Refuting the Case for a CO2 Tax: William Nordhaus's "DICE Model" Reconsidered
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.