Rolling the DICE: William Nordhaus's dubious case for a carbon tax.

• Author: Murphy, Robert P.
• Position: Dynamic Integrated Model of Climate and the Economy - Report

The 2007 Nobel Peace Prize awarded to AI Gore and the Intergovernmental Panel on Climate Change (IPCC) underscores the public's growing awareness of and concern about anthropogenic (man-made) global warming. Many climatologists and other relevant scientists claim that emissions of greenhouse gases (GHGs) from human activity will lead to increases in the earth's temperature, which in turn will spell potentially catastrophic hardship for future generations. If this forecast proves to be accurate, economists will recognize "what former World Bank chief economist Nicholas Stern described in his famous report to the British government as "the greatest example of market failure we have ever seen" (2007, 1).

With the science of global warming so stipulated, most economists' standard reaction is to recommend a government policy to internalize the externality; the debate has largely revolved around the best mechanism to deal with carbon emissions (for example, "cap and trade" versus a carbon tax) and the appropriate magnitude of the corrective penalty on emissions. Although the most important implementation of emission curbs to date, the Kyoto Protocol, relies on tradable permits, increasingly more economists have concluded that a carbon tax can achieve a desired level of emissions more efficiently (Pizer 1997; Nordhaus 2008). It would seem that the "consensus" in the natural sciences on anthropogenic global warming has carried over into the social sciences in the form of an emerging consensus on a carbon tax as the best way to balance present economic growth against future losses caused by avoidable climate change. Indeed, as of this writing, I am not aware of a single peer-reviewed economics article that challenges the basic case for a carbon tax (although the preceding citations contain several criticisms of a cap-and-trade system).

In this article, I argue that this consensus is unjustified because the case for a carbon tax is much weaker than most economists are probably aware. I illustrate the problems with a thorough analysis of the assumptions underlying William Nordhaus's Dynamic Integrated Model of Climate and the Economy (hereafter, "DICE model"), which is an excellent representative of the orthodox approach. I first document that each critical step in Nordhaus's case reties on numerical estimates that are quite uncertain and to which the magnitude of the "optimal" carbon tax may be very sensitive. After this immanent critique, to assess the danger of Nordhaus' approach I examine some of the drawbacks of real-world government action.

Summary of the DICE Model and the IPCC Fourth Assessment Report

Before closely examining the potential problems of Nordhaus's case for a carbon tax, I provide in this section a quick overview of his DICE model and the IPCC scientific analysis to which his economics is anchored.

Nordhaus and the DICE Model

A professor at Yale University since 1967, William Nordhaus has been chosen as the representative of the mainstream in climate-change economics for his longstanding career in an area in which he literally wrote the book (originally Nordhaus 1979 and more definitively Nordhaus 1994b). Although my criticisms are directed at Nordhaus, they are relevant to most other proposals for a carbon tax as well. (1) As one expert told me, "A lot of economists interested in climate change start--and end-with Nordhaus."

In the early 1990s, Nordhaus and his collaborators developed the earliest versions of the Regional Dynamic Integrated Model of Climate and the Economy (RICE) and the aggregated DICE models. These models have evolved over time, incorporating revised estimates from the natural sciences as well as structural improvements. Nordhaus and Boyer 2000 describes the RICE and DICE models as of 1999, and Nordhaus 2008 (which serves as the reference for the present article) describes the DICE model as of September 2007. For a brief description of the model's mechanics, we turn to Nordhaus himself:

The DICE model views the economics of climate change from the perspective of neoclassical economic growth theory.... The DICE model extends this approach by including the "natural capital" of the climate system as an additional kind of capital stock. In other words, we can view concentrations of GHGs as negative natural capital, and emissions reductions as investments that raise the quantity of natural capital. By devoting output to emissions reductions, economies reduce consumption today but prevent economically harmful climate change and thereby increase consumption possibilities in the future....

In the DICE model, the world is assumed to have a well-defined set of preferences, represented by a "social welfare function," which ranks different paths of consumption.... The relative importance of different generations is affected by two central normative parameters: the pure rate of time preference and the elasticity of the marginal utility of consumption.... In the modeling, we set the parameters to be consistent with observed economic outcomes as reflected by interest rates and rates of return on capital....

Output is produced with a Cobb-Douglas production function in capital, labor, and energy. Energy takes the form of either carbon-based fuels (such as coal) or non-carbon-based technologies (such as solar or geothermal energy or nuclear power). Technological change takes two forms: economy-wide technological change and carbon-saving technological change. Carbon-saving technological change is modeled as reducing the ratio of C[O.sub.2] emissions to output. Carbon fuels are limited in supply. Substitution from carbon to noncarbon fuels takes place over time as carbon-based fuels become more expensive, either because of resource exhaustion or because policies are taken to limit carbon emissions. (Nordhaus 2008, 32-35)

The DICE model ultimately yields a large matrix of output, describing the trajectories (in ten-year increments) of variables such as total global emissions, the damages from climate change, the social cost of carbon, and the optimal tax on carbon (expressed as 2005 dollars per ton).

The IPCC Fourth Assessment Report

The IPCC is the world authority on climate-change science. (2) It was established by the World Meteorological Organization and the United Nations Environment Program in 1988. Its periodic reports do not contain new research, but instead "make policy-relevant--as opposed to policy-prescriptive assessments of the existing worldwide literature on the scientific, technical and socio-economic aspects of climate change" (Jarraud and Steiner 2007, v). Working Group I's contribution to the Fourth Assessment Report (abbreviated AR 4), The Physical Science Basis, contains chapters "written by 152 coordinating lead authors and lead authors from over 30 countries and reviewed by over 600 experts" (Jarraud and Steiner 2007, v).

The AR4 is the best single repository for the natural-science relationships to which Nordhaus calibrates the DICE model. The basic story of the AR4 is that human activities are emitting carbon dioxide (C[O.sub.2]) and other GHGs, which allow sunlight to pass through them, but trap some of the lower-frequency infrared radiation that bounces back from Earth. This "enhanced greenhouse effect" leads to global warming, which many scientists and economists warn will have dramatic effects on human well-being over the next several hundred years.

Weaknesses in the DICE Model's Recommended Carbon Tax Profile

Nordhaus's method for calculating the optimal carbon tax (as a function of time) is straightforward. He assumes that economic activity releases GHGs, thereby raising their concentration in the atmosphere. The increased concentration leads to higher temperatures, which in turn cause net economic damages to future generations. Because the present generation is assumed to care about the welfare of its descendants, the emission of the marginal ton of carbon into the atmosphere today translates into a (discounted) loss in present utility. Market prices do not fully reflect this aspect of the situation, and so (Nordhaus concludes) a Pigovian tax on carbon usage is justified. For economic efficiency, the tax should just compensate for the present discounted value of the reduction in future utility flows owing to the warming that the marginal emission will cause.

The calibrated ideal tax (which varies over time) depends on the numerical estimates undergirding the DICE model. Yet, as we shall see, every step in Nordhaus's argument relies on estimates subject to great uncertainty. Therefore, even if mainstream economists accept the argument's basic premise for a carbon tax, they should hesitate to clamor for implementation of the tax. In the remainder of this section, I summarize these key areas of uncertainty.

Uncertainty Area One: Future GHG Atmospheric Concentrations May Be Overstated

Unlike some other negative externalities, the impact of a given quantity of GHG emissions depends crucially on the concentration already in the atmosphere. Therefore, an efficient carbon tax regime must incorporate projections of future GHG concentrations as a function of time and of the taxes themselves. Yet these projections are not as straightforward as one might think. A major source of uncertainty concerns carbon "sinks," such as the oceans. As humans pump tons of carbon dioxide into the atmosphere, the oceans absorb some of it. This absorption mitigates the growth in atmospheric GHG concentrations and hence reduces the projected damages from a given amount of emissions. The problem for modelers is that the oceans are vast but finite sinks. In response to critics of earlier versions of his DICE model, Nordhaus explicitly adopted a "three-reservoir" model of carbon flows in his 1999 and subsequent versions (Nordhaus and Boyer 2000, 57). By its very nature, this particular model cannot be simply calibrated with historical measurements on carbon concentrations because the...