Mar 31, 2016 | Systems Analysis
By Melina Kourantidou, MSA 2015 participant, PhD student, Department of Environmental and Business Economics, University of Southern Denmark
In summer 2015 I participated in the Summer Academy on Economic Growth and Governance of Natural Resources in Lomonosov Moscow State University. I was inspired by the interdisciplinary lectures there as well as by recent developments in Arctic marine governance to propose a game-theoretical model for Arctic fisheries management.
While commercial fishing in the central Arctic Ocean is unlikely to become common anytime soon, fisheries management in the region includes complex decision making challenges. © Fernbach Antal – Fotolia | Dollar Photo Club
In July 2015, representatives from the five Arctic Ocean coastal states (Canada, Denmark, Norway, Russia and the United States) signed the Declaration Concerning the Prevention of Unregulated High Seas Fishing in the Central Arctic Ocean. In the declaration text it is clearly stated that “commercial fishing in the high seas portion of the central Arctic Ocean is unlikely to occur in the near future.” This approach increases the stature of the Precautionary Principle, a strategy that copes with possible risks in cases where scientific information is limited. The declaration is the first official attempt to regulate international waters of the Central Arctic Basin. While commercial fishing in the central Arctic Ocean is unlikely to become common anytime soon, fisheries management in the region includes complex decision making challenges, while it is also complicated by multiple factors, including transboundary fish stocks—those crossing boundaries of Exclusive Economic Zones (EEZs) — and straddling stocks (those typically found in the high seas adjacent to the EEZ) arising from the unsettled maritime boundary lines, thus often calling for the establishment of an effective bilateral or multilateral regime.
The contentious and divisive issue of how to handle Arctic fisheries has mostly been discussed so far in literature from a biodiversity standpoint rather than an economic one. Yet looking at the problem from an economic standpoint could help provide information that could prevent optimal use of resources and thus contribute to preventing irrational behaviors that may lead to the collapse or disruption of the ecosystem. Optimization theory provides critical insights for individual fishers or countries pursuing the most profitable strategy (higher payoffs). At the same time it can also prove useful for broader decision-making processes whereby all interested parties cooperate on the management of Central Arctic fish stocks.
A map of the Central Arctic Ocean shows the many countries that border the ocean. © Shephard et al., 2016
Game theory can potentially contribute in a more complex setting, with two or more actors—states in our case—involved in fishing resource management and with each state being able to choose among a set of available options, with their payoff dependent on other states’ choices.
There are a number of different types of games available in the game theoretical framework. Given the existing risks and uncertainties over Arctic marine resources I would propose a differential game setting as a baseline scenario. A differential game is a mathematical formulation used for either conflict or cooperation where players’ strategies are changing over time.
A differential game seems suitable since there is an underlying assumption that the “Arctic players” involved make decisions at all time points and not necessarily in specific time intervals. Furthermore a repeated static game (players deciding simultaneously with no prior knowledge of other players’ choices), such as the Prisoner’s Dilemma, would probably not work as well here, since the payoff functions of our players would not be time-dependent.
If we are looking for a solution where all involved Arctic states agree to cooperate on the management of marine resources in the Central Arctic, we would probably need to solve it as a standard optimal control problem, through the use of maximum principle or dynamic programming. In other words the outcome of optimizing a joint welfare function should be examined regarding its efficiency, which brings together the different Arctic players in a joint effort to maximize their average individual welfare.
Another theory known as Nash equilibrium could provide useful insights with regard to incentives and motivations, especially in cases, like the one described here, where it is rather daunting to predict how different players will behave in a game. A Nash equilibrium comes down to a set of different strategies for each one of the players included in the game, indicating that neither player has incentive to change their choice (taking others’ choices as given) since their payoffs are not improving anyway.
An open-loop solution that gives Nash equilibrium would result in all players having absolutely no incentive to deviate from their specific strategic path, given the path of other players or in other words having the players at a Nash Equilibrium would make them unwilling to act differently, since they would be worse off if they did.
An Open Loop Nash Equilibrium can be examined where there is exclusive dependence on the time variable; if a player deviates from the equilibrium control, even if briefly, and decides to return to its former behavior, the equilibrium is broken. Conversely, in a feedback (or closed-loop) Nash Equilibrium which is strongly time consistent, the dependence lies on the current state of the system. Differential games can generally help towards answering whether a potential cooperative solution can be achieved through a Nash equilibrium of a non-cooperative game.
Yet another question is whether countries would prefer to cooperate instead of competing for fishing in the Central Arctic. A cooperative scenario would require a Net Present Value (sum of benefits minus sum of costs, both in present values) larger than the non-cooperative scenario, thus covering the opportunity costs arising from the cooperative case. If this condition is not satisfied we will have to accept that there will be a non-cooperative behavior up to the point that cooperation turns lucrative for all players.
Game theoretic approaches with regard to stock management have provided useful insights and directed new lines of inquiry, but the dynamically changing Arctic raises issues that call for coordinated responses, for example through the use of more robust tools such as evolutionary game theory. Given that many species are expected to expand to yet unexploited parts of Arctic waters, one major concern is the consequences of coastal states’ harvesting activities on society’s wellbeing, and the ways in which it will be made possible to leave a positive legacy for future generations.
Looking at the interplay of ecology and economic behavior is one way that scientists can begin to answer these questions. Meticulous research on strategies of defection, cooperation and enforcement can be a cornerstone for establishing and managing effective ways to protect the Arctic marine environment, taking into account the current dearth of research in existing and future biodiversity.
Read my full report on the MSA 2015 Web site (PDF)
Note: This article gives the views of the author, and not the position of the Nexus blog, nor of the International Institute for Applied Systems Analysis.
Mar 22, 2016 | Water
By Taher Kahil, IIASA Water Program
This year’s theme of the UN World Water Day is “Water and Jobs.” It focuses on how adequate water management can change workers’ lives. Indeed, water management and job creation are tightly linked. Nearly all jobs depend on water, and without reliable and safe access to water, neither small activities nor major global industries can endure. Similarly, labor is necessary to build, maintain, operate, and manage the water system, and to run water-based projects. Furthermore, job creation can be a thirsty business in both developing and developed countries. In many developing countries irrigation projects, requiring significant amounts of water, are considered the main engine for the economy and source of employment. In developed countries, less water is needed but it still requires sufficient quality for manufacturing and service projects creating job opportunities.
(cc) Albert Gonzlez Farran – UNAMID
Freshwater bodies such as rivers and aquifers supply the water that people and businesses rely on. But pressures on these bodies have been mounting worldwide during the last century. Population and economic growth have led to greater water use and increased pollution, with many basins around the world undergoing pervasive water shortages and quality degradation. Researchers expect the impacts of climate change to exacerbate these damages. At the same time, the global economy needs to continue growing to be able to adequately sustain the world’s rising population. However, the linkage between water and economic growth has increased global concerns about the impacts of water-related risks such as scarcity, droughts, floods, and pollution on economies’ ability to grow and create jobs. In fact, the World Economic Forum’s 2016 Global Risks Report ranks water as the highest global risk on economies over the next ten years.
When we talk about water and jobs, it is also important to mention that nearly 750 million people lack access to safe water and 2.5 billion live without adequate sanitation across the developing countries. People in these countries are constantly searching for water, which leaves limited time for productive work and skills building that yield better employment.
As we look towards the future, the link between water and employment becomes even more crucial. Water-related risks, which are expected to intensify due to climate change, will likely have adverse impacts on economy and employment, leading to major consequences beyond the water industry. For instance, researchers have linked the extreme drought in Syria between 2007 and 2010 to the uprising that began there in 2011. Several years of drought caused an extensive crop failure and massive losses of livestock, which resulted in 2 to 3 million people driven into unemployment and poverty. This situation contributed to a mass rural exodus into economically depressed cities, deepening existing instability in that country.
How do we avoid more crises like this? The complex and evolving water challenges of the future can only be addressed by investing in sustainable and integrated water management solutions such as those being identified and tested by the Water Futures and Solutions (WFaS) initiative at IIASA . WFaS is a cross-sector, collaborative, global initiative aimed at developing plausible scenarios of future water supply and demand, and identifying robust and no-regret portfolio of solutions for balancing water systems. The initiative brings together researchers and decision makers from governmental and non-governmental organizations as well as from the private industry and from a wide variety of sectors influencing water management. The potential water solutions include improved water policies and governance structures and the adoption of more innovative and environmentally friendly water technologies. Sustainable water resource management does not only address water-related risks, but it can also create green job opportunities for local and disadvantaged communities, for example in efficiency improvement works, in the production of alternative water sources, and in aquatic ecosystem restoration projects.
World Water Day © UN-Water
Note: This article gives the views of the author, and not the position of the Nexus blog, nor of the International Institute for Applied Systems Analysis.
Mar 18, 2016 | Alumni, Systems Analysis, Young Scientists
By Célian Colon, PhD student at the Ecole Polytechnique in France & IIASA Mikhalevich award winner
How can we best tackle risks in our complex and interconnected economies? With globalization and information technologies, people and processes are increasingly interdependent. Great ideas and innovations can spread like wildfire. However, so can turbulence and crises. The propagation of risks is a key concern for policymakers and business leaders. Take the example of production disruption: with global supply chains, local disasters or man-made accidents can propagate from one place to another, and generate significant impact. How can this be prevented?
Risk propagation is like a domino effect. Credit: Martin Fisch (cc) via Flickr
As part of my PhD research, I met professionals on the ground and realized that supply risk propagation is a particularly tricky issue, since most parts of the chains are out of their control. Supply chains can be very long, and change with time. It is difficult to keep track of who is working with whom, and who is exposed to which hazard. How then can individual decisions mitigate systemic risks? This question directly connects to the deep nature of systemic problems: everyone is in the same boat, shaping it and interacting with each other, but no one is individually able to steer it. Surprising phenomena can emerge from such interactions, wonderfully illustrated by bird flocking and fish schooling.
As an applied mathematician thrilled by such complexities, I was enthusiastic to work on this question. I built a model where firms produce and interact through supply chain relationships. Pen and paper analyses helped me understand how a few firms could optimally react to disruptions. But to study the behavior of truly complex chains, I needed the calculation power of computers. I programmed networks involving a large number of firms, and I analyzed how localized failures spread throughout these networks, and generate aggregate losses. Given the supply strategy adopted by each firm, how could systemic risk be mitigated?
With my collaborators at IIASA, Åke Brännström, Elena Rovenskaya, and Ulf Dieckmann, we have highlighted the key role of coordination in managing risks. Each individual firm affects how risks propagate along the chain. If they all solely focus on maximizing their own profit, significant amounts of risk remain. But if they cooperate, and take into account the impact of their decisions on the risk profile of their trade partners, risk can be effectively mitigated. Reducing systemic risks can thus be seen as a common good: costs are heterogeneously borne by firms while benefits are shared. Interestingly, even in long supply chains, most systemic risks can be mitigated if firms only cooperate with only one or two partners. By facilitating coordination along critical supply chains, policy-makers can therefore contribute to the reduction of risk propagation.
Colon’s model analyzes how firms produce and interact through supply chain relationships. Credit: Jan Buchholtz (cc) via Flickr
Drawing robust conclusions from such models is a real challenge. On this matter, I benefited from the experience of my IIASA supervisors. Their scientific intuitions greatly helped me focusing on the most fertile ground. It was particularly exciting to borrow techniques from evolutionary ecology and apply them to an economic context. Conceptually, how economic agents co-adapt and influence each other shares many similarities with the co-evolution of individuals in an ecological environment. To address such complex issues, I strongly believe in the plurality of approaches: by illuminating a problem from different angles, we can hope to see it more clearly!
Note: This article gives the views of the author, and not the position of the Nexus blog, nor of the International Institute for Applied Systems Analysis.
Oct 14, 2015 | Systems Analysis
By Brian Fath, IIASA Advanced Systems Analysis Program and Towson University
Brian Fath. © Matthias Silveri | IIASA
The seminal book The Limits to Growth by Donella Meadows and colleagues was a first attempt to make a world model that integrated environment, economics, population, and industrial pollution. Without drastic changes to curb human population growth, consumption of non-renewable resources and industrial effluence, the model scenario projected a collapse of the world social-industrial system, because physically it is not possible to keep growing on a finite planet. This important message spurred many people in the environmental sciences, but was largely ignored, or worse ridiculed, by the dominant economic and political leaders. Perhaps their work was too pessimistic (although some could say realistic) and called for change for which society was not yet ready.
My co-authors and I feel their message was interpreted incorrectly. The restrictions imposed by The Limits to Growth do not entail stagnation and strife but rather give us an opportunity for new priorities, greater equity, and greater well-being. Living within the limits can offer agreeable, pleasant, even thriving and wonderful living conditions.
Therefore we have written a book, which shows that following nature provides guidance and pathways to Flourishing within Limits to Growth.
People today are confronted with a number of very serious problems: poverty, increased inequalities among countries and people, refugees, regional conflicts and civil wars, global climate change, accelerating exploitation of the global non-renewable and renewable resources, rapid land use change and urbanization, and increased emissions of harmful chemicals into the environment. History has shown us that we cannot solve these problems using traditional methods based on short-sighted economic growth.
Additionally, we know from natural laws that continuous growth in a finite environment is not possible. How can we ensure sustainable development for society on Earth? It would be possible by imitating the system that understands how to sustain long-term development: to learn from nature and follow nature’s way. Nature shifts from quantitative biomass growth when the resources become limiting to qualitative development by increasing resource use efficiency, in terms of both improved network connectivity and information on process regulation and feedbacks. The two main ecosystem functions, flow of energy and transfer of nutrients, are accomplished by renewable energy and complete recycling of the needed elements. Nature also originated and perfected the use the 3Rs: Reduce, Reuse, and Recycle.
“The restrictions imposed by The Limits to Growth do not entail stagnation and strife but rather give us an opportunity for new priorities, greater equity, and greater well-being” Photo: Innsbruck, Austria ©Nikolai Sorokin | Dollar Photo Club
Our book employs a global model to experiment with applying these properties of nature in society. Using global statistics, the model considers how the development will change if:
- A revenue-neutral, resource-based Pigovian tax is increased significantly and along with commensurate tax reduction to enhance recycling and application of renewable energy
- We increase investment in education, innovation, and research significantly to raise the level of understanding by the population and to develop new progressive ideas to address our global problems.
- We increase pollution abatement considerably to reduce its negative impacts on our health, nature, and production.
- We increase aid from the developed to the developing countries to 0.8% of GNP, which would enhance the cooperation among countries, reduce poverty and population growth and thereby also the number of refugees. In this context, it is important that the aid is given as support to education, health care, and family planning and not at all as military aid.
The model calculations show that it is possible to obtain a win-win situation, where both industrialized and developing nations can achieve a better standard of living – the developing countries mostly quantitatively and the developed countries mostly qualitatively. The calculations are compared with scenarios based on “business as usual” practices. The business as usual scenario shows a major collapse around the year 2060, which is in accordance to the Limits to Growth results from 1972 and the follow-up-publications from the Club of Rome.
Furthermore, the book demonstrates calculations of ecological footprints and sustainability by assessing our consumption and loss of work energy due to our use of resources and destruction of nature. These calculations lead to the following conclusions:
- Maintain natural areas and the ecosystem services they provide.
- Improve agricultural production by increasing efficiencies and technologies.
- Shift our thoughts and actions from quantitative growth to qualitative development, for instance by using the three R’s.
- Shift to renewable energy.
- Leave today’s policy focused entirely on short-sighted economic considerations and start to discuss how we can improve environmental management, increase the level of education and research, and achieve greater equality in society.
- Develop and promote alternative measures of welfare and well-being.
- Reduce, rather than reward, financial speculations, exorbitant profits, and stock market gambling.
More information: Listen to an interview with Brian Fath on WCBN Radio.
References
Jørgensen SE, Fath BD, Nielsen SN, Pulselli F, Fiscus D, Bastianoni S. 2015. Flourishing Within Limits to Growth: Following nature’s way. Earthscan Publisher.
Meadows, DH, Meadows, DL, Randers J., Behrens, W.H. III, (1972) Limits to Growth, New York: New American Library.
Note: This article gives the views of the author, and not the position of the Nexus blog, nor of the International Institute for Applied Systems Analysis.
Jan 19, 2015 | Energy & Climate
By Armon Rezai, Vienna University of Economics and Business Administration and IIASA,
and Rick van der Ploeg, University of Oxford, U.K., University Amsterdam and CEPR
The biggest externality on the planet is the failure of markets to price carbon emissions appropriately (Stern, 2007). This leads to excessive fossil fuel use which induces global warming and all the economic costs that go with it. Governments should cease the moment of plummeting oil prices and set a price of carbon equal to the optimal social cost of carbon (SCC), where the SCC is the present discounted value of all future production losses from the global warming induced by emitting one extra ton of carbon (e.g., Foley et al., 2013; Nordhaus, 2014). Our calculations suggest a price of $15 per ton of emitted CO2 or 13 cents per gallon gasoline. This price can be either implemented with a global tax on carbon emissions or with competitive markets for tradable emission rights and, in the absence of second-best issues, must be the same throughout the globe.
The most prominent integrated assessment model of climate and the economy is DICE (Nordhaus, 2008; 2014). Such models can be used to calculate the optimal level and time path for the price of carbon. Alas, most people including policy makers and economists view these integrated assessment models as a “black box” and consequently the resulting prescriptions for the carbon price are hard to understand and communicate to policymakers.
© Cta88 | Dreamstime.com
New rule for the global carbon price
This is why we propose a simple rule for the global carbon price, which can be calculated on the back of the envelope and approximates the correct optimal carbon price very accurately. Furthermore, this rule is robust, transparent, and easy to understand and implement. The rule depends on geophysical factors, such as dissipation rates of atmospheric carbon into oceanic sinks, and economic parameters, such as the long-run growth rate of productivity and the societal rates of time impatience and intergenerational inequality aversion. Our rule is based on the following premises.
- First, the carbon cycle dynamics are much more sluggish than the process of growth convergence. This allows us to base our calculations on trend growth rates.
- Second, a fifth of carbon emission stays permanently in the atmosphere and of the remainder 60 percent is absorbed by the oceans and the earth’s surface within a year and the rest has a half-time of three hundred years. After 3 decades half of carbon has left the atmosphere. Emitting one ton of carbon thus implies that is left in the atmosphere after t years.
- Third, marginal climate damages are roughly 2.38 percent of world GDP per trillion tons of extra carbon in the atmosphere. These figures come from Golosov et al. (2014) and are based on DICE. It assumes that doubling the stock of atmospheric carbon yields a rise in global mean temperature of 3 degrees Celsius. Hence, the within-period damage of one ton of carbon after t years is
- Fourth, the SCC is the discounted sum of all future within-period damages. The interest rate to discount these damages r follows from the Keyes-Ramsey rule as the rate of time impatience r plus the coefficient of relative intergenerational inequality aversion (IIA) times the per-capita growth rate in living standards g. Growth in living standards thus leads to wealthier future generations that require a higher interest rate, especially if IIA is large, because current generations are then less prepared to sacrifice current consumption.
- Fifth, it takes a long time to warm up the earth. We suppose that the average lag between global mean temperature and the stock of atmospheric carbon is 40 years.
We thus get the following back-of-the-envelope rule for the optimal SCC and price of carbon:
where r = ρ+ (IIA-1)x g. Here the term in the first set of round brackets is the present discounted value of all future within-period damages resulting from emitting one ton of carbon and the term in the second set of round brackets is the attenuation in the SCC due to the lag between the change in temperature and the change in the stock of atmospheric carbon.
Policy insights from the new rule
This rule gives the following policy insights:
- The global price of carbon is high if welfare of future generations is not discounted much.
- Higher growth in living standards g boosts the interest rate and thus depresses the optimal global carbon price if IIA > 1. As future generations are better off, current generations are less prepared to make sacrifices to combat global warming. However, with IIA < 1, growth in living standards boosts the price of carbon.
- Higher IIA implies that current generations are less prepared to temper future climate damages if there is growth in living standards and thus the optimal global price of carbon is lower.
- The lag between temperature and atmospheric carbon and decay of atmospheric carbon depresses the price of carbon (the term in the second pair of brackets).
- The optimal price of carbon rises in proportion with world GDP which in 2014 totalled 76 trillion USD.
The rule is easy to extend to allow for marginal damages reacting less than proportionally to world GDP (Rezai and van der Ploeg, 2014). For example, additive instead of multiplicative damages resulting from global warming gives a lower initial price of carbon, especially if economic growth is high, and a completely flat time path for the price of carbon. In general, the lower elasticity of climate damages with respect to GDP, the flatter the time path of the carbon price.
Calculating the optimal price of carbon following the new rule
Our benchmark set of parameters for our rule is to suppose trend growth in living standards of 2 percent per annum and a degree of intergenerational aversion of 2, and to not discount the welfare of future generations at all (g = 2%, IIA = 2, r = 0). This gives an optimal price of carbon of $55 per ton of emitted carbon, $15 per ton of emitted CO2, or 13 cents per gallon gasoline, which subsequently rises in line with world GDP at a rate of 2 percent per annum.
Leaving ethical issues aside, our rule shows that discounting the welfare of future generations at 2 percent per annum (keeping g = 2% and IIA = 2) implies that the optimal global carbon price falls to $20 per ton of emitted carbon, $5.5 per ton of emitted CO2, or 5 cents per gallon gasoline.
If society were to be more concerned with intergenerational inequality aversion and uses a higher IIA of 4 (keeping g = 2%, r = 0), current generations should sacrifice less current consumption to improve climate decades and centuries ahead. This is why our rule then indicates that the initial optimal carbon price falls to $10 per ton of carbon. Taking a lower IIA of one and a discount rate of 1.5% per annum as in Golosov et al. (2014) pushes up the initial price of carbon to $81 per ton emitted carbon.
A more pessimistic forecast of growth in living standards of 1 instead of 2 percent per annum (keeping IIA = 2, r = 0) boosts the initial price of carbon to $132 per ton of carbon, which subsequently grows at the rate of 1 percent per annum. To illustrate how accurate our back-of-the-envelope rule is, we road-test it in a sophisticated integrated assessment model of growth, savings, investment and climate change with endogenous transitions between fossil fuel and renewable energy and forward-looking dynamics associated with scarce fossil fuel (for details see Rezai and van der Ploeg, 2014). The figure below shows that our rule approximates optimal policy very well.
The table below also confirms that our rule also predicts the optimal timing of energy transitions and the optimal amount of fossil fuel to be left unexploited in the earth very accurately. Business as usual leads to unacceptable degrees of global warming (4 degrees Celsius), since much more carbon is burnt (1640 Giga tons of carbon) than in the first best (955 GtC) or under our simple rule (960 GtC). Our rule also accurately predicts by how much the transition to the carbon-free era is brought forward (by about 18 years). No wonder our rule yields almost the same welfare gain as the first best while business as usual leads to significant welfare losses (3% of world GDP).
Transition times and carbon budget
|
|
Fossil fuel Only |
Renewable Only |
Carbon used |
maximum temperature |
Welfare loss |
| IIA=2 |
First best |
2010-2060 |
2061 – |
955 GtC |
3.1 °C |
0% |
| Business as usual |
2010-2078 |
2079 – |
1640 GtC |
4.0 °C |
– 3% |
| Simple rule |
2010-2061 |
2062 – |
960 GtC |
3.1 °C |
– 0.001% |
Recent findings in the IPCC’s fifth assessment report support our findings. While it is not possible to translate their estimates of the social cost of carbon into our model in a straight-forward manner, scenarios with similar levels of global warming yield similar time profiles for the price of carbon.
Our rule for the global price of carbon is easy to extend for growth damages of global warming (Dell et al., 2012). This pushes up the carbon tax and brings forward the carbon-free era to 2044, curbs the total carbon budget (to 452 GtC) and the maximum temperature (to 2.3 degrees Celsius). Allowing for prudence in face of growth uncertainty also induces a marginally more ambitious climate policy, but rather less so. On the other hand, additive damages leads to a laxer climate policy with a much bigger carbon budget (1600 GtC) and abandoning fossil fuel much later (2077).
In sum, our back-of-the-envelope rule for the optimal global price of carbon and gives an accurate prediction of the optimal carbon tax. It highlights the importance of economic primitives, such as the trend growth rate of GDP, for climate policy. We hope that as the rule is easy to understand and communicate, it might also be easier to implement.
References
Dell, Melissa, Jones, B. and B. Olken (2012). Temperature shocks and economic growth: Evidence from the last half century, American Economic Journal: Macroeconomics 4, 66-95.
Foley, Duncan, Rezai, A. and L. Taylor (2013). The social cost of carbon emissions. Economics Letters 121, 90-97.
Golosov, M., J. Hassler, P. Krusell and (2014). Optimal taxes on fossil fuel in general equilibrium, Econometrica, 82, 1, 41-88.
Nordhaus, William (2008). A Question of Balance: Economic Models of Climate Change, Yale University Press, New Haven, Connecticut.
Nordhaus, William (2014). Estimates of the social cost of carbon: concepts and results from the DICE-2013R model and alternative approaches, Journal of the Association of Environmental and Resource Economists, 1, 273-312.
Rezai, Armon and Frederick van der Ploeg (2014). Intergenerational Inequality Aversion, Growth and the Role of Damages: Occam’s Rule for the Global Carbon Tax, Discussion Paper 10292, CEPR, London.
Stern, Nicholas (2007). The Economics of Climate Change: The Stern Review, Cambridge University Press, Cambridge.
Note: This article gives the views of the authors, and not the position of the Nexus blog, nor of the International Institute for Applied Systems Analysis.
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