Curbing Emissions through a Carbon Liabilities Market: A note from a climate skeptic s perspective

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1 Curbing Emiion hrough a Carbon Liabiliie Marke: A noe from a climae kepic perpecive Eienne Billee de Villemeur, Juin Leroux Série Scienifique Scienific Serie Monréal Février 2014/February Eienne Billee de Villemeur, Juin Leroux. Tou droi réervé. All righ reerved. Reproducion parielle permie avec ciaion du documen ource, incluan la noice. Shor ecion may be quoed wihou explici permiion, if full credi, including noice, i given o he ource.

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3 Curbing Emiion hrough a Carbon Liabiliie Marke: A noe from a climae kepic perpecive * Eienne Billee de Villemeur, Juin Leroux Réumé/abrac We argue for he creaion of a carbon liabiliie marke o addre climae change. Each period, counrie would be made liable for heir hare of reponibiliy in curren climae damage. Becaue liabiliie could be raded like financial deb, robune o raegic manipulaion and efficiency enue. Moreover, hi decenralize he choice of he rae by which counrie dicoun fuure benefi and damage. Raher han being baed on an expeced dicouned um of fuure marginal damage (a wih a carbon ax or radable emiion permi) our propoal relie only on oberved realized damage and on he well-documened emiion hiory of counrie. Mo clé/keyword: Carbon Liabiliie, Climae Policy, Marke Inrumen. Code JEL : Q54, H23. * The auhor wih o hank Geir Aheim, Haan Benchekroun, Yann Bramoullé, Aleio D.Amao, George Dionne, Paul Ekin, Gérard Gaude, André Grimaud, Chriian Gollier, Jérémy Lauren-Luchei, Peer Harley, Marcu Hermann, Loui Hoe, Shi-Ling Hu, Yann Kervinio, Séphane Lambrech, Derek Lemoine, Lelie Marin, Sephen Salan, Marc Sanugini, Charle Séguin, Jen Seffek, Nicola Treich, Edilio Valenini, Bruno Veraevel, Mirko Wiederhol, Ralph Winkler a well a paricipan of he 2012 Occaional California Workhop on Environmenal and Reource Economic, he Monreal Reource and Environmenal Economic Workhop, and he 2012 Pari Environmenal and Energy Economic Seminar (PEEES). EQUIPPE, Univerié de Lille, France. HEC Monréal, CIRANO & CIRPEE, Canada, juin.leroux@hec.ca.

4 1 Inroducion Climae policie ha rely on economic inrumen, uch a emiion axe or cap-and-rade program, exac immediae paymen on he bai ha climae damage will occur in he fuure. In principle, an opimal carbon ax ak emier o pay oday he expeced dicouned marginal damage of emiion, according o ome climae damage cenario over he nex decade, omeime cenurie ha may or may no maerialize. Likewie, he number of radable permi iued in an effi cien cap-and-rade program i alo coningen on aid cenario, effecively coing emier he full expeced conequence of heir emiion flow upon emiing. Should hee cenario or mankind reponibiliy in hem prove inaccurae, uch anicipaory cheme would caue needle dirupion o he economy. Inead, we argue in favor of holding counrie liable for climae damage ariing from heir greenhoue ga emiion hrough he creaion of a marke for liabiliie. Concreely, emiing CO 2 in he amophere 1 would be accompanied by he iuance of a carbon liabiliy: a legal duy for he bearer o pay damage over ime a climae damage occur. 2 In oher word, he bearer of carbon liabiliie would be repaying heir deb o he world in inallmen raher han upfron. Carbon liabiliie would no expire, bu would inead decay a he ame rae a amopheric CO 2, all he while holding i bearer accounable for paying carbon damage a climae damage occur. Carbon liabiliie could be old o oher counrie, by paying hem o honor heir newly acquired reponibiliy in fuure climae damage. 3 effi ciency. Free rade on he global marke would enure The idea of uing liabiliie a a mean o conrolling exernaliie race back 1 For expoiional purpoe, we hall peak only in erm of CO 2. 2 Clearly, he iue of deermining he magniude of anhropogenic climae damage i a diffi cul one. Noe, however, ha hi queion i by no mean reolved wih a carbon ax. In fac i i made even wore, becaue eimaing he value of he damage caued by a on of carbon emied oday decade or cenurie ino he fuure i a much more heroic fea han aeing he reponibiliy of pa emiion in (oberved) damage ocurring oday. Ye, very few objecion o he carbon ax eem o be raied on hoe ground. 3 Thank o he financiariaion of climae liabiliie, carbon damage would add o he naional deb. Therefore, here i no reaon o be more concerned by counrie defauling on he paymen of carbon damage han by heir defauling on he repaymen of naional deb. However, here i a difference in he naure of hee deb. In he unlikely cae of defaul on financial deb, hoe affeced are credior who choe o expoe hemelve o financial rik. By conra, hoe affeced by defaul on carbon deb are likely o be reiden of vulnerable counrie ha did no chooe o expoe hemelve o climae rik. We hank Yann Kervinio for hi obervaion. 2

5 o Calabrei (1970) and wa recenly compared o correcive axaion in Shavell (2011). On he one hand, regulaion (axaion) i coly even in he abence of damage, wherea a liabiliy approach only kick in when harm acually occur. On he oher hand, a liabiliy approach i ypically more informaionally demanding becaue i require eablihing or (Kolad e al, 1990; Shavell, 2011). Hence, a liabiliy approach i likely o be more appropriae in iuaion where damage i highly uncerain bu where i ource can be eaily eablihed. Thi i preciely he cae of climae change, where he magniude of damage i ypically unknown bu he reponibiliy of counrie oward CO 2 concenraion can be readily eablihed hank o available daa on cumulaed CO 2 emiion per counry (e.g., from he World Reource Iniue or he World Bank daabae). 4 2 Effi ciency Le {D } + =0 = { } + i Di denoe he flow of ochaic damage borne by all =0 counrie, indexed by i, a aached o anhropogenic climae change. A any period, he occurrence and he magniude of hi damage i aumed o be an increaing funcion of Z, he curren ock of anhropogenic CO 2 in he amophere. Our propoal coni in convering CO 2 emiion ino financial deb. More preciely, in each period, all counrie are required o conribue o an inernaional climae fund o he une of µ Z j where µ = dd /dz i he marginal climae damage due o anhropogenic emiion 5 and where Z j = = γ X j i he conribuion of counry j o he ock Z (i i he dicouned um of i pa emiion X j, for all, accouning for heir naural decay a rae 1 γ). 6 4 The liabiliy approach i uually dicued in he conex of or law, involving privae parie and legal co aached o lawui, o eablihing due care and negligence. By conra, he liabiliy approach we conider here i public, in he ene ha i involve counrie, and would coni in an auomaic procedure where he negligence rule play no role. Counrie would be held reponible for climae damage according o heir pa emiion. 5 Unlike in or law, we do no aim for "full liabiliy" becaue i i no opimal o cover all he co. Raher, we require counrie o pay for he marginal damage hey induce, hence our ue of he phrae "effi cien carbon liabiliie". 6 I i acually no required o race back emiion o infiniy. In fac, accouning only for, ay, po-1990 emiion would reul in he very ame emiion paern. Indeed, he runcaion imply amoun o lump-um ranfer o counrie while preerving incenive a he margin. 3

6 Propoiion 1 Under he uual Pigovian aumpion ha no ingle agen ha an impac on he marginal damage, 7 uch a carbon deb cheme yield fir-be emiion paern. Proof. benefi a: Under raional expecaion, counry i evaluae i preen ne B i = + =0 β B i ( ) X i µ Z i ], (1) ( ) where B i X i i he per-period benefi of counry i reuling from i emiion in he curren period. Counry i hen chooe an emiion ream { X i uch ha: B i X i = E β µ Z i X i ] = E (γβ) D Z ] } + =0 under he aumpion ha no ingle agen ha an impac on marginal damage. Each counry equalize i marginal benefi wih he expeced dicouned value of marginal climae damage, hu achieving fir-be effi ciency. Noice ha he only informaion required of he planner o implemen our cheme, on op of he well-documened emiion hiory of counrie, i µ = dd dz : he marginal impac of curren anhropogenic CO 2 concenraion on he curren flow of climae damage. While obaining hi informaion accuraely may be no mall ak, i eem far le dauning o be working wih oberved daa han wih predicion over fuure decade or cenurie. Indeed, he informaion required o implemen an effi cien carbon ax, τ, or he equivalen cap-and-rade program i he expeced, dicouned um of he marginal impac of curren emiion on fuure climae damage: τ = E β Z i D X i Z ] = E (γβ) D Z From a policy andpoin, implemening our carbon deb policy i impler han implemening a cap-and-rade program. Under our cheme, carbon deb i iued and allocaed yemaically baed on each counry oberved emiion. 7 We hall work under hi aumpion hroughou. I follow ha we hall ignore raegic iue aociaed wih he relaive ize of counrie a dicued in he nex ecion. ]. (2) 4

7 By conra, cap-and-rade cheme require a planner o iue and allocae permi wih he obviou rik of micalculaion and miallocaion, repecively. The upho of requiring le of he planner i ha much more freedom i lef o he counrie, hu allowing for more decenralizaion han, ay, a harmonized carbon ax policy or a global cap-and-rade program. 8 Specifically, counrie make heir own predicion abou fuure damage and work wih heir own dicoun facor. However, here i a limi o decenralizaion: making firm liable would increae defaul rik and lead o kewed incenive. By conra, aigning liabiliie a he counry level enure olvabiliy and correc incenive becaue naion are long-lived. In addiion, hi give counrie overeigny on how o finance heir carbon damage. Secion 3 addree how rade can mainain effi ciency in he cae where counrie have differen dicoun facor and differen expecaion abou fuure anhropogenic climae damage. 3 Robune If deb can be raded, our approach i robu o heerogeneiy in dicoun facor and o diverging foreca. If dicoun facor and foreca are counry-pecific Expreion (2) become: B i X i ] = E i (γβ i ) µ where β i and E i are he dicoun facor and he expecaion of counry i, repecively. Counry heerogeneiy yield rade opporuniie: a marke for deb leave i o counrie o deermine how much deb hey wih o hold baed on heir predicion of fuure climae change damage. Should opinion differ on he likelihood and magniude of fuure damage, or on he dicoun rae, effi ciency i mainained hrough rade a we now how. Specifically, given a compeiive marke price, p, counrie may chooe o buy carbon deb and be paid o do o or o ell hem, by paying oher o 8 Seing a number of permi i anamoun o chooing a dicoun facor and o adoping a pecific predicion of fuure climae damage. Thu, from hi perpecive, a global capand-rade program i acually cloer o cenralizaion han o decenralizaion (even hough effi ciency call again he fragmenaion of permi marke). 5

8 hold deb in heir ead. Propoiion 2 Conider a carbon liabiliie cheme where inallmen are e o curren marginal climae damage: µ = D Z. Allowing carbon deb o be raded mainain effi ciency while decenralizing preference and belief. Proof. We how ha effi ciency i robu o heerogeneiy in counrie dicoun facor. The proof auming counrie formulae differen expecaion abou fuure damage, E i, proceed imilarly. Suppoe counrie have heerogeneou dicoun facor. Aume counry j ell Y j uni of he deb aociaed o i curren emion, X j + Y j. I expeced ne preen benefi wrie a follow: B j = + =0 β je 0 B j ( X j + Y j ) ( )]] p Y j µ Z j + c j p Z j, where c j i he co of holding financial deb for counry j a dae and Z j = γz j 1 + Xj i he amoun of carbon deb held by counry j a dae. The ole purpoe of inroducing a co of holding financial deb i o enure an inerior oluion. We inerpre i a counry defaul rik and herefore aume i o be negligible for uual level of deb. We aume c j o be increaing, ricly convex, and uch ha c j (0) = 0. Similarly, aume counry i purchae Y i uni of deb, a meaured in carbon ock uni. I expeced ne preen benefi wrie a follow: B i = + =0 β ie 0 B i ( X i ) + p Y i µ Z i + c i ( p Z i )]], where he carbon ock for which counry i i conidered o be reponible now wrie: Z i = γz i 1 + X i + Y i From he poin of view of a ne eller of carbon deb, he fir-order condiion 6

9 wrie a follow: B j X j B j Y j = E = E = p β Z j j X j µ + p c j ( p Z i )] ] ( ) D γβj + p c j ( p Z j ) ]] Z From he poin of view of a ne buyer of carbon deb, he fir-order condiion are he following: B i X i I follow ha, for all i: and for all j yielding effi ciency. + = E β Z i i µ X i + p c i ( p Z i )] ] + = E (γβ i ) D + p c i ( p Z i ) ]] Z + p = E β Z i i µ Y i + p c i ( p Z i )] ] + = E (γβ i ) D + p c i ( p Z i ) ]] Z B i X i p = Bj Y j = p, = Bj X j, Propoiion 2 can be een a an analog of he Fir Welfare Theorem, whereby allowing carbon deb o be raded yield allocaive effi ciency hrough decenralizaion. 9 Furhemore, anoher conequence of Propoiion 2 i ha our cheme allow for diverging opinion regarding climae change. I i alo noeworhy ha our mechanim i robu in he ene of being immune o raegic ma- 9 I would be inereing o explore wheher an equivalen of he Second Welfare Theorem hold. For an aemp o conjugae allocaive effi ciency wih he rediribuive apec of global warming, ee Billee de Villemeur and Leroux (2011). 7

10 nipulaion boh in he dicoun facor and in he expecaion becaue he final allocaion of deb i a compeiive marke oucome. To um up, he inroducion of a marke for carbon deb make our mechanim robu o mirepreenaion and o mireporing. Morever: Remark 3 Becaue our cheme financialize he carbon deb, failure o honor he laer i now no differen han a defaul in he repaymen of financial deb. If counrie ake par in hi cheme, hey are unlikely o renege on heir paricipaion. Naurally, here i he queion of wheher counrie will paricipae in he fir place, leading o he general heme of coaliion formaion in inernaional environmenal agreemen. Becaue he expeced ne dicouned payoff of counrie are idenical under our approach a wih an opimal carbon ax, we do no expec o obain in our eing markedly differen concluion from hoe of ha lieraure. Of coure, hoe very imporan queion deerve o be addreed more carefully, which we leave o fuure work. 4 Liabiliy Alhough here i ome evidence ha climae change already ha an impac on economic oucome, climae damage remain highly uncerain and volaile. I follow ha ex ane approache o climae policy exhibi he unappealing feaure of poibly requiring high paymen when realized damage i low. A liabiliy approach avoid hi diconnecedne by linking paymen o realized harm. 10 The key feaure of our mechanim i ha he propec of being liable for fuure damage creae incenive o reduce emiion oday. I i a general principle of juice ha no pary can be liable in he abence of "conrucive noice". 11 In oher word, a counry hould no be aked o pay for he climae conequence of emiion made before he dicovery of he impac of greenhoue gae on he climae. A already menioned, however, our mechanim doe no require racing back emiion o infiniy, bu can accoun for anhropogenic 10 In or law, one apec of he debae beween he regulaory and he liabiliy approache we did no ye menion i he fac ha paymen reflec realized harm in he laer wherea hey are baed on he poibiliy of harm in he former. On hi, ee Shavell (1984, 2011) and Kolad e al (1990). 11 We hank Shi-Ling Hu for bringing hi iue o our aenion. 8

11 emiion aring a ome agreed-upon reference dae only. I hu doe no violae hi baic legal principle. 12 Becaue i require a conenu only on he principle and on a aring dae, one can expec an agreemen o be more eaily reached wih a liabiliy approach han wih axaion. Indeed, he laer require a conenu on he magniude of ye unrealized climae even far off in he fuure, a much more ambiiou goal. We now urn o a formal preenaion of our liabiliy cheme. Aume ha paymen are adjued according o realized damage, D (Z ). More preciely, aume ha counrie are acually required o pay µ Z i I D, where I D = D (Z ) E D (Z )] i he raio of he realized over he expeced damage. 13 Propoiion 4 The liabiliy rule µ Z i I D i fir-be effi cien, robu and yield paymen proporional o realized climae damage. Proof. By definiion, E I D ] = 1 for all, o ha expeced paymen are unchanged. Hence, from Propoiion 1, he liabiliy rule i fir-be effi cien. For he ame reaon, from Propoiion 2, i i robu o mirepreenaion and deviaion. Furhermore, µ ZI i D i indeed proporional o realized harm: µ ZI i D = dd Z i D (Z ) dz E D (Z )] = Zi Z (dd /dz ) E D (Z ) /Z ] D (Z ). If he damage funcion, D, were linear, paymen would exacly cover oal damage and counrie would pay in proporion o heir emiion conribuion: µ Z i I D = Zi Z D (Z ). If he damage funcion i convex, oal paymen add up o more han he realized damage becaue fir-be effi ciency require going beyond full liabiliy Obviouly, for incenive o exi, "acual noice" i alo needed; i.e., counrie mu no only be aware of he fac ha hey are cauing harm (conrucive noice), bu mu alo be informed ha hey will be conidered liable for fuure climae damage. 13 Expecaion i aumed o be aken a he beginning of he period. 14 The incompaibiliy beween fir-be effi ciency and budge balance i well-known. See, e.g., Billee de Villemeur and Leroux (2011). 9

12 Remark 5 Full liabiliy coniue a conervaive policy where paymen rely only on realized damage, and no even on ome eimae of he marginal damage funcion. In Europe and in he U.S., he field of environmenal damage eimaion i already well developed. Reference 1] Calabrei, G., The Co of Acciden: A Legal and Economic Analyi, New Haven, CN.: Yale Univeriy Pre, ] Billee de Villemeur, E. and J. Leroux (2011) Sharing he Co of Global Warming, The Scandinavian Journal of Economic, 113(4), ] Hammond, Peer J., (1981) Ex-Ane and Ex-Po Welfare Opimaliy under Uncerainy, Economica, 48 (n.191), ] Kolad, C. D., T.S. Ulen and G.V. Johnon (1990), "Ex Po Liabiliy for Harm,v. Ex Ane Safey Regulaion: Subiue of Complemen?", American Economic Review, 80(4), ] Shavell, S. (1984) "Liabiliy for Harm Veru Regulaion of Safey", Journal of Legal Sudie, June 1984, 13, ] Shavell, Seven, (2011), Correcive axaion veru liabiliy, American Economic Review, Paper and Proceeding, 101(3),