Journal of Public Economics

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1 PUBEC-0330; No of Pages 0 Journal of Publc Economcs xxx (0) xxx xxx Contents lsts avalable at ScenceDrect Journal of Publc Economcs journal homepage Regonal ntatves the cost of delayng bndng clmate change agreements Julen Beccherle a, Jean Trole b, a Mnstère du Développement Durable, France b Toulouse School of Economcs, France artcle nfo abstract Artcle hstory Receved 7 May 00 Receved n revsed form 0 Aprl 0 Accepted 7 Aprl 0 Avalable onlne xxxx JEL classfcaton D6 F5 H3 Q5 The Kyoto Copenhagen Protocols on clmate change mtgaton postponed the specfcaton of bndng commtments to a future negotaton. Ths paper analyzes the strategc mplcatons of delayed negotatons. Whle, as s well-understood, the ncentve to free rde leads to excessve emssons pror to a bndng agreement, the cost of delay s magnfed by players' attempt to secure a favorable barganng poston n the future negotaton. A brnkmanshp, an effort substtuton, a rasng rval's cost effects all concur to generate hgh post-agreement emssons. The paper apples ths general nsght to the ssuance of forward or bankable permts. 0 Elsever B.V. All rghts reserved. Keywords Internatonal negotatons Clmate change Cap trade Bankable permts. Introducton Clmate change s a global ssue n need of a global answer. The frst attempt at an ntegrated approach to mtgaton, the 997 Kyoto Protocol, dd not specfy frm commtments from ratfyng countres to cut ther emssons. The 009 Copenhagen conference was meant to defne the contours of the post-kyoto world. Despte wdespread agreement on the urgency to act, Copenhagen dd not delver an agreement wth bndng commtments to emssons cuts, left the defnton of objectves ther verfcaton to future negotatons. A low-am deal, drafted by a small group of countres led by the US, Chna, Brazl, South Afrca Inda, had to be struck n a hurry to avod returnng home empty hed. It was only taken note of by the assembly. The falure of the Copenhagen negotaton to delver a legally bndng commtment to emssons reductons beyond 0 (the year of expraton of the Kyoto Protocol), has multple orgns. Frst, the lack of measurement enforcement protocols of consensus on The authors are grateful to partcpants at the World Congress of Envronmental Resource Economcs (Montreal, 00) at the College de France conference on Managng Global Warmng (Pars, 00), to Sören Blomqust, Domnque Bureau, Domnk Grafenhofer, Bll Nordhaus, Jean-Perre Ponssard, Nck Stern, two anonymous referees especally to Bard Harstad for very helpful comments on an earler draft. Correspondng author. Tel ; fax E-mal addresses julen.beccherle@developpement-durable.gouv.fr (J. Beccherle), jean.trole@tse-fr.eu (J. Trole). nstruments made t dffcult to even desgn a sustanable agreement. Second, poltcal wll was lackng; ndeed no draft had been serously dscussed by heads of states pror to the conference. Fnally, the negotaton revealed a hgh level of dstrust among countres. The paper argues that extendng the watng game untl Kyoto 3 (say, 00) would have serous consequences, that go well beyond the celebrated free-rdng ncentve. Namely, not only wll countres engage n suboptmal efforts to reduce ther emssons n the next ten years, but they wll also consder how ther behavor wll mpact the outcome of negotatons n 00. We consder a two-perod framework. In perod, each regon of the world chooses a publc polcy, antcpatng the negotaton of a global agreement at date. In the generc verson of the model, ths polcy refers to any nstrument that mpacts the regon's date- welfare It may determne ts date- technologcal feasblty set, ts nstalled base of pollutng equpments, or, n a key applcaton of our theory, the domestc allocaton of property rghts on polluton allowances. The essental feature of the date- polcy choce s that t affects the regon's margnal cost of date- abatement, whch n turn Of course there wll be some progress. Carbon permts markets exst or may be created n Europe, the US, Japan some other developed economes. Emergng countres are takng some acton as well. A mxture of collateral damages (the emsson of SO, a local pollutant, jontly wth that of CO by coal plants), the drect mpact of own producton of CO for large countres lke Chna, the desre to placate domestc opnon avod nternatonal pressure wll all lead to some carbon control /$ see front matter 0 Elsever B.V. All rghts reserved. do0.06/j.jpubeco Please cte ths artcle as Beccherle, J., Trole, J., Regonal ntatves the cost of delayng bndng clmate change agreements, J. Publc Econ. (0), do0.06/j.jpubeco

2 J. Beccherle, J. Trole / Journal of Publc Economcs xxx (0) xxx xxx mples that the regon's date- choce of publc polcy s made wth an eye on the future negotaton. The paper's frst contrbuton s to nvestgate the exact nature of the resultng commtment effect. A natural benchmark s regonal optmzaton or cost mnmzaton. Because the date- polcy affects the date- ncentves for abatement, regonal optmzaton ams at mnmzng the total (ntertemporal) cost to the regon. Cost mnmzaton obtans both n the frst best, n whch a bndng agreement s reached at date, n the complete absence of negotaton. Under delayed negotaton, two extra effects concur to push date- emssons up. A decrease n one's margnal ncentve to abate frst mples that the regon would pollute more, were the negotaton to fal. The brnkmanshp effect works through a reducton n the other regon's payoff when the negotaton fals; t changes the regon's threat pont n the negotaton enables t to extract more of the surplus; t s partcularly potent when the regon has substantal barganng power n the negotaton. Second, the outcome n the negotaton depends on one's own welfare, were the negotaton to fal. Thus a regon's date- polcy s n part guded by ts own welfare when negotatons break down at date. Because emssons are hgher when negotatons break down, the country can afford a lower date- nvestment n polluton control; ths ntertemporal substtuton effect by contrast s most potent when the country's barganng power s weak. These two effects both mply that a delay n negotatng a global agreement ncreases post-negotaton polluton not only the pre-negotaton one. When envronmental damage costs are convex, a thrd strategc effect arses, that renforces the other two by commttng to a hgher polluton level, a regon rases the margnal damage cost of all regons therefore nduces others to cut down on ther emssons. Ths s the rasng the other's margnal envronmental cost effect, or rasng rval's cost effect for short. We show that delayng negotaton always rases date- emssons compared to the frst-best. Indeed, t may even be the case that a delayed negotaton nduces more date- emssons than n the complete absence of negotaton, ths despte the reducton n emssons brought about by the date- agreement. Thus, delayed negotaton may be worse than no negotaton at all. The paper's second contrbuton s to apply these generc nsghts to the ssuance of future allowances to the bankablty of polluton allowances (as embedded n the Waxman Markey bll). In partcular, we predct that regons wll ssue too many forward or bankable allowances. Proponents of regonal cap--trade systems, such as the one exstng n Europe or those that are/were under consderaton n the Unted States a number of other developed countres, take the vew that regonal markets wll jump-start clmate change mtgaton later lead to convergence to a sngle, worldwde clmate treaty. We nvestgate the strategc mplcatons of a delayed agreement n the context of the ssuance of forward allowances; we also show that smlar nsghts apply to the ssuance of bankable permts. In ether case, the regon puts today nto prvate hs allowances that can be used to cover future emssons. Focusng on lnear envronmental damage costs for expostonal smplcty, we frst show that, followng the logc of the Coase conjecture, regons ssue forward allowances nether n the complete absence of negotaton nor n the frst best (n whch the negotaton takes place at date ). By contrast, n the ntermedate stuaton n whch the negotaton s delayed, the brnkmanshp ntertemporal substtuton effects both mply that regons ssue forward allowances whenever date- emssons ncrease wth the number of such allowances. The latter property holds for example f the regons aucton off date- new (spot) allowances face a shadow cost of publc funds; because regons put some weght on revenue, they have a tendency to over ssue spot permts at date, thereby lowerng the prce of carbon. Alternatvely, the government could nternalze only partally the welfare of the holders of forward permts. Or else, the new permts could be dstrbuted for free at date, but the government mght at date negotate domestcally wth a powerful ndustral lobby, whose status-quo welfare s stronger, the larger the number of allowances t receved at date. Ether way, delayed negotatons lead to hgh future emssons through an excessve ssuance of forward or bankable permts, even though they can be retred or fewer spot permts ssued. A poltcal mplcaton of our analyss s that f an ambtous clmate treaty s mpossble today, countres should at least agree to lmt bankng forward-sellng. Further, we show that markets can be merged under symmetrcal condtons, but that the agreement wll otherwse content tself wth a specfcaton of the volume of emssons n mantaned regonal markets. The paper s organzed as follows Secton sets up the generc model. Secton 3 dentfes the brnkmanshp, ntertemporal substtuton, rasng rval's cost effects, derves llustrates the excess polluton result. Secton 4 develops the applcaton to forward allowances bankable polluton permts. Secton 5 concludes... Lterature revew contrbuton Ths paper bulds on several lteratures. Frst, the forward-market applcaton relates to, among others, Allaz Vla (993) Mahenc Salané (004), who nvestgate the dea that forward markets can be used to nfluence rvals. Allaz Vla fnd that f competng frms set quanttes of forward rghts over tme, then they wll sell more than they would n a spot market. Sellng one unt today reduces the compettors' future margnal benefts therefore ncreases the frm's proft. In much of the paper, we abstract from the Allaz Vla (rasng rval's cost) effect by assumng that margnal polluton damages are lnear n total polluton focus on the mpact of negotaton, a queston that s moot n Allaz Vla's olgopoly framework. Laffont Trole (996a,b) study cap--trade polces wth spot forward markets analyze how regulatory commtment flexblty to news can be made consstent. Lke Allaz Vla, these papers however do not consder negotatons among multple regulators/countres, whch s the focus of the current paper. 3 Second, by takng the vew that negotatons take tme, we mplctly study the role of ncomplete contracts the mportance of property rghts allocatons n a context of global externaltes. Our paper thereby bulds on the ncomplete contracts hold up lterature (Grossman Hart, 986; Hart Moore, 990; Wllamson, 985). The common thread wth that lterature s the dea that ex-ante nvestments nfluence the outcome of ex-post negotatons. Our paper does not add to the theoretcal body of knowledge on ncomplete contractng. Indeed the dea that one's barganng power n a future negotaton affects one's ncentve to nvest can be found n Grossman Hart the entre ncomplete-contract lterature. Smlarly, the brnkmanshp effect, accordng to whch a regon may want to harm the other regon's outsde opton, s akn to the ncomplete-contract dea that partes bas ther technologcal choces so as to enhance ther own outsde opton to worsen the other party's outsde opton (e.g. Holmström Trole(99); the lterature on second sourcng Farrell Galln (988), Shepard (987) also makes the pont that outsde optons ought to be manpulated n antcpaton of a future negotaton). Fnally, the rasng rval's cost effect bears resemblance not only wth the forward-market lterature, but also wth the lterature on free-rdng n Of course bankablty has the (well-known) beneft of smoothng the carbon prce when transtory shocks to economc actvty or technologcal progress would make ths prce very volatle. 3 There s also a growng lterature on closed-economy, optmal dynamc multnstrument polces (for example, carbon prce R&D subsdes, as n Acemoglu et al. (009) Grmaud Rouge (008)). Please cte ths artcle as Beccherle, J., Trole, J., Regonal ntatves the cost of delayng bndng clmate change agreements, J. Publc Econ. (0), do0.06/j.jpubeco

3 J. Beccherle, J. Trole / Journal of Publc Economcs xxx (0) xxx xxx 3 mult-perod contrbutons to publc goods, whch emphaszes that current future contrbutons may be strategc substtutes (Admat Perry (987) Fershtman Ntzan (99); for example the latter fnds that forward-lookng behavor results n lower contrbutons to the publc good as partes want to pressure the other partes to contrbute more n the future). Thus, the pont of our paper s to descrbe what mplcatons ncomplete-contract nsghts have for envronmental negotatons. The paper further derves a perhaps unexpected applcaton to the desgn of emssons tradng systems. Thrd, ths paper contrbutes to the growng lterature on clmate change agreements 4 casts some lght on the effects of delayed negotatons on nternatonal clmate change agreements. Our contrbuton s to nclude dynamcs nto the analyss to put forward the potental cost of delayed negotatons. An early paper emphaszng the potental of R&D reducton when nvestments can be held up n future negotatons s Buchholz Konrad (994). The most closely related paper s Harstad (009) who develops a very nterestng analyss of the dynamcs of clmate change agreements. Harstad studes an economy where soveregn countres repeatedly make nvestment emsson decsons. The cost of polluton depends on the total stock of emssons, accumulated over tme. Harstad demonstrates, as we do, that under some condtons short-lastng agreements lead to hgher polluton than no agreement at all. Notably, he establshes ths result n an nfnte horzon model whle we have only two perods. Under some assumptons, 5 Harstad's state space, whch aprorhas (n+) dmensons (the exstng stock of polluton, together wth the technologcal state of each the n countres), collapses to a twodmensonal recursve one, n whch outputs are fully determned by the exstng stock of polluton the latter's evoluton depends on these outputs the global stock of knowledge. We chose to be more general n terms of technologes to allow for asymmetres (n partcular, n our model, whch country s more technology advanced mpacts the contnuaton equlbrum) at the expense of a two-perod analyss. Ths added generalty allows us to nvestgate nterestng polcy nstruments such as forward bankable allowances, whch the Harstad assumptons cannot capture, as well as the consequences of asymmetrc preferences barganng powers. We also dentfy the three effects at stake.. A generc model.. Tmng utlty functons The model has two perods, t=, two regons of the world, =A, B. 6 For notatonal smplcty, wthout loss of generalty, we normalze date- payoffs so that regons do not dscount the future. In perod, regonal authortes (regulators) non-cooperatvely smultaneously choose sngle-dmensonal 7 polcy varables, a for regon. At ths stage a R may st for any date- nstrument avalable to the regulator that affects the regon's date- ncentve to emt pollutants. We normalze a such that a hgher a s less envronment-frendly. For example, a hgh a may correspond to a lax polluton stard, a low nvestment n green technology or a hgh level of ssuance of forward allowances. Thus a n general s not date polluton, although the case of costly adjustment (n whch a s ndeed date- polluton the regon ncurs an adjustment cost related to the dstance between a a ) fts our framework. 4 See e.g., Aldy Stavns (007) Barrett (005). The paper also bulds on the extensve lterature on coalton formaton n nternatonal agreements (e.g., Carraro Snscalco (993)). 5 See Secton 3.3 for a statement of these assumptons. 6 The analyss s generalzed to an arbtrary number of regons n Secton The results carry over to a mult-dmensonal date- acton space, provded that the stard supermodularty assumptons are satsfed (see e.g., Mlgrom Roberts (990)). The negotaton wth the other regon s delayed untl perod (see the dscusson below). The absence of date- agreement mples that the choces of date- emssons are drven by the famlar free-rdng ncentve. Wthout loss of generalty unless otherwse stated, 8 we omt the correspondng analyss for clarty of exposton. At date, the regulators wll agree on second-perod polluton levels a R + n both regons on a sde payment, for example through an allocaton of polluton allowances or drect cash transfers. Whle a can st for any (envronment-unfrendly) polcy that changes regon 's date- emssons ncentves, a denotes the actual level of date- emssons. 9 Regons' date- date- welfares, gross of polluton damages, are denoted U (a ) U (a, a ). These functons are ncreasng n a a respectvely, twce dfferentable. U s twce dfferentable strctly concave n a. Regon 's polluton damage depends lnearly 0 on the total amount of emssons at date ; f c s regon 's margnal damage, then ts envronmental cost s c a where a a A + a B. Let c c A +c B denote the total margnal damage cost. Assumpton. () A regon's margnal utlty of pollutng n the second perod s decreasng wth ts frst-perod polluton control U N 0 a a () Let Γ a du da a + U a a ; a where n o a arg max U a ; a ca for all a There exsts a FB such that Γ (a FB )=0, Γ (a )N0 f a ba FB Γ (a )b 0 f a Na FB. Condton () smply states that a lax envronmental polcy at date (a hgher a )rasesregon's margnal cost of polluton abatement, or equvalently rases ts margnal utlty of emssons. Delayng polluton abatement then rases the cost of polluton mtgaton at a latter stage. Ths assumpton just captures the noton of a lax envronmental polcy n our model. In the followng, hats refer to the values of the parameters that emerge from an effcent date- agreement, whle star superscrpts correspond to the Nash outcome that would result from a falure to agree. Thus, denotes regon 's second-perod polluton control after the agreement. Condton () s a quas-concavty condton n whch the jontly effcent date- reacton to the frst perod polcy, a,s factored n; ths assumpton wll guarantee the unqueness of the frstbest polcy a FB allow us to sgn the bas nduced by delayed negotatons. We wll check that Assumpton s satsfed n all our applcatons. 8 Date- date- emssons are nterdependent n the case of bankable allowances (Secton 4.). There, we wll formally ntroduce date- polluton. 9 As we wll later dscuss, ths s unrestrctve snce any date- polluton-control polcy corresponds to a unque level of emssons. 0 We make the assumpton that the envronmental costs depend lnearly on the total amount of polluton for smplcty, but we show n Secton 3 that the results obtaned n the lnear case can be extended to a general envronmental cost functon. The beneft of assumng lnear damage functons s that we rule out Allaz Vla style effects. Thnk for nstance of electrc utltes that nvest massvely today n coal-fred power plant ths nvestment choce wll have long lastng consequences on the ablty to cheaply abate polluton. Please cte ths artcle as Beccherle, J., Trole, J., Regonal ntatves the cost of delayng bndng clmate change agreements, J. Publc Econ. (0), do0.06/j.jpubeco

4 4 J. Beccherle, J. Trole / Journal of Publc Economcs xxx (0) xxx xxx Were the negotaton to break down at date, regonal regulators would choose non-cooperatvely second-perod polluton levels, a * for regon. Ths benchmark defnes the outsde optons n the date- negotaton. Both a are functons of regon 's pror polcy.... Example nvestments n green equpments Authortes start wth a mass of (exstng or potental) brown equpments or buldngs. In each perod, they choose ther nvestment levels n perod, regon 's regulator makes a fracton X of ts equpments polluton-free for date (agan, we neglect date- polluton). Alternatvely, X mght be the fracton of green buldngs or equpments bult at date becomng operatonal at date. We assume that the regon has some technology for revampng, summarzed by a cost functon ϕ (X ) whch s ncreasng convex, wth ϕ (0)=0 ϕ ()=+. Smlarly, let Y denote the fracton of revamped equpment after the date- nvestment (so Y s the remanng fracton of brown buldngs or equpments). The date- nvestment costs ϕ (Y X ). Lettng a Y a X, the frst-perod secondperod utltes U U are equal to (mnus) the nvestment costs U (a )= ϕ ( a ) U (a, a )= ϕ (a a ). Snce ϕ s convex, U (a, a ) s concave n a. For gven (a, a j ), a * (a ) a are unquely defned. We can check that Assumpton s satsfed.... Dscusson (delayed negotaton) Our approach follows the large lteratures on ncomplete contracts on repeated contractng n assumng that no complete long-term contract s sgned at date. Regons may ntally fal to agree for dfferent reasons. Frst, the complance envronment may not yet be n place; for example, the Kyoto Copenhagen negotatons were hampered by the absence of a relable measurement of emssons by uncertanty as to how these would be measured n the future. Furthermore, there was no consensus on the use of economc nstruments on the nature of enforcement. Second, f a regon s governed by a poltcal party opposed to nternatonal negotatons on clmate change, the other regon may choose to wat for ths government to be defeated replaced by a more favorable government before enterng real negotatons. Compensatng the reluctant government s too expensve so the envronmentallyconcerned regon prefers to wat untl an equally envronmentallyconcerned government s nstalled n the other country to negotate. 3 Frst, dfferentatng U wth respect to a a U a a = ϕ a a N 0 snce ϕ s convex. Second, from the frst-order condton n the negotated case ϕ a a = c Thus Γ a = ϕ a ϕ a a = ϕ a c Snce ϕ (0)=0 ϕ () =, snce ϕ s convex, the functon Γ s decreasng admts a zero. Thus Assumpton s satsfed. 3 To llustrate the mpact of a synchronzed poltcal agendas n a smpler envronment than ours, take two perods ( ) two symmetrc regons (A B), consder a pro-envronment polcy that creates gross per-regon utlty u relatve to ts no-agreement utlty. However, the date- government of regon A has valuaton u b0 for ths polcy, unlke the date- government who wll value t at u. Regon B values t at u at both dates. The dscount factor s δ. If no agreement exsts by date, Nash barganng then wll ensure that each regon receves u. Antcpatng an agreement at date, the date- government of regon A s wllng to take a proenvronment stance at date f t receves compensaton T from regon such that ½u + TŠ δu. Smlarly, regon s wllng to accept an agreement f [u T] δu. Thus, f ð δþðu + u Þb0,.e., u + u b0, no agreement s sgned at date. Thrd, another possble explanaton s an ntal asymmetry of nformaton between regons, leadng to a barganng breakdown n early stages. The smplest such stuaton consstent wth our modelng has the regons hold prvate nformaton about some fxed component of ther utlty functon, such as some nfra-margnal cost of mplementng a pro-envronment polcy. Provded that ths nformaton becomes common knowledge before date, t can create a breakdown of negotaton at date wthout mpactng any of the analyss below. In general, though, prvate nformaton relates to the margnal cost of abatement or the regon's tolerance to emssons; the analyss s then more complex than depcted n the paper, as t nvolves screenng/sgnalng, but the basc forces unveled n the paper are robust. Fourth, there may be an agreement at date, but some nvoluntary (but antcpated) loopholes allow regons to devate from ts sprt. 4 Our analyss then refers to the degrees of freedom nvoluntarly allowed by the date- agreement... Welfare functons date- barganng Lettng T denote the transfer receved by regon as part of the date- agreement (T A +T B =0), the second-perod welfares of the world of regon, W W, respectvely, can be wrtten as W a A ; a B ; a A ; a B W a ; aj ; a U A a A ; a A + T U a ; a + U B a B ; a B Let, for gven date- actons, Ŵ a A ; ab A W aa B ; ab ; a A ; ab ; W a ; a j W a a ; a j a j ; a ; where n o a a arg max U a ; a c a a n o arg max U a ; a ca ba a ; c a A + a B ðþ c a + a j + T ðþ usng revealed preference a successful negotaton reduces date- emssons for any gven date- polces. 5 Revealed preference also mples that the functons a * are monotonc n the frst-perod effort Lemma. a * are non-decreasng (strctly ncreasng f c N0 for all ) functons of a. Furthermore, for all a, a a N a. Thus, the more strngent the frst-perod polluton control polcy, the lower the second-perod polluton. In partcular, appled to the case n whch negotatons are delayed, by adoptng loose polluton control polces n the frst-perod a regon can credbly commt to hgh date- polluton, were the negotaton to break down. Ths commtment s a key element of our analyss. 4 See Trole (009) for an analyss of pre-contractual cognton ts consequences for contract desgn ncompleteness. 5 Interestngly, the European Unon ETS prce fell by % n 009 as t became more more unlkely that a satsfactory agreement would be drawn. Whle some of ths decrease may be due to news about the economc recesson, the 9% drop n prce mmedately after the Copenhagen Accord s a clear sgn. Please cte ths artcle as Beccherle, J., Trole, J., Regonal ntatves the cost of delayng bndng clmate change agreements, J. Publc Econ. (0), do0.06/j.jpubeco

5 J. Beccherle, J. Trole / Journal of Publc Economcs xxx (0) xxx xxx 5 Date- barganng At date the two regulators agree on ther polluton levels on a sde payment. We model the barganng outcome by the Nash barganng soluton. 6 Callng α A α B the barganng powers of regons A B (wth α A +α B =), 7 regon {A, B}'s ntertemporal payoff after negotaton, W neg, s gven by W neg a ; a j = U a + W a ; a j + α Ŵ a ; a j W A a ; a j + W B a ; a j ð3þ The term U (a ) n Eq. (3) s the date- utlty assocated wth choosng polcy a. Ths term s fxed (sunk) at date. W *(a, a j )s the outsde opton of regon, whle α Ŵ a ; aj W A a ; aj + W B a ; aj s the share of the total surplus extracted by regon durng the negotaton..3. Benchmarks frst best autarky Before tacklng the case of delayed negotatons, let us look at the two polar cases n whch negotatons take place at both dates (frst best) 8 or never take place (autarky)..3.. Frst best The polluton levels agreed upon durng the negotaton A ; B are optmal gven the frst-perod choces (a A, a B ). From the envelope theorem, the frst best can be obtaned by dfferentatng U A a A + U B a B + U A a A ; a A + U B a B ; a B c a A + a B n o wth respect to {a A, a B A }, evaluatng t at ; B. Ths gves, for {A, B} Γ a du da a a + U a a ; a =0 ð4þ As announced n Assumpton, let a FB denote the unque value of satsfyng ths equaton..3.. Autarky The outcome when there s never any negotaton s gven by a smlar regonal optmzaton equaton du da a + U a + U a a ; a a a ; a a = Γ a U a! a ; =0 a ð5þ 3. The cost of delayng negotatons 3.. The ntertemporal substtuton brnkmanshp effects Suppose now that regons negotate only at date. We assume that the game wth payoff functons {W neg (a, a j j ), W neg (a, a j )} admts a unque Nash equlbrum, {a DN, a jdn }, where DN sts for Delayed Negotaton. Before provng our man result, we dentfy more precsely the effects mentoned above. Regon chooses a so as to maxmze W neg as defned by Eq. (3). Note that, whle W neg depends on a j, ts dervatve wth respect to a does not. From the envelope theorem, the frst-order condton s W neg a a = du da a! + U a ; a a + α U! a a ; a a U a a ; a ð6þ + α c j da a da =0 The regonal optmzaton term s 0 a da + U a a ; a A s nl at a =a FB. The ntertemporal substtuton term s gven by α U a ; a! a a U a ; a a It s postve snce a a N a for all a (the negotaton leads to less polluton) U (a, a )/ a a N0. Furthermore, t s larger, the smaller s α. A regon wth a low barganng power behaves as f t antcpated autarky, therefore a hgh date- emssons level. The brnkmanshp term s gven by α c j da a da Because a ncreases wth a from Lemma, thstermsalways postve. It s larger when α s large a country wth substantal barganng power s able to extract most of the surplus created by an agreement therefore benefts from lowerng the other party's outsde opton. Also the brnkmanshp effect s more mportant, the larger the other regon's envronmental cost. Indeed, f regon j s senstve to polluton (c j s large), then regon 's threat s all the more effectve. And so Γ a DN b 0 Let a *Na FB denote the soluton to Eq. (5), whch we wll assume s unque. 6 They are other approaches to modelng barganng. It seems reasonable to assume that the outcome of a negotaton depends at least partally on the outsde optons avalable to the partes. 7 Barganng theory has so far had relatvely lttle to say about the determnants of barganng power, so t s reasonable to allow arbtrary sharng coeffcents n our theory. 8 It does not matter whether the two regons negotate at date a long-term agreement for the two perods, or negotate at each date t an agreement specfyng the countres' short-term polces. Assumpton () then mples that a DN Na FB. In equlbrum there s an overprovson of a relatve to the frst-best level Proposton. Delayed negotatons rase the post-negotaton polluton by encouragng lax envronmental polces a DN pror to the negotaton for all, a DN Na FB so a DN a DN N a FB Comparson wth autarky Comparng condtons (5) (6), we note that under autarky, the negotaton-related brnkmanshp effect dsappears, whle the ntertemporal substtuton effect has full strength. Please cte ths artcle as Beccherle, J., Trole, J., Regonal ntatves the cost of delayng bndng clmate change agreements, J. Publc Econ. (0), do0.06/j.jpubeco

6 6 J. Beccherle, J. Trole / Journal of Publc Economcs xxx (0) xxx xxx Further assumptons are needed n order to compare the autarky level a wth the equlbrum value a DN under perod--only negotaton. For example, n the nvestment-n-green-equpments llustraton ntroduced earler, the date- nvestment s the same a DN =a ( so there s more date- polluton under autarky). But one can also fnd examples n whch the brnkmanshp effect s partcularly strong relatve to the ntertemporal substtuton one so, not only a DN Na, but also date- polluton s hgher under delayed negotaton than under autarky (see our dscusson paper, Beccherle Trole (00)). Proposton. The date- polluton under delayed negotaton may be hgher or smaller than under autarky. 3.. n-regon verson The analyss generalzes straghtforwardly to n regons. Lettng α denote regon 's barganng power (Σ α =), condton (6) remans vald provded that c j be replaced by (Σ j c j ) n the brnkmanshp term. A small regon s lkely to have lttle barganng power so the ntertemporal substtuton effect has full strength. The brnkmanshp effect by contrast s lkely to vansh provded that the externalty (Σ j c j ) does not ncrease fast when the country becomes small. For example, an ncrease n the number of regons stemmng from the breakup of allances reduces the brnkmanshp effect renforces the ntertemporal substtuton one. 3.. Non-lnear polluton damages rasng the rval's cost The lnear envronmental-costs assumpton allowed us to cleanly focus on the effect of the date- negotaton on the date- ncentve. Yet the effects of greenhouse gases (GHG) seem to be convex rather than lnear. The nonlnearty n the envronmental damage functon actually magnfes the strategc ncentve. The ntuton resembles that developed n Allaz Vla (993) n a dfferent context. Let C (a ) denote the envronmental cost functon of regon. Let C(a ) C A (a )+C B (a ) denote the total envronmental cost. We assume that C s twce dfferentable s ncreasng convex (that s dc ða ÞN 0, d C ða da da ÞN 0). The second-perod welfare functons are now W a A ; a B ; a A ; a B W a ; a j ; a = U A a A ; a A + U B a B ; a B Cða Þ ð7þ = U a ; a C ða Þ ð8þ Under autarky, a regon's second-perod emssons mpact the other regon's margnal damage cost. Regons play a Nash equlbrum of the game wth payoff functons W a ; a j ; a n o Let a a ; aj denote the Nash equlbrum of the game fa;bg n o whch, we assume, s unque stable. Smlarly, a ; aj maxmzes W (a A, a B, a A, a B ) s assumed to be unque. For gven date- actons, let Ŵ a A ; a B A W a A ; a B B ; a A ; a B ; a A ; a B ; W a ; a j W a a A ; a B ; a j a A ; a B ; a fa;bg Regon 's ntertemporal payoff after negotaton, W neg, s W neg a ; a j W neg a = U a + W a ; a j + α Ŵ a A ; a B W a ; a j + W j a ; a j From the envelope theorem, the frst-order condton s a 0 du a ; a aj + U a da a ; a ; aj A + α U a ; a! a ; a j U a ; a ; a j a + α C j a a A ; a B a a ; a j a 0 + α C a a A ; a B a ; a j A =0 Condton (9) s very smlar to Eq. (6); the three effects dentfed earler (regonal optmzaton, ntertemporal substtuton brnkmanshp) are stll at work. But ntroducng non-lnear envronmental costs adds a fourth term 0 α C a a A ; a B a a ; a j A An ncrease n a makes date- abatement more costly to regon so commts that regon to hgh emssons n the absence of agreement. Ths rases regon j's margnal damage cost thus nduces regon j to reduce ts own emssons under autarky. Regon j faces a hgher margnal cost of polluton reduces ts second-perod polluton Because we assumed that the Nash equlbrum s stable, a j s decreasng n a ( ncreasng n a j ). Ths s the rasng rval's cost effect. (to use an expresson coned by Salop Sheffman (983)). Ths effect s larger, the larger s α, that s, the smaller the barganng power of the regon. The new effect renforces the ntertemporal substtuton brnkmanshp effects. We thus conclude that Proposton holds a fortor The symmetrc addtve specfcaton Harstad (009) assumes that regon derves an ncreasng concave beneft B(y ) from date- consumpton y. 0 Symmetry obtans, as B( ) as well as the damage functon C( ) are the same for both regons. Fnally, emssons take an addtve form a = y + a Thus B a a = C a ; wherea Σ a 9 Ths analyss agan generalzes to n regons. The addtonal term assocated wth the convexty of the damage functons s then " α C a a j # h a a + α C j a a k j a a a j k j; a where a =(a, a, a n ). 0 Recall that hs model has an nfnte horzon. We recast t n our two-perod framework for the sake of comparson. a ð9þ Please cte ths artcle as Beccherle, J., Trole, J., Regonal ntatves the cost of delayng bndng clmate change agreements, J. Publc Econ. (0), do0.06/j.jpubeco

7 J. Beccherle, J. Trole / Journal of Publc Economcs xxx (0) xxx xxx 7 B a =C ð Þ; where Σ And so, lettng a Σ a, ψ(x) (B ) (C (x)), ψ ðxþ ðb Þ ðc ðxþþ (ψ ψ are decreasng), a = a + ψ a = a + ψ ðþ The lnear addtve assumpton of Harstad's model mples that knowledge s a pure publc good, on par wth envronmental qualty. The outcomes n the presence or absence of negotaton are ndependent of who made the pror nvestments n green technologes (only a matters). We can push the analyss a bt further allow for asymmetrc barganng weghts n the symmetrc addtve specfcaton. The ntertemporal substtuton, brnkmanshp rasng rval's costs effects are gven by the followng three terms, respectvely Δða h Þ α C ðð a ÞÞ C a ð a Þ 0 + α C a ψ a ð a ð a Þ ψ a A ð a Þ 0 + α C a ψ a ð a ð a Þ ψ a A ð a Þ For symmetrc barganng powers (α =/ as s assumed n Harstad), the total strategc effect s Δ = C ðða ÞÞ. Another smple case arses when damage costs are lnear (ψ =0). Then Δ s ndependent of the barganng powers da = da = d = da = The followng result s a drect applcaton of these formulas Proposton 3. Consder the symmetrc addtve specfcaton assume that the damage functon C(a ) s lnear. Then date- efforts are the same whether or not negotaton occurs at date a DN = a. And so a DN b a for all. An applcaton of the symmetrc addtve specfcaton s to the choce at date of a polluton stard that defnes the envronmental qualty of equpments that wll not be revamped at date. Lettng a denote the resultng date- polluton y denote the new polluton at date, then a =y +a. Ths s but a renterpretaton of our example wth nvestments n green equpments. 4. Market consoldaton under forward or bankable allowances 4.. Forward allowances 4... Overvew As the Unted States, the emergng countres actually most of the world resst bndng agreements, many experts place ther hopes n the emergence of regonal polluton permt markets such as the Examples nclude CO emsson stards for automobles n Europe, n the Unted States, a mnmum mleage legslaton for cars trucks (mles traveled per gallon of gasolne). In France, an envronmental law package called Grenelle de l'envronnement ntroduced upper lmts on housng consumpton (by 0 every new buldng wll have to consume less than 50 kwh/m /year). already exstng European Unon Emsson Tradng System (ETS) for CO emsson permts. Proponents of regonal ETS ntatves take the vew that regonal markets wll jump-start clmate change mtgaton wll pave the way for an nternatonal bndng agreement over regon's emssons. However a deal wll not happen overnght. We nvestgate the strategc mplcatons of a delayed agreement. As we prevously dd, we ensure strategc ndependence under autarky by assumng that the damages depend lnearly on total emssons. We frst focus on strategc choces regardng forward allowances; we later show that smlar nsghts apply to the ssuance of bankable permts. In ether case, the regon puts today nto prvate hs allowances that can be used to cover future emssons. We also assume, as we dd before, that the date- agreement defnes both regons' emssons. The resultng outcome s equvalent to a merger of the two ETS systems only n a symmetrc confguraton. The brnkmanshp effect apples provded that country 's date- polluton under autarky ncreases wth the number of forward allowances dstrbuted or sold at date. The ntertemporal substtuton effect further requres that domestc polluton be reduced by an nternatonal agreement. We post that the government faces a shadow cost of publc funds auctons off date- allowances, show that these propertes are ndeed satsfed. But the propertes may hold even f permts are dstrbuted for free at date. For example, the government mght at date negotate domestcally wth a powerful ndustral lobby, whose status-quo welfare s stronger, the larger the number of allowances t receved at date. Let us prevew our results. We frst consder a stuaton n whch the two regons sell forward allowances at date n a non-coordnated way. In the absence of future negotaton, we show that t s suboptmal for a regon to sell forward. Ths regonal optmzaton effect s a renterpretaton of the Coase conjecture. If a regon sells some allowances at date, at date t wll not fully nternalze the decrease n value of these forward allowances when ssung spot allowances. Antcpatng ths ncentve, the buyers of forward allowances buy the allowances below the prce that would preval f only a spot market exsted. A regon that chooses to sell allowances forward ends up sellng more allowances than t would n a date- spot market. By contrast, t becomes proftable for a regon to sell some allowances forward when regons negotate over emssons at date. As earler, the outsde optons n the date- negotaton consst n sgnng no agreement choosng noncooperatvely the number of spot allowances. To underst the two effects at work t s useful to consder the polar case n whch one regon has all the barganng power. Because fewer allowances are ssued than n the absence of an agreement, the date- prce of allowances (P ) s hgher than n the noncooperatve case (p ). The buyers of forward allowances, ratonally antcpatng the negotaton outcome, are wllng to purchase the forward allowances at a prce P greater than p. For a regon wth no barganng power, ssung some allowances forward ncreases ts mmedate proft byp per unt, whle only decreasng ts outsde opton by p. So the regon has an ncentve to free-rde on the negotated outcome by sellng at date forward allowances at the post-agreement prce. The ntertemporal substtuton effect thus creates an ncentve for the regon wthout barganng power to sell forward allowances. The regon wth full barganng power also has an ncentve to sell forward allowances albet for a dfferent reason It benefts from lowerng the other regon's outsde opton. The lower the other regon's outsde opton, the larger the surplus that t wll be able to extract n the negotaton. By sellng allowances forward, the regon credbly commts to ncrease ex post the total number of allowances t Exstng or planned ETS schemes, whle dstrbutng most allowances for free, plan to move to a full auctonng approach (of course there s some uncertanty as to the credblty of such commtments). Please cte ths artcle as Beccherle, J., Trole, J., Regonal ntatves the cost of delayng bndng clmate change agreements, J. Publc Econ. (0), do0.06/j.jpubeco

8 8 J. Beccherle, J. Trole / Journal of Publc Economcs xxx (0) xxx xxx wll sell n the absence of agreement. Ths brnkmanshp effect gves an ncentve for the regon wth barganng power to sell allowances forward Descrpton of the forward allowance game In the case of forward tradng, the frst-perod strategc acton a s the number of forward allowances regon sells at date. Smlarly, the second-perod strategc acton a, that s the level of emssons produced by regon n perod, s the total number of allowances ssued n regon (a s equal to a plus the number of spot allowances ssued at date ). Frms are captve wthn regons. 3 In each regon, the frms take the prce of allowances n ther regon as gven when choosng ther output. We call p (a ) regon 's nverse dem functon for allowances. p s non-ncreasng n a. The regon's second-perod utlty, U, s made of two terms. Frst, the regulator values the polluton of frms producng on ts sol to the extent that ths economzes on abatement costs, generatng more profts, employment or taxes. We stay as general as possble assume that the value assocated wth domestc frms emttng a unts of polluton s V (a ). The functon V s ncreasng n a concave. In the absence of taxes or other externaltes on the rest of socety, one can assume that V (a ) s equal to the domestc frms' proft π (a ), so that V (a )=π (a )=p (a ) but we do not mpose such a restrcton for the moment. Second, the regulator nternalzes part of the cash generated by the sale of allowances; ndeed we assume that the regons face a shadow cost of publc funds λ, that s that rasng $ of publc money costs socety $(+λ). And so h U a ; a λ a a p a + V a ð0þ Snce V (a ) s concave, then for ether small λ or decreasng margnal revenue, U (a, a ) s concave n a. For gven (a, a j ), a a a are unquely defned. The frst-perod utlty assocated wth the sale of forward allowances s λ tmes the revenues from the sale. 4 More precsely, the forward allowances a are sold at prce p a as agents ratonally antcpate that the date- agreement wll lead to a prce p.let U a λa p a ðþ 4... Checkng assumpton. These two functons satsfy the assumptons of the generc model. 5 In partcular Γ a = du da a + U a a ; a = λp a d a da 3 That s, we assume that outsourcng costs are mportant, so that frms are fxed therefore oblged to buy permts from the regon where they were ntally located. Ths s typcally the case for utltes snce electrcty cannot be transported over long dstances, electrcty producers must have power plants located relatvely close to ther end consumers. 4 Whether forward allowances are sold or dstrbuted for free at date s rrelevant for the argument. 5 Frst, we have U a ; a a a = λp a N 0 Second, du d a da + U a ; a a = λp a a a da has the same sgn as ( a ). Assumpton () s satsfed wth a FB =0, Proposton apples. The frst-order condton takes the specfc form " # W neg = λp d a a a + α a da h λ p + α c j da a da a p a a 4... Polcy mplcatons. Appled to forward tradng, Lemma mples that the level of date- emssons n regon (under autarky or negotaton) s an ncreasng functon of the number of ts forward allowances. Thus, ssung forward allowances s a credble commtment to emt more n the future. Proposton n turn mples that forward allowances are ssued whle none would be n the frst best, that delayed negotaton results n more polluton at date Comparson wth autarky. Under autarky, ratonal agents antcpate second-perod prce of allowances p a a. Therefore U a = λa p a a. 6 The ntertemporal welfare functon of regon n the autarky stuaton s W aut a ; a j = U a + U a h a ; a c a a + a j a j = λp a a a a + V a h a c a a + a j a j ðþ Snce a a s non-decreasng, then a =0. The effect of ntroducng a date- negotaton s to nduce regons to sell allowances forward, whle n autarky they would have refraned from sellng forward. The followng proposton s proved n the Appendx. Proposton 4. For lnear dem functons when V s equal to proft, the strategc ncentve to be n a stronger barganng poston the reducton of polluton acheved through date- negotaton cancel out a DN =a Merger of emsson tradng systems Wthout loss of generalty, we have assumed that at date the two regons agree on a vector of emssons, one for each regon. When regons are completely symmetrc (c A =c B =c/, α A =α B =/, V A (x)=v B (x) p A (x)=p B (x) for all x) barganng over regonal allowances amounts (on the equlbrum path) to mergng the regonal markets settng a total number of allowances. The optmalty of mergng markets requres that the optmal agreement leads to equal prces of CO n both regons. Ths condton however s not n general satsfed. It does not hold n the symmetrc case off the equlbrum path (that s, when one of the regons devates from the equlbrum number of forward permts) or n the asymmetrc case. Intutvely, the date- carbon prce determnes the rent enjoyed by those prvate actors who acqured forward permts at date. Because such rents are costly to the regons, the latter at date cooperatvely set regonal allowances prces wth an eye on lmtng them. Ths ncentve for prce dscrmnaton mples that settng equal prces for the two regons a corollary of market merger s not optmal n general. Wth a few adaptatons, though, our model can deal wth the case where the negotaton s constraned to focus on mergng the two systems on settng the total allowances world-wde. We here content ourselves wth a sketch of the man nsghts. 6 U a dffers from the frst-perod utlty under delayed negotaton Under autarky forward allowances sell at prce p a a, whle they sell at prce p a N p a a under delayed negotaton. Please cte ths artcle as Beccherle, J., Trole, J., Regonal ntatves the cost of delayng bndng clmate change agreements, J. Publc Econ. (0), do0.06/j.jpubeco

9 J. Beccherle, J. Trole / Journal of Publc Economcs xxx (0) xxx xxx 9 Under carbon-prce equalzaton, the regonal optmzaton the brnkmanshp effects reman. The ntertemporal substtuton effect however can go n the opposte drecton. Ths effect s drven by the prcedfferencebetweentheautarkyoutcome(thethreatpont)the negotated outcome. If regons dffer suffcently n ther ndustry structures ( thus abatement costs), the autarky prce n one regon may be larger than the negotated prce. In that case, the ntertemporal substtuton effect becomes negatve for ths regon. By contrast, f both autarky prces are below the negotated prce, the analyss of the general model remans vald. The followng proposton s proved n the Appendx. Proposton 5. For lnear nverse dem functons, when the negotaton bears on mergng the two allowance markets () When regons have the same technology (.e. p (x)=p j (x) for all x), then both regons sell forward. () When regons have dfferent technologes, then provded that technologes are dfferentated enough (alternatvely that envronmental costs are low enough), only the regon wth the most performng technology (regon such that p (x)bp j (x) for all x) sells forward. 4.. Bankng of polluton allowances Another polcy through whch the authortes can put future permts nto prvate hs s the bankng clause n Emsson Tradng Systems. For example, the Waxman Markey bll whch passed the House of Representatves n June 009 (but not the Senate) had bult n such a scheme. The bll adopted a cap--trade approach, set the quantty of permts to be ssued over the next 0 years, allowed permt holders to bank ther permts for future use Strategc actons utlty functons Let n denote regon 's number of allowances ssued at date. These allowances can be used n perod or banked for use at tme. The amount of allowances banked by the prvate sector s a.son a +q where q s the number of allowances used n perod. As earler, a denote emssons n regon n perod. For notatonal convenence, we assume that the pollutng frms' payoff functon s the same n both perods. Frms' net beneft functon n perods, π (q )π (a ), respectvely, s ncreasng convex. They antcpate a post-negotaton second-perod allowance prce p a. So, assumng that there s bankng n equlbrum, they wll bank untl ther margnal beneft to produce s equal to that prce π n a = p a = π a so n a = a ð3þ Because the beneft s convex the nverse dem functon of regon s decreasng, condton (3) defnes an ncreasng functon a (n ). Regons therefore maxmze ndfferently over a or over n.we choose a as the frst-perod strategc acton. The polluton at date has a drect cost c q to regon. 7 The regulator values a share λ of the proceedngs from the sale of the allowances. We therefore have U a ; a j = λp a a + a c a j + aj + π a 7 If all effects of polluton are delayed there s no regeneraton, then c =c (the second-perod cost). In general c can be greater or smaller than c. Regon 's second-perod utlty s U a ; a = λp a a a + π a 4... Checkng assumpton We verfy that U = λp a a a N 0. So Assumpton () s satsfed. We wll assume that Assumpton () s also satsfed. We have checked that ths s ndeed the case for lnear dem functons. Although U depends on both a a j, the general result apples snce U (a, a j ) s separable n a a j. Proposton 6. A delayed negotaton ncreases the quantty of banked allowances yelds an overprovson of allowances n the frst perod. 5. Alleys for future research The ntroducton has already summarzed the man nsghts of the analyss. These concludng notes rather focus on how t could be enrched. Besdes the obvous extenson to a longer horzon, several alleys for research seem partcularly promsng. Frst, whle our model already covers a wde range of nstruments, ts generalty could be further enhanced. Consder for nstance the clean development mechansm (CDM) set up n the aftermath of Kyoto. Ths mechansm allows countres that have commtted to emsson abatement targets to mplement these n part through projects n countres that have ratfed the Kyoto protocol but are not subject to such targets. The developed countres' wllngness to go along wth the CDM mpacts not only ther own effort pror to the negotaton of a bndng agreement (through the earned credts), but also the effort of the emergng countres' regon. The basc model could be enrched to account for such nterdependences. A second promsng alley s to consder asymmetrc nformaton between regons regardng, say, ther poltcal resolve to combat clmate change. As we noted, such asymmetres may be one of the causes of delay, as regons are engaged n a form of war of attrton. Furthermore, ths extenson could generate nterestng nsghts regardng sgnalng strateges. For example, before negotatng n Copenhagen, Europe made a commtment to a 0% emsson reducton relatve to 990 (30% n case of a satsfactory agreement ) several countres added a carbon tax for those economc agents who are not covered by the ETS system. Some observers argued that European poltcans were thereby puttng themselves n a weak barganng poston because they made concessons before negotatng over-sgnaled ther eagerness to reach an agreement; others dsagreed vewed ths move as a way to sgnal good ntentons to jump-start real negotatons. We have consdered only a global agreement between the regons. Whle we feel that negotatng a global agreement s the most reasonable way to go, many advocate a sectoral agreement approach. The study of multple negotatons could be fascnatng, as nterest group poltcs would then play a major role. Fnally, a common poltcal argument n favor of tough polluton control at home s that strct ant-polluton polces gve the country's ndustry a technologcal edge by stmulatng R&D n green technologes help create tomorrow's green growth. Ths strategc trade effect mght allevate the mpact of the strategc effects of delayed negotaton. We leave these open questons other exctng ssues on the clmate negotaton research agenda to future work. Please cte ths artcle as Beccherle, J., Trole, J., Regonal ntatves the cost of delayng bndng clmate change agreements, J. Publc Econ. (0), do0.06/j.jpubeco