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4. Uncertainty and worst-case risks

Climate change entails relatively predictable, reasonably bad expected or average outcomes — and catastrophically worse outcomes that are unlikely but not impossible. How should economics incorporate uncertainty about catastrophic worst-case risks?


Uncertainty and climate treaties: Does ignorance pay?
Dellink, R. & Finus, M.
Resource and Energy Economics, 2012, 34, 565 - 584
Uncertainty and learning play an important role in the management of many environmental and resource problems and in particular in climate change. In stylized game-theoretic models of international environmental treaty formation, which capture the strategic interactions between nations, learning usually has a negative impact on the success of cooperation. We use a richer climate model that captures the large heterogeneity between different world regions and considers uncertainty about the benefits and costs from climate mitigation. By explicitly exploiting differences between regions and allowing transfers to mitigate free-rider incentives, we derive much more positive conclusions about the role of learning.

Uncertain outcomes and climate change policy
Pindyck, R. S.
Journal of Environmental Economics and Management, 2012, 63, 289 - 303
I incorporate distributions for temperature change and its economic impact in an analysis of climate change policy. As a measure of willingness to pay (WTP), I estimate the fraction of consumption w*(t) that society would be willing to sacrifice to ensure that any increase in temperature at a future point is limited to t. Using information on distributions for temperature change and economic impact from recent studies assembled by the IPCC and others, I fit displaced gamma distributions for these variables. These fitted distributions, which roughly reflect the "state of knowledge" regarding warming and its impact, generally yield values of w*(t) below 2%, even for small values of t, consistent with moderate abatement policies. I also calculate WTP for shifts in the mean and standard deviation of the temperature distribution, and show how WTP, and thus the demand for abatement, are driven more by outcome uncertainty than expected outcomes.

Fat Tails, Thin Tails, and Climate Change Policy
Pindyck, Robert S.
Review of Environmental Economics and Policy, 2011, 5 (2): 258-274.
Climate policy is complicated by the considerable uncertainties concerning the benefits and costs of abatement. We do not even know the probability distributions for future temperatures and impacts, making benefit–cost analysis based on expected values challenging to say the least. There are good reasons to believe that those probability distributions are fat-tailed, which implies that if social welfare is based on the expectation of a constant relative risk aversion utility function, then we should be willing to sacrifice close to 100 percent of gross domestic product to reduce greenhouse gas emissions. I argue that unbounded marginal utility makes little sense and that once we put a bound on marginal utility, this implication of fat tails goes away: Expected marginal utility will be finite even if the distribution for outcomes is fat-tailed. Furthermore, depending on the bound on marginal utility, the index of risk aversion, and the damage function, a thin-tailed distribution can actually yield a higher expected marginal utility (and thus a greater willingness to pay for abatement) than a fat-tailed one.

Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change
Weitzman, Martin L.
Review of Environmental Economics and Policy, 2011, 5 (2): 275-292.
In this article, I revisit some basic issues concerning structural uncertainty and catastrophic climate change. My target audience here are general economists, so this article could also be viewed as a somewhat less technical exposition that supplements my previous work. Using empirical examples, I argue that it is implausible that low-probability, high-negative impact events would not much influence an economic analysis of climate change. I then try to integrate the empirical examples and the theory together into a unified package with a unified message that the possibility of catastrophic climate change needs to be taken seriously.

Fat tails, exponents, extreme uncertainty: Simulating catastrophe in DICE
Frank Ackerman, Elizabeth A. Stanton, and Ramón Bueno
Ecological Economics, 2010, 69(9): 1657-1665.
The problem of low-probability, catastrophic risk is increasingly central to discussion of climate science and policy, but integrated assessment models (IAMs) in climate economics rarely incorporate this possibility. What modifications are needed to analyze catastrophic economic risks in an IAM? This article explores the question using DICE, a well-known IAM, examining the implications of a fat-tailed probability distribution for the climate sensitivity parameter, a focus of recent work by Martin Weitzman, and the shape of the damage function, one of the issues raised by the Stern Review.

Uncertainty and risk in climate projections for the 21st century: comparing mitigation to non-intervention scenarios
Lorenzo Tomassini, Reto Knutti, Gian-Kasper Plattner, Detlef P. van Vuuren, Thomas F. Stocker, Richard B. Howarth and Mark E. Borsuk
Climatic Change, 2010, 103(3-4): 399-422.
Probabilistic climate projections based on two SRES scenarios, an IMAGE reference scenario and five IMAGE mitigation scenarios (all of them multi-gas scenarios) using the Bern2.5D climate model are calculated. Probability distributions of climate model parameters that are constrained by observations are employed as input for the climate model. The sensitivity of the resulting distributions with respect to prior assumptions on climate sensitivity is then assessed. Due to system inertia, prior assumptions on climate sensitivity play a minor role in the case of temperature projections for the first half of the 21st century, but these assumptions have a considerable influence on the distributions of the projected temperature increase in the year 2100. Upper and lower probabilities for exceeding 2°C by the year 2100 are calculated for the different scenarios. Only the most stringent mitigation measures lead to low probabilities for exceeding the 2°C threshold. This finding is robust with respect to our prior assumptions on climate sensitivity. Further, probability distributions of total present-value damages over the period 2000–2100 for the different scenarios are calculated assuming a wide range of damage cost functions, and the sensitivity of these distributions with respect to the assumed discount rate is investigated. Absolute values of damage costs depend heavily on the chosen damage cost function and discount rate. Nevertheless, some robust conclusions are possible.

Accounting for the risk of extreme outcomes in an integrated assessment of climate change
Michael D. Gerst, Richard B. Howarth and Mark E. Borsuk
Energy Policy, 2010, 38(8): 4540-4548.
The potential for climate catastrophes, represented by ‘fat-tailed’ distributions on consequences, has attracted much attention recently. To date, however, most integrated assessment models have either been largely deterministic or deterministic with ex-post sensitivity analysis. The conclusions of such analyses are likely to differ from those employing models that accurately characterize society’s joint preferences concerning time and risk, especially when distributions are fat-tailed. Using a dynamic stochastic general equilibrium model adapted from Nordhaus’s DICE model, we show that failing to accurately account for risk can lead to substantial underestimation of the net benefits of greenhouse gas abatement. A robust finding of our analysis is that a lenient ‘policy ramp’ emissions reduction strategy is preferable over a more aggressive strategy—such as that advocated by the Stern Review—only if the model does not account for uncertainty about the climate system, the carbon cycle and economic damages, and specifies a consumption discount rate that is counterfactually higher than the historical global weighted average cost of capital of 4.0%. In the debate over uncertainty and time discounting, our results imply that what matters most in climate change assessment is the inclusion and particular specification of uncertainty rather than the precise choice of discount rate.

How should the distant future be discounted when discount rates are uncertain?
Christian Golliera and Martin L. Weitzman
Economics Letters, 2010, 107(3): 350-353.
The so-called "Weitzman–Gollier puzzle" is the fact that two seemingly symmetric and equally plausible ways of dealing with uncertain future discount rates appear to give diametrically opposed results. The puzzle is resolved when agents optimize their consumption plans. The long run discount rate declines over time toward its lowest possible value.

How should the distant future be discounted when discount rates are uncertain?
Martin L. Weitzman and Christian Gollier
Economic Letters (2010) 107(3): 350-353.
The so-called "Weitzman–Gollier puzzle" is the fact that two seemingly symmetric and equally plausible ways of dealing with uncertain future discount rates appear to give diametrically opposed results. The puzzle is resolved when agents optimize their consumption plans. The long run discount rate declines over time toward its lowest possible value.

What is the "damages function" for global warming - and what difference might it make?
Martin L. Weitzman
Climate Change Economics (2010) 1(1): 57-69.
The existing literature on climate change offers little guidance on why one specification or another of a "damages function" has been selected. Ideally, one wants a functional form that captures reality adequately, yet is analytically sufficiently tractable to yield useful results. This paper gives two plausible risk aversion axioms that a reduced form utility function of temperature change and the capacity to produce consumption might reasonably be required to satisfy. These axioms indicate that the standard-practice multiplicative specification of disutility damages from global warming, as well as its additive analogue, are special cases of this paper's theoretically derived utility function. Empirically, the paper gives some numerical examples demonstrating the surprisingly strong implications for economic policy of the distinction between additive and multiplicative disutility damages.

Economics of climate change under uncertainty: Benefits of flexibility
Jon Anda, Alexander Golub and Elena Strukova
Energy Policy (2009) 37(4): 1345-1355.
The selection of climate policy has to be made in an extremely uncertain environment: both benefits and costs of a particular climate policy are unknown and in the best case could be described by the probability distribution of various outcomes. The expected value approach to cost-benefit analysis relies on the aggregated estimation of various outcomes of climate policy weighted and averaged by probabilities. The variance, skewness, and kurtosis are important characteristics of uncertainties but can be easily lost in the process of aggregation. Real option analysis explicitly accounts for both the expected value of underling assets and the variance of the expected value (as well as skewness and kurtosis that are important to describe a fat tail phenomenon). In the paper, we propose an application of real option analysis in order to formulate rules for the selection of a climate policy (emission target) and estimate the economic value of the future flexibility created by interim climate policy, which may be corrected in the future in response to new knowledge that hopefully reduces uncertainties. The initially selected interim policy has an option value and methodology for its valuation presented in the paper.

Uncertainty and assessment of the issues posed by urgent climate change. An editorial comment
Paul Baer and James S. Risbey
Climatic Change (2009) 92(1-2): 31-36.
Climate change raises a number of difficult issues concerning the management of scientific uncertainty. Urgent decisions seem to call for quantified probability statements as the basis of rational policy-making. Yet the answers to many important questions such as the likely rate of sea level rise are not easily quantified, and the utilization of any estimates based on ‘collective subjective probability’ necessarily depends on value-laden judgments about burden-of-proof and the distribution of risk. We suggest that there is a need for a new form of risk assessment that is based in, but not limited to, the scientific community, in which rapid but credible processes address the critical questions that we are now facing.

On modeling and interpreting the economics of catastrophic climate change
Martin L. Weitzman
Review of Economics and Statistics (2009) 91(1): 1-19.
With climate change as prototype example, this paper analyzes the implications of structural uncertainty for the economics of low-probability, high-impact catastrophes. Even when updated by Bayesian learning, uncertain structural parameters induce a critical "tail fattening" of posterior-predictive distributions. Such fattened tails have strong implications for situations, like climate change, where a catastrophe is theoretically possible because prior knowledge cannot place sufficiently narrow bounds on overall damages. This paper shows that the economic consequences of fat-tailed structural uncertainty (along with unsureness about high-temperature damages) can readily outweigh the effects of discounting in climate-change policy analysis.

Additive damages, fat-tailed climate dynamics, and uncertain discounting
Martin L. Weitzman
Economics: The Open-Access, Open-Assessment E-Journal (2009) 3(29): 1-29.
This paper in applied theory argues that there is a loose chain of reasoning connecting the following three basic links in the economics of climate change: 1) additive disutility damages may be appropriate for analyzing some impacts of global warming; 2) an uncertain feedback-forcing coefficient, which might be near one with infinitesimal probability, can cause the distribution of the future time trajectory of global temperatures to have fat tails and a high variance; 3) when high-variance additive damages are discounted at an uncertain rate of pure time preference, which might be near zero with infinitesimal probability, it can make expected present discounted disutility very large. Some possible implications for welfare analysis and climate-change policy are briefly noted.

Uncertainty and climate change policy
John Quiggin
Economic Analysis and Policy (EAP) (2008) 38(2): 203-210.
The paper consists of a summary of the main sources of uncertainty about climate change, and a discussion of the major implications for economic analysis and the formulation of climate policy. Uncertainty typically implies that the optimal policy is more risk-averse than otherwise, and therefore enhances the case for action to mitigate climate change.

Why economic dynamics matter in assessing climate change damages: Illustration on extreme events
Stéphane Hallegatte, Jean-Charles Hourcade and Patrice Dumas
Ecological Economics (2007) 62(2): 330-340.
Extreme events are one of the main channels through which climate and socioeconomic systems interact, and it is likely that climate change will modify the probability distribution of the losses they generate. The long-term growth models used in climate change assessments, however, cannot capture the effects of such short-term shocks. To investigate this issue, a non-equilibrium dynamic model (NEDyM) is used to assess the macroeconomic consequences of extreme events. This exercise allowed us to define the economic amplification ratio, as the ratio of the overall production loss due to an event to its direct costs. This ratio could be used to improve the cost-benefit analysis of prevention measures. We found also that, unlike a Solow-like model, NEDyM exhibits a bifurcation in GDP losses: for each value of the capacity to fund reconstruction, GDP losses remain moderate if the intensity and frequency of extremes remain under a threshold value, beyond which GDP losses increase sharply. This bifurcation may partly explain why some poor countries that experience repeated natural disasters cannot develop. Applied to the specific issue of climate change, this model highlights the importance of short-term constraints in the assessment of long-term damages, and shows that changes in the distribution of extremes may entail significant GDP losses in absence of specific adaptation. It suggests, therefore, that to avoid inaccurately low assessments of damages, researchers must take into account the distribution of extremes instead of their average cost and make explicit assumptions on the organization of future economies.

Integrating economic analysis and the science of climate instability
Darwin C. Hall and Richard J. Behl
Ecological Economics (2006) 57(3): 442-465.
Scientific understanding of climate change and climate instability has undergone a revolution in the past decade with the discovery of numerous past climate transitions so rapid, and so unlike the expectation of smooth climate changes, that they would have previously been unbelievable to the scientific community. Models commonly used by economists to assess the wisdom of adapting to human-induced climate change, rather than averting it, lack the ability to incorporate this new scientific knowledge. Here, we identify and explain the nature of recent scientific advances, and describe the key ways in which failure to reflect new knowledge in economic analysis skews the results of that analysis. This includes the understanding that economic optimization models reliant on convexity are inherently unable to determine an "optimal" policy solution. It is incumbent on economists to understand and to incorporate the new science in their models, and on climatologists and other scientists to understand the basis of economic models so that they can assist in this essential effort. 

Uncertainty and economic analysis of climate change: A survey of approaches and findings
Sonja Peterson
Environmental Modeling and Assessment (2006) 11: 1-17.
The analysis of climate change is confronted with large uncertainties that need to be taken into account to arrive at meaningful policy recommendations. The main contribution of economics to this interdisciplinary task is to provide formal frameworks and techniques for analyzing climate policy in the context of uncertainty. This paper will give an overview of existing approaches and findings to provide a broad picture of what economics can contribute to the debate.

Optimal climate policy is a utopia: From quantitative to qualitative cost-benefit analysis
Jeroen C.J.M. van den Bergh
Ecological Economics (2004) 48: 385-393.
The dominance of quantitative cost-benefit analysis (CBA) and optimality concepts in the economic analysis of climate policy is criticised. It is based in a misplaced interpretation of policy for a complex climate&-economy system as being analogous to individual inter-temporal welfare optimisation. The application of quantitative CBA and optimality concepts to climate policy reflects an overly ambitious approach that does more harm than good. An alternative approach is to focus the attention on extreme events, structural change and complexity. A qualitative rather than quantitative CBA that takes account of these aspects can support the adoption of a minimax regret approach or precautionary principle in climate policy. This means: implement stringent GHG reduction policies as soon as possible.

Is the uncertainty about climate change too large for expected cost-benefit analysis?
Richard S. J. Tol
Climatic Change (2003) 56(3): 265-289.
Cost-benefit analysis is only applicable if the variances of both costs and benefits are finite. Finiteness is hard to prove; the opposite is easier to establish as one only needs to show that there is one possible climate change scenario with infinite variance. The paper shows that all relevant current variables of the FUND climate economics model have finite variances. However, there is a small chance that climate change reverses economic growth in some regions. In that case, the discount rate becomes negative and the present value of benefits of greenhouse gas emission reduction become so large that the variance is unbounded. One could interpret this as an indication that cost-benefit analysis is invalid. Alternatively, one could argue that the infinity is present in both the base case and the policy scenario, and therefore irrelevant — implying that cost-benefit analysis remains a valid tool.

Climate change policy: Quantifying uncertainties for damages and optimal carbon taxes
Tim Roughgarden and Stephen H. Schneider
Energy Policy (1999) 27: 415-429.
To calculate an "optimal" control rate or carbon tax a climate-economy model can be used on estimates of climate damages resulting from warming scenarios. The dynamic integrated climate-economy (DICE) model, in its original specification, suggested that an efficient policy for slowing global warming would incorporate only a relatively modest amount of abatement of greenhouse gas emissions, via the mechanism of a small carbon tax. Here, the DICE model is reformulated to incorporate several alternate damage estimates, resulting in a significantly more aggressive optimal policy than that suggested by the original model. In addition, statistical distributions of these damage estimates are constructed and used in a probabilistic analysis of optimal carbon tax rates, resulting in mostly much larger (but occasionally smaller) carbon taxes than the DICE defaults. In view of the large uncertainties in estimates of climate damages, a probabilistic formulation that links many of the structural and data uncertainties is essential to policy analysis, since point values or "best guesses" deny policy makers the opportunity to consider low probability, but policy-relevant, outliers.