Production technology and carbon emission: Long-run relation with short-run dynamics

Dinda, Soumyananda A icle P oduc ion echnology and ca bon emission: Long- un ela ion wi h sho - un dynamics Jou nal o Applied Economics P o ided in Coope a ion wi h: Uni e si y o CEMA, Buenos Ai es Sugges ed Ci a ion: Dinda, Soumyananda (2018) : P oduc ion echnology and ca bon emission: Long- un ela ion wi h sho - un dynamics, Jou nal o Applied Economics, ISSN 1667-6726, Taylo & F ancis, Abingdon, Vol. 21, Iss. 1, pp. 106-121, h ps://doi.o g/10.1080/15140326.2018.1526871 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/314042 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. 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I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ Jou nal o Applied Economics ISSN: 1514-0326 (P in ) 1667-6726 (Online) Jou nal homepage: www. and online.com/jou nals/ ecs20 P oduc ion echnology and ca bon emission: long- un ela ion wi h sho - un dynamics Soumyananda Dinda To ci e his a icle: Soumyananda Dinda (2018) P oduc ion echnology and ca bon emission: long- un ela ion wi h sho - un dynamics, Jou nal o Applied Economics, 21:1, 106-121, DOI: 10.1080/15140326.2018.1526871 To link o his a icle: h ps://doi.o g/10.1080/15140326.2018.1526871 © 2018 The Au ho (s). Published by In o ma UK Limi ed, ading as Taylo & F ancis G oup Published online: 28 No 2018. Submi you a icle o his jou nal A icle iews: 3739 View ela ed a icles View C ossma k da a Ci ing a icles: 36 View ci ing a icles Full Te ms & Condi ions o access and use can be ound a h ps://www. and online.com/ac ion/jou nalIn o ma ion?jou nalCode= ecs20 P oduc ion echnology and ca bon emission: long- un ela ion wi h sho - un dynamics Soumyananda Dinda Depa men o Economics, Uni e si y o Bu dwan, Bu dwan, India ABSTRACT Using a ec o e o co ec ion model, his pape in es iga es he long- un ela ion wi h sho - un dynamics among CO 2 emission, echnological p og ess and economic g ow h. I obse es a speci- fic kind o causali y unning om echnological p og ess o educ- ion o CO 2 emission in he Uni ed S a es du ing 1963–2010, while pas income gene a ion is he cause o ising ca bon emission. Policy make s should emphasise R&D o upda ed p oduc ion echnology, while aising income helps o educe CO 2 emission. Technological p og ess is he cen al o ce ha causes income g ow h as well as emissions’ educ ion. Con inuous change and adap ion o new and upda ed echnology is he main d i ing o ce owa ds sus ainable de elopmen . ARTICLE HISTORY Recei ed 29 Augus 2016 Accep ed 1 Sep embe 2017 KEYWORDS CO 2 emission; economic g ow h; pa en ; echnological p og ess 1. In oduc ion The linkage be ween clima e change and economic g ow h is an impo an issue in ecen esea ch; howe e , he e is no much ocus on he ela ionship be ween echnological p og ess and clima e change o ca bon emission. Ca bon dioxide (CO 2 )emissionis he main culp i o global clima e change (Coondoo & Dinda, 2002). Ca bon emission ises o e he yea s while he numbe o pa en egis a ion also inc eases in a de eloped coun y like he Uni ed S a es. Now, ques ions a ise abou he ela ionship be ween pa en egis a- ion and ca bon emission, o he ela ionship be ween clima e change and echnological p og ess. 1 Se e al s udies (Coondoo & Dinda, 2002; Dinda & Coondoo, 2006;S e n,2000; Yang, 2000) obse e he causal linkage be ween economic g ow h and ca bon emission (o ene gy consump ion). Applying econome ic ools, his s udy in es iga es he ela ion among echnological p og ess, economic g ow h and CO 2 emission. Le us conside a specific le el o income, up o which one may easonably expec high g eenhouse gas-in ensi e income g ow h o affec ad e sely he clima e; bu beyond a ce ain c i ical le el, clima ic deg ada ion may each a s age whe e u he income g ow h becomes impossible. Thus, clima e change is a global public good ha may ac as a cons ain o income g ow h a his la e s age i g eenhouse gas-in ensi e income g ow h p ocess is con inued (Dinda, 2009a; Hol z-Eakin & Selden, 1995; CONTACT Soumyananda Dinda [email p o ec ed] Depa men o Economics, Uni e si y o Bu dwan, Golapbag Campus, Bu dwan, Wes Bengal 713104, India I am also g a e ul o he Edi o o he JAE o aluable sugges ions. 1 Pa en egis a ion is conside ed as he p oxy o echnology and i s change o e ime is he echnological p og ess. JOURNAL OF APPLIED ECONOMICS 2018, VOL. 21, NO. 1, 106–121 h ps://doi.o g/10.1080/15140326.2018.1526871 © 2018 The Au ho (s). Published by In o ma UK Limi ed, ading as Taylo & F ancis G oup This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License (h p://c ea i ecommons.o g/licenses/ by/4.0/), which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. Schmalensee, S oke , & Judson, 1998; Wo ld Bank, 1992). The global economy aces se ious challenges om he global clima e change. To o e come i , he e is in e na ional p essu e o educe ca bon emission o all na ions. This s udy in es iga es echnological p og ess and i s linkage wi h CO 2 emission, which is a c ucial ac o o global clima e change. I ocuses on p oduc ion echnology and i s p og ess which is obse ed in numbe o g an ed u ili y pa en s o e ime. 2 These pa en s imp o e p oduc ion p ocesses. Gene ally, echnological p og ess 3 esul s in a g ea e efficiency in he use o ene gy and ma e ials. T uly, upg aded echnology imp o es wi h economic g ow h and helps o p oduce ce ain amoun o goods using less ene gy and ma e ials, which defini ely educe p essu e o bu den on na u al esou ces and en i onmen successi ely. The e is a g owing end among indus ies o econside hei p oduc ion p ocesses and he eby ake en i onmen al consequences o p oduc ion in o accoun . Lindma k (2002) obse es ha he echnological change associa ed wi h he p oduc ion p ocess may also esul in changes o he inpu mix o ma e ials and uels. Ul ima ely ene gy equi emen pe uni o ou pu will be less o new p oduc ion echnology. Any imp o emen in p oduc ion sys em h ough ce ain change in echnology, edesign p oduc o /and p oduc ion p ocess helps o sa e ene gy and educe emission. 4 In ui i ely, echnological p og ess is one o he main causes o educ ion o ca bon emission (Dinda, 2009b). Does echnological p og ess mo e in he igh di ec ion owa ds he low ca bon emission associa ed wi h economic g ow h? A ca e ul s udy is necessa y o unde s and he causal linkage be ween echnological p og ess, income and ca bon emissions. I ce ainly helps o o mula e p ope policy o mi iga ing clima e change o a coun y and he wo ld. In his con ex , his s udy ocuses on he Uni ed S a es, a de eloped economy, whe e numbe o pa en egis a ion (bo h design and u ili y pa en ) is e y high o e se e al decades. So, logically he Uni ed S a es should be he leas pollu e in he wo ld, bu in con as , he Uni ed S a es is on he op o ca bon emi e s lis . 5 Why is he Uni ed S a es on he op pollu e s lis while i holds he majo pa en s o inno a ions o upg aded echnology? Does he ising inno a ion educe ossil- uel consump ion and he eby ca bon emission? This pape a emp s o answe hese ques ions wi h a possible heo e ical explana ion and empi ical e idence. 2 Numbe o u ili y pa en s g an ed in he US Pa en and T adema k Office (USPTO) is aken, he e, as a p oxy o echnology o gi en yea . O e ime, i ep esen s echnological p og ess. Se e al s udies also used USPTO da a; see Cao (2014), Hall e al. (2001), and G iliches (1998). 3 Technological p og ess may also play a majo ole in his p ocess o ans o ma ion o a cleane en i onmen by accele a ing economic g ow h and a he same ime by helping in he subs i u ion o di y and obsole e echnologies by cleane ones. This is he so-called echnique effec o economic g ow h (see Dinda, 2004; S e n, 2004). The goal o cleane and upg aded echnology is o educe emissions o pollu an s. Applica ions o hese echnologies defini ely gene a e less emission and decline he emission le el, “clean coal echnologies”like PFBC, which ini ial goal was o educe emission o pa icula es and acidifica ion. Ano he example is ha ca aly ic con e e s o ca s dec ease emissions ha affec he local en i onmen and u n i in o o he emissions such as CO 2 emission. This s udy ocuses on CO 2 emission only. 4 Ene gy sa ing echnology educes ossil- uel consump ion and he eby less ca bon emissions. Some imes, an ex e nal shock may also o ce he s uc u e o he economy o change. Fo example, oil shocks o he 1970s ha e caused an eno mous s uc u al economic ansi ion wo ld o e owa ds en i onmen - iendly echnology ha helped o educe emission (Moomaw & Un uh, 1997; Un uh & Moomaw, 1998). 5 China and he Uni ed S a es a e in he op lis o o al ca bon emission. China and he Uni ed S a es hold fi s and second posi ion in CO 2 emission in he wo ld, espec i ely. Fo de ails, see he Ca bon Dioxide In o ma ion Analysis Cen e (CDIAC) o Oak Ridge Na ional Labo a o y (ORNL), he Uni ed S a es. JOURNAL OF APPLIED ECONOMICS 107 The pape is o ganised as ollows: Sec ion 2 highligh s he ela ed li e a u e and discusses on echnological p og ess ocusing on u ili y pa en . Sec ion 3 p o ides a simple heo e ical backg ound ollowing Dinda (2009b), which shows how p oduc ion echnologies help o educe pollu ion in a g owing economy. Sec ion 4 desc ibes he da a and he empi ical me hodology. Sec ion 5 analyses he esul s, and Sec ion 6 concludes. 2. Li e a u e e iew 2.1. Rela ed li e a u e Se e al socio-economic ac o s (including consume s’choices) a e esponsible o imp o ing en i onmen al quali y (Gawande, Boha a, Be ens, & Wang, 2000,2001; Lopez & Mi a, 2000; Lieb, 2002; McConnel, 1997; Ro hman, 1998); howe e , en i on- men al quali y imp o es also wi h echnological p og ess (And eoni & Le inson, 2001; B ock & Taylo , 2010; Dinda, 2004; G ossman & K uege , 1995; Komen, Ge king, & Folme , 1997). Loschel (2002) p o ides an o e iew o he ea men o echnological change in economic models o en i onmen al policy. The assessmen o clima e change mi iga ion policies h ough economic modelling depends c ucially on assump ions unde which echnological change has been inco po a ed in he model (Loschel & Schymu a, 2013). Ea lie economics modelling a e hea ily elied on he assump ion o exogenous echnological change, which is also a unc ion o ime. Al hough many p oblems associa ed wi h modelling o exogenous echnological change ha e been esol ed, nume ous ques ions s ill emain unanswe ed. Few ene gy–economy–en i onmen models conside echnological change as endogenous, esponding o socio-economic a iables. Loschel (2002) poin s ou o h ee main elemen s in models o echnological inno a ion: (1) in es men in R&D, (2) spillo e s om R&D and (3) echnology lea ning, o lea ning-by-doing. Technological change is an unce ain phenomenon. These unce ain ies ha e o be inco po a ed in la ge-scale models mo e ca e ully. Ano he impo an dimension o echnical change is he po en ial o pa h-dependency, ine ias and lock-in si ua ions. Ene gy–economy models can accoun o such effec s by a ca e ul inclusion o lea ning-by-doing, ime lags, assump ions abou he diffusion a es o inno a ions and di ec ed (o biased) echnological change (Cao, 2014; G iliches 1998; Ha ne , 2005; Hall, Jaffe, & T aj enbe g, 2001; Loschel & Schymu a, 2013). The e a e wo majo ends in he li e a u e –one ocuses on shi ing he use o p oduc ion echnologies which is diffe en om hei p oduc ion in ensi y (S okey, 1998) and o he analyses he cha ac e is ics o he aba emen echnology (John & Pecchenino, 1994; Selden & Song, 1995). B ock and Taylo (2010) p o ide a G een Solow model ha includes emission, aba emen and s ock o pollu ion. Ande sson and Ka pes am (2013) demons a e ha he economic g ow h p omo es a educ ion o ene gy and ca bon emissions. They analyse he sho - e m and long- e m de e minan s o ene gy in ensi y, ca bon in ensi y and scale effec s o eigh de eloped and wo eme ging economies om 1973 o 2007. A de ailed li e a u e su ey on ene gy–g ow h nexus can be ound in he s udy o Oz u k (2010). B unne meie and Cohen (2003) iden i y he de e minan s o 108 S. DINDA en i onmen al inno a ion in he US manu ac u ing indus ies. Using a panel o 127 manu ac u ing indus ies o e he pe iod 1989–2004, Ca ion-Flo es and Innes (2010) s udy he po en ial bidi ec ional causal links be ween en i onmen al inno a ion and oxic ai pollu ion and find ha en i onmen al inno a ion is an impo an d i e o educ ions in US oxic emissions. Le inson (2009) obse es ha he US manu ac u ing sec o ai pollu an s (such as SO 2 ,NO 2 , CO and VOC) declined wi h echnological ad ancemen du ing 1987–2001. Se e al s udies (Ape gis & Payne, 2009; Bu ns, G oss, & S e n, 2013; Cheng, 1996,1999; Cheng & Lai, 1997; Coondoo & Dinda, 2002; Daghe & Yacoubian, 2012; Kalime is, Richa dson, & Bi as, 2014; S e n, 2000; Yang, 2000) examine he causal ela ionship be ween income and ene gy consump ion (emission), bu ew (Ausubel, 1995) in es iga e he causali y be ween echnological p og ess and ca bon emission. This pape mainly ocuses on he long- un equilib ium ela ionship among CO 2 emission, income and echnological p og ess wi h hei sho - un dynamics in a de eloped economy like he Uni ed S a es. 2.2. Technological p og ess Technological p og ess is possible h ough inno a ions, which a e p o ec ed by pa en igh s. Pa en s a e impo an legal documen s, issued by an au ho ised go e nmen agen , g an ing he igh o exclude anyone else om he p oduc ion o use o a specific new de ice o p ocess o defined numbe o yea s. They a e issued, gene ally, o he in en o o he de ice o p ocess a e a ho ough examina ion ocusing “on bo h he no el y o he claimed i em and i s po en ial u ili y”(G iliches, 1990). As s a ed in G iliches (1990): “The igh embedded in he pa en can be assigned by he in en o o somebody else, usually o his employe , a co po a ion, and/o sold o o licensed o use by somebody else”. The main pu pose o he pa en sys em is “ o encou age in en ion and echnical p og ess bo h by p o iding a empo a y monopoly o he in en o and by o cing he ea ly disclosu e o he in o ma ion necessa y o he p oduc ion o his i em o he ope a ion o he new p ocess”(G iliches, 1990). Thus, pa en egis a ion is conside ed as a p oxy o inno a ion and i p o ides coun y’s echnological capabili ies (A chibugi & Coco, 2004,2005; G iliches, 1990, 1998; Lall, 1992). So, he pa en egis a ion o a coun y shows he end in he imp o emen o echnological s eng h (Tong and F ame 1994). This s udy mainly concen a es on echnological s eng h o a na ion. This pape conside s he u ili y pa en (UTPAT) as a p oxy o p oduc ion echnology, 6 which is he main conce n o ca bon emission in he p oduc ion p ocess. Ma ke ambi ions a e he p ime mo e o new inno a ions in a ma u ed capi alis ic economy (Lall, 1992). Technological p og ess is cap u ed in e ms o u ili y pa en s which mus be eflec ed wi h less pollu ion in he efficien p oduc ion p ocess. As numbe o pa en on p oduc ion inno a ion inc eases, he ene gy consump ion o ca bon emission may educe. Thus, his pape ies o a gue ha g owing u ili y pa en migh be he cause 6 Pa en egis a ion is conside ed as a p oxy o echnological inno a ion and i also eflec s he coun y’s echnological capabili ies (A chibugi & Coco, 2004; G iliches, 1990; Lall, 1992). Bo h u ili y and design pa en a e egis e ed. Howe e , u ili y pa en is conside ed a gene al indica o o echnological p og ess ela ed o ca bon- educing echnologies. In his con ex , u ili y pa en is mo e app op ia e compa e o design pa en . JOURNAL OF APPLIED ECONOMICS 109 o educ ion o ca bon emission. This is impo an o ackle he global clima e change wi h app op ia e policy and o mula e s a egy o economic de elopmen wi h R&D. 3. Theo e ical backg ound 3.1. P oduc ion unc ion, pollu ion and clean echnology Following Solow (1956)and Dinda (2009b), conside ing one-good economy, ou pu is p oduced by only composi e capi al, k, o gi en echnology. P oduc ion unc ion o his economy (in ensi e o m) is y¼ ðkÞ; k>0and kk <0 (1) The p oduc ion o he economy, y, depends only on composi e capi al k, which also gene a es pollu ion as a by-p oduc and is he echnology in his sys em. Pollu ion is una oidable and i has an inhe en ela ion wi h he p oduc ion p ocess. Only echnological imp o emen s elimina e pollu ion. Pollu ion pe uni ou pu (μ) may be a dec easing (inc easing) unc ion o echnological imp o emen . Fo simpli- ci y, ini ially his pape assumes a cons an μ. Pollu ion is gene a ed di ec ly wi h p oduc ion bu in e sely wi h a ailable cleane echnology. The pollu ion flow a each momen is p opo ional o ou pu p oduc ion and in e se o he echnological a ail- abili ies, i.e., p¼μy A;0<μ<1 (2) whe e pis he pollu ion and Ais he numbe o a ailable clean echnologies in he economy. A highe alue o Asugges s mo e a ailable clean echnology (Dinda, 2009b; Reis, 2001) in he economy. A lowe alue o Asugges s a limi ed choice se , whe eas highe alue o Ap o ides g ea e choice se wi h mo e al e na i es and ee o choose be e and/o cleane echnologies. The choice o echnology depends on i s a ailabili y and accessibili y o all. The basic assump ion is ha an upg aded p oduc ion echno- logical inno a ion (in e ms o ei he p oduc i i y o ene gy efficiency) is conside ed a cleane echnology. I sugges s ha any p oduc ion inno a ion inc eases ou pu o gi en inpu s. So, pe capi a ou pu equi es less inpu . Wi h p oduc ion echnological inno a ions, he inpu –ou pu a io dec eases and consequen ly p essu e on en i on- men educes. Pollu ion is gene a ed di ec ly wi h p oduc ion o a gi en echnology a a gi en ime. Howe e , o e ime, a na ion mo es owa ds mo e and mo e clean echnology h ough con inuous upg ade o /and inno a ion. Clean echnology also changes o e ime. The inno a ion ou come depends on he R&D expendi u e, physical and human capi al. Thus, s ock o capi al and echnological p og ess join ly de e mine pollu ion, p, in long un. 7 Taking log o Equa ion (2), he long- un ela ion is ln p¼ln μþln yln A(3) 7 Acco ding o And eoni and Le inson (2001), inc easing e u n o scale ope a es in he aba emen echnology and educes pollu ion. 110 S. DINDA 3.2. S eady s a e The s eady-s a e ela ionship be ween he g ow h a e o pollu ion, income and ech- nology is de i ed om Equa ion (3) (diffe en ia ing wi h espec o ime), i.e., _ p p¼ _ y y _ A A(4) Equa ion (4) sugges s ha echnological p og ess defini ely educes he pollu ion g ow h a e. When pollu ion pe uni ou pu (μ) may change o e ime as μ¼μ0eθ (5) whe e μ0(>0) is he ini ial alue, and i s g ow h a e, θ(θ0;o ; hi 0), is a cons an and is ime a iable, hen ln μ¼ln μ0þθ (6) Now plugging Equa ion (6) in o (3), we ge ln p¼ln μ0þθ þln yln A(7) and co esponding s eady-s a e ela ionship will be _ p p¼θþ _ y y _ A A(8) Theo e ically, θshould be nega i e and pollu ion declines o e ime. Equa ion (8) sugges s ha pollu ion’s g ow h a e ( _ p p) inc eases wi h economic g ow h a e ( _ y y), bu echnological p og ess ( _ A A) in p oduc ion p ocess educes pollu ion in long un. In his con ex , we e i y i s empi ical alidi y using a coun y specific da a. 4. Empi ical s a egy 4.1. Da a sou ces U ili y pa en (UTPAT) is conside ed as a p oxy o a p oduc ion echnology ha is supposed o educe ca bon emission. In his s udy, i is measu ed as he numbe o u ili y pa en s g an ed pe yea . Time se ies da a on UTPAT o he pe iod 1963–2013 a e aken om he US pa en and adema k office (USPATO) websi e. The co esponding annual ime se ies da a on pe capi a CO 2 emission 8 (PCCO 2 ) (exp ess in me ic ons) o he pe iod 1961−2010 a e ob ained om Ca bon Dioxide In o ma ion Analysis Cen e 9 (CDIAC), he Uni ed S a es; and pe capi a GDP 8 He e, we conside CO 2 emission as p oxy o pollu ion. T uly, pollu ion and CO 2 emission is a om equal, o he e is a diffe ence be ween emission and pollu ion. Emission is one pa o pollu ion. Emission is a flow and affec s local en i onmen only, while concen a ion o CO 2 emission is he s ock ha accumula e o e ime and affec he local as well as he global en i onmen . Measu emen o CO 2 emission is compa a i ely easie han ha o concen a ion o CO 2 , and widely he CO 2 emission da a a e a ailable, bu less CO 2 concen a ion da a. Mo eo e , CO 2 emission is one o he g eenhouse gases, bu i is he mos impo an a he global le el. 9 This ca bon dioxide emission da a gene a e om manu ac u ing indus y, which is app op ia e o his s udy. See Oak Ridge Na ional Labo a o y (ORNL) o he Uni ed S a es, h p://www.cdiac.o nl.go . JOURNAL OF APPLIED ECONOMICS 111 (PCGDP) a e aken om he Wo ld Bank (a cons an p ice 2005). CO 2 emission pe dolla (CO 2 pe dolla ) is calcula ed o he pe iod o 1961–2010. Combining hese da a se s oge he , we compile ime se ies da a se o he Uni ed S a es du ing 1963–2010. Fossil- uel ca bon emission gene a ed by he Uni ed S a es has been inc easing con inuously o e he long pas se e al decades (see Figu e A1), while a he same ime, he numbe o u ili y pa en s has been inc easing apidly (see Panel a in Figu e 1). Du ing 1963–2010, pe capi a ca bon emission emi ed by he Uni ed S a es inc eased yea ly 0.22% and pe dolla ca bon emission declined by 1.85%, while he g an ed u ili y pa en g ew 3.27%. Figu e 1 shows he ising ends o u ili y pa en and pe capi a CO 2 emission, while pe dolla CO 2 emission is con inuously declining. I shows clea e idence ha pe capi a CO 2 emission has been inc easing (o a leas non-declining) o e se e al decades, whe eas CO 2 emission pe dolla is s eadily alling. Du ing he pe iod, u ili y pa en s con inuously inc ease. The p elimina y obse a ion is ha he e is an associa ion be ween u ili y pa en and CO 2 emission pe dolla o e ime. 4.2. Me hodology We ha e o examine wea he da a a e s a iona y o non-s a iona y and apply app o- p ia e econome ic echniques o da a analysis. Va iables a e non-s a iona y i hey ha e a uni oo . He e, we apply he augmen ed Dickey–Fulle (ADF) and Phillips– Pe on (PP) uni oo es . In case o wo o mo e non-s a iona y a iables, he e is a possibili y o coin eg a ing ela ion among hem. Coin eg a ion es s a e equi ed when all a iables a e in eg a ed o o de one, i.e., I(1). Hence, i needed, we examine he coin eg a ion (Johansen, 1988). Engle and G ange (1987) show ha i wo se ies a e I(1), hen G ange causali y may exis in a leas one di ec ion in I(0) a iables. Acco ding o Engle and G ange (1987), coin eg a ion shows he long- un equilib ium ela ionship among a iables and sho - un dynamics. Fo sho - un ela ion, ec o au o eg essi e model is cons uc ed in e ms o hei fi s diffe ences. In case, wo se ies a e I(1); VAR wi h e o co ec ion e m is he ec o e o co ec ion model (VECM), which cap u es sho - un dynamics wi h he long- un equilib ium ela ion. VECM is a s a is ical echnique ha helps o de ec he na u e o ela ionship in long- un and sho - un dynamics among a iables in a ime se ies da a se . Le he s ochas ic (o andom dis u bance) e m (ν) be added o he coin eg a ing equa ion o o m he model: CO2pe dolla ¼λ1UTPAT þλ2PCGDP þν (9) and he ec o e o co ec ion (o VAR wi h e o co ec ion e m) is ΔX ¼ΩΔX iþηEC 1þε (10) whe e X is he ec o o diffe ence o a iables and EC is he e o co ec ion e m de i ed om he long- un coin eg a ing ela ionship [E ^ C ¼^ ν ¼CO2pe dolla  ^ λ1UTPAT  ^ λ2PCGDP  ]. 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