J. Scott Holladay* and Michael A. Livermore Regional variation, holdouts, and climate treaty negotiations

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1 DOI /jbca Journal of Beneft-Cost Analyss 2013; 4(2): J. Scott Holladay and Mchael A. Lvermore Regonal varaton, holdouts, and clmate treaty negotatons Abstract: We develop a model of nternatonal agreements to prce a transboundry externalty and provde a new heurstc to ad n nterpretng negotaton behavor. Under conservatve assumptons, a country s net benefts wll be postve under an effcent polluton prce f ts share of global damages s less than half ts share of worldwde abatement costs. We solve for a permt allocaton scheme consstent wth that heurstc such that every regon wll have postve net benefts n an agreement to prce the polluton externalty at the globally effcent level. We then apply ths framework to clmate change usng regonal data from Integrated Assessment Models and test the feasblty of a global clmate change treaty. The results ndcate that several regons have postve net benefts from a globally effcent prce on carbon, ncludng Western Europe, South Asa (ncludng Inda), and Latn Amerca. We then solve for a permt allocaton scheme that should produce worldwde agreement on a clmate treaty. Usng the same model, we show that dfferental carbon taxes amed at producng unversal agreement would produce tax rate dfferences of an order of magntude. We also argue that shares of global DP mght be an approprate proxy for exposure to clmate damages and fnd that a global clmate treaty would be cost-beneft justfed for all countres wthout transfers when that assumpton s used. Keywords: clmate change; developng countres; nternatonal clmate polcy; transboundry polluton. JEL classfcaton: Q54; F51; H23 Correspondng author: J. Scott Holladay, Assstant Professor, Department of Economcs, Unversty of Tennessee; Fellow, Howard H. Baker Center, Tel.: , e-mal: jhollad3@utk.edu Mchael A. Lvermore: Assocate Professor of Law, Unversty of Vrgna School of Law 1 Introducton There are substantal obstacles to achevng effcent polcy solutons to global externaltes. In the best of crcumstances, soveregn natons cooperate to produce

2 132 J. Scott Holladay and Mchael A. Lvermore (at least nomnally) bndng agreements. But negotatng these agreement s complcated by the strategc behavor of the partes, each seekng to maxmze ts own ndvdual share of the net benefts. Internal poltcal obstacles may also prevent countres from actng n the nternatonal arena even when t s n ther own best nterest. These strategc and publc choce ssues can delay, or even scuttle, agreement on nternatonal treates that would generate large net benefts. In ths paper, we propose a new test to suss out whch countres would experence postve net benefts under an agreement to nternalze a global externalty. The results can be used to separate partes that requre a sde-payment to jon such a treaty from countres behavng strategcally to secure unnecessary sde payments or freerde off other countres emssons reductons. Such a test would be useful n ensurng that welfare-enhancng efforts to reduce transboundry externaltes are not waylad by strategc acton on the part of negotators. To descrbe ths test, we develop a stylzed model of the costs and benefts of nternalzng a global externalty. The model can be used to estmate a country s net benefts based on shares of global costs and benefts rather than levels. Ths can be partcularly useful when nformaton about the shares of global costs and benefts s more readly avalable (or more certan) than estmates of total cost and beneft levels. We begn by modelng the condtons for net benefts of elmnatng a global externalty for a gven country. We use the model to descrbe a permt allocaton scheme that would equate prvate and socal cost whle transferrng wealth to countres wth negatve net benefts under the ntal condtons. The wealth transfer takes the form of grantng holdout countres permts n excess of ther share of global emssons whle reducng the allocaton to countres that clearly beneft from nternalzng the externalty. We also use the model to llustrate the dffcultes of usng dfferental tax rates across countres. We then use data on the dstrbuton of clmate change rsks and greenhouse gas abatement costs to explore the model n the context of a specfc global envronmental externalty. Usng data produced by ntegrated assessment models (IAMs), we apply the smple test descrbed above to dentfy countres that are extremely lkely to be better off under a globally effcent clmate treaty vs-à-vs the status quo and n the absence of transfers. We dentfy several global regons, ncludng Chna and the Unted States, that mght be holdouts to a clmate treaty that prces greenhouse gas emssons at the effcent level. We then solve for a permt allocaton scheme that would ensure all global regons are ncentvzed to jon a global clmate change treaty that prces carbon at the socal optmum. The results suggest that permt allocaton to Western Europe and South Asa, ncludng Inda, would be far below ther share of global emssons (n the effcent emsson pathway) and that addtonal permts

3 Regonal varaton, holdouts, and clmate treaty negotatons 133 rangng from 3.8% to 10% of global emssons would be allocated to Chna and the Unted States. Fnally, we test the effcacy of schemes that would allow dfferental emssons tax rates across countres. Huge dfferentals n tax rates suggest that ths would not be a cost effectve scheme for reducng emssons to the effcent level. There s a volumnous lterature on the cost and benefts of controllng greenhouse gas emssons. 1 We focus on brngng together the strand of the lterature that estmates the magntude of damages under clmate change [see Tol (2012), Wetzman (2010), and Nordhaus (2008) among many others] wth the lterature that examnes nternatonal negotatons to address clmate change [see Carraro and Snscalco (1993), Fnus, Altamrano-Cabrera, and Van Ierland (2005), and Bréchet, erard, and Tulkens (2011) for some examples]. Ths paper provdes a straghtforward method for evaluatng the net benefts of correctng a global externalty for ndvdual countres or regons. We beleve that t provdes several benefts compared to the exstng lterature. Most mportant, the net beneft estmates are transparent and calculated n shares rather than levels. Further, these estmates can be used to calculate the sde payments necessary to ncentvze agreement to a globally effcent treaty as well as estmate the neffcency of unlateral acton to address clmate change. We also employ a novel measure of possble damages from future clmate change. There are relatvely few models of clmate change damages at the natonal level, and even regonal shares of damages tend to be extremely senstve to parameter assumptons. For that reason, we use share of global DP as a proxy for share of potental clmate change damages. Ths could be an attractve measure f clmate change damages are best understood as affectng the global economy, wth each country s ndvdual harm allocated on the bass of ther partcpaton n that economy. Share of global DP would then better reflect how much each country has to lose. In addton, share of future global DP s subject to much less uncertanty than the IAMs damage predctons. The paper proceeds as follows. In Secton 2 we develop a straghtforward cost-beneft-based model of nternatonal envronmental agreement formaton and descrbe the smple estmate of net benefts. The next secton descrbes the data taken from IAMs to estmate net benefts n nternatonal clmate treaty negotatons. Secton 4 apples the test to clmate data and Secton 5 concludes. 1 See Barrett (2005) for a summary of the lterature.

4 134 J. Scott Holladay and Mchael A. Lvermore 2 Model We model the costs and benefts of a straghtforward negotaton to mpose an effcent soluton to a global envronmental externalty. 2 The model s stylzed but provdes a framework for dentfyng countres that are most lkely to be better off under an effcent envronmental agreement. 3 Countres are faced wth a choce of jonng a global treaty that oblgates sgnatores to reduce emssons to the globally effcent level through means of an envronmental tax or polluton permt scheme. 4 If every country ratfes, then the treaty goes nto force, but f there s a sngle holdout, then the treaty lapses and no country reduces emssons. Potental sgnatores compare the benefts from global emssons reductons aganst the cost of domestc abatement, and f the benefts outwegh the costs, then they choose to sgn the treaty. Ths structure elmnates the possblty of sub-global coaltons creatng ther own treaty and allows us to focus on globally effcent, cost mnmzng agreements. 5 By estmatng whch countres clearly beneft from a globally effcent emsson level vs-à-vs the status quo, we can dentfy those countres least lkely to requre a sde-payment to acheve postve net benefts. Country faces a domestc margnal damage functon of MD (E), where E s the global emssons level. Country s margnal abatement cost functon s MAC (e ), where e s the quantty of domestc emssons. Margnal damages are monotoncally ncreasng n global emssons and margnal abatement costs are monotoncally decreasng n domestc emssons. Country wll have postve net max benefts from an agreement to reduce emssons from the unregulated level (e max for domestc emssons and E for global emssons) to the globally effcent level ( e domestcally and E globally) wthout need of sde-payments f: max E max e MD (E) MAC (e ), (1) E e 2 We choose to focus on an effcent soluton to a global externalty, but our model s suffcently flexble to allow for any level of reducton n the externalty. 3 We abstract from the treaty negotaton process and complance ssues to focus on dentfyng potental free rders. See Barrett (2005) and Barrett and Stavns (2003) for analyss of those ssues. 4 We put off the form ths treaty takes (emssons taxes or permt schemes) tll the next secton. 5 These sub-global clmate coaltons and the assocated free-rder problem s mportant n the context of nternatonal clmate change negotatons. See Nagashma and Dellnk (2008). Ths assumpton allows us to detect potental free rders by dentfyng natons wth postve net benefts under a clmate agreement. If those countres attempt to hold out of an agreement, they wll be recognzed as free rders, presumably reducng ther barganng power. Ths assumpton allows us to focus on the cost-beneft justfcaton of nternatonal envronmental agreements whle puttng asde the ssues of external or nternal stablty that have been debated n the lterature.

5 Regonal varaton, holdouts, and clmate treaty negotatons 135 Ths equaton can be arranged nto a beneft-cost rato: max D(E ) + AC (e ) max AC (e ) + D(E ) 1, (2) where D and AC are the damage and abatement cost functons of country, respectvely. If the nequalty holds, country s better off at the globally effcent level of emssons. The rato behaves n an ntutve way: t s ncreasng n E max and e and max decreasng n e and E. It s also ncreasng n margnal damages and margnal abatement costs. Ths s smply a condton that the domestc beneft-cost rato must be greater than one for a country to jon the globally effcent treaty. We assume a functonal form on the margnal abatement cost and margnal damage functons to allow us to elmnate level varables and work wth shares of damages and abatement costs. In partcular, we assume that the damage and abatement cost functons are lnear. These assumptons are conservatve for dentfyng countres lkely to be better off at the globally effcent emssons level, n the sense that type II errors are mnmzed. The more convex the MAC curve, the smaller the share of global damages that are necessary to compensate for domestc costs; concave MAC curves n the clmate context are unlkely. 6 The consequences of non-lnear damage curves for settng optmal carbon polcy are dscussed n Wetzman (2009) and Ackerman, Stanton, and Bueno (2010) among many others. Under these assumptons, the costs of entry nto an effcent envronmental treaty s equal to the area under the margnal abatement cost functon: a trangle wth area equal to MAC(e)(e 1 max e). The benefts of entry 2 nto the effcent envronmental treaty are the domestc damages abated: 1 (E max E){MD(E max ) MD (E )} Usng ths notaton and the smplfyng assumptons above, the model confrms that a country wll be better off under an agreement to reduce emssons to the globally effcent level: max max max (E E){MD(E ) + MD (E )} (e e)md (E ), 6 Lnear MAC curves are consstent wth the metastudy conducted by Fscher (2006). Ellerman (1998) fnds quadratc functons ft most regonal MACs very well, but (wth the excepton of Brazl) the coeffcents on the quadratc term are very small. 7 To see ths smply, separate the area of benefts nto two peces, the rectangle below the optmal tax rate (E max E )MD (E ) and the remanng area below the margnal damages curve and 1 above the tax rate: (E max E ){MD(e max ) MD (E )}. 2 Sum these two areas and then combne terms.

6 136 J. Scott Holladay and Mchael A. Lvermore where MD (E) = Σ MD (E) s the global margnal damages at emssons level E, whch s smply the sum of each country s margnal damages at that emssons level. The globally effcent level of emssons E s the one that equates MD (E) and MAC (E). 8 Ths s smply a condton that the benefts (on the left hand sde of the nequalty) must exceed the costs of jonng a globally effcent treaty. The value of global emssons reductons s based on the domestc margnal damages, and the cost of domestc abatement s based on the global margnal damages. We wll explot ths fact to move from dollar denomnated measures of damages and abatement costs to shares of global totals. Rearrangng these terms [assumng MD (E ) > 0], the condtons become that country should enter the clmate treaty f: max max MD (E ) + MD(E) e e max, MD (E ) E E (3) The term on the left hand sde of the nequalty s country s share of global damages tmes a constant based on the slope of the margnal damage functon. The rght hand sde s the share of global emsson reducton. The model can confrm that a country s better off under an effcent clmate treaty, even wth a constant damage functon, f ts share of global damages exceeds one-half ts MD (E) share of global emsson reductons. As ncreases, the share of global E damages requred to fulfll the nequalty decreases. Ths formulaton elmnates the level of costs and benefts and focuses on shares, whch may be easer to observe. If every country s share of emssons reductons were exactly equal to ts share of global benefts, the nequalty wll be satsfed for each country and a global treaty wll come nto force. The more nequtable the proportonal dstrbuton, the less lkely t becomes that all countres wll be better off under an agreement to reduce emssons to the globally effcent level. As the share of abatement becomes more concentrated n countres that wll not receve sgnfcant benefts, the lkelhood of gettng agreement on an effcent prce decreases. Whle stylzed, the model provdes a bass for a smple test that can be taken to the data to dentfy countres that would be better off under an effcent clmate treaty. Ths concept, based on the costs and benefts of domestc acton, s dstnct but related to the stablty concept n the lterature. 9 Ths approach allows 8 Ths equalty holds comes from the defnton of the effcent tax, whch equates global margnal damages wth global margnal costs. 9 D Aspremont, Jacquemn, abszewcz, and Weymark (1983) frst descrbe coalton stablty n collusve prce cartels, but the Internatonal Envronmental Agreement lterature has adopted

7 Regonal varaton, holdouts, and clmate treaty negotatons 137 us to assess global and sub-global envronmental treates and determne whch coaltons would be cost-beneft justfed on a country-by-country bass. The heurstc descrbed above s especally useful f we have more relable data about the max MD (E ) ratos and e e than about the values of the ndvdual terms. max MD (E ) (E E) 2.1 Permt allocaton schemes If the dstrbuton of global emssons reductons and rsks are relatvely uneven, achevng agreement on an effcent emsson prce wll be dffcult. It s has been shown that, under these condtons, t may be possble to use emssons permts to redstrbute abatement costs from hgh-cost to hgh-rsk regons, whch could nduce all countres to jon an effcent nternatonal treaty. 10 We now use the same framework to develop a permt allocaton scheme that produces the globally effcent level of emssons whle provdng the wealth transfers necessary to ncentvze countres whose costs exceed benefts to jon a treaty. We magne a permt scheme n whch a socal planner dstrbutes permts to pollutng regons. 11 We follow the lterature n assumng that utlty s lnear and that the socal planner weghts welfare equally across countres. 12 The number of permts s fxed at the effcent level of emssons E, but the dstrbuton of those permts s flexble, to encourage agreement. If the socal planner allocates permts to each country n proporton to ts emssons at the globally effcent level, then the costs wll mmc an effcent emsson tax. By dstrbutng fewer permts to regons that are clearly better off under the envronmental agreement, and more permts to other regons, the planner can use the permts to produce an agreement. Emssons permts n excess of a regon s effcent share of global emssons can be traded at a prce equal to global margnal damages. Ths represents a ths termnology as well. See Barrett (1994) for an early paper that analyzes coalton stablty usng a smlar cost-beneft-style framework. 10 See Chander and Tulkens (1992) for an early example of how nternatonal transfers can help form cooperatve agreements and Rotllon and Tazdat (1996) for an example of the form those transfers mght take. 11 Of course, much of the dffculty n creatng effcent nternatonal envronmental polcy s due to the lack of a socal planner. 12 See Eyckmans and Tulkens (2003), Carraro, Eyckmans, and Fnus (2006, p. 3), and Carraro and Snscalco (1993). Ths ensures that utlty s transferable across countres, meanng that transfers are equally weghted. It would be straghtforward to extend ths analyss to unequal weghts usng a socal welfare matrx that weghts transfers. Ths approach gnores numerous equty and poltcal ssues wth these transfers that are beyond the scope of ths paper.

8 138 J. Scott Holladay and Mchael A. Lvermore beneft to recpent countres. By ncludng ths beneft on the left hand sde of the nequalty from equaton 3 and rearrangng, we can solve for the requred number of permts to ensure that each country s better off under an envronmental treaty and that the global coalton s potentally cost-beneft justfed for each member: (E max E){MD(E max ) + MD (E )} + (P)MD(E) MD (E )( e max e ), max max e e MD (E ) + MD(E) max P=, (E E) MD (E ) (4) where P s the share of global permts n excess of a country s share of global e emssons at the effcent level. The number of permts s ncreasng n E the quantty of abatement relatve to the globally effcent emssons level and decreasng n the share of global damages. 2.2 Suboptmal taxes The dstrbuton of permt allocaton descrbed above reles on the transfer of polluton rghts across countres. Certan types of transfers may be dffcult for practcal or poltcal reasons. In the absence of a mechansm to facltate transfers, the effcent outcome may only be achevable f net benefts are dstrbuted relatvely equally across all countres. We use the same model to examne two possble second-best strateges requrng less nternatonal cooperaton and compare the results to the globally effcent outcome. For the frst second-best strategy, we assess the mpact of an envronmental tax set at less than the effcent level. Such a tax would decrease the costs and benefts of a global envronmental treaty. The costs would decrease more quckly than the benefts, 13 mplyng that more natons would be lkely to jon the treaty as the tax rate declned. It s straghtforward to use our framework to show the mpact of unform suboptmal envronmental taxes: max α max α MD (E ) + MD(E ) e e α α max α, MD (E ) E E (5) 13 The constructon of the margnal damage and margnal benefts curves ensure that the last unt of polluton abated generates the least net benefts. Ths means any reducton n the envronmental tax wll ncrease the average net benefts of emssons reductons.

9 Regonal varaton, holdouts, and clmate treaty negotatons 139 where E α and e α are the global and domestc level, respectvely, of emssons under an emssons tax of αmd (E ). Ths formulaton presents a smple translaton of the cost-beneft heurstc derved above for suboptmal envronmental taxes. A country wll jon an envronmental treaty that sets an envronmental tax at 50% of the globally effcent level, for example, f ts share of global benefts tmes the constant based on the slope of the margnal damage functon exceeds half of ts share of global abatement. We can solve the same cost-beneft formulaton for the threshold domestc emssons tax (as a functon of the globally effcent level) that would ncentvze a country to jon a globally effcent treaty as another second-best approach. It s mportant to note that we are consderng a globally effcent treaty, despte the fact that countres may each be abatng ether above or below the globally effcent level. Ths s the analog of the permt scheme descrbed above. Some countres must tax at above the effcent level to compensate for the fact that other countres wll tax at below the globally effcent level. Ths holds E max E, MD, max and e e constant by assumpton, allowng us to solate the MD s needed to produce an agreement. After solvng for the MD s, we can test the plausblty of that assumpton. Usng the structure lad out above, we can easly determne the level at whch countres become clearly better off under an envronmental treaty. Rearrangng equaton 3 we have: MD (E ) + MD(E) e e ρ, MD (E ) (E E ) max max = max (6) max e e MD (E ) max max + ρ =, (E E)MD (E ) MD(E)) (7) The ρ dentfed from these equatons s the tax level (as a fracton of the globally effcent level) that brngs a regon to the potental coalton member category. We can then test the plausblty of the assumpton that a globally effcent clmate treaty s possble by evaluatng ndvdual natons ρ to assess whether they wll have an mpact on the globally effcent emssons level. 3 Internatonal clmate treaty negotatons We now explot the framework descrbed above to analyze nternatonal clmate treaty negotatons. Clmate change s a clear example of a global envronmental

10 140 J. Scott Holladay and Mchael A. Lvermore externalty. Emssons from any country generate damages that are experenced worldwde. Negotatons to create lmts on the emssons of greenhouse gases (Hs) have consstently faled to acheve bndng reductons and suffer from numerous holdouts. The actual abatement costs and damages assocated wth clmate change are dffcult to predct [see Tol (2005)], makng the theoretcal framework descrbed above partcularly useful. Several IAMs are avalable that predct global emssons reductons and damages assocated wth clmate change at a regonal level. 14 Usng ths data, t s possble to test for the feasblty of a global clmate change treaty usng the heurstc descrbed above. A number of papers assess the stablty of clmate change treaty coaltons usng data from IAMs. Perhaps most smlar to ths paper, Bossett et al. (2009) examne the stablty of every possble coalton that could emerge from a 12-regon IAM and tests for the ablty of those coaltons to delver envronmentally sgnfcant emssons reductons. Bosett, Carraro, De Can, Massett, and Tavon (2012) explore how changng assumptons about the pure rate of tme preference, socal welfare aggregaton, and clmate change damage scenaros can affect the stablty of the most envronmentally effectve coaltons. Ths paper dffers from the exstng lterature by usng the nsght from the smple model above to test for the domestc-level cost-beneft justfcaton of a global clmate change treaty usng shares of global costs and benefts from a clmate change treaty rather than ther levels. The results, partcularly for external stablty, are straghtforward and ntutve and potentally more accurate f the IAMs are better at predctng the dstrbuton of clmate change damages and abatement costs than ther magntudes. 3.1 Data The deal dataset to dentfy holdouts n clmate change negotatons would nclude country-level estmates of the cost of reducng emssons and the potental damages from clmate change. Specfcally, such a dataset would estmate the present value of the dscounted stream of future costs of mplementng the optmal carbon prce at the country level. These values would be merged wth country-level estmates of the dscounted stream of future damages from clmate change. Unfortunately, due to the lack of necessary country-level data and the 14 See chapter 6 of Stern (2006) for descrptons of the ssues and technques used n Integrated Assessment Modelng and the current state of the IAM lterature as well as Tol (2009) for a metaanalyss of recent models.

11 Regonal varaton, holdouts, and clmate treaty negotatons 141 Table 1 WITCH regon defntons. Regons USA WEURO EEURO KOSAU CAJAZ TE MENA SSA SASIA CHINA EASIA LAM Countres Unted States Western European EU Countres Eastern European EU Countres South Korea, South Afrca, and Australa Canada, Japan, and New Zealand Russa and Non-EU Eastern European Countres Mddle East and North Afrca Sub-Saharan Afrca South Asa ncludng Inda Chna ncludng Tawan South East Asa Latn Amerca, Mexco, and the Carbbean The composton of global regons used n the WITCH model. See Bosett et al. (2009) for a full descrpton of the regonal defntons. nablty to quantfy the consderable uncertantes at mcro levels, no such dataset exsts. Whle country-level data s typcally unavalable, there are several estmates of costs and damages at the regonal level from IAMs. To the extent that regons are carefully selected to be homogeneous, regonal estmates should serve as a good proxy for the actons of ndvdual countres. Estmates of the costs of reducng emssons at the regonal level are avalable from the WITCH (World Induced Techncal Change Hybrd) Polcy Smulator produced by Fondazone En Enrco Matte (FEEM). Ths project develops an ntegrated energy-economc- envronment model to assess the mpact of clmate change polcy on varous economc varables. The model s descrbed n Bosett, De Can, Sgobb, and Tavon (2009). Results are avalable for 12 regons desgned to be reasonably homogenous n ther response to emssons reductons. Specfcally, Bosett et al. (2009) argue that ther regons are desgned to share smlartes n terms of the structure of the economy, energy supply and demand and resource endowments. 15 The model can be used to predct regonal DP and H emssons from 2010 to 2100 under a varety of dfferent emssons levels and polcy scenaros. By comparng emssons under a busness as usual scenaro to forecasts under a varety of polcy frameworks that cap atmospherc concentratons of Hs, t s possble to calculate the share of global emssons reductons by regon. These regonal abatement estmates are pared wth regonal damage estmates taken from several dfferent sources. Nordhaus and Boyer (2000) provde 15 Detaled regonal defntons for the WITCH model are detaled n Table 1.

12 142 J. Scott Holladay and Mchael A. Lvermore regonal damage functons for 13 global regons usng the Regonal Integrated Clmate-Economy (RICE) model. The RICE model provdes estmates of damages from clmate change through a regonal level damage functon that translates changes n surface temperature to changes n consumpton. Ths s accomplshed by calculatng the effects of temperature change on a sector-by-sector level and then summng for each regon. Results are reported as a fracton of DP loss under 2.5 C and 6 C warmng by The regonal defntons are slghtly dfferent than those used n the WITCH model, but they are suffcently close to allow comparson for the regons that play an mportant role n nternatonal clmate polcy. These efforts to quantfy damages from clmate change are ncomplete. Many of the damages are currently unquantfed and some damages may be dffcult to predct ex ante. However, even f damages are systematcally under- (or over-) estmated, ths should not affect nference from exstng data so long as all regons are equally lkely to face unquantfed and unpredctable damages. Of course, these probabltes cannot be determned. The theoretcal specfcaton s flexble enough to employ any estmated regonal breakdown of clmate change damages and abatement costs. As the scence of clmate modelng advances, the estmates can be plugged drectly nto ths model. 4 Assessng a global clmate change treaty The theoretcal framework lad out above requres comparng the porton of total world emssons reductons and damages avoded assocated wth an effcent global carbon prce. Usng a varety of data sources, we compare the fracton of world abatement and benefts at the regonal level for whch relatvely precse estmates are avalable. The IAMs descrbed above provde data that s consstent wth the theoretcal framework and can be used to dentfy regons that could see postve net benefts under a global clmate treaty. We then consder several polcy scenaros that may elmnate the unprced externalty whle addressng the global nature of damages from H emssons. We begn by estmatng the fracton of emssons reductons borne by dfferent regons usng data from the WITCH model. The model s used to estmate H emssons under a varety of scenaros: busness as usual, an emssons reducton suffcent to reduce atmospherc concentraton to 640 parts per mllon (whch s assocated wth warmng of around 24 C), and an emssons reducton suffcent to reduce atmospherc concentraton to 535 ppm (assocated wth warmng of 2.6 C). The 535 ppm emssons scenaro can be pared

13 Regonal varaton, holdouts, and clmate treaty negotatons 143 wth an mplementaton polcy opton to analyze how proposed cost contanment strateges affect costs. The least expensve mplementaton scenaro employs all technologes and polces to mnmze costs, ncludng emssons tradng, offsets, and renewable technologes. The most expensve polcy opton s labeled no backstop technology, whch assumes no technologcal mprovement n ether the energy or non-energy sector over the remander of the century. The WITCH model projects emssons every 5 years from 2010 to 2100 n each scenaro. We comple those projectons and subtract the dfference between emssons under a busness-as-usual scenaro and under each polcy opton. Usng these projected emssons reductons, t s straghtforward to estmate the share of global reductons expected n each regon. We then fnd the scenaro wth the maxmum and mnmum emssons reducton shares for each regon. Ths range of possble reducton shares s reported n Table 2. Though there s a great deal of heterogenety across regons, the dfferent scenaros provde remarkably smlar emssons reductons predctons. Chna wll face the hghest level of emssons reductons over the remander of the century at around 25%, whle Eastern European countres wll only provde 1.5% of global emssons reductons. Due to the long halflfe of carbon and the slow movement of the global clmate cycle, even sharp reductons n emssons wll not guarantee full avodance of Table 2 Share of global emssons reductons by regon. Regon Mn Max USA WEURO EEURO KOSAU CAJAZ TE MENA SSA SASIA CHINA EASIA LAM The range of emssons reductons shares from eleven dfferent parameterzatons of the WITCH model. Unts for each column are regonal share of global clmate emssons reductons. The varaton across dfferent versons of the model s consderably less than the varaton across regons.

14 144 J. Scott Holladay and Mchael A. Lvermore these damages. 16 When determnng whether to enter a treaty to reduce emssons, governments are presumably comparng the present value of abatement costs to the margnal reductons n damages that abatement wll generate. The IAMs we use do not provde mappngs from current emssons reductons nto damages averted, but they do provde estmates of damages (typcally measured as a fracton of output) assocated wth varous temperature ncreases. In the absence of data on the proportonal beneft of margnal decreases n H emsson, we use the proporton of total exposure as a proxy. Usng temperature-based measures of total exposure may also be the approprate measure for modelng the treaty formaton process f the decsons of negotators are based on these measures of damages, whch are the best currently avalable. We use the RICE [descrbed n Nordhaus and Boyer (2000)] for regonal clmate change damages. 17 Addtonally, we use projected future DP as a proxy for share of global damages. Clmate change s lkely to generate damages that spll across nternatonal boundares, such as generatng frctons n nternatonal trade markets or causng unrest that requres the expendture of natonal defense resources. These cost spllovers make regonal attrbuton of damage dffcult. For that reason, regonal DP provdes a useful alternatve measure of exposure to clmate change damages. In Fawcett (2009), the EPA suggests shares of global DP to approxmate the fracton of global clmate change damages to whch the Unted States mght be exposed. To our knowledge, no other paper n ths lterature has used ths approach when assessng the feasblty of a global clmate change treaty. Havng compled estmates of the costs of abatement and the possble damages from clmate change at the regonal level, we can determne whch countres are least lkely to be worse off under a global clmate treaty. We use the mdpont of the range of possble emssons reducton shares from the WITCH model. 18 We then calculate each regon s share of global damages as estmated under the RICE and WITCH models. Because both models damages are reported as fractons of DP n future years, t s necessary to translate these estmates nto a common unt of measure before calculatng each regon s fracton of world costs. To do ths, we use DP projectons from the WITCH model busness-asusual scenaro. One addtonal dffculty remans: the two dfferent models used 16 Clmate damages are a functon of the stock of polluton, whle emssons are drectly related to abatement costs. We use the terms abatement and emssons avoded nterchangeably. 17 It s mportant to note that these estmates are senstve to the IAMs used to calculate margnal benefts and margnal damages. If these models are ncorrect about the dstrbuton of future damages from clmate change, that error wll be propagated n our estmates. 18 Because of the relatvely consstent emssons reductons estmates, the results are not senstve to usng other plausble measures.

15 Regonal varaton, holdouts, and clmate treaty negotatons 145 to calculate abatement costs and damages defne ther regons slghtly dfferently. Some large economes are defned consstently across the models, but smaller regons are nconsstent. To compare the fracton of world costs and damages, we choose to combne regons from the two damage estmates to match the WITCH regons that nclude the most aggregated regonal defntons. By multplyng the estmated clmate change damages from RICE and DP shares by the approprate WITCH DP forecast, t s possble to report damages n bllons of 2005 US $ (the unt of measure used by WITCH). By summng the dollar value of damages, we can estmate the total world damages from clmate change and then fnd each regon s fracton of those damages. Ths generates an estmate of damages from clmate change consstent wth the stylzed model at the regonal level. Pared wth cost estmates from the WITCH model, we can compare the fracton of world damages to the fracton of world costs and apply the heurstc to dentfy regons that are least lkely to have an ncentve to avod mposton of a globally effcent carbon prce. Ths analyss s predcated on a globally effcent emssons treaty wth a commtment perod of Dfferental growth rates n DP, emssons, and damages across regons mply that treates wth dfferent commtment perods would requre a separate analyss, but ths method wll effectvely estmate net benefts across any commtment perod. To smplfy notaton and focus on our clmate change case study, we take advantage of the concept of the socal cost of carbon, whch represents the margnal damages generated by a ton of carbon emssons at a gven global emssons level: SCC = MD (E). A flat damage functon mples that SCC s the same for all values of E. The global socal cost of carbon can be consdered the sum of the domestc socal costs of carbon for every country n the world. We denote the global socal cost of carbon as SCC and domestc socal cost of carbon as SCC. Settng the effcent global tax at SCC would generate MAC (e ) = MD (e ). We further assume that the MD (E) s a constant for all countres. Ths s a conservatve assumpton that further reduces the rsk of false postves for a postve domestc net beneft country. 19 These estmates represent a lower bound on the level of clmate treaty partcpaton that could be expected at the globally effcent prce. To the extent that margnal damages are ncreasng, regons on the margn become more lkely to jon a treaty. Usng ths new notaton and our more conservatve assumpton on the shape of the MD curve, the condton for a country to jon an effcent global clmate change treaty becomes: 19 The assumpton s conservatve n the sense that constant margnal damages mnmzes the total benefts of jonng a clmate change treaty to lower emssons to a gven level. Any country that would agree to a clmate change treaty under constant margnal damages would agree f ts margnal damage functon was ncreasng.

16 146 J. Scott Holladay and Mchael A. Lvermore SCC e e max 1 > max SCC 2(E E) (8) If regon s share of global benefts exceeds half ts share of global costs, then they are better off under an effcent nternatonal agreement. If every regon satsfes ths nequalty, then net benefts are postve everywhere and the global treaty wll come nto force. As the slope of the margnal damage curve ncreases, ths one-half weght falls, and the lkelhood of a regon beng better off under a treaty and an agreement beng cost-beneft justfed ncreases. Table 3 provdes three estmates of SCC based on dfferent sources of SCC max e e damage estmates n columns 1 3 and n column 4. Comparng the max (E E) damage estmates to one-half of the abatement estmates allows us to dentfy clear wnner (CW) regons under these conservatve assumptons. Focusng on ndvdual regons, Western Europe and South Asa appear most exposed to clmate change damages, whle Chna and the Unted States face the largest abatement requrements. Several regons are clearly better off under a globally effcent clmate change treaty no matter whch damage specfcaton s used (Western Europe, South Asa, Latn Amerca); other regons are senstve to the source of the damage estmates. If damages are lkely to spll over natonal borders, then the DP share may be the best proxy for true damages. In that case, jonng a clmate treaty would be cost-beneft justfed for both Chna and the Unted States. 20 Table 4 provdes a summary of whether a regon would jon a global clmate treaty based on a gven damage estmate. If each regon satsfes the nequalty above, then a global clmate change treaty would be cost-beneft justfed for all countres. The results suggest that under the RICE damage estmates a global coalton would not be feasble, as several regons, ncludng the largest emtters, would be holdouts. The damage estmates based on DP shares suggest that a global treaty would be cost-beneft justfed for all countres. Each global regon satsfes the nequalty, but Russa 20 It should be noted that these estmates are based on the conservatve assumptons lad out above. As the slope of the margnal damage curve ncreases, there are thresholds over whch both countres become better off under a globally effcent clmate treaty. If the damages curve for Chna s steep enough so that MD (E max ) s 10.5 tmes greater than MD(E ), then Chna would be better off under a global clmate change treaty even f ts share of global damages s only 2.2%. For the US, the comparable fgure s 3.9. If the unregulated level of damages exceeds the domestcally effcent level by more than 3.9 tmes, then the US would be better off under a global clmate treaty usng even the smallest share of global benefts as the bass for our estmate.

17 Regonal varaton, holdouts, and clmate treaty negotatons 147 Table 3 Regonal share of damages and abatement. Column RICE WITCH 2.5 C 6 C DP Share Abatement USA WEURO EEURO KOSAU CAJAZ TE MENA SSA SASIA CHINA EASIA LAM Columns 1 and 2 dsplay each regon s share of global clmate change damages as estmated by the RICE model. Column 3 lsts each regon s share of global DP n 2100 as approxmated by the WITCH model, whch may be consdered a proxy for exposure to future damages. Column 4 lsts the mdpont of the range of each regon s share of abatement as predcted by the WITCH model. Table 4 Regonal share of damages and abatement. Column RICE WITCH 2.5 C 6 C DP Share USA N N Y WEURO Y Y Y EEURO N N Y KOSAU Y Y Y CAJAZ N Y Y TE N N N MENA Y N Y SSA Y N Y SASIA Y Y Y CHINA N N Y EASIA Y Y Y LAM Y Y Y Columns 1 3 dsplay whether a regon would jon a globally effcent clmate treaty usng the share of global damage estmate from the source lsted n the column header. Y ndcates the regon would jon the treaty. N ndcates that the regon would requre a sde-payment to jon.

18 148 J. Scott Holladay and Mchael A. Lvermore and Eastern Europe have close to zero net benefts under a globally effcent treaty. 4.1 Permt allocatons Hgh-rsk countres can choose to receve less than ther proportonal share of permts and provde permts to countres that face a hgh fracton of the requred total emssons reductons. A careful dstrbuton of permts wll provde ncentves for all countres to jon an effcent nternatonal clmate treaty. Numerous papers have attempted to solve for permt schemes that produce stable clmate change coaltons, 21 but we take advantage of the heurstc descrbed above, whch may be more robust to measurement error snce t operates on shares rather than levels. By constructon of the model, there must be enough regons that experence net gans from emssons reductons to provde permts to those that do not, ensurng that under ths framework a global coalton s feasble. It s stll useful to trace the flow of permts and assess the poltcal feasblty and equty mpacts of these coaltons. Smplfyng equaton 4 to account for our lnear damage functon produces the followng equaton: max e e SCC max E E 1 P =, 2 SCC (9) where P s the share of global permts n excess of a country s share of global e emssons at the effcent level. E The number of permts s smply the gap between the share of damages and half the share of abatement. Usng the data descrbed above, we are able to determne the number of permts relatve to a regon s share of emssons requred to produce a global treaty prcng emssons at the effcent carbon prce. Table 5 descrbes the mnmum number of permts requred to nduce regons to jon a global treaty, or the number of permts that regons would be wllng to provde to encourage other regons to sgn on. The entres n the table represent the number of permts above (or below) ther share of global emssons. The unts are ndexed such that the globally effcent level of emssons s 100. For example, usng the RICE model 2.5 C damage estmates, Chna would need to receve an excess allocaton of permts equal to 10.5% of global emssons reductons and 21 See Eyckmans and Tulkens (2003), Carraro et al. (2006), and erman, Tont, Tulkens, and de Zeeuw (2003), among many others.

19 Regonal varaton, holdouts, and clmate treaty negotatons 149 Table 5 Permt flows across regons. RICE WITCH 2.5 C 6 C DP Share USA WEURO EEURO KOSAU CAJAZ TE MENA SSA SASIA CHINA EASIA LAM The share of addtonal permts requred to ncentvze agreement to a globally effcent carbon prce measure relatve to the globally effcent emssons level (E ). Unts are ndexed such that the globally effcent level of emssons s 100. Negatve numbers represent permt outflows. Western Europe would be wllng to accept an allocaton of permts 17.7% of global emssons less than ts share. The Unted States would need to receve permts totallng 1% 4% of total emssons reductons under the damage estmates produced by the RICE model, but t would provde permts equal to 9% of total emssons reductons based on the DP proxy for damage. Ths permt scheme represents a straghtforward method to encourage all regons to jon a global clmate agreement. Whle such an agreement mght be techncally feasble, t mght face domestc poltcal backlash. It may be dffcult to convnce Latn Amercans to forgo permts n exchange for the Unted States agreement, or for South Asa to send permts to Chna. However, because Western Europe s wllng to gve up a relatvely large number of permts, t may be possble to provde adequate compensaton from ts pool of permts. It appears that under these damage scenaros, globally effcent clmate treates are possble f Western Europe s wllng to provde sgnfcant transfers to the Unted States and Chna. A global clmate treaty would be domestcally cost-beneft justfed for all countres wthout any transfers f global DP shares are used as a measure of damages. The negatve numbers ndcate each regon would be wllng to gve away permts n ths scenaro, although none should have to do so.

20 150 J. Scott Holladay and Mchael A. Lvermore 4.2 Suboptmal carbon prces Usng the heurstc and data descrbed above, there are several regons that we cannot confrm would be better off under a globally effcent carbon prce wthout permt transfers. Recall that equaton 5 allows us to fnd a suboptmal carbon prce at whch countres that do not experence postve net benefts would be wllng to jon a self-enforcng treaty. Under our smplfyng assumptons, a suboptmal carbon tax reduces the break even rato of share of benefts and share of costs from one-half to somethng less. Specfcally, a country wll be better off jonng a clmate treaty mposng a carbon tax at α of the globally effcent level f ts share of global damages avoded s more than 1 α ts share of global 2 abatement. For example, f an nternatonal clmate treaty were proposed that set a carbon prce at half the global socal cost of carbon for a sngle country, then that country would be better off jonng a global clmate treaty f ts share of global benefts exceeded 1 ts ther share of global emssons reductons. Other natons 4 would have to pay a hgher tax rate so the emssons-weghted average tax was at the globally effcent level. We now turn to estmatng what level of domestc carbon tax these countres would accept to jon a treaty that reduces emssons to the globally effcent level. Ths scenaro magnes a global treaty wth dfferental carbon taxes based on each regon s share of global damages and abatement. The emssons-weghted average tax would be equal to the global margnal damages producng an effcent emssons level. Recall that SCC s the global margnal damages of a ton of carbon emssons, or n other words, the globally effcent carbon prce. Usng our estmates of regonal abatement costs and damages and equaton 7, we can fnd the ρ that solves: 1 ρ =, 2(E E) SCC max e e SCC max for each regon. Ths ρ represents the threshold fracton of the global socal cost of carbon that exactly equates the regonal costs and benefts of jonng a global clmate treaty, whch we refer to as the break-even tax rate. Table 6 lsts the threshold fracton of the globally effcent carbon prce that would leave each regon on the margn of jonng a global treaty for each of our three damage share estmates. For example, usng the RICE model s damage estmates, the Unted States should be wllng to jon an agreement to reduce total emssons to the effcent level f t were allowed to prce carbon at 52% of the globally effcent level. A globally effcent clmate treaty s possble f the emssons-weghted average of each regon s ρ s equal to or larger than the globally effcent tax level. Recall (10)

21 Regonal varaton, holdouts, and clmate treaty negotatons 151 Table 6 Break-even carbon tax rates for varous damage estmates. RICE WITCH DP 2.5 C 6 C DP Share USA WEURO EEURO KOSAU CAJAZ TE MENA SSA SASIA CHINA EASIA LAM The break-even carbon tax rate measures the maxmum percentage of the globally effcent prce on carbon that regons would be wllng to mpose domestcally as part of a globally effcent clmate treaty. that ths specfcaton assumes that E max E max, SSC and e e do not change despte country nsttutng a carbon prce dfferent from the global optmum. By constructon, the emssons-weghted average of ρ s < 1, suggestng that t would be possble to produce a globally effcent level of emssons usng dfferental taxes, but ths s not suffcent to ensure that these assumptons are reasonable. We can evaluate ths assumpton by lookng at the ndvdual ρs and determnng whether the globally effcent level of emssons s lkely to change. For example, usng the RICE model 2.5 C damage estmates, Western Europe would be wllng to pay a carbon tax over sx tmes the globally effcent level, but Chna would only pay a tax at 17% of the effcent level. Ths mples that abatement costs are lkely to be sgnfcantly hgher n Western Europe than n Chna, thus ncreasng the globally effcent level of emssons and volatng our assumpton. Allowng ndvdual countres to set ther own carbon tax s unlkely to generate anythng approachng a globally effcent clmate treaty. If an agreement ncludng dfferental tax rates allowed for emssons offsets for abatement undertaken n low-cost regons, Western Europe could pay for abatement n Chna; however, ths arrangement s very smlar to the wealth transfer through permt allocaton scheme descrbed above. Wthout such a scheme, dfferental carbon tax rates across countres based on shares of global abatement and damages are not partcularly useful.