A Case of Reverse Causation?

Tomorrow’s Emission Determine Today’s Social Cost of Carbon

Here’s the weird thing: the social cost of carbon today, depends significantly on the year-by-year emissions of carbon in the future, which we obviously don’t know. (Because it depends on our own future actions!)  It takes some explanation to show why that’s true and how it matters.

If you know a bit about climate policy, you know that the SCC — the social cost of carbon — is the amount of harm done by adding an additional ton of CO2 to the atmosphere. You also know that actually putting a number on the SCC is really hard because of scientific uncertainties about the severity of harm and parameters that economists either don’t know at all or can’t agree on. But the idea itself seems simple.

Actually, things turn out to be more complicated.  That extra ton of carbon is going to be in the atmosphere a long time — centuries, essentially — and so we need to know how much harm it is going to each moment for the entire time. Basically, the temperature increase in proportion to emissions, so the effect of each ton on temperature is effectively a constant.  So far, so good.

But — and this is an important “but” — the harmful effects of climate change aren’t proportional to the temperature change.  For example, in one of the leading models, the harmful effects are  driven by the square of the temperature change. Models vary, but they all view the relationship between temperature and cost as non-linear (and upward curving, for that matter).  What this means is that the harmful effect of an additional ton depends on how much carbon is also in the air  each moment that ton is in the atmosphere.  An extra ton causes very little harm at times when total carbon is low; much more harm when total carbon is high.

Remember that we want to trace how much harm our extra carbon causes over time.  But to do that, we need to know how much other carbon is already in the atmosphere at that future time.  And to do that we need to know the future trajectory of emissions.  That’s why the social cost of carbon is not an absolute; it’s relative to a future emissions trajectory.  Integrated Assessment Models (IAMs) pick emission scenarios when they are trying to determine the social cost of carbon, but they don’t bother to explain why.  So it can easily slip by the reader.

Maybe this is interesting, but why is it significant?  Here are a few reason:

1.  It introduces another element of uncertainty into calculations of the social cost of carbon, besides the uncertainties about climate impacts from the scientific side and the uncertainties about how those affect the economy from the economic side.

2.  It suggests that maybe early carbon emitters  should not be held responsible for climate change.  Even if they had known as much s we do about climate science, they might not have foreseen that atmospheric emissions would rise so much as to cause significant harm, at least not nearly so quickly.

3.  It requires some subtle revision in the standard idea that we should set an emissions tax equal to the marginal cost of the pollutant.  Before we impose a carbon tax, the social price of carbon will be one number.  But that’s not what we want to use as the carbon tax. After we impose a tax, the future emissions trajectory will shift and so will the social cost of carbon.  If we pick the right number, the carbon tax will indeed equal the new social cost of carbon, but not to the old one. The social cost of carbon is a product of the carbon tax, not vice versa.

There are a lot of other problems with figuring out the social cost of carbon, enough so that even some economists think we should take some other approach to setting carbon targets.  But this one is particularly interesting because it involves a fundamental aspect of the climate problem, its nonlinearity.

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Reader Comments

2 Replies to “A Case of Reverse Causation?”

  1. Dan, your article appears to relate surface temperature increases with harm, and with costs, but you offer nothing to explain those relations. Some people will appreciate increasing temperatures, others, not so much. Plants will thrive on increasing atmospheric CO2. You also mention “social costs,” which sounds like a really fuzzy concept, a political concept filled with subjectivity.

    You wrote that “the temperature increases in proportion to emissions, so the effect of each ton on temperature is effectively a constant.” Wow!! Probably not even 1 in 100 of those people who self-describe themselves as climate science experts would agree with you on that one.

    It is widely accepted (based on assumptions) that increasing amounts of carbon in the atmosphere will result in non-linear increases in surface temperatures, but the relationship is not known.

    IPCC Published reports, (TAR3), estimate or assume (no proof) that the effective temperature increase caused by growing concentrations of CO2 in the atmosphere (following a logarithmic relationship) diminishes with increasing concentrations. This information has been presented in the IPCC reports. (Chapter 6. Radiative Forcing of Climate Change: section 6.3.4 Total Well-Mixed Greenhouse Gas Forcing Estimate). This logarithmic function is the reason that increasing emissions will have decreasing impacts, even according to the IPCC.

    According to most “studies”:

    As the amount of man-made CO2 goes up, surface temperatures do not rise at the same rate. In fact, although estimates vary – climate sensitivity is a highly debated topic in climate science – the last IPCC report (AR4) described the likely range as between 2 and 4.5 degrees C, for double the amount of CO2 compared to pre-industrial levels.

    There is no agreement on climate sensitivity and if there was, that would call into question the integrity of those agreeing on something that has not and cannot be measured or tested. Theorize all you want, build models to express your theories. Run your models on supercomputers to the extent you can afford (please don’t use tax dollars). But don’t confuse the theory with reality.

    So far, the average global temperature (whatever that means, since that cannot be measured) has gone up by about 0.8 degrees C (1.4 F), since 1880, according to the IPCC. Which is nowhere near the climate sensitivity now predicted by the IPCC. There has been (according to IPCC) roughly a 42% increase in CO2 in the atmosphere since 1880, and that would produce a linear-response increase (your statement) in atmospheric temperature so that global mean temperatures would now be over 270 deg. F, too hot for human survival outdoors.

    All human life not protected by massive cooling systems has not perished.

    The important thing to remember is that climate science is full of uncertainties and that the models are all based on assumptions that have not been – and cannot be – tested and verified. The earth is not a closed experiment.

    The truth is that the future of climate change cannot be predicted, because that future has yet to be determined. The fact that some people want to choose a preferred prediction, and then pass laws to coercively alter the way we all live based on their prediction, is frightening.

    There is no rational basis for assuming that climate change can be predicted , let alone that it can be controlled and regulated by men and women with guns. Ultimately, that is the only power that governments have, the power to coerce, with violence and threats of violence.

    Why on earth would anyone want to surrender their freedom to false science-driven fascists? And why on earth would anyone trust a scientist who trusts politicians to make intelligent choices on behalf of everyone else?

    When climate change comes as it inevitably will, since it always has (there is no climate equilibrium!), thinking human beings who are free to take risks and to adapt to changing conditions, will be the best resource for coping with that change, as they are always coping with any other change. Human and climate futures are unpredictable.

    Live free, and prosper.

  2. There’s another nonlinearity – the temperature increase is proportional not to the CO2e concentration, but to its logarithm. Each doubling of CO2e concentration in the atmosphere is expected to produce a temperature increase of around 1.5 degrees Celsius. See http://earthguide.ucsd.edu/virtualmuseum/rotary/global_warming/03.shtml. This means that the emission of a tonne of GHG causes twice as much harm when the concentration is 300 ppm than when it is 600 ppm. In a sense, as the problem gets worse, the SCC per emitted tonne goes down.

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About Dan

Dan Farber

Dan Farber has written and taught on environmental and constitutional law as well as about contracts, jurisprudence and legislation. Currently at Berkeley Law, he has al…

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