Economists, regulators, and activists all try to calculate the social cost of carbon—that is, the economic and ecological damage caused each time we add a ton of carbon dioxide to the atmosphere by burning fossil fuels. If we know how much harm each additional ton of carbon dioxide causes, the thinking goes, regulators can offset the effects by putting a price on in it, in the form of taxes or regulations. Unfortunately, they calculate that price using dubious computer models. The results are an example of an old programming adage: garbage in, garbage out.

Consider the White House Interagency Working Group, which in May issued a technical document aiming to calculate carbon's costs. To estimate the monetary value of the damages caused by carbon emissions, the group focused such things as projected changes in net agricultural productivity, human health, flood damage, and ecosystem services due to climate change.

To get this figure, the Working Group ran three different integrated assessment computer models (IAMs) that combine climate science models with econometric models. The models were each run with various discount rates to obtain a range of estimates for the social cost of carbon. Discount rates recognize the fact that a dollar today is worth more than a dollar tomorrow, a year from now, or a hundred years from now. (How much interest would you require to put off getting a dollar for 10 years? Congratulations: You've just estimated a discount rate.) Many analysts believe the discount rate should be inferred from market rates of return, since spending today to reduce greenhouse gas emissions will be financed out of current consumption, just like any other investment.

The Working Group cranked the IAMs with discount rates of 2.5, 3, and 5 percent, and it also supplied a high-end estimate to account for possible higher-than-expected impacts of future climate change. Interestingly, the Working Group evidently ignored the Office of Management and Budget (OMB) directive that 3 and 7 percent discount rates should be generally applied to determining the costs and benefits of regulatory decisions and that the outputs should be confined to domestic impacts. The 7 percent rate is an estimate of the average before-tax rate of return to private capital in the U.S. economy, and the 3 percent rate is real rate of return on long-term government debt.

In any case, the White House group's new estimates for the social cost of carbon in 2020 are $12, $43, and $65 per ton of carbon dioxide in 2007 dollars (at the 5, 3, and 2.5 percent discount rates, respectively). The Working Group derived a high-end figure of $129 per ton in 2020 by looking at the worst 5 percent of the distribution of possible damages using a 3 percent discount rate. The corresponding figures for 2050 are $27, $71, $98, and $221 per ton.

Can regulators, companies, and consumers take these figures to the bank? I'm afraid not.

In an incisive new study, Massachusetts Institute of Technology economist Robert Pindyck rips the social cost of carbon estimates derived from integrated assessment computer models to pieces. In his National Bureau of Economic Research working paper, "Climate Change Policy: What Do the Models Tell Us?," Pindyck concludes that the models all "have crucial flaws that make them close to useless as tools for policy analysis: certain inputs such as the discount rate are arbitrary, but have huge effects on the social cost of carbon estimates that models produce." Pindyck adds that the "models' descriptions of the impact of climate change are completely ad hoc, with no theoretical or empirical foundation; and the models can tell us nothing about the most important driver of the social cost of carbon, the possibility of a catastrophic climate outcome."

Pindyck is clearly right with regard to how choosing the discount rate affects estimates for the social cost of carbon. By tweaking the rate, the Working Group reported estimates for 2020 ranging from a low of $12 to $65 per ton – a fivefold difference. As Institute for Energy Research economist Robert Murphy testified before the Senate Environment and Public Works Committee in July, had the Working Group applied the 7 percent discount rate as part of its cost-benefit analysis, as required by the OMB, the estimate for the social cost of carbon would have been negligible. Murphy also noted that the OMB requires cost/benefit analysis to be reported in terms of domestic impacts, with global impacts being optional. The Working Group reported estimates using global figures only. Using the Working Group's own data, Murphy reckons that the domestic social cost of carbon could be as low as $2 per ton.

Pindyck points out the inputs for the IAMs must include projections of future carbon dioxide emissions, the amount of carbon released per dollar of GDP, future concentrations of greenhouse gases in the atmosphere, average global temperature changes, changes in rainfall, hurricane frequency, sea level, economic losses due to higher temperatures, costs of abating carbon dioxide emissions, and make assumptions about the discount rate. All of these parameters can be modified to conform to the views of the modelers. "Thus these models can be used to obtain almost any result one desires," writes Pindyck.

Let's look at a couple of his examples, climate sensitivity and how future damages are calculated. Climate sensitivity is defined how much temperature would increase from doubling the amount of carbon dioxide over pre-industrial levels in the atmosphere. As Pindyck points out, climate scientists have not yet succeeded in nailing down this number. In its 2007 Fourth Assessment Report the Intergovernmental Panel on Climate Change estimated that climate sensitivity was between 2°C and 4.5°C, with 3°C the most probable figure. Yet more recent studies are reporting values that are significantly lower. Lower climate sensitivity suggests that humanity has more time to develop low- and no-carbon energy technologies as a way to avoid harmful man-made global warming. In any case, modelers can pick among lots of different estimates of how much and how fast future warming is likely to be. Higher warming estimates mean a higher social cost of carbon, and vice versa.

The models also try to estimate how much various increased temperatures would reduce future GDP. But Pindyck points out that no economic theory underlies such estimates; there is just not much in the way of data correlating temperature changes with economic output. Consequently, modelers use "guesswork" to come up with plausible values as damage function inputs. "The bottom line here is that the damage functions used in most IAMs are completely made up, with no theoretical or empirical foundation," asserts. Pindyck He argues that model-based "analyses of climate policy create a perception of knowledge and precision, but that perception is illusory and misleading."

As hard as he is on the delusions of precision promised by the computer models, Pindyck does not want to just throw up his hands when it comes to addressing problems caused by man-made climate change. The best we can do, he argues, is to sketch out "a plausible range of catastrophic outcomes" and then calculate how much it would cost now to avert those outcomes. He admits that "'plausible' would mean acceptable to a range of economists and climate scientists."

Because catastrophic climate change cannot be ruled out, Pindyck favors imposing a carbon tax that is roughly equal to the social costs of carbon concocted by the Working Group. "This," he argues, "would help establish that there is a social cost of carbon, and that social cost must be internalized in the prices consumers and firms pay."

Pindyck makes a devastating argument that recent estimates of the social cost of carbon amount to garbage. But his suggestion that we count on the fever dreams of smart economists and climate scientists to formulate global warming policy doesn't seem all that plausible either.