Climate: The Implication of Uncertainty

Anyone who looks seriously at climate issues should recognize that the consequences of climate change are very uncertain. My own view, defended in my first post here, is that they are sufficiently uncertain to raise serious doubts about the sign as well as the size of the effect, that warming due to human production of greenhouse gases might well make us better off rather than worse off. My belief that the net effect of climate change might be positive is consistent with the current scientific orthodoxy, although I attach a higher probability to the possibility of net positive outcomes and pay more attention to it than most. Rennert et. al. 2022, an article recently published in Nature and currently being considered by the EPA as a possible basis for regulatory decisions, attempts to estimate the net cost from producing an additional ton of carbon dioxide. Its Figure 2 shows the probability distribution, according to its calculations, for the net cost. The far left end of the distribution is below zero, representing the possibility of a net positive effect.

Even if I am wrong and the effect is almost certainly negative, how negative it will be is very uncertain. CO₂ emissions might fall sharply due to increases in the cost of fossil fuels or decreases in the cost of alternatives. For a given value of emissions, varying estimates of climate sensitivity imply at least a factor of two range for the resulting temperature increase. For a given increase in temperature, the effect on humans depends on what humans will be doing for the next century. The effect of climate on agricultural output is difficult to predict; Rennert found it large and negative, one of the previous studies found it positive. Diking against a meter of sea level change could be a serious problem for Bangladesh if it happened tomorrow. If Bangladesh follows the pattern of China, where GDP per capita has increased more than seventy fold since Mao's death, by the time it happens they can pay the cost out of small change.

A possible response to this point is to argue that uncertainty is no argument against action. One should simply replace the uncertain range of outcomes with the best estimate one can provide of its expected value, the average of costs weighted by their probability, and act as if that were the known consequence of warming.

It is a possible response and a popular one, but it is wrong. The question we are answering is not "what should we do?" but "what should we do now?" Waiting will raise the cost of dealing with the problem but will also provide additional information. The more information we have, the better our ability to decide what precautions are worth taking. Or not worth taking. Uncertainty that will be reduced over time is an argument against immediate action.

The usual rhetorical response is to claim that we barely have time to act at all, that if we wait more than a very short time it will be too late. This claim becomes less persuasive the more times it is made, and it has  been made, by various people, quite a large number of times over the past thirty years. It largely depends on picking some arbitrary temperature change, most commonly two degrees C, and treating it as if it were the end of the world. As salesmen commonly put it, "Buy Now—This Is Your Very Last Chance To Take Advantage of Our Special Offer."

For a more realistic opinion, consider an estimate of the cost of waiting by William Nordhaus, an economist who has specialized in climate issues. In the course of a piece arguing for immediate action against climate change, he reported his estimate of how much greater the cost of climate change would be if we waited fifty years to deal with it instead of taking the optimal action at once.  The number was $4.1 trillion. He took that as an argument for immediate action, writing that "Wars have been started over smaller sums." 4.1 trillion sounds like a large number but it is a cost spread out over the entire globe and a long period of time. Annualized, it comes to less than a tenth of a percent of world GNP.[1]  

"Thought before action, if there is time."

(from a character in a Dick Francis novel)

And there usually is.

The Optimal Policy

I have been comparing a policy of acting today on the basis of our current estimate of the expected cost of climate change with a policy of waiting until we have more information and only acting then. There are other alternatives. Suppose we are uncertain what the cost from an additional ton of CO₂ is but are confident that it is at least five dollars. It would follow that any policy to reduce emissions justified at a cost of five dollars a ton was worth taking now although we might want to wait for more information before implementing more expensive policies.

To generalize this approach imagine, as economists often do, that we have complete information not of cost but of the probability distribution for cost — not merely, in this case, the probability distribution for the cost of climate change based on our present information but the probability distribution for changes in that distribution over time due to additional information. We could then, in principle, calculate an optimal policy for today, perhaps a modest carbon tax, and the rules for modifying that policy, increasing or decreasing the tax year by year as additional information came in.

A Statistical Digression

The US has just joined the allies in World War II and you are a government official with the job of deciding whether batches of ammunition produced for the war effort are of acceptable quality, whether too many of the rounds are duds. You consult a statistician who tells you that the correct procedure is to test a fixed number of rounds, accept or reject according to how many are duds, with the number tested and the acceptance criteria depending on facts about the cost of testing, the value of quality, and what you know about how likely defective batches are.

It occurs to you that that cannot be the right answer. Suppose his formula tells you that a batch should be rejected if, after testing ten thousand rounds, more than fifty are defective. If the first fifty-one rounds are defective there is no point to testing the rest of the ten thousand. Generalizing the result, what you want is not a fixed number to test and a fixed criterion for failure but a stopping rule, a way of recalculating your estimate of the percentage of duds in the batch and your confidence in that estimate after each round is tested and stopping the tests when you become sufficiently confident that the batch either is or is not acceptable.

This is a true story, somewhat condensed. The original insight seems to have been due to Garret L. Schuyler, a captain in the navy, in a conversation with W. Allen Wallis, head of the Statistical Research Group during the war. It was followed up by Wallis and my father, which is how I heard the story. They eventually got Abraham Wald interested. He solved the theoretical problem of finding a rule for the stopping point and in the process invented sequential analysis, later described by Wallis as “one of the most powerful and seminal statistical ideas of the past third of a century.” I have just described the application of the same approach, continually revising the decision as additional information comes in, to climate policy.[2]

Nordhaus devotes a chapter of his book to “Dealing with Uncertainty in Climate-Change Policy.” Unless I missed it, he never mentions the fact that, if information is improving over time, uncertainty is an argument for delay.

Sometimes it is worth reinventing the wheel.

The Problem with my Optimal Policy

My discussion so far exhibits an error commonly made by economists writing about policy, the implicit assumption that they are writing for an intelligent and benevolent despot, that if only they can figure out what ought to be done the government will do it. For evidence against that assumption in the climate context, consider biofuels policy. Legal rules to force the conversion of corn into ethanol to be used as fuel were initially justified on the theory that, by substituting biofuels for fossil fuels, they would decrease the output of CO₂. Academics investigating the question eventually concluded that they didn’t, that at least as much CO₂ was produced in the process of growing corn and converting it into ethanol as would be produced by burning the equivalent amount of gasoline.

We still have the biofuels policy, still convert more than a third of the U.S. output of maize, roughly fifteen percent of world production, into alcohol. Doing so may not slow climate change but it does rise the price of maize — and farmers vote. Think of it as our contribution to world hunger.[3]

I have spent a good deal of time and effort over the past two months researching and writing a critique of Rennert et al. 2022, arguing that it greatly exaggerates the cost of carbon, and have sent a version of that critique to the EPA, which had asked for comments. I believe my arguments are correct. I will be pleasantly surprised if they have any effect on the EPA’s decision of whether to adopt a higher cost of carbon.

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[1] Nordhaus gets his figure from Table 5-1 of his book A Question of Balance. So far as I can tell he never says how long a period he is summing the cost over, but the first line of the table shows the results of doing nothing for 250 years, so it is presumably at least that long. For simplicity I am assuming that global GNP increases at the discount rate, making the present value of 250 years of global GNP equal to 250 times GNP in the first year. 

[2] My source for the details of the history is W. Allen Wallis, “The Statistical Research Group, 1942-1945,” Journal of the American Statistical Association, Jun., 1980, Vol. 75, No. 370, pp. 320-330. Reading it, I came across the following passage by Wallis:

“He brought up the problem of the necessary sample size for comparing two percentages and gave me a memorandum prepared for him on that subject by a certain John von Neumann. I had never before heard of this von Neumann fellow, but the memorandum was obviously pretty smart for a man who apparently knew little about statistics”

[3] Al Gore, to his credit, has publicly conceded both that the biofuels policy he supported was a mistake and that "One of the reasons I made that mistake is that I paid particular attention to the farmers in my home state of Tennessee, and I had a certain fondness for the farmers in the state of Iowa because I was about to run for president."