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

Abstract

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).

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Acknowledgments

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.

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Correspondence to Richard S. J. Tol.

Appendix: Bandwidth Selection for Kernel Regression with Restrictions

Appendix: Bandwidth Selection for Kernel Regression with Restrictions

Section 4 introduces restricted kernel regression by adding an artificial data point representing the restriction. (This is readily generalized to multiple restrictions.) The bandwidth of the restriction should be selected such that the kernel regression is not materially affected where there are observations while maintaining smoothness. Figure 7 shows that, if the same bandwidth is chosen for the restriction as for the actual observations, the kernel function is lower for the first observations. If the bandwidth is 100 times smaller, the kernel function sharply bends near zero. A bandwidth of one-tenth is an acceptable, yet ad hoc compromise.

Fig. 7
figure 7

Kernel regression of impact on temperature where the restriction \(I(T=0) = 0\) has the same bandwidth as the observations (‘1’), one-tenth of that bandwidth (‘0.1’) or 100th (‘0.01’); the unrestricted kernel function is shown for comparison

The Matlab code can be found at http://ideas.repec.org/c/sus/susesa/0313.html.

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Tol, R.S.J. Bootstraps for Meta-Analysis with an Application to the Impact of Climate Change. Comput Econ 46, 287–303 (2015). https://doi.org/10.1007/s10614-014-9448-5

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Keywords

  • Impacts of climate change
  • Kernel regression
  • Bootstrap
  • Risk aversion
  • Ambiguity aversion

JEL Classification

  • C14
  • Q54