Journal of Appled Economcs. Vol IX, No. 1 (May 2006), 19-47 PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 19 PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS JUAN-CARLOS ALTAMIRANO-CABRERA Wagenngen Unversty MICHAEL FINUS * Unversty of Hagen and Natonal Unversty of Sngapore Submtted June 2004; accepted May 2005 We analyze the mplcaton of dfferent allocaton schemes of CO 2 -emsson permts for stablty and the success of nternatonal clmate agreements. Our model combnes a game theoretcal wth an emprcal module that comprses 12 world regons and captures mportant dynamc aspects of the clmate change problem. We consder seven dfferent permt allocaton schemes. Two pragmatc schemes allocate permts accordng to a unform emsson reducton quota, fve equtable schemes allocate permts based on some normatve crtera frequently dscussed n the lterature permt tradng can rase partcpaton and the success of clmate agreements, but pragmatc schemes are superor to equtable ones. JEL classfcaton codes: C72, Q25, Q28 Key words: clmate agreements, tradable emsson permts, coalton formaton, self-enforcng agreements I. Introducton Emsson permts have been proposed as an effcent nstrument to tackle both natonal and nternatonal envronmental problems. Recently, ths market-based * Mchael Fnus (correspondng author): Insttute of Economc Theory, Department of Economcs, Unversty of Hagen, Proflstr. 8, 58084 Hagen, Germany, mchael.fnus@fernunhagen.de. Juan-Carlos Altamrano-Cabrera: Envronmental Economcs and Natural Resources Group, Wagenngen Unversty, Department of Socal Scences, Hollandseweg 1, 6706 KN Wagenngen, The Netherlands, juan-carlos.altamrano-cabrera@wur.nl. The authors would lke to thank two anonymous referees and the co-edtor Marana Conte Grand for ther comments that substantally mproved the qualty of ths paper. They would lke to acknowledge that these comments nfluenced n partcular sectons IV and V. The paper has also benefted from dscussons wth Alfred Endres and Ekko van Ierland. Needless to say, the authors assume responsblty for all remanng errors.
20 JOURNAL OF APPLIED ECONOMICS nstrument has ganed ncreasng attenton n the context of the Kyoto Protocol, amng at controllng global warmng. Snce greenhouse gas emsson affects all countres, t can be expected that a suffcent hgh partcpaton n permt tradng wll guarantee a well-functonng market. However, there has been much debate about the dstrbutonal effects of dfferent permt allocaton schemes. Rose et al. (1998) took a promnent lead n ths dscusson, classfyng dfferent allocaton schemes, clarfyng ther motvaton and analyzng ther mpact on dfferent countres. The dscusson ntated many other papers (e.g., Kverndokk 1995 and Böhrnger et al. 2002) dealng wth varous notons of far allocatons of permts. It s recognzed that not only effcency but also farness aspects may play an mportant role for the partcpaton and success of a global warmng treaty. However, ths lterature only studes the mpact of dfferent allocaton schemes on net abatement costs of ndvdual partcpants (abatement costs plus/mnus the outlay/recept from permt tradng). Hence, not much can be concluded about whether and whch countres have an ncentve to jon an nternatonal envronmental agreement (IEA) and whether such a treaty wll be self-enforcng. In order to analyze partcpaton and stablty, two more steps are necessary. Frst, not only abatement costs but also benefts from jont abatement polces have to be taken n consderaton. Only ths gves a complete pcture of the basc ncentves to partcpate n an agreement. That s, we can test whether cooperaton s not only globally but also ndvdually ratonal. We call a treaty ndvdually ratonal f each partcpant receves a net beneft exceedng that n the noncooperatve status quo. As shown for nstance n Eyckmans et al. (1994) and German and van Steenberghe (2003), not all permt allocaton schemes that are deemed to be far guarantee ndvdual ratonalty to all partcpants. For nstance, a permt allocaton based on per capta may appear to be far ( one-man-one vote ), but leads to very large transfers from ndustralzed to developng countres that may volate the nterests of donors. Second, even though ndvdual ratonalty may be seen as a necessary condton for cooperaton, t s by no means a suffcent condton. Snce abatement consttutes a publc good, countres may be better off not partcpatng n an ndvdually ratonal IEA, savng abatement costs and beneftng from the efforts of sgnatores. Consequently, n vew of the fact that there s no supranatonal nsttuton that can enforce a global treaty, IEAs must also be self-enforcng. We check ths wth the concept of nternal and external stablty whch has been wdely appled n the game theoretcal lterature on IEAs (e.g., Barrett 1994 and Carraro and Snscalco 1993). 1 Dfferent from ths lterature, however, we combne our game theoretcal 1 For an overvew of ths lterature see Fnus (2003).
PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 21 analyss wth an emprcal model that captures twelve world regons. That s, we nether model heterogenety n a stylzed way as for nstance n Fnus and Rundshagen (1998) and Hoel (1992), nor do we consder stylzed transfer rules as for nstance n Botteon and Carraro (1997) and Eyckmans and Tulkens (2003). The objectve of ths paper s to test whether stable coaltons exst under varous permt allocaton schemes and f ths s the case whether they mprove upon the non-cooperatve outcome. We consder two pragmatc scenaros that allocate permts accordng to a unform emsson reducton quota and fve equty scenaros that allocate permts based on some normatve crtera frequently dscussed n the lterature. Dfferent from Bosello, Buchner and Carraro (2003), Eyckmans and Fnus (2003) and Wekard, Fnus and Altamrano-Cabrera (2004) that test stablty of outcome-based allocaton rules, we consder allocaton basedrules. 2 It turns out that permt tradng can mprove upon the success of selfenforcng clmate agreements but pragmatc are superor to equty schemes. Thus, moral motves may not always be a good gude for the desgn of effectve and selfenforcng treates. In the followng, we ntroduce the game theoretcal and emprcal module n Secton II. We motvate our permt tradng schemes and dscuss some fundamental features n Secton III and report about results of our stablty analyss n Secton IV. Secton V wraps up wth a summary and draws some conclusons. II. The model A. Game theoretcal module Coalton formaton s modeled as a two-stage game. In the frst stage, countres or regons ( I={1,...,N}) decde on ther membershp strategy; n the second stage, they choose ther abatement strateges. In the frst stage, we assume that countres have two membershp strateges: strategy σ = 0 means I do not want to jon the agreement and σ = 1 means I want to become a member of a clmate treaty. Countres that announce σ = 0 form a sngleton coalton and those that announce 2 Ths categorzaton s due to Rose et al. (1998). Permts may be allocated based on some crtera amng at nfluencng the ntal allocaton (allocaton-based), the fnal allocaton after trade has taken place (outcome-based) or mportant factors assocated wth tradng (processbased). Snce governments and ther representatves usually bargan on the allocaton of permts (though they may determne ther barganng poston by conjecturng the outcome or some varables assocated wth the process of tradng), we beleve that allocaton-based rules should receve suffcent attenton n the analyss.
22 JOURNAL OF APPLIED ECONOMICS σ = 1 become members of a non-trval coalton (.e., a coalton of at least two members). Hence, a vector of announcements σ = (σ 1, σ 2,, σ N ), σ Σ, leads to coalton structure c = (s, 1,..., 1), c C, wth s ether a non-trval coalton f at least two countres have announced σ = 1 or s = {} f ether all countres have announced σ = 0 or only one country has announced σ = 1. Hence, there exst 4096 dfferent membershp vectors but only 4084 dfferent coalton structures n the context of twelve players (regons). 3 If s = {}, ths s called the sngleton coalton structure and f s = I, ths s called the grand coalton structure. In the second stage, countres choose ther abatement strateges q based on the followng payoff functon: N π = B( q) C(q), = 1 (1) assumng a concave beneft functon from global abatement, B, and a convex abatement cost functon from ndvdual abatement, C. For a gven coalton structure c, we assume that non-sgnatores (σ = 0) pursue ther self-nterests, maxmzng π wth respect to q, takng the abatement level of all other countres as gven. Assumng an nteror equlbrum, ths leads to the followng frst-order condton: N = 1 B ( q) = C (q) s, (2) where prmes denote dervatves. In contrast, sgnatores (σ = 1) are assumed to maxmze the aggregate welfare of ther coalton. Ths leads to the followng frst order condtons: B ( q) C (q) N = s = 1 s. (3) The smultaneous soluton of the frst order condtons of non-sgnatores and sgnatores leads to abatement vector q * (c). Ths abatement vector can be nterpreted as a partal Nash equlbrum between coalton s and the sngleton players (Chander * * and Tulkens 1997). Hence, n equlbrum, C(q) = C(q) j j for all and j that belong to s. That s, the abatement vector of the coalton s effcent for the coalton. Of course, ths does not extend to outsders. Consequently, the grand coalton 3 Ths should not be confused as meanng that the mappng of membershp strateges nto coalton structures would not be unque.
PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 23 structure (s = I), representng full cooperaton, chooses a globally optmal abatement vector and the sngleton coalton structure (s={}), representng no cooperaton, corresponds to the classcal Nash equlbrum. Any other coalton structure may be seen as partal cooperaton. If q * (c) s unque for all c C, then the payoff vector π(q * (c)) wth π (q * (c)) N * * = B ( q 1 (c)) C (q (c)) s unque n the second stage. In secton II.C, we wll = argue that ths s ndeed the case and that q * (c) les n the nteror of the abatement space. At ths stage, t suffces to notce that π(q * (c)) represents the case wthout permt tradng. In the case of permt tradng, payoffs have to be modfed. For smplcty, we assume that permts are only traded among cooperatng countres,.e., among coalton members (see secton V for a dscusson of ths assumpton). Hence, a coalton member s payoff can be wrtten as * * * π % (q (c),q (t)) =π(q (c)) p (q (t) q (c)), (4) where p s the permt prce and q(t)s the assgned abatement resultng from some allocaton under a partcular permt tradng system t T. The second term on the * rght hand sde of equaton (4) s postve f a country s a permt seller ( q(t) < q(c) ) * and negatve f a country s a permt buyer ( q(t) > q(c) ). The prce of permts s equal to margnal abatement costs n equlbrum and follows mmedately from the frst order condtons of sgnatores n (3). Thus, the fnal payoff π% n (4) can be nterpreted as the payoff from cooperaton wthout transfers, π, plus or mnus a transfer that depends on the allocaton of abatement, q(t). In secton IV, we wll dscuss varous permt schemes that determne q(t). At ths stage, t suffces to notce that because π(q * * (c)) s unque also π% (q (c),q (t)) s unque for each coalton structure c C and any permt scheme t T. Taken together, payoffs to country depend on the coalton structure c C determned n the frst stage of the game and on abatement strateges q Q and the permt tradng systems t T chosen n the second stage of the game, π (c, q, t). Snce abatement q follows from the assumpton of jont welfare maxmzaton of coalton members and the allocaton of permts follows from the assumpton about a partcular permt tradng system, we can thus defne stablty of coalton structure c as follows: Stable Coalton Structures. Coalton structure c C resultng from * announcement σ Σ s called stable f for all I, σ σ : * * * π( σ, σ ) π( σ, σ ) assumng some permt tradng scheme t T and that q Q follows from the assumpton of jont welfare maxmzaton of coalton members.
24 JOURNAL OF APPLIED ECONOMICS Obvously, our defnton mples that a coalton structure s called stable f membershp strateges consttute a Nash equlbrum. Ths defnton s smlar to the concept of nternal and external stablty: n equlbrum, no sgnatory has an * ncentve to leave the coalton by changng ts announcement from σ = 1 to σ = 0 (nternal stablty) and no non-sgnatory has an ncentve to jon the coalton * by announcng σ = 1 nstead of σ = 0(external stablty). The advantage of our defnton s that exstence of an equlbrum s guaranteed. The reason s that the sngleton coalton structure can always be supported as a Nash equlbrum: suppose all countres announce σ = 0, then no sngle country can change ths coalton structure by unlaterally changng ts membershp strategy. The advantage of the other defnton s that t allows separatng stablty nto two dmensons. Hence, when dscussng stablty n the followng, we dstngush between nternal and external stablty. It s evdent that the defnton of stable coalton structures mples voluntary partcpaton snce sgnatores can leave ther coalton f they fnd t more attractve to free-rde and non-sgnatores can jon the agreement f ths pays. B. Emprcal module In ths secton, we explan our emprcal module - called STACO-model. Snce the model has been lad out n much detal n Fnus, Altamrano-Cabrera and van Ierland (2004), we brefly descrbe here only ts man features. The man dea of STACO s to calbrate the followng payoff functon: T t t t t t t= 1 π (q) = (1 + r ) (B (q ) C (q )), (5) where the phlosophy behnd the model comprses three tems. Frst, the model should reflect mportant dynamcs of clmate models. Therefore, STACO consders a perod of 100 years, startng n 2010 and bases ts calbraton on the wdely known DICE-model of Nordhaus (1994) for the development of global emssons and concentraton. Second, n order to make the model nterestng for a game theoretcal analyss, there should be a suffcent number of dfferent players. Therefore, STACO uses abatement cost estmates of Ellerman and Decaux (1998) for twelve world regons. For global benefts and regonal benefts from abatement (n the form of reduced damages), STACO uses estmates of Fankhauser (1995) and Tol (1997). Thrd, the model must be smple enough to be tractable for a game theoretcal analyss. Therefore, STACO assumes statonary abatement strateges, fts the parameters to ths specfcaton, leadng to the followng dscounted payoff functon:
PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 25 N 1 3 1 2 π (q) =γµ Bδb q δ 1 c 3 α q + 2 β q =, (6) 100 where q s the total abatement over 100 years, q = q t= 1 t. The global beneft parameter s µ B, the regonal beneft parameter s γ, representng the shares of the N dfferent world regons n global benefts, 0 γ 1, γ =1 = 1 and α and β are regonal abatement cost parameters. The parameters δ b and δ c capture dscountng n STACO; n the case of δ b t further ncludes the decay of greenhouse gases. In our standard case we assume a dscount rate of 2 percent. 4 Note that µ B δ b represents global margnal benefts. It turns out that µ B δ b =37.4 US$ per ton of carbon, a fgure that s much n lne wth other studes (e.g., Plambeck and Hope 1996). The regonal parameters reflect dfferences of twelve world regons: USA, Japan (JPN), European Unon (EU-15), other OECD countres (O-OECD), Eastern European countres (EE), former Sovet Unon (FSU), energy exportng countres (EEX), Chna, Inda, dynamc Asan economes (DAE), Brazl and rest of the world (ROW). We use the abbrevatons n brackets n the followng. 5 The parameters are lsted n the Appendx n Table A.1 and ther mplcatons are vsualzed n Fgure 1 and 2 below. Fgure 1 lsts regons n descendng order of regonal beneft shares. It s evdent that the large ndustralzed regons are the man benefcares of global abatement whereas EEX, DAE and Brazl receve the smallest share of global benefts. From Fgure 2, t s evdent that margnal abatement costs never ntersect. Moreover, margnal abatement costs vary wdely: Chna and USA have the flattest curves whereas Brazl as well as Japan have the steepest. Roughly speakng, those regons wth low ntal emssons (e.g., Brazl and Japan) face steep margnal abatement cost curves (see Table A.1 n the Appendx) snce cheap abatement optons have already been exploted and substtuton to more effectve abatement technologes s expensve. For regons wth hgh ntal emssons (e.g., Chna and USA) just the opposte holds. 4 For a dscount rate of 2 percent, δ b =1385 and δ c =43.1 n STACO. The parameter µ B represents damages n terms of a loss of GDP for a doublng of greenhouse gas concentraton, expressed n percentages. We take µ B = 0.027 (meanng a 2.7 percent loss) from Tol (1997). In secton 4, these assumptons wll be subject to a comprehensve senstvty analyss. 5 EU-15 comprses the 15 countres of the European Unon as of 1995. O-OECD ncludes among other countres Canada, Australa and New Zealand. EE ncludes for nstance Hungary, Poland, and Czech Republc. EEX ncludes for example the Mddle East Countres, Mexco, Venezuela and Indonesa. DAE comprses South Korea, Phlppnes, Thaland and Sngapore. ROW ncludes for nstance South Afrca, Morocco and many countres n Latn Amerca and Asa.
Fgure 1. Regonal benefts from global abatement 26 25 20 % of global benefts 15 10 JOURNAL OF APPLIED ECONOMICS 5 0 EU-15 USA Japan FSU ROW Chna Inda O-OECD EEX DAE Brazl EE
Fgure 2. Margnal abatement cost functons m argnal abatem ent costs (US dollar 3000 2500 2000 1500 1000 500 0 B r a z l M ax. 13 G ton at 4564 $/ton Japan EEX EU-15 O -O O E U S A FSU EE D A E R O W Inda C h n a 0 20 40 60 80 100 120 140 160 180 200 220 240 abatem ent (ggatons carbon doxde) PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 27
28 JOURNAL OF APPLIED ECONOMICS C. General features of the model In ths secton, we dscuss some general features of our model, relatng to the game theoretcal and the emprcal module. Frst, n secton II.A, we ponted out that a unque abatement vector for each coalton c C guarantees a unque payoff vector. Consderng the emprcal specfcaton of the payoff functon (see equaton (6)), t s evdent that regons have a domnant strategy because the frst order condtons of 2 sgnatores are µδ B b γ=δ c( α s q +β q ) and those of non-sgnatores 2 are µδγ=δ B b c( α q +β q ). Thus, unqueness s evdent. An nteror soluton follows from two peces of nformaton. a) C(q) s an ncreasng functon, C(q = 0) = 0and B =µ s = Bδb γ s B =µ Bδbγ > 0,hence q * > 0 I and for any coalton structure. Notce that ths mples that even n the sngleton coalton structure, correspondng to the classcal Nash equlbrum, some abatement s undertaken compared to the busness-as-usual scenaro, and hence BAU Nash BAU e > e I, where e s defned as emsson level n the busness-asusual scenaro and e as emsson level n the Nash equlbrum. b) Generally, we Nash max can choose a suffcent hgh upper bound q to guarantee an nteror soluton. However, n our model abatement means to reduce emssons from the busnessas-usual emsson level, e BAU max BAU. Hence, t seems sensble to requre q e. Snce 2 * t follows from µδ B b γ=δ s c( α q +β q ) that q takes on the largest value f s=i (correspondng to the classcal global optmum), we only have to check * BAU whether q(s = I) e holds for all I. In our model, t turns out that ths s ndeed the case. Second, n our model, superaddtvty holds. That s, whenever a country j jons coalton s, so that coalton structure changes from c to c%, aggregate welfare of countres s {j} ncreases, π (c, t) (c) (c, t) s +π j < π % s {j}. The reason s smple. Frst, the aggregate payoff to coalton s and s {j} s not affected by the knd of permt tradng scheme: permt tradng only affects ndvdual payoffs of coalton members through transfers but transfers add up to zero. (Recall that nonsgnatores are not nvolved n tradng.) Second, outsders I\{s {j}} have a domnant strategy. Hence, they wll not change ther abatement level n c% compared to c. Hence, f we let q s, q s {j} and q j denote the abatement vector of sgnatores before and after country j joned coalton s and abatement of country j, respectvely, then max s π+ max π< max s j s {j} q π must hold. q s {j} j q Thrd, n our model, cooperaton generates postve externaltes. That s, whenever a country j jons coalton s, so that coalton structure c changes to c%, outsders k s {j} gan π k(c) <π k(c) %. From the frst order condtons of
PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 29 sgnatores, t s evdent that abatement of each member ncreases because the sum of margnal benefts ncreases from µδ B B γ s to µδ B B γ s {j}. Hence, global abatement ncreases, outsders benefts ncrease from c to c% but ther abatement costs reman the same. Fourth, superaddtvty together wth postve externaltes mply that global welfare s rased f partcpaton s gradually ncreased. Nevertheless, membershp matters. That s, global welfare may well be dfferent n two coaltons s 1 and s 2 that are of the same sze but comprse dfferent members. Ffth, n the Introducton we mentoned that an agreement must be ndvdually ratonal and self-enforcng to be stable. Evdently, we check the self-enforcng part through Defnton 1 of stable coalton structures. Less evdent s that ths automatcally mples to check also for ndvdual ratonalty. The reason s that nternal stablty mples ndvdual ratonalty (but not vce versa). Suppose coalton s s not ndvdually ratonal for member, then member can leave the agreement and because of the postve externalty property (see tem 3 above), he wll be (strctly) better off than n the sngleton coalton structure (provde s\{} comprses at least two members). Sxth, generally, the advantage of partcpatng n a coalton s that ths ncreases global abatement. Moreover, own abatement efforts are matched by others. Ths ncreases benefts from global abatement but also ncreases abatement costs. The relatve sze of both effects determnes whether t pays to jon a coalton. As a tendency, the hgher partcpaton n an agreement, the less attractve t becomes to jon a coalton and the more attractve t becomes to leave a coalton due to the strct concavty of the payoff functon. Therefore, stable coaltons are usually only small. Seventh, partcpaton n a stable agreement wll also depend on membershp and on the permt tradng system. Snce countres have dfferent beneft and cost functons, jont welfare maxmzaton may mply a very asymmetrc dstrbuton of the gans from cooperaton. For nstance, a coalton member, say, wth a flat margnal abatement cost functon wll have to contrbute more to abatement than a member, say j, wth a steep margnal abatement cost functon. If has also lower margnal benefts than j, then may well be worse off from cooperaton or at least receves a low payoff. Consequently, t may pay country to free-rde. Ths may be dfferent f country receves a transfer from country j whch may be accomplshed va a permt tradng system that allocates a suffcent amount of permts to country. In our model, a regon s for nstance EE, DAE, Chna and Inda and a regon j for nstance EU-15 and Japan.
30 JOURNAL OF APPLIED ECONOMICS III. Fundamentals about permt tradng A. Motvaton of permt schemes In secton II.A, we observed that payoffs n a coalton structure c are affected N * by the global abatement level q(c) = 1 and the ndvdual abatement level * N * * q(c), π = B( q(c)) 1 C(q(c)) =. Ths holds for non-sgnatores. For sgnatores, payoffs also depend on the assgned abatement level q(t)that follows from the allocaton of permts under some permt scheme t, * π % =π p(q(t) q(c)). Notng that emsson permts of regon, e, mean to allocate a fracton 0 λ 1of the total amount of permts e s, to each member, e =λ e s, λ =1 s, and recallng that abatement s defned as BAU * * BAU * q = e e n our model, e s = e s wth e s = e s q s, then the allocaton of abatement can be expressed as follows: BAU BAU * q(t). (7) = e λ e q(c) s s Thus, dfferent permt schemes t T can be related to dfferent weghts λ. In the lterature, several schemes have been proposed of whch we consder seven n ths paper. We only brefly comment on these schemes and refer the reader to a more extensve dscusson of ther motvaton to Cazorla and Toman (2000) and Rose et al. (1998). The frst two schemes are called pragmatc schemes, the next fve are called equtable schemes. The names that we attach to each scheme are shown n the frst row and the mathematcal specfcatons of weghts are dsplayed n the second row n Table 1. For the grand coalton, weghts (expressed as percentage) are dsplayed for each regon n the subsequent rows. Ths gves a frst dea of the relatve mpact of dfferent schemes n terms of weghts, though t has to be ponted out that weghts are dfferent n other coalton structures. The base data for computatons of weghts s provded n the Appendx, Table A.2. Pragmatc schemes Our pragmatc schemes belong to so-called soveregnty rules because they do not much nterfere wth the status quo. Both schemes assume that all members receve emsson permts that represent the same percentage from some base emsson level. Ths mples to allocate unform emsson reducton quotas to each member. Such a scheme has been appled n the Helsnk Protocol on Sulfur Reducton n Europe and n many other IEAs. However, dfferent from these treates,
Table 1. Permt schemes and shares n the grand coalton Regons Pragmatc schemes Equtable schemes Quota Quota Egaltaran Hstorcal Ablty Ablty Energy BAU Nash responsblty to pay to pollute effcency (1) (2) (3) (4) (5) (6) (7) BAU Nash BAU 1 1 BAU 1 BAU 1 e e Pop ( e ) ( GDP Pop ) ( e Pop) ( e GDP) BAU Nash 1 e e Pop BAU 1 BAU 1 BAU ( e ) ( GDP Pop) ( e Pop) ( e GDP) s s s USA 20.2 19.8 4.8 1.9 0.5 1.6 9.8 Japan 4.7 4.8 1.9 8.2 0.3 2.8 26.8 EU-15 11.7 11.7 5.8 3.3 0.6 3.4 18.4 O-OECD 5.2 5.3 2.2 7.4 1.1 2.9 8.2 EE 4.3 4.5 1.9 9.0 4.4 3.0 2.1 FSU 8.4 8.3 4.5 4.6 8.2 3.6 1.3 EEX 10.2 10.6 24.9 3.7 14.8 16.7 3.6 Chna 19.7 19.4 20.9 1.9 18.5 7.2 1.2 Inda 5.3 5.4 17.8 7.3 37.0 23.1 2.0 DAE 3.4 3.5 3.2 11.1 3.2 6.4 6.4 Brazl 1.1 1.1 3.0 35.2 3.6 18.6 16.0 ROW 5.9 5.8 9.1 6.5 7.8 10.6 4.3 Total 100 100 100 100 100 100 100 BAU Notes: All fgures are expressed as a percentage. e = emssons n the BAU scenaro for country ; e country ; Pop = level of populaton n country ; GDP = level of GDP n country. s s Nash s = emssons n the Nash equlbrum for s 1 PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 31
32 JOURNAL OF APPLIED ECONOMICS n our model such quotas can be traded as ntended under the Kyoto Protocol. Quota BAU (scheme 1) assumes base emssons n the busness-as-usual BAU scenaro, e ; Quota Nash (scheme 2) assumes base emssons n the classcal Nash Nash equlbrum, e, correspondng to those n the sngleton coalton structure. Both emsson levels may be nterpreted as the status quo before an agreement s sgned. The alternatve assumptons allow us to check whether our results are senstve to the choce of the base-lne emsson level. From Table 1, we observe that weghts between scenaro 1 and 2 dffer only slghtly. Ths s because the Nash equlbrum mples only a mnor emsson reducton from BAU-emssons (see Table A.2 n the Appendx). Snce base lne emssons are strongly concentrated n USA and Chna, those regons receve the hghest weghts. We now turn to our equtable schemes. Equtable schemes Egaltaran (scheme 3) allocates emsson permts on a per capta bass. Ths rule acknowledges that all men should have the same rght to emt: one man one vote. Evdently, energy exportng countres (EEX), Chna and Inda, receve the hghest shares n the grand coalton snce a large porton of total populaton lves n these regons. Hstorcal responsblty (scheme 4) allocates permts nversely to BAUemssons because those countres that have contrbuted to current greenhouse gas concentraton should contrbute more to mtgate ths problem. Thus, weghts under ths scheme are the mrror mage of Quota BAU, and therefore Brazl and dynamc Asan economes (DAE) receve hgh weghts. Ablty to pay (scheme 5) allocates permts nversely to welfare levels measured as gross domestc product (GDP). Ths rule argues that wealther natons should take on more responsblty n global clmate change control than poorer natons. However, ths rule may also be seen as a vehcle of development ad through envronmental polcy by allocatng more permts to poorer natons. Agan, those regons that receve hgh shares of emsson permts are those mentoned under the Egaltaran scheme and are manly developng countres. The scheme Ablty to pollute (scheme 6) s smlar n sprt to Hstorcal responsblty, except that weghts are not based on emssons but on emssons per capta. It has also some connecton to Egaltaran where weghts are based on populaton. Thus, ths scheme may be defended by argung that every man has the same responsblty for preservng the clmate system. Snce the USA has the hghest emsson per capta rato, they receve the lowest weght. In contrast, due
PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 33 to low current emssons and hgh populaton densty, developng countres receve hgh weghts under ths scheme. Energy effcency (scheme 7) allocates emsson permts nversely to the emsson/gdp rato. It therefore rewards regons wth advanced envronmental technology lke Japan and European Unon (EU-15) but gves low weghts to Chna, Inda and Eastern European countres (EE) that have drty ndustres. B. Illustraton of permt schemes: Some fundamental relatons In ths subsecton, we llustrate some of the mplcatons of the seven dfferent permt tradng schemes n Table 2. As a reference pont, we also dsplay the base case of no permt tradng. Agan, we choose the grand coalton to llustrate some fundamental relatons. For each scenaro, the gans from cooperaton are measured n relaton to the sngleton coalton structure, correspondng to the classcal Nash equlbrum. Snce the payoff to a regon can be nterpreted as ts payoff wthout tradng plus or mnus a transfer (see secton II.A), we also dsplay transfers as mpled by the varous permt schemes. A postve number means to pay a transfer (permt buyer) and a negatve number means to receve a transfer (permt seller). In order to gan some nsghts about the dmenson of tradng, we also dsplay total transfers, that s, the sum of all postve or negatve numbers. Moreover, n order to get an dea about the dstrbuton of the gans from cooperaton, we compute the standard devaton of the gans from cooperaton. From Table 2 the followng observatons are nterestng: Frst, the total gan from cooperaton n the socal optmum s wth 4,071 bllon US$ large gven the fact that the global payoff n the Nash equlbrum s only 1,960 bllon US$. Second, the standard devaton of the gans from cooperaton s generally large. However, there are sgnfcant dfferences: The two pragmatc schemes show the lowest standard devaton and some of the equtable schemes have a very hgh standard devaton, exceedng that wthout permt tradng to a large extent. The large spread of the gans also shows up n large transfers mpled by the varous permt tradng schemes. Obvously, the equty schemes mply a major reshuffle of the gans from cooperaton through permt tradng, but most of them replace the asymmetry wthout tradng through another asymmetry that s even larger. Thrd, nether the base case of no permt tradng nor any of the permt schemes mples that cooperaton s proftable for all partcpants. There are always at least two regons that are worse off than n the Nash equlbrum. For the equty schemes, ndvdual ratonalty s sometmes severely volated for almost half of all regons.
Table 2. Gans and transactons under varous permt schemes: Grand coalton 34 Regons No permt Pragmatc Equtable schemes tradng schemes Hstorcal Ablty Quota BAU Quota Nash Egaltaran responsblty Ablty to pay to pollute Energy ntensty (1) (2) (3) (4) (5) (6) (7) Gans Trans- Gans Trans- Gans Trans- Gans Trans- Gans Trans- Gans Trans- Gans Trans- Gans Trans- Fers fers fers fers fers fers fers fers USA 1,241-721 520 577 664-4,709 5,950-5,716 6,957-6,200 7,441-5,815 7,056-2,941 4,182 Japan 1,236-926 310 976 260-30 1,266 2,160-923 -596 1,832 286 950 8,703-7,467 EU-15 1,569-1,051 518 1,037 531-1,006 2,574-1,917 3,486-2,857 4,426-1,862 3,430 3,370-1,801 O-OECD 133-17 115 45 87-1,029 1,162 767-634 -1,421 1,554-785 918 1,068-936 EE -33 - -68 35-24 -9-936 904 1,487-1,520-63 31-561 528-860 827 FSU 269-189 81 179 90-1,190 1,460-1,165 1,434 196 74-1,483 1,752-2,289 2,559 EEX 38 - -475 513-330 368 4,710-4,672-2,746 2,784 959-922 1,811-1,773-2,786 2,824 Chna -866-820 -1,686 698-1,564 1,233-2,099-5,424 4,558 679-1,545-3,563 2,696-5,696 4,830 Inda 83-378 -295 378-294 4,765-4,682 1,002-919 11,411-11,328 6,499-6,416-826 910 DAE 33-88 -55 116-83 30 3 2,845-2,813-2 35 1,177-1,145 1,150-1,117 Brazl 103-27 76 45 58 691-588 12,141-12,038 921-817 6,283-6,180 5,327-5,223 ROW 265-397 -133 375-110 1,542-1,278 637-372 1,044-780 2,082-1,818-149 414 JOURNAL OF APPLIED ECONOMICS Total 4,071-4,071 2,168 4,071 2,058 4,071 13,319 4,071 19,219 4,071 15,393 4,071 17,330 4,071 16,546 Standard devaton 651-442 - 399-2491 - 4,450-3,886-3,446-3,787 - Note: All fgures are expressed n bllon US$.
PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 35 For the base case, t s not surprsng that ndvdual ratonalty s volated for EE and Chna because ther margnal benefts and abatement costs are far below average levels. Hence, these regons contrbute above average to global polluton control but beneft only below average. Obvously, none of the permt schemes smultaneously repars ths defcency for these two regons, lettng alone the volaton of ndvdual ratonalty of other regons. Fourth, even though we can mmedately conclude that the grand coalton s not a stable coalton structure because ndvdual ratonalty s volated under all schemes, t may nevertheless be possble to form smaller coaltons that are ndvdually ratonal. Nevertheless, also for smaller coaltons stablty may be a problem as wll be apparent from the next secton. IV. Stablty analyss In ths secton, we present results of our stablty analyss. We start wth the standard case n secton IV.A, reflectng the parameter values as reported and dscussed n secton III. In secton IV.B, we report on the results of our senstvty analyss. A. Standard case For each scenaro, we test all 4084 coalton structures for stablty wth an algorthm programmed n Matlab. In the base case wthout permt tradng, t turns out that more than 1000 coalton structures are externally stable but only 14 coalton structures are nternally stable. None of the 13 non-trval coalton structures (.e., ncludng a coalton of at least two members) that are nternally stable are also externally stable and hence no non-trval coalton structure s stable. On the one hand, ths stresses that nternal stablty s the man problem of stablty and therefore we focus n partcular on ths part of stablty n the followng dscusson. On the other hand, ths stresses the strong free-rder ncentves n general, but, n partcular, n the context of heterogeneous regons. Under the scenaro Quota-BAU, ths changes somehow. Now 28 coalton structures are nternally stable of whch two are also externally stable. The frst coalton structure ncludes a coalton between the European Unon (EU-15) and Chna and the second a coalton between Inda and the Rest of the World (ROW). In order to explan the drvng forces of permt tradng, we exemplarly have a closer look at the coalton between EU-15 and Chna n Table 3, though smlar relatons are also true for other stable coaltons.
36 JOURNAL OF APPLIED ECONOMICS Table 3. Coalton between the European Unon and Chna: No permt tradng and permt tradng under the Quota BAU scenaro Regons Total Margnal Payoffs Payoffs Transfers ICM ICM emsson abatement (wthout (wth (wthout (wth reducton costs permt permt permt permt tradng) tradng) tradng) tradng) gton US$/ton bln US$ bln US$ bln US$ bln US$ bln US$ (over over over over over over 100 100 100 100 100 100 years) years years years years years * q q ð ð% USA 16-8.5 683 683-137.8-132.6 Japan 1-6.5 559 559-107.9-25.0 EU-15 8 20 11.1 733 595 137-268.6-131.3 O-OECD 2-1.3 111 111 - -13.5-52.3 EE 1-0.5 42 42 - -19.4-40.8 FSU 5-2.5 215 215 - -13.7-64.2 EEX 1-1.1 97 97 - -21.3-139.2 Chna 46 34 11.1-6 131-137 118.0-19.3 Inda 3-1.9 160 160 - -30.2-11.2 DAE 1-0.9 81 81 - -18.1-33.5 Brazl 0-0.6 50 50 - -0.4-18.7 ROW 4-2.5 217 217 - -14.3-24.1 World 87 - - 2,942 2,942 - - - * * * Note: ICM means ncentve to change membershp measured as π( σ, σ ) π( σ, σ ). See secton II.A. From Table 3, t s evdent that wthout permt tradng the coalton between the EU-15 and Chna (ndcated n talcs n the frst column) s not nternally stable because Chna would gan by leavng ths coalton (ndcated n the second last column). Clearly, wthout transfers, EU-15 s the man benefcary n ths coalton at the expenses of Chna. Because Chna s a cheap provder of abatement, also USA and Japan have an ncentve to jon ths coalton (ndcated n the second last column) and therefore ths coalton would also not be externally stable. Wth permt tradng, the stuaton changes. Under the Quota BAU scenaro,
PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 37 Chna receves a suffcent amount of emsson permts ( q s low; see equaton 7) that can be sold to EU-15. Thus, Chna receves a large transfer of 137 bllon US$ as ndcated n the column Transfers. Thus, whereas before there was a slack of enforcement power on the sde of EU-15 and lack on the sde of Chna wthout permt tradng, ths asymmetry s now somehow mtgated wth permt tradng, as ths s evdent from the last column. Now Chna would loose from leavng the coalton. Also no outsder has an ncentve to jon the coalton. In partcular, USA and Japan have no nterest anymore n jonng ths coalton because transfers to Chna would exceed ther gans from cooperaton. For the other coaltons and permt tradng schemes, results are summarzed n Table 4. In Table 4, the sngleton coalton structure, whch s stable by defnton, and the grand coalton structure, whch s not stable under any scenaro, are lsted as benchmarks to measure the success of stable coalton structures. Also the reference case wthout permt tradng s lsted. It s evdent that under the pragmatc schemes the number of nternally stable coalton structures s hgher than n the base case wthout permt tradng but under the equty schemes ths s substantally lower. Ths confrms the conjecture from the grand coalton n secton III.B that equty schemes may remove an asymmetry but replace t by a dfferent and even stronger asymmetry. Dfferent degrees of asymmetry also show up n terms of stable coalton structures (nternally and externally stable coalton structures). Only under the pragmatc schemes, we fnd stable coalton structures. Those stable coalton structures mprove upon the non-cooperatve stuaton n envronmental and welfare terms, though they close the gap between no and full cooperaton only to a small extent. The results also confrm that membershp matters and that from the number of partcpants success cannot be nferred. For example, the coalton between EU-15 and Chna s more successful than any other stable coalton, though the coalton between EU-15, Eastern European countres (EE) and Inda counts one more member. B. Senstvty analyss A typcal feature of emprcal work s that results depend on assumptons about polcy scenaros and on parameter values, whch are subject to some uncertanty. In terms of polcy scenaros, we consdered above two pragmatc and fve equty allocaton schemes of permts. It s evdent that a much longer lst of schemes could be generated and checked for stablty. We refran from ths exercse. However, gven that the two pragmatc schemes perform rather well whereas all
38 JOURNAL OF APPLIED ECONOMICS Table 4. Stable coalton structures Scenaro Number of Stable coaltons Global Global nternally emsson payoff stable coaltons reducton () sngleton coalton - stable 55 1,960 () no permt tradng 14 no stable coaltons - - () (1) quota BAU 28 {EU-15, Chna} 87 2,942 {Inda, ROW} 60 2,107 (2) quota Nash 53 {EU-15, EE, Inda} 68 2,372 {Japan, Inda} 61 2,151 (v) (3) egaltaran 3 no stable coaltons - - (4) hstorcal responsblty 1 no stable coaltons - - (5) ablty to pay 0 no stable coaltons - - (6) ablty to pollute 1 no stable coaltons - - (7) energy effcency 1 no stable coaltons - - (v) grand coalton - not stable 256 6,031 Notes: Global emsson reducton = gga tons over 100 years. Global payoff = bllon US dollar over 100 years. Stable coaltons means nternally and externally stable. Scenaros 1 and 2 correspond to the pragmatc schemes and scenaros 3 to 7 to the equtable schemes. fve equty schemes perform badly for our model, one may wonder whether a combnaton of a pragmatc and an equty rule would perform better. Thus, we tested a combnaton of every of the two pragmatc schemes wth every of the fve equty schemes. We consder apart from a 50%/50% allocaton rule of permts, also a 25%/75% and 75%/25% rule. 6 Surprsngly, we fnd no non-trval coalton structure that s stable. Apparently, the equty rules ntroduce too much asymmetry, or, put dfferently, the asymmetry of the equty schemes cannot be suffcently balanced by the pragmatc schemes. Thus, the superorty of the pragmatc schemes over the equty schemes n our model s confrmed by our senstvty analyss. In terms of parameters and gven the large number of parameters that enter our model, some selecton s necessary for a senstvty analyss. We beleve that the hghest uncertanty concerns benefts from global abatement and dscountng. Hence, n terms of benefts, we conduct a senstvty analyss where we unformly 6 Ths means that we tested 30 addtonal scenaros.
PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 39 rase the level of benefts from global abatement. That s, we rase the base value of the global beneft parameter µ B from 100 to 200 and 300 percent. 7 In terms of the dscount factor, we recall that our standard case assumed a dscount rate of 2 percent. Ths s roughly n lne wth Wetzman (2001) who suggests that f a constant dscount rate has to be chosen, n the context of global warmng, then a dscount rate of 2 percent or less s approprate to capture long-term effects. Ths means that we are at the upper bound. Hence, we test also for a dscount factor of 1 percent and - n order to get a more complete pcture of the drvng forces - consder addtonally also a dscount rate of 3 percent. It s evdent that dscountng affects not only benefts but also abatement costs. In lne wth more sophstcated models, a lower (hgher) dscount rate means n our model STACO to put a hgher (lower) weght on benefts compared to abatement costs because of the long terms effects of clmate change. More specfcally, a change n the dscount rate affects the beneft parameter δ B and the cost parameter δ c n STACO. Snce both parameters are level parameters (see equaton (6); as ths s also true for µ B ), only the change of the relaton δ B / δ c s mportant. Hence, a dscount rate of 1 percent has the same effect as rasng the global beneft parameter µ B from 100 to 120 percent and a dscount rate of 3 percent has the same effect as lowerng the global beneft parameter µ B from 100 percent to 85 percent. Hence, taken together, our senstvty analyss compares our standard scenaro, whch s the 100 percent scenaro, wth a 85, 120, 200 and 300 percent scenaro. Table 5 summarzes the results that confrm our qualtatve results from above. Frst, the grand coalton, though t would rase global welfare substantally compared to no cooperaton, s not stable under all scenaros. Second, wthout permt tradng, there s now one stable coalton structure n the 120, 200 and 300 percent scenaros that nvolves a coalton between Japan and EU-15. 8 Ths suggests that a suffcent hgh recognton of the benefts from controllng global warmng may mprove upon the prospects of cooperaton a conjecture confrmed for the pragmatc permt tradng schemes. However, ths coalton only slghtly mproves upon the non-cooperatve outcome: both regons have steep margnal abatement costs and therefore only margnally ncrease abatement efforts above non-cooperatve levels. Thrd, pragmatc permt tradng schemes are superor to equtable schemes for 7 Recall, µ B = 0.027 n the base case and hence 200 (300) percent mples µ B = 0.054 (µ B = 0.081) whch means a substantal ncrease n the valuaton of the benefts from a reducton of greenhouse gases. Ths s certanly a optmstc vew wth respect to the recognton of envronmental benefts by governments. 8 It turns out that 120 percent s the lower benchmark for whch ths change occurs.
40 JOURNAL OF APPLIED ECONOMICS Table 5. Senstvty analyss Percentage Coaltons Scenaros Total parameter emsson µ B reducton Global payoff No (1) (2) (3) gton bln US$ permt to (over 100 (over 100 tradng (7) years) years) Sngleton coalton structure x x x x 50 1,493 Coalton Japan, EU-15 - - - - 53 1,567 Coalton Inda, ROW - x - - 54 1,607 85 % Coalton Japan, Inda - - x - 55 1,641 Coalton EU-15, EE, Inda - - x - 62 1,814 Coalton EU-15, Chna - x - - 78 2,253 Grand coalton - - - - 234 4,656 Sngleton coalton structure x x x x 55 1,960 Coalton Japan, EU-15 - - - - 59 2,056 100 % Coalton Inda, ROW - x - - 60 2,107 Base Coalton Japan, Inda - - x - 61 2,151 Case Coalton EU-15, EE, Inda - - x - 68 2,372 Coalton EU-15, Chna - x - - 87 2,942 Grand coalton - - - - 256 6,031 Sngleton coalton structure x x x x 62 2,655 Coalton Japan, EU-15 x - - - 67 2,784 Coalton Inda, ROW - x - - 67 2,850 120 % Coalton Japan, Inda - x x - 69 2,909 Coalton EU-15, EE, Inda - - - - 77 3,199 Coalton EU-15, Chna - x - - 98 3,962 Grand coalton - - - - 284 8,053 Sngleton coalton structure x x x x 87 6,161 Coalton Japan, EU-15 x - - - 92 6,453 Coalton Inda, ROW - x - - 93 6,588 200 % Coalton Japan, Inda - x x - 95 6,720 Coalton EU-15, EE, Inda - - - - 105 7,343 Coalton EU-15, Chna - x x - 133 9,045 Grand coalton - - - - 377 18,000
PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 41 Table 5. (Contnued) Senstvty analyss Percentage Coaltons Scenaros Total parameter emsson µ B reducton Global payoff No (1) (2) (3) gton bln US$ permt to (over 100 (over 100 tradng (7) years) years) Sngleton coalton structure x x x x 112 11,910 Coalton Japan, EU-15 x - - - 119 12.466 Coalton Inda, ROW - x - - 119 12,704 300 % Coalton Japan, Inda - x x - 122 12,950 Coalton EU-15, EE, Inda - - - - 135 14,094 Coalton EU-15, Chna - x x - 169 17,280 Grand coalton - - - - 470 33,903 Note: x means stable and means not stable. Frst column refers to percentages of the beneft parameter µ B. The 85 and 120 percent scenaro correspond to a dscount rate of 3 and 1 percent, respectvely, as explaned n the text. Scenaros 1 and 2 correspond to the pragmatc schemes and scenaros 3 to 7 to the equtable schemes. all scenaros. Apart from the sngleton coalton structure, there s no stable coalton structure under any equtable scheme but two or three under the pragmatc schemes. Thus, our concluson from above s confrmed that moral motvatons (.e., equty concerns) may not always be a good gude for successful treatymakng. Fourth, n case there are stable coalton structures, they nvolve only small coaltons and only margnally mprove upon the non-cooperatve outcome n terms of global welfare and global emsson reducton. Thus, even though a cleverly desgned permt tradng scheme may balance some asymmetres between coalton members, t cannot totally overcome strong free-rder ncentves. V. Summary and conclusons We studed the effect of permt tradng on the stablty of global clmate agreements wth a model that combnes a game theoretcal wth an emprcal module.
42 JOURNAL OF APPLIED ECONOMICS The game theoretcal module models coalton formaton as a two-stage game n whch regons choose ther partcpaton n an agreement n the frst stage and ther abatement strateges n the second stage. Apart from membershp, payoffs depend on the permt tradng scheme, mplyng dfferent ntal allocatons of emsson allowances. The emprcal module provded beneft and costs estmates for twelve world regons. Though t captures long-run effects of greenhouse gas accumulaton over 100 years, t assumes statonary abatement strateges for game theoretcal tractablty. We consdered seven dfferent permt tradng schemes that were dvded nto two categores: pragmatc and equtable schemes. Pragmatc schemes are closely related to the current status quo and allocate permts accordng to unform emsson reductons from some base emsson level. We consdered emssons n the busness-as-usual scenaro wthout abatement and those n the Nash equlbrum as base lnes. Equtable schemes could be motvated by dfferent notons of farness that have been proposed n the lterature as for nstance hstorcal responsblty or ablty to pay. From the many results we would lke to menton three key results. Frst, the gans from partal and full cooperaton would be very large n terms of global welfare but also measured n envronmental varables lke global emsson reducton. However, the gans are qute unevenly dstrbuted because of the large heterogenety between regons. Dependng on the permt scheme, ths nequalty can be mtgated, as for nstance the pragmatc schemes do. However, the equtable schemes frequently replace one type of asymmetry by ntroducng another asymmetry, mplyng large transfers from one group of countres to another group. For nstance, a scheme that allocates permts on a per capta bass mples large transfers from ndustralzed to developng countres. Second, the large asymmetres under the equtable rules found for full cooperaton also showed up for partal cooperaton, mplyng that there was no stable coalton under equtable schemes. In contrast, some coaltons are stable under the pragmatc schemes. Thus, our fndngs do not support the conjecture that equty can enhance the success of agreements. Of course, ths fndng cannot clam generalty. Nevertheless, t provdes an ndcaton that equty prncples alone mght not be able to offset strong-free-rder ncentves. In fact, desgnng permt tradng schemes based on pragmatc prncples may appear to be less far but more successful n mtgatng the clmate problem. Thrd, even cleverly desgned permt tradng schemes that reduces the dsparty of the allocaton of the gans from cooperaton cannot overcome strong free-rder ncentves. In our model, only small coaltons turned out to be stable that mprove upon the status quo, though not much. Nevertheless, t became evdent that the