Recently, the United States Environmental Protection Agency (EPA) increased its estimate for the net societal cost of an additional ton of carbon dioxide (CO2) that is released into the atmosphere to \$36 from \$22. One of the immediate effects was a change of energy standards for household appliances, for example microwave ovens. Other consequences are expected to follow, for example possibly in emission standards for automobiles and power plants, and in other regulations.
What exactly is the definition of the “social cost of carbon” (SCC)? Who is interested in determining this quantity? Who is interested in its value? Can this even be done and, if so, how accurately? And how is it done? Is there any mathematics in it?
The social cost of carbon is generally defined as the net economic damage (overall cost minus overall benefits, accumulated over time, and discounted) of a small additional amount of CO2 (a metric ton, 1,000 kg, produced by burning about 440 liters of gasoline) that has been released into the atmosphere. Mathematically, it’s a rate of change; economically, it’s a marginal cost. Economists have been trying to determine this in order to estimate the cost of mitigation of climate change: In an ideal situation, the cost of mitigating the effects of an additional ton of CO2 in current dollars should be equal to the SCC, and if a tax were assessed on releasing CO2, it should equal the SCC.
Concretely, suppose a new regulation is proposed with the goal of reducing greenhouse gas emissions. Implementing the regulation will cost money. If the expected cost exceeds the SCC, it is unlikely to be enacted, at least in the US and in the EU. Regulators have to include a cost-benefit analysis, and the new regulation will come up short. Therefore, the SCC furnishes an immediate connection between climate science and climate policy. It’s one way to “monetize” the results of anthropogenic climate change. Since a higher SCC is expected to make regulations easier, it will generate resistance from groups that are opposed to regulation.
It is very difficult to obtain a reasonable number for the SCC. Clearly, climate science models that connect the release of greenhouse gases to climate changes must be used (and that’s where mathematics comes in, but it’s not the only place). But there are many additional input variables that influence it. Climate system variables include the overall climate sensitivity to CO2 emissions, the extent to which a climate model can predict abrupt climate changes, and the level of geographic detail in the model. Higher climate sensitivity, the inclusion of abrupt changes, and more details all tend to increase the SCC. There are also economic variables and model details that influence SCC, such as the discount rate (used to turn future costs into present day costs), the economic value placed on the quality of human life and ecosystems, the capacity of a society to adapt to changes in climate conditions, and the extent to which indirect costs of climate change are incorporated. A lower discount rate (meaning a long-term view into the future), high economic valuation of ecosystems, and detailed inclusion of indirect costs will all increase the SCC. In addition, the SCC is generally expected to increase in the future as economies become more stressed due to results of previous climate change. A ton of CO2 that is released in 2030 will be more expensive. Current models used by the United States EPA try to assess costs up to the year 2300 – which may be longer than the time horizon of many climate models that are currently being used.
It is perhaps no surprise that all SCC calculations end up with a range of numbers, rather than with a fixed value, and that these ranges vary widely. In fact, there are low estimates of an SCC of -\$2 (that is, a small net benefit of increased CO2 emissions) and high estimates of \$200 or more. Generally, research in this important area lags behind the state-of-the-art of physical climate models, mainly due to the additional economic components that have to be included.
I mentioned that the mathematical connection comes from climate models which are used to make predictions. But there is a broader, more general connection. Using models that include physical, social, and economic factors, all with their own uncertainties, presents new challenges to the emerging mathematical field of uncertainty quantification. Perhaps over time mathematics can contribute to improving the methods by which the SCC is computed.