When discussing climate change, we have frequently found it useful to bring up a 2005 paper by Richard Tol, one of the most frequently cited economists who writes in the peer reviewed literature on climate change. In that paper, Tol reviews 28 published studies on the marginal damage costs associated with climate change. Those studies — generated by 18 independent teams of scholars — produced a total of 103 estimates. The median estimate for the cost of emitting a ton of carbon in those studies is $26. The mean estimate is $97 per ton. The modal estimate is $6 per ton (all numbers rounded to the nearest dollar).

Because the 103 estimates come from only 28 studies and are therefore not really 103 independent estimates, Tol produces weighted estimates of the mean, mode, and median that proportionately reduce the weight given to multiple estimates from a given study. If a study produces one estimate of the mean, it gets a weight of one. If a study has seven estimates of the mean, they each get a weight of one seventh. Calculated this way, the median estimate for the cost of emitting a ton of carbon in those studies is $14. The mean estimate is $93 per ton. And the modal estimate is $2 per ton (all numbers rounded to the nearest dollar).

Tol then calculates estimates that vary the weight of each study along several subjective dimensions. Was the study peer reviewed? Was the study based on an independent impact assessment of climate change? Did the study rely on dynamic climate change scenarios? Was the study based on explicit economic scenarios? Did the study estimate marginal damage costs rather than average costs? Each “yes” to the above questions earned the study one point (meaning a 5-point study was given proportionally more weight than a 1-point study). He then gave each study an additional 0.1 point for each year in which the study was published since 1990, thus giving more weight to newer rather than older studies.

The median cost estimate for carbon emissions in Tol’s quality-weighted data set is $16 per ton ($2 more than without quality weights). The mean estimate is $129 per ton ($36 more than without quality weights). The modal estimate remains at $2 per ton.

When Tol eliminated the studies that weren’t peer reviewed, the median quality-weighted cost estimate fell to $14 per ton, the mean to $50 per ton, and the mode increased to $5 per ton.

The large difference between the mean and median estimates as well as the low modal estimate highlight the large variation in the carbon-cost estimates as well as a large “right-tail” in the distribution. That variation is explained for the most part by (1) the discount rate applied to future costs and benefits, and (2) the manner in which monetarized costs were aggregated across countries. That is, it’s not so much that study x found high costs because the authors of study x concluded that sea level rise would be more economically devastating than, say, study z. It’s that study x used a 1% discount rate for those future sea-level-rise costs while study z used, say, a 3% discount rate. And study x weighted damages in poorer countries more than in wealthier countries.

Tol reports that, if he removes those studies engaged in “equity weighting” from the dataset, median carbon emissions costs are $10 per ton. Mean costs are $90 per ton. Modal costs are $2 per ton. And when he removes studies from the dataset using a 1% or lower discount rate, he found that median carbon emissions costs were $7 per ton, mean $16 per ton, and mode $2 per ton.

“If we take all studies without discriminating between them, the best guess for the marginal damage costs of carbon dioxide emissions is $5 per ton,” writes Tol, but “there are good reasons to discriminate between studies … it appears that studies with better methods yield lower estimates with smaller uncertainties than do studies with worse methods. If one excludes the studies in the gray literature, the combined marginal damage cost estimate falls further, and so does its uncertainty. It seems as if the most pessimistic estimates of climate change impacts do not withstand a quality test.”

Given that, what’s the “best” guess available from the literature published through 2004? When asked that question by Danish statistician Bjorn Lomborg, the answer he gave was $2 a ton (an answer reported in Lomborg’s book *Cool It*). $2 a ton is the most frequent value in the data, or mode. Because environmentalists worship at the alter of “consensus” when discussing the science of climate change, a similar emphasis on a show of hands in the economics professions suggests a modal — not a mean or median — calculation. Hence, we have been comfortable using Tol’s $2 per ton figure when discussing what the economics literature has to say about the cost of carbon emissions.

In a recent on-line debate with Joe Romm, however, Tol’s 2005 review of the literature was dismissed by Joe because it was old and has been superseded by more recent work; in particular, the IPCC’s 4th assessment on climate change (published last year) and the Stern Review on the economics of climate change(released in 2006). More importantly, Tol updated his literature review last August — of which we were unaware — and, according to one blogger, “Taylor’s quoting of old numbers that Tol has himself moved away from looks like cherry-picking and in any case will not convince anyone who has moved on from 2004.”

So what does Tol report now?

Well, it’s certainly true that the literature has expanded a bit. Nineteen studies have been published since Tol’s 2005 paper and, as a consequence, there are now 108 new marginal cost estimates to consider. Yet this explosion of published work is somewhat misleading given that all of those studies are based upon only 12 underlying papers estimating the total costs of climate change, and only two of those studies were published since Tol’s 2005 survey of the literature. The (raw unweighted) median estimate for the cost of emitting a ton of carbon from the 211 estimates in those studies is $29. The mean is $105 per ton. And the mode is $6 per ton (all numbers rounded to the nearest dollar). Those numbers are remarkably similar to the raw 2005 estimates of $26, $97, and $6 respectively.

If one thinks of the 211 estimates as a sample of data drawn from an unobserved population, what type of population is it? Is it normally distributed or something else? In his 2005 paper, Tol assumed normality. In his 2008 paper, Tol now considers three possible distributions: the normal distribution; the normal distribution with normalized standard deviations (standard deviation divided by the mean, which is also called coefficient of variation), and Fisher-Tippett (which, unlike the normal distribution, is skewed right). Given the right skew to the 2005 data (mean>median>mode), this would seem to be an obvious addition.

Table 1 summarizes the median, mean, mode, and standard deviation findings for each of these three probability density functions after Tol’s 2005 quality-weights are applied to the 2008 data set. Standard deviations are also offered. Findings are then further subdivided based on discount rate, peer review, and publication date.

Some observations about Table 1.

First, the widely-held belief that recent studies argue that the costs of climate change will be higher than previously thought — an argument presented in the most recent IPCC report and by Joe Romm in our recent on-line exchange — is incorrect with one exception. That is the mode, median, and mean estimates of costs are highest in the oldest studies and lowest in the most recent studies. The one exception is the median estimate in the normal distribution using the coefficient of variation, which increases with time from $14 a ton to $16 and $17, but that change is very small.

Second, some of Tol’s 2008 estimates are larger than his 2005 cost estimates and some are not. Recall that Tol’s quality-weighted 2005 median, mean, and mode findings were $16, $129, and $2 per ton respectively. His 2008 cost estimate using the normal distribution (coefficient of variation) is lower: $15, $102, and $0 per ton respectively. The 2008 estimates using normal distribution (standard deviation) and Fisher-Tippett have higher medians, lower means, and higher modes: $47, $88, and $33 and $74, $127 and $35, respectively.

Third, just as in 2005, the “better” (peer reviewed) studies in the literature produce lower cost estimates relative to non peer reviewed studies with the exception of the mode in the normal (coefficient of variation), which rises from $0 to $3.

Fourth, just as in 2005, large cost estimates flow from low discount rates (pure rate of time preference) and low cost estimates flow from higher rates of pure time preference.

The contention that Tol has “moved away” from his 2005 numbers is literally true. The most important difference between Tol 2008 and Tol 2005 is that Tol 2008 considers three probability density functions rather than the one employed in Tol 2005. Two of those three probability density functions report more varied (higher and lower) cost estimates than those reported in Tol 2005.

Tol argues in his 2008 paper that the social cost of carbon emissions is positive, that there is so much uncertainty regarding costs that “a considerable risk premium is warranted,” and that, consequently, “greenhouse gas emission reduction today is justified.” Those declarations did not appear in his 2005 paper, but they are not inconsistent with the findings of that paper. There is a difference, of course, between a discussion about the social cost of carbon emissions and a discussion about appropriate carbon taxes. The former informs but does not dictate the latter. Tol 2005 discussed only the former. Tol 2008 discusses primarily the former but briefly touches on the latter as well.

Regardless, one can embrace the findings of Tol’s meta-analysis without embracing Tol’s interpretation of how best to translate that meta-analysis into public policy. The literature suggests that the social cost of carbon emissions is likely positive, but that alone does not justify a carbon tax. If the social cost is only a few dollars a ton, the political and economic transaction costs associated with imposing a carbon tax would likely exceed the benefits. Moreover, there may be less expensive ways of reducing harm than imposing carbon taxes or emission trading regimes. Uncertainties there may be, but if we discount the future by 3 percent annually (a discount rate that seems appropriate given opportunity costs), the high-cost scenarios that so heavily weight these analyses vanish into thin air. That’s because most of the damages associated with climate change will occur many decades in the future and even small differences regarding the economic impact of those damages produces highly variant estimates. Discount the future, however, and the (economic) importance of those disagreements all but disappears.

So what does Tol 2008 tell us about the social cost of carbon emissions (assuming that the underlying science from the IPCC is correct)? Given our skepticism about the underlying logic of discount rates of 1% or less, any number between $3 per ton and $24 per ton seems defensible. The lower end of that distribution would seem to be more reasonable, however, keeping in mind that the better and more recent studies produce lower cost estimates than do others.