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Refuting the Case for a CO2 Tax: William Nordhaus’s “DICE Model” Reconsidered

By Robert Murphy -- October 19, 2009

Editor Note: Robert Murphy’s peer-reviewed article in The Independent Review, “Rolling the DICE: William Nordhaus’ Dubious Case for a Carbon Tax”, is available online [.pdf].

When I first began working for the Institute for Energy Research, my preliminary research indicated that William Nordhaus (now a co-author of Paul Samuelson’s famous economics textbook) was a great representative of the mainstream case for a Pigovian carbon tax. I have gone on to study his case, presented in articles and a book, in great detail. What I have found is an eager willingness to spot “market failure” coupled with a naive faith in government “solutions.” The full article deals with these big picture issues, but this post will dwell on the narrow technical results–using Nordhaus’s own numbers–that should give average economists pause when it comes to the typical recommendation of a carbon tax to “internalize the externality” of greenhouse gas emissions.

Most Damages Come From Ill-Specified “Catastrophic” Outcomes. In Nordhaus’s DICE model [Dynamic Integrated Model of Climate and the Economy], he relies on a simplified model of the global climate system and economy, calibrated to the latest numbers put out by the IPCC and other groups. The model can then simulate the climate damage impacts of a marginal ton of emissions on human welfare, allowing Nordhaus to derive the “optimal carbon tax.”

When I delved into the numbers behind Nordhaus’s damage function–which related a given increase in global temperatures to a percentage loss of global GDP–I was quite surprised. The DICE model (at least as of the time I wrote the paper) assumed that a warming of 2.5C would yield a loss of 1.5% of global GDP, averaged across various sectors. For example, the agricultural sector (worldwide) would contribute to a 0.13% reduction in global GDP, the toll on coastal regions would yield another 0.32% of GDP in damages, and so forth.

The single biggest contributor, however, was a 1.02% GDP loss attributed to a “catastrophic impact.” (See Table 2 on page 209 of my paper, hyperlinked above.) So to repeat, Nordhaus’s optimal carbon tax was based on a damage function that said 2.5C of warming would yield 1.50% GDP losses, and 1.02% was due to a “catastrophic impact.”

Now this in itself is a bit disturbing, since the lion’s share of Nordaus’s recommended tax is coming from the nebulous “catastrophic impact” category. In other words, it would be one thing if careful, sectoral studies assessed the likely impact from various amounts of warming, and then Nordhaus rounded up the final number because of the “kicker” of ill-defined catastrophic impacts. But that’s not what happened–fully 68% of Nordhaus’s damage function (calibrated at the 2.5C warming level) results from this one category of impacts.

What’s even more disturbing is the way in which Nordhaus got this figure. It’s too involved to reproduce the whole account here, but I encourage the interested reader to look at pages 206-208 in the journal article for the full story. Here is the summary of the episode I gave in the article:

Nordhaus in 1994 asked experts to estimate (among other things) the probability of global GDP loss of 25 percent in the event of 3.0C warming…The surveyed experts gave him their answers, from which he computed the mean. By 1999, further research had made these scenarios seem more plausible or catastrophic. So Nordhaus and Boyer took the original average of probabilities reported by the experts, doubled it, and then assigned this new figure as the probability for a 30 percent loss of GDP rather than the 25 percent the experts had been told to consider, for a less significant warming of 2.5C rather than the 3.0C mentioned in the original survey. More recent research suggests that at least some of these catastrophic scenarios were false alarms. [Emphasis in original, footnotes and citations removed.]

Before leaving this section, I want to clarify that I’m not accusing Nordhaus of academic dishonesty. I believe part of the reason for the changes described above, was that it was more convenient to fit into his model. (For example, the IPCC’s best guess for the warming from a doubling of CO2-eq. concentrations fell from 3C when Nordhaus originally conducted the survey down to 2.5C when he was re-calibrating his model, so it’s not suprising that he took the experts’ original answers and applied them to the less-severe warming scenario.)

Yet since so much of Nordhaus’s empirical case for a carbon tax rests on the probabilistic damage from an unlikely-but-catastrophic scenario, I think it’s very important for economists to realize the tenuous foundation of those huge estimates of GDP losses.

The Wrong Climate Target Could Be Much Worse Than Doing Nothing. The other finding I want to highlight is that Nordhaus’s own simulations show the extreme danger in trusting politicians to dabble in carbon legislation. It’s true, a theoretically optimal carbon tax–one that is consistently implemented by all governments around the world, and that updates its magnitude to reflect the changing “social cost of carbon” over the years–would, in Nordhaus’s simulation, yield net benefits of some $3 trillion (in present-discounted value terms). The optimal carbon tax saddles the economy with about $2 trillion in compliance costs, but this downside is more than compensated by the reduction of about $5 trillion of expected future climate damages. Thus, on net Nordhaus’s model shows a perfect carbon tax making the world $3 trillion richer than it would otherwise be.

To his extreme credit, Nordhaus also simulated other policies. Since they deviate from the theoretically optimal policy (at least according to an economist’s criteria), these other policies obviously do not yield $3 trillion in net benefits. What should alarm economists, however, is that Nordhaus shows just how destructive some proposed policies would be, at least in the world of his DICE model.

The worst offender in this regard is Al Gore’s 2007 proposal to reduce CO2 emissions 90% by the year 2050. According to the DICE model, this extreme goal would yield benefits of a $12 trillion reduction in future climate damages. However, Gore’s plan would so cripple the economy that the world would suffer almost $34 trillion in compliance costs. (See Table 4 on page 211.) In other words, Nordhaus’s own model shows that Gore’s proposal would make the world $21 trillion poorer than if governments did nothing about climate change.

Conclusion. Even if we stipulate the natural science results in the IPCC, it does not follow that governments should implement interventions in the economy to reduce fossil fuel use as “a move in the right direction.” William Nordhaus is certainly no “denier” or “skeptic” when it comes to climate change and the case for government activism. Yet his own DICE model shows that the empirical case for a carbon tax is much more dubious than many economists realize. Once we consider the possibility that governments won’t implement the “optimal” tax as conceived by economists, I would argue that the case falls apart.


  1. Ed Reid  

    The International Energy Agency estimated in 2008 that the global investment required to reduce global annual emissions by 50% by 2050 would total approximately $45 trillion. It is reasonable to assume that those making the requisite investments would choose the most productive and least costly investments first. Therefore, it is also reasonable to assume that extending the global reductions from 50% to 83% would require the investment of at least an additional $30 trillion; and, more likely, an additional $45 trillion since the additional projects would be expected to be more difficult and expensive. Achieving a 99.95% reduction would likely require a global investment approaching $150 trillion. The global investment required to achieve “350” is currently incalculable and arguably inestimable.


  2. Tom Tanton  

    “I want to clarify that I’m not accusing Nordhaus of academic dishonesty. I believe part of the reason for the changes described above, was that it was more convenient to fit into his model.” But, Bob, doesn’t that DEFINE academic dishonesty?


  3. Bob Murphy  

    Heh heh good point Tom, but what I meant was, I don’t think he necessarily made at least that particular change because it bumped up the optimal carbon tax. (Or rather, kept it from falling.) Mainstream economists have to use simplifying shortcuts all the time, so I wouldn’t say somebody acted dishonestly unless I were sure the motivation for the tinkering was to arrive at a pre-ordained answer.

    There are some people, like Nicholas Stern for example, who I am pretty sure adjusted all the knobs on his modeling so that the carbon tax would be as big as possible. In contrast, Nordhaus’ uses a proxy for market discount rates etc., in order to come up with a decent guess of the ideal Pigovian tax (if you assume away all the flaws in government schemes).


  4. Tom Tanton  

    ok, granted he wasn’t necessarily being “malicious”—but changing “reality” to “fit the model” is backwards–change the model to fit reality sure seems like a more honest approach. I’ll grant that the changes he made were actually just simplifying in this instance.


  5. Ben  

    Tom, I think that it is best described as “doing the best you can with the data you have”. It’s not an unreasonable thing in many cases (I have estimated flowrates by applying the Beaufort wind scale to written descriptions). If he didn’t have the time or money to redo his survey, then the adjustsments aren’t unreasonable.

    However, where I draw the line is putting this vague, adjusted number as a cornerstone of his argument. The error bars on his estimate are far too large to use for policy making.

    Furthermore, extremely rare, ultra-high-damage events tend to twist things. For example, there is about 1 in a million chance that an asteroid will end life as we know it (damage ~quintillion dollars, the replacement value of Earth). Does this mean that we should spend a trillion dollars a year to develop anti-asteroid technology? Of course not. Argument ad absurdum aside, this same sort of analysis is applied to climate change. I find it questionable at best.


  6. Noblesse Oblige  

    Granting your points regarding the fuzziness of Nordhaus’ ‘catastrophic impacts,’ it is an example of the common practice in economics: “If you don’t know the answer and you can’t figure it out, VOTE ON IT.” Still it is indeed telling that one has to work hard to achieve a benefit/cost ratio that exceeds 2. No responsible business I know of would invest with that expectation, given the long payback period and the uncertainties involved. Only governments do this kind of thing, since there is no competition to enforce a penalty for failure, and in fact they usually achieve negative returns.

    Norhaus’ analyses are indeed useful for comparing the optimal strategy with alternatives, including Gore and Stern, as well as Kyoto-type policies. Also if I recall correctly, the optimal tax is not much better than waiting a few decades before enacting anything. Presumably this allows the world to become richer and then better afford mitigation measures. Ah, but that kind of solution ‘doesn’t sell newspapers.’

    In any event, the world will not warm by 2.5 degrees. It will be about 1 degree plus or minus natural variations. That alone will drive the benefit/cost ratio toward zero, but it is after all the cost part of the ratio that drives government — the ability to tax and spend. Benefits are nice but don’t really matter.


  7. Elba Patti  

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