press.Google Scholar
  23. Nordhaus, W. D., & Boyer, J. G. (2000). Warming the world: Economic models of global warming. Cambridge, MA: The MIT Press.Google Scholar
  24. Nordhaus, W. D., & Yang, Z. (1996). RICE: A regional dynamic general equilibrium model of optimal climate-change policy. American Economic Review, 86(4), 741–765.Google Scholar
  25. Pindyck, R. S. (2013). Climate change policy: What do the models tell us? Journal of Economic Literature, 51(3), 860–872.CrossRefGoogle Scholar
  26. Plamberk, E. L., & Hope, C. W. (1996). PAGE95: An updated valuation of the impacts of global warming. Energy Policy, 24(9), 783–793.CrossRefGoogle Scholar
  27. Rehdanz, K., & Maddison, D. J. (2005). Climate and happiness. Ecological Economics, 52(1), 111–125.CrossRefGoogle Scholar
  28. Roson, R., & van der Mensbrugghe, D. (2012). Climate change and economic growth: Impacts and interactions. International Journal of Sustainable Economy, 4(3), 270–285.CrossRefGoogle Scholar
  29. Silverman, B. W. (1986). Density estimation. London: Chapman and Hall.CrossRefGoogle Scholar
  30. Stern, N., Peters, S., Bakhshi, V., Bowen, A., Cameron, C., Catovsky, S., et al. (2006). Stern review: The economics of climate change. London: HM Treasury.Google Scholar
  31. Takezawa, K. (2006). Introduction to nonparametric regression. Hoboken: Wiley.Google Scholar
  32. Tibshirani, R. (1988). Variance stabilization and the bootstrap. Biometrika, 25(3), 433–444.CrossRefGoogle Scholar
  33. Tol, R. S. J. (1995). The damage costs of climate change toward more comprehensive calculations. Environmental and Resource Economics, 5(4), 353–374.CrossRefGoogle Scholar
  34. Tol, R. S. J. (2002a). Estimates of the damage costs of climate change—part 1: benchmark estimates. Environmental and Resource Economics, 21(1), 47–73.CrossRefGoogle Scholar
  35. Tol, R. S. J. (2002b). Estimates of the damage costs of climate change–part II: dynamic estimates. Environmental and Resource Economics, 21(2), 135–160.CrossRefGoogle Scholar
  36. Tol, R. S. J. (2009). The economic effects of climate change. Journal of Economic Perspectives, 23(2), 29–51.CrossRefGoogle Scholar
  37. Tol, R. S. J. (2012). On the uncertainty about the total economic impact of climate change. Environmental and Resource Economics, 53(1), 97–116Google Scholar
  38. van der Ploeg, F., & Withagen, C. (2012). Too much coal, too little oil. Journal of Public Economics, 96(1–2), 62–77.CrossRefGoogle Scholar
  39. Webster, M. D., Forest, C., Reilly, J. M., Babiker, M. H., Kicklighter, D. W., Mayer, M., et al. (2003). Uncertainty analysis of climate change and policy response. Climatic Change, 61, 295–320.CrossRefGoogle Scholar
  40. Weitzman, M. L. (2012). GHG targets as insurance against catastrophic climate damages. Journal of Public Economic Theory, 14(2), 221–244.CrossRefGoogle Scholar
  41. Weitzman, M. L. (2009). On modelling and interpreting the economics of catastrophic climate change. Review of Economics and Statistics, 91(1), 1–19.CrossRefGoogle Scholar
  42. Yohe, G. W., & Tol, R. S. J. (2002). Indicators for social and economic coping capacity: Moving towards a working definition of adaptive capacity. Global Environmental Change, 12(1), 25–40.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of SussexFalmerUK
  2. 2.Institute for Environmental StudiesVrije UniversiteitAmsterdamThe Netherlands
  3. 3.Department of Spatial EconomicsVrije UniversiteitAmsterdamThe Netherlands
  4. 4.Tinbergen InstituteAmsterdamThe Netherlands
  5. 5.CESifoMunichGermany

Personalised recommendations