Optmal Transfers and Partcpaton Decsons n Internatonal Envronmental Agreements 1 by Carlo Carraro 2, Johan Eyckmans 3 and Mchael Fnus 4 Abstract The lterature on nternatonal envronmental agreements has recognzed the role transfers play n encouragng partcpaton n nternatonal envronmental agreements (IEAs), but the few results acheved so far are overly specfc and do not explot the full potental of transfers for successful treaty-makng. Therefore, n ths paper, we develop a framework that enables us to study the role of transfers n a more systematc way. We propose a desgn for transfers usng both nternal and external fnancal resources and makng welfare optmal agreements self-enforcng. To llustrate the relevance of our transfer scheme for actual treaty-makng, we use a well-known ntegrated assessment model of clmate change to show how approprate transfers may be able to nduce almost all countres nto sgnng a self-enforcng,.e. nternally and externally stable, clmate treaty. Keywords: Self-enforcng Internatonal Envronmental Agreements, Clmate Polcy, Transfers JEL Classfcaton: C72, H23, Q25, Q28. Revsed Verson: February 2006 1 2 3 4 Ths paper has been wrtten whle M. Fnus was a vstng scholar at the Katholeke Unverstet Leuven, Centrum voor Economsche Studën (K.U.Leuven-CES, Belgum). He acknowledges the fnancal support by the CLIMNEG 2 project funded by the Belgan Federal Scence Polcy Offce and the knd hosptalty of K.U.Leuven. Fondazone En Enrco Matte FEEM and Unversty of Vence. EHSAL- Europese Hogeschool Brussel and Katholeke Unverstet Leuven, Centrum voor Economsche Studën. Unversty of Hagen, Department of Economcs.
1 1. Introducton Transfers play a promnent role n the analyss of self-enforcng nternatonal envronmental agreements (IEAs). There are two reasons why ths s not surprsng. Frst, large asymmetres n the cost and beneft structure between countres may lead to a hghly asymmetrc dstrbuton of the gans from cooperaton that may hamper successful treaty-makng. Second, IEAs provde a publc good and therefore face strong free-rder ncentves that mght be mtgated through the use of transfers. A revew of current lterature (see Carraro and Snscalco, 1998; Fnus, 2001, 2003a and Tulkens, 1998) suggests that contrbutons n ths feld can be broadly dvded nto two categores. The frst category analyzes IEAs usng the tools of cooperatve coalton theory. The analyss s based on the characterstc functon that assgns a worth to every coalton, whch s calculated as the aggregate payoff that a coalton can secure for ts members rrespectve of the confguraton of the players remanng outsde ths coalton. As well as testng whether the coalton ncludng all players (grand coalton) s stable (n the sense of the core, for example), the man focus s on the axomatc foundaton of normatvely motvated sharng schemes such as the Nash barganng soluton, the Shapley value and the Chander-Tulkens transfer scheme. Applcatons are found n the context of global warmng (Chander and Tulkens, 1995, 1997; Eyckmans and Tulkens, 2003; German et al., 1998), acd ran (German et al., 1996; Katala et al., 1995), hgh seas fsheres (Katala and Lndroos, 1998; Lndroos, 2004; Lndroos and Katala, 2001, Pntasslgo, 2003) and water management (Ambec and Sprumont, 2002; Lejano and Davos, 1999). Ths approach may be regarded as the classcal cooperatve method of studyng coaltons. The strength of ths approach les n the generalty
2 of results that can often be establshed on the bass of some standard propertes, lke superaddtvty. 5 The second category of contrbutons analyzes IEAs usng the tools of non-cooperatve coalton theory. The analyss s based on the valuaton functon that assgns an ndvdual payoff to every coalton member. The value s calculated by takng nto account the entre coalton structure,.e. the partton of players nsde and outsde a coalton. The man focus s on explanng free-rdng behavor n the context of externaltes, dentfyng the man economc factors that determne the relatve success of partal cooperaton and suggestng nstruments for dscouragng free-rdng. The advantage of the non-cooperatve over the cooperatve approach s that t better captures externaltes between players and coaltons (Bloch 2003). However, ths advantage comes at the cost of complexty, mplyng that results are usually less general. In the context of the non-cooperatve approach, transfers have been analyzed n ther ex-ante and ex-post forms. 6 Ex-ante means that countres commt to a certan transfer rule before they decde upon ther partcpaton n an IEA. Ex-post means that after an agreement has formed, transfers are used to broaden an exstng coalton. The frst putatve paper on transfers goes back to Carraro and Snscalco (1993). In lne wth ntuton, they prove that transfers have no effect n the standard model wth symmetrc countres, gven the constrant that IEAs must be nternally and externally stable, and that transfers must be self-fnanced. They proceed to analyze varous forms of commtment that wll enable coaltons to expand va ex-post transfers. They suggest two drectons of ex-post transfers that may mprove upon the status quo: 1) nsders (coalton members) brbng outsders 5 6 Roughly speakng, supperaddtvty means that the worth of coaltons ncreases wth ncreasng partcpaton. See secton 3 for a formal defnton. For an overvew, see Fnus (2003).
3 (non-coalton members) to jon ther coalton and 2) outsders brbng other outsders to jon the coalton. The dea of varous forms of commtment and ex-post transfers was also pursued n later papers by Botteon and Carraro (1997), Jeppesen and Andersen (1998) and Petraks and Xepapadeas (1996), though commtment s certanly not an assumpton n lne wth the noton of self-nterested players. Therefore, t was mportant to llustrate that expansons of coaltons va ex-post transfers may also be possble wthout commtment as ths has been done by Botteon and Carraro (1997) n a smple emprcal model wth fve heterogeneous countres. Moreover, the postve effect of ex-ante transfers was llustrated for the Nash barganng soluton and the Shapley value. A smlar concluson was confrmed by Barrett (1997) for the Shapley value usng a stylzed smulaton model where heterogenety s modeled va two types of countres. Later papers have looked at the effect of varous ex-ante and ex-post transfers rules on the success of coalton formaton and on the possblty of expandng stable coaltons (see Altamrano-Cabrera and Fnus, 2004; Bosello et al., 2003, 2004; Carraro and Snscalco, 2001; Eyckmans and Fnus, 2003, 2004a; Fnus et al., 2004; Wekard et al., 2004). Most of these papers used a more elaborate emprcal model, looked not only at stylzed transfer schemes derved from cooperatve game theory, but also consdered schemes that are based on varous moral motves for far sharng, consdered transfers va permt tradng and allowed for the possblty of multple coaltons. Roughly speakng, all papers bascally confrm earler studes n concludng that transfers can be conducve to the success of selfenforcng agreements, but that outcomes crucally depend on the partcular transfer rule, the model and the data set. For nstance, Barrett (2001) draws a rather pessmstc pcture of the Chander-Tulkens transfer rule n the context of a non-cooperatve coalton model, whereas Eyckmans and Fnus (2003) come to a more optmstc concluson. Moreover, Bosello et al.
4 (2003) fnd some evdence that equtable sharng rules can enhance effcency by ncreasng the number of sgnatores of an envronmental treaty, whereas Altamrano-Cabrera and Fnus (2004) derve the exact opposte concluson. The mxed evdence and the specfc results motvate us to look for a more general approach to studyng the role of transfers n the context of non-cooperatve coalton theory. In partcular, we want to determne the full potental of transfers. To ths end, we go back to the roots of the analyss of IEAs, removng n ths paper any unnecessary complcaton as a frst step. That s, we assume a smple cartel formaton game and apply the concept of nternal and external stablty. We do not consder commtments or any complcaton lke nontransferable utlty (Buchholz and Konrad 1995), montorng and moral hazard problems (Petraks and Xepapadeas 1996); reputaton effects (Jeppesen and Andersen; 1998; Hoel and Schneder 1997) are also dscarded n favor of the noton of optmal transfer schemes. Wth optmal transfers we mean transfers desgned to maxmze global welfare under the constrant that the underlyng IEA s self-enforcng. The mportance of ths research ssue for polcy makng s evdent when consderng for nstance the crucal role fnancal or technology transfers play a n current dscussons on possble post-kyoto clmate polces n the framework of the Unted Natons Framework Conventon on Clmate Change (UNFCCC). Frst, mportant multlateral fnancal transfers take place under the so-called Global Envronment Faclty 7 (GEF) program. As the fnancal mechansm of the UNFCCC, GEF allocates and dsburses about 250 mllon dollars per year n projects for mprovng energy effcency, fosterng renewable energy use, and pushng for sustanable transportaton. Moreover, t manages two specal funds the Least Developed 7 The Global Envronment Faclty or GEF was establshed n 1991 by UNEP (Unted Natons Envronmental Program), UNDP (Unted Natons Development Program) and the World Bank. For more nformaton, see www.thegef.org. Although ts ams are broader than only clmate change polcy, t has become the man fnancal nstrument of the UNFCCC.
5 Countres Fund 8 and the Specal Clmate Change Fund 9 as well the Adaptaton Fund 10 under the Kyoto Protocol. Second, the flexble mechansms (.e. Emssons Tradng ET, Jont Implementaton JI and Clean Development Mechansm CDM) foreseen n the Kyoto Protocol are expected to generate mportant flows of fnancal resources among the Protocol member states and even between sgnatores and non-sgnatores n the case of CDM projects. For nstance, den Elzen and de Moor (2002) estmate that the former Sovet Unon mght reap about 2.3 bllon dollar revenues (about 0.3% of GDP) annually from permt tradng under the Kyoto Protocol. Moreover, CDM projects mght lead to revenues of about 500 mllon dollar for developng countres, even under rather conservatve assumptons. 11 It s mportant to note that these fnancal mechansms (GEF and specfc clmate funds) and flexble Kyoto mechansms (ET, JI, CDM) can be nterpreted as multlateral transfer schemes. Therefore, our paper s contrbuton to the polcy debate s that t provdes mportant new nsghts on how the exstng transfer schemes should be optmzed n order to acheve maxmum partcpaton and envronmental effectveness of future, voluntary nternatonal clmate polcy agreements. In what follows, we present our model n secton 2. Ths comprses not only a theoretcal part but also an emprcal part n order to llustrate the usefulness and practcal applcaton of our concepts. The emprcal part s based on a modfed verson of RICE, a well-known ntegrated 8 9 10 11 The Least Developed Country Fund (LDCF) was created to address the extreme vulnerablty and lmted adaptve capacty of least developed countres and has supported ther preparaton of Natonal Adaptaton Programmes of Actons. The Specal Clmate Change Fund (SCCF) supports actvtes n the areas of adaptaton, technology transfer, energy, transport, ndustry, agrculture, forestry, waste management and economc dversfcaton. The Adaptaton Fund (AF) wll assst developng countres n copng wth the adverse effects of future clmate change. Two percent of the proceeds of Clean Development Mechansm (CDM) projects under the Kyoto Protocol wll be drected to ths AF. Note that these numbers are only revenues and are not corrected yet for the cost of emsson reducton projects. However, these costs are beleved to be very low n the Former Sovet Unon and n developng countres.
6 assessment model of clmate change polcy (Nordhaus and Yang, 1996). In secton 3, we ntroduce two propertes of coalton formaton that are sutable for analyzng all aspects of transfers n secton 4. Secton 5 wraps up the man fndngs and hghlghts some drectons for future research. 2. Model 2.1 Theoretcal Background Coalton formaton s modeled as a two-stage game. There are n players N = {1,...,n} that are countres or world regons n our emprcal model and whch we smplfy refer to as countres n the followng dscusson. In the frst stage, countres choose ther membershp: a country can ether jon coalton S and become a sgnatory or reman a sngleton and non-sgnatory. These decsons lead to coalton structure C = {S,{ },...,{n}},.e., a partton of players, wth s sgnatores (s denotes the cardnalty of S) and n-s non-sgnatores. Gven the smple structure of the frst stage, a coalton structure C s fully characterzed by coalton S. 12 In the second stage, countres choose ther economc strateges. In the context of our emprcal model, economc strateges are emsson abatement and captal nvestment (see subsecton 2.2 for detals). At ths stage, t suffces to denote the vector of economc strateges by ω (S) = ( ω1(s),..., ω n(s)), gven that a coalton S has formed n the frst stage; we can also note that n the second stage countres receve ndvdual payoffs π ( ω (S)) that depend on the economc strateges of all countres. 13 12 13 Ths smplfcaton would not be possble f we were to allow for multple non-trval coaltons as for nstance consdered n Bosello et al. (2003, 2004), Carraro (2000), Eyckmans and Fnus (2003) and Fnus (2003b). Ths smple theoretcal framework has often been adopted n the lterature on nternatonal envronmental agreements where the assumpton of a coalton structure wth a sngle coalton s the most obvous and realstc and where the game s characterzed by postve externaltes. A
7 We compute the subgame-perfect equlbra of ths two-stage game by backward nducton. To do ths, t s suffcent for strateges to consttute a Nash equlbrum at every stage. For the second stage, ths entals that economc strateges form a Nash equlbrum between coalton S and the n-s non-sgnatores. 14 That s: π ( ω (S), ω (S)) π ( ω (S), ω (S)) ω (S) and S S: * * * S S S S S S * * * * * S S π ( ω (S), ω, ω (S)) π ( ω (S), ω (S), ω (S)) ω (S). (1) where ω S (S) s the economc strategy vector of coalton S, ω S (S) the vector of all other countres not belongng to S, ω (S) the strategy of non-sgnatory, and ω (S) the strategy vector of all other non-sgnatores except under coalton structure S. An astersk denotes equlbrum strateges. Computatonally, ths mples that non-sgnatores S wll choose ther economc strateges so as to maxmze ther ndvdual payoff π ( ω ), whereas all sgnatores S jontly maxmze π S ( ω ), the aggregate payoff of ther coalton. Strategcally, ths means that the behavor of non-sgnatores towards all other countres s selfsh and non-cooperatve; sgnatores behave cooperatvely towards ther fellow members (otherwse cooperaton would not be worthwhle analyzng), but non-cooperatvely towards outsders. Economcally, ths means strateges are group (but not globally) effcent wthn coalton S. Hence, the equlbrum economc strategy vector ω * (S) corresponds to the socal optmum f coalton S comprses all countres (S=N),.e. the grand coalton forms, and corresponds to the Nash equlbrum f coalton S comprses only one member (s={}) - both concepts whch are known outsde the context of coalton formaton. Hence, any more general framework s sometmes used n coalton theory (Bloch, 2003) but would not be useful for the purpose of showng our man results. 14 Ths has been called a partal agreement Nash equlbrum by Chander and Tulkens (1997). Our assumpton s n lne wth the manstream of the lterature on coalton theory. For an overvew see Bloch (2003) and Y (2003).
8 neffcency,.e., global welfare loss compared to the global Pareto optmum, stems from the fact that S s not the grand coalton. Gven that the second stage of the game has been solved, we defne v (S) =π( ω (S)) as the * valuaton of country f coalton S forms. Ths defnton succnctly summarzes all nformaton relevant to the second stage. For the frst stage, we defne a Nash equlbrum n terms of partcpaton. 15 The followng two condtons must be met: nternal stablty: v(s) v(s\{}) S. (2) external stablty: v(s) v(s {}) S. (3) That s, n equlbrum, no sgnatory belongng to coalton S has an ncentve to leave ts coalton n order to become a non-sgnatory, gven the partcpaton decsons of all other countres. By the same token, no non-sgnatory has an ncentve to jon coalton S, gven the decsons of all other countres. Regardless of whether we consder ex-ante or ex-post transfers, n a TU-framework, optmal economc strateges are not affected by transfers. Thus, valuatons wth transfers ˆv (S) are related to those wthout transfers v (S) smply through the relaton ˆv (S) = v (S) + t where t > 0 means recevng and t < 0 means payng a transfer. We make the standard assumpton that transfers balance,.e., and hence ˆv (S) = v(s) t N 0 =. 16 Note that n any N N 15 16 Ths defnton of coaltonal stablty s due to d Aspremont et al. (1983) and has been frequently appled n the lterature on IEAs as for nstance by Barrett (1994), Carraro and Snscalco (1993), Hoel (1992) and by many scholars afterwards. The condton that transfers balance s equvalent to the self-fnanced transfer constrant n Carraro and Snscalco (1993).
9 case (wth and wthout transfers), coalton S={} s always nternally stable and coalton S=N always externally stable, whch smply follows by defnton. 2.2 Emprcal Background In order to llustrate the mportance of transfers for the success of coalton formaton, we derve valuatons from the CLIMNEG World Smulaton Model (hereafter abbrevated as CWSM). CWSM s an ntegrated assessment, economy-clmate model that extends the semnal RICE model by Nordhaus and Yang (1996). 17 It captures the endogenous feedback of clmate change damages on producton and consumpton. The economc module of the CWSM conssts of a dynamc, long-term, perfect foresght, Ramsey-type optmal growth model. The envronmental module conssts of a carbon cycle and temperature change module. The decson varables n the CWSM are nvestment and carbon emsson reducton. In the CWSM, the world s dvded nto sx regons: USA, JPN (Japan), EU (European Unon), CHN (Chna), FSU (Former Sovet Unon) and ROW (Rest of the World). In every regon, and at every tme t, the followng budget equaton descrbes how potental GDP, Y,t, can be allocated to consumpton, Y,tC ( μ,t), and clmate change damages, Y,tD ( Δ T) t : Z,t, nvestment, I,t, emsson abatement costs, ( ) ( ) Y = Z + I + Y C μ + Y D Δ T (4),t,t,t,t,t,t t Output Y,t s produced wth captal and labor. Captal s bult up through nvestment and deprecates at some fxed rate. Labour supply s assumed to be nelastc. Therefore, nvestment I,t s the only endogenous producton nput and consttutes the frst choce varable n the model. 17 Almost all parameter values are taken from the RICE model of Nordhaus and Yang (1996). A complete overvew of the equatons and parameter values of the CWS model can be found n Eyckmans and Tulkens (2003).
10 Abatement costs Y,t C ( μ,t ) are expressed as loss of potental GDP : C s the share of potental GDP devoted to abatement, whch s a functon of μ,t [ 0,1], a varable that measures the relatve emsson reducton compared to the busness-as-usual scenaro wthout any abatement polcy. Damages Y D ( T ),t t Δ are also expressed as loss of potental GDP : D s the share of potental GDP destroyed by clmate change damages, whch s a functon of temperature change ΔT t. Temperature change depends on the stock of greenhouse gases, whch n turn depends on emssons that accumulate n the atmosphere. Fnally, emssons are proportonal to producton, but can be reduced by the abatement rate μ,t. Hence, the second choce varable n ths model s the emsson abatement rate μ,t. Both choce varables (nvestment and abatement) affect output, abatement costs, damage costs and therefore also consumpton, not only domestcally but also abroad. Ths s mmedately evdent wth regard to abatement because remanng emssons (after abatement) ncreases the stock of greenhouse gases, whch affects envronmental damages n every country. However, t s also true for nvestment, snce captal s an nput n the producton process and emssons are proportonal to producton. Technologcal progress s captured by the CWSM n an exogenous fashon (the tme path s taken from RICE). It ncreases producton potental and decreases the emsson-output rato (.e. ncreases energy effency) over tme. Welfare s measured as total lfetme dscounted consumpton: π ( ω ) = where Z Ω,t (5) t t= 0[ 1+ρ ] ρ stands for the dscount rate of regon, Ω denotes the tme horzon and ω s an economc strategy vector. Vector ω = {I,t, μ,t} N;t = 0,, Ω conssts of a tme path of 35
11 decades 18 for emsson abatement and nvestment for all sx regons and hence ts length s 2x35x6=420. For every possble coalton S, we compute the Nash equlbrum ω * (S) between S and N\S n order to derve valuatons * v (S) =π( ω (S)) as descrbed n subsecton 2.1. Gven that our emprcal model comprses sx players, we have 58 dfferent coaltons and therefore a full table of valuaton vectors of dmenson 58x6. If valuatons are modfed through transfers, ths happens n a one-shot fashon snce t does not affect equlbrum economc strateges n the CWSM as proved n Eyckmans and Tulkens (2003). Thus, we are operatng wthn a TU-framework. We fnsh ths secton wth fve remarks about the basc ncentve structure obtaned by calbratng the CWSM. Frst, we assume a relatvely low dscount rate of 1.5 percent, except for CHN and ROW where we assume a dscount rate of 3 percent n order not to overestmate the ncentves for these regons to mplement clmate change polces. However, much hgher dscount rates would smply gnore the long term effects of clmate change, provdng no ncentve for countres to cooperate and therefore would render our analyss unnterestng. The dscount rates chosen are n lne wth the recommendatons n Wetzman (2001). Second, the parameters set for the CWSM mply that USA, JPN and EU face steep abatement cost curves, whle CHN and ROW face flat ones. The regonal dfferences n abatement costs manly reflect dfferences n energy effcency. Intutvely, energy effcent regons face hgher margnal costs when cuttng back emssons than regons characterzed by low energy effcency because they have already exploted the cheapest energy savng technques. Thrd, damage functons are partcularly steep n EU and ROW, less steep n USA and JPN and relatvely flat n FSU and CHN. The hgh damage estmate (as a percentage of potental 18 We choose a suffcently long tme perod to avod an end pont bas. However, due to dscountng, only a shorter perod s strategcally relevant for players.
12 GDP ) for ROW s due to the fact that clmate change s beleved to affect developng countres more strongly than ndustralzed countres, because ther economes tend to depend more on clmate related producton processes lke agrculture, fshery and forestry (IPCC 2001). The low damage estmate for FSU s due to some expected benefts from moderate temperature ncrease, lke the ncreased avalablty of arable land. Fourth, n a gven coalton S, the steeper the margnal damage cost curves and the flatter the margnal abatement cost curves of the members of S are, the hgher the optmal abatement of coalton members wll be, whch follows from the frst-order condtons of jont welfare maxmzaton of coalton S (see Barrett, 1994 and Eyckmans and Tulkens, 2003). It follows that n any perod, coalton members should abate up to the pont where ther margnal abatement costs are equal to the dscounted sum of all coalton members avoded future margnal clmate change damages. Ffth, coalton members wth a flatter margnal abatement cost curve have to contrbute more than those wth a steeper curve, all else beng equal, whch also follows from the frst order condtons (cost effcency) of coalton S. 3. Propertes of Valuatons In ths secton, we dscuss two mportant propertes that hold for the valuatons derved from our emprcal model CWSM and whch determne the general ncentve structure of countres n the coalton formaton game. The frst property s called superaddtvty and means that the aggregate valuaton of country j and coalton S ncreases f country j jons coalton S. Property 1: Superaddtvty A coalton game s superaddtve f and only f for all S { j} S j S N and j S : v(s {j}) > v(s) + v (S).
13 That s, there s coaltonal gan from cooperaton and hence cooperaton s group ratonal or coaltonally ratonal. It s evdent that superaddtvty s a necessary condton to make cooperaton attractve for those countres partcpatng n an IEA. Ths property means that startng from any coalton S and ncreasng the degree of cooperaton by movng to S {j} or even larger coaltons, t s generally possble to allocate the coalton gan such that t consttutes a Pareto-mprovement to all regons nvolved n cooperaton. 19 We can defne the second property wth the term postve externaltes, meanng that f country j jons coalton S, all countres that do not belong to S {j} are better off. Property 2: Postve Externaltes A coalton game exhbts postve externaltes f and only f for all S N, j S and all S { j} : v(s {j}) > v(s). Consequently, there s an external gan or a postve spllover from cooperaton, makng free-rdng attractve. From a non-sgnatory s pont of vew, the most favorable condton s the one n whch all other countres partcpate n the agreement. 20, 21 It s then clear that a regon s decson to jon a coalton as well as the stablty of an IEA depends on the ntensty of the superaddtvty effect whch, together wth the sharng rule of the coaltonal gan, determnes the nsde optons of cooperaton relatve to the ntensty of the postve externalty effect whch n turn determnes the outsde optons of cooperaton. We 19 20 21 Superaddtvty s a property frequently encountered n cooperatve coalton theory, but not much used n non-cooperatve coalton theory, despte the fact that t helps to structure deas mmensely. Postve (and negatve) externaltes s a property that plays an mportant role n recent lterature on non-cooperatve coalton theory. See for nstance Bloch (2003), Y (2003) and Maskn (2003). The mportance of the propertes superaddtvty and postve externalty n theoretcal models on IEAs s hghlghted for nstance n Fnus (2003b).
14 wll study these effects n more detal n secton 4, but note here that superaddtvty and postve externalty together mply that global welfare ncreases through cooperaton. That s, gven a coalton S, whenever a sngle or several countres jon coalton S, global welfare s rased. That s, cooperaton s globally ratonal - a central property that motvates our effort of analyzng measures to mtgate the problems of free-rdng n transboundary polluton control. Table 1 llustrates the magntudes at stake for our emprcal applcaton usng the CWSM model. It dsplays for a selecton of coaltons welfare (global welfare) and two envronmental varables (carbon concentraton and global emssons) n absolute (n the legend) and relatve terms (n the table). The relatve magntudes can be nterpreted as a closng the gap ndex, measurng how close a coalton comes to the global optmum where the performance n the global optmum s 100 percent and the performance wth no cooperaton s 0 percent by defnton. Apart from stressng that both full and partal cooperaton can make a large dfference n welfare and ecologcal terms compared to no cooperaton, Table 1 llustrates that not only the sze of a coalton matters for the global success of cooperaton, but also the dentty of ts members. Put dfferently, the commonly held vew that hgh partcpaton automatcally ndcates the success of an IEA may be wrong. For nstance, coalton no. 32 ncludng fve members (USA, JPN, EU, CHN, FSU) ranks lower than many coalton structures comprsng coaltons of only three or four members and even lower than coalton no. 31 wth only two members (JPN and ROW). From Table 1, t s also clear that, as a general tendency, the mportance for global welfare of partcpaton of partcular countres decreases wth the followng sequence: ROW, CHN, EU, USA, FSU and JPN. ROW s and CHN s mportant role stems from the fact that they can provde cheap abatement. Smlarly, JPN s lesser mportance s due to ts steep margnal abatement cost curve. However, there s also an addtonal dmenson related to envronmental damages. If a gven coalton maxmzes ts jont welfare, the hgher the margnal damages of
15 coalton members are, the hgher jont abatement efforts wll be, all else beng equal. Ths explans the mportance of EU for cooperaton. These remarks also explan why the old Kyoto coalton comprsng USA, JPN, EU and FSU n our model ranks relatvely low snce the two key players CHN and ROW are outsders. A smlar concluson apples to the present Kyoto coalton, after the wthdrawal of the USA n 2001. It s evdent that the US decson mples a dramatc drop n welfare and envronmental effectveness, almost to non-cooperatve levels. Thus, our model provdes support for the efforts of many governments and non-governmental organzaton to convnce the US to rejon the Kyoto Protocol. However, t also provdes support for the concern of the US and many others that an effectve clmate polcy must nclude developng countres (.e., ROW) and countres n transton (.e., CHN). 22 4. Stable Coaltons In ths secton, we analyze coalton formaton under the assumpton of no transfers and varous forms of transfers. Results and arguments are llustrated wth the CWSM model. In subsecton 4.1, we start wth no transfers. Subsecton 4.2 deals wth ex-ante transfers and shows the advantage of optmal transfers, as defned n Eyckmans and Fnus (2004b), compared to smple transfer schemes, as assumed n most papers up to now. The purpose of ths secton s apart from a non-techncal exposton of the concept of optmal transfers to quantfy ths advantage n the context of clmate change. 23 Subsecton 4.3 analyzes the expanson of coaltons va ex-post transfers. It s demonstrated that when optmal transfers are used ex-ante, no further mprovement s possble va ex-post transfer usng nternal means, 22 23 Smlar conclusons can also be found n Buchner et al. (2002) where an ntegrated economyclmate model based on RICE s also used. The man dfference s that n the model used by Buchner et al. (2002) techncal change s endogenous. The formal proofs n ths partcualr subsecton are provded n Eyckmans and Fnus (2004b).
16 ths s only possble by external means. The condtons under whch such an expanson s possble are derved and mplcatons for polcy makng are dscussed. To gan an understandng of the drvng forces of coalton formaton, t s mportant to recall that stablty s defned by two components nternal and external stablty and that valuatons are characterzed by superaddtvty as well as postve externaltes. Moreover, t s helpful to note that the postve externalty property mples that a necessary condton for nternal stablty s ndvdual ratonalty. Indvdual ratonalty, also sometmes called proftablty (see Carraro and Snscalco, 1993), means that every coalton member S receves at least the same valuaton n coalton S as t does under condtons of no cooperaton ( S:v (S) v ({}). In other words, a mnmum requrement for coalton S to be nternally stable (and therefore stable) s that cooperaton should, for all members of S, consttute a (weak) Pareto-mprovement compared to no cooperaton. The reason s smply explaned. Suppose a member n S would receve a lower valuaton than under no cooperaton,.e., v(s) < v({}). If regon were to leave coalton S, t would receve valuaton v(s\{}) for whch v(s\{}) v({}) holds (wth strct nequalty f s 3) due to postve externaltes. Consequently, leavng coalton S would always pay and therefore S could not be nternally stable. 4.1 No Transfers In the case of no transfers, only 11 out of 58 coaltons are ndvdually ratonal n our CWSM model analyss (see Table 2). None of the top 20 ranked coaltons (n terms of global welfare) s ndvdually ratonal. No coalton wth 5 members and only one wth 4 members s ndvdually ratonal (see Table 2). Nether the old (no. 47) nor the present (no. 50) Kyoto coalton s ndvdually ratonal. Notably, not a sngle coalton that ncludes Chna the key player wth cheap abatement optons s ndvdually ratonal. Thus, n the absence of
17 transfers, although cooperaton may be coaltonally (because of superaddtvty) and globally (because of superaddtvty and postve externalty) ratonal, t may not be ndvdually ratonal to all coalton members. The reason s that an effcent allocaton of abatement burdens wthn a coalton S would result n a hghly asymmetrc allocaton of the net gans from cooperaton among coalton members that face a markedly heterogeneous beneft and cost structure. For nstance, the EU has a relatvely steep margnal abatement and margnal damage cost curve. Therefore, f the EU s a member of a coalton S, t wll be a major benefcary of cooperaton, because t contrbutes relatvely lttle to cooperaton, but n proporton benefts much. The opposte s true for Chna, whch faces a flat margnal abatement cost and damage cost curve and whch therefore s a typcal loser from cooperaton wthout transfers. Thus, even a smple check for ndvdual ratonalty ndcates that wthout transfers a key player lke Chna cannot be convnced to jon a clmate treaty. Moreover, we can already conjecture that wthout transfers even moderate partal cooperaton wll prove very dffcult. Ths s confrmed by a detaled analyss of nternal and external stablty as shown n Table 2. The two ndvdually ratonal coaltons wth the hghest global welfare (no. 21 and 22) are not nternally stable, though all other ndvdually ratonal coaltons are nternally stable. However, none of the nternally stable coaltons s also externally stable. Hence, there s no stable coalton wthout transfers when valuatons are derved from the CWSM model (see also Table 3). Ths observaton renforces the startng pont for our analyss,.e. the need for a systematc analyss of the possbltes of transfers to enhance the success of nternatonal clmate agreements. 4.2 Ex-Ante Transfer Schemes In the lght of the above negatve concluson, we consder dfferent ex-ante transfer schemes. That s, the membershp decson n the frst stage of the game s based on the assumpton that
18 coalton S wll not only choose ts optmal economc strateges n the second stage, but wll also allocate the coalton gan from cooperaton among ts members wth a partcular transfer scheme. From secton 2, we may recall that ˆv (S) = v(s) + t and that transfers balance,.e., and hence ˆv (S) = v(s) t S 0 =. S S We start by consderng three transfer schemes that have played an mportant role n prevous analyses of self-enforcng IEAs (see the lterature cted n the Introducton). We call these schemes smple n order to dstngush them from our optmal transfer schemes that we ntroduce subsequently. Through the llustraton of both optmal and smple transfer schemes, the full potental of an optmal desgn of transfers wll become apparent. 4.2.1 Smple Transfer Schemes All three smple transfer schemes that we consder orgnate from cooperatve coalton theory. Nevertheless, they have been frequently adopted n the context of the valuaton functon approach. Ths requres only a slght modfcaton of ther orgnal defntons to account for the fact that coalton S may not only be the grand coalton but can be any subcoalton of N. The followng formulas descrbe valuatons of player beng a member of a gven coalton S N. The frst transfer scheme s the Shapley Value and mples valuatons of the followng form: t!(s t 1)! ˆv = v (T {}) v (T) S (6) SV k k T S s! k T {} k T T wth coalton S N, T S a subgroup of S and t and s the sze of group S and T. Roughly speakng, the Shapley Value gves every country a valuaton accordng to ts average margnal contrbuton over every possble subcoalton T of S (term between square brackets n (6)), weghted by the probablty that ths subpartton forms (frst factor n (6)).
19 The second smple transfer scheme s the Nash Barganng soluton (wth equal weghts): NB 1 ˆv = v ({}) + v j(s) v j({}) S s js js (7) Every member n S receves ts valuaton under no cooperaton (frst term) plus an equal share of the coaltonal surplus compared to no cooperaton (second term). Thus, no cooperaton serves as the threat pont. The thrd smple transfer scheme s the Chander and Tulkens transfer scheme n the verson as appled n Eyckmans and Tulkens (2003): ˆv = v ({}) + v (S) v ({}) S ' CT D ' j j D j js js js (8) wth ' D dscounted margnal damages of member. It s evdent that ths scheme s a verson of the Nash barganng rule wth unequal weghts. Ths rule gves a hgher share of the gans from cooperaton to those that are most affected by clmate change. It s straghtforward to show that all three smple transfer schemes are all coaltonally ratonal,.e. S N: ˆv j(s) v(s) j, and ndvdually ratonal,.e., S js js : ˆv (S) v({}) snce superaddtvty holds. The results of our applcaton, as summarzed n Tables 2 and 3, confrm our ntuton and also many prevous studes on transfers: smple transfers mprove upon the outcome wthout transfers. However, t s mportant to realze that ths result s by no means general. Of course, all smple transfer schemes guarantee ndvdual ratonalty, but ndvdual ratonalty s only a necessary condton for nternal stablty. Though ths s not the case n our example, assumng dfferent parameter values or swtchng to a dfferent model, may mply that a coalton s stable wthout transfers and ths leads to a hgher global welfare than any other
20 stable coalton wth a smple transfer scheme. Already from Table 2, t can be seen that there are three coaltons of sze 3 that are nternally stable wthout transfers, but none under the Shapley Value and the Chander and Tulkens transfer rule. Hence, we cannot generally conclude that smple transfer schemes would always enhance nternal stablty. Smlarly, no general concluson s possble wth respect to external stablty ether. Moreover, n our applcaton, the Nash barganng soluton leads to a stable coalton (no. 16) wth hgher global welfare than n any other stable coalton under the other two transfer schemes. However, other parameter values or other models could yeld dfferent results. Fnally, we have no nformaton about whether we could do any better than the Nash Barganng soluton n ths example and f so what the best transfer scheme would be and whch coalton could be acheved. 4.2.2 Optmal Transfer Schemes In order to address the ssues rased above n a systematc way, we frst focus on nternal stablty. For ths purpose, we ntroduce the concept of a Potentally Internally Stable Coalton (PISC) whch we defne as follows (see Eyckmans and Fnus, 2004b and Botteon and Carraro, 1997 for a smlar concept): Defnton 1: Potentally Internally Stable Coalton (PISC) A coalton S s sad to be potentally nternally stable (PIS) f and only f v(s) v(s\{}). S S Thus, f a coalton S s not PIS, ths smply means that there s no transfer scheme that can ensure nternal stablty to all members of S and hence ths coalton cannot be stable. Conversely, f a coalton S s PIS, then ths means that coalton S has suffcent resources to prevent a coalton member from leavng coalton S. Thus, what s requred now s to
21 construct a transfer scheme that ensures nternal stablty to all members of S, provded S s PIS. Gven the desgn of most smple transfer schemes, t seems approprate to construct a transfer scheme that gves every member of S ts outsde opton v (S \{}) plus a share of the coalton surplus compared to the free-rder valuaton: Defnton 2: Optmal Transfer Schemes (OPTS) A transfer scheme can be termed optmal f t satsfes OP S N, S : ˆv (S) = v(s\{}) + λ (S) j Sv j(s) j Sv j(s\{}) s 1 s wth λ(s) Δ = { λ + j Sλj = 1}. By the constructon of OPTS, t s easy to see that any transfer scheme that belongs to the class of OPTS wll make any PISC nternally stable. The desgn of OPTS suggests that we have much leeway n choosng weghts λ (S). As long as the surplus of cooperaton over the free-rdng valuatons as well as all weghts λ (S) are postve, the resultng allocaton wll be nternally stable regardless of the choce of weghts. It s nterestng to note the smlartes and dfferences between OPTS on the one hand and the Chander-Tulkens and Nash Barganng soluton on the other hand. The smlarty s that all three transfer schemes gve each player a reference or threat pont payoff plus some share of the surplus. Moreover, also for OPTS coaltonal ratonalty holds because ˆv (S) = v (S). However, OPTS s dfferent from the other transfer schemes S OP S because t chooses the correct threat pont (frst term of the defnton of ˆv OP (S) n Defnton 2) and defnes the coalton surplus (second term of the defnton of ˆv OP (S) n Defnton 2) wth respect to ths threat pont. Moreover, f S s not PIS, then the total
22 coaltonal payoff s nsuffcent to satsfy the free-rdng clams of all members of S and OPTS becomes a loss sharng nstead of a surplus sharng formula. It s evdent that any transfer scheme that belongs to the class of OPTS wll lead to the same set of nternally stable coaltons. Less evdent but nterestng s that ths robustness result also carres over to the set of externally stable coaltons. Ths s because for any OPTS, ether a coalton S s nternally stable for all members (f t s PIS) or fals to be nternally stable for all members (f t s not PIS) and nternal stablty/nstablty s lnked to external stablty/nstablty n a drect way More specfcally, pck a coalton S and suppose S s PIS. Then, under any OPTS, S s nternally stable for all coalton members,.e., S: ˆv (S) v (S\{}) by the very OP defnton of PIS and OPTS and regardless of the partcular sharng vectors λ. Hence, for all S, all coaltons S\{} are externally unstable wth respect to accesson of regon S. Suppose now that S s not PIS. Then, followng a smlar lne of argument, under OPTS for all S, all coaltons S\{} are externally stable wth respect to accesson of regon S because coalton members receve less than ther free-rdng payoff v (S \{}), regardless of the partcular sharng vectors λ. Therefore, any famly of weghts of an OPTS wll lead to the same set of nternally and externally stable coaltons. As s clearly confrmed by Table 2, every coalton that s nternally stable under a smple transfer scheme wll also be nternally stable under an optmal transfer scheme, but not vce versa. Ths s not true however for external stablty. For nstance, coalton no. 16 s externally stable under Nash Barganng, but s not externally stable under an optmal transfer scheme. Hence, one may wonder whether some effort should be made to search for a transfer scheme that acheves not only nternal, but also external stablty n an optmal way. A closer nspecton of the underlyng fundamentals reveals that ths s not necessary. Frst, f
23 coalton S s not externally stable aganst accesson of player j, then coalton S {j} s nternally stable wth respect to a wthdrawal of j. Ths follows smply from the defnton of stablty (see subsecton 2.1). Second, we know from above that f S {j} s nternally stable wth respect to a wthdrawal of j, t s also nternally stable for all other members of S {j} under OPTS. Thrd, due to superaddtvty and postve externaltes, global welfare of coalton S {j} s hgher than global welfare of coalton S. Thus, we do not need to worry about external stablty from a global pont of vew. If a coalton S s not externally stable, then there s a larger coalton wth hgher global welfare that wll be stable. In partcular, we can conclude that the coalton wth the hghest global welfare among all PISC, say S *, s also externally stable. (If * S were not externally stable, then there would exst a larger PISC wth hgher global welfare, volatng the ntal assumpton that S * generates the hghest global welfare.) To sum up, any transfer scheme that belongs to the class of OPTS leads to the same set of nternally and externally stable coaltons. Thus, results are robust and ndependent of specfc dstrbutonal weghts. Moreover, any OPTS explots the full potental of self-enforcng cooperaton. The coalton wth the hghest global welfare among the potentally nternal stable coaltons wll be nternally stable and externally stable and hence stable. The mportance of these fndngs are evdent from Table 2 and 3. In our applcaton, the three smple transfer schemes lead to very dfferent equlbra. Under the smple transfer schemes, the Nash Barganng soluton generates the hghest global welfare (wth 68.2 percent of total maxmum welfare), whereas OPTS acheves 94.5 percent of total maxmum welfare for coalton no. 5 {USA, EU, CHN, ROW}, whch s the coalton yeldng the hghest global welfare among all PIS coaltons.
24 We fnsh ths subsecton wth two general observatons. Frst, there always exsts a stable non-trval coalton under OPTS. 24 In contrast, under no transfers or smple transfer schemes, a stable non-trval coalton may fal to exst, though ths apples only to the no transfer case n our applcaton wth the CWSM model. Second, there s no general guarantee that all coaltons are ndvdually ratonal under OPTS, whereas ths s the case for all smple transfer schemes. However, ths poses no problem: () all coaltons that are PIS are nternally stable under any OPTS and therefore ndvdually ratonal due to the postve externalty property and () coaltons that are not PIS mght not be ndvdually ratonal but they cannot be stablzed anyway. 25 4.3 Ex-Post Transfer Schemes In ths subsecton, we consder ex-post transfers. Ths means that after a coalton has formed, transfers are used to modfy the status quo. The status quo s a stable coalton that has emerged from the coalton formaton process based ether on no transfers or on some ex-ante transfer scheme. 26 In our applcaton, the status quo s represented by the stable coaltons lsted n Table 2 and 3. The status quo can be modfed usng transfers to expand a coalton S. Followng Carraro and Snscalco (1993), we cte two cases. In the frst case, a coalton S uses transfers to expand ts agreement by brbng outsders to jon the coalton (subsecton 24 25 26 Due to superaddtvty, all coaltons wth two members are nternally stable under OPTS. If one of them s externally stable, the clam s obvous. If none of them s externally stable, then there exst larger coaltons that are nternally stable. Agan, f they are externally stable, the clam s confrmed and f not, then there are even larger coaltons that are nternally stable. The argument contnues, notng that at least the grand coalton s externally stable by defnton. Ths explans why n the column denoted by #IR n Table 2, no exact numbers can be gven under OPTS - ths would requre us to assume a partcular set of weghts. It wll become evdent below that our arguments also apply to a wder nterpretaton of the status quo, whch also ncludes non-stable coaltons.
25 4.3.1); n the second case, an outsder j S uses transfers to brbe another outsder k S to jon coalton S. Agan, we mpose budget neutralty, meanng that transfers must balance. 4.3.1 Expanson of Coaltons Through Internal Means The standard procedure to analyze the expanson of coaltons through nternal means s to pck a stable coalton (see Botteon and Carraro, 1997). For nstance, n the case of the Nash Barganng soluton, one may pck coalton no. 16. Subsequently, we check to see whether expanson of coalton S s possble, where current members of S compensate an outsder j for jonng ther coalton. It can be argued that expanson s possble f and only f 1) the expanson consttutes a Pareto-mprovement to all members of S and 2) the enlarged coalton S {j} s nternally stable. The frst requrement follows from the presumpton that current members of S wll only brbe outsder regon j to jon f they are better off once t does so. The second requrement smply follows from the defnton of stablty. The frst requrement means that S: v(s {j}) + t v(s) (9.a) v(s j {j}) + tj v(s) j (9.b) and the second requrement that S: v (S {j}) + t v (S {j}\{}) (10.a) v(s j {j}) + tj v(s) j (10.b) must hold where typcally t 0 and t j 0. By addng (9.a) and (9.b), summng over all regons S {j} nvolved n the expanson and notng that t S {j} 0, we get = v(s {j}) v(s). (11) S {j} S {j}
26 Condton (11) s a necessary condton for (9. a) and (9.b to hold and may be called Potentally Pareto-Improvement (PPI). However, by consultng Defnton 1, t s evdent that ths condton s nothng else than the condton of superaddtvty. Snce superaddtvty holds n our global emsson game (as n many other models), PPI s a non-bndng constrant. A smlar manpulaton of the second requrement reveals that a necessary pre-requste for condton (10.a) and (10.b) to hold s v(s {j}) v(s {j}\{}) (12) S {j} S {j} whch s nothng other than the condton of potental nternal stablty (PIS). Hence, expanson from coalton S s possble f there exsts a coalton S {j} that s PIS. Gven these remarks, the analyss of coalton expansons s straghtforward snce all theoretcally and emprcally relevant nformaton s already known from the prevous subsecton 4.2 on ex-ante transfers. More specfcally, we can argue as follows. Whch coaltons qualfy as potental canddates from whch expanson starts? All coaltons that are PIS and whch are ndcated n bold n Table 2 under OPTS. In contrast, under smple transfer schemes, not all potental canddates are known. From whch of the potental canddates s expanson actually possble? From all that are not externally stable because ths means that coalton S {j} s PIS. In contrast, under a smple transfer scheme, we cannot conclude that f S s externally unstable, then S {j} s nternally or potentally nternally stable. Of course, f we know that f S {j} s nternally stable, S {j} s PIS and hence an expanson from S to S {j} s possble. However, f S {j} s not nternally stable, we cannot conclude anythng under a smple transfer scheme, so we are requred to make the addtonal check (12), namely whether S {j} s PIS.
27 Fnally, and probably most mportantly: should we be concerned about expansons from a global welfare pont of vew? Not really! The coalton wth the hghest global welfare among PISC s nternally and externally stable as we argued n subsecton 4.2. Hence, no expanson va nternal means s possble from ths coalton. Thus, the ntroducton of the concept of optmal transfer schemes renders the analyss of ex-post transfers va nternal means redundant. As regards expanson va nternal resources for our data set, t follows that we cannot do better than coalton no. 5. 4.3.2 Expanson of Coalton by External Means We now turn to the queston of whether the expanson of a coalton S s possble through external means. Ths means that an outsder k S brbes another outsder j S to jon coalton S. Stable coaltons for whch expansons va nternal means are not possble are the best, although not exclusvely, potental canddates for expansons va external means. 27 From the prevous subsecton, we know that the condton of Pareto-mprovement s not bndng n the context of superaddtvty. Therefore, we can concentrate on the condton of potental nternal stablty. By assumpton, we know that f S s nternally and externally stable, then under OPTS, S {j} s not PIS. Consequently, expanson s only possble f and only f the enlarged coalton receves suffcent transfers to compensate for the lack of PIS and, n addton, the external player s better off despte provdng these resources. That s, the condtons: v (S {j}) + t v (S {j}\{}) (13.a) S {j} S {j} S {j} v k(s {j}) + tk v k(s) (13.b) 27 Indeed, as long as expanson va nternal means s possble, outsders wll beneft for free from expanson through postve spllovers, knowng that expanson s n the nterest of all current members of coalton S.