Analyzing Climate Uncertainty and Risk with an Integrated Assessment Model

Robert Repetto and Robert Easton

Uncertainty over the consequences of unprecedented global warming is central to environmental insecurity. Global warming threatens to exacerbate all other ecological stresses and menaces human populations and economies. Despite scientific efforts, great uncertainties still pervade crucial aspects of the climate change process and its consequences. Yet integrated assessment models widely used to analyze climate policy options, such as the Nordhaus DICE model,1 establish that model outputs are highly sensitive to plausible alternative parameter values. This paper further explores uncertainties by substituting probability distributions for pre-determined values of key parameters in the DICE model. It then draws randomly from these probability distributions to implement a Monte Carlo analysis of policy outcomes, generating hundreds of policy simulations. An important finding is that the sacrifice in world consumption entailed in keeping the rise in global temperatures below two degrees centigrade would likely be negligible if emitting countries cooperate in adopting efficient mitigation policies. In other words, the cost of insurance against dangerous climate change is close to zero. Thus, the result of this analysis suggests that science and economics agree on keeping climate change below a level threatening serious damage.

In the twenty-first century, global warming is the dominant source of environmental insecurity. The global climate is changing rapidly on a scale unprecedented over the course of human civilization, so the consequences have no historical parallels. Because carbon dioxide stays in the atmosphere and oceans react slowly to changes in atmospheric heat build-up, global warming is irreversible over many decades. Moreover, scientists warn that the climate system has poorly understood tipping points beyond which positive feedbacks, such as melting ice and methane releases, will accelerate change.2 The paleo-climate record includes episodes of very rapid change over the span of a few decades.3 In its consequences, global warming is acting as a “force multiplier” for almost all other serious environmental problems: exacerbating deficiencies of water availability and quality, compounding air pollution, threatening a mass biodiversity extinction disaster, further degrading oceanic ecosystems and life, accelerating forest losses by fire and pest outbreaks, spreading infectious diseases, and compromising public health. Among the most serious consequences of climate change are the increasing frequency and intensity of extreme weather events, such as

Robert Repetto is a senior fellow at the International Institute for Sustainable Development (IISD) and a senior fellow for the Energy and Climate programs at the United Nations Foundation. He is a leading environmental economist and is known for his writings and research on the interface between environment and economics and on policies to promote sustainable economic development.

Robert Easton is a professor emeritus in the department of applied mathematics at the University of Colorado at Boulder. His research interests are in dynamical systems, Hamiltonian mechanics, statistics, macro economics, and environmental economics. droughts, heat waves, floods, coastal cyclones, and storm surges. Although such extreme weather events are often disastrous, forecasting is difficult, which makes preparation for them equally challenging. The uncertainty surrounding many important aspects of the climate problem compounds this insecurity. The future course of greenhouse gas emissions, with or without policy restraints, will vary with uncertain future economic and population growth and the supply conditions for carbon-based and alternative energy sources. The future availability of oceanic and terrestrial carbon sinks is uncertain, as is the sensitivity of global temperatures to the build-up of greenhouse gases. How damaging future global warming will be to human economies and populations is uncertain, especially since damages will stem largely from sudden and extreme weather events. Secondary responses, including mass migrations, social and political unrest, famines, and pandemics, have led national security bodies to rank climate change among the foremost security threats of this century.4 On the other side, the pace of technological change and energy sector improvements is also uncertain. The ability to predict the evolution of these variables over several decades into the future is quite limited, especially when they are inter- linked. Not only does uncertainty make policy responses far more difficult, interests opposed to any policy intervention to reduce carbon emissions have also used it repeatedly as an excuse or rationale for inaction.5 Many experts have argued that policies to deal with climate change threats should be fashioned in ways that address these uncertainties. Some have recommended reliance on the precautionary principle, which would give heavy weight to avoidance of worst-case outcomes.6 Others have formulated policy models that incorporate a greater degree of risk aversion in weighing gains and losses.7 Others have invoked an analogy to insurance models, which treat mitigation costs as the premium needed to insurance against catastrophic outcomes.8 Nonetheless, most influential models that are being used for climate policy analysis have largely assumed away uncertainties. They have been deterministic, in the sense that all important relationships and quantitative parameters are specified as if known with certainty even over an analytical span of a century. Uncertainty is then introduced by testing the effects of altered parameters on modeled results. The leading example of this approach is the DICE model (Dynamic Integrated model of Climate and the Economy) created by William Nordhaus, Sterling Professor of Economics at Yale University. The DICE model has been widely used and highly influential, partly because Professor Nordhaus has updated the model several times and has generously made accessible and public the model’s details, including its computer code. The DICE model has been cited at least a thousand times. Professor Nordhaus’ work with the model was cited no less than a dozen times in the recent report on mitigation options by the International Panel on Climate Change. It was used and cited by the White House Interagency Working Group report on the social cost of carbon and referenced several times in the Executive Office of the President 2014 report, “The Cost of Delaying Action to Stem Climate Change.”9 For these reasons, the DICE model is the foundation on which our study has built an effort to treat major uncertainties intrinsically in a policy analysis. Rather than assuming that important parameters are known with certainty, this study treats them as inherently uncertain and known only within a range of probabilities. The underlying probabilities are derived from estimates available in published scientific literature. These estimates may span considerable ranges. Using this approach, model results are also limited to probabilities rather than certainties. The core of the DICE model is a highly aggregated optimal growth model: world output is produced with autonomously rising efficiency by the capital stock and a labor force that grows at the same assumed rate as world population grows. Growth of the capital stock depends on the fraction of world output devoted to investment, net of capital depreciation. The remaining world output is available for consumption and per capita consumption—along with the level of population—determines global welfare. The core analytical problem in the growth model is to choose investment levels in such a way as to maximize a welfare function defined over all future time periods. The welfare function implies declining values to consumption further in the future and to successive increments to consumption in any period. Building on this core, the DICE model assumes that producing world output generates emissions of greenhouse gases at an assumed base rate that gradually declines over time because of structural changes in the world economy. To these are added emissions from changes in land use, which also decline at an assumed rate. A mitigation option in the model allows some fraction of output to be devoted to reducing industrial emissions. That fraction rises sharply with the proportion of emissions that are mitigated, up to a maximum value that is assumed to shrink over time at a known rate. Emissions that are not abated contribute to an increase in atmospheric concentrations. A compact climate sub-model allocates these concentrations between oceanic and terrestrial sinks, with the remainder residing in the atmosphere. Atmospheric concentrations contribute to the rise in surface temperatures through an assumed forcing function. Climate change damages are modeled as a non-linear function of the rise in surface temperatures and represented as a loss in world output. The DICE model is then also programmed to find the best fraction of output to devote to mitigation in each time period and, correspondingly, the best fraction of output to sacrifice in climate change damages. In other words, the model chooses both the savings rate and the mitigation rate to achieve the highest level of welfare over the entire time period. Because of its prominence and accessibility, the DICE model has received its fair share of scrutiny and criticism. Sir Nicholas Stern, principal author of the Stern Review of the Economics of Climate Change for the British Treasury Department, debated Professor Nordhaus on the proper rate at which to discount future welfare over long periods of time.10 As mentioned above, Harvard Professor Martin Weitzman has argued for a higher degree of risk aversion because of the possibility of catastrophic damages.11 The DICE model’s assumed damage function, which rises indefinitely as a quadratic function of the temperature increase, has been criticized because it implies that world income could continue to increase even at extreme double-digit temperature increases. It has also been criticized because it implicitly rejects the possibility of climate tipping points that might propel the world into catastrophic, irreversible states.12 In addition, it has been proposed that damages from climate change might adversely affect not only the level of output but also the capital stock and its productivity, reducing potential growth.13 Other critics have focused on the assumed sensitivity of the climate to increased greenhouse gas concentrations, arguing that the scientific literature admits the possibility of significantly higher sensitivities.14 These re-examinations have established that the DICE model conclusions are sensitive to changes in these parameters. Specifically, greater climate sensitivity, greater risk aversion, and more extreme damage potentials tip the model’s economically maximizing solutions toward higher carbon prices and more abatement of emissions.15 Previous research using the DICE model to analyze uncertainty has therefore focused primarily on the sensitivity of the climate to atmospheric carbon build-up and on the damages caused by climate change.16 Probability functions have been postulated to represent these parameters of the model. With these, Monte Carlo simulations have been carried out by drawing randomly many times from these distributions and using those draws to solve the model repeatedly. The results in this Monte Carlo approach are then presented as frequency distributions of model outputs. This research has explored the risk implications of reaching a global warming tipping point at which a more severe relationship between damages and further warming could come into play. These studies have found that these risks should lead to higher carbon prices and more stringent emissions reductions.

Sensitivity Analysis

In the light of these previous findings, our analysis has focused primarily on other important uncertainties in the climate problem—those related to the generation and abatement of carbon emissions. Both the future rate of emissions growth in the absence of abatement and the future costs of abatement are uncertain. Future economic growth, leading to higher emissions, is partly driven by increasing world population. The DICE model accepts the current medium projection from the United Nations (UN) Population Division that world population will stabilize during this century at 10.5 billion people. This exogenous model assumption is invariable over all temperature increases, even those implying severe climate change impacts on food and water supply and human settlements. Moreover, the UN projections themselves are unrelated to socio- economic projections, relying instead on extrapolations from demographic histories.17 UN projections are often revised and have not proven to be very accurate forecasts. For sensitivity analysis, this study adopts a stabilization level of nine billion people and in Monte Carlo analysis postulates a uniform distribution ranging between nine and eleven billion people. Another important uncertainty arises in the future course of emissions per unit of world output in the absence of mitigation. The DICE model relates emissions to total world output, which increases in substantial part because of productivity improvements. The model implicitly assumes that increases in physical inputs and increases in the efficiency with which those inputs are used result in the same emissions—a questionable assumption. The model represents all improvements in energy efficiency with a single parameter representing changes over time in emissions per unit of world output and assumes that this emission-intensity declines at a rate of 1 percent per year. This ratio is actually the product of emissions per unit of energy consumed— known as “decarbonization”—and energy consumed per dollar of output, or energy efficiency. Both have improved over time. The latter has historically improved by 2 percent per year, but improvement slowed to 0.9 percent per year in the last two decades because of structural changes in the world economy, as a larger share of world output has been generated in countries with poor but rapidly improving energy efficiency, particularly Brazil, Russia, India, China, and South Africa—the BRICS.18 “Decarbonization” has improved by 0.4 percent per year over the twentieth century, but has stalled in the last two decades for essentially the same reason, as an increasing share of output has been generated in countries that are greatly dependent on coal— mainly India and China.19 In the future, as growth slows in the BRICS countries and their energy efficiency approaches that of developed countries, these structural changes will shrink in significance. Both the Intergovernmental Panel on Climate Change (IPCC) and the Energy Modeling Forum at Stanford University have found that different models imply quite different projections of future ratios of emissions to output.20 These differences arise from implicit assumptions about the pace of structural economic change, technological change, limits on the use of nuclear power, future fossil fuel prices, and other uncertainties. Studies agree that the scope for continuing improvements in energy efficiency is vast. Moreover, carbon intensity is likely to improve more rapidly for several reasons: China, India, and other countries are closing inefficient coal plants and investing in alternatives because of intolerable levels of air pollution. Also, the relative costs of coal and natural gas are shifting, as coal extraction faces a rising cost curve and gas extraction costs are falling because of horizontal drilling and hydraulic fracturing, or “fracking.” Finally, as wind and solar power approach grid parity in more regions and applications, their use will increase even without explicit mitigation policies. In sensitivity analysis, emissions per unit of output are assumed to decline by 2 percent per year; a range of 1 to 2 percent is used in the Monte Carlo analysis. Another important uncertainty is the future cost of abating emissions through energy efficiency, use of non-carbon fuels, and carbon capture and storage. The DICE model assumes that technological improvements reduce abatement costs by 0.5 percent per year, regardless of the abatement policy adopted. This assumption denies the likelihood of induced technological change and “learning-by-doing” improvements achieved with greater deployment of non-carbon technologies. In recent decades, the costs of renewable energy have declined at a much faster rate than assumed by the DICE model—exceeding 2 percent per year—and energy saving technologies have achieved faster market penetration than the model accounts for. This study’s alternative assumption for sensitivity analysis is a continuing annual rate of 2 percent in cost improvement. For Monte Carlo simulations, a range between 0.5 and 2 percent per year is assumed. A final important change regards the economic effects of abatement costs. In the DICE model, both abatement costs and climate damage costs are represented as fractional reductions in the world output available for investment or consumption. This assumption implies that, other things being equal, both mitigation and damage costs will rise with the growth of world output. With respect to damage costs, this assumption is reasonable because, at any level of temperature increase, damages will be greater if there is more value at risk. However, abatement costs depend only on the tonnage of emissions, the fraction of those abated, and the costs per ton of abatement. With those given, abatement costs will not rise just because there has been growth in the underlying economy. In both sensitivity and Monte Carlo analyses, this study has modified the specification of the DICE model to effectuate this change in assumption, making abatement costs independent of the growth of the economy for any fixed level of emissions. The following graphics show the results of a sensitivity analysis that changes these key parameters cumulatively. In order to align these results with previous analyses, we have included as the last parameter change an assumption in the climate damage function that makes damages a cubic power of the temperature increase rather than a quadratic, which better represents the possibility of extreme damages at high levels of climate change. Under what we consider to be a more realistic portrayal of the generation and abatement of carbon emissions, there is a pronounced change in the preferred emissions trajectory implied by the original DICE model. As shown in figure 1, instead of rising throughout the twenty-first century (the topmost trajectory), lower population growth, faster gains in carbon efficiency, and a more realistic portrayal of the economic impact of abatement costs in combination lead to a consistently declining emissions trajectory. If a more optimistic assumption regarding improvements in abatement cost technologies is also adopted, then emissions in the preferred policy scenario fall by almost 75 percent over the century. Recognition of more extreme damage risks adds further to the case for drastic emissions reductions, which fall to virtually zero by the end of the century.

Figure 1 Projected Emissions 2015-2100 90

80

70

60 Baseline2

50 Baseline3

CO2 Populaon Gt 40 Emissions/GDP 30 AbatecostExp

20 DamageExp

10

0 2000 2020 2040 2060 2080 2100 2120 Year

Turning to the temperature implications of these emissions trajectories, the graphic in figure 2 shows that, under the alternative assumptions regarding emissions generation and abatement, the lower trajectory of emissions is sufficient to keep the temperature increase below two degrees Celsius over the twenty-first century. Adding the damage sensitivity component implies that temperature should be kept well below the two degree limit. In other words, the sensitivity analysis shows that under reasonable alternative assumptions, economic analysis supports the international consensus that global warming should be contained within “safe” limits.21 Thus, there is no conflict between science and economics.

Figure 2 Temperatures 2015-2100 3.5

3

2.5 Baseline2

2 Baseline3

Populaon 1.5 Emissions/GDP

1 AbatecostExp

DamageExp Temperature increase from baseline 0.5

0 2000 2020 2040 2060 2080 2100 2120 Years

Figure 3 depicts the impact on more ambitious abatement policies on future consumption. What is remarkable is how insensitive future consumption is to changes in emissions. Contrary to political claims, future consumption continues to grow at an almost unchanged rate under all scenarios. The reason for this result is easily understood: higher abatement costs imply reduced emissions and lower climate change damages. These costs largely cancel, leaving little net effect on consumption. It is worth noting that these results of the sensitivity analysis have not invoked any greater degree of risk aversion or valuation of future consumption than assumed in the original DICE model.

Figure 3 World Consumpon 2015-2100 400

350

300

250 Baseline2 Baseline3 200 Populaon

150 Emissions/GDP AbatecostExp 100 Consumpon in trillions of dollars DamageExp

50

0 2000 2020 2040 2060 2080 2100 2120 Years

Monte Carlo Analysis

With this sensitivity analysis as background, probability distributions have been specified for these parameter values spanning DICE model assumptions and our alternatives. The following table (table 1) lays out these distributions. The Monte Carlo analysis drew randomly from each of these distributions five hundred times and solved the model with each set of parameters. This procedure led to probability distributions for variables of interest, including the emissions at all points in time, the cumulative emissions over the century, the temperature increase at all points in time, the levels of output, and the levels of aggregate consumption.

Table 1. Monte Carlo Probability Distributions

Parameter Distribution Range Population uniform 9-11 Emissions/GDP Decline uniform 1%-2% per year Mitigation Cost Decline uniform 0.5%-2% per year 1.5%-2% at 2 degrees Damage Values uniform 20%-50% at 6 degrees22

A key finding is that there is no conflict between a policy based on keeping global warming to a safe limit and a policy based solely on economic criteria. This finding differs from the position implied by the original DICE model and discussed in the recent book by Professor Nordhaus, The Climate Casino, which concludes that an economically optimum temperature increase, even with all countries participating efficiently, would be well above 2 degrees.23 As the cumulative distribution function in figure 4 indicates, in a majority of cases—55 percent— the economically preferred mitigation policy would also keep the temperature increase below two degrees over this century. In more than 80 percent of cases, each representing a possible combination of circumstances and conditions, the economically preferred policy would let temperature rise no more than 2.1 degrees by 2100, within 5 percent of the target. In no case would temperature rise more than 2.3 degrees. Without invoking any heightened degree of risk aversion or any heavier weighting on the welfare of future generations, the analysis finds that the prudential policy approach and the economic policy approach are in agreement.

Figure 4 Projected Temperature Increase 2100

3

2.5

2

1.5 Temperature 1

0.5

Temperature Increase Above Baseline 0 1 47 24 70 93 116 139 162 185 415 438 461 484 208 231 254 277 300 323 346 369 392 Trial Results Sorted From Lowest to Highest

The analysis also finds that an ambitious mitigation approach designed to keep global warming to a safe limit would not sacrifice aggregate consumption per capita. As demonstrated in the sensitivity analysis, aggregate consumption is almost independent of the climate policy adopted and varies within a narrow band across all 500 simulations. More spent on mitigation leads to smaller damage losses from global warming; less spent on mitigation means greater damage losses. Over the range of policy outcomes in the model, these two costs largely net out, leaving aggregate consumption little changed. Moreover, over the range of solutions in the analysis, less global warming leads to higher levels of per capita consumption. The correlation between them over the five hundred Monte Carlo solutions is fairly close: -0.68. Over the wide range of conditions sampled in the analysis, policies result in per capital consumption levels about 0.4 percent higher in 2010 for every 0.1 degree less warming (figure 5). In other words, these results imply that insurance against unsafe global warming is available at virtually zero cost if countries cooperate in adopting efficient mitigation policies.

Figure 5 World Consumpon 2100 450

400

350

300

250

200 Consumpon Trillions of Dollars 150

100

50

0 0 100 200 300 400 500 600 Trial Number

In summary, the analysis of uncertainty and risk with the DICE integrated assessment model leads first to the unsurprising conclusion that the model outputs of interest are sensitive to changes in key parameters and assumptions that are uncertain over the time scale of the analysis. Realistic, but less pessimistic, assumptions lead to the conclusion that an economically optimal policy would lead to rapidly falling world emissions and a temperature increase below the agreed-upon safe limit of 2 degrees Celsius. When those parameters and assumptions are treated as inherently uncertain and known only within a range of probabilities, the analysis concludes that under most future conditions, it would still be economical to keep the temperature increase below 2 degrees, and almost always economical below 2.1 degrees. In addition, the analysis finds that global consumption would not be significantly affected by policies designed to limit global warming to a tolerably safe degree, implying that insurance against dangerous climate change is virtually free if countries cooperate in implementing economically efficient mitigation policies.

Notes

1 For background information on the DICE model, see William Nordhaus, “Scientific and Economic Background on DICE-2013R Model,” Yale University Department of Economics, http://www.econ.yale.edu/~nordhaus/homepage/DICE-science.htm. 2 Intergovernmental Panel on Climate Change, Fifth Assessment Report – Climate Change 2013: The Physical Science Basis (Paris, France: World Meteorological Organization and United Nations Environment Programme, 2013), http://www.ipcc.ch/report/ar5/wg1/. 3 Committee on Abrupt Climate Change, “Abrupt Climate Change,” National Research Council, 2015, http://www.nap.edu/openbook.php?record_id=18373. 4 Center for Naval Analyses (CNA) Military Advisory Board, National Security and the Accelerating Risks of Climate Change (Alexandria, VA: CNA, 2014). 5 Naomi Oreskes, Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming (London, England: Bloomsbury Press, 2011). 6 Jonathan Aldred, “Climate Change Uncertainty, Irreversibility and the Precautionary Principle,” Cambridge Journal of Economics 36, no. 5 (July 30, 2012), http://cje.oxfordjournals.org/content/36/5/1051.full. 7 Martin Weitzman, “Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change,” Review of Environmental Economics and Policy 5, no. 2 (2011), http://scholar.harvard.edu/weitzman/publications/fat-tailed- uncertainty-economics-catastrophic-climate-change-0. 8 Executive Office of the President, The Cost of Delaying Action to Stem Climate Change (Washington, DC: WhiteHouse.Gov, 2014), http://www.whitehouse.gov/sites/default/files/docs/the_cost_of_delaying_action_to_stem_climate_change.pdf. 9 Interagency Working Group on Social Cost of Carbon, United States Government, Technical Support Document: Technical Update of the Social Cost of Carbon for Regulatory Impact Analysis under Executive Order 12866 (Washington, DC: WhiteHouse.Gov, 2013), http://www.whitehouse.gov/sites/default/files/omb/inforeg/social_cost_of_carbon_for_ria_2013_update.pdf. 10 Nicholas Stern, The Economics of Climate Change: The Stern Review (Cambridge, UK: Cambridge University Press, 2007), http://www.cambridge.org/us/academic/subjects/earth-and-environmental-science/climatology-and- climate-change/economics-climate-change-stern-review. 11 Weitzman, “Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change.” 12 Michael W. Hanemann, What is the Economic Cost of Climate Change? (Berkeley, CA: University of California—Berkley, 2008), http://escholarship.org/uc/item/9g11z5cc. 13 Frances C. Moore and Delavane B. Diaz, “Temperature Impacts on Economic Growth Warrant Stringent Mitigation Policy,” Nature Climate Change 5 (January 12, 2015), http://www.nature.com/nclimate/journal/v5/n2/full/nclimate2481.html?WT.ec_id=NCLIMATE-201502. 14 Derek Lemoine and Christian Traeger, “Watch Your Step: Optimal Policy in a Tipping Climate,” American Economic Journal: Economic Policy 137, no. 166 (February 2014), http://www.researchgate.net/profile/Derek_Lemoine/publication/263610103_Watch_Your_Step_Optimal_Policy_in _a_Tipping_Climate/links/53d032f70cf2fd75bc5d1ab9.pdf. 15 Robert E. Kopp et al., “The Influence of the Specification of Climate Change Damages on the Social Cost of Carbon,” Economics 6 (April 30, 2012), https://rucore.libraries.rutgers.edu/rutgers-lib/39292/. 16 Frank Ackerman and Elizabeth A. Stanton, “Climate Risks and Carbon Prices: Revising the Social Cost of Carbon,” Economics 6 (April 4, 2012), http://www.economics-ejournal.org/economics/journalarticles/2012-10. 17 Toshiko Kaneda and Jason Bremner, Understanding Population Projections: Assumptions behind the Numbers (Washington, DC: Population Reference Bureau, 2014), http://www.prb.org/pdf14/understanding- population-projections.pdf. 18 International Energy Agency, Worldwide Trends in Energy Use and Efficiency: Key Insights from IEA Indicator Analysis (Paris, France: IEA, 2008), http://www.iea.org/publications/freepublications/publication/Indicators_2008.pdf. 19 Dustin LeClair, “US and Global Carbon Intensity Trends,” George C. Marshall Institute, http://marshall.org/climate-change/u-s-and-global-carbon-intensity-trends/. 20 Allen A. Fawcett et al., “Overview of EMF 22 US Transition Scenarios,” Energy Economics 31 (October 2009), https://web.stanford.edu/group/emf-research/docs/emf22/fawcettOverview22.pdf.

21 Further results, not shown here, show that if climate sensitivity is estimated to be greater, even more abatement of emissions would be called for. 22 A uniform distribution ranging from 1.5 to 2.5 percent of output has been assumed for the extent of damage at two degrees of warming. A uniform distribution ranging from 20 to 50 percent of output has been assumed for a warming of five degrees, in view of the wide range of uncertainties regarding impacts, irreversible factors, and discontinuities under extreme warming. 23 William Nordhaus, “Climate Policy by Balancing Costs and Benefits,” in The Climate Casino: Risk, Uncertainty and Economics for a Warming World (New Haven: Yale University Press, 2013).