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Damage Functions (Or Why I Am Mad at Economists)


Madison Condon (@MadisonECondon) is Associate Professor at Boston University School of Law.

This post is part of our ongoing series on climate, economics, and “green capitalism.” Read the rest of the posts here.


I think I had never heard of William Nordhaus until he was awarded the Nobel Prize in Economics in 2018. The award was bestowed in recognition of his work modeling the costs and benefits of acting on climate change through limiting emissions. At the time, I worked with climate economists, who remarked (like others) that it was surprising the award had not been at least co-granted to Martin Weitzman. Nordhaus, I later learned, was similarly surprised.

Like Nordhaus, Weitzman argued that the economics of climate change must be guided by the science. But he disagreed with Nordhaus’s approach to discounting the future, and instead referenced ideas like risk aversion and the precautionary principle to conclude it would be worth it to spend a lot of money right now to prevent the worst from possibly happening. Weitzman pointed out tremendous uncertainty in the forecasts of climate impacts, including tipping points, large error bars, and unknown unknowns. In economics-speak, he characterized this as enormous “downside risk,” including a potentially small—but fundamentally unknown—chance of total human annihilation.

But the Swedish central bank’s prize was given to Nordhaus rather than Weitzman. That decision represents the many ways the field of economics has helped to steer us toward our present crisis.

Global-Average Land”

While I didn’t know his name until 2018, I had become familiar with Nordhaus’s work without realizing it. His Dynamic Integrated Model of Climate and the Economy, or DICE model, was one of the three climate cost-benefit models used by the Obama Administration to estimate the “social cost of carbon” (SCC) at $51/ton of CO2. The SCC puts a monetary number on the damages caused by one additional ton of carbon dioxide today by adding up all those future damages and discounting them to the present—this figure is meant to serve as a guide of how much it would be worth to “sacrifice” today for the future.

In the long five years since 2018, there has been a growing understanding both inside and outside of economics departments that Nordhaus’s DICE model is really quite bad. The Environmental Protection Agency now proposes to raise the SCC to $190, using more complex methods and realistic assumptions than the original. But the new SCC, like the old one, rests on economic methods that continue to make a mess of climate science, social science, and the limits of uncertainty.

Excellent critiques of DICE and similar neoclassical models have already elucidated their flawed approach to discounting, technology, growth, and complexity and systems theory, so here I would like to focus on the part of mainstream economic models that really drive me up the wall: damage functions, or the equation representing economic output lost each year as a function of average global temperature rise. In the DICE model, this relationship is assumed to be quadratic, i.e., damages each year are some damage factor x multiplied by T2 that year–meaning the very simple damage function is a gently upward-swooping line.

In the 1990s, climate science was primarily interested in figuring out how hot we were going to make ourselves, using models that broke the earth into a large grid representing feedbacks between the atmosphere and the oceans. It was the very early days of “regional” climate modeling and the development of techniques for predicting localized impacts, like floods. Damage functions were built in this context, and focused on the projected costs of global average temperature rise–a value that itself was an average of forecasted temperature rise across all the grid squares of the global climate models (and across all their model runs).

In 1994, Nordhaus published two different methods of estimating the cost of climate damages. The first, which is used in all versions of the DICE model for constructing the damage function, uses “enumeration:” or adding up all the different categories of costs by climate impact (like drought) and sector of the economy (like agriculture). One large and unresolved problem with these models is that they make no attempt to estimate large categories of damages, yet this omission is typically given little significance by the users of the model outputs.

Nordhaus’s second method of estimation in 1994 was “expert elicitation,” i.e., he asked a group of 19 men what they personally thought the cost of climate change would be. Included in the survey were ten economists (among them Larry Summers), four social scientists, and five experts in natural sciences and engineering. The published results highlight the divergence of opinion between economists and scientists, presented by Nordhaus as an unresolvable toss-up between those “who view the prospect of greenhouse warming with little concern, confident that human societies will adapt handily to such changes” and those who “worry about major and irreversible impacts on natural systems [and] unpredictable extreme events.”

Professor Steve Keen has poked fun at some of the more outrageous elicited responses from economists, but the one I want to highlight is the following, from a climate scientist:

I must tell you that I marvel that economists are willing to make quantitative estimates of economic consequences of climate change where the only measures available are estimates of global surface average increases in temperature. As [one] who has spent his career worrying about the vagaries of the dynamics of the atmosphere, I marvel that they can translate a single global number, an extremely poor surrogate for a description of the climatic conditions, into quantitative estimates of impacts of global economic conditions.

This respondent was baffled by how economists were purporting to leap-frog the scientists: if science was still far from being able to tell us what 2°C of warming would look like in New York City versus Nairobi, how could the economists begin to predict its economic effects? Scientists could describe what may happen based on their knowledge of the climate system (it could be very bad), but they balked at the idea of attempting to assign probabilities to those scenarios, let alone translate them into dollar signs. 

Three decades later and climate science has progressed. Global climate models represent topography, clouds, and weather systems on a smaller scale, and methods have developed to improve regional climate forecasts. But, as I explain in detail in my forthcoming article, Climate Services: The Business of Physical Risk, global climate models have their own limits: they are much better at forecasting “simple,” chronic, processes like global sea-level rise than they are complex, acute, hazards like hurricanes in a particular place. For their part, economic models simultaneously ignore these improvements in granularity, for the sake of computational simplicity, while failing to respect what the scientific models still cannot tell us. The model used by many of the world’s central banks, for example, relies on a damage function that relates regional economic and labor productivity to annual temperature and precipitation. The problem, to quote my new favorite scientist, is that “nobody lives in ‘global-average-land’!” The storm following a drought that dumps a season of rainfall in a day likely has implications for financial risk, but is not captured in metrics of average annual precipitation in a region.

But the most annoying thing to me about the damage function is its reliance on econometrics, or statistics, a tool that seems to have become synonymous with mainstream economics. Econometrics is the analysis of data to deduce mathematical relationships. Through this method, economists plot equations between economic output and “climate”—as measured either by differences in climate between places (e.g., cool places are historically richer), or past changes in climate (e.g., by looking at the economic impact ~1°C of warming that has occurred over my lifetime). But to state what really should come across to most readers as something beyond the obvious: under a climate changed future, the future will not look like the past, and there is no reason to expect that these relationships between historic temperatures and economic output will hold. International financial regulators use econometrically deduced relationships to conclude that 3.5°C of warming by 2100 would reduce global output 7-14%. I’m sorry, but if you think the journey from 1.2 to 2°C and beyond is going to resemble the journey from normal temperatures to 1.2°C, just more so… you are wrong.

Econometric calculations based on past behavior ignore not only the big scary tipping points like methane releases from the melting permafrost, but also the ones that are far easier to wrap one’s mind around, like the Great Salt Lake running dry. Society, too, has tipping points; infrastructure has breaking points; ecosystems have thresholds; after some level of temperature rise, crops don’t lose productivity, they just die—same with humans.

Moving Beyond Gently-Swooping Lines

The passage of the Inflation Reduction Act last summer prompted a discussion of the ways Leah Stokes had been right: clinging to the economist-advised carbon tax and a fixation on externalities, efficiency, and cost-benefit analysis had thwarted progress on climate policy. I tweeted that economists had done damage beyond recommending poor policy instruments: they had significantly contributed to the downplaying of climate harms throughout my lifetime. I pledged that when I was less mad, I would write about it. I’m still mad, actually. Because this matters.

In a moving piece following Weitzman’s death in 2019, Eric Roston highlighted that his work on the economics of “fat-tails” was crucial in gathering support for the 1.5 and 2°C goals enshrined in the 2015 Paris Agreement. Nordhaus’s work did the opposite. In Merchants of Doubt, Naomi Oreskes and Eric Conway document the pivotal role Nordhaus and his colleagues played in casting doubt on the wisdom of fighting climate change. Over the years, Nordhaus has made slight updates to his model, the latest version raises damages slightly, while noting that the damage function omits “potentially significant climate change impact channels, such as biodiversity loss, ocean acidification, extreme events, social unrest, etc.” In his Nobel Prize Lecture, Nordhaus made much of climate science, showing carbon ice core data and warning of irreversible tipping points. But his conclusion remained the same: Whether policymakers adopted his cost-benefit analysis suggesting “optimal warming” of 3°C, “or the Paris Accord’s target of 2°C, we must be realistic and realize that the world is not close to attaining those goals.”

These models continue to have influence beyond the world of policy, including on investors. Until recently Big Four accounting firm KPMG proudly advertised its own reliance on DICE in climate risk analysis. But with financial regulators picking them up, the failings of these models are finally attracting attention. This winter, KPMG’s new climate risk advisor Mark Cliffe attacked the Federal Reserve for relying on DICE-like models, pointing out how absurdly at odds they are with “climate scientist’s frantic warnings.” At an online event, Cliffe, who was formerly chief economist at ING, again dismissed the models, referring to them as “neoclassical equilibrium models [that] abstract from volatility.” While I agree with him, it is fascinating how long it took the world to catch on. I recently unearthed a 2018 text message I sent to a friend shortly after the Nobel announcement that kicked off my continued obsession: “he predicts GDP losses in single digits from warming that will literally melt all the ice.”

These models have also shaped public understanding of climate risk. Last summer, Ezra Klein argued in the New York Times that people should not decline to have children out of fear of the world they will face: “No mainstream climate models suggest a return to a world as bad as the one we had in 1950, to say nothing of 1150.” Klein here should have specified that he was talking about mainstream climate economic models, not the scientific global climate models predicting we may return to a world like the one we had in the Pliocene. I agree wholeheartedly with Kate Marvel, quoted by Klein as rejecting “the notion that children are somehow doomed to an unhappy life;” but I do, personally, think that in the U.S. they may be doomed to a world with less wealth—at the very, very least, one with less coffee.

One reason why economic models perform so poorly—and why we shouldn’t hold our breath that we can make them much better without borrowing approaches from other fields—is because we don’t have data on what the economy looks like when all the ice melts. The hotter it gets, the more unpredictable it becomes, and even our science models running on supercomputers start to lose forecasting power as we depart the climate conditions from which we have gathered all of our data. I don’t need a model to tell you that we should be trying very hard to avoid the worst.