Thursday, June 18, 2009

Costs multiply

A post from last month at Climate Progress points us to a new MIT study in the Journal of Climate, which makes a frightening median projection of 5.2 degrees Celsius (9.4 degrees Fahrenheit) warming by 2100, along with a 5% chance of warming greater than 7.4 degrees Celsius (13.3 degrees Fahrenheit). The research program's website makes a critical point in its explanation of the results:
There is no single revision that is responsible for this change. In our more recent global model simulatations, the ocean heat-uptake is slower than previously estimated, the ocean uptake of carbon is weaker, feedbacks from the land system as temperature rises are stronger, cumulative emissions of greenhouse gases over the century are higher, and offsetting cooling from aerosol emissions is lower. No one of these effects is very strong on its own, and even adding each separately together would not fully explain the higher temperatures. Rather than interacting additively, these different affects appear to interact multiplicatively, with feedbacks among the contributing factors, leading to the surprisingly large increase in the chance of much higher temperatures.
By interacting multiplicatively, even small errors in several parts of a climate model can combine to produce massive swings in the final result. And it doesn't stop there: these uncertainties in climate modeling then interact multiplicatively with uncertainties in economic modeling, producing even larger swings in the estimated cost of global warming. As I explained in a post on the topic a little less than a year ago, the results can be overwhelming:
When considering the implications of the three concerns I have raised, one question is particularly important to keep in mind. What happens if the concerns are simultaneously valid—if the Nordhaus/Manzi damage estimates are biased down by more than one of the weaknesses I mention? To a first approximation, they multiply. This means that if the failure to analyze extreme uncertainty, the high discount rates, and the crude worldwide aggregation of damages present in Nordhaus's model each lower the optimum carbon tax by a factor of two, a better estimate would have a starting carbon tax approximately eight times as high. Since Nordhaus's "optimal policy ramp" starts with a tax of $7.40 per ton of carbon dioxide, such a recalculation would bring us to almost $60 per ton, which is close to what many carbon tax advocates suggest. More interestingly, if each of the above failures causes a miscalculation by a factor of three, the total estimate may be off by twenty-seven. This brings us to a very high carbon tax of $200.
Unfortunately, these costs are all too plausible. At the very minimum, I think that the failure to appreciate the uncertainty in our models deflates our cost estimates by a factor of four, unreasonably high discount rates lower them by a factor of two, and using aggregate world GDP rather than country-by-country modeling also lowers them by a factor of two. This already means that we're off by approximately a factor of 16—so while economist William Nordhaus's models of climate change suggest an optimal carbon tax of $7.40 per ton, a more appropriate level is at least $120.

And I'm not exaggerating when I say "at a minimum": these are incredibly conservative estimates for the gap between analyses like Nordhaus's and more complete models that throw away the false certainties and simplifications. If you have any doubt about the effect of "fat-tailed" uncertainty on the costs of climate change, you should read Martin Weitzman's brilliant analysis of the problem. Meanwhile, the effects of even small changes in the discount rate are mathematically inevitable: the difference between damages 100 years from now discounted by 2% and discounted by 3.1% is already a factor of three.

The moral? Don't let artificially low, "rigorous" estimates of the costs of climate change lull you into complacency. As I've said before, if superficially valid estimates defy all reasonable intuition, you ought to see whether there's a problem with the underlying analysis. When global warming threatens to move average temperatures more than our transition out of the Ice Age, melting the ice caps and disrupting climates throughout the world, there's probably something wrong with any calculation that the optimal policy is to nudge up the price of coal power by less than a cent per kilowatt-hour.

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