This is a crosspost for Critique of “Comprehensive evidence implies a higher social cost of CO2” by David Friedman, published on 30 July 2023.

(Originally written to be submitted to Nature, which rejected it, edited for the substack. Versions were also sent to the EPA and the authors of Rennert.)

A recent Nature article, Rennert et al. 2022, estimates the social cost of CO₂ summed through 2300. The authors find a total cost of $185 per ton of CO₂ [Bressler 2021 estimated 258 $], more than three times the value of $51 used in current U.S. regulatory decisions. $90 of that is due to increased mortality from higher temperatures, $84 to reduced agricultural output, $2 to sea level rise and $9 to energy costs for residential and commercial buildings.

Mortality

The mortality calculation in Rennert is based on regional figures for increased mortality per degree of temperature rise from Cromar et al. 2022. Temperature-related mortality depends, among other things, on income since richer people can afford air conditioning and better insulated homes and have less need to go out in unfavorable weather. The economic model in Rennert implies per capita GNP roughly tripling by 2100, increasing about eleven-fold by 2300^[1], but since Cromar does not include income in the relation between temperature and mortality Rennert ignores the effect of that increase on temperature-related mortality. Socioeconomic conditions are mentioned in Cromar as a factor to be considered in future work but the implicit assumption of the two articles taken together is that, despite the large projected increase of income, the relation between temperature and mortality will remain at the level of the recent past.

Temperature Distribution Over the Year

The article estimates the effect of increases in average temperature without specifying the distribution over the year. An increase of 2°C in winter and 0°C in summer would have a very different effect on mortality than an increase of 0°C in winter and 2°C in summer. Increases in temperature due to anthropogenic climate change, as projected in the IPCC reports, are greater in winter than in summer, so reduce mortality from cold more and increase mortality from heat less than a uniform increase with the same average. The data in the articles used by Cromar to deduce temperature-related mortality are from temperature variation little of which is due to climate change so have no reason to reproduce that pattern.

Carleton et al. 2022, a more recent and more sophisticated calculation of the contribution to the Social Cost of Carbon from temperature-related mortality, uses the same time period and discount rate as Rennert but takes account of the effect on mortality of both income and the temperature distribution. It found a value of $36.6 for a high emissions scenario (RCP 8.5) and $17.1 for a moderate emissions scenario (RCP 4.5). The latter is much closer than the former to the assumptions in Rennert.

Technology

Temperature-related mortality depends on medical, heating, cooling, and insulating technologies. We do not know how much those technologies will improve over the next three centuries but that there will be no change is not a plausible assumption. Yet that is the assumption implicit in Rennert, which applies the increase in temperature-related mortality per degree of warming calculated in Cromar from past data to project the increase from now to 2300. Changes in mortality over recent history suggest that the effect they are ignoring would be large.

Two examples:

Sidney et al. find an annual decline in cardiovascular mortality in the United States from 2000 to 2011 of 3.79%. Continued for the rest of the century that would reduce cardiovascular disease, one of the sources of temperature-related mortality, to about one twentieth of its present value by 2100.

Lay et al., calculating temperature-related mortality rates first with 1973-82 data and then with 2003-13 data, found that the predicted increase in temperature-related mortality in the U.S. for a 2°C increase fell by more than 97%, for a 6°C increase by 84%, due to changes in mortality rates over thirty years.

Rennert projects mortality rates on the assumption that the relation between temperature and mortality will remain constant for almost three hundred years.

Migration

A fourth factor ignored in Cromar is adaptation by migration. Currently, 280,000,000 people, about 3.5% of the world population, live in a different country than they were born in. If some parts of the world become less attractive due to climate change and some more, populations can be expected to shift in response, reducing temperature-related mortality.

In summary, I found four problems with the mortality calculation from Cromar as used in Rennert^[2]: neglecting the effect of income on temperature-related mortality, ignoring the pattern of temperature change implied by greenhouse warming, neglecting the effect of technological change, ignoring adaptation by migration. The first two can be corrected by substituting the result in Carleton for that in Cromar, reducing the SCC due to temperature-related mortality from $90/ton to something between $17.1/ton and $36.6/ton. Correcting the third and fourth should further reduce it by a large but unknown amount.

Effect of Climate Change on Agriculture

Rennert bases its estimate of the effect of climate change on agriculture on Moore et al. 2017. I find three problems with its calculations.

Technological Change

One way of adapting agriculture to a changed environment is by modifying crop varieties. Biotech is a rapidly progressing field so we can expect our ability to modify crop varieties to improve over time. A more primitive form of biotech, selective breeding, adapted maize to the cooler climate of North America. As our biotechnology improves we should be able to do the same thing with other crops in the other direction in decades instead of millennia. Research in adapting wheat to hotter temperatures is currently ongoing^[3].

Moore vs Challinor

“The yield–temperature response functions used in this paper are derived from a database of studies estimating the climate change impact on yield compiled for the IPCC 5th Assessment Report, also described in a meta-analysis by Challinor et al.” (Moore)

That quote makes puzzling the striking difference between the two papers. Figure 1 in Challinor shows the effect of temperature on yield for wheat, maize, and rice both with and without adaptation, in temperate and tropical regions. Without adaptation yield falls in all cases. With adaptation, yield rises with temperature for wheat and maize in temperate regions, rice definitely in tropical and perhaps also in temperate regions, falls for wheat above 2°C and maize throughout the temperature range shown, in tropical regions.  Since most wheat is grown in temperate regions, most rice in tropical regions, and a majority of maize in temperate regions, that should result in an increase, not a decrease, in yield with temperature.

CO₂ Fertilization

Increases in CO₂ concentration in the atmosphere increase the yield of C3 crops and reduce water requirements for both C3 and C4 crops. Moore uses a figure of 11.5% increase in C3 yield with a doubling of CO₂ concentration, writing “This is very close to estimates from experimental field studies for C3 crops” and footnoting the claim to Long et al. 2006.  Long, however, found increases of 12%, 13%, and 14% (rice, wheat, and soybeans) from an increase to 550 ppm from the ambient concentration, which implies an increase of about 17.5% [should this be (0.12 + 0.13 + 0.14)/3*370/(550 - 370) = 26.7 %?] for a doubling^[4]. Kimball 2016, a survey of FACE (Free-air CO₂ Enrichment) studies of which Long is one, found that “Yields of C₃ grain crops were increased on average about 19%” by increasing CO2 from 353 ppm to 550, which implies a 23% [should this be 0.19*353/(550 - 353) = 34.0 %?] increase for a doubling.

Taylor and Schlenker 2022 used random variation in CO₂ concentration observed by NASA’s Orbiting Carbon Observatory-2 satellite, combined with county level crop yield data, to directly observe the effect of varying CO₂ concentration on crop yields in actual agricultural practice. They found that a 1 ppm increase in CO₂ equates to a 0.4%, 0.6%, 1% yield increase for corn, soybeans, and wheat, respectively. Their article includes a discussion of reasons why the FACE studies may have substantially underestimated the effect^[5].

Moore’s modeling produces an anomalously low value for CO₂ fertilization of C3 crops — 2/3 the value in the source they cite, half the value found in the most recent survey of FACE results, lower still relative to the results in Taylor and Schlenker 2022. That is at least part of the reason that they get a much more negative result for the social cost of carbon than earlier studies that used earlier and higher estimates from enclosed rather than free air studies — FUND, which found a net benefit, or AgMIP, which found a cost but a substantially smaller one^[6]. Replacing Moore’s 11.5% by Kimball’s 23%  would substantially reduce the contribution of the effect of climate change on agriculture to the cost of carbon.

Conclusion

Correcting the neglect of technological change and using a more realistic value for CO₂ fertilization would reduce Moore’s estimate  substantially, might make the net effect of climate change on agriculture positive.

The General Problem

Over the past two centuries, technological change has replaced sailing ships with jet planes for long distance transportation. Over the past century, medicine has progressed from a point where almost no contagious diseases were curable to one where almost all are. Over the past fifty years, computer technology has progressed to the point where the typical member of a developed society carries in his pocket a computer more powerful than any that existed fifty years ago. There is no reason to believe that the process has stopped and no way of predicting its effects on the world beyond the very short term. As I wrote in a book published fifteen years ago:

… with a few exceptions, I have limited my discussion of the future to the next thirty years or so. That is roughly the point at which both AI and nanotech begin to matter. It is also long enough to permit technologies that have not yet attracted my attention to start to play an important role. Beyond that my crystal ball, badly blurred at best, becomes useless; the further future dissolves into mist. (Friedman 2008)

Rennert sums costs over the next three centuries, with about two-thirds of the total coming after 2100^[7].Their solution to the problem of predicting technological change over that period is, with the exception of their estimates of CO₂ production and energy costs, to ignore it, implicitly assume technological stasis. That is the wrong solution — but any projection of technological change that far into the future would be science fiction not science.

What they claim to do cannot be done.

References

Carleton, T et al. (2022) Valuing the Global Mortality Consequences of Climate Change Accounting for Adaptation Costs and Benefits, QJE, Vol. 137, Issue 4, November, Pages 2037–2105. https://doi.org/10.1093/qje/qjac020

Cromar KR et al. (2022) Global Health Impacts for Economic Models of Climate Change: A Systematic Review and Meta-Analysis. Ann Am Thorac Soc. 2022 Jul;19(7):1203-1212.

Friedman, D (2008) Future Imperfect: Technology and Freedom in an Uncertain World, Cambridge University Press, NY.

Kimball, Bruce A. (2016) Crop responses to elevated CO₂ and interactions with H₂O, N, and temperature, Current Opinion in Plant Biology, Vol. 31, pp. 36-43. https://doi.org/10.1016/j.pbi.2016.03.006

Lay, CR, Sarofim, MC, Zilberg, AV, Mills, DM, Jones, RW, Schwartz, J, Kinney, PL (2021) City-level vulnerability to temperature-related mortality in the USA and future projections: a geographically clustered meta-regression, The Lancet, Planetary Health. https://doi.org/10.1016/S2542-5196(21)00058-9

Long, SP, Ainsworth, E A, Leakey, ADB, Nösberger, J, Ort, DR (2006) Food  for thought: lower-than-expected crop yield stimulation with rising CO₂ concentrations. Science 312, 1918–1921. DOI: 10.1126/science.1114722

Moore, FC, Baldos, U, Hertel, T et al. (2017) New science of climate change impacts on agriculture implies higher social cost of carbon. Nat Commun 8, 1607. https://doi.org/10.1038/s41467-017-01792-x

Rennert, K, Errickson, F, Prest, BC et al. (2022) Comprehensive evidence implies a higher social cost of CO₂. Nature 610, 687–692. https://doi.org/10.1038/s41586-022-05224-9

Sidney S, Quesenberry CP, Jaffe, MG, et. al. (2016)  Recent Trends in Cardiovascular Mortality in the United States and Public Health Goals. JAMA Cardiol. 2016;1(5):594–599. doi:10.1001/jamacardio..1326

Taylor, CA, Schlenker, W  Environmental Drivers of Agricultural Productivity Growth: CO₂ Fertilization of US Field Crops.

Zabel, F, Putzenlechner, B, Mauser,W (2014) Global Agricultural Land Resources – A High Resolution Suitability Evaluation and Its Perspectives until 2100 under Climate Change Conditions, PLOS One, vol. 9, Issue 9, September. https://doi.org/10.1371/journal.pone.0107522

Ramankutty, N et al (2002) The global distribution of cultivable lands: current patterns and
sensitivity to possible climate change, Global Ecol. Biogeogr. 11 377–92. https://doi.org/10.1046/j.1466-822x.2002.00294.x

Zhang, X and Cai, X (2011) Climate change impacts on global agricultural land availability Environ. Res. Lett. 6 014014.). DOI 10.1088/1748-9326/6/1/014014

1. ^{^}

   Calculated from Figure 2b in Rennert. Even an eleven-fold increase in income would still leave countries such as India, Nigeria, and Indonesia with incomes substantially lower than current U.S. incomes.

2. ^{^}

   These are not errors in Cromar et al. viewed as an estimate of current effects of temperature change but become errors when incorporated into Rennert et al. and used to project effects into the far future.

3. ^{^}

   At the John Innes Centre in Norwich.

4. ^{^}

   “Such an adjustment is justified because to a first approximation growth responses by plants to elevated CO₂ are generally linear between 300 and 900 ppm” (Kimball). Ambient CO₂ in 2000 was about 370 ppm. I am using that figure, starting with 13%, the average of the three values reported.

5. ^{^}

   Observed variation was only over a range of about 15 ppm so their results do not tell us how large the effect would be for much greater increases in CO₂ concentration but they suggest that the FACE results seriously underestimate the yield increases from CO₂ fertilization. According to the authors, “recent work has pointed out potential measurement error, arguing that FACE estimates should be adjusted upward by 50% to account for the effect of air turbulence and CO2 fluctuations (Allen et al. 2020)”

6. ^{^}

   Moore et al. Fig. 4.

7. ^{^}

   As estimated from Extended Data Fig. 2 in Rennert et al.