[updated] Global development interventions are generally more effective than Climate change interventions

Pre­vi­ously ti­tled “Cli­mate change in­ter­ven­tions are gen­er­ally more effec­tive than global de­vel­op­ment in­ter­ven­tions”. Be­cause of an er­ror the con­clu­sions have sig­nifi­cantly changed. [old ver­sion]. I have ex­tended the anal­y­sis and now provide a more de­tailed spread­sheet model be­low.

Word count: ~1800

Read­ing time: ~9 mins

Key­words: Cli­mate change, cli­mate policy, global de­vel­op­ment, global health, cause pri­ori­ti­za­tion, pri­ori­ti­za­tion re­search, com­par­ing di­verse benefits

Epistemic sta­tus: Uncer­tain and spec­u­la­tive. I don’t ex­ces­sively hedge my claims through­out for clar­ity’s sake (#‘bet­ter wrong than vague’, #“say wrong things”, #”cor­rect me if I’m wrong”, #”All mod­els are wrong, but some are use­ful”).

Ac­knowl­edg­ments: Thanks to John Halstead, Danny Bressler, Sahil Shah, and mem­bers on the Effec­tive Altru­ism fo­rum, es­pe­cially AGB, for helpful com­ments. Any er­rors are mine.

Com­par­a­tive cost-effec­tive­ness of cli­mate change and global development

Summary

Does cli­mate change de­serve more at­ten­tion within the effec­tive al­tru­ism com­mu­nity?[1]

What is more effec­tive: cli­mate change in­ter­ven­tions to avert emis­sions per tonne or sin­gle re­cip­i­ent global de­vel­op­ment in­ter­ven­tions such as cash trans­fers?

Are tar­geted in­ter­ven­tions to more fun­da­men­tally trans­form the lives of the poor­est more effec­tive than sup­ply­ing broad global pub­lic goods such as a sta­ble cli­mate with com­par­a­tively small benefits to ev­ery­one on the planet?

To an­swer these ques­tions, the fol­low­ing ques­tion is cru­cial:

“What value should we use for the so­cial cost of car­bon to ad­e­quately re­flect the greater marginal util­ity of con­sump­tion for low-in­come peo­ple?”[2]

Here, I tried to an­swer this ques­tion. Sur­pris­ingly, I find that global de­vel­op­ment in­ter­ven­tions are gen­er­ally more effec­tive than cli­mate change in­ter­ven­tions.

My spread­sheet model be­low shows that cli­mate change in­ter­ven­tions are only more effec­tive than global de­vel­op­ment in­ter­ven­tions, if and only if:

  • Money is worth only 100 times as much to the global poor than peo­ple in high-in­come coun­tries (i.e. if util­ity to con­sump­tion is log­a­r­ith­mic) and not more

  • AND cli­mate change in­ter­ven­tions are very effec­tive (less than $1 per tonne of car­bon averted) AND/​OR

  • un­der quite pes­simistic as­sump­tions about cli­mate change (if the so­cial cost of car­bon is higher than $1000 per tonne of car­bon).

Key claims

I base the above con­clu­sion on the fol­low­ing three em­piri­cal claims:

1. New re­search on the in­come-ad­justed coun­try-level so­cial cost of car­bon al­lows us to com­pare global de­vel­op­ment in­ter­ven­tions to cli­mate change in­ter­ven­tions.

The new re­search is the first to use cli­mate model pro­jec­tions, em­piri­cal cli­mate-driven eco­nomic dam­age es­ti­ma­tions, and also so­cio-eco­nomic pro­jec­tions which take into ac­count greater marginal util­ity of con­sump­tion for ev­ery coun­try in­di­vi­d­u­ally.[3]

In other words, this takes into ac­count “your dol­lar does (>)100x or more good if you give to the poor­est rather than peo­ple in high-in­come coun­tries”). More on in­come weight­ing in Ap­pendix 2.

Other more canon­i­cal In­te­grated Assess­ment Models (IAM) such as DICE have only have one value for the whole world, and, while the RICE IAM has 12 re­gions,[4] this still un­der­states the het­ero­ge­neous ge­og­ra­phy of cli­mate dam­age.

The new re­search first es­ti­mated the so­cial cost of car­bon for ev­ery coun­try in the world. Then, the au­thors summed up all the coun­try-level costs of car­bon to ar­rive at the global cost of car­bon: US$417 per tonne of CO2 (66% CI: US$177–805, data ex­plorer).

Di­vid­ing this value by how much more worth a dol­lar is for the poor­est vs. peo­ple in high-in­come coun­tries, e.g. 100x, al­lows us to di­rectly com­pare cli­mate change to cash-trans­fers to the poor­est and other global de­vel­op­ment in­ter­ven­tions. For in­stance, di­vidin by 100 re­sults in ~$4.17 per tonne of CO2 (66% CI: $1.77–8.05)).[5]

While this global es­ti­mate also in­cludes costs to more priv­ileged peo­ple…

  • ...in ad­vanced economies (e.g. US, EU),

  • …in the fu­ture who are richer due to eco­nomic growth,

  • …in coun­tries that are not as af­fected by cli­mate change due to ge­og­ra­phy (e.g. some rich cold coun­tries might ac­tu­ally benefit a lit­tle)

… these do not weigh as heav­ily in these calcu­la­tions be­cause the mod­el­ling ad­justs for de­creas­ing marginal util­ity of in­come.

The key point here is that the new model ac­counts more thor­oughly for ge­o­graph­i­cal het­ero­gene­ity and diminish­ing re­turns to con­sump­tion. We now need no longer worry as much that the so­cial cost of car­bon es­ti­mates ob­scure that cli­mate change will be much worse for the poor­est peo­ple in ge­ogra­phies more af­fected by cli­mate change (who we could send un­con­di­tional cash trans­fers to).

The new pa­per’s so­cial cost of car­bon figure is con­tro­ver­sial and has been crit­i­cized for be­ing too high for var­i­ous method­olog­i­cal rea­sons.[6] For in­stance, one very crit­i­cal new pa­per also now es­ti­mates the so­cial cost of car­bon on a coun­try-level, sug­gest­ing that the global so­cial cost of car­bon is only $24 (and, us­ing var­i­ous sen­si­tivity analy­ses, val­ues rang­ing from $3.38/​tCO2e to $21,889/​tCO2e).[7]

To ac­count for the new pa­per over­es­ti­mat­ing or un­der­es­ti­mat­ing the so­cial cost of car­bon, be­low, we use sen­si­tivity anal­y­sis to show how our model re­sponds to over- or un­der­es­ti­mat­ing the true so­cial cost of car­bon by 10x.

2. Only some cli­mate change in­ter­ven­tions avert a tonne of CO2 for less than the global in­come-ad­justed cost of car­bon.

Only if a cli­mate change in­ter­ven­tion has a cost-effec­tive­ness of so­cial cost of car­bon /​ in­come ad­just­ment /​ X per tonne of CO2 averted, then it is X times as effec­tive as cash-trans­fers.

So gen­er­ally, cli­mate change in­ter­ven­tions cre­ate x more util­ity than cash-trans­fers, where


For in­stance, a cli­mate change in­ter­ven­tion with an effec­tive­ness of $1 per tonne of CO2 averted would be ~4.17x more effec­tive than cash-trans­fers if the so­cial cost of car­bon /​ 100 is $4.17. This is just the ba­sic model. We com­pli­cate this anal­y­sis in the spread­sheet be­low with more pa­ram­e­ters. For in­stance, some global de­vel­op­ment in­ter­ven­tions are 17.5 more effec­tive than cash-trans­fers.

3. Scal­able cli­mate change in­ter­ven­tions are not gen­er­ally as cost-effec­tive com­pared to global de­vel­op­ment in­ter­ven­tions.

Cash-trans­fers can ab­sorb more fund­ing with con­sis­tently high cost-effec­tive­ness than any other in­ter­ven­tion.

So even if many other high-risk, high-re­ward pro­jects have a higher benefit-cost ra­tio than cash-trans­fers in ex­pec­ta­tion, they usu­ally have smaller fund­ing gaps and one needs to do more re­search to find them.

But cli­mate change can also ab­sorb large amounts of fund­ing at scale with con­sis­tently high cost-effec­tive­ness and only slowly diminish­ing re­turns.

Ex­am­ples of in­ter­ven­tions with cost-effec­tive scal­able in­ter­ven­tions are:

  1. Ocean alkalinity might be a way to ab­sorb large amounts of car­bon up to 100 billion tonnes /​ year) for as lit­tle as $10 per tonne of CO₂ averted.[8],[9]

  2. Trop­i­cal re­foresta­tion be­tween 2020–2050 could be in­creased by 5.7 billion tonnes (5.6%) at a car­bon price of $20 per tonne of CO2 averted or by 15.1 billion tonnes (14.8%) at $50 per tonne of CO2 averted.[10]

  3. Avoided de­foresta­tion can pre­vent 55.1 billion tonnes at $20 per tonne of CO2 averted or 108.3 billion tonnes at $50 per tonne of CO2 averted.[11]

  4. The lev­elized costs of cap­tur­ing CO2 from the at­mo­sphere are pro­jected to be $94-232 per tonne CO2[12] and could de­crease to $35 by 2050.[13]

Mul­ti­ply­ing the num­ber of tonnes avertable by the (av­er­age) cost per tonne averted equals the fund­ing gap. For some of these in­ter­ven­tions this is in the trillions.[14] To get a rough es­ti­mate of the over­all fund­ing gap of cli­mate change, we can mul­ti­ply global emis­sions—roughly 37 billion tonnes per year—and as­sume an av­er­age cost-effec­tive­ness of $50 per tonne. This sug­gests a fund­ing gap of $1.85 trillion/​year.

Yet, none of these scal­able in­ter­ven­tions can avert a tonne of car­bon at scale for less than $4.17.

The figure be­low shows the cost-effec­tive­ness of some more in­ter­ven­tions and their over­all abate­ment po­ten­tial (though we should be skep­ti­cal of “free lunch” in­ter­ven­tions with nega­tive costs).[15]

Im­pli­ca­tions for cause prioritization

If none of these three claims above can be falsified, then it fol­lows that, as a rule, we should con­sider pri­ori­tiz­ing global de­vel­op­ment over cli­mate change in­ter­ven­tions. In other words, avert­ing car­bon should not re­place un­con­di­tional cash-trans­fers to the poor­est as the new ‘bench­mark’ or re­place global de­vel­op­ment as the new ‘main­stream EA flag­ship cause’.

How­ever, un­der some pes­simistic mod­el­ling as­sump­tions, some se­lect cli­mate change in­ter­ven­tions might be more effec­tive than global de­vel­op­ment in­ter­ven­tions and should be pri­ori­tized. Read on for our up­dated model on this.

When are cli­mate change in­ter­ven­tions more effec­tive than global de­vel­op­ment in­ter­ven­tions?

Con­sider the fol­low­ing spread­sheet (Google sheet). A more de­tailed de­scrip­tion of the pa­ram­e­ters, as­sump­tions and sce­nar­ios are in Ap­pendix 1.

Op­ti­mistic scenario

As­sump­tions:

  • So­cial cost of car­bon is only $17.7

  • an η of 2 (i.e. cash-trans­fers to the poor­est are worth 13,610x as much as to peo­ple in rich coun­tries)

  • a high cost of $232 per tonne of car­bon averted at scale,

  • and global de­vel­op­ment in­ter­ven­tions be­ing 17.5x as effec­tive as cash.

This re­sults in cli­mate change in­ter­ven­tions be­ing only 0.00003% as effec­tive as cash-trans­fers.

Real­is­tic scenario

As­sump­tions:

  • So­cial cost of car­bon is $417

  • η of 1.5 (i.e. cash-trans­fers to the poor­est are worth 1,260x as much as to peo­ple in rich coun­tries)

  • $10 per tonne of car­bon averted at scale (e.g. de­foresta­tion pre­ven­tion)

  • and global de­vel­op­ment in­ter­ven­tions be­ing 7.95x as effec­tive as cash (me­dian Givewell char­ity effec­tive­ness)

This re­sults in cli­mate change in­ter­ven­tions be­ing only 0.42% as effec­tive as cash-trans­fers.

Pes­simistic scenario

As­sump­tions:

  • So­cial cost of car­bon is high $8,050

  • η of 1 (i.e. cash-trans­fers to the poor­est are worth 120x as much as to peo­ple in rich coun­tries)

  • $0.02 per tonne of car­bon averted at scale (e.g. lob­by­ing for de­foresta­tion pre­ven­tion)

  • and global de­vel­op­ment in­ter­ven­tions are cash-trans­fers, which are give 83 cents of ev­ery dol­lar to the poorest

This re­sults in cli­mate change in­ter­ven­tions be­ing 4,041x more effec­tive than cash-trans­fers.

Conclusion

Global de­vel­op­ment in­ter­ven­tions seem gen­er­ally more effec­tive than cli­mate change in­ter­ven­tions. How­ever, un­der pes­simistic mod­el­ling as­sump­tions, se­lect cli­mate change in­ter­ven­tions might be more effec­tive than global de­vel­op­ment in­ter­ven­tions.

Only if util­ity to con­sump­tion is log­a­r­ith­mic (i.e. only if a dol­lar go­ing to the poor­est is not more than 100x as much as go­ing to peo­ple in rich coun­tries) AND a given cli­mate change in­ter­ven­tion is very effec­tive (less than $1 per tonne of car­bon averted) OR un­der quite pes­simistic as­sump­tions about cli­mate change (if the so­cial cost of car­bon is higher than $1000 per tonne of car­bon), then cli­mate change in­ter­ven­tions are more effec­tive than global de­vel­op­ment in­ter­ven­tions.

So for those want­ing to max­i­mize ex­pected util­ity, one should sup­port cli­mate change in­ter­ven­tions only if they are very cost-effec­tive (i.e. lower than $1/​tCo2e averted).

The re­sults of the model are also very sen­si­tive to the in­come ad­just­ment pa­ram­e­ter η – if it’s just 1, i.e. re­turns to con­sump­tion are log­a­r­ith­mic, and money to the poor­est is only 100x as good at go­ing to the poor­est, and the so­cial cost of car­bon is just in the hun­dreds of dol­lars, then some effec­tive, but not su­per scal­able in­ter­ven­tions such as de­foresta­tion pre­ven­tion on the or­der of $1 per tonne of car­bon averted can beat some global de­vel­op­ment in­ter­ven­tions.

Be­cause the con­fi­dence in­ter­vals be­tween cli­mate and de­vel­op­ment are wide and over­lap­ping, the value of in­for­ma­tion of re­duc­ing un­cer­tainty is high. For in­stance, the value of bet­ter in­for­ma­tion on the tran­sient cli­mate re­sponse has been es­ti­mated to be $10 trillion.[16] In other words, if new re­search would show that the so­cial cost of car­bon is ac­tu­ally much higher, then this might lead to more op­ti­mal al­lo­ca­tion of re­sources.

Ap­pendix 1: Ad­di­tional info on model parameters

So­cial cost of carbon

Gen­eral note on so­cial cost of car­bon: Gen­er­ally, cli­mate mod­el­ling is much more un­cer­tain than global de­vel­op­ment in­ter­ven­tions (which can be stud­ied with RCTs) and the effects of cli­mate change are in the fu­ture (see Ap­pendix 3). Altru­ists with high risk /​ un­cer­tainty aver­sion and/​or high dis­count rates might want to not sup­port cli­mate change in­ter­ven­tions for that rea­son.

Yet, the es­ti­mate from above so­cial cost of car­bon mod­el­ling uses sen­si­tivity analy­ses to ac­count for un­cer­tainty and uses dis­count­ing and so the es­ti­mates are at least some­what ro­bust to differ­ent speci­fi­ca­tions.

Also, some com­menters note that the quan­tifi­ca­tion of cli­mate mod­el­ling is es­sen­tially use­less (also see Ap­pendix 3). How­ever, one study es­ti­mated a lower bound of the global so­cial cost of car­bon at US$125 and ar­gues that:

“Quan­tify­ing the true SCC value is com­pli­cated be­cause of var­i­ous difficult-to-quan­tify dam­age cost cat­e­gories and the in­ter­ac­tion of dis­count­ing, un­cer­tainty, large dam­ages and risk aver­sion [...] The best that can be offered is a lower bound based comes from a con­ser­va­tive meta-es­ti­mate that ag­gre­gates stud­ies us­ing high and low dis­count rates, it does not ac­count for var­i­ous cli­mate change dam­ages ow­ing to a lack of re­li­able in­for­ma­tion, and it does not con­sider a min­i­max re­gret ar­gu­ment ad­dress­ing dam­ages as­so­ci­ated with ex­treme cli­mate change.”

Also, as an aside, out­side of pri­ori­ti­za­tion, for op­ti­mal policy the so­cial cost of car­bon should be:

  1. Set to the marginal abate­ment cost, which can be op­ti­mal and eas­ier to es­ti­mate.[17] or

  2. Set to err on the side of over­es­ti­mat­ing ex­ter­nal­ities[18] (while re­duc­ing other non-Pi­go­vian taxes).

Op­ti­mistic as­sump­tion: The new study’s es­ti­mate is 10x higher than more canon­i­cal es­ti­mates such as the EPA’s $42 per tonne, which is based on IAMs. This be­cause it con­tentiously as­sumes im­pacts on GDP growth per­ma­nently al­ter a coun­try’s GDP [19] us­ing differ­ent dam­age func­tions, not be­cause they are ac­count­ing for greater marginal util­ity of con­sump­tion to in­di­vi­d­u­als with lower con­sump­tion lev­els.[20]

For that rea­son, in our op­ti­mistic sce­nario, we down­ward ad­just by 10x on the pa­per’s lower 66% CI, so that the so­cial cost of car­bon is $17.8. Note that this is con­ser­va­tive in the sense of be­ing much lower even than the es­ti­mated lower bound of the so­cial cost of car­bon.

Real­is­tic as­sump­tion: In the re­al­is­tic as­sump­tion, we use the study’s cen­tral es­ti­mate ($417), and as­sume that the model is cor­rect.

Pes­simistic as­sump­tion: This as­sumes that the study’s es­ti­mate is ac­tu­ally 10x too low and ad­justs for this.

This is plau­si­ble be­cause of con­trib­u­tors to so­cial cost of car­bon not fully cap­tured by em­piri­cal, macroe­co­nomic dam­age func­tions, and their likely im­pacts on the so­cial cost of car­bon (see Table S5 in the pa­per’s sup­ple­men­tary ma­te­rial and Table 1 in[21]). For in­stance:

  • Ad­just­ment costs (short-term costs of adap­ta­tion)

  • Non-mar­ket dam­ages (bio­di­ver­sity loss, cul­tural losses, etc.)

  • Tip­ping points in the cli­mate sys­tem (catas­trophic cli­mate events, hys­tere­sis etc.)

  • High in­er­tia effects of CO2 (ocean acid­ifi­ca­tion, sea level rise)

  • Gen­eral equil­ibrium effects (spillover, trade, etc.)

  • Macro-scale adap­ta­tion (long-term re­struc­tur­ing of econ­omy)

  • Poli­ti­cal in­sta­bil­ity and vi­o­lent conflicts

  • Large mi­gra­tion flows

  • More ex­treme weather and nat­u­ral disasters

  • Bresler finds that ex­plic­itly ac­count­ing for cli­mate mor­tal­ity costs triples the welfare costs of cli­mate change.[22]

  • The high­est so­cial cost of car­bon es­ti­mate in the liter­a­ture is on the same or­der of mag­ni­tude ($1687[23]), and the high­est figure amongst many in a re­cently pub­lished pa­per find that for 6 de­grees of warm­ing the cost will be (which has a sub­stan­tial prob­a­bil­ity) is $21889 /​ per tonne) [24]

In­come adjustment

The in­come ad­just­ment takes into ac­count that “your dol­lar does (>)100x or more good if you give to the poor­est rather than peo­ple in high-in­come coun­tries”). More on in­come weight­ing in Ap­pendix 2. The op­ti­mistic case has an η value of 2, the re­al­is­tic of 1.5, and the pes­simistic of 1 (Source). This cor­re­sponds to 1 dol­lar be­ing worth 120-13,610 more when it goes to the poor­est peo­ple on the planet (e.g. via un­con­di­tional cash-trans­fers) than some­one on Me­dian US in­come (120 might be an un­der­es­ti­mate ac­cord­ing some of my calcu­la­tions and it might be 250). For higher val­ues go­ing to­wards 2, this can dom­i­nate the anal­y­sis.[25]

Cost per tonne of CO2 averted

Op­ti­mistic case: The lev­elized costs of cap­tur­ing CO2 from the at­mo­sphere are pro­jected to be $94-232 per tonne CO2[26] and could de­crease to $35 by 2050.[27] We use the up­per bound ($232) for the op­ti­mistic case.

Real­is­tic case: For the mid­dle case, we use ocean alkalinity which might be a way to ab­sorb large amounts of car­bon up to 100 billion tonnes /​ year) for as lit­tle as $10 per tonne of CO₂ averted.[28],[29] This is also roughly in line with the cost per tonne of CO2 averted through new clean en­ergy gen­er­a­tion over coal and other in­ter­ven­tions, wind pro­duc­tion tax credit in the United States, which have es­ti­mated car­bon abate­ment costs rang­ing from $2-260 (Car­bon cap­ture and stor­age is on a similar or­der of mag­ni­tude, also see figure be­low for other in­ter­ven­tions).[30]

Op­ti­mistic case: Prevent­ing de­foresta­tion can have a cost-effec­tive­ness of $0.57 per averted ton of CO2 at scale.[31] Dona­tions to “Coal­i­tion for Rain­for­est Na­tions” for ad­vo­cacy on de­foresta­tion pre­ven­tion has been es­ti­mated to avert a tonne of CO2e for $0.12, with a plau­si­ble range of $0.02 - $0.72.[32] We use the lower bound, $0.02, as the op­ti­mistic case. Note that this is per­haps com­par­ing ap­ples to or­anges, by com­par­ing ad­vo­cacy to di­rect in­ter­ven­tions and that a fairer com­par­i­son would high-risk, high-re­ward global de­vel­op­ment sci­ence or policy in­ter­ven­tions which have been sug­gested to be per­haps 100x more effec­tive than cash.[33]

Global de­vel­op­ment in­ter­ven­tions effectiveness

Op­ti­mistic case: Some global de­vel­op­ment in­ter­ven­tions have been es­ti­mated to be 17.5x more effec­tive than cash-trans­fers (e.g. de­worm­ing).[34] We use this as the op­ti­mistic case.

Real­is­tic case: The me­dian Givewell char­ity effec­tive­ness vs. cash is 7.95.[35]

Pes­simistic case: The pro­por­tion of to­tal ex­penses that GiveDirectly has de­liv­ered di­rectly to re­cip­i­ents is ap­prox­i­mately 83%.[36]

Ap­pendix 2: In­come-weighting

A re­cent pa­per es­ti­mates the coun­try-level so­cial cost of car­bon, us­ing not only cli­mate, but also so­cio-eco­nomic pro­jec­tions.[37] For the marginal util­ity sub­sti­tu­tion, they use a μ-value of 1.5 as a cen­tral value.

What con­cretely does this mean?

All else be­ing equal, money go­ing to poorer coun­tries or peo­ple is bet­ter than money go­ing to richer coun­tries or peo­ple. Weyl sug­gests that as­sum­ing log­a­r­ith­mic util­ity giv­ing 1 dol­lar to an ex­tremely poor per­son is like giv­ing 66 dol­lars to an Amer­i­can[38]. (“That is, if marginal util­ity is de­clin­ing in lev­els of in­come, say util­ity is the nat­u­ral log of con­sump­tion, then the marginal util­ity is 1/​con­sump­tion. This im­plies a dol­lar’s worth of con­sump­tion in util­ity terms of a per­son at the global poverty line is worth 64 times as much as a dol­lar to per­son in the high­est decile of con­sump­tion in the USA (63.6=(1/​(1.9*365))/​(1/​44,152) so trans­fer­ring in­come from a rich per­son in the USA to a globally poor per­son pro­duces, in and of it­self, mas­sively higher to­tal global util­ity (even if not Pareto im­prov­ing).”[39]).

Weyl sug­gests that log­a­r­ith­mic util­ity is canon­i­cal in eco­nomics and sup­ported by a wide range of data, “in­clud­ing re­cent hap­piness stud­ies (Steven­son and Wolfers, 2008) and labour sup­ply de­ci­sions (Chetty, 2006)”. This is also in line with work that finds a cor­re­la­tion be­tween log in­come and hap­piness [40]:

The law of log­a­r­ith­mic util­ity can be found in other ar­eas such as re­search fund­ing as well [41].

The gen­eral form of mod­el­ling util­ity con­sump­tion re­la­tion­ships us­ing isoe­las­tic util­ity func­tion is: [42]:

Ord [43] ex­plains this func­tion as fol­lows:

“This equa­tion has one free pa­ram­e­ter, known as η (‘eta’, which sounds ‘e’ for ‘elas­tic­ity’), which rep­re­sents how steeply re­turns to con­sump­tion diminish. η must be be­tween 0 and ∞, and can be es­ti­mated em­piri­cally.

The equa­tion, for util­ity (u) at a given con­sump­tion level (c), and elas­tic­ity (η) is:

From this it fol­lows that for η = 0 util­ity is lin­ear in con­sump­tion, for η = ½ util­ity is the square root of con­sump­tion, and for η = 1 util­ity is log­a­r­ith­mic in con­sump­tion. Values of η above 1 cor­re­spond to util­ity hav­ing a finite up­per bound, which is ap­proached hy­per­bol­i­cally as con­sump­tion in­creases.

How­ever, the main use of the equa­tion is to just com­pare the slope of the curve at one con­sump­tion level to the slope at an­other con­sump­tion level. For ex­am­ple the ra­tio of the slope at $1,000 per an­num to the slope at $10,000 per an­num shows us the rel­a­tive value of giv­ing an ex­tra dol­lar to some­one with an­nual con­sump­tion $1,000 ver­sus to some­one with $10,000. When perform­ing this calcu­la­tion, the equa­tion is very sim­ple:

Giv­ing a dol­lar to some­one with k times as much con­sump­tion is worth only:

(1/​k)^2

times as much.

There have been many at­tempts to mea­sure η, and it is typ­i­cally found to be be­tween about 1 and 2. If η equals 1, then we have log­a­r­ith­mic util­ity of con­sump­tion and we have the very sim­ple rule that a dol­lar is worth 1/​k times as much if you are k times richer (and that dou­bling some­one’s in­come is worth the same amount no mat­ter where they start). If η equals 2, then we have to raise this to the power of 2, so be­ing 10 times richer would mean a dol­lar is worth just 1/​100th as much (and dou­bling your in­come is worth much less the higher your start­ing in­come). The truth is prob­a­bly in be­tween these limits.”

Ap­pendix 3: Uncer­tainty around cli­mate change modelling

In­te­grated as­sess­ment mod­els have been heav­ily crit­i­cised. Con­sider the fol­low­ing quote by MIT Eco­nomics Pro­fes­sor Robert S. Pindyck from his pa­per “The Use and Mi­suse of Models for Cli­mate Policy”:[44]

“In a re­cent ar­ti­cle, I ar­gued that in­te­grated as­sess­ment mod­els (IAMs) “have cru­cial flaws that make them close to use­less as tools for policy anal­y­sis.” In fact, I would ar­gue that call­ing these mod­els “close to use­less” is gen­er­ous: IAM-based analy­ses of cli­mate policy cre­ate a per­cep­tion of knowl­edge and pre­ci­sion that is illu­sory, and can fool policy-mak­ers into think­ing that the fore­casts the mod­els gen­er­ate have some kind of sci­en­tific le­gi­t­i­macy. IAMs can be mis­lead­ing – and are in­ap­pro­pri­ate – as guides for policy, and yet they have been used by the gov­ern­ment to es­ti­mate the so­cial cost of car­bon (SCC) and eval­u­ate tax and abate­ment poli­cies. What are the cru­cial flaws that make IAMs so un­suit­able for policy anal­y­sis? They are dis­cussed in de­tail in Pindyck (2013b), but the most im­por­tant ones can be briefly sum­ma­rized as fol­lows: 1. Cer­tain in­puts – func­tional forms and pa­ram­e­ter val­ues – are ar­bi­trary, but have huge effects on the re­sults the mod­els pro­duce. An ex­am­ple is the dis­count rate. There is no con­sen­sus among economists as to the “cor­rect” dis­count rate, but differ­ent rates will yield wildly differ­ent es­ti­mates of the SCC and the op­ti­mal amount of abate­ment that any IAM gen­er­ates. For ex­am­ple, these differ­ences in in­puts largely ex­plain why the IAMbased analy­ses of Nord­haus (2008) and Stern (2007) come to such strik­ingly differ­ent con­clu­sions re­gard­ing op­ti­mal abate­ment. Be­cause the mod­eler has so much free­dom in choos­ing func­tional forms, pa­ram­e­ter val­ues, and other in­puts, the model can be used to ob­tain al­most any re­sult one de­sires, and thereby le­gi­t­imize what is es­sen­tially a sub­jec­tive opinion about cli­mate policy. 2. We know very lit­tle about cli­mate sen­si­tivity, i.e., the tem­per­a­ture in­crease that would even­tu­ally re­sult from a dou­bling of the at­mo­spheric CO2 con­cen­tra­tion, but this is a key in­put to any IAM. The prob­lem is that the phys­i­cal mechanisms that de­ter­mine cli­mate sen­si­tivity in­volve cru­cial feed­back loops, and the pa­ram­e­ter val­ues that de­ter­mine the strength (and even the sign) of those feed­back loops are largely un­known, and are likely to re­main un­known for the fore­see­able fu­ture. 3. One of the most im­por­tant parts of an IAM is the dam­age func­tion, i.e., the re­la­tion­ship be­tween an in­crease in tem­per­a­ture and GDP (or the growth rate of GDP). When as­sess­ing cli­mate sen­si­tivity, we can at least draw on the un­der­ly­ing phys­i­cal sci­ence and ar­gue co­her­ently about the rele­vant prob­a­bil­ity dis­tri­bu­tions. But when it comes to the dam­age func­tion, we know vir­tu­ally noth­ing – there is no the­ory and no data that we can draw from. 4. IAMs can tell us noth­ing about the like­li­hood or pos­si­ble im­pact of a catas­trophic cli­mate out­come, e.g., a tem­per­a­ture in­crease above 5°C that has a very large im­pact on GDP. And yet it is the pos­si­bil­ity of a cli­mate catas­tro­phe that is (or should be) the main driv­ing force be­hind a stringent abate­ment policy.”

Yet, in a later pa­per Pindyck es­ti­mates the so­cial costs of car­bon through ex­pert sur­veys to be in the hun­dreds of dol­lars range. This is in line with IAMs and leads me to be­lieve that

The So­cial Cost of Car­bon Re­vis­ited:[45]

“An es­ti­mate of the so­cial cost of car­bon (SCC) is cru­cial to cli­mate policy. But how should we es­ti­mate the SCC? A com­mon ap­proach uses an in­te­grated as­sess­ment model (IAM) to simu­late time paths for the at­mo­spheric CO2 con­cen­tra­tion, its im­pact on tem­per­a­ture, and re­sult­ing re­duc­tions in GDP. I have ar­gued that IAMs have defi­cien­cies that make them poorly suited for this job, but what is the al­ter­na­tive? I pre­sent an ap­proach to es­ti­mat­ing an av­er­age SCC, which I ar­gue can be a use­ful guide for policy. I rely on a sur­vey of ex­perts to elicit opinions re­gard­ing (1) prob­a­bil­ities of al­ter­na­tive eco­nomic out­comes of cli­mate change, but not the causes of those out­comes; and (2) the re­duc­tion in emis­sions re­quired to avert an ex­treme out­come, i.e., a large cli­mate-in­duced re­duc­tion in GDP. The av­er­age SCC is the ra­tio of the pre­sent value of lost GDP from an ex­treme out­come to the to­tal emis­sion re­duc­tion needed to avert that out­come. I dis­cuss the sur­vey in­stru­ment, ex­plain how ex­perts were iden­ti­fied, and pre­sent re­sults. I ob­tain SCC es­ti­mates of $200/​mt or higher, but the vari­a­tion across ex­perts is large. Trim­ming out­liers and fo­cus­ing on ex­perts who ex­pressed a high de­gree of con­fi­dence in their an­swers yields lower SCCs, $80 to $100/​mt, but still well above the IAM-based es­ti­mates used by the U.S. gov­ern­ment.”[46]

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