2011/94 The Kyoto Protocol, the Copehage Accord, the Cacu Agreemets, ad Beyod: A Ecoomic ad Game Theoretical Exploratio ad Iterpretatio Parkash CHANDER Hery TULKENS
CORE DISCUSSION PAPER 2011/51 The Kyoyo Protocol, the Copehage Accord, the Cacu Agreemets, ad beyod: A ecoomic ad game theoretical exploratio ad iterpretatio Parkash CHANDER 1 ad Hery TULKENS2 October 2011 Abstract The paper is ot iteded for game theorists uless they are iterested i learig how their theories, ad the theory of evirometal games as developed i a forthcomig book, are beig used for studyig the curret problem of climate chage Similarly for ecoomists I geeral, the presetatio is addressed to those who have a iterest i seeig how theory ca shape policy i the area of climate chage After a summary presetatio of the relevat features of the Protocol, followed by the sketchig out of a ecoomic model servig as support for the theoretical costruct, we cosider a series of aspects of it such as referece emissios, efficiecy ad stability, competitive tradig, desirability of free trade i emissios ad the clea developmet mechaism, ot to defed it ad idepedetly of the subsequet developmets, but rather as a bechmark for uderstadig the various issues cocerig the climate chage problem i geeral The, we exted this exercise to a appraisal of the situatio of the world climate regime that is curretly prevailig, after the Protocol has etered ito force Fially, we discuss four aspects of the world climate regime that is likely to prevail after the expiry of the Kyoto commitmet period 2008-2012 Our message is a o-covetioal oe, compared with the commo wisdom of commetaries of the Kyoto Protocol ad of its follow-ups It is ispired by research o the foudatios of iteratioal cooperatio i geeral ad o climate chage i particular Keywords: iteratioal evirometal agreemets, climate chage, Kyoto Protocol, applied game theory, applied microecoomics JEL Classificatio: Q540, Q58, F020, D7, C7 1 Natioal Uiversity of Sigapore Uiversité catholique de Louvai, CORE, B-1348 Louvai-la-Neuve, Belgium E-mail: herytulkes@uclouvaibe 2 Provisioal versio of a chapter to appear i A Theory of Evirometal Games, by Parkash Chader ad Hery Tulkes, Oxford Uiversity Press, forthcomig, 2012 This paper presets research results of the Belgia Program o Iteruiversity Poles of Attractio iitiated by the Belgia State, Prime Miister's Office, Sciece Policy Programmig The scietific resposibility is assumed by the authors
2 The Kyoto Protocol, the Copehage Accord, the Cacu Agreemets ad beyod: A ecoomic ad game theoretical exploratio ad iterpretatio Parkash Chader ad Hery Tulkes Outlie Itroductio 3 1 Mai features of the Protocol 5 2 A basic model to deal with the ecoomic issues at stake 6 3 A world treaty i the makig 7 31 Referece emissios 7 32 Efficiecy ad coalitioal stability: the role of trasfers10 33 Competitive emissios tradig i lieu of trasfers 11 34 Agreeig o referece emissios 13 35 Coalitioal stability of the tradig equilibrium 15 36 Desirability of free trade i emissios16 37 The clea developmet mechaism as a alterative form of emissios tradig18 4 Appraisig the first commitmet period 20 41 The post-ratificatio situatio 21 42 A game theoretic iterpretatio 21 5 Post- Kyoto prospects: Copehage, Cacu ad the road ahead 24 (i) Time periods 25 (ii) The ature of strategies: cap ad trade vs commad ad cotrol, atioal vs sectoral, emissios vs temperature chage 25 (iii) A fragmeted vs global world climate regime27 (iv) The participatio of developig coutries 29 Refereces 32
3 Itroductio As the title suggests, this paper iterprets the situatio created by the Kyoto Protocol ad reflects o its likely successors i the light of the theory of evirometal 4 games itroduced ad fully developed i a forthcomig book Callig upo both positive ad ormative ecoomics, it aalyzes the issues at stake i the curret iteratioal egotiatios o climate chage The paper is meat maily for practitioers ad makers of policy o climate chage It is writte i a style that is accessible eve to those who may ot wat to master the theory It is self-cotaied ad refereces to the material i the book are itetioally kept at the miimum 5 The egotiatios o climate chage, that have bee takig place sice the late 1980's withi the Uited Natios istitutios, are obviously a worldwide process, judgig by 6 the legth of the list of coutries which have take part i the successive meetigs But these egotiatios, prior to the Kyoto meetig, had led oly to a "framework covetio", siged i 1992 i Rio de Jaeiro, that was little more tha a declaratio of 7 itet The real issue the was: will the cotiuig egotiatios evetually lead to a sustaiable agreemet bearig o effective actios that is also worldwide? Or will they lead to a breakig up of the coutries ito idepedet separate blocks each actig or ot actig at all to the best of its ow iterests? The Kyoto Protocol, siged i December 1997, has bee a major developmet i the post-rio evolutio of these egotiatios Its importace lies maily i the fact that it requires some coutries to take effective actios that would become bidig o them oce they ratify it 4 A Theory of Evirometal Games, by Parkash Chader ad Hery Tulkes, Oxford Uiversity Press, forthcomig, 2012 5 For a thorough accout of the scietific evidece o the state of the problem, the reader is referred to the assessmet reports issued by the Itergovermetal Pael o Climate Chage, refereced i the bibliography as IPCC 1990, 1995, 2001, 2007 The egotiatios themselves take place i a body created by the Geeral Assembly of the Uited Natios i 1992 uder the ame of Uited Natios Framework Covetio o Climate Chage (UNFCCC) ad established i Geeva 6 Accordig to the relevat UNFCCC websites of October 2009, 165 coutries were preset at the time of sigig of the 1992 Covetio i Rio, 84 were preset at the December 1997 Coferece of the Parties (COP) 3 to sig the Kyoto Protocol, ad 192 were preset at the December 2009 COP 15 held i Copehage 7 It should be metioed that the little more metioed above is far from beig egligible as far as the future was cocered: for the implemetatio of ay policy, a essetial ad prelimiary compoet is that emissios be kow To that effect, the sigatories to the Covetio committed themselves to submit iformatio regardig ivetories of their emissios, aually for the coutries listed i Aex 1, less frequetly for the others A UN admiistratio has bee set up, located i Geeva ad Bo, which is i charge of receivig, reviewig, compilig ad publishig atioal commuicatios cotaiig these ivetories (which did ot exist before) as well as other reports o actios take to reduce the emissios It also orgaizes the successive COPs
4 After a summary presetatio i Sectio 1 of the mai features of the Protocol that are relevat for our aalysis, we sketch out i Sectio 2 the ecoomic model that serves as the basic support for our theoretical costruct We the proceed i two stages First, takig the Protocol as it was siged, we cosider i Sectio 3 a series of its characteristics, features ad properties such as referece emissios, efficiecy ad stability, competitive tradig, desirability of free trade i emissios ad the clea developmet mechaism as a form of tradig Idepedetly of the subsequet developmets cocerig the actual implemetatio of the Protocol, we use it as a bechmark for uderstadig the various issues cocerig the climate chage 8 problem i geeral Our theoretical referece had led us to offer at the time a essetially costructive view of the Protocol That view still ispires our reewed presetatio here It remais i cotrast with more critical views offered by other 9 commetators I Sectio 4, we exted this exercise to a appraisal of the situatio of the world climate regime that has bee actually prevailig durig the first commitmet period 2008-2012 i view of the subsequet o uaimous ratificatio of the Protocol Sice the Protocol does ot require all coutries to commit to achieve quatified reductios of their emissios, a list of the parties which agreed to reductios of their emissios 10 appears as Aex B to the Protocol The role of the other coutries i the agreemet, although ot igored, is less precisely specified Therefore, a cetral questio is whether the Kyoto Protocol is to be cosidered as just a Aex B agreemet, or is it to be see, after further thought ad beyod the appearaces, as a worldwide agreemet? I the two Sectios 3 ad 4 we defed ad substatiate the secod thesis Fially, i Sectio 5 we discuss the world climate regime that is likely to prevail after the expiry of the commitmet period 2008-2012 ad the ature of egotiatios that may lead to it, give the Copehage 2009 Accord ad its follow up 8 I a paper writte ad circulated i 1998 It was evetually published as Chader, Tulkes, va Ypersele ad Willems (2002) 9 For istace, Nordhaus ad Boyer (1999) have argued that the strategy behid the Kyoto Protocol has o groudig i ecoomics or evirometal policy The approach of freezig emissios at a give level for a group of coutries is ot related to a particular goal for cocetratios, temperature, or damages Nor does it bear ay relatio to a ecoomically orieted strategy that would balace the costs ad beefits of greehouse-gas reductios 10 Aex B to the Kyoto Protocol is distict from Aex I to the Rio Covetio but both essetially list the OECD coutries, the former Soviet Uio coutries, ad the Easter Europea ecoomies i trasitio The group is ofte referred to as the developed coutries
5 1 Mai features of the Protocol 11 Let us briefly ote the mai features of the Protocol that are importat from the poit of view of our aalysis: (i) The Protocol proposes dated quotas of yearly emissios, expressed i percetages of 1990 emissios, for Aex B coutries, to be met o average over the period 20082012 (ii) It proposes the priciples of (a) emissio tradig by coutries (or by their etities) ad of (b) joit implemetatio by Aex B coutries (iii) It proposes a clea developmet mechaism (CDM) as a way to ivolve the oaex B coutries (especially developig oes) i some particular form of joit implemetatio ad emissio tradig (iv) It allows trade i emissios oly amog those coutries which ratify the Protocol It is also proposed that trade i emissios will ot be allowed with coutries that do ot fulfill their obligatios uder the Protocol We may also ote some of the features that the Protocol does ot have: (i) The Protocol does ot set targets i terms of the accumulated stock of greehouse gases Its object is ot a trajectory of stock of greehouse gases, but it is emissio flows per year averaged over the commitmet period (ii) No explicit emissios ceiligs have bee proposed for o-aex B coutries ad such ceiligs, if at all, have to be egotiated i future rouds (iii) The parties to the Protocol are expected to eforce the commitmets made by them withi their ow coutries But the text does ot specify sactios if a ratifyig coutry does ot fulfill its obligatios uder the Protocol, except for the above provisio o beig excluded from emissio tradig 11 I Kyoto, the text of the protocol was adopted uaimously by the delegates of the 84 coutries that participated i the egotiatios Sigig of the text by govermets ad ratificatio by parliamets was to take place later o The Protocol was to eter ito force oly if 55 coutries, represetig 55% of the world total emissios ratified it This occurred i February 2005, but ratificatios by more coutries cotiued ad by October 2009, 189 coutries had ratified the Protocol I the meatime, the US, uder the Bush admiistratio, decided ot to ratify, that is, ot to submit the Protocol for ratificatio to the US Cogress
6 However, a compliace regime, icludig details of sactios for o-compliace, has bee set up i subsequet egotiatios ad evetually established by the Marrakech Accord of 2001, which is bidig o all ratifyig coutries 2 A basic model to deal with the ecoomic issues at stake Cosider the coutries of the world (idexed by i = 1,, ) each of which ejoys a aggregate cosumptio level xi, equal to the aggregate value of its productio activities yi mius damages Di which cosist of lost productio due to global 12 pollutio The productio activities of coutry i are described most simply by a icreasig ad strictly cocave productio fuctio yi = gi (ei ) where ei is the fossil fuel 13 eergy iput Assume that the uits have bee so defied that a uit of fossil fuel use geerates a uit of emissios as a by-product The emissios of coutry i are thus equal to ei Accordigly, gi!(ei )!!(= dgi (ei ) / dei ) is the margial product of fossil fuel eergy or the margial cost of abatemet, depedig o the cotext Damages i each coutry deped o the total emissios of all coutries, ie, o a icreasig damage cost fuctio Di = di (! e They are represeted by i =1 i! e ), which for simplicity is take to be j =1 j 14 liear Each coutry's et output is thus give by the expressio xi = gi (ei )! di " e j, (1) j =1 where di > 0 is the damage per uit of emissios or, equivaletly, the beefit per uit of abatemet of coutry i Igorig distributioal issues, the optimal world cosumptio is equal to the maximum of! x with respect to the variables e1, e Let (e1!,, e! ) be the vector i=1 i of emissios of the coutries that achieve such a world optimum These are obtaied as a solutio to the first order coditios for a maximum, ie, gi!(e ) = " d j,i = 1,, * i 12 (2) j =1 Several studies give estimates of these damage costs (see eg Fakhauser (1995), Nordhaus ad Yag (1996)), Ster (2006) ad Tol (2009)) Accordig to some estimates, damages for developig coutries as a percetage of GDP from a hypothetical doublig of CO2 cocetratio are substatially larger tha for developed coutries The mai reasos for the high estimates for developig coutries are health impacts ad the high proportio of global wetlads foud i these coutries The estimates, however, vary widely 13 Despite developmet of alterative sources of eergy, more tha 95% of world eergy still comes from fossil fuels 14 Numerical estimates of damages i some regios of the world are give i Table 1 below
7 Thus, at the world optimum, the margial abatemet cost of each coutry must be equal to the sum of margial damages of all coutries Notice that the world efficiet emissios are idepedet of the actual or curret emissios of the coutries They deped oly o the total margial damage! j =1 d j of all coutries15 I our iterpretatio, we assume that egotiatios o climate chage aim, at least i priciple, at achievig world efficiet emissios Theory however teaches us that attaiig this goal may be jeopardized, that is, a agreemet o efficiet emissios may be ustable, if for each coutry the costs ad beefits are ot properly balaced However, the theory also shows that appropriately desiged trasfers betwee coutries ca remedy for that We show i Sectio 3 that a system of tradable permits with iitial allowaces properly specified ca play the same role as such trasfers We therefore argue i the sectios to follow that the Kyoto Protocol, thaks to its cap ad trade architecture ad with appropriately selected referece emissios, ca be see as a step i the directio of a efficiet ad stable regime for the world climate, ad that a sequece of such steps ca ideed lead the coutries of the world ultimately to a efficiet ad stable trajectory of emissios ad cosumptios 3 A world treaty i the makig 31 Referece emissios How does a coutry decide how much to emit? Low emissios imply low productio accordig to the fuctio gi, whereas high emissios etail high damages accordig to the fuctio Di Followig classical ecoomics reasoig, we argue i Chapter 3 that each coutry ca achieve its domestic optimum by maximizig with respect to ei its cosumptio level xi as defied i (1), takig as give all variables with j! i If all coutries adopt such behavior, a Nash equilibrium betwee coutries prevails, which i the framework of the above basic model cosists of the vector of 16 emissios such that gi!(ei ) = di, i = 1,, 15 (3) However, the productio fuctios gi may chage over time because of chages i techology ad/or i productio capacity Cosequetly, the world efficiet emissio levels may also chage eve if the margial damages remai uchaged 16 Uiqueess of this vector is esured uder our assumptios of strict cocavity of the fuctios gi ad liearity of the fuctios Di
8 We ote two characteristics of this Nash equilibrium: (i) the equilibrium emissios (e1,, e ) are clearly ot equal to the world efficiet emissios (e1!,, e! ), as ca be see by comparig (2) ad (3), ad (ii) ei > ei* for each i, sice gi is cocave ad! j =1 d j > di for each i Thus, the world efficiet emissios are lower tha those prevailig at the o-cooperative Nash equilibrium Fulfillmet of coditios (3) that characterize the Nash equilibrium requires domestic policies that ivolve either a eergy tax or appropriately priced pollutio permits such that the eergy price icludig the tax or the permit price be equal to the domestic margial damage cost Such domestic policies, which are atioally ratioal, are ofte called o regrets policies However, there is little empirical evidece to support that the coutries do ideed decide their emissio levels i this ratioal maer If the firms i a coutry have strog lobbyig power, they may be able to ifluece their govermet to keep the 17 eergy prices low Sice profit maximizatio by firms implies equality betwee the! margial product ad the price of eergy, this will lead to emissios ei which are higher tha! ad such that gi!(ei ) < di, thus prevetig the atioally ratioal policy from beig adopted If the firms ad the govermet i each coutry behave i this maer, a differet equilibrium - also o-cooperative i ature - results, called the "market solutio" by Nordhaus ad Yag (1996) or "busiess-as-usual" by others Aother reaso why a atioally ratioal policy may ot be followed is that firms i a coutry may simply ot be profit maximizers, as is the case with large public sector eterprises i some o-market ecoomies I such cases, the domestic equilibria are either of the "atioally ratioal" or of the "busiess-as-usual" type, ad eergy prices do ot iduce ay well defied emissio policy - except for a geerally low cocer for efficiet use of eergy I sum, at least three types of coutry behavior are possible But whatever be a coutry s behavior, if its firms maximize profits ad markets are competitive, its margial abatemet cost must be equal to the (average) domestic fossil fuel price i real terms Give the strict cocavity of the productio fuctio, it follows that the higher the domestic fossil fuel price, the higher the margial cost of abatemet As see 18 from Table 1 below such a relatioship ideed holds (except i case of Chia, where, 17 Not just firms: other ecoomic agets may do the same I some coutries, govermets subsidize fuels like kerosee used by the poor 18 This is a expaded versio of Table 21 i Chapter 2 i that two more colums have bee added
9 19 as is kow, state owed firms do ot ecessarily maximize profits) I particular, the eergy prices i the US are systematically lower ad so is the margial abatemet cost Moreover, for the three market ecoomies of the US, the EU, ad Japa, the higher the 20 eergy prices, the higher the margial abatemet costs For the other coutries, we caot say much, ot oly because of lack of data, but also because they are either omarket or less developed ecoomies, or both The margial abatemet cost of the US is low compared to that of the EU or Japa, it is ext oly to that of Chia, ad sigificatly below that of Idia Sice the margial damage cost of the US, which is the largest ecoomy i the world, caot be lower tha, say that of the EU, this suggests that the US emissios are determied by the Table 1 Retail prices (i US$ per uit) of idustrial fossil fuels, margial abatemet ad damage costs i some regios *Source: Eergy Prices ad Taxes 1996 **Source: Ellerma ad Decaux (1998) ***Source: Fakhauser (1995) 21 "busiess-as-usual" policy rather tha by optimizatio at the atioal level O the other had, domestic oil prices are kept high i Idia by imposig import tariffs ot out of cocer for the eviromet but to avoid a adverse balace of paymet The last colum of Table 1 presets a educated guess about the type of domestic equilibrium that is likely to be prevailig i each coutry/regio 19 The margial cost of abatemet may seem exceptioally high i case of Japa, but this is because of its large depedece o atural gas, price of which is relatively high, ad less o coal ad oil 20 21 Coal i Japa is a oticeable exceptio; but its use there is cosiderably lower This is clearly a case of govermet, ad ot market, failure
10 32 Efficiecy ad coalitioal stability: the role of trasfers Let (e1,, e ) be some vector of referece emissios They may be the Nash equilibrium or the busiess-as-usual emissios Or worse, they may be the outcome of a geerally low cocer for the efficiet use of eergy I either case, the referece emissios are likely to be higher tha the world efficiet emissios Reducig the emissios from the referece levels to the world efficiet levels requires each coutry i to reduce its emissios by ei! ei* As this etails abatemet cost, ie, gi (ei )! gi (e1" ), ad beefits, ie, di " j =1 (e j! e*j ), the latter should exceed the former for each i to esure that the emissio reductios be agreed upo volutarily by all coutries Now this is ulikely to be the case: some coutries may have high abatemet costs ad low beefits, while others may have low abatemet costs ad high beefits This is oe of 22 the ratioales behid the scheme of trasfers specified by the followig equatio: Ti = {gi (ei )! gi (ei* )}! di " dj { j =1 j =1 } " g j (e j )! " g j (e*j ),i = 1,,, (4) j =1 where Ti > 0 meas a receipt by coutry, while Ti < 0 meas a paymet by i Its ecoomic sigificace is as follows: the first expressio withi braces o the right is equal to coutry i s total abatemet cost, ad the secod expressio withi braces is equal to the world s total abatemet cost abatemet costs which i either case are those etailed by the move from the referece emissios to the world efficiet oes The scheme thus requires coutry i ot to bear its ow abatemet cost gi (ei )! gi (e1" ) but to bear istead a damage-weighted proportio, di / abatemet cost Clearly,!! j =1 d j, of the world s total T = 0, which esures a balaced budget if a i =1 i iteratioal agecy were established to implemet the scheme Most importatly, the mai virtue of the above scheme is that, if implemeted together with the efficiet emissio levels (e1!,, e! ), it guaratees that beefits after trasfers exceed costs for all coutries, be they cosidered idividually or after formig 23 coalitios of ay kid Briefly stated, the solutio so described ejoys the properties of idividual ad coalitioal ratioality Not oly each coutry is idividually better off, but 22 This formula is adapted to the preset cotext from the cetral equatio (15) i Chapter 4 of the aouced forthcomig book It was origially itroduced i Chader ad Tulkes 1995 ad 1997 23 The proof of this property, which is cetral to our theory, results from establishig that, for the cooperative game associated with the evirometal ecoomic model here uder discussio, optimal world emissios together with the said trasfers costitute a solutio i the core of that game
11 also each coalitio of coutries is better off compared to what they would get by adoptig ay alterative arragemet amog themselves i terms of emissios ad trasfers Notice the role played by the referece emissios (e1,, e ) i the calculatio of the trasfers (T1,,T) I our book, we oly assume the referece emissios to be equal to the Nash equilibrium emissios ad show that together with world efficiet emissios the scheme ejoys idividual ad coalitioal stability But what if the referece emissios are ot equal to the Nash equilibrium emissios? I particular, if these are equal to the busiess-as-usual emissios of the type discussed above? It turs out that the core-theoretic property of the scheme is robust with regard to the referece emissios If (e1,, e ) are equal to the busiess-as-usual emissios, the the correspodig trasfers (T1,,T ) have the same game theoretic properties as whe they are equal to the Nash equilibrium emissios This is see ituitively as follows: (a) the busiess-as-usual emissios are geerally higher tha the Nash equilibrium emissios, ad (b) give (a) the payoff that a coalitio ca achieve for itself is lower, sice the emissios of members ot i the coalitio are higher Therefore the core is larger ad icludes more imputatios The first row of Table 2 provides a example of a vector of referece emissios These have bee estimated by Ellerma ad Decaux (1998) o the basis of MIT s EPPA multi-regioal ad multi-sector computable geeral equilibrium model of ecoomic activity, eergy use ad carbo emissios We use such estimated emissio levels at several stages of our argumets below ad shall for obvious reasos refer to them as the busiess-as-usual emissios 33 Competitive emissios tradig i lieu of trasfers Ulike the scheme of trasfers specified i (4), the Kyoto Protocol does ot propose ay trasfers amog the coutries It oly proposes ceiligs or caps o the emissios of some coutries, ad these caps are probably ot equal to the world efficiet emissios Yet, as we argue below, the caps o emissios of the Protocol, together with the trade that they iduce, ca be iterpreted as a scheme of trasfers ad therefore its whole architecture as a step towards reachig emissios that would be both world efficiet ad coalitioally stable To see this, we ow redefie the above scheme of trasfers i terms of emissio quotas ad trades This requires us to first itroduce the cocept of a competitive emissios tradig equilibrium
12 A competitive emissios tradig equilibrium with respect to emissio quotas ( e10,, e0 ) is a vector of emissios ( e 1,, e ) ad a price!ˆ > 0 (expressed i uits of the cosumptio good per uit of emissios) such that for each coutry i = 1,,, e i = arg max ( gi (ei ) +!ˆ (ei0 " ei )), (5) ad i =1 i =1! e i =! ei0 (6) Assumig a iterior solutio, the first order coditios for maximizatio imply gi!(e i )= "ˆ,!!i = 1,, This implies that competitive trade i emissios eables the coutries to relocate the productio ad emissio activities so as to maximize their! total output while keepig their total emissios restricted to defiitio! 0 i =1 i e, sice by e =! i =1 ei0 ad gi!(e i ) = g!j (e j ) for all, i, j = 1,, i =1 i I a competitive emissios tradig equilibrium, the coutries trade i part or all of their pollutio rights (which are equal to their emissio quotas ( e10,, e0 )), at a give market price, ad at that price the demad ad supply of pollutio rights are equal For each i the amout!ˆ (ei0 " e i ) represets the value of paymet, i uits of the cosumptio good, for the purchase of pollutio rights at the world market price if (e! e i ) is egative, or receipt from the sale of pollutio rights if (e! e i ) is positive 0 i 0 i Let us ow defie emissio quotas (e10,, e0 ) from the world efficiet emissios (e1*,, e* ) ad the referece emissios (e1,, e ) such that for each coutry i (ei0! ei* )" d j = { gi (ei )! gi (ei* )}! j =1 di " dj { j =1 j =1 } " g j (e j )! " g j (e*j ) (7) j =1 The left had side of this expressio is what coutry pays (or receives) if it buys (sells) pollutio rights i amout (ei0! ei* ) at price! " * # j =1 d j I view of (2),! * = gi"(ei* ) = g"j (e*j ),i, j = 1,, Which meas that (e1*,, e* ) ad are othig but the competitive emissios tradig equilibrium relative to the pollutio quotas advocated above as (e10,, e0 ) Ad the right had side is equal to the trasfer sufficiet to iduce coalitioal stability of the world efficiet emissios Note that while the world efficiet emissios (e1*,, e* ), as defied i (2), are idepedet of the referece emissios (e1,, e ), the pollutio quotas (e0,, e0 ), as
13 defied i (7), are ot I fact, sice the world efficiet emissios are idepedet of the referece emissios ad thus fixed, there is a oe-to-oe correspodece betwee (e1*,, e* ) ad (e1,, e ) This meas that if the coutries are agreeable to the referece emissios (e1,, e ), the they should also be agreeable to the assigmet of pollutio quotas (e10,, e0 ) ad competitive trade i emissios, sice by defiitio these would ot oly lead to the world efficiet emissios (e1*,, e* ), but also to trasfers that make each coutry or coalitio of coutries better-off relative to the referece emissios ad cosumptios This shifts the argumet from a agreemet o pollutio quotas to a agreemet o referece emissios (e1,, e ) 34 Agreeig o referece emissios However, reachig a agreemet o referece emissios might ot be easy For the followig two reasos First, the curret Nash or busiess-as-usual referece emissios (e 1,, e ) that determie the pollutio quotas (e10,, e0 ) ad the trasfers (T1,,T ) may be cosidered ufair, especially by those coutries which are i the early stages of their ecoomic developmet They curretly have comparatively low emissios, while the emissios of developed coutries are high I the future, whe they will have developed, the curretly developig coutries will have higher emissios ad they might argue that those should be used as referece emissios istead of the curret oes Thus, the scheme of trasfers, although Paretia (everyoe is better off) with respect to the curret Nash or busiess-as-usual referece emissios, might be cosidered usatisfactory by the developig coutries For istace, as see from the first row of Table 2, Idia s estimated referece emissios are early oe-fourth of 24 those of the US ad substatially less tha oe-third of Chia Obviously, Idia is ulikely to accept such low referece emissios compared to those of Chia ad the 25 US Secod, if the reductios to be achieved i the emissios, ie ei! ei*, are very large (as proposed by some coutries), they are politically ifeasible, at least i the short ru The Kyoto Protocol ca be see to address both issues Sice the emissios of developig coutries i geeral ad of Idia ad Chia i particular have ot bee subjected to ceiligs, their emissios will rise as a result of their ogoig ecoomic 24 Table 2 uses data from the MIT s EPPA model 1998 That model has ot bee updated, but Chia ad Idia have grow faster tha aticipated, especially Chia whose emissios ow exceed those of US 25 The Prime Miister of Idia made a propositio at the G-8 summit held i November 2007 that the developig coutries would ever udertake aythig that does ot match the per capita emissios of developed coutries
14 developmet ad those of the Aex B coutries will fall as a result of abatemets ad remai fixed at the levels agreed upo at Kyoto util at least further egotiatios take place With time the emissios of developig coutries will become comparable to those of Aex B coutries likely to be sooer i case of Chia tha Idia ad these might be the subjected to ceiligs Furthermore, the Kyoto Protocol oly requires relatively small reductios for the immediate future, leavig further reductios to later periods I other words, the Kyoto Protocol is ot icosistet with the ultimate goal of reachig a agreemet o appropriate referece emissios (e1,, e ) i some future roud of egotiatios, typically i the secod or a later commitmet period For reachig a agreemet o referece emissios the coutries may have to first agree o adoptig some equity priciple As discussed above, the curretly cosidered baselies of busiess-as-usual or historically gradfathered 26 emissios are clearly problematic Similarly, the uiform per capita emissios, beig advocated by Idia ad Chia, are also uacceptable: if emissios caot be gradfathered the by the same logic populatio size caot be gradfathered either A scheme of differetial stadards of emissios per uit of GDP is more likely to be acceptable, but it does ot resolve the problem completely As all the ecoomies grow ad their emissios rise, the stadards may have to be revised from time to time ad made more striget 27 Somethig that is time cosistet ad free of ormative priciples is eeded Whatever be the equity priciple for determiig the pollutio rights, it seems ulikely from the figures i the first ad secod rows of Table 2 that the miimal emissio reductios or o-reductios implied by the Kyoto Protocol would be icosistet with it This seems to be especially true i case of Idia, which ulike Chia has rather low emissios What this meas i policy terms is that the developig coutries should ot oppose the Kyoto Protocol ad leave the issue of iitial allocatio of pollutio rights, o which they have repeatedly isisted, to future egotiatios I the meatime, implemetatio of the Kyoto Protocol will ot oly reduce the emissios of Aex B coutries ad thus improve the global eviromet, but will also stregthe the positio of the developig coutries i future rouds of egotiatios as their emissios will cotiue to rise as their ecoomies grow ad become comparable to those of Aex B coutries 26 Historically gradfathered emissios are busiess-as-usual emissios of some fixed year, ot ecessarily of the curret year 27 The iterested reader may wat to refer back to the discussio of this issue i Chapter7
15 35 Coalitioal stability of the tradig equilibrium If each Aex B coutry meets its Kyoto commitmet output is equal to! i =1 gi (ei0 ), which by defiitio is less tha o its ow, the world! i =1 gi (e i ), where s are the competitive tradig equilibrium emissios, as defied i (5) ad (6) I fact, as ca be easily see, competitive emissios tradig allows the coutries of the world to restrict the total world emissios to their aggregate Kyoto commitmet e0 =! 0 i =1 i e at least cost Competitive trade i emissios thus eables the coutries to reduce the world emissios efficietly As see above, each coutry or coalitio of coutries gais from competitive trade i emissios However, this does ot imply that each coutry or coalitio of coutries would be willig to participate i competitive emissio tradig For that to be true we must show further that o coutry or coalitio of coutries ca gai eve more by formig a separate bloc ad tradig emissios oly amog themselves A argumet based o the theory of market games ideed shows that o coalitio of coutries ca be better off compared to the competitive emissios tradig equilibrium by formig a separate bloc Let S! N be a bloc of coutries whose members decide, give their aggregate emissios quota " 0 i!s i e, to adopt some joit policy of their ow such as tradig oly amog themselves or egagig i some other bilateral/multilateral agreemets The maximum payoff of such a bloc of coutries ca obtai is the w(s) = max " gi (ei ) subject to i!s " e = " i!s ei0, (8) i!s i 28 give their aggregate emissios quota Cosider agai (e 1,, e ), the competitive tradig equilibrium emissios relative to 0 i (e,, e0 ) We show that the payoff of members of S uder the competitive equilibrium is ot lower tha their payoff whe they form a separate bloc as defied i (8) This would establish that o coutry or coalitio of coutries will have icetives to form a separate bloc ad ot participate i world-wide competitive emissio tradig 28 We igore the damages because they remai the same, sice the aggregate emissio quota fixed " i!n ei0 is
16 To that effect, we show that % i$s # i"s gi (e i )! w(s) Usig (5), this is equivalet to (gi (e i ) +!ˆ (ei0 " e i )) # % i$s gi (e!i ) where (e!i )i!s is the solutio to (8) Sice " i!s " e! = " i!s ei0, we must show that i!s i gi (e i ) +!ˆ ($ i#s e!i " $ i#s e i )! # i"s gi (e!i ) This iequality is true sice each is cocave ad!ˆ = gi"(e i ) i competitive emissios tradig equilibrium Therefore, gi (e i ) +!ˆ (e!i " e i ) # gi (e!i ), i!s, irrespective of whether (e!i! e i ) is positive or egative This leads to the coclusio that o coutry or coalitio of coutries will have a icetive to form a separate bloc ad ot participate i world-wide competitive emissio tradig Thus, the outcome of worldwide competitive trade i emissios amog the coutries caot be improved upo by the formatio of coalitios of coutries, such as separate tradig blocs We are thereby rediscoverig i fact, just applyig a geeral property of competitive equilibria kow as their "core" property, which says that competitive equilibria belog to the core of a appropriately defied cooperative 29 game 36 Desirability of free trade i emissios While the Kyoto Protocol allows trade i emissios amog the Aex B coutries, it leaves ope the questios of extet ad ature of such tradig Ecoomic ad game theoretic cosideratios ca be further called upo to deal with these issues As to the extet of tradig, that is, the umber of participats i the trade, the market equilibrium theory geerally favors trade amog the largest umber of ecoomic agets This is also implied by the previous argumet agaist the formatio of separate tradig blocs or ay other form of coalitios that restrict trade Ideed, it is ot to the beefit of ay coutry or group of coutries to form a coalitio ad act idepedetly of the other coutries 29 The preset game is a pure market game where exteralities play o role, sice, oce the emissio quotas are fixed, the public good aspect of the problem disappears Oe is left with oly the private goodstype problem of allocatig the emissios betwee the coutries Note, however, that this game represets a productio ecoomy ad ot a stadard pure exchage ecoomy
17 Thus, it is i the world's overall ecoomic iterest that o-aex B coutries, whose emissios are ot subject to quotas, be evertheless allowed to participate i the tradig process We shall argue below that the clea developmet mechaism (CDM) cotais provisios to that effect A policy implicatio is that this mechaism be desiged so as to make it as ope as possible to the largest umber of coutries The fact that o quotas were assiged to these coutries is irrelevat if the full beefits of 30 trade i emissios are to be realized As to the ature of tradig, the same body of theory advocates that the istitutios goverig the trades be desiged so as to esure that they be as competitive as possible competitiveess meaig here that all participats behave as price takers It is ideed oly for markets with that property that efficiecy, coalitioal stability ad worldwide maximal beefits are established Regulatory provisios that restrict competitiveess i the emissios tradig process are thus to be avoided Such as, for istace, provisios allowig for market power to be exerted by some traders so as to ifluece price formatio to their advatage, as well as regulatory cotrols that would impede sufficiet price flexibility; or still, as proposed by some, limitig the quatities that ca be traded As is well kow, the larger the umber of participats, the more competitive the market is likely to be: our argumet favorig a large extet of the market is thus also 31 oe that favors competitio Large umbers are admittedly either the oly way or a sufficiet coditio to esure the competitive character of a market, but they are a powerful factor Table 2 below gives a umerical illustratio of the outcome of world-wide 32 competitive trade i emissios The competitive equilibrium price of emissios estimated to be equal to $2475 per to i 1985 dollars Coutry is a exporter of emissio reductios if ei0 > e i ad a importer if ei0 < e i Coutry 30 is gai from Oe might eve argue that it is similarly irrelevat whether or ot a coutry ratifies the Protocol or has ot met its commitmet uder the Protocol Excludig a coutry from trade i emissios o ay pretext hurts all However, exclusio from trade is the oly threat that ca be exerted agaist a o complyig coutry: the loss so icurred is thus to be see as a cost to isure compliace As to icludig CDM activities takig place i o ratifyig coutries, it may raise accoutig issues i the host coutry However, it has become oly a academic questio, sice all coutries, except the US, have ratified the Kyoto Protocol 31 Our argumet o the role of markets to achieve coalitioal stability is also reiforced by a cetral result i ecoomic theory (Debreu ad Scarf (1963); Edgeworth (1881)) accordig to which oly competitive equilibria are coalitioally stable, if the umber of traders is large 32 Additioal details ca be foud i Ellerma ad Decaux (1998), who also cosider other tradig regimes
18 emissios trade is equal to!ˆ (ei0 " e i ) " (gi (ei0 ) " gi (e i )) if it is a exporter ad gi (e i )! gi (ei0 )! "ˆ (e i! ei0 ) if it is a importer both are positive, sice the price is equal to the margial cost of abatemet at e i ad gi is cocave Exportig coutry will ot gai from trade if it is paid oly its actual cost of abatemet, ie gi ( e i )! gi ( eˆi" ) : all the gais from trade i that case would go to the importig coutries Competitive emissios tradig thus distributes the gais from trade amog the exporters ad importers i exactly the same way as it does i the case of competitive trade i commodities Amog the developig coutries, Chia turs out to be the sigle largest exporter of 33 emissios followed by Idia Amog the Aex B coutries, the US turs out to be the sigle largest importer followed by the EU But all coutries gai from emissio tradig as the umerical example illustrates, ad the gais are substatial for both sides This idicates the eed for cooperatio amog the developed ad developig coutries by istitutioalizig such trade Yet, for several reasos there might be oppositio to such trade from both developed ad developig coutries alike 37 The clea developmet mechaism as a alterative form of emissios tradig For the reasos metioed i Sectio 36, restrictig trade i emissios amog Aex B coutries aloe may affect both Aex ad o Aex B coutries This raises the questio of how to ivolve the o Aex B coutries i emissios trade without 34 havig them committed to ay emissio quotas That seems difficult, but it is ot 35 impossible 33 There is however a practical differece betwee Aex B tradig ad the modelig of global tradig which tries to mimic a perfect CDM, which may implicitly impose omial quotas o o Aex B coutries 33 Oe colleague has expressed this problem as follows: should we allow Mexico to sell permits to the US if it is ot guarateed that Mexico will really reduce emissios accordigly? 34 Oe colleague has expressed this problem as follows: should we allow Mexico to sell permits to the US if it is ot guarateed that Mexico will really reduce emissios accordigly? 35 For example, oe ca calculate the impact of a tax icrease o fossil fuel eergy i a developig coutry ad offer to trasfer to the developig coutry a amout that is equal to the market value of the cosequet reductio i its emissios The recetly proposed uclear agreemet betwee Idia ad the US is a case i poit, as it promises cleaer techologies to help Idia meet its eergy eeds What would be the impact of this agreemet o Idia s emissios ad therefore how much emissio reductios ca the US claim to have imported?
19 I fact, it is the mai purpose of the clea developmet mechaism I essece, 36 trade occurs through certified project activities located i o Aex B coutries The certificatio determies the amout of emissios reductio ( certified uits ) that the project geerates, i compariso to a baselie that specifies what the emissios would be i the absece of the project The amout of the reductio so achieved ca the be sold by the iitiator of the project to ay ecoomic aget belogig to a Aex B coutry, with the certified amouts beig credited to meet the commitmet of the coutry to which the purchasig party belogs The price at which the certified uits are sold ad purchased is determied by supply ad demad for them, which are i tur determied by the supply of project activities ad the demad of those Aex B coutries for which buyig such uits is cheaper tha reducig their ow emissios That competitive coditios prevail i the formatio of this price is as ecessary as i the formatio of the price of the quotas i the emissios tradig scheme of Sectio 36 However, the developig coutries might fear that participatio i ay form of trade i emissios will amout to some sort of acceptace of emissio quotas o their part Developig coutries like Idia ad Chia have ofte expressed the view that the problem of climate chage has bee created by the idustrialized coutries ad therefore it is these coutries which should first reduce their emissios, o matter how, before the developig coutries ca cosider acceptig ay quotas I additio, the clea developmet mechaism is ofte iterpreted by them as a form of trade that distributes the gais from trade etirely to the carbo credit importig (read Aex B) coutry ad oe to the carbo credit exportig (read o 37 Aex B) coutry More specifically, it has bee ofte proposed that rather tha payig the exportig developig coutry the market value at the competitive price, ie!ˆ (ei0 " e i ), the importig coutries may pay oly the actual cost of abatemet, ie gi (ei0 )! gi (e i ), which (give the strict cocavity of the fuctio gi (ei ) ) is strictly less tha!ˆ (ei0 " e i ) This form of trade i emissios ca be give effect by the importig coutries by systematically offerig to cover the cost, ad cost aloe, of abatemet activities i developig coutries o a project - by - project basis But the developig coutries may accept this form of tradig oly if carbo credit importers collude so as 36 37 As per the vocabulary of Article 12 of the Protocol It is iroic that the coutries which geerally extol the virtues of competitive markets should look for other forms of tradig whe it suits them
20 to behave moopolistically Agaist this bias, there is the coutervailig force of competitio amog the buyers, if there are may I the CDM costruct, the determiatio of the baselie is of fudametal importace As with emissios tradig, the referece to it i the operatio of the CDM poits to the fact that the ultimate solutio rests o the determiatio of referece emissios We showed above how these ca lead to well-defied emissio quotas for each coutry, which i tur ca iduce efficiet competitive trades i emissios With the CDM beig part of it, the efficiecy properties of the istitutioal architecture of the Kyoto Protocol are thus much ehaced Fially, besides facilitatig competitive emissios trade amog Aex ad o Aex B coutries which would reduce the burde of Aex B coutries of meetig their Kyoto commitmets, the assigmet of quotas to developig coutries would create stroger icetives for developmet ad adoptio of cleaer techologies by them More geerally, eve regardless of whether or ot the established trade i emissios is competitive, the developig coutries stad to beefit from the implemetatio of the Kyoto Protocol If the Aex B coutries meet their Kyoto commitmets, the iteratioal prices of fossil fuels will fall which would accelerate ecoomic growth i 38 developig coutries The eergy exportig o Aex B coutries, however, might suffer ecoomic losses because of (a) less reveue from eergy exports ad (b) higher prices of eergy-itesive exports from Aex B coutries But other o Aex B coutries such as Idia ad Chia with a differet mix of imports ad exports might be better off, as show by Babiker, Reilly ad Jacoby (2000) 4 Appraisig the first commitmet period We ow wish to cosider how the situatio that has bee prevailig durig the commitmet period 2008-2012 ca be iterpreted ad appraised i the light of the book s theories I the fial Sectio 5, we shall also express some views that these theories ispire us to have o the situatio that may prevail after the expiry date of 2012 38 I fact, the o Aex B coutries would beefit eve more if, as some Aex B coutries have suggested, o trade i emissios were to be established amog Aex B coutries ad each coutry is to meet its Kyoto commitmet o its ow That is so because the Aex B coutries will ot have access to the Russia hot air ad therefore their actual total reductios i emissios will be much larger
21 41 The post-ratificatio situatio By the ed of 2009, the UNFCCC website listed, i its Status of ratificatio report of the Rio Covetio, that 193 member coutries of the Uited Natios, have siged 39 ad ratified the Covetio which had etered ito force o March 21, 1994 With these 193 coutries havig thus take part for more tha 15 years i the implemetatio of the Rio Covetio, our first claim earlier i this paper that the egotiatios o climate chage are a truly worldwide process is obviously verified But, as also metioed at the begiig of the paper, the Covetio has established oly a framework for actio i climate matters Worldwide egotiatios have take place withi this framework betwee the 193 coutries, which have cosisted i defiig, comparig ad evaluatig a large variety of possible courses of actio by the various coutries I other words, they have bee explorig the players strategy sets i the game After some time, the egotiatios evetually led to the Kyoto Protocol, which was siged i 1997 ad later by several govermets, ad subsequetly (ad more importatly) submitted for ratificatio to their coutries respective legislative bodies The official date of etry ito force of the Protocol is February 16, 2005, which is the date at which the required miimum umber 40 of ratificatios by coutries was reached Some additioal coutries ratified it durig the subsequet moths By the ed of 2009, 189 coutries had ratified the Protocol, while oe sigatory-coutry the 41 US has declared havig o itetio to do so 42 A game theoretic iterpretatio The text of the Protocol expresses a collective choice of specific actios to be take by each oe of the 190 coutries which siged it However, due to the o ratificatio by the US, the situatio that prevails after all ratificatios have take place is differet Rather tha the text of the Protocol, it is this factual situatio that we cosider as a outcome of the egotiatios ivolvig the 190 coutries By a outcome we mea what the coutries decide to do, or formally commit themselves to do i terms of their emissios, after ratificatios have take place ad from the momet of etry ito force of the Protocol 39 The o ratifyig coutries beig at that date Adorra ad the Holy See Recall from footote 9 that this is 55 coutries, represetig 55% of the world total emissios i 1990 41 Three coutries, although havig siged ad ratified the Rio Covetio, either siged or a fortiori ratified the Kyoto Protocol These are Afghaista, Sa Mario ad Somalia 40
22 This situatio has a coalitio structure aki to what we call i Chapter 4 (Sectio 42 423) a Nash Equilibrium relative to a coalitio (NERC), i which the coalitio i questio is the set of 189 ratifyig coutries whose joit strategy is what they have committed themselves to do accordig to the provisios of the Protocol The strategy of the oly o ratifyig coutry the US is what emissios it decides to choose itself, which are likely to be higher tha the emissios stated i the text it siged i Kyoto I game theoretical termiology, we thus have prevailig, as the factual situatio for the period 2005-2012, a strategy profile of the 190 players of the whole world, cosistig of (a) joitly agreed upo strategies for the members of the coalitio of 189, ad (b) a idividually decided strategy for oe outsider What do the strategies i this profile precisely cosist of? If we formulate them i terms of levels of emissios, there are three categories of them: (a) For the 189 members of the coalitio of ratifyig coutries: (i) For 37 coutries listed i Aex B of the Protocol, the strategies are the levels of their emissios resultig from the assiged amouts of quatified emissios reductio or limitatio obligatio with respect to 1990 metioed i that Aex; (ii) For the other 152 o Aex B coutries, the strategies are the levels of their emissios resultig from the busiess as usual evolutio of their ecoomies (b) For the o ratifyig coutry, amely the US: The strategy is also the level of its emissios resultig from its busiess as usual evolutio For the coalitio of ratifyig coutries, the time spa of their commitmet is the period 43 2008-2012 The outsider coutry may joi the coalitio at ay time, if it so wishes The NERC thus appears to be a cocept whose structure describes fairly well the situatio prevailig durig the commitmet period 2005-2012 Strictly speakig, the situatio itself might ot be called a equilibrium because oe caot prove it to cosist of best reply strategies i the techical sese; but oe caot claim the opposite 42 This cocept is idetical to the oe itroduced i our earlier writigs of 1995-1997 uder the alterative termiology of partial agreemet Nash equilibrium with respect to a coalitio 43 A few weeks after Presidet Obama s electio, oe US official stated publicly i early 2009: We are back i the game While pleasat to read, this statemet makes little game theoretic sese: o player ca leave a game with exteralities whe these are global sice by defiitio they affect all players I the climate chage game, all coutries of the world are ecessarily i, irrespective of whether ay oe of them is i or out of a possibly existig agreemet