Even after the update, I’m confused by this model. I’ll restrict my attention to the “Realistic case” for simplicity.
The global social cost of carbon when constructed from the country-level estimates is effectively:
CCG=CCa+CCb+CCc+…
where CCG is the global social cost of carbon and CCa, CCb, CCc, etc. are the country level social costs of carbon for countries ‘a’, ‘b’, ‘c’, etc.
The spreadsheet model then uses an income adjustment factor of 1,260 expressing that a dollar means more to a poor person than a rich person. We can also think of this as a unit conversion factor: 1,260 American median income dollars = 1 GiveDirectly recipient dollar. We can write this conversion factor as 1260$A1$GD=1.
The next step in the model is to divide the global social cost of carbon by the income adjustment factor. If we expand global social cost of carbon, this looks like:
CCG1260=CCa1260+CCb1260+CCc1260+…
If we just look at the units, this is:
$G$GD$A=$a$GD$A+$b$GD$A+$c$GD$A+…
where $G is a country-level-cost-of-carbon-weighted dollar, $a is a dollar in country ‘a’, etc. Converting country ‘a’ dollars to GiveDirectly recipient dollars via $GD1260$A is only appropriate if country ‘a’ is in fact America. Otherwise, the units don’t line up.
It seems like what we’d actually want as far as income adjustment is something like:
CCG−GD=$a$GD$a+$b$GD$b+$c$GD$c+…
where CCG−GD is the global social cost of carbon expressed in GiveDirectly recipient dollars.
In other words, we can’t just apply the same income-adjustment factor to every country’s social cost of carbon because not every country has the same income. We need per-country income adjustment factors. Applying the 1,260 income adjustment factor to American social cost of carbon works but in applying this adjustment to the global cost of carbon, we are also implicitly saying that the social cost of carbon in Burkina Faso ought to be discounted just as heavily.
I think the only way the current approach works is if we assume that country-level costs have somehow already been adjusted into American median income dollars.
Thanks for this comment and apologies for the delay in replying.
As mentioned I had emailed the authors and they didn’t get back to me, and also the author of this paper this paper, “A social cost of carbon for (almost) every country” had apparently trouble replicating their analysis.
But both these papers do cite individual costs of carbon for each country—for instance here:
There you can for instance see that India’s SCC is $85.4 . I think this is based average income till the end of the century taking into account growth (“socioeconomic projections” (perhaps $20k/capita ).) and how much they’re hurt by climate damages given how rich they are. This figure is then income adjusted so that it is comparable with present day Americans (it might actually downward adjust the damages of rich countries which will be richer than present day US by the end of the century). Because then it can be interpreted as “this is what the Indian government should spend right now in USD to avert per tonne”, which seems to make most sense.
These costs are then all added together to arrive at the global social cost of carbon and what we should spend collectively to avert a tonne of CO2. This is why I think we can compare this with Givedirectly and the analysis is roughly correct.
I think my current model is suboptimal in that it mixes up different income adjustment factor eta = 1.5 and combining it with a different eta they use in the paper. It might be good to standardize this in one analysis. This might change the results.
I’m sorry that I didn’t understand quite the point you’re making, but you might legitimately be onto something. I think to get to the bottom of this it might be best to create a new model with open and transparent code to figure this out. I saw that you did very good quantitative analysis in a different post, so perhaps you could take this on. But maybe this would be more something for a slightly bigger org with more research capacity to take on. Not sure how productive this is or whether there’s really demand for such an analysis though.
Not sure which explanation will work better so I’ve included both a prose description of what I think is going on and a model. Look at whichever seems most useful.
Words
This figure is then income adjusted so that it is comparable with present day Americans (it might actually downward adjust the damages of rich countries which will be richer than present day US by the end of the century). Because then it can be interpreted as “this is what the Indian government should spend right now in USD to avert per tonne”, which seems to make most sense.
I think this is the crux of the discrepancy. I interpret the country-level social cost of carbon as expressing the cost in terms of that country’s citizens’ consumption. More concretely, if the social cost of carbon is $85/tonne of CO2 in India and everyone in India emits 5 tonnes of CO2, everyone’s welfare in India is as though their income is actually $425 (5 * 85) lower. I understand you to be saying that if everyone in India emits 5 tonnes at $85/tonne, it’s actually as though their income is reduced by $12.5 (5 * 85 / 34 where 34 is the poverty multiplier using an eta of 1.5 and an Indian income of $2000). The lower number comes because you believe the $85/tonne to be quoted in terms of dollars for the American median income and it needs to be adjusted to account for the fact that each dollar “means more” in lower-income India. Is that description intelligible? Is it an accurate account of your views?
Supposing that’s right, I can now explain why I believe my version. I think the relevant parts of the paper and model are the damages module and the discounting module.
I don’t think the sort of adjustment-to-America (i.e. “income adjusted so that it is comparable with present day Americans”) would happen in the damages module. Indeed, a quick skim of the damage function reference shows it to be talking purely about macroeconomic indicators. So the output of the damages module very likely is in local terms (e.g. a 1% decline in India’s GDP) rather than American terms.
Based just on the name, if this sort of adjustment-to-America were present, I’d expect it to take place in the discounting module. But the Ricke paper doesn’t describe any sort of adjustment for disparate incomes at time T=0. The income-relevant adjustments they perform are an: (1) an optional rich-poor damage specification which affects how damages grow over time for countries in each bin; (2) an optional elasticity of marginal utility adjustment to account for how the cost diminishes as economies grow [1]. So it doesn’t look like the discounting module does the required adjustment-to-America either.
Model
I’ve also made a quick spreadsheet model trying to explain what I think is going on.
The first two tabs are just data—the country level social costs of carbon and the GDP per capita (median income probably would have been better but alas).
The next tab to look at is probably “Hillebrandt Analogue”. It replicates your calculation using country-level data. It applies your uniform “Realistic” poverty multiplier to each country and then sums rather than summing before applying the poverty multiplier. Reassuringly, we get basically the same result: a global social cost of carbon of $0.32.
The other two tabs show roughly how I think the modeling should be done.
“CSSC in American Dollars” uses American GDP per capita as a reference income to compute separate poverty multipliers for each country based on its GDP per capita. The multiplier is 1 for America, less than 1 for countries richer than America and much greater than 1 for countries much poorer than America. Applying each country’s poverty multiplier to its country-level social cost of carbon and summing gives us a global social cost of carbon $36,834. If 100% of the social cost of a tonne of CO2 fell on an American making $62,641 (US GDP per capita), this would be the welfare-equivalent of a $36,834 reduction in income.
“CSSC in GiveDirectly Dollars” follows the same procedure but uses GiveDirectly annual consumption ($180) as the reference income. Thus the poverty multiplier is near 0 for most developed countries and is only over 0.5 for extremely poor countries like Burundi. Applying each country’s poverty multiplier to its country-level social cost of carbon and summing gives us a global social cost of carbon of $5.67. If 100% of the cost of a tonne of CO2 fell on a typical GiveDirectly recipient, this would be the welfare-equivalent of a $5.67 reduction in income.
Interestingly, this $5.67 figure makes climate change interventions within a factor of 2 of GiveDirectly in terms of cost-effectiveness (assuming $10 tonne/CO2 averted).
I think it’s pretty clear from context that this income adjustment is only applied within countries over time rather than across countries at time T=0: “We thus used growth-adjusted discounting determined by the Ramsey endogenous rule, with a range of
values for the elasticity of marginal utility (μ) and the pure rate of time preference (ρ), but we also report fixed discounting results to demonstrate the sensitivity of SCC calculations to discounting methods.”
Even after the update, I’m confused by this model. I’ll restrict my attention to the “Realistic case” for simplicity.
The global social cost of carbon when constructed from the country-level estimates is effectively:
CCG=CCa+CCb+CCc+…
where CCG is the global social cost of carbon and CCa, CCb, CCc, etc. are the country level social costs of carbon for countries ‘a’, ‘b’, ‘c’, etc.
The spreadsheet model then uses an income adjustment factor of 1,260 expressing that a dollar means more to a poor person than a rich person. We can also think of this as a unit conversion factor: 1,260 American median income dollars = 1 GiveDirectly recipient dollar. We can write this conversion factor as 1260$A1$GD=1.
The next step in the model is to divide the global social cost of carbon by the income adjustment factor. If we expand global social cost of carbon, this looks like:
CCG1260=CCa1260+CCb1260+CCc1260+…
If we just look at the units, this is:
$G$GD$A=$a$GD$A+$b$GD$A+$c$GD$A+…
where $G is a country-level-cost-of-carbon-weighted dollar, $a is a dollar in country ‘a’, etc. Converting country ‘a’ dollars to GiveDirectly recipient dollars via $GD1260$A is only appropriate if country ‘a’ is in fact America. Otherwise, the units don’t line up.
It seems like what we’d actually want as far as income adjustment is something like:
CCG−GD=$a$GD$a+$b$GD$b+$c$GD$c+…
where CCG−GD is the global social cost of carbon expressed in GiveDirectly recipient dollars.
In other words, we can’t just apply the same income-adjustment factor to every country’s social cost of carbon because not every country has the same income. We need per-country income adjustment factors. Applying the 1,260 income adjustment factor to American social cost of carbon works but in applying this adjustment to the global cost of carbon, we are also implicitly saying that the social cost of carbon in Burkina Faso ought to be discounted just as heavily.
I think the only way the current approach works is if we assume that country-level costs have somehow already been adjusted into American median income dollars.
Thanks for this comment and apologies for the delay in replying.
As mentioned I had emailed the authors and they didn’t get back to me, and also the author of this paper this paper, “A social cost of carbon for (almost) every country” had apparently trouble replicating their analysis.
But both these papers do cite individual costs of carbon for each country—for instance here:
https://country-level-scc.github.io/explorer/
There you can for instance see that India’s SCC is $85.4 . I think this is based average income till the end of the century taking into account growth (“socioeconomic projections” (perhaps $20k/capita ).) and how much they’re hurt by climate damages given how rich they are. This figure is then income adjusted so that it is comparable with present day Americans (it might actually downward adjust the damages of rich countries which will be richer than present day US by the end of the century). Because then it can be interpreted as “this is what the Indian government should spend right now in USD to avert per tonne”, which seems to make most sense.
These costs are then all added together to arrive at the global social cost of carbon and what we should spend collectively to avert a tonne of CO2. This is why I think we can compare this with Givedirectly and the analysis is roughly correct.
I think my current model is suboptimal in that it mixes up different income adjustment factor eta = 1.5 and combining it with a different eta they use in the paper. It might be good to standardize this in one analysis. This might change the results.
I’m sorry that I didn’t understand quite the point you’re making, but you might legitimately be onto something. I think to get to the bottom of this it might be best to create a new model with open and transparent code to figure this out. I saw that you did very good quantitative analysis in a different post, so perhaps you could take this on. But maybe this would be more something for a slightly bigger org with more research capacity to take on. Not sure how productive this is or whether there’s really demand for such an analysis though.
Not sure which explanation will work better so I’ve included both a prose description of what I think is going on and a model. Look at whichever seems most useful.
Words
I think this is the crux of the discrepancy. I interpret the country-level social cost of carbon as expressing the cost in terms of that country’s citizens’ consumption. More concretely, if the social cost of carbon is $85/tonne of CO2 in India and everyone in India emits 5 tonnes of CO2, everyone’s welfare in India is as though their income is actually $425 (5 * 85) lower. I understand you to be saying that if everyone in India emits 5 tonnes at $85/tonne, it’s actually as though their income is reduced by $12.5 (5 * 85 / 34 where 34 is the poverty multiplier using an eta of 1.5 and an Indian income of $2000). The lower number comes because you believe the $85/tonne to be quoted in terms of dollars for the American median income and it needs to be adjusted to account for the fact that each dollar “means more” in lower-income India. Is that description intelligible? Is it an accurate account of your views?
Supposing that’s right, I can now explain why I believe my version. I think the relevant parts of the paper and model are the damages module and the discounting module.
I don’t think the sort of adjustment-to-America (i.e. “income adjusted so that it is comparable with present day Americans”) would happen in the damages module. Indeed, a quick skim of the damage function reference shows it to be talking purely about macroeconomic indicators. So the output of the damages module very likely is in local terms (e.g. a 1% decline in India’s GDP) rather than American terms.
Based just on the name, if this sort of adjustment-to-America were present, I’d expect it to take place in the discounting module. But the Ricke paper doesn’t describe any sort of adjustment for disparate incomes at time T=0. The income-relevant adjustments they perform are an: (1) an optional rich-poor damage specification which affects how damages grow over time for countries in each bin; (2) an optional elasticity of marginal utility adjustment to account for how the cost diminishes as economies grow [1]. So it doesn’t look like the discounting module does the required adjustment-to-America either.
Model
I’ve also made a quick spreadsheet model trying to explain what I think is going on.
The first two tabs are just data—the country level social costs of carbon and the GDP per capita (median income probably would have been better but alas).
The next tab to look at is probably “Hillebrandt Analogue”. It replicates your calculation using country-level data. It applies your uniform “Realistic” poverty multiplier to each country and then sums rather than summing before applying the poverty multiplier. Reassuringly, we get basically the same result: a global social cost of carbon of $0.32.
The other two tabs show roughly how I think the modeling should be done.
“CSSC in American Dollars” uses American GDP per capita as a reference income to compute separate poverty multipliers for each country based on its GDP per capita. The multiplier is 1 for America, less than 1 for countries richer than America and much greater than 1 for countries much poorer than America. Applying each country’s poverty multiplier to its country-level social cost of carbon and summing gives us a global social cost of carbon $36,834. If 100% of the social cost of a tonne of CO2 fell on an American making $62,641 (US GDP per capita), this would be the welfare-equivalent of a $36,834 reduction in income.
“CSSC in GiveDirectly Dollars” follows the same procedure but uses GiveDirectly annual consumption ($180) as the reference income. Thus the poverty multiplier is near 0 for most developed countries and is only over 0.5 for extremely poor countries like Burundi. Applying each country’s poverty multiplier to its country-level social cost of carbon and summing gives us a global social cost of carbon of $5.67. If 100% of the cost of a tonne of CO2 fell on a typical GiveDirectly recipient, this would be the welfare-equivalent of a $5.67 reduction in income.
Interestingly, this $5.67 figure makes climate change interventions within a factor of 2 of GiveDirectly in terms of cost-effectiveness (assuming $10 tonne/CO2 averted).
I think it’s pretty clear from context that this income adjustment is only applied within countries over time rather than across countries at time T=0: “We thus used growth-adjusted discounting determined by the Ramsey endogenous rule, with a range of values for the elasticity of marginal utility (μ) and the pure rate of time preference (ρ), but we also report fixed discounting results to demonstrate the sensitivity of SCC calculations to discounting methods.”
Thank you so much for this thoughtful comment.
Unfortunately, I won’t have the time to give it the time it deserves to engage with it properly (e.g. rework the analysis etc.).
I think you raise interesting points and people looking to extend this work further should take your comment into account.
Okay, thanks. I will likely write this up as a post then so that the concern doesn’t get lost here in the comments.
Thanks this is a great idea!
I’m really sorry that I don’t have more time for this.