Abstract
This paper proposes an operationally simple and easily generalizable methodology to incorporate climate change damage uncertainty into Integrated Assessment Models (IAMs). First uncertainty is transformed into a risk measure by extracting damage distribution means and variances from an ensemble of socio economic and climate change scenarios. Then a risk premium is computed under different degrees of risk aversion, quantifying what society would be willing to pay to insure against the uncertainty of the damages. Our estimates show that the premium for the risk is a potentially significant addition to the “standard average damage”, but highly sensitive to the attitudes toward risk. In the last research phase, the risk premium is incorporated into the climate change damage function of a widely used IAM which shows, consequently, a substantial increase in both mitigation and adaptation efforts, reflecting a more precautionary attitude by the social planner. Interestingly, adaptation is stimulated more than mitigation in the first half of this century, while the situation reverses afterwards.
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Source: authors’ elaboration. There are two possible states of the world/temperature: T1 associated to low and T2 associated to high damages, with probability P1 and P2 respectively. Due to risk aversion the dis-utility function is convex in damages. The utility loss associated to the expected damage UL(E(D(T))) (corresponding to loosing E(D(T)) with certainty) is lower than the expected utility loss E(UL(D(T))). The Damage Certainty Equivalent CE(D(T)) is thus larger than the expected damage E(D(T)). The difference, is the risk premium
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Notes
Uncertainty about objective probabilities does not prevent agents from forming subjective probabilities.
Exercises like EMF (https://emf.stanford.edu/), ISI-MIP (https://www.pik-potsdam.de/research/climate-impacts-and-vulnerabilities/research/rd2-cross-cutting-activities/isi-mip) and AgMIP (http://www.agmip.org/) well illustrate this approach.
See Anderson et al. (2014) for a discussion and new approaches on sensitivity tests.
The risk adjusted rate is given by r where r = rf + βπ, where rf is the risk free discount rate, β is the elasticity of net benefit of the investment with respect to a change in aggregate consumption and π is the systematic risk premium. A value of β > 1, that is what authors find in relation to mitigation policies, implies an increase in the discount rate to be applied.
See Kousky et al. (2011) for a review of the different methodologies to measure risk premium to be included in the social cost of carbon.
Applications of the theory to understand investments decisions in finance are commonplace. See for example, Levy (1994) and Blake (1996) as well as the excellent notes of Professor Norstad. http://www.norstad.org/finance/util.pdf. An application to environmental decision-making is Krupnick et al. (1993). Note that we are using the concept of expected utility to elicit the risk premium but we are not applying the expected utility framework in the full sense of the CCAPM model, which we regard as inappropriate for this kind of analysis.
In practice all the links in the chain from temperature to damages may be multiplicative. Certainly the relationship between temperature and economic damages is, but if the others were not, the use of the log normal will be more of an approximation.
The literature on risk aversion indicates that the coefficient of relative risk aversion may increase with the size of the income loss or gain (Arrow 1965; Holt and Laury 2002). In this respect an alternative utility function (the exponential function) may be more appropriate. This takes the form: \(U(x) = \frac{{ - \exp^{ - \gamma x} }}{\gamma }\). In this case the coefficient of relative risk aversion is given by γx. Studies show, however that for variations in x that are small relative to total x (which in our case is GDP) a constant relative risk aversion function is a reasonable approximation.
The WITCH model outcomes are amply referenced in the Fifth Assessment Report of the IPCC (Clarke et al. 2014) and in many model inter-comparison exercises (Bosetti et al. 2015, Lessmann, et al. 2015, Tavoni et al 2014) placing WITCH among the established models in the integrated assessment community. For detailed information on the WITCH model we address the interest reader to: http://www.witchmodel.org/.
The WITCH model thus, sharing this feature with a whole stock of IAMs, uses reduced form climate change damage functions. I.e. all the complexities of impact assessments are compacted in few parameters. This simplification is particularly useful for the present exercises. For more discussion on the pros and cons of reduced form damage functions see Bosello (2014).
We also performed some sensitivity tests (see supplementary Appendix Table 4) showing, in general, a relatively small effect of forcing the two values to be the same. The sensitivity analysis also shows that for some values of ƞ in the WITCH utility function, the model cannot find an equilibrium. Specifically, assuming ƞ = 2, optimization for high-damage regions, such as Sub Saharan Africa, can be solved only if the pure rate of time preference ρ is adjusted downward. The economic intuition is the following: the case ƞ = 2 corresponds to a situation of high relative risk aversion and low willingness to substitute consumption inter-temporally. In this case future damages are high, as they incorporate a large premium for the risk, and representative agents in the model would have a stronger preference to consume everything today. Thus, from the Ramsey equation, an increase in ƞ reduces the growth rate of consumption, and, in our simulations, the reduction is “too much” to find a feasible intertemporal optimum. The resulting lower sensitivity of consumption growth to the gap between the interest rate and the pure rate of time preference can be compensated by reducing the pure rate of time preference ρ. Gollier (2002) shows how uncertainty in future consumption modifies the Ramsey equation in a similar way. The pure rate of time preference would be lower in order to induce precautionary savings. In the context of the debate on climate change discounting, Gollier (2008) and Dasgupta (2008) have also suggested a parameter combination of ƞ = 2 and ρ = 0.
The quantitative characterization on the evolution of main social economic variables in the scenario (namely GDP and population) have been extracted from: https://secure.iiasa.ac.at/web-apps/ene/SspDb/dsd?Action = htmlpage&page = about.
This computation is scarcely meaningful in a non-cooperative set up as almost all of the climate policy relies upon adaptation.
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Acknowledgements
Part of the research leading to the completion of this paper has been funded by the European Community’s Seventh Framework Program under Grant Agreement No. 308337 (BASE) and No 298436 (DYNAMIC).J.M.P.M. was funded by a Basque Government post-doctoral fellowship.
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Appendix
Appendix
We ran the SSP2 with and without adjustment in the ηcoefficient in the model and results show that the adjustment to set it equal to the coefficient of risk aversion does not have a big impact when the non–cooperative solution is implemented (Table 4). The same applies when we make small changes to the pure rate of time preference (ρ) (See Tables 4, 5, 6, 7, 8, 9, Fig. 8).
Akaike Information Criteria (AIC) of the fitting of damages with different distribution (the lower the better)
The sensitivity analysis also shows that for some values of ƞ in the WITCH utility function, the model cannot find an equilibrium. Specifically, assuming ƞ = 2, optimization for high-damage regions, such as Sub Saharan Africa, can be solved only if the pure rate of time preference ρ is adjusted downward. The economic intuition is the following: the case ƞ = 2 corresponds to a situation of high relative risk aversion and low willingness to substitute consumption inter-temporally. In this case future damages are high, as they incorporate a large premium for the risk, and representative agents in the model would have a stronger preference to consume everything today. Thus, from the Ramsey equation, an increase in ƞ reduces the growth rate of consumption, and, in our simulations, the reduction is “too much” to find a feasible intertemporal optimum. The resulting lower sensitivity of consumption growth to the gap between the interest rate and the pure rate of time preference can be compensated by reducing the pure rate of time preference ρ. Gollier (2002) shows how uncertainty in future consumption modifies the Ramsey equation in a similar way. The pure rate of time preference would be lower in order to induce precautionary savings. In the context of the debate on climate change discounting, Gollier (2008) and Dasgupta (2008) have also suggested a parameter combination of ƞ = 2 and ρ = 0.
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Markandya, A., De Cian, E., Drouet, L. et al. Building Risk into the Mitigation/Adaptation Decisions simulated by Integrated Assessment Models. Environ Resource Econ 74, 1687–1721 (2019). https://doi.org/10.1007/s10640-019-00384-1
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DOI: https://doi.org/10.1007/s10640-019-00384-1