Thank you for this post on a very important topic! And thank you for the kind words on my Mortality Cost of Carbon paper.
I think that, at least from the perspective of using my paper, the analysis is actually much simpler than what you do above. Instead of using the 83 million cumulative 2020-2100 excess deaths, use the mortality cost of carbon itself: i.e. the number of lives saved per ton of carbon dioxide reduced, which is provided by the paper. So instead of the equation you show above, the equation now becomes:
Marginal Cost Per Life Saved = (Marginal Cost Per Ton CO_2 reduced)/(The Mortality Cost of Carbon)
Future pessimistic - $5.50 per tonne, so $23,400 to avert 4,255 tons*
Future realistic - $0.29 per tonne, so $1,234 to avert 4,255 tons
Future optimistic - $0.03 per tonnes, so $127 to avert 4,255 tons
The issue with your original equation above is that you are implicitly assuming linearity, i.e. assuming that the marginal cost of saving a life from marginally reducing emissions is equivalent to the average cost of saving a life if we were to reduce emissions all the way to zero. However, one of the findings of the Mortality Cost of Carbon paper is that the system is actually nonlinear and highly convex, so the number of lives saved from marginally reducing emissions is actually much greater than the average number of lives saved that you would get per ton if you were to reduce all the way to zero (see figure 4). This is all a fancy way to say that there are diminishing marginal returns in terms of saving lives from reducing carbon dioxide on a planetary scale. So to determine the marginal impact of reducing emissions, use the marginal estimates provided by the paper (the mortality cost of carbon).
And of course, as you mention above, the mortality cost of carbon is just the projected number of excess deaths from 2020-2100 caused by marginal emissions due to temperature-related mortality—i.e. the net effect of more hot days (bad for mortality) and fewer cold days (good for mortality). It leaves out potentially important climate-mortality pathways such as the effect of climate change on infectious disease, civil and interstate war, food supply, flooding, as well as the co-benefit from less air pollution. Despite these limitations, Louis was still finding that these projections were cost-competitive with Givewell’s top recommendations.
*Note that Louis was using the 2020 Working Paper version of the Mortality Cost of Carbon, which included all mortality sources from the 2014 WHO paper (one of three papers used to construct the mortality damage function, which Andrew also mentions in the post), whereas the 2021 published version of the paper in Nature Communications used just the temperature-related mortality estimates from the 2014 WHO report. This ends up leading to a slight difference in the mortality cost of carbon estimate, from 1⁄4255 in the working paper version to 1⁄4434 in the published paper version. Recalculating Louis’s analysis with the published paper version numbers yields:
Future pessimistic - $5.50 per tonne, so $24,387 to avert 4,434 tons*
Future realistic - $0.29 per tonne, so $1,286 to avert 4,434 tons
Future optimistic - $0.03 per tonnes, so $133 to avert 4,434 tons
Thank you for commenting! I felt like I was relying on your paper without fully understanding it. I’m afraid that much of my post is just an attempt to reinterpret your work.
It’s encouraging that Founder’s Pledge thinks they can get such a low price on carbon! Interventions at that price really might be effective.
One major question I had about your paper is; what’s the breakdown of harms between direct deaths, economic harms, and other losses (like non-fatal hunger)? When the WHO estimates 250,000 deaths each year from 2030-2050, should I interpret a multiplier on that to account for other harms like productivity lost from sickness?
I knew I was making a bad linearity assumption, but I think I might have underestimated how much error it was introducing. If I use my naive model to match your work, I get 50,000 tons/death, which is an order of magnitude off from your estimate. Is that because of an improper linearity assumption?
No worries! I’m glad you found the paper useful and interesting!
The mortality cost of carbon is just the number of excess deaths from temperature-related mortality in units of excess deaths from emitting one metric ton of CO_2. So it’s just excess deaths and nothing else. The social cost of carbon is the full monetized value of all climate impacts from emitting one ton of CO_2, which includes the monetized value of those excess deaths in addition to other sources of climate damages. You can see that before the model accounted for temperature-related mortality, the social cost of carbon was $37, but after accounting for temperature-related mortality, it is $258. However, note my caveat from the conclusion: “It is important to note that recent literature has identified other shortcomings in the DICE model including other issues with the climate-economy damage function and the climate module. Besides adding the effect of climate change on mortality and subsequent feedbacks, DICE-EMR takes the rest of the DICE model as given without updating other factors.”
It’s hard for me to determine how much the different simplifying assumptions from your back-of-the-envelope formula are affecting your estimate. The linearity assumption is certainly causing a big difference because the system is highly convex. Also, the DICE-EMR model has the DICE climate model built into it that can show the climatic effect of changes in emissions. I’m not sure how much error you’re introducing with the back-of-the envelope climate assumptions, but that could also be an issue.
All this to say, if estimating the marginal impact (either the mortality cost of carbon or the full social cost of carbon) were as simple as a back-of-the envelope calculation, then there wouldn’t be a need to give William Nordhaus the Nobel Prize for his work on the original DICE model (the first one for environmental economics), nor for me to do this work. I think Louis Dixon’s original post is basically all you need to do for this exercise (at least for leveraging my paper’s results). Or as @jh suggested above, a $1/ton estimate just gets you to $4.4K per life saved using my paper’s results.
Also, see this one quote from the end of the paper: “Separate from policy, the MCC and SCC can be useful in informing the decision-making of individuals, households, companies, charities, and other organizations in determining the social impact of the emissions generated by their activities. The emissions contributions of these groups are usually marginal relative to the aggregate emissions of the world economy from the industrial revolution through the twenty-first century. Therefore, the social impact of changes in their activities that either reduce or increase emissions should be quantified using estimates of marginal impacts: i.e. the SCC and the MCC.”
Thank you for your responses! I added edits to the essay to reflect this.
Overall, as I noted in the edits, this exercise has made me shift from being skeptical about all climate change interventions to considering shifting some donations from global poverty to climate change interventions. Not entirely convinced, but it seems a lot more plausibly effective than I first suspected.
Some things I don’t understand though:
It makes sense that with a convex harms curve, marginal harms will be worse than this back of the envelope linear calculation suggests. But it’s surprising that they’re 10 times higher. I guess it’s just very nonlinear, as you say, but that’s surprising to me.
The $1/ton estimate comes from CATF, which is a lobbying organization. Their cost effectiveness calculations account for money they spend lobbying, but not deadweight loss caused by taxes and regulations. How reasonable is it accept that sort of accounting?
1. To your question on accounting for deadweight losses etc., it is true that this is not included, rather this is an estimate of marginal changes from donations. But the factors not included in the calculation are not only deadweight losses (and other costs), but also lots of benefits, e.g. economic benefits from technological leadership. This is parallel to GiveWell analyses which only focus on mortality/direct income gains and ignore a lot of other follow-on benefits and costs.
2. The air pollution benefits of clean energy advocacy are plausibly in the same ballpark as climate benefits (depends on how severe climate change turns out) and benefits from overcoming energy poverty are also very significant (though hard to causally pin-down given the relationship between energy demand growth and human welfare is bidirectional, I explore this a bit more here).
3. One thing that is very different between GiveWell recommendations on global health and FP recommendations on climate is the attitude towards uncertainty—GiveWell recs have a high uncertainty avoidance whereas CATF and other estimates are meant to be risk-neutral estimates leveraging a fairly indirect theory of change (policy advocacy > policy change > technological change > changed emissions trajectory). So, in that sense the absence of risk-neutral global health recommendations biases the argument in favor of climate.
Thank you for this post on a very important topic! And thank you for the kind words on my Mortality Cost of Carbon paper.
I think that, at least from the perspective of using my paper, the analysis is actually much simpler than what you do above. Instead of using the 83 million cumulative 2020-2100 excess deaths, use the mortality cost of carbon itself: i.e. the number of lives saved per ton of carbon dioxide reduced, which is provided by the paper. So instead of the equation you show above, the equation now becomes:
Marginal Cost Per Life Saved = (Marginal Cost Per Ton CO_2 reduced)/(The Mortality Cost of Carbon)
@Louis_Dixon performed this analysis before in a really nice post Does using the mortality cost of carbon make reducing emissions comparable with health interventions? - EA Forum (effectivealtruism.org) and found that using carbon dioxide reduction estimates from a Founder’s Pledge report:
Future pessimistic - $5.50 per tonne, so $23,400 to avert 4,255 tons*
Future realistic - $0.29 per tonne, so $1,234 to avert 4,255 tons
Future optimistic - $0.03 per tonnes, so $127 to avert 4,255 tons
The issue with your original equation above is that you are implicitly assuming linearity, i.e. assuming that the marginal cost of saving a life from marginally reducing emissions is equivalent to the average cost of saving a life if we were to reduce emissions all the way to zero. However, one of the findings of the Mortality Cost of Carbon paper is that the system is actually nonlinear and highly convex, so the number of lives saved from marginally reducing emissions is actually much greater than the average number of lives saved that you would get per ton if you were to reduce all the way to zero (see figure 4). This is all a fancy way to say that there are diminishing marginal returns in terms of saving lives from reducing carbon dioxide on a planetary scale. So to determine the marginal impact of reducing emissions, use the marginal estimates provided by the paper (the mortality cost of carbon).
And of course, as you mention above, the mortality cost of carbon is just the projected number of excess deaths from 2020-2100 caused by marginal emissions due to temperature-related mortality—i.e. the net effect of more hot days (bad for mortality) and fewer cold days (good for mortality). It leaves out potentially important climate-mortality pathways such as the effect of climate change on infectious disease, civil and interstate war, food supply, flooding, as well as the co-benefit from less air pollution. Despite these limitations, Louis was still finding that these projections were cost-competitive with Givewell’s top recommendations.
*Note that Louis was using the 2020 Working Paper version of the Mortality Cost of Carbon, which included all mortality sources from the 2014 WHO paper (one of three papers used to construct the mortality damage function, which Andrew also mentions in the post), whereas the 2021 published version of the paper in Nature Communications used just the temperature-related mortality estimates from the 2014 WHO report. This ends up leading to a slight difference in the mortality cost of carbon estimate, from 1⁄4255 in the working paper version to 1⁄4434 in the published paper version. Recalculating Louis’s analysis with the published paper version numbers yields:
Future pessimistic - $5.50 per tonne, so $24,387 to avert 4,434 tons*
Future realistic - $0.29 per tonne, so $1,286 to avert 4,434 tons
Future optimistic - $0.03 per tonnes, so $133 to avert 4,434 tons
Thank you for commenting! I felt like I was relying on your paper without fully understanding it. I’m afraid that much of my post is just an attempt to reinterpret your work.
It’s encouraging that Founder’s Pledge thinks they can get such a low price on carbon! Interventions at that price really might be effective.
One major question I had about your paper is; what’s the breakdown of harms between direct deaths, economic harms, and other losses (like non-fatal hunger)? When the WHO estimates 250,000 deaths each year from 2030-2050, should I interpret a multiplier on that to account for other harms like productivity lost from sickness?
I knew I was making a bad linearity assumption, but I think I might have underestimated how much error it was introducing. If I use my naive model to match your work, I get 50,000 tons/death, which is an order of magnitude off from your estimate. Is that because of an improper linearity assumption?
(50,000 tons/life) = (2 Tt/°C) * (2.5°C/AGW) / (100 million lives / AGW)
When I have time later, I’ll edit the post to include some of your feedback.
No worries! I’m glad you found the paper useful and interesting!
The mortality cost of carbon is just the number of excess deaths from temperature-related mortality in units of excess deaths from emitting one metric ton of CO_2. So it’s just excess deaths and nothing else. The social cost of carbon is the full monetized value of all climate impacts from emitting one ton of CO_2, which includes the monetized value of those excess deaths in addition to other sources of climate damages. You can see that before the model accounted for temperature-related mortality, the social cost of carbon was $37, but after accounting for temperature-related mortality, it is $258. However, note my caveat from the conclusion: “It is important to note that recent literature has identified other shortcomings in the DICE model including other issues with the climate-economy damage function and the climate module. Besides adding the effect of climate change on mortality and subsequent feedbacks, DICE-EMR takes the rest of the DICE model as given without updating other factors.”
It’s hard for me to determine how much the different simplifying assumptions from your back-of-the-envelope formula are affecting your estimate. The linearity assumption is certainly causing a big difference because the system is highly convex. Also, the DICE-EMR model has the DICE climate model built into it that can show the climatic effect of changes in emissions. I’m not sure how much error you’re introducing with the back-of-the envelope climate assumptions, but that could also be an issue.
All this to say, if estimating the marginal impact (either the mortality cost of carbon or the full social cost of carbon) were as simple as a back-of-the envelope calculation, then there wouldn’t be a need to give William Nordhaus the Nobel Prize for his work on the original DICE model (the first one for environmental economics), nor for me to do this work. I think Louis Dixon’s original post is basically all you need to do for this exercise (at least for leveraging my paper’s results). Or as @jh suggested above, a $1/ton estimate just gets you to $4.4K per life saved using my paper’s results.
Also, see this one quote from the end of the paper: “Separate from policy, the MCC and SCC can be useful in informing the decision-making of individuals, households, companies, charities, and other organizations in determining the social impact of the emissions generated by their activities. The emissions contributions of these groups are usually marginal relative to the aggregate emissions of the world economy from the industrial revolution through the twenty-first century. Therefore, the social impact of changes in their activities that either reduce or increase emissions should be quantified using estimates of marginal impacts: i.e. the SCC and the MCC.”
Thank you for your responses! I added edits to the essay to reflect this.
Overall, as I noted in the edits, this exercise has made me shift from being skeptical about all climate change interventions to considering shifting some donations from global poverty to climate change interventions. Not entirely convinced, but it seems a lot more plausibly effective than I first suspected.
Some things I don’t understand though:
It makes sense that with a convex harms curve, marginal harms will be worse than this back of the envelope linear calculation suggests. But it’s surprising that they’re 10 times higher. I guess it’s just very nonlinear, as you say, but that’s surprising to me.
The $1/ton estimate comes from CATF, which is a lobbying organization. Their cost effectiveness calculations account for money they spend lobbying, but not deadweight loss caused by taxes and regulations. How reasonable is it accept that sort of accounting?
(Working at Founders Pledge)
1. To your question on accounting for deadweight losses etc., it is true that this is not included, rather this is an estimate of marginal changes from donations. But the factors not included in the calculation are not only deadweight losses (and other costs), but also lots of benefits, e.g. economic benefits from technological leadership. This is parallel to GiveWell analyses which only focus on mortality/direct income gains and ignore a lot of other follow-on benefits and costs.
2. The air pollution benefits of clean energy advocacy are plausibly in the same ballpark as climate benefits (depends on how severe climate change turns out) and benefits from overcoming energy poverty are also very significant (though hard to causally pin-down given the relationship between energy demand growth and human welfare is bidirectional, I explore this a bit more here).
3. One thing that is very different between GiveWell recommendations on global health and FP recommendations on climate is the attitude towards uncertainty—GiveWell recs have a high uncertainty avoidance whereas CATF and other estimates are meant to be risk-neutral estimates leveraging a fairly indirect theory of change (policy advocacy > policy change > technological change > changed emissions trajectory). So, in that sense the absence of risk-neutral global health recommendations biases the argument in favor of climate.