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tied to climate change. How will temperatures change after a doubling of CO2 levels? What economic impact will result from an increase in global mean temperatures of 3\ufffdC? These are extreme events, and extreme events have a low sample size. There is little or no data for these observations, and it is difficult to extrapolate the outcomes based on the available data because there are likely highly nonlinear mechanisms at work, and, furthermore, the extent of these nonlinearities is unknown, again because of lack of sufficient data in the rele- vant areas. Climate Change and Policy | Dealing with the Uncertainty About Climate Change 33 One popular method of addressing the uncertainty inher- ent in climate change (used by Christopher Hope and Nicholas Stern, for example) is the use of Monte Carlo analysis, in which the model is solved numerous times using a variety of param- eter values that are drawn from assumed distributions. The shortcoming here, as can be determined by the preceding discussion, is that the result of this analysis depends largely on the choice of distribution, which is precisely what one does not know enough about. Assuming a normal distribution can give us precise probability measures for extreme events, but these measures are only as good as the normality assumption that drives them. Furthermore, some authors tend to \u2018bound\u2019 their distributions by ignoring high-impact, very low probabil- ity outcomes. The major argument in favor of this approach is that one has such a weak understanding of the likelihood of these events that taking them into account and having them overtly influence policy would be foolish. Indeed, it might lead to extreme risk aversion and policy actions that may cripple the economy. In further support of this approach, William Nordhaus found that his optimal policy in a model which focused on the \u2018best guesses,\u2019 or mean estimates for parameter values, was a good approximation of the policy for the expected value model, which would introduce some risk pre- mium to avoid extreme events. However, other authors have found that the risk premium associated with extreme events would indeed be substantial, including Richard Tol, Megan Ceronsky, David Anthoff, and Cameron Hepburn. Numerous authors, from Nordhaus and Weitzman to Robert Pindyck, have put forth arguments for why the distri- bution of climate change outcomes is unlikely to have a nor- mal \u2018thin-tailed\u2019 distribution. They argue that the distribution is likely to possess \u2018fat tails,\u2019 meaning that the probability de- creases at a less than exponential rate. For fat-tailed distribu- tions, the probability assigned to events located many standard deviations from the mean are much higher than what would be predicted in a thin-tailed distribution. Figures 3 and 4 present a comparison of two probability density functions (PDFs). In the figures, both distributions possess the same mean (1.667) and variance (2.222), but one distribution is fat tailed and the other is thin tailed. The thin-tailed PDF is a normal distribu- tion and the thick-tailed PDF is a generalized Pareto distribu- tion with K¼0.4, s¼0.4, and m¼1. There are several reasonable motivations for assuming a fat- tailed distribution to key IAM parameters like climate sensitiv- ity and economic damages. One plausible reason is the largely unknown extent to which feedback loops could create large nonlinearities in climate sensitivity, species extinction, and the like. Even if it is believed that the parameter in question follows a thin-tailed distribution, uncertainty about the variance may lead one to treat the distribution as fat tailed. This is put succinctly by Pindyck: . . . suppose we don\u2019t know the variance of the distribution, and therefore we estimate the variance using all available data, with Bayesian updating of our estimate as new data becomes available. In that case the posterior distribution for [the variable] (i.e., the distri- bution conditional on our estimation process for the variance) is necessarily fat-tailed (from \u2018Fat Tails, Thin Tails, and Climate Change Policy\u2019 in the Review of Environmental Economics and Policy volume 5, p. 259). Weitzman goes further, arguing that the combination of fat- tailed distributions and typical formulations of utility that are used in IAMs can lead to the unpalatable conclusion that governments should devote almost 100% of GDP toward curbing the effects of climate change (this is Weitzman\u2019s \u2018dismal theorem\u2019). When low levels of consumption possess marginal utilities that approach infinity, the marginal utility of avoiding damages from extreme events can approach infinity. When the distribution of climate change outcomes is fat tailed, the rising marginal utility of avoiding extreme events outpaces the falling probability of these extreme events occurring, creating infinite or near-infinite returns to climate change policy. This can be viewed as a call to far greater mitigation efforts, although it is more widely regarded as validation for bounding marginal utility in IAMs. This is the perspective Nordhaus takes when he provides several examples, from asteroids to nuclear weapons, suggesting that one does not treat \u2018zero consump- tion\u2019 as an outcome yielding infinite disutility. He also argues that the dismal theorem applies most directly for issues where no learning can take place (the creation of strangelets in parti- cle colliders, for example), whereas climate change is a more gradual process in which learning can occur. Pindyck acknowl- edges the importance of distributional assumptions regarding climate change parameters but also argues that tail properties 0.08 0.07 0.06 0.05 0.04 P ro b ab ili ty 0.03 0.02 0.01 0 1 2 3 4 5 6 Standard deviations from mean 7 8 9 Thin tail Fat tail Figure 3 Example of fat- and thin-tailed distributions. 34 Climate Change and Policy | Dealing with the Uncertainty About Climate Change alone do not dictate the level of optimal intervention. He notes that \u201cWhat matters here is the entire distribution for outcomes, and not necessarily whether that distribution has fat or thin tails (from \u2018Fat Tails, Thin Tails, and Climate Change Policy\u2019 in the Review of Environmental Economics and Policy volume 5, p. 276).\u201d The Implications of Uncertainty The implications of uncertainty are somewhat unclear. Uncer- tainty often can be resolved (or lessened) over time using a \u2018wait and see\u2019 attitude. As Pindyck has noted, the attractiveness of this position depends on the relative weight of two distinct irreversibilities. Working against the \u2018wait and see\u2019 attitude is the potential irreversibility of climate damage or the existence of tipping points regarding climate damage. If the impacts of climate change are largely irreversible, waiting can have severe consequences. Uncertainty regarding potential environmental irreversibilities can urge policymakers into greater and earlier intervention through the \u2018precautionary principle.\u2019 The other irreversibility which favors the \u2018wait and see\u2019 approach relates to the irreversibility of investment decisions. Investing in mit- igation and adaptation may prove ineffective or unnecessary due to the high uncertainty faced when making policy deci- sions. As an example, investment in sea walls will not yield tangible benefits if sea level rise is inconsequential, or if sea level rise is well beyond what the sea walls can control. In both cases, investment in the sea walls will be largely lost and useless. Uncertainty regarding the effectiveness and necessity of costly mitigation and adaptation investments suggest that these investments