Acke man, F ank; S an on, Elizabe h A.
Wo king Pape
Clima e isks and ca bon p ices: Re ising he social cos o
ca bon
Economics Discussion Pape s, No. 2011-40
P o ided in Coope a ion wi h:
Kiel Ins i u e o he Wo ld Economy – Leibniz Cen e o Resea ch on Global Economic Challenges
Sugges ed Ci a ion: Acke man, F ank; S an on, Elizabe h A. (2011) : Clima e isks and ca bon p ices:
Re ising he social cos o ca bon, Economics Discussion Pape s, No. 2011-40, Kiel Ins i u e o he
Wo ld Economy (I W), Kiel
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Clima e Risks and Ca bon P ices:
Re ising he Social Cos o Ca bon
F ank Acke man and Elizabe h A. S an on
S ockholm En i onmen Ins i u e – U.S. Cen e , Some ille
Abs ac The social cos o ca bon – o ma ginal damage caused by an addi ional on
o ca bon dioxide emissions – has been es ima ed by a U.S. go e nmen wo king g oup
a $21 in 2010. Tha calcula ion, howe e , omi s many o he bigges isks associa ed
wi h clima e change, and downplays he impac o ou cu en emissions on u u e
gene a ions. Ou eanalysis explo es he e ec s o unce ain y abou clima e
sensi i i y, he shape o he damage unc ion, and he discoun a e. We show ha he
social cos o ca bon is unce ain ac oss a b oad ange, and could be much highe han
$21. In ou wo s case, i could be almos $900 in 2010, ising o $1,500 in 2050.
The mos ambi ious scena ios o elimina ing ca bon dioxide emissions as apidly as
echnologically easible ( eaching ze o o nega i e ne global emissions by he end o
his cen u y) equi e spending up o $150 o $500 pe on o educ ions in ca bon
dioxide emissions by 2050. Using a easonable se o al e na i e assump ions,
he e o e, he damages om a on o ca bon dioxide emissions in 2050 could exceed
he cos o educing emissions a he maximum echnically easible a e. Once his is
he case, he exac alue o he social cos o ca bon loses impo ance: he clea policy
p esc ip ion is o educe emissions a apidly as possible, and cos -e ec i eness
analysis o e s be e insigh s o clima e policy han cos -bene i analysis.
Pape submi ed o he special issue
The Social Cos o Ca bon
JEL Q54, Q58
Keywo ds Social cos o ca bon; cos -bene i analysis; clima e policy; clima e
economics
Co espondence F ank Acke man, S ockholm En i onmen Ins i u e – U.S. Cen e ,
44 Teele A e., Some ille, MA 02144, USA; e-mail: ank.ack[email p o ec ed].
Discussion Pape
No. 2011-40 | Sep embe 23, 2011 | h p://www.economics-ejou nal.o g/economics/discussionpape s/2011-40
© Au ho (s) 2011. Licensed unde a C ea i e Commons License - A ibu ion-NonComme cial 2.0 Ge many
2
1. In oduc ion
Wi h he U.S. En i onmen al P o ec ion Agency’s ecen his o ic s ep owa d egula ion o
g eenhouse gas emissions, cos -bene i analyses o p oposed Ame ican egula ions can now
include an es ima e o damages done by g eenhouse gas emissions – o con e sely, he bene i s
o educing hose emissions. I is, howe e , a e y small s ep: he “social cos o ca bon” (SCC),
i.e. he damage pe on o ca bon dioxide, is es ima ed a $21 o 2010 (In e agency Wo king
G oup 2010).1 Equi alen o $0.21 pe gallon o gasoline,2 such a low cos is di icul o
econcile wi h he belie ha i is u gen o ake ac ion o add ess se ious clima e isks.3
The analysis by he ede al In e agency Wo king G oup is signi ican o i s ole in se ing U.S.
clima e policy. I is also no ewo hy as a a e ins ance whe e economic heo ies and analyses
ha e been newly in oduced in o he public policy deba e.4 Thus i is impo an o examine he
uses o clima e economics in he Wo king G oup analysis, pa icula ly he ea men o he
c ucial unce ain ies ha cha ac e ize he ield. This pape p esen s an examina ion and e-
analysis o he SCC, inding ha ou majo unce ain ies in he economics o clima e change
could imply much la ge es ima es. In each case, he Wo king G oup has chosen he op ion ha
minimizes es ima es o clima e isks and damages.
We begin wi h a discussion o he choice o models and scena ios o he SCC calcula ion. Ou
e-analysis elies on DICE, one o he models used by he In e agency Wo king G oup ha
p oduced he $21 es ima e; we use he Wo king G oup’s modi ied e sion o DICE, and he
same i e scena ios on which hey based hei calcula ions.
We hen in oduce ou majo a eas o unce ain ies ha a ec he calcula ion: he sensi i i y o
he clima e o g eenhouse gases; he le el o damages expec ed a low empe a u es; he le el o
damages expec ed a high empe a u es; and he discoun a e. We ecalcula e he SCC based on
combina ions o high and low al e na i es o each o hese ac o s, yielding an a ay o 16
possible alues, bo h o 2010 and o 2050.
Some o he esul an alues o he SCC a e ex emely high; he highes ones exceed $800 pe
on in 2010 and $1,500 in 2050. In con as , a e iew o scena ios ha each ze o o nega i e ne
global emissions wi hin his cen u y inds ha hey o en imply ca bon p ices, and ma ginal
aba emen cos s, o $150 o $500 pe on o CO2 by 2050. Se e al o ou al e na i e SCC alues
a e well abo e his ange.
1 All dolla igu es in his a icle a e in cons an 2007 U.S. dolla s.
2 Acco ding o he U.S. En i onmen al P o ec ion Agency, he e a e 8.8 kg o CO2 emissions om a gallon o
gasoline, implying ha 114 gallons o gasoline yield one me ic on o emissions ( he s anda d uni o analysis o
emissions); 103 gallons yield one sho on o emissions (see h p://www.epa.go /oms/clima e/420 05001.h m,
accessed Ap il 22, 2011). Thus a use ul ule o humb is ha $1 pe on o CO2 is equi alen o oughly $0.01 pe
gallon o gasoline. The es ima e in he ex o $0.21 pe gallon is o e ed solely o he sake o compa ison; he e a e
no exis ing o p oposed ede al egula ions ha would add a ca bon cha ge o he p ice paid o gasoline.
3 On he u gency o ac ion, see IPCC (2007). On he implica ions o low SCC alues, see Acke man and S an on
(2010).
4 I is new only o U.S. policy; o he coun ies, no ably he Uni ed Kingdom, a e se e al yea s ahead o he Uni ed
S a es in his espec . The U.S. policy p ocess is un o una ely pa ochial, howe e , so ha he in oduc ion o clima e
economics in o policy analysis is p esen ed wi h almos no e e ence o o he coun ies’ expe ience.
3
We conclude wi h a discussion o he meaning o e y high SCC es ima es. Once he SCC
exceeds he cos o b inging ne emissions o ze o, i s exac alue becomes less impo an ; i he
SCC we e wice as la ge, i would ha e he same policy implica ions. A such high SCC alues,
cos -bene i analysis o indi idual policies p o ides no use ul in o ma ion; wha is needed
ins ead is a cos -e ec i eness analysis o he leas -cos , mos e icien pa hway o each ze o o
nega i e ne emissions.
2. Choice o models
The In e agency Wo king G oup used h ee well-known models o clima e economics: DICE,
PAGE, and FUND. They an each o he models on he same i e scena ios, and a e aged he
esul s. Unde hei “cen al case” o p e e ed assump ions, he alue o he SCC, a e aged
ac oss he i e scena ios, was $28 in DICE, $30 in PAGE, and $6 in FUND, o a h ee-model
a e age o $21.
Ou e-analysis uses only he DICE model. I is p obably he bes -known and mos widely used
clima e economics model, and i is he easies o modi y o ou pu poses. Mo eo e , i s es ima e
is he closes o he Wo king G oup’s h ee-model a e age. As sugges ed by he Wo king
G oup’s cen al case esul s, i is likely ha FUND would ha e p oduced lowe es ima es han
hose epo ed below, while PAGE would ha e p oduced highe es ima es. Rega ding he la e ,
PAGE has an explici ea men o po en ial clima e ca as ophes, using a Mon e Ca lo analysis
ha allows a ia ion in he size o ca as ophes, he empe a u e h eshold a which hey become
possible, and he likelihood o ca as ophe once he h eshold has been passed. DICE, in con as ,
includes he ce ain y-equi alen o expec ed alue o ca as ophe in i s damage unc ion. As a
esul , PAGE es ima es a highe SCC han DICE a lowe discoun a es o highe clima e
sensi i i y.5 Ou analysis includes bo h lowe discoun a es and highe clima e sensi i i y, so ou
SCC es ima es would ha e been highe i we had used PAGE.
3. Choice o scena ios
The Wo king G oup analysis ejec s, wi h li le discussion, he widely used In e go e nmen al
Panel on Clima e Change (IPCC) clima e scena ios, and ins ead uses scena ios om ou o he
models: he business-as-usual scena ios om IMAGE, MERGE, MESSAGE, and MiniCAM,
and a 550 ppm s abiliza ion scena io.
The s anges aspec o his choice is he inclusion o he 550 ppm scena io. Does i imply a
guess ha unde business-as-usual condi ions, he e is a 20-pe cen chance ha he wo ld will
each ag eemen on s abiliza ion a ha le el? No explana ion is o e ed. Mo eo e , he 550 ppm
scena io is no e en a single, in e nally consis en scena io; a he , i s GDP, popula ion, and
emissions ajec o ies a e a e ages o he alues in he 550 ppm scena ios om he o he ou
models (see In e agency Wo king G oup 2010, p.16).
None heless, inclusion o he 550 ppm scena io makes li le di e ence in p ac ice. Excluding i
would cause only a $1 inc ease o he $21 SCC es ima e om DICE, FUND, and PAGE, o he
5 A lowe discoun a e inc eases he impo ance o e en s a he in he u u e, when empe a u es a e highe and
ca as ophes a e mo e likely. Highe clima e sensi i i y makes highe empe a u es and inc eased isks o
ca as ophe occu soone . Fo hese easons, PAGE es ima es a la ge SCC han DICE a a 2.5% discoun a e, and a
95 h pe cen ile clima e sensi i i y; see In e agency Wo king G oup on Social Cos o Ca bon (2010), Table 3.
4
$28 es ima e om DICE alone. Fo he SCC es ima es in ou analysis, p esen ed below,
exclusion o he 550 ppm scena io would cause an a e age inc ease o 1 pe cen ; no indi idual
es ima e would change by mo e han 15 pe cen in ei he di ec ion. Thus we ha e e ained he
550 ppm scena io in ou calcula ions, o inc ease compa abili y wi h he Wo king G oup esul s.
The ou business-as-usual scena ios used by he Wo king G oup we e adop ed om an Ene gy
Modeling Fo um (EMF) exe cise which compa ed en models; no hing is said abou why hese
ou we e selec ed om among he en EMF models. The mo e amilia IPCC scena ios a e
dismissed in a single sen ence, on g ounds o hei age and he unexplained asse ion ha hey
now appea o be ex eme ou lie s in some a iables.
Fo hose who a e no amilia wi h EMF, i may be help ul o con as he selec ed EMF
scena ios wi h s anda d IPCC SRES scena ios.6 Figu es 1 and 2 compa e he cumula i e ca bon
dioxide emissions and cu en me hane emissions om he ou EMF scena ios and h ee IPCC
scena ios, A2, B2, and B1.7 As Figu e 1 shows, ca bon dioxide emissions in he ou EMF
scena ios (solid lines) a e close o he B1 and B2 scena ios o he i s hal o his cen u y,
sp eading ou o oughly span he in e al om A2 o B2 by 2100.
Figu e 1: Compa ing EMF and IPCC CO2 emission scena ios
Sou ce: See ex .
Fo me hane emissions, Figu e 2 shows ha h ee o he ou EMF scena ios s a ou well below
he le el o he B1 and B2 scena ios; by 2100, all ou a e oughly a o below he le el o B2.
6 IPCC scena io da a a e om h p://s es.ciesin.o g/ inal_da a.h ml , downloaded Ma ch 1, 2011. EMF scena io da a
a e om
h p://em .s an o d.edu/e en s/em _b ie ing_on_clima e_policy_scena ios_us_domes ic_and_in e na ional_policy_a
chi ec u es , downloaded Feb ua y 15, 2011.
7 Figu e 1 p esen s cumula i e emissions because CO2 pe sis s in he a mosphe e o long pe iods o ime; Figu e 2
p esen s cu en emissions because me hane is emo ed om he a mosphe e much mo e quickly.
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
CO2 : cumula i e G since 2000
MERGE
MiniCAM
IMAGE
MESSAGE
A2
B2
B1

5
Thus he emissions ajec o ies o he EMF scena ios a e b oadly wi hin, bu owa d he lowe
end o , he spec um o IPCC scena ios, pe haps closes o B2.
Figu e 2: Compa ing EMF and IPCC CH4 emission scena ios
Sou ce: See ex .
All else being equal, lowe emissions imply lowe damages, and he e o e a lowe es ima e o he
SCC. Use o an IPCC scena io in which emissions g ow mo e apidly, such as A2, would likely
ha e led o highe alues o he SCC. Rela i e o IPCC scena ios, he EMF emission ajec o ies
a e pa icula ly low in he i s hal o his cen u y; his is o g ea es impo ance a high discoun
a es, which weigh he ea lie yea s mo e hea ily.
Fo he sake o compa abili y wi h he Wo king G oup esul s, we ha e adop ed he same i e
scena ios in ou analysis o unce ain ies. No e ha his is a conse a i e choice o scena ios, as
well as models; epe i ion o ou analysis wi h he PAGE model and highe -emission IPCC
scena ios would lead o la ge SCC alues. Kopp and Mignone (2011) p o ide a mo e de ailed
e alua ion o he Wo king G oup’s emission scena ios as pa o a discussion o he ull se o
assump ions used in he Wo king G oup’s analysis.
4. Fou unce ain ies
This sec ion explo es ou majo unce ain ies ha a ec he SCC calcula ion: he alue o he
clima e sensi i i y pa ame e ; he le el o clima e damages expec ed a low empe a u es; he
le el o damages a high empe a u es; and he discoun a e. The nex sec ion p esen s mul iple
es ima es o he SCC, based on al e na i es o each o hese unce ain ies.
4.1. Clima e sensi i i y
The clima e sensi i i y pa ame e is he long- e m empe a u e inc ease expec ed om a doubling
o he concen a ion o ca bon dioxide in he a mosphe e. This c ucial pa ame e , which
measu es he pace o global wa ming, emains unce ain, and he e a e easons o belie e ha
signi ican unce ain y abou clima e sensi i i y is inescapable (Roe and Bake 2007).
250
300
350
400
450
500
550
600
650
2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
M CH
4
emissions
MERGE
MiniCAM
IMAGE
MESSAGE
A2
B2
B1
6
On his opic, he Wo king G oup analysis is imp essi ely ho ough. They discuss he scien i ic
e idence on likely alues o clima e sensi i i y, and adop a p obabili y dis ibu ion which
assumes a wo- hi ds p obabili y ha clima e sensi i i y is be ween 2.0oC and 4.5oC. The
minimum is ze o and he maximum is 10oC; he dis ibu ion has a median o 3.0oC and a 95 h
pe cen ile o 7.14oC. They hen pe o m a Mon e Ca lo analysis, epea edly selec ing a clima e
sensi i i y alue om his p obabili y dis ibu ion and unning he model wi h ha alue; he
inal SCC es ima e is he a e age esul om hese uns.8
The Wo king G oup epo s, bu does no emphasize, he 95 h pe cen ile esul s as a measu e o
he po en ial impac o unce ain y abou clima e sensi i i y. Resul s o DICE, and o he h ee-
model a e age used by he Wo king G oup, a e p esen ed in Table 1.
Table 1: SCC es ima es, 2010 and 2050, 3% discoun a e
Sou ce: In e agency Wo king G oup (2010).
We ollow he Wo king G oup in epo ing esul s o bo h a e age and 95 h pe cen ile clima e
sensi i i y, in each o he a ia ions desc ibed below. In p ac ice, hese esul s may co espond o
clima e sensi i i y somewha below 3.0oC and 7.1oC, espec i ely, since ac ual clima e
sensi i i y in DICE (and se e al o he in eg a ed assessmen models) is lowe han he epo ed
alues. DICE uses a de aul clima e sensi i i y o 3.0oC, bu ac ually esponds o a doubling o
a mosphe ic ca bon dioxide wi h a long- un empe a u e inc ease o 2.77oC ( an Vuu en e al.
2011).
4.2. Damage unc ion es ima es
Like clima e sensi i i y, he ela ionship be ween empe a u e inc eases and economic damage is
unce ain. The Wo king G oup says li le abou he es ima es o economic damages om clima e
change, excep o call o addi ional esea ch. Implici ly, i adop s wi hou ques ion he app oach
aken by each model. Kopp e al. (2011) modi y he Wo king G oup’s e sion o he DICE
model by including unce ain y in he damage unc ion and a ying he le el o isk a e sion in
he discoun a e. We ake a simple app oach: he damage unc ion emains a ce ain y
equi alen , bu we explo e al e na i e unc ional o ms and pa ame e alues.
DICE assumes ha as empe a u es ise, an inc easing ac ion o ou pu is los o clima e
damages. We will use D o damages as a ac ion o he GDP ha would be p oduced in he
8 In PAGE and FUND, he e a e o he Mon e Ca lo a iables ha a e d awn om p obabili y dis ibu ions o each
un; in DICE, as used by he Wo king G oup, clima e sensi i i y is he only Mon e Ca lo a iable.
Emissions
yea
Clima e
sensi i i y
DICE
3-Model
A e age
2010 A e age $28 $21
2010
95
h
pe cen ile $56 $65
2050 A e age $64 $45
2050
95
h
pe cen ile $123 $136
7
absence o clima e change; R = 1 – D o he ne ou pu a io, o ou pu ne o clima e damages as
a ac ion o ou pu in he absence o clima e change; and T o global a e age empe a u e
inc ease in oC abo e 1900. The DICE damage unc ion is:
(1) 𝑅𝑅=1
1+.00284 𝑇𝑇2
O equi alen ly,
(2) 𝑅𝑅=1
1+�𝑇𝑇18.8
��2
The DICE ne ou pu a io can be iewed as combining wo sepa a e es ima es: i s , o low
empe a u es, William No dhaus, he c ea o o DICE, es ima es ha damages a e 1.8 pe cen o
ou pu a 2.5oC (No dhaus 2007); second, a high empe a u es, i is assumed by de aul ha he
quad a ic ela ionship o damages o empe a u e in (1) o (2) con inues o apply. Sepa a e
esea ch add esses he low- empe a u e and high- empe a u e es ima es, sugges ing al e na i es
o each.
The DICE low- empe a u e damage es ima e is based on an e alua ion o se e al ca ego ies o
clima e damages a 2.5oC (No dhaus 2008; No dhaus and Boye 2000). In a e iew and c i ique
o he No dhaus es ima es as applied o he Uni ed S a es, Michael Hanemann de elops
al e na i e es ima es o damages a 2.5oC, which a e, in o al, almos exac ly ou imes he
No dhaus alue (Hanemann 2008). I he same ela ionship applies wo ldwide, hen a easonable
al e na i e a low empe a u es is o keep he o m o equa ion (1) o (2), bu ecalib a e damages
o 7.1 pe cen o ou pu a 2.5oC. This yields he equa ion:
(3) 𝑅𝑅=1
1+�𝑇𝑇9.1
��2
Nei he he No dhaus no he Hanemann 2.5oC es ima e p o ides a basis o p ojec ing damages
a much highe empe a u es.9 I has become con en ional o ex apola e he same quad a ic
ela ionship o highe empe a u es, bu he e is no economic o scien i ic basis o ha
con en ion. The ex apola ion implies ha damages g ow a a leisu ely pace, especially in he
No dhaus e sion: om equa ions (2) and (3), i is easy o see ha hal o wo ld ou pu is no los
o clima e damages un il empe a u es each18.8oC acco ding o DICE, o 9.1oC in he
Hanemann a ian .
In a discussion o damage unc ions and ca as ophic isks, Ma in Wei zman a gues ha e en i
he No dhaus es ima e is app op ia e o low- empe a u e damages, he inc easingly ominous
scien i ic e idence abou clima e isks implies much g ea e losses a highe empe a u es
(Wei zman 2010). He sugges s ha damages should be modeled a 50 pe cen o ou pu a 6oC
and 99 pe cen a 12oC as be e ep esen a ions o he cu en unde s anding o clima e isks; he
la e empe a u e can be aken as ep esen ing he end o mode n economic li e, i no human
li e in gene al. In suppo o his disas ous p ojec ion o 12oC o wa ming, Wei zman ci es
ecen esea ch showing ha a ha empe a u e, a eas whe e hal he wo ld’s popula ion now
9 No dhaus p esen s some nume ical es ima es o damages a 6oC, sugges ing hey a e be ween 8 pe cen and 11
pe cen o ou pu (No dhaus 2007); hese es ima es a e no well documen ed, and do no appea o be used in he
calib a ion o DICE.
8
li es would expe ience condi ions, a leas once a yea , ha human physiology canno ole a e –
esul ing in dea h om hea s oke wi hin a ew hou s (She wood and Hube 2010).
Wei zman c ea es a damage unc ion ha ma ches he DICE es ima e a low empe a u es, bu
ises o his sugges ed alues a 6oC and 12oC. He modi ies (2) by adding a highe powe o T o
he denomina o :10
(4) 𝑅𝑅=1
1+�𝑇𝑇20.2
��2
+�𝑇𝑇6.08
��6.76
When T is small, he quad a ic e m in (4) is mo e impo an , p o iding a close ma ch o he
o iginal DICE damage unc ion; when T is la ge, he highe -powe e m is mo e impo an ,
allowing he damage unc ion o ma ch Wei zman’s alues o highe empe a u es.
The same me hod can be applied o he Hanemann low- empe a u e es ima e in (3); calib a ing o
Hanemann’s alue a 2.5oC, and Wei zman’s alues a 6oC and 12oC, we ob ain:
(5) 𝑅𝑅=1
1+�𝑇𝑇9.2
��2
+�𝑇𝑇6.47
��7.41
Equa ions (2), (3), (4), and (5) inco po a e all combina ions o wo low- empe a u e al e na i es
(No dhaus and Hanemann), and wo high- empe a u e al e na i es (No dhaus and Wei zman).
Using hei ini ials, hese can be labeled as he N-N, H-N, N-W, and H-W damages unc ions,
espec i ely. They a e displayed in Figu e 3 ( he g aph p esen s damages as a sha e o GDP, i.e.
1 - R), wi h la ge do s indica ing he poin s used o calib a ion. Below 3oC, he low- empe a u e
al e na i es a e dominan , and he high- empe a u e al e na i es make no isible di e ence; a
6oC and abo e, he high- empe a u e al e na i es de e mine he shape o he damage unc ion. In
pa icula , he wo damage unc ions wi h he Wei zman high- empe a u e assump ion a e nea ly
iden ical abo e 6oC.11
10 This equa ion ollows Wei zman’s me hod bu di e s sligh ly om his nume ical es ima es. He appea s o ha e
aken he DICE coe icien in (1) o be .00239 a he han .002839. Ou equa ions (4) and (5) we e i ed o minimize
he sum o squa ed de ia ions om he No dhaus and Hanemann damage es ima es, espec i ely, a 2.5oC, and he
Wei zman poin es ima es a 6oC and 12oC.
11 A small anomaly is ha be ween 6oC and 12oC he N-W damage unc ion, despi e i s lowe low- empe a u e
damages, is sligh ly highe han H-W; he gap is g ea es a 6.9oC, whe e N-W damages a e 3.8 pe cen abo e H-W.
This anomaly, which is an a i ac o ou cu e- i ing p ocedu e, may explain one aspec o he esul s p esen ed
below: unde condi ions whe e high- empe a u e damages a e likely o be impo an , he SCC can be g ea e wi h
he N-W han wi h he H-W damage unc ion. See, in pa icula , he uppe es ima es in Figu e 5.
15
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