If a climate change intervention has a cost-effectiveness of $417 /ā X per tonne of CO2 averted, then it is X times as effective as cash-transfers.
Wait a second.
Iām very confused by this sentence. Suppose, for the sake of argument, that all the impacts of emitting a tonne of CO2 are on people about as rich as present-day Americans, i.e. emitting a tonne of CO2 now causes people of that level of wealth to lose $417 at some point in the future. There is then no income adjustment necessary (I assume everything is being converted to something like present-day USD for present-day Americans, but Iām not actually sure and following the links didnāt shed any light), so the post-income-adjustment number is still $417. Also suppose for the sake of argument that we can prevent this for $100.
This seems clearly worse than cash transfers to me under usual assumptions about log income being a reasonable approximation to wellbeing (as described in your first appendix), since we are effectively getting a 4.17x multiplier rather than a 50-100x multiplier. Yet the equation in the quote claims it is 4.17x more effective than cash transfers*.
What am I missing?
*Mathematically, I think the equation works iff. the cash transfers in question are to people of comparable wealth to whatever baseline is being used to come up with the $417 figure. So if the baseline is modern-day Americans, that equation calculates how much better it is to avert CO2 emissions than to transfer cash to modern-day Americans.
I was about to say this and then saw your comment. My impression from the paper is the $417 is a sum of costs to different countries, and for each of them the cost is a present value to the people in that country, with discounting being applied based on the expected amount of economic growth in that country. So I donāt think itās calibrated to present-day Americans, but I donāt think itās calibrated to the worldās poorest either, and I agree the argument doesnāt go through.
Thereās another problem with the quoted claim, which becomes clear if you pick a value like X = 1/ā1000. Paying $417,000 to avert a tonne of carbon is a huge net bad and not just a much smaller net good.
It seems to me another problem is that if the social cost of carbon comes from effects on growth, you have to compare that to the effects on growth of cash transfers. Itās generally easy for small changes in growth rate to outweigh small changes to level in the long run, so if you compare the growth effects of one intervention to the level effects of another intervention, itās no surprise that the former would seem more effective.
I agree with this. I would have assumed they would do (i), and other responses from people who actually read the paper make me think it might effectively be (iii). I donāt think itās (ii).
I mentioned it in my comment elsewhere, butāfrom a quick look at the paper and the supplementary materialāI donāt think itās much like any of these. They donāt make any special mention that I could find of trying to translate purely economic measures into welfare. The only mention I could find about income adjustment is ārich/āpoor specificationsā which appears to be about splitting the formula for growth of damages into one of two forms depending on whether the country is rich or poor.
Edit: They do mention āelasticity of marginal utilityā in the discounting module section which is also known as āintergenerational inequality aversionā.
My nonconfident best guess at an interpretation is that, according to these estimates, for every tonne of carbon:
Future Indians suffer damages utility-equivalent to the present population of India paying a total of $76
Future Americans suffer damages utility-equivalent to the present population of the USA paying a total of $48
Future Saudis suffer damages utility-equivalent to the present population of Saudi Arabia paying a total of $47
Next are China, Brazil, and the UAE, all with $24, and then a lot of other countries, and the sum of all these numbers is $417. So itās as if the $417 is paid by this particular mix of the worldās people, making it iii), something in between. These numbers are totals that donāt divide by population, so an individual inhabitant of Saudi Arabia or the UAE pays a greater absolute amount than an individual American, who pays a greater absolute amount (but a smaller percentage of income) than an individual Indian.
But I think the social cost of carbon figures should generally be interpreted as current US dollars. They are then discounted for decreasing returns to consumption for future people who live in countries with higher consumption.
So we should divide the $417 figure by the 100x multiplier (or more, see my sensitivity analysis).
It would have been reasonable for them to use the mean global income as the baseline, rather than dollars to the mean US citizen.
If I understand correctly, that would boost things by about a factor of 3 in favour of climate change (mean global income is about $20k, vs. mean US income of about $60k). Though, I suppose thatās a fairly small uncertainty compared to the others listed here.
The assumption is that a policymaker will use these results to shape how strict climate policy is. Stricter climate policies will reduce present-day consumption in the policymakerās jurisdiction. The goal is to have a climate policy that is just strict enough to balance the future utility gain from improved climate with current utility loss from reduced consumption.
For most real world applications it is convenient to have marginal damages expressed in monetary terms, rather than in utility units. In a final step, the marginal damage estimate therefore must be converted into monetary units. In principle one would just divide the marginal damage estimate expressed in utility units by marginal utility of income or consumption in the present to convert from utility to monetary units. Income inequality in the present however implies that the marginal utility of income is difference between regions and therefore the conversion depends on the choice of the reference or normalization region. Unless potentially very large transfers equating marginal utilities are allowed this yields different monetary values for different reference regions of the aggregated marginal damages as shown in Anthoff et al. (2009a)
I think itās conventional in the literature to use the US as the reference region: āIn order to make the numerical results comparable with previous studies we take the US as reference region x throughout this paperā (ibid).
My current understanding of how we should interpret a social cost of carbon of $y is:
āGiven certain assumptions about future climate effects, emissions trajectories, how utility scales with consumption, and how much we discount future utility, a utilitarian policymaker in country x should be willing to reduce current consumption in his country by up to $y in order to abate 1 ton of carbon emissionsā
This also means that, due to assumptions about diminishing marginal utility, the choice of reference region majorly affects the SCC. For example, Anthoff and Emmerling show how reference region affects their results. (Remember that this, like all SCC estimates, is subject to lots of assumptions about the effects of climate change and discounting.)
(Sorry for the huge image)
If the SCC estimate is low enough it can actually be negative for some regions, meaning that any reduction in present-day consumption in those countries to mitigate climate change would reduce utility.
I wanted to jump in here while the discussion is active, but Iāll also flag that John, Johannes and I are working on this and should have a post on comparing climate vs. global health/ādevelopment interventions in the not-too-distant future.
Great, thank you for this! Look forward to seeing more work also.
And just a quick thought: if we know what the SCC of carbon is for Africa (looks like ~$10), and itās defined in the way you say, then we could also do the comparison directly with the Africa-SCC figure, rather than converting into US equivalent first e.g.:
1 tonne of CO2 averted ā equivalent to $10 of consumption in Africa
If it costs $1 to avert a tonne, then $1 ā $10 consumption
$1 cash transfer ā $1 of consumption in Africa (or maybe ~$5 to a GiveDirectly-recipient)
$1 to AMF ā ~$50 African-consumption-equivalent (thinking of it as 10x GiveDirectly)
So with these figures, carbon offsets are better than cash transfers, but AMF is 5x better than carbon offsets.
I had emailed all the authors of this analysis and asked them, but they didnāt get back to me, so I think itās ambiguous and not really replicable. But yes I agree itās a fairly small uncertainty compared to the others.
Wait a second.
Iām very confused by this sentence. Suppose, for the sake of argument, that all the impacts of emitting a tonne of CO2 are on people about as rich as present-day Americans, i.e. emitting a tonne of CO2 now causes people of that level of wealth to lose $417 at some point in the future. There is then no income adjustment necessary (I assume everything is being converted to something like present-day USD for present-day Americans, but Iām not actually sure and following the links didnāt shed any light), so the post-income-adjustment number is still $417. Also suppose for the sake of argument that we can prevent this for $100.
This seems clearly worse than cash transfers to me under usual assumptions about log income being a reasonable approximation to wellbeing (as described in your first appendix), since we are effectively getting a 4.17x multiplier rather than a 50-100x multiplier. Yet the equation in the quote claims it is 4.17x more effective than cash transfers*.
What am I missing?
*Mathematically, I think the equation works iff. the cash transfers in question are to people of comparable wealth to whatever baseline is being used to come up with the $417 figure. So if the baseline is modern-day Americans, that equation calculates how much better it is to avert CO2 emissions than to transfer cash to modern-day Americans.
I was about to say this and then saw your comment. My impression from the paper is the $417 is a sum of costs to different countries, and for each of them the cost is a present value to the people in that country, with discounting being applied based on the expected amount of economic growth in that country. So I donāt think itās calibrated to present-day Americans, but I donāt think itās calibrated to the worldās poorest either, and I agree the argument doesnāt go through.
Thereās another problem with the quoted claim, which becomes clear if you pick a value like X = 1/ā1000. Paying $417,000 to avert a tonne of carbon is a huge net bad and not just a much smaller net good.
It seems to me another problem is that if the social cost of carbon comes from effects on growth, you have to compare that to the effects on growth of cash transfers. Itās generally easy for small changes in growth rate to outweigh small changes to level in the long run, so if you compare the growth effects of one intervention to the level effects of another intervention, itās no surprise that the former would seem more effective.
Am I right that what we need to know is whether, when assessing the total global social cost of carbon:
i) they multiplied harms to the worldās poorest people, measured in equivalent dollars of their income, by ~100x;
ii) they divided the harms to the world richest people, measured in equivalent dollars of their income, by ~100x;
iii) or something in between?
HHās argument only goes through if itās the second of the three.
I agree with this. I would have assumed they would do (i), and other responses from people who actually read the paper make me think it might effectively be (iii). I donāt think itās (ii).
I mentioned it in my comment elsewhere, butāfrom a quick look at the paper and the supplementary materialāI donāt think itās much like any of these. They donāt make any special mention that I could find of trying to translate purely economic measures into welfare. The only mention I could find about income adjustment is ārich/āpoor specificationsā which appears to be about splitting the formula for growth of damages into one of two forms depending on whether the country is rich or poor.
Edit: They do mention āelasticity of marginal utilityā in the discounting module section which is also known as āintergenerational inequality aversionā.
My nonconfident best guess at an interpretation is that, according to these estimates, for every tonne of carbon:
Future Indians suffer damages utility-equivalent to the present population of India paying a total of $76
Future Americans suffer damages utility-equivalent to the present population of the USA paying a total of $48
Future Saudis suffer damages utility-equivalent to the present population of Saudi Arabia paying a total of $47
Next are China, Brazil, and the UAE, all with $24, and then a lot of other countries, and the sum of all these numbers is $417. So itās as if the $417 is paid by this particular mix of the worldās people, making it iii), something in between. These numbers are totals that donāt divide by population, so an individual inhabitant of Saudi Arabia or the UAE pays a greater absolute amount than an individual American, who pays a greater absolute amount (but a smaller percentage of income) than an individual Indian.
Thanks for catching this mistake.
Iāve updated the analysis to reflect this.
I emailed the authors but they didnāt reply.
But I think the social cost of carbon figures should generally be interpreted as current US dollars. They are then discounted for decreasing returns to consumption for future people who live in countries with higher consumption.
So we should divide the $417 figure by the 100x multiplier (or more, see my sensitivity analysis).
Iām still a bit worried about this.
It would have been reasonable for them to use the mean global income as the baseline, rather than dollars to the mean US citizen.
If I understand correctly, that would boost things by about a factor of 3 in favour of climate change (mean global income is about $20k, vs. mean US income of about $60k). Though, I suppose thatās a fairly small uncertainty compared to the others listed here.
The assumption is that a policymaker will use these results to shape how strict climate policy is. Stricter climate policies will reduce present-day consumption in the policymakerās jurisdiction. The goal is to have a climate policy that is just strict enough to balance the future utility gain from improved climate with current utility loss from reduced consumption.
(Anthoff and Emmerling, 2016, p. 5, emphasis added).
I think itās conventional in the literature to use the US as the reference region: āIn order to make the numerical results comparable with previous studies we take the US as reference region x throughout this paperā (ibid).
My current understanding of how we should interpret a social cost of carbon of $y is:
āGiven certain assumptions about future climate effects, emissions trajectories, how utility scales with consumption, and how much we discount future utility, a utilitarian policymaker in country x should be willing to reduce current consumption in his country by up to $y in order to abate 1 ton of carbon emissionsā
This also means that, due to assumptions about diminishing marginal utility, the choice of reference region majorly affects the SCC. For example, Anthoff and Emmerling show how reference region affects their results. (Remember that this, like all SCC estimates, is subject to lots of assumptions about the effects of climate change and discounting.)
(Sorry for the huge image)
If the SCC estimate is low enough it can actually be negative for some regions, meaning that any reduction in present-day consumption in those countries to mitigate climate change would reduce utility.
I wanted to jump in here while the discussion is active, but Iāll also flag that John, Johannes and I are working on this and should have a post on comparing climate vs. global health/ādevelopment interventions in the not-too-distant future.
Great, thank you for this! Look forward to seeing more work also.
And just a quick thought: if we know what the SCC of carbon is for Africa (looks like ~$10), and itās defined in the way you say, then we could also do the comparison directly with the Africa-SCC figure, rather than converting into US equivalent first e.g.:
1 tonne of CO2 averted ā equivalent to $10 of consumption in Africa If it costs $1 to avert a tonne, then $1 ā $10 consumption $1 cash transfer ā $1 of consumption in Africa (or maybe ~$5 to a GiveDirectly-recipient) $1 to AMF ā ~$50 African-consumption-equivalent (thinking of it as 10x GiveDirectly)
So with these figures, carbon offsets are better than cash transfers, but AMF is 5x better than carbon offsets.
I had emailed all the authors of this analysis and asked them, but they didnāt get back to me, so I think itās ambiguous and not really replicable. But yes I agree itās a fairly small uncertainty compared to the others.