A corrected model suggests climate change interventions may be within a factor of two of direct cash transfers

Link post

In an ear­lier EA fo­rum post, data from a new pa­per on coun­try-level so­cial cost of car­bon is used to es­ti­mate the com­par­a­tive cost-effec­tive­ness of cli­mate change in­ter­ven­tions and global de­vel­op­ment in­ter­ven­tions (cost-effec­tive­ness of the lat­ter as de­ter­mined by GiveWell’s mod­els). A cen­tral com­po­nent of the ear­lier post (hence­forth GDvCC[1]) is sup­posed to be in­come[2]-weight­ing---$10 dol­lars of lost in­come means a great deal more in terms of util­ity for some­one that makes $200 per year than for some­one that makes $20,000 per year. More gran­u­lar, coun­try-level data on the so­cial cost of car­bon gets us closer to ac­count­ing for this dis­tri­bu­tional con­sid­er­a­tion[3] and al­lows us to ex­press the so­cial cost of car­bon in a way that’s di­rectly com­pa­rable with the out­puts of GiveWell’s mod­els. GDvCC’s model finds that, in its “re­al­is­tic” sce­nario, cli­mate change in­ter­ven­tions are 3% as cost-effec­tive as GiveDirectly and 0.4% as cost-effec­tive as GiveWell’s me­dian top char­ity. How­ever, I think there’s an er­ror in the way the coun­try-level so­cial cost of car­bon (CSCC) is in­ter­preted in GDvCC which leads to in­cor­rect in­come-weight­ing. Cor­rect­ing for this er­ror sug­gests that cli­mate change in­ter­ven­tions (again, un­der “re­al­is­tic” as­sump­tions) are 57% as cost-effec­tive as GiveDirectly.

In­ter­pret­ing coun­try-level so­cial cost of car­bon: the discrepancy

In­ter­pret­ing CSCC data seems to be difficult (for ex­am­ple, there was also an ear­lier ver­sion of GDvCC which in­ter­preted it in a third way). Given that, I’m go­ing to ex­plain my in­ter­pre­ta­tion and how it differs from that in GDvCC in a va­ri­ety of ways—once/​if one of the ex­pla­na­tions works for you, feel free to skip the rest. After this sec­tion, we’ll talk about why I pre­fer my in­ter­pre­ta­tion.

Con­crete example

In one of GDvCC’s au­thor’s com­ments, he ex­plains that, “There you can for in­stance see that In­dia’s SCC is $85.4 . [...] This figure is then in­come ad­justed so that it is com­pa­rable with pre­sent day Amer­i­cans[.]”. I don’t see any rea­son to be­lieve that that ad­just­ment-to-Amer­ica hap­pens in the CSCC data. On my in­ter­pre­ta­tion, an $85 SCC in In­dia means that if we could re­ar­range the so­cial costs of some sin­gle tonne of car­bon so that they fell en­tirely on an In­dian of av­er­age in­come—roughly $2000---the welfare-equiv­a­lent in­come is $1915. In other words, the vic­tim of our strange sce­nario would be roughly in­differ­ent be­tween an in­come of $1915 with­out the so­cial costs of that tonne of car­bon and $2000 with the so­cial costs of that tonne of car­bon. In the GDvCC in­ter­pre­ta­tion, the welfare-equiv­a­lent in­come is roughly $1997.5. This re­sults from be­liev­ing that the origi­nal $85/​tonne figure is quoted in dol­lars pegged to Amer­i­can av­er­age in­come and then di­vid­ing by 34 to ac­count for the lower in­come in In­dia and the cor­re­spond­ing fact that a dol­lar “means more” there ( which fol­lows the calcu­la­tions in GDvCC’s model and sets—a pa­ram­e­ter ex­press­ing how the value of a marginal dol­lar changes with in­come—to 1.5).

Data-based model

Be­cause the GDvCC post op­er­ates on the be­lief that all the coun­try-level so­cial costs of car­bon have already been “in­come ad­justed so that [they are] com­pa­rable with pre­sent day Amer­i­cans”, it sim­ply ap­plies a uniform poverty mul­ti­plier (1260) to trans­late these Amer­i­can-ad­justed dol­lars to GiveDirectly-re­cip­i­ent dol­lars. On my in­ter­pre­ta­tion, the coun­try-level so­cial costs of car­bon have not already been ad­justed to some com­mon nu­meraire so each CSCC must be ad­justed us­ing a sep­a­rate poverty mul­ti­plier which ac­counts for that coun­try’s av­er­age in­come. Us­ing sup­ple­men­tary data from Coun­try-level so­cial cost of car­bon and GDP per cap­ita data from the World Bank, I’ve pro­duced a quick spread­sheet model of these in­ter­pre­ta­tions.

The “GDvCC analogue” tab repli­cates the calcu­la­tions performed in the origi­nal post us­ing this more gran­u­lar data—it ap­plies the uniform “re­al­is­tic” poverty mul­ti­plier to each coun­try and then sums rather than ap­ply­ing the poverty mul­ti­plier af­ter sum­ming. Re­as­sur­ingly, the es­ti­mated global cost of car­bon matches that found in the “re­al­is­tic” sce­nario in GDvCC’s model---$0.32. The key part to no­tice is that the poverty mul­ti­plier is the same for each coun­try.

The “CSCC in Amer­i­can dol­lars” tab gives each coun­try a sep­a­rate poverty mul­ti­plier us­ing Amer­i­can GDP per cap­ita as the refer­ence in­come. 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.

The “CSSC in GiveDirectly dol­lars” tab 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.

(Both the “CSCC in Amer­i­can dol­lars” tabs and “CSCC in GiveDirectly dol­lars” mod­els ex­press valid calcu­la­tions. They just pro­duce fi­nal figures ex­pressed in terms of differ­ent nu­meraires. We can in fact con­vert be­tween the two us­ing a poverty mul­ti­plier of 6,492 (con­cep­tu­ally the same as the 1260 ap­pear­ing in GDvCC but in­stead of be­cause of our World Bank GDP per cap­ita data for US in­come in­stead of me­dian).)

Unit analysis

We can also think of this a bit more ab­stractly in terms of unit anal­y­sis. This is a gen­er­ally use­ful way to check mod­els by mak­ing sure that all the units of mea­sure line up; we don’t want to add 20 sec­onds to 4 dol­lars be­cause the re­sult­ing quan­tity doesn’t have any sen­si­ble phys­i­cal in­ter­pre­ta­tion. Once we re­al­ize that not all dol­lars are equal and we should treat dol­lars of con­sump­tion for the av­er­age In­dian differ­ently than dol­lars of con­sump­tion for the av­er­age Amer­i­can, we can get a lot of mileage out of this ap­proach.

The global so­cial cost of car­bon when con­structed from the coun­try-level es­ti­mates is effec­tively where is the global so­cial cost of car­bon and , , , etc. are the coun­try level so­cial costs of car­bon for coun­tries ‘a’, ‘b’, ‘c’, etc.

The GDvCC model then uses a poverty mul­ti­plier 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 write this con­ver­sion fac­tor as where is a dol­lar in Amer­ica and is a dol­lar for a GiveDirectly re­cip­i­ent.

The next step in the GDvCC model di­vides the global so­cial cost of car­bon by the uniform poverty mul­ti­plier. If we ex­pand global so­cial cost of car­bon, the calcu­la­tion looks like: .

If we just look at the units, this is

where is a coun­try-level-cost-of-car­bon-weighted dol­lar, is a dol­lar in coun­try ‘a’, etc. Con­vert­ing coun­try ‘a’ dol­lars to GiveDirectly re­cip­i­ent dol­lars via is only ap­pro­pri­ate if coun­try ‘a’ is in fact Amer­ica. Other­wise, the units don’t line up.

The “CSCC in GiveDirectly dol­lars” model looks like where is the global so­cial cost of car­bon ex­pressed in GiveDirectly re­cip­i­ent dol­lars. In this case nu­mer­a­tor and de­nom­i­na­tor of each term on the right-hand side can­cel leav­ing us with a global so­cial cost of car­bon ex­pressed in terms of GiveDirectly dol­lars.

To sum­ma­rize, unit anal­y­sis sug­gests that sim­ply adding the coun­try-level so­cial costs of car­bon and then ap­ply­ing a sin­gle poverty mul­ti­plier (as the GDvCC model does) is in­ap­pro­pri­ate be­cause the con­cept of a dol­lar of con­sump­tion ac­tu­ally dis­guises sub­stan­tial het­ero­gene­ity across coun­tries. We need to ho­mog­e­nize the units with tai­lored poverty mul­ti­pli­ers be­fore sum­ming the coun­try-level so­cial costs of car­bon is a sen­si­ble op­er­a­tion.

Which in­ter­pre­ta­tion to pre­fer?

Ex­am­i­na­tion of study methodology

My ba­sic ar­gu­ment against the GDvCC in­ter­pre­ta­tion is that the ad­just­ment-to-Amer­ica it sup­poses is an ad­di­tional step that is not de­scribed any­where in the pa­per and doesn’t seem to nat­u­rally fit in any com­po­nent of the model as de­scribed. Fur­ther­more, I don’t think this ad­just­ment is so com­mon and ex­pected as to not merit men­tion. Thus, the ab­sence of ev­i­dence is ev­i­dence of ab­sence.

Coun­try-level so­cial cost of car­bon and so­cial cost of car­bon mod­els gen­er­ally, as far as I un­der­stand, con­sist of four mod­ules:

  • a so­cio-eco­nomic mod­ule wherein the fu­ture evolu­tion of the econ­omy, which in­cludes the pro­jected emis­sions of CO2, is char­ac­ter­ized with­out the im­pact of cli­mate change;

  • a cli­mate mod­ule wherein the earth sys­tem re­sponds to emis­sions of CO2 and other an­thro­pogenic forc­ings;

  • a dam­ages mod­ule, wherein the econ­omy’s re­sponse to changes in the Earth sys­tem are quan­tified; and

  • a dis­count­ing mod­ule, wherein a time se­ries of fu­ture dam­ages is com­pressed into a sin­gle pre­sent value.

Of these four mod­ules, dam­ages and dis­count­ing seem like the only places where the re­quired ad­just­ment could hap­pen.

I don’t think that “in­come [is] ad­justed so that it is com­pa­rable with pre­sent day Amer­i­cans” in the dam­ages mod­ule. It doesn’t seem to fit the de­scrip­tion of the dam­ages mod­ule which talks about “the econ­omy’s re­sponse to changes in the Earth sys­tem”. In­deed, a quick skim of the dam­age func­tion pa­per refer­enced in Coun­try-level so­cial costs of car­bon shows it to be talk­ing purely about macroe­co­nomic in­di­ca­tors. The refer­enced pa­per says “The im­pact of warm­ing on global eco­nomic pro­duc­tion is a pop­u­la­tion-weighted av­er­age of coun­try-level im­pacts in Fig. 4a.” where Fig 4a is about “Change in GDP per cap­ita (RCP8.5, SSP5) rel­a­tive to pro­jec­tion”. So the out­put of the dam­ages mod­ule in that pa­per is a pop­u­la­tion-weighted func­tion of lo­cal, purely eco­nomic im­pacts (e.g. a 1% de­cline in In­dia’s GDP).

The dis­count­ing mod­ule seems like the most likely can­di­date lo­ca­tion for this sort of ad­just­ment to hap­pen. The dis­count­ing mod­ule already han­dles tem­po­ral dis­count­ing and we can think of the re­quired ad­just­ments as ge­o­graphic or in­come dis­count­ing. But, in this case, I don’t think the dis­count­ing mod­ule ac­tu­ally in­cludes these ad­just­ments. The high-level de­scrip­tion of the mod­ule—”wherein a time se­ries of fu­ture dam­ages is com­pressed into a sin­gle pre­sent value”—de­scribes only tem­po­ral dis­count­ing. Look­ing at the method­ol­ogy in more de­tail, the only men­tions of in­come-re­lated ad­just­ments are: (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 effec­tive so­cial cost diminishes as economies grow [4]. So, as ex­pected, all the par­tic­u­lars of the method­ol­ogy are about how in­come effects change over time. None of the men­tioned ad­just­ments take ac­count of differ­ing in­comes and con­sump­tion at the be­gin­ning of the model i.e. the pre­sent day.

San­ity check on data

A quick in­spec­tion of the coun­try-level data also pro­vides rea­son to doubt that the coun­try-level so­cial costs have already been in­come-ad­justed. For ex­am­ple, it strikes me as fairly im­plau­si­ble that In­dia’s in­come-ad­justed CSCC is less than twice the United States’ ($85 vs $48) given that In­dia has 4 times the pop­u­la­tion, a cli­mate much more sus­cep­ti­ble to the nega­tive im­pacts of global warm­ing, and a much poorer pop­u­la­tion.


If we ac­cept the above ar­gu­ments the coun­try-level so­cial costs of car­bon are each ex­pressed in lo­cal terms and the rough, cor­rected model which ac­counts for this sug­gests that the so­cial cost of car­bon ex­pressed in terms of in­come for a typ­i­cal GiveDirectly re­cip­i­ent is $5.67. In other words, a typ­i­cal GiveDirectly re­cip­i­ent would be in­differ­ent be­tween bear­ing the full so­cial costs of a tonne of car­bon with an an­nual con­sump­tion of $180 and bear­ing none of the costs with a con­sump­tion of $174.33. If we use GDvCC’s “re­al­is­tic” es­ti­mate of $10/​tonne CO2 averted, this means that such cli­mate change in­ter­ven­tions pro­duce 57% as much benefit per dol­lar donated as a dona­tion to GiveDirectly.

  1. I’m refer­ring to it as GDvCC to keep the fo­cus on the ideas rather than the peo­ple in­volved. Thank you to the origi­nal au­thor for the work he did—most of which I am reusing—and for dis­cus­sion in the com­ments on the origi­nal post. ↩︎

  2. Apolo­gies if I get a bit sloppy with “in­come” vs “con­sump­tion”. The thing we care about di­rectly as far as welfare is con­cerned is con­sump­tion, but of­ten in­come data is all that’s available. I’ll also use “in­come” to match the lan­guage in a source un­der dis­cus­sion. The two are gen­er­ally closely cor­re­lated over the long-run but may di­verge due to things like sub­sidies (e.g. SNAP in the U.S. counts for con­sump­tion but not in­come.). Also, I’ll pre­tend GDP per cap­ita is the same as in­come which is not strictly cor­rect. ↩︎

  3. A full ac­count of this con­sid­er­a­tion would en­tail hav­ing house­hold- or in­di­vi­d­ual-level con­sump­tion data and do­ing the weight­ing on that ba­sis. The dis­crep­ancy be­tween coun­try-level and house­hold-level weight­ing in­creases as within-coun­try con­sump­tion in­equal­ity in­creases. ↩︎

  4. 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.” ↩︎