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The bias of integrated assessment models that ignore climate catastrophes

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Abstract

Climate scientists currently predict there is a small but real possibility that climate change will lead to civilization threatening catastrophic events. Martin Weitzman has used this evidence along with his controversial “Dismal Theorem” to argue that integrated assessment models of climate change cannot be used to determine an optimal price for carbon dioxide. In this paper, I provide additional support for Weitzman’s conclusions by running numerical simulations to estimate risk premiums toward climate catastrophes. Compared to the assumptions found in most integrated assessment models, I incorporate into the model a more realistic range of uncertainty for both climate catastrophes and societal risk aversion. The resulting range of risk premiums indicates that the conclusions drawn from integrated assessment models that do not incorporate the potential for climate catastrophes are too imprecise to support any particular policy recommendation. The analysis of this paper is more straightforward and less technical than Weitzman’s, and therefore the conclusions should be accessible to a wider audience.

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Notes

  1. It should be noted that the analysis of this paper is not only applicable to the DICE model. The FUND and PAGE models use logarithmic utility functions (Plambeck and Hope 1995; Tol 2005), which are equivalent to the CES preference specification used by the DICE model with a CRRA coefficient equal to 1. The FUND model uses Monte Carlo analysis on uncertain parameters of the model. The PAGE model represents key input parameters by probability distributions, and random sampling is used to build up an approximate probability distribution for the model results. Despite this additional flexibility to address uncertainty compared to the DICE model, both FUND and PAGE truncate the distributions of input parameters and therefore ignore the possibility of “extreme weather events” (Tol 2005). The developers of these models have noted these limitations of their models. For instance, developers of the FUND model recently noted that higher levels of risk aversion can lead to extremely high values for the social cost of carbon (Anthoff et al. 2009). However, they still refer to their results as “optimal” policies, and policymakers have done the same when referencing their work in draft regulations (Interagency Working Group 2010).

  2. In climate models this parameter is generally called “climate sensitivity,” which refers to the equilibrium change in global mean near-surface air temperature that would result from a sustained doubling of the atmospheric carbon dioxide concentration. According to Yohe (2009), “current understanding puts the range of this critical parameter between 1.5 degrees Celsius and more than 5 degrees Celsius.”

  3. For example, NASA’s chief climate scientist called the 2009 U.S. House legislation a “counterfeit climate bill” (Hansen 2009) because it proposed such a low price on carbon emissions.

  4. These are mean global surface temperature changes relative to pre-industrial revolution levels. Warming until now has been less than 1 degree Celsius according to the National Oceanic and Atmospheric Administration.

  5. Various studies have described the “catastrophic premium puzzle” in regard to the higher-than-expected risk premiums embedded in the yields of catastrophic bonds. Bantwal and Kunreuther (2000) speculate that these abnormally large premiums are due to “ambiguity aversion, loss aversion and uncertainty avoidance.” Even these catastrophic bonds are attractive to some investors as a hedge against large drops in the market as a whole. In contrast, climate catastrophes that could threaten human civilization would obviously not serve as a hedge against any event.

  6. Theoretically speaking, it is not clear whether a risk premium or a measure of willingness-to-pay will be higher. All else equal, the optimal willingness-to-pay will be lower than the risk premium in this setting if it is preferable to allow for a significant probability of catastrophe to remain, while the risk premium will be lower if the level of expected consumption is significantly lower than the consumption level that results when a climate catastrophe does not occur.

  7. To follow the economic definition of a risk premium, the representative agent in the model actually receives the expected value of global consumption in the case of no uncertainty.

  8. A 70% loss in global consumption is an extremely conservative estimate for a civilization threatening catastrophe. If the event were to occur in 200 years following an average annual GDP growth of 2%, a 70% decrease in GDP would result in a global GDP that is still over 15 times today’s level.

  9. The use of recursive utility functions over deterministic consumption paths goes back at least to Koopmans (1960) who showed V(c0,c1,…)=W(c0,V(c1,c2,…)), for the utility function V and “aggregator" function W. Kreps and Porteus (1978) extended the use of recursive utility functions to stochastic consumption streams. Finally, while the Kreps and Porteus framework had the ability to incorporate only two-period lotteries, Epstein and Zin (1989) extended the formulation of the space of temporal lotteries to an infinite horizon framework. Normandin and St. Amour (1998) used this utility function to assess the relative contribution of risk aversion, intertemporal substitution and taste shocks on monthly U.S. equity premiums.

  10. Many economists and philosophers since Ramsey (1928) have argued that weighing all generations equally is the only ethically defensible practice. Heal (2009) describes a pure rate of time preference above zero as “intergenerational discrimination.”

  11. To test this, I computed a model of up to six generations, with various model lengths and methods of “ramping-up” the probabilities for climate catastrophes. Please see the Appendix for these results.

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Appendix

Appendix

In this section I provide sensitivity analysis to three features of the model: 1) the number of periods in the model; 2) the probability of an occurrence of a climate catastrophe; and 3) the range of CRRA coefficients.

Figures 4, 5 and 6 display six period, five period and three period models that are in other respects equivalent to the four period model results of Fig. 3. Each of these models runs for a length of 200 years. The length of a generation has been shortened for the models with a greater number of periods. In each model, the probability of a climate catastrophe starts at zero percent in the first period and grows to five percent in the last period.

Fig. 4
figure 4

Six Period Risk Premiums with Recursive Preferences. (Assumptions: 6 generation model with 33.3 years per generation; probabilities of catastrophe are 1%, 2%, 3%, 4% and 5% in periods 2, 3, 4 and 5, respectively; damages increase by 2.5% of global consumption in each period)

Fig. 5
figure 5

Five Period Risk Premiums with Recursive Preferences. (Assumptions: 5 generation model with 40 years per generation; probabilities of catastrophe are 1.25%, 2.5%, 3.75%, and 5% in periods 2, 3 and 4, respectively; damages increase by 3.3% of global consumption in each period)

Fig. 6
figure 6

Three Period Risk Premiums with Recursive Preferences. (Assumptions: 3 generation model with 66.7 years per generation; probabilities of catastrophe are 2.5% and 5% in periods 2 and 3, respectively; damages increase by 10% of global consumption in each period)

The results are similar to that of Fig. 3. The models with more periods (and therefore shorter generations) tend to have higher risk premiums, especially when the potential damages are the largest.

Figure 7 displays a four period model in which the probability of a climate catastrophe has been cut in half in each period (and remains zero in the first period) but in other respects is equivalent to the model displayed in Fig. 3. As expected, the risk premiums in Fig. 7 are smaller than those in Fig. 3, but they are still substantial, and the overall trends are the same.

Fig. 7
figure 7

Low Probability Risk Premiums with Recursive Preferences. (Assumptions: 4 generation model with 50 years per generation; probabilities of catastrophe are 0.5%, 1.5% and 2.5% in periods 2, 3 and 4, respectively; damages increase by 5% of global consumption in each period)

Finally, Fig. 8 displays a wider range of CRRA coefficients (1–100). The risk premiums on the higher end of this range are significantly larger than those of the base model, and the rate of increase in risk premiums remains relatively consistent throughout the range.

Fig. 8
figure 8

Wider Range of CRRA coefficients with Recursive Preferences. (Assumptions: 4 generation model with 50 years per generation; probabilities of catastrophe are 1%, 3% and 5% in periods 2, 3 and 4, respectively; damages increase by 5% of global consumption in each period)

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Kaufman, N. The bias of integrated assessment models that ignore climate catastrophes. Climatic Change 110, 575–595 (2012). https://doi.org/10.1007/s10584-011-0140-7

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