Li, Xiaoyu; Wang, Miao; Wan, Wenxuan
A icle
E alua ion o ma ginal aba emen cos and po en ial educ ion in
China's indus ial ca bon emissions: A quad a ic di ec ional ou pu
dis ance unc ion app oach
Jou nal o Inno a ion & Knowledge (JIK)
P o ided in Coope a ion wi h:
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Sugges ed Ci a ion: Li, Xiaoyu; Wang, Miao; Wan, Wenxuan (2024) : E alua ion o ma ginal
aba emen cos and po en ial educ ion in China's indus ial ca bon emissions: A quad a ic
di ec ional ou pu dis ance unc ion app oach, Jou nal o Inno a ion & Knowledge (JIK), ISSN
2444-569X, Else ie , Ams e dam, Vol. 9, Iss. 2, pp. 1-11,
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E alua ion o ma ginal aba emen cos and po en ial educ ion in China’s
indus ial ca bon emissions: A quad a ic di ec ional ou pu dis ance
unc ion app oach
Xiaoyu Li
a
, Miao Wang
b,
*, Wenxuan Wan
a
a
School o Accoun ing, Chongqing Technology and Business Uni e si y, Chongqing 400067, China
b
School o Business, Zhengzhou Uni e si y, Zhengzhou 450001, China
ARTICLE INFO
A icle His o y:
Recei ed 18 No embe 2023
Accep ed 25 Ap il 2024
A ailable online 3 May 2024
ABSTRACT
As a ele an indica o o quan i ying he alue o ca bon emissions, he ma ginal aba emen cos (MAC) o
ca bon emissions has ecei ed inc easing a en ion om academics and policymake s. This s udy uses a qua-
d a ic di ec ional ou pu dis ance unc ion o analyse he echnical e ficiency, po en ial emission educ ion
and shadow p ices o China’s indus ial ca bon emissions. The esul s show ha he echnical e ficiency o
China’s indus y g adually dec eased du ing he sample pe iod. F om he pe spec i e o egions wi h di e -
en ca bon in ensi y and indus ial ou pu , egions wi h lowe ca bon in ensi y and highe indus ial ou pu
g adually closed o he op imal on ie o he echnology use le el and had ela i ely high echnical e fi-
ciency. Rising echnical ine ficiency and ca bon emissions led o a po en ial emission educ ion ha also
exhibi s an upwa ds end. In addi ion, he MAC o indus ial ca bon emissions exhibi s a U-shaped ajec-
o y, wi h 2011 as he u ning poin . Gene ally, in ecen yea s, egions wi h lowe ca bon in ensi y and hose
wi h highe indus ial ou pu ha e a ela i ely high MAC o indus ial ca bon emissions. The empi ical find-
ings e eal ha a ca bon emission educ ion policy should be o mula ed and a ge ed o each p o ince, and
he p inciple o ‘easy be o e di ficul ’can be ollowed o p omo e emission educ ion.
© 2024 The Au ho s. Published by Else ie España, S.L.U. on behal o Jou nal o Inno a ion & Knowledge. This
is an open access a icle unde he CC BY-NC-ND license
(h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
Keywo ds:
Pa ame e app oach
Ma ginal aba emen cos
Technical e ficiency
Regional disc epancies
JEL classifica ion:
Q52
Q54
Q56
In oduc ion
As he la ges emi e o ca bon dioxide (CO
2
) emissions in he
wo ld, China is unde eno mous p essu e o educe i s emissions.
China is now in he in e media e and la e s ages o indus ial de el-
opmen , and he Chinese indus y has been labelled ‘high consump-
ion and high emissions’. China’s indus ial ossil ene gy use and CO
2
emissions accoun o 70 % o China’s o al ene gy consump ion and
CO
2
emissions (Wang & Feng, 2018a,b). To p omo e low-ca bon
de elopmen , he Chinese go e nmen se se e al emissions mi iga-
ion a ge s. The 13 h Fi e-Yea Plan se a a ge o achie e ca bon
aba emen pe uni o GDP by 40 %−45 % by 2020 compa ed o he
2005 le el, wo king owa ds achie ing he goal o peak ca bon emis-
sions by 2030 and aiming o ca bon neu ali y by 2060. To each
hese a ge s, he Chinese go e nmen ook se e al emission educ-
ion measu es, such as compelling he elimina ion o ou da ed p o-
duc ion acili ies and echnologies in high-ene gy consump ion
indus ies ia adminis a i e and legisla i e means and p omo ing
new ene gy echnologies.
The Chinese go e nmen has also s a ed o emphasise and
s eng hen i s ma ke posi ion o deploy en i onmen al esou ces,
g adually s eng hening he c ucial ole o ma ke mechanisms in he
alloca ion o en i onmen al esou ces (Guo & Feng, 2021). In 2011,
pilo ca bon ading p ojec s led by he Na ional De elopmen and
Re o m Commission we e launched in Beijing, Tianjin, Shanghai,
Chongqing, Guangdong, Hubei and Shenzhen. On 19 Decembe 2017,
he Na ional Ca bon Emission T ading Ma ke Cons uc ion Plan
(Powe Gene a ion Indus y) was issued, and he amewo k o Chi-
na’s ca bon emissions ading sys em was comple ed, es ablishing a
na ional ca bon emissions ading ma ke o he fi s ime.
Assessing he alue o ca bon emissions has eme ged as a signifi-
can a ea o esea ch and policy ocus ollowing he incep ion o he
Kyo o P o ocol (Jin & Chen, 2022). In ecen yea s, he Chinese go -
e nmen has implemen ed a ange o measu es o acili a e ca bon
educ ion. Wha is he oppo uni y cos o con inuing measu es such
as he abo e emission educ ion policies? Wha a e he influencing
ac o s o oppo uni y cos o ca bon emission educ ion? How can
mi iga ion measu es o achie ing ca bon emission educ ion be
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (M. Wang).
h ps://doi.o g/10.1016/j.jik.2024.100493
2444-569X/© 2024 The Au ho s. Published by Else ie España, S.L.U. on behal o Jou nal o Inno a ion & Knowledge. This is an open access a icle unde he CC BY-NC-ND license
(h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
Jou nal o Inno a ion & Knowledge 9 (2024) 100493
Jou nal o Inno a ion
&Knowledge
h ps://www.jou nals.else ie .com/jou nal-o -inno a ion-and-knowledge
achie ed a a lowe cos ? De e mining he answe s o hese ques ions
could ad ance ca bon emission educ ion and he e ficien ope a ion
o ca bon ading ma ke s. The shadow p ice o ca bon emissions,
namely he heo e ical equilib ium p ice o ca bon emission ading,
is he ma ginal emission educ ion cos (ma ginal aba emen cos ,
MAC) o CO
2
emissions.
1
The s udy’sfindings p o ide a significan
e e ence o he go e nmen o conduc a ional alloca ions o ca -
bon emissions, compensa e o en e p ises’emission educ ion and
o e ele an insigh s o ca bon emissions ading p ices in he p i-
ma y ma ke and guiding he ma ke ading p ice.
As a ‘bad’ou pu , ca bon emissions lack ac ual ading alue; hus,
no clea ma ke p ice is e iden . As he embodimen o social cos ,
he shadow p ice (MAC) can e ec i ely eflec he ading p ice o
such bad ou pu . The e o e, accu a ely measu ing he ca bon emis-
sion shadow p ice is c ucial o de e mining a ional ca bon emission
p ices. Among all ela ed es ima ion app oaches, he di ec ional dis-
ance unc ion (DDF) is mo e ele an o p ac ical needs due o i s
cha ac e is ic o allowing non-desi ed and desi ed ou pu s o a y in
di e en p opo ions. In addi ion, wi h he inno a ion o p oduc ion
echnology and he inc ease in g een g ow h equi emen s, he DDF
p o ides an e ec i e way o expand desi ed ou pu s while cu ing
non-desi ed ou pu s. Conside ing his, DDF is inc easingly a ou ed
by mo e esea che s. Addi ionally, di e en Chinese egions exhibi
a ious ea u es. To examine egional disc epancies and p o ide an
e idence-based e e ence o he go e nmen o assign ca bon emis-
sion educ ion asks, his s udy measu es he shadow p ice o indus-
ial CO
2
emissions (ICE) a di e en g oup le els. Fo he abo e wo
issues, we use p o incial panel da a om China’s indus ial sec o
and de elop a quad a ic di ec ional ou pu dis ance unc ion
app oach o measu ing he shadow p ice o indus ial CO
2
emissions.
This s udy also calcula es di e en egions’po en ial indus ial ca -
bon educ ions, which may o e a aluable e e ence o he go e n-
men o assign ca bon emission educ ion asks. In b ie , analysing
he shadow p ice o ICE can p o ide a ele an e e ence o he go -
e nmen o accu a ely implemen ICE alloca ions and compensa e
en e p ises’emission educ ion, and i is also ele an o he p icing
o ca bon emissions ading in he p ima y ma ke and guiding he
ma ke ading p ices.
The emainde o his s udy is s uc u ed as ollows. Sec ion ``Li -
e a u e e iew’’ e iews he p e ious ela ed s udies. Sec ion ``Mod-
els and da a’’ de ails he model cons uc ion and in oduces he da a
used o p ocessing. Sec ion ``Empi ical esul s and discussion’’ dis-
cusses he shadow p ice and po en ial ca bon emission educ ion a
he na ional, g oup and p o incial le els. Sec ion ``Conclusions and
policy implica ions’’ summa ises he ull ex and o e s some ele-
an policy p oposals.
Li e a u e e iew
P e ious esea ch has p ima ily used wo di e en me hods o
measu ing shadow p ice: compu able gene al equilib ium and he
dis ance unc ion. The dis ance unc ion me hod only equi es his o -
ical inpu −ou pu da a o es ima e he shadow p ice and does no
equi e an abundance o assump ions ega ding u u e o ms o eco-
nomic de elopmen and echnological p og ess (Wang e al., 2018).
In addi ion, he es ima ed esul s can e ec i ely measu e he MAC
and po en ial emission educ ions; hus, he dis ance unc ion has
been ex ensi ely used o quan i ying pollu an shadow p ices
(Zhang e al., 2019).
The Shepha d dis ance unc ion and DDF a e he wo mos com-
monly employed dis ance unc ions (Mu y & Kuma , 2002). The
Shepha d dis ance unc ion app oach only equi es he ac ual pollu-
ion emissions and does no equi e inpu −ou pu p ice in o ma ion.
By using he dual ela ionship be ween ou pu dis ance and income
unc ions, we can ob ain he pollu an shadow p ice, which p o ides
a clea e economic meaning. Gi en he ad an ages o he dis ance
unc ion, his me hod has been widely used o pollu an shadow
p ice measu emen . Fo ins ance, Reig-Ma ı
nez e al. (2001) es i-
ma ed he shadow p ice o wo indus ial was es in he ce amic pa e-
men indus y in Spain using he Shepha d ou pu dis ance unc ion.
Pa k and Lim (2009) also applied he ou pu dis ance unc ion o cal-
cula e he shadow p ice o CO
2
emissions om elec ic powe plan s
in Ko ea.
Howe e , he Shepha d dis ance unc ion only allows o he
change a e o good ou pu o be he same as ha o bad ou pu , and
ha does no sui he needs o policymake s, o whom good ou pu
should inc ease while bad ou pu dec eases (Cheng & Kong, 2022;Li
e al., 2023;Wu e al., 2023). Unde his ci cums ance, Chambe s e
al. (1996) p oposed he DDF, which elimina es he angula cons ain
by simul aneously adjus ing he inpu and ou pu in di e en di ec-
ions. Chung e al. (1997) fi s applied he DDF o a s udy con ain-
ing bad ou pu s. The basic idea o DDF is o inco po a e good and
bad ou pu s ha occu in he p oduc ion cou se in o he model,
enabling disp opo iona e scale changes in bo h o ms o ou pu ;
ha is, as good ou pu inc eases, bad ou pu can dec ease. This
model also means ha he obse a ion poin mee s he on ie
o e ficiency only when good ou pu is unable o con inue o
expand and bad ou pu is unable o con inue o sh ink. DDF con-
o ms o he ac ual ci cums ances and has conside able flexibili y
and low da a equi emen s (i.e. DDF only equi es he co e-
sponding inpu and ou pu da a, which a e ex emely easy o
ob ain); hus, he echnique is mo e a ac i e o schola s o
measu ing shadow p ice (o MAC).
Examples o ele an DDF−shadow p ice s udies include Du and
Mao (2015), who examined he CO
2
MAC o Chinese coal-fi ed powe
plan s, combining p oduc ion heo y wi h ou pu DDF. Molinos-Sen-
an e e al. (2015) used pa ame ic quad a ic DDF o calcula e he CO
2
shadow p ice o was ewa e ea men plan s. Kaneko e al. (2010)
used non-pa ame ic DDF o e alua e he sul u dioxide (SO
2
) emis-
sions MAC o China’s he mal powe sec o . Liu and Feng (2018) es i-
ma ed he CO
2
emissions shadow p ices o 165 coun ies using a
quad a ic ou pu DDF and examined i s influencing ac o s. He e al.
(2018) es ima ed he p o incial CO
2
MAC o China employing
pa ame ic DDF. Wang e al. (2020) also used DDF o measu e he
MAC o China’s egional CO
2
emissions. Ji and Zhou (2020) employed
a mul i-pollu an pa ame ic ou pu DDF o e alua e he MACs o
CO
2
,SO
2
and ni ogen oxide (NOx) emissions in 105 ci ies ac oss
China om 2006 o 2014. Wu e al. (2020) adop ed he quad a ic DDF
model o calcula e he CO
2
emissions MAC o he Chinese 30 p o in-
ces and de e mined quo as o CO
2
emissions among p o inces based
on he esul s. Wu e al. (2021) used DDF and slacks-based measu e
(SBM) echniques o measu e he shadow p ices o SO
2
and CO
2
in
China. Wang e al. (2022) used non-pa ame ic DDF o calcula e ca -
bon shadow p ices in 152 coun ies wo ldwide. Thuy e al. (2023)
applied DDF o es ima e he MAC o h ee wa e con aminan s in he
sea ood p ocessing indus y in Vie nam.
Pa ame ic and non-pa ame ic app oaches ha e p ima ily been
used o calcula e he dis ance unc ion (Ma e al., 2019;Oh e al.,
2020;Xian e al., 2020). The non-pa ame ic me hod p edominan ly
employs da a en elopmen analysis (DEA). Examples o esea che s
who ha e used non-pa ame ic app oaches include Choi e al. (2012),
Wang and He (2017),Wu e al. (2019),Chen e al. (2021),Kuma and
Jain (2021)),Shen e al. (2021),Bale
zen is e al. (2022),Yue e al.
(2023) and Sil a and Magalh~
aes (2023). In pa ame ic me hods, he
dis ance unc ion is app oxima ely exp essed using a anslog o qua-
d a ic unc ion, and he co esponding pa ame e s a e es ima ed
using linea p og amming o s ochas ic on ie analysis (SFA). As
one o he non-pa ame ic me hods, DEA may ha e he de ec o he
es ima ion esul no being unique when es ima ing he shadow
1
The meaning o MAC is equal o he shadow p ice in his manusc ip .
X. Li, M. Wang and W. Wan Jou nal o Inno a ion & Knowledge 9 (2024) 100493
2
p ice. Addi ionally, by pa ame e ising he DDF, he bounda y o p o-
duc ion is ep esen ed in he o m o a specific p oduc ion unc ion,
and he shadow p ice o bad ou pu can be ob ained h ough di e -
en ia ion, bu using he non-pa ame ic me hod o calcula e he
shadow p ice o bad ou pu h ough di e en ia ion is di ficul .
Many schola s ha e adop ed pa ame ic app oaches o es i-
ma e DDF when in es iga ing shadow p ices. Fo example, Tang
e al. (2016) employed a pa ame ic DDF app oach o es ima e
he MACs o China’sCO
2
and SO
2
emissions om 2003 o 2012.
Zhang and Jiang (2019) applied a pa ame ic me a- on ie inpu
dis ance unc ion o calcula e he shadow p ice o SO
2
emissions
o 93 o China’scoal-fi ed powe plan s loca ed in China’skey
‘en i onmen al p o ec ion ci ies’.Adenuga e al. (2020) applied a
anslog unc ion ha is specified in an SFA amewo k o alue
he shadow p ice and cos a io o pollu ion o su plus P in dai y
a ms in No he n I eland. Wei and Zhang (2020) p oposed a pa -
ial pa ame ic en i onmen al p oduc ion on ie o es ima e CO
2
and SO
2
emissionsshadowp ices o 93coal-fi ed powe plan s
in China. Qi and Choi (2020) examined DDF calcula ed by SFA o
es ima e he CO
2
MAC o 92 coal- uel gene a o s loca ed in
Shanghai, China. Mazio is e al. (2020) used a pa ame ic
app oach o es ima e he shadow p ice o educing unplanned
wa e supply in e up ions o 21 Chilean wa e companies. He e
al. (2021) used he pa ame e me hod o se a quad a ic DDF o
calcula e he shadow p ice o ag icul u al g eenhouse gases. Ji e
al. (2021) pa ame e ised DDF using he quad a ic unc ion and
applied he pa ame e isa ion me hod o es ima e he shadow p i-
ceso ou pollu an sinmajo ci iesinChina.Rekke e al.
(2023) used a pa ame ic quad a ic DDF o calcula e he MAC o
CO
2
in he Eu opean chemical indus y.
In e ms o esea ch ega ding he en i onmen al emissions
shadow p ice in China’s indus ial sec o , Chen e al. (2013) used DDF
o e alua e he MAC o indus ial CO
2
emissions in China and analyse
he MAC di e ences among a ious indus ial sec o s. Wu e al.
(2020) measu ed CO
2
shadow p ices in China’s 36 indus ial sec o s
om 2006 o 2015 using an en i onmen al p oduc ion on ie DDF
based on a non-pa ame ic app oach. Cheng e al. (2020) adop ed he
by-p oduc ion DEA model’s dual o mula ion o in es iga e indus ial
ca bon shadow p ices based on Chinese p o incial panel da a. Liu e
al. (2020) applied a join p oduc ion DEA-based model o analyse he
MAC change and i s decomposed ac o s o SO
2
emissions in China’s
indus ial sec o . Wang e al. (2020) applied he dual model o he
adi ional SBM o measu e he CO
2
MAC o China’s indus ial sec o
om a p o incial pe spec i e. Shen e al. (2021) used he e ised
backp opaga ion-DEA model o measu e he ca bon shadow p ices
gene a ed in China’s indus ial sec o om 1998 o 2017. Zhang e al.
(2022) used quad a ic DDF and SFA me hods o es ima e SO
2
and CO
2
emissions shadow p ices in China’s indus ial sec o .
The abo e indus ial sec o s udies p oduced many meaning ul
esul s, p o iding ele an e e ences o China’s u u e emission educ-
ion in he indus ial sec o . Howe e , hese p e ious s udies ha e wo
no able limi a ions. Fi s , mos indus ial ca bon MAC s udies we e con-
duc ed om he pe spec i e o di e en sub-indus ies. Al hough a ew
s udies examined indus ial CO
2
shadow p ices a he p o incial le el,
hese s udies we e no conduc ed acco ding o he cha ac e is ic clus e -
ing g oups o di e en p o inces. Second, as no ed abo e, non-pa ame -
ic me hods ca y he de ec o he es ima ion esul no being unique
when es ima ing shadow p ices. Reg e ably, s udies ha conduc ed
shadow p ice analysis a he p o incial le el all adop ed he non-
pa ame ic app oach. As poin ed ou abo e, a non-pa ame ic app oach
may ha e he de ec o he es ima ion esul no being unique when
es ima ing he shadow p ice. In addi ion, he bounda y o p oduc ion is
ep esen ed in he o m o a specific p oduc ion unc ion, and hen he
shadow p ice o ‘bad’ou pu can be ob ained by di e en ia ing h ough
pa ame ic DDF, whe eas i is di ficul o calcula e he shadow p ice o
‘bad’ou pu by di e en ia ing h ough he non-pa ame ic me hod.
Conside ing his, his s udy conduc s ex ended esea ch in he
ollowing wo ways. Fi s , we use he da a om each p o ince in
China’s indus ial sec o om 2000 o 2017 o es ima e echnical
e ficiency by adop ing a quad a ic di ec ional ou pu dis ance
unc ion me hod (which is a kind o pa ame ic app oach) o
CO
2
shadow p ice and po en ial CO
2
emission educ ion (PCR).
Second, his s udy classifies he 30 p o inces in o di e en g oups
based on he cha ac e is ics o geog aphical loca ion, ca bon
in ensi y and pe capi a indus ial ou pu alue o examine he
disc epancies in echnical e ficiency, shadow p ice and PCR in di -
e en g oups.
Models and da a
Di ec ional ou pu dis ance unc ion
In he p oduc ion p ocess, he desi ed p oduc and i s by-p oduc s
(such as pollu an s) a e o en p oduced simul aneously. We assume
ha ndecision-making uni s use Minpu s x¼ðx1;x2;⋯xmÞ2Rþ
M o
p oduce Sgood ou pu (y¼ðy1;y2;⋯ysÞ2Rþ
S) and Jbad ou pu
b¼ðb1;b2;⋯bjÞ2Rþ
J. Subsequen ly, he p ocess o p oduc ion can be
o mula ed as ollows:
PxðÞ¼ y;bðÞ:xðÞcan p oduce y;bðÞ g ð1Þ
Acco ding o Chung e al. (1997), he possibili y se o p oduc ion
is bounded and closed, and inpu and good ou pu can be mo e easily
disposed. Fu he mo e, acco ding o he co-p oduc ion ela ionship
o good and bad ou pu , he ollowing wo assump ions mus also be
sa isfied: (1) null-join ness, i ðy;bÞ2PðxÞand b ¼0; hen y¼0; (2)
weak disposable o bad ou pu , i ðy;bÞ2PðxÞand 0u1¼0; hen
ðuy;ubÞ2PðxÞ.
Combining he inpu −ou pu (x, y, b) and di ec ion ec o
g¼ðgy;gbÞ, he ollowing is he defini ion o he di ec ional ou pu
DDF:
~
Dox;y;b;gy;gb
¼sup b:yþbgy;bbgb
2PxðÞ
ð2Þ
This DDF mani es s ha i is easible o maximise he good ou pu
along he di ec ion ec o g¼ðgy;gbÞwhile minimising he bad ou -
pu unde a gi en p oduc ion easibili y se P(x).
Fig. 1 illus a es he DDF, e ealing ha i he p oduce is a he
bounda y o he P(x) se , ~
Doðx;y;b;gy;gbÞ¼0 (i.e. b¼0), his is he
mos e ficien s a us. I he p oduce p oduces wi hin he P(x) se , ~
Doð
x;y;b;gy;gbÞ>0 (i.e. b>0), his indica es ha he ou pu is ine fi-
cien , and he e is po en ial o u he expand good ou pu and
educe bad ou pu . B iefly, a highe b alue indica es ha p oduc ion
e ficiency is lowe .
Fu he mo e, he DDF has he ollowing ansla ion p ope ies:
~
Dox;yþbgy;bbgb;gy;gb
¼~
Dox;y;b;gy;gb
bð3Þ
Eq. (3) indica es ha i he good ou pu ises by bgyand he bad
ou pu simul aneously dec eases by bgb, hen he p oduce is mo e
e ficien and he DDF dec eases by b.
Shadow p ices o bad ou pu s
The bad ou pu ’s shadow p ice is ob ained om he dual ela ion
o DDF and p ofi unc ion. Suppose ha he p ice ec o o good ou -
pu is p¼ðp1;p2;⋯psÞ2Rþ
Sand he p ice ec o o bad ou pu is ¼ðq1;
q2;⋯qjÞ2Rþ
J.
In addi ion, because ~
Doðx;y;b;gy;gbÞ0, he p ofi unc ion is
defined as ollows:
Wx
0;p;qðÞ¼maxy;bpy qb :~
Dox;y;b;gðÞ0
no
ð4Þ
X. Li, M. Wang and W. Wan Jou nal o Inno a ion & Knowledge 9 (2024) 100493
3
whe e x0indica es he p ices o inpu s. Eq. (4) can be u he w i en
as ollows:
Wx
0;p;qðÞpy qbðÞþp~
Dox;y;b;gðÞgyþq~
Dox;y;b;gðÞgbð5Þ
The le -hand side o Eq. (5) indica es he maximum possible ben-
efi allowed wi hin he p oduc ion easibili y se . By con as , he
igh -hand side is he ac ual benefi plus he benefi om elimina ing
ine ficiencies by inc easing good ou pu while educing bad ou pu .
When he ine ficiencies a e elimina ed along he di ec ion ec o and
each he ou pu on ie , we ob ain he ollowing:
~
Dox;y;b;gðÞ¼minp;q
Wx
0;p;qðÞpy qbðÞ
pgyþqgb
ð6Þ
Take he ollowing de i a i e o good and bad ou pu :
y~
Dox;y;b;gðÞ¼
p
pgyþqgb
0;
b~
Dox;y;b;gðÞ¼
q
pgyþqgb
0:
8
>
>
<
>
>
:
ð7Þ
Subsequen ly, he bad ou pu shadow p ice can be exp essed as ollows:
qj¼ps
@~
DOx;y;b;gðÞ=@bj
@~
DOx;y;b;gðÞ=@ys
j¼1;2;⋯;J;s ¼1;2;⋯;S:
8
>
<
>
:
ð8Þ
Pa ame e ised quad a ic di ec i i y ou pu dis ance unc ion
T anslog and quad a ic o ms a e o en used o pa ame e ise dis-
ance unc ions. Among he o ms, he anslog o m canno sa is y
he ans e p ope y o DDF and is gene ally used in pa ame e ising
he Shepa d ou pu dis ance unc ion (Lee & Zhang, 2012). The qua-
d a ic o m is a quad a ic app oxima ion o he unknown dis ance
unc ion, which sa isfies he cha ac e o he di ec ional ou pu dis-
ance unc ion well. The e o e, his s udy adop s he quad a ic o m
o pa ame e ise he DDF. We se he di ec ional ec o g= (1, 1),
which indica es ha o a gi en inpu , good ou pu expands by a uni
and bad ou pu dec eases by a uni .
This s udy se s labou (x
1
), capi al s ock (x
2
) and ene gy (x
3
)asinpu s,
and g oss indus ial ou pu alue (y)andCO
2
emissions (c)as hegood
and bad ou pu s, espec i ely (Yang e al., 2021; Tian & Feng, 2022;
Feng e al., 2018, 2024). No ably, he quad a ic unc ion includes a
egion dummy a iable (ID
k
) and a ime dummy a iable (T
) o
cap u ing he e ec s o indi iduals and ime. Subsequen ly, he qua-
d a ic DDF o he k
h
p o ince in yea can be exp essed as ollows:
~
Dox
k;y
k;b
k;1;1
¼a0þX
3
n¼1
anx
nk þb1y
kþg1b
k
þ1
2X
3
n¼1X
3
n0¼1
ann0x
nkx
n0kþ1
2b2y
k
2þ1
2g2b
k
2
þX
3
n¼1
dnx
nkb
kþX
3
n¼1
enx
nky
kþmy
kb
kþX
K1
k¼1
λkIDk
þX
T1
¼1
T
ð9Þ
This s udy es ima es he pa ame e s o quad a ic DDF using he
ollowing linea p og amming algo i hm:
MinX
T
¼1X
K
k¼1
~
Dox
k;y
k;b
k;1;1
0
hi
s: :iðÞ~
Dox
k;y
k;b
k;1;1
0;k¼1;⋯;K; ¼1;⋯;T:
iiðÞ
~
Dox
k;y
k;0;1;1
0;k¼1;⋯;K; ¼1;⋯;T:
iiiðÞ
@~
Dox
k;y
k;b
k;1;1
@b0;k¼1;⋯;K; ¼1;⋯;T:
i ðÞ
@~
Dox
k;y
k;b
k;1;1
@y0;k¼1;⋯;K; ¼1;⋯;T:
ðÞ@~
Dox
k;y
k;b
k;1;1
@xn
0;n¼1;2;3;k¼1;⋯;K; ¼1;⋯;T:
iðÞ
b1g1¼1;b2¼g2¼m;dnen¼0;n¼1;2;3:
iiðÞ
ann0¼an0n;n;n0¼1;2;3:
8
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
:ð10Þ
A e es ima ing he pa ame e s o DDF ( he pa ame e alues a e
lis ed in Appendix Table A.1), he shadow p ices o indus ial CO
2
emissions in p o ince kno yea can be calcula ed as ollows:
q¼pg1þg2bþP3
n¼1dnxnþmy
b1þb2yþP3
n¼1enxnþmbð11Þ
In he cu en s udy, ICE is he unexpec ed ou pu , and he
expec ed ou pu is g oss indus ial ou pu ; hus, he economic signifi-
cance o he calcula ed ICE shadow p ice is he amoun o g oss
indus ial ou pu o be educed o educe one ICE uni , ep esen ing
he MAC o ICE.
Fig. 1. Di ec ional ou pu dis ance unc ion.
X. Li, M. Wang and W. Wan Jou nal o Inno a ion & Knowledge 9 (2024) 100493
4
Da a
This s udy is conduc ed using panel da a o he 30 Chinese p o -
inces om 2000 o 2017 and calcula ing echnical e ficiency, aba e-
men po en ial and shadow p ices based on a ious inpu −ou pu
da ase s. Among he da ase s, labou o ce, ene gy consump ion and
capi al s ock a e se as inpu −ou pu da ase s (i.e. x). Con e sely,
g oss indus ial ou pu and indus ial CO
2
emissions a e se as good
ou pu (y) and bad ou pu (b), espec i ely (Liu & Feng, 2023; Wang
& Feng, 2020, 2021a,b; Zheng e al., 2023). The da a sou ces and p oc-
essing a e desc ibed as ollows.
(1) The labou da a om 2000 o 2016 a e ob ained om he S a-
is ical Yea book o he Chinese Indus y (2001−2017), and he
labou da a in 2017 use he a e age alue be ween 2016 and 2018.
The labou da a in 2018 a e ob ained om he China Economic Cen-
sus Yea book—2018. (2) We use he ‘pe pe ual in en o y me hod’ o
calcula e capi al s ock da a, p ocessing he ele an da a e e encing
Chen (2011). (3) Ene gy consump ion da a o he indus ial sec o
a e ob ained om he China Ene gy S a is ics Yea book o China
(2001−2018), and we con e he physical quan i y o ene gy con-
sump ion da a in o s anda d coal equi alen . (4) G oss indus ial ou -
pu alue da a om 2000 o 2011 a e ob ained om CISY (2001
−2012), and he da a o 2012−2017 a e es ima ed using indus ial
sales alues and he a e age p oduc ion−sales a io. All cu ency-
ela ed da a (yand k) a e con e ed o cons an p ices in 2000. (5)
Finally, we calcula e CO
2
emissions om ossil ene gy, e e encing Mi
e al., (2017),Wang and Feng, (2017) es ima ing he indi ec CO
2
emissions induced om elec ici y using he CO
2
coe ficien o elec-
ici y, o he CO
2
emissions pe uni o he mal powe gene a ion.
Fu he mo e, o examine he di e ences be ween egions wi h
di e en cha ac e is ics, his s udy g oups he 30 p o inces in o di -
e en egions acco ding o geog aphical loca ion, ca bon in ensi y
and pe capi a g oss indus ial ou pu alue (see Table 1). In e ms o
ca bon in ensi y and pe capi a g oss indus ial ou pu alue, he op
10 p o inces wi h high ca bon in ensi y and pe capi a g oss indus-
ial ou pu a e se as ‘high ca bon in ensi y’and ‘high indus ial ou -
pu ’, he lowe 10 p o inces a e se as ‘low ca bon in ensi y’and ‘low
indus ial ou pu ’and he middle 10 p o inces a e se as ‘middle ca -
bon in ensi y’and ‘middle indus ial ou pu ’.
Empi ical esul s and discussion
Technical e ficiency
Technical e ficiency measu es he deg ee o which he op imal ou -
pu is achie ed wi h a gi en inpu , exp essing he le el o echnology
use in a p oduc ion p ocess. In he p esen s udy, echnical e ficiency is
eflec ed by DDF. I he alue o DDF equals 1, p oduc ion is a i s mos
e ficien . Con e sely, i he alue o DDF is g ea e han 1, a dis ance o
each i s mos e ficien poin is e iden , whe ein a g ea e DDF alue
indica es lowe echnical e ficiency. As his s udy includes good ou pu
(g oss indus ial ou pu alue) and bad ou pu (ICE), DDF can also eflec
p oduc ion e ficiency and po en ial emission educ ion e ficiency. Fig. 2
p esen s he echnical e ficiency le el ia DDF.
F om a na ional pe spec i e (see Fig. 2A), he a e age alues o
na ional DDF o e all p esen an ascending endency om 2000 o 2017,
sugges ing ha echnical e ficiency in China’s indus y has g adually
dec eased since 2000. Fig. 2B shows he a e age DDF a ia ions o he
eas e n, cen al and wes e n egions in he same ime pe iod. Fi s , he
DDF in he eas e n egion fi s exhibi ed g ow h, which declined in 2009
as a u ning poin , p esen ing an in e ed U-shaped change end sugges -
ing ha he echnical e ficiency in he eas e n egion dec eased om 2000
o 2009 and has inc eased since 2009. Fu he mo e, he DDF in he cen al
egion ose om 2000 o 2012 and gen ly d opped om 2012 o 2016,
hen sha ply inc eased o mo e han 0.8 in 2017. This esul indica es ha
he cen al egion’s echnicale ficiency dec eased om 2000 o 2012, had
a sligh inc ease om 2012 o 2016, bu significan ly dec eased in 2017.
In con as o he cen al and eas e n egions, he DDF o he wes e n
egion exhibi ed an inc easing endency in he whole sample pe iod, bu
i s g ow h a e has been ex emely minimal since 2014, sugges ing ha
he wes e n egion’s echnical e ficiency dec eased in all s udy yea s.
Compa ed o he DDF alues in he o he h ee egions, we find ha he
eas e n egion had he highes ine ficiency le el om 2000 o 2012, ol-
lowed by he cen al and wes e n egions. Ne e heless, since he ise o
he eas e n egion’s echnical e ficiency and he dec ease o he wes e n
egion’s echnical e ficiency, he DDF alue o he wes e n egion has
g adually exceeded ha o he eas e n egion since 2013. F om 2013 o
2017, he eas e n egion’s echnical e ficiency was he highes , whe eas i
was he lowes in he wes e n egion excep o 2017.
Fig. 2C shows he dispa i y o DDF change ends in egions wi h
di e en ca bon in ensi y le els. The esul s demons a e ha he
ajec o y o echnical e ficiency in egions wi h low ca bon
in ensi y fi s dec eased and hen inc eased in 2008 as a u ning
poin , and he echnical e ficiency in egions wi h middle ca bon
in ensi y also exhibi ed a simila change ajec o y. Howe e , he
echnical e ficiency in egions wi h high ca bon in ensi y exhib-
i ed a dec easing end om 2000 o 2017. Toge he wi h he
inc ease in echnical e ficiency in low-ca bon egions and he
dec ease in echnical e ficiency in ca bon-in ensi e egions, low
ca bon in ensi y egions ha e g adually had he highes echnical
e ficiency since 2011, ollowed by middle and high ca bon in en-
si y egions. Fig. 2D compa es he dispa i y o echnical e ficiency
change in egions wi h di e en indus ial ou pu s. The esul s
e eal ha he echnical e ficiency o high indus ial ou pu
egions dec eased om 2000 o 2008 and inc eased om 2008 o
2017. In addi ion, he echnical e ficiency in middle indus ial
ou pu egions dec eased om 2000 o 2014, exhibi ing a so
inc ease since 2014; howe e , he echnical e ficiency in low
indus ial ou pu egions showed an o e all dec easing end in
he s udy pe iod. In conclusion, he egions wi h lowe ca bon
in ensi y and highe indus ial ou pu g adually came close o
he op imal on ie o echnology use.
Table 1
G oup di isions and associa ed p o inces.
G oup di ision Associa ed p o inces
Geog aphical p oximi y
Eas Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Hainan
Cen al Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan, Shanxi
Wes Inne Mongolia, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang, Guangxi
Ca bon in ensi y
Low ca bon in ensi y Guangdong, Shanghai, Beijing, Tianjin, Jiangsu, Zhejiang, Shandong, Fujian, Jilin, Hainan
Middle ca bon in ensi y Liaoning, Jiangxi, Henan, Hubei, Sichuan, Chongqing, Hunan, Shaanxi, Anhui, Heilongjiang
High ca bon in ensi y Guangxi, Hebei, Yunnan, Gansu, Inne Mongolia, Xinjiang, Guizhou, Qinghai, Shanxi, Ningxia
Pe capi a g oss indus ial ou pu alue
High indus ial ou pu Tianjin, Shanghai, Jiangsu, Zhejiang, Guangdong, Shandong, Beijing, Fujian, Liaoning, Jilin
Middle indus ial ou pu Inne Mongolia, Chongqing, Hubei, Hebei, Henan, Anhui, Ningxia, Jiangxi, Sichuan, Hunan
Low indus ial ou pu Shaanxi, Qinghai, Shanxi, Guangxi, Heilongjiang, Hainan, Xinjiang, Gansu, Yunnan, Guizhou
X. Li, M. Wang and W. Wan Jou nal o Inno a ion & Knowledge 9 (2024) 100493
5
Aba emen po en ial o indus ial CO
2
emissions
Sec ion “Technical e ficiency” eflec s he p oduc ion e fi-
ciency and po en ial e ficiency o educing emissions by DDF;
hus, DDF is employed o de e mine he uppe limi o good ou -
pu expansion and he po en ial educ ion in bad ou pu . Fo
example, he na ional a e age DDF om 2000 o 2017 was
0.3112, and he na ional a e age ICE in he same ime pe iod
was 5284.97 M , sugges ing ha he na ional a e age ICE could
be educed o 5284.97 M £0.3112 = 1644.46 M . Fig. 3 illus-
a es he a e age PCR in he whole na ion and di e en egional
g oups in he s udy pe iod.
Fig. 2. A e age DDF in all o China and di e en egional g oups.
Fig. 3. A e age po en ial ca bon educ ion in he whole na ion and di e en egional g oups.
X. Li, M. Wang and W. Wan Jou nal o Inno a ion & Knowledge 9 (2024) 100493
6
As demons a ed in Fig. 3A, he indus ial a e age PCR inc eased
om less han 300 M in 2000 o app oxima ely 4400 M in 2017.
This esul is pa ially a ibu able o ising echnical ine ficiency and
pa ially a ibu able o inc easing ICE. Fig. 3B indica es ha he PCR
in he eas e n egion main ained an inc easing end om 2000 o
2011 and hen dec eased a e 2011. The eas e n egion’s PCR was
he highes in mos yea s un il 2015. The cen al egion wi h he sec-
ond-la ges PCR exhibi ed an upwa ds end in almos all s udy yea s.
In 2017, he cen al egion’s PCR exceeded he eas e n and wes e n
egions and had he la ges PCR. Addi ionally, he wes e n egion had
he lowes (bu ising) PCR in mos yea s. Since 2015, he PCR in he
wes e n egion has exceeded ha o he eas e n a ea.
Fig. 3C shows he PCR change dispa i y be ween egions wi h di -
e en ca bon in ensi ies, e ealing ha he PCR change o low ca bon
in ensi y egions exhibi ed an in e ed U-shaped cu e du ing he
s udy pe iod and had he lowes PCR since 2011. Combined wi h he
esul s in Fig. 2C, we can asse ha he dec ease in he low ca bon
in ensi y egion’s PCR was a ibu able o an imp o emen in echni-
cal e ficiency. F om 2000 o 2011, he PCR in middle and high ca bon
in ensi y egions we e almos simila ; howe e , since 2011, he PCR
in middle ca bon in ensi y egions has g adually dec eased, becom-
ing he egion wi h he lowes PCR. By con as , he PCR in high ca -
bon in ensi y egions significan ly inc eased, becoming he egion
wi h he la ges PCR. Fig. 3D shows he dispa i ies in PCR change
be ween egions wi h di e en indus ial ou pu s. F om 2000 o
2010, he PCR o he high indus ial ou pu egions exhibi ed an
inc easing end and had he la ges PCR, dec easing since 2010 and
becoming he egion wi h he lowes PCR since 2015. The PCR in mid-
dle and low indus ial ou pu egions all exhibi ed an o e all inc eas-
ing end h oughou he s udy pe iod. Some no able di e ences a e
e iden . The g ow h a io o PCR in he middle indus ial ou pu
egions was ela i ely la ge p io o 2011 and hen became smoo h
om 2011 o 2017; howe e , he g ow h a io o PCR in he low
indus ial ou pu egions was ela i ely so be o e 2016 and became
sha p om 2016 o 2017.
Table 2 p esen s he a e age PCR o he 30 Chinese p o inces om
2000 o 2017. Hebei P o ince had he la ges emission educ ion
po en ial, wi h an a e age annual PCR o 388.23 M , sugges ing ha
he p o ince has he po en ial o u he educe CO
2
emissions by
app oxima ely 388.23 M i i eaches he on ie o echnology use.
Table 2 indica es ha he easons ha led o Hebei ha ing he la ges
PCR a e a ibu able o i s high le el o echnical ine ficiency and he
high CO
2
emissions, pa icula ly he o me . The a e age DDF in
Hebei was as high as 0.9096, sugges ing ha ine ficien p oduc ion
accoun ed o 90.96 % o o al p oduc ion in Hebei, and he emission
educ ion po en ial a io also eached 90.96 %; he e o e, Hebei
P o ince may be ela ed o a se ious p oblem o ine ficien p oduc-
ion. Addi ionally, Hebei P o ince was a conside able ca bon
emi e (i.e. a e age CO
2
emissions we e 426.81 M ). These wo
ci cums ances led o high PCR in Hebei P o ince. Shandong P o -
ince ollowed Hebei wi h an a e age o 259.04 M . As shown in
Table 2, he main eason o Shandong’s high PCR was i s consid-
e able CO
2
emissions. In addi ion, Shanxi, Guangdong, Jiangsu,
Henan and Inne Mongolia exhibi ed a ela i ely high a e age
PCR, wi h a e age DDF alues ha we e all g ea e han 0.5, sug-
ges ing ha hese p o inces may all benefi om echnical ine fi-
ciency o di e en deg ees.
In con as , Hainan exhibi ed he smalles educ ion po en ial, and
i s a e age annual PCR was only 0.47 M , which indica es ha Hainan
may be able o u he educe i s CO
2
emissions by app oxima ely
0.47 M i he p o ince p oduces a he on ie o echnology use.
The emission educ ion space o Hainan is ex emely small and has
p ima ily benefi ed om i s high echnical e ficiency and low CO
2
emissions. As epo ed in Table 2, he DDF in Hainan was 0.0301, sug-
ges ing ha he e was only 3.01 % ine ficien indus ial p oduc ion in
Hainan. The a e age annual CO
2
emissions in Hainan we e only 15.61
M . Beijing, Qinghai, Chongqing and Jilin also exhibi ed low a e age
PCR, which was p ima ily a ibu able o ela i ely high echnical
e ficiency and low CO
2
emissions.
Shadow p ices o indus ial CO
2
emissions
Shadow p ice in he whole na ion and di e en g oups
As no ed in Sec ion “In oduc ion”, he MAC is ep esen ed by
he shadow p ice o ICE in his s udy. Fig. 4A illus a es he a e -
age shadow p ice o ICE be ween 2000 and 2017. Compa ed o
p e ious esea ch, he esul s o his s udy appea o be eason-
able. The shadow p ice p esen s h ee dis inc s ages. Fi s , om
2000 o 2011, a significan downwa ds end in he shadow p ice
is shown, dec easing om 2.45 (10
4
yuan pe on) in 2000 o 2.1
(10
4
yuan pe on) in 2011, sugges ing ha he educed cos
dec eased du ing his pe iod, wi h some appa en fluc ua ions.
The second s age occu ed om 2011 o 2016, when he shadow
p ice o ICE exhibi ed an upwa ds end wi h a ela i ely la ge
g ow h a e, sugges ing ha con olling ICE became expensi e in
his pe iod. Finally, in he hi d s age (2016−2017), he shadow
p ice dec eased om mo e han 2.3 (10
4
yuan pe on) o app ox-
ima ely 2.2 (10
4
yuan pe on).
Fig. 4B−D shows he shadow p ices o ICE in each egion. Compa -
ing he h ee figu es e eals ha he shadow p ice change ajec o-
ies in he eas e n egion, low ca bon in ensi y egions and high
indus ial ou pu egions we e simila , achie ing a sha p, fluc ua ing
Table 2
A e age annual po en ial CO
2
emission educ ion ac oss p o inces (M ).
P o inces A e age DDF A e age emissions A e age PCR P o inces A e age DDF A e age emissions A e age PCR
Hebei 0.9096 426.81 388.23 Fujian 0.1662 146.61 24.37
Shandong 0.5550 466.71 259.04 Anhui 0.1485 162.59 24.15
Shanxi 0.7803 317.57 247.79 Guangxi 0.2046 115.86 23.71
Guangdong 0.6969 333.27 232.26 Guizhou 0.2001 105.88 21.18
Jiangsu 0.5615 391.92 220.06 Shanghai 0.1598 116.09 18.55
Henan 0.5879 304.38 178.94 Gansu 0.1826 88.00 16.07
Inne Mongolia 0.6004 213.64 128.26 Jiangxi 0.1633 96.43 15.74
Sichuan 0.3931 207.96 81.75 Heilongjiang 0.1250 108.44 13.55
Liaoning 0.2999 255.13 76.52 Ningxia 0.1628 78.85 12.84
Zhejiang 0.2798 238.67 66.78 Tianjin 0.1595 79.19 12.63
Hubei 0.2502 202.94 50.77 Jilin 0.1131 100.10 11.32
Xinjiang 0.4085 123.99 50.64 Chongqing 0.0942 92.40 8.70
Hunan 0.2804 159.79 44.81 Qinghai 0.1156 45.81 5.30
Yunnan 0.3100 127.15 39.42 Beijing 0.1025 47.30 4.85
Shaanxi 0.2933 115.90 33.99 Hainan 0.0301 15.61 0.47
X. Li, M. Wang and W. Wan Jou nal o Inno a ion & Knowledge 9 (2024) 100493
7
dec ease om 2000 o 2011 as he egions wi h he lowes shadow
p ice. Since 2011, he change a e o he shadow p ice has become
milde , p esen ing a ising end. The esul s indica e ha he cos o
educing ICE g adually became mo e cos ly as he s udy pe iod p o-
g essed. Addi ionally, he shadow p ice change ajec o y in he cen-
al egion, middle ca bon in ensi y egions and middle indus ial
ou pu egions p esen ed an in e ed U shape. Fu he mo e, as
shown in Fig. 4B, he shadow p ice in he wes e n egion fi s
exhibi ed a s eady and mild dec ease om 2000 o 2011, main-
aining a significan ise a e 2011. In ecen yea s, he wes e n
egion has become he egion wi h he highes ICE shadow p ice.
The shadow p ice in he high ca bon in ensi y egions also p e-
sen ed a U-shaped a ia ion, wi h 2011 as he u ning poin .
Since 2010, he middle ca bon in ensi y egion has had he la g-
es shadowp ice, ollowedby hehighandlowca bonin ensi y
egions. Fo egions wi h di e en indus ial ou pu , since 2004,
low indus ial ou pu egions ha e had he cos lies MAC,
whe eas high indus ial ou pu egions ha e had he smalles
MAC (see Fig. 4D).
Shadow p ice disc epancies ac oss p o inces
Fig. 5 illus a es he indus ial ca bon shadow p ices ac oss he
30 Chinese p o inces. F om Fig. 5A, he ou p o inces wi h he
lowes a e age shadow p ice we e Hebei, Shandong, Jiangsu and
Guangdong, wi h p ices o 1.7120, 1.7598, 1.8848 and 1.9775,
espec i ely (10
4
yuan pe on). This esul sugges s ha hese
ou p o inces ha e a ela i ely low ma ginal cos o u he
educing ICE and should be China’s p e e ed choice o indus ial
ca bon educ ion. In con as , Shaanxi, Heilongjiang and Beijing
exhibi ed he highes a e age shadow p ice, a 2.6855, 2.6000
and 2.4953, espec i ely (10
4
yuan pe on). This esul indica es
ha hese h ee p o inces ha e a ela i ely high ma ginal cos
o u he educing hei ICE.
Fig. 5B p esen s he changing end o indus ial ca bon shadow
p ices om 2000 o 2017. The 30 p o inces can be classified in o ou
g oups acco ding o hei ea u es. The fi s g oup ep esen s p o in-
ces wi h ICE shadow p ices ha showed an o e all inc easing end
du ing he s udy pe iod, which includes Beijing, Heilongjiang,
Yunnan, Shaanxi and Xinjiang. Fo hese fi e p o inces, he cos o
u he educing ICE became inc easingly expensi e. The second
g oup ep esen s p o inces wi h ICE shadow p ices ha exhibi ed a
U-shaped change end, which includes Liaoning, Jilin, Shanghai,
Henan, Hubei, Hunan, Sichuan, Guizhou and Gansu. The hi d g oup
ep esen s p o inces wi h ICE shadow p ices ha showed an o e all
downwa ds end, which includes Tianjin, Hebei, Shanxi, Inne Mon-
golia, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Shandong and Guang-
dong. Fo hese 11 p o inces, he cos o u he educing ICE
g adually dec eased. The ou h g oup ep esen s p o inces wi h ICE
shadow p ices ha we e s eady and did no change conside ably du -
ing his s udy.
Ac ually, he e a e la ge di e ences in he es ima ions o he
MACs o ICE in China in he p e ious li e a u e. Fo example, Chen e
al. (2013) and Wu e al. (2020) all applied non-pa ame ic DDF o
es ima e he MAC o China’s indus ial sec o s. The o me s udy
o ecas ed he MACs o ICE a 2731 and 4012 yuan pe on o ca -
bon emissions du ing he 12 h and 13 h Fi e-Yea Plans, espec-
i ely. By con as , he la e s udy ound ha he a e age MAC
o he op fi e indus ial sec o s wi h he highes ca bon in ensi y
is 373.92 yuan/ on, and he op fi e sec o s wi h he lowes ca -
bon in ensi y a e 50,254.54 yuan/ on. We find ha bo h s udies
a e based on China’s indus ial sec o da a and used a simila
es ima ion app oach; howe e , he calcula ed MAC esul s a e
qui e di e en . This may be a ibu ed o he ac ha non-
pa ame ic me hods ha e a de ec in es ima ing ICE esul s ha
a e no unique. Conside ing his, his s udy adop ed a pa ame ic
DDF model o es ima e he MAC o ICE and hen discussed he
MACs acco ding o he cha ac e is ic clus e ing g oups o di e -
en p o inces, which may p o ide mo e de ailed e e ences o
local go e nmen o o mula e emission educ ion measu es a -
ge ed o each p o ince’s ac ual si ua ion.
Fig. 4. A e age indus ial ca bon shadow p ice in he whole na ion and di e en egional g oups. (Uni : 10
4
yuan RMB pe on).
X. Li, M. Wang and W. Wan Jou nal o Inno a ion & Knowledge 9 (2024) 100493
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