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The Question of Global Warming

I begin this review with a prologue, describing the measurements that transformed global warming from a vague theoretical speculation into a precise observational science.

There is a famous graph showing the fraction of carbon dioxide in the atmosphere as it varies month by month and year by year (see the graph). It gives us our firmest and most accurate evidence of effects of human activities on our global environment. The graph is generally known as the Keeling graph because it summarizes the lifework of Charles David Keeling, a professor at the Scripps Institution of Oceanography in La Jolla, California. Keeling measured the carbon dioxide abundance in the atmosphere for forty-seven years, from 1958 until his death in 2005. He designed and built the instruments that made accurate measurements possible. He began making his measurements near the summit of the dormant volcano Mauna Loa on the big island of Hawaii.

Concentration of Carbon Dioxide in the Atmosphere

He chose this place for his observatory because the ambient air is far from any continent and is uncontaminated by local human activities or vegetation. The measurements have continued after Keeling’s death, and show an unbroken record of rising carbon dioxide abundance extending over fifty years. The graph has two obvious and conspicuous features. First, a steady increase of carbon dioxide with time, beginning at 315 parts per million in 1958 and reaching 385 parts per million in 2008. Second, a regular wiggle showing a yearly cycle of growth and decline of carbon dioxide levels. The maximum happens each year in the Northern Hemisphere spring, the minimum in the Northern Hemisphere fall. The difference between maximum and minimum each year is about six parts per million.

Keeling was a meticulous observer. The accuracy of his measurements has never been challenged, and many other observers have confirmed his results. In the 1970s he extended his observations from Mauna Loa, at latitude 20 north, to eight other stations at various latitudes, from the South Pole at latitude 90 south to Point Barrow on the Arctic coast of Alaska at latitude 71 north. At every latitude there is the same steady growth of carbon dioxide levels, but the size of the annual wiggle varies strongly with latitude. The wiggle is largest at Point Barrow where the difference between maximum and minimum is about fifteen parts per million. At Kerguelen, a Pacific island at latitude 29 south, the wiggle vanishes. At the South Pole the difference between maximum and minimum is about two parts per million, with the maximum in Southern Hemisphere spring.

The only plausible explanation of the annual wiggle and its variation with latitude is that it is due to the seasonal growth and decay of annual vegetation, especially deciduous forests, in temperate latitudes north and south. The asymmetry of the wiggle between north and south is caused by the fact that the Northern Hemisphere has most of the land area and most of the deciduous forests. The wiggle is giving us a direct measurement of the quantity of carbon that is absorbed from the atmosphere each summer north and south by growing vegetation, and returned each winter to the atmosphere by dying and decaying vegetation.

The quantity is large, as we see directly from the Point Barrow measurements. The wiggle at Point Barrow shows that the net growth of vegetation in the Northern Hemisphere summer absorbs about 4 percent of the total carbon dioxide in the high-latitude atmosphere each year. The total absorption must be larger than the net growth, because the vegetation continues to respire during the summer, and the net growth is equal to total absorption minus respiration. The tropical forests at low latitudes are also absorbing and respiring a large quantity of carbon dioxide, which does not vary much with the season and does not contribute much to the annual wiggle.

When we put together the evidence from the wiggles and the distribution of vegetation over the earth, it turns out that about 8 percent of the carbon dioxide in the atmosphere is absorbed by vegetation and returned to the atmosphere every year. This means that the average lifetime of a molecule of carbon dioxide in the atmosphere, before it is captured by vegetation and afterward released, is about twelve years. This fact, that the exchange of carbon between atmosphere and vegetation is rapid, is of fundamental importance to the long-range future of global warming, as will become clear in what follows. Neither of the books under review mentions it.


William Nordhaus is a professional economist, and his book A Question of Balance: Weighing the Options on Global Warming Policies describes the global-warming problem as an economist sees it. He is not concerned with the science of global warming or with the detailed estimation of the damage that it may do. He assumes that the science and the damage are specified, and he compares the effectiveness of various policies for the allocation of economic resources in response. His conclusions are largely independent of scientific details. He calculates aggregated expenditures and costs and gains. Everything is calculated by running a single computer model which he calls DICE, an acronym for Dynamic Integrated Model of Climate and the Economy.

Each run of DICE takes as input a particular policy for allocating expenditures year by year. The allocated resources are spent on subsidizing costly technologies—for example, deep underground sequestration of carbon dioxide produced in power stations—that reduce emissions of carbon dioxide, or placing a tax on activities that produce carbon emissions. The climate model part of DICE calculates the effect of the reduced emissions in reducing damage. The output of DICE then tells us the resulting gains and losses of the world economy year by year. Each run begins at the year 2005 and ends either at 2105 or 2205, giving a picture of the effects of a particular policy over the next one or two hundred years.

The practical unit of economic resources is a trillion inflation-adjusted dollars. An inflation-adjusted dollar means a sum of money, at any future time, with the same purchasing power as a real dollar in 2005. In the following discussion, the word “dollar” will always mean an inflation-adjusted dollar, with a purchasing power that does not vary with time. The difference in outcome between one policy and another is typically several trillion dollars, comparable with the cost of the war in Iraq. This is a game played for high stakes.

Nordhaus’s book is not for the casual reader. It is full of graphs and tables of numbers, with an occasional equation to show how the numbers are related. The graphs and tables show how the world economy reacts to the various policy options. To understand these graphs and tables, readers should be familiar with financial statements and compound interest, but they do not need to be experts in economic theory. Anyone who knows enough mathematics to balance a checkbook or complete an income tax return should be able to understand the numbers.

For the benefit of those who are mathematically illiterate or uninterested in numerical details, Nordhaus has put a nonmathematical chapter at the beginning with the title “Summary for the Concerned Citizen.” This first chapter contains an admirably clear summary of his results and their practical consequences, digested so as to be read by busy politicians and ordinary people who may vote the politicians into office. He believes that the most important concern of any policy that aims to address climate change should be how to set the most efficient “carbon price,” which he defines as “the market price or penalty that would be paid by those who use fossil fuels and thereby generate CO2 emissions.” He writes:

Whether someone is serious about tackling the global-warming problem can be readily gauged by listening to what he or she says about the carbon price. Suppose you hear a public figure who speaks eloquently of the perils of global warming and proposes that the nation should move urgently to slow climate change. Suppose that person proposes regulating the fuel efficiency of cars, or requiring high-efficiency lightbulbs, or subsidizing ethanol, or providing research support for solar power—but nowhere does the proposal raise the price of carbon. You should conclude that the proposal is not really serious and does not recognize the central economic message about how to slow climate change. To a first approximation, raising the price of carbon is a necessary and sufficient step for tackling global warming. The rest is at best rhetoric and may actually be harmful in inducing economic inefficiencies.

If this chapter were widely read, the public understanding of global warming and possible responses to it would be greatly improved.

Nordhaus examines five kinds of global-warming policy, with many runs of DICE for each kind. The first kind is business-as-usual, with no restriction of carbon dioxide emissions—in which case, he estimates damages to the environment amounting to some $23 trillion in current dollars by the year 2100. The second kind is the “optimal policy,” judged by Nordhaus to be the most cost-effective, with a worldwide tax on carbon emissions adjusted each year to give the maximum aggregate economic gain as calculated by DICE. The third kind is the Kyoto Protocol, in operation since 2005 with 175 participating countries, imposing fixed limits to the emissions of economically developed countries only. Nordhaus tests various versions of the Kyoto Protocol, with or without the participation of the United States.

The fourth kind of policy is labeled “ambitious” proposals, with two versions which Nordhaus calls “Stern” and “Gore.” “Stern” is the policy advocated by Sir Nicholas Stern in the Stern Review, an economic analysis of global-warming policy sponsored by the British government.* “Stern” imposes draconian limits on emissions, similar to the Kyoto limits but much stronger. “Gore” is a policy advocated by Al Gore, with emissions reduced drastically but gradually, the reductions reaching 90 percent of current levels before the year 2050. The fifth and last kind is called “low-cost backstop,” a policy based on a hypothetical low-cost technology for removing carbon dioxide from the atmosphere, or for producing energy without carbon dioxide emission, assuming that such a technology will become available at some specified future date. According to Nordhaus, this technology might include “low-cost solar power, geothermal energy, some nonintrusive climatic engineering, or genetically engineered carbon-eating trees.”

Since each policy put through DICE is allowed to run for one or two hundred years, its economic effectiveness must be measured by an aggregated sum of gains and losses over the whole duration of the run. The most crucial question facing the policymaker is then how to compare present-day gains and losses with gains and losses a hundred years in the future. That is why Nordhaus chose “A Question of Balance” for his title. If we can save M dollars of damage caused by climate change in the year 2110 by spending one dollar on reducing emissions in the year 2010, how large must M be to make the spending worthwhile? Or, as economists might put it, how much can future losses from climate change be diminished or “discounted” by money invested in reducing emissions now?

  1. *

    See Nicholas Stern, The Economics of Climate Change: The Stern Review (Cambridge University Press, 2007).

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