Economic targets and loss-aversion in international environmental cooperation

Transcription

1 MPRA Munch Personal RePEc Archve Economc targets and loss-averson n nternatonal envronmental cooperaton Doruk İrş Sogang Unversty 5 September 5 Onlne at MPRA Paper No. 694, posted 5 February 6 6:8 UTC

2 Economc Targets and Loss-Averson n Internatonal Envronmental Cooperaton Doruk İrş Sogang Unversty September 5, 5 Abstract In the standard emsson problem, each country s rulng party decdes on an optmal level of emssons by analyzng the cost and beneft to the country. However, such polcy decsons are often nfluenced by poltcal partes ncentves to be elected. Voters tend to gve hgher prorty to economc ssues than they do to envronmental ones. As a result, poltcal partes have addtonal ncentves to reach a crtcal economc beneft level, at a cost of hgher emsson level, n order to satsfy voters expectatons n economc ssues. Therefore, ths study explores the mplcatons of poltcal partes beng averse to nsuffcent economc performance relatve to a crtcal economc target level on sustanng an nternatonal envronmental agreement on emsson levels. In dong so, we allow countres to have asymmetrc concerns about economc targets, as well as asymmetrc technology levels. We fnd that stronger concerns about economc targets deter the most cooperatve emsson levels countres could jontly sustan. Furthermore, technologcal asymmetry could ether deepen or offset ths mpact. These results suggest that efforts on achevng substantal nternatonal envronmental agreements should be supported at the ctzen level to elmnate the adverse effects. Keywords: Emsson Problem; Economc Targets; Loss-Averson; Internatonal Envronmental Agreements; Repeated Game. JEL classfcaton: Q5; Q58; D3 Poltcs s too serous a matter to be left to the poltcans. Charles de Gaulle Introducton In many economc models, we assume that governments make optmal choces for ther country by takng nto account the benefts and the costs to the country. However, n realty governments objectves often dffer from ther countres, snce they have addtonal ncentves to be re-elected. In ths paper, we argue dorukrs@gmal.com; Phone: ; Sogang Unversty, School of Economcs, -74, Seoul, S. Korea.

3 that smlar stuaton also exsts when governments decde on ther emsson cuts. It s wdely known that poltcal partes consder economc benefts to be of greater mportance, snce these benefts are more vsble and certan to voters than are the results of envronmental polces. As a result, they would have addtonal ncentves to ntroduce some populst polces n order to acheve some economc targets. Poltcal partes could perceve these targets as crtcal levels below whch voters would be unsatsfed wth the economc performance. Furthermore, poltcal partes would be averse to perform poorly n these economc aspects, snce t mght cost them the next electon. For example, an ncrease n tax, say on gasolne, could be better for the country but not eventually mplemented due to such dstortonary ncentves of the rulng party. relevant ncentves on nternatonal envronmental cooperaton. In ths paper, we am to understand the mplcatons of such possbly To model ths, we assume that poltcal partes perceve economc benefts from emsson not only n absolute levels but also as gans or losses relatve to ther economc targets, and that they are averse to nsuffcent economc performances. More specfcally, economc targets are reference levels such that, f a country s economc beneft from emssons s hgher than ts economc target, then ts leaders fnd the economc performance suffcent (.e., a gan). However, f the beneft s less than ts economcs target, then ts leaders fnd the economc performance nsuffcent (.e., a loss). Thus, ths paper ntroduces the wdely used phenomena of reference levels and loss-averson nto the nternatonal envronmental cooperaton. Kahneman and Tversky (979) argue that people perceve outcomes as gans and losses relatve to a reference level, whch may be current assets, the status-quo, or expectatons, rather than fnal wealth or a welfare level. Furthermore, people exhbt loss-averson, whch s the tendency to strongly prefer avodng losses to acqurng gans. The theory of loss-averson has been employed to provde nsght nto varous phenomena such as n fnancal markets (Benartz and Thaler, 995), consumpton and savng behavor (Bowman et al., 999), housng markets (Genesove and Mayer, ), voter behavor (Alesna and Passarell, 4) at the ndvdual level; and also, n nternatonal trade (Freund and Ozden, 8) and poltcal partes electon platform changes (Schumacher et al., 5) at the government level. More specfcally, Schumacher et al. (5) explan why governments change ther electon platform more than opposton partes. They argue and fnd emprcal evdence that partes wth low aspraton change more when they are n government than n opposton due to loss-averson. For example, when the German Green Party moves nto offce frst tme as the coalton partner of Socal Democratc Party n 998, they changed ts platform sgnfcantly. In short, the economc ssues became more mportant, whle the envronmental ones became less mportant. Even though t costed the party some actvst and many loyal voters, t was able to reman as an attractve coalton partner and acheved hghest natonwde votes ever. In addtonal to Schumacher et al. (5), Smon (985) also argues that poltcal partes exhbt bounded ratonalty, especally when decsons are complex. Bendor et al. (), n ther recent book on behavoral theores of electon, show that poltcal partes and/or voters aspraton (reference) levels For nstance, the followng lnk descrbes recent surveys that show how voters prortze economc ssues more hghly than they do envronmental ssues n the Unted States. See the supportng nformaton provded n Schumacher et al. (5) for more detaled poltcal hstory of the German Green Party.

4 nfluence party competton, turnout, and voters choces of canddates. Alternatvely, poltcal partes can be ratonal. Stll, smlar mpacts on achevng economc targets can be observed f they take actons to maxmze not only the net beneft to the country, but also ther own prvate nterests (Besley, 6; Persson and Tabelln, ). Ratonal poltcal partes may be reluctant to change to greener polces f voters are averse to economc losses (Alesna and Passarell, 4), or f they are nfluenced by specal nterest groups (Grossman and Helpman, 994). In the latter case, partes may strve to reach an economc target because of ndustral lobbysts, who are possbly stronger than the green lobbysts, expectng some economc targets to be acheved. 3 As a result, to be elected, poltcal partes would value the economc benefts from emssons more hghly n order to satsfy some economc targets, thus, to attract voters or specal nterest groups. 4 Several studes examne how behavoral economcs can advance the scence of envronmental and resource economcs, and note that loss-averson could be crucal for non-market valuatons (Shogren et al., ) and whether clmate change s framed as a loss or a gan (Gsottbauer and van den Bergh, 3). To the best of our knowledge, İrş and Tavon (5) s the only other study (a work n progress), whch employs loss-averson to examne nternatonal envronmental agreements. They nvestgate the mpact of loss-averson wth respect to a threshold amount of envronmental damage, whch s vewed as ndcatve of an approachng catastrophe. Our study dffers sgnfcantly from that of İrş and Tavon (5), because the latter focuses on coalton formaton, and partcularly the sze of coaltons and the types of countres that form a coalton n the case of asymmetry n ther belefs on envronmental safe operatng lmts (references) and n ther perceved vulnerablty when a threshold s exceeded (lossaverson). A country s economc target could be determned, among others, by ts past performance and targets, current and expected future performances, performances of other countres, and poltcal partes declaratons. For nstance, overly-optmstc declaratons mght cause ambtously hgh economc targets, 5 and whle economc busts lower the voters expectatons, t also rases attenton n economc ssues relatve to envronmental ones and, thus, can ncrease the economc targets. 6 In ths paper, we assume countres economc targets and economc target concerns (.e., how much are targets valued comparng to the beneft and the cost of emssons and, how averse poltcal partes are to nsuffcent economc performances) to be exogenous and allow them to dffer between the countres. Furthermore, we also allow countres to dffer n ther development levels, partcularly n ther technology levels. In ths context, a 3 Detz et al. () study the mplcatons of domestc lobbyng, partcularly on IEAs. See also Oates and Portney (3) for a revew of lobby groups on envronmental polces. 4 Buchholz et al. (5) provde a theoretcal examnaton of the mplcatons of the electoral process for IEAs, and fnd sgnfcant adverse effects. Based on emprcal evdence, Cazals and Sauquet (5) show that poltcal leaders levels of commtment to IEAs dffer wth the tmng of electons. In our model, we abstract completely from the electoral process and focus on the potental consequences. 5 Mler (9), usng personal ntervews wth poltcal eltes and a quas-expermental desgn, fnds that poltcans often use decson heurstcs and suffer from over-optmstc forecasts. Smlarly, Frankel () studes the forecasts of real growth rates made by offcal government agences n 33 countres. He fnds that forecasts have a postve average bas and that ths bas s even stronger n economc booms. 6 For nstance, publc polls show that voters prortze economc ssues and neglect envronmental ones more durng 8 crss. 3

5 technologcally advanced (developed) country needs to emt less than a (developng) country that s not as technologcally advanced n order to generate the same economc surplus. To address the consequences for IEAs of economc targets and loss-averson, we develop a dynamc game n whch countres face a free-rdng publc goods problem and attempt to mantan cooperaton n ther natonal emsson strateges. Here, emtted polluton s assumed to be transboundary. We restrct our attenton to IEAs that are self-enforcng, as n Ferrara et al. (9) and Hadjyanns et al. (), snce there s no supranatonal authorty to enforce envronmental polcy mechansms. In ths context, a country prefers to sustan cooperaton on agreed-upon emsson polces, as long as the dscounted future welfare losses from a breakdown n nternatonal envronmental cooperaton outwegh the onetme gan of a unlateral devaton from the cooperatve path. Note that we abstract completely from any partcpaton consderatons, whch have been at the center of IEA lterature (Barrett, 994; Carraro and Snscalco, 993; D Aspremont et al., 983; Hoel, 99). 7 Instead, we look for the sustanablty of a cooperatve emsson level, partcularly the most cooperatve emsson level, by countres amng to acheve ther economc targets and that are averse to economc losses, wthn the context of a selfenforcng IEA nvolvng full partcpaton. We compare the sustanablty of a cooperatve emsson level by dfferent set of countres that vary n terms of ther economc targets, economc target concerns, and technology levels. We examne sets of countres that are both symmetrc and asymmetrc n terms of these characterstcs. 8 We fnd that f a country has stronger economc target concerns, that s, t values ts economc targets more and/or becomes more averse to economc losses, then ths country fnds t more dffcult to sustan cooperaton, but that ths stuaton facltates the sustanablty n other countres owng to strategc substtutablty of emsson levels. In the case that all countres have stronger economc target concerns, sustanng an agreed-upon cooperatve emsson level mght become easer for some suffcently developed countres but harder for some developng countres. So, an agreed cooperatve emsson level could not be sustaned after all countres havng stronger economc target concerns f there s no transfer mechansm. Furthermore, we show that a decrease n a country s ablty to sustan cooperaton means the most (lowest) cooperatve emsson level ths country can sustan ncreases. Thus, the most cooperatve emssons countres can sustan can be ordered as follows: lowest n the case that no country cares about economc targets; all countres reach ther targets; and hghest f no countres reach ther targets. We also fnd that t s more dffcult to sustan a cooperatve emsson level f countres become more asymmetrc n ther technology levels. In ths case, the mpact of further asymmetry n the level of economc target concerns s ambguous. Asymmetry n economc target concerns may correct the negatve mpact of asymmetry n technology levels on sustanng cooperaton f developng countres have weaker and developed countres have stronger economc target concerns. Otherwse, t enters as another obstacle for countres to support a greater degree of nternatonal envronmental cooperaton. These results 7 See also the followng more recent revews of the lterature: Barrett (5) and Fnus (8). 8 Much of the lterature on IEAs examnes the case of symmetrc countres. However, some studes provde a theoretcal examnaton of countres that are asymmetrc n terms of ther sze and margnal damage from polluton (Kolstad, ), margnal costs and benefts of abatement (McGnty, 7; Pavlova and de Zeeuw, 3), and technologes (Mendez and Trelles, ). 4

6 provde another perspectve on why leaders have to be further motvated for greener polces by ctzens when they are to negotate n the nternatonal arena. The remander of ths paper s organzed as follows. Secton sets out the bascs. Secton 3 characterzes the statc Nash equlbrum of our model. Secton 4 analyzes the dynamc game. Secton 5 provdes two numercal analyss: the frst one studes the mpact of economc target concerns on the most cooperatve emssons. The second one analyzes the model for technologcally asymmetrc countres, gves nsghts of North-South model. Fnally, Secton 6 proposes concludng remarks and relates the predctons of our model to the ongong U.N. Clmate Summts. The appendx contans some calculatons and all the proofs of propostons and lemma. The Model We assume the world conssts of n countres. 9 The countres have perfect nformaton about the world, and decde smultaneously on an emsson level of a pollutant substance, x (, ). Emssons have a negatve envronmental effect and gve rse to negatve externaltes owng to transboundary effects. In other words, emssons n country pollute the envronment n country, as well as n other countres. However, emssons are unavodable for producton, whch creates surpluses for producers and consumers. Our model bulds on the work of Mendez and Trelles () and ncorporates countres economc targets nto the problem. The net-beneft functon for country, whch also ams to reach ts economc target, s as follows: B (x,...,x n )=b (x ) p (x,...,x n )+ t x,b R, () where country s economc beneft b (x ) depends only on ts emssons, the cost of polluton p (x,...,x n ) depends on all countres emsson levels, and the target utlty t x,b R depends on the country s emssons and economc target b R. The scalng factor > measures how much country cares about ts target utlty relatve to the benefts and costs of emssons. We assume the followng functonal forms: b (x ) = x () p (x,...,x n ) = x x + X x j (3) j6= ( t x,b R b (x ) b R, f b (.) b R = b (x ) b R, otherwse. (4) A hgher value of the country s exogenously determned technologcal neffcency (, ) requres hgher emssons to reach a gven economc beneft. We call country developng f t s technologcally neffcent (relatvely hgh ), and developed f t s technologcally effcent (relatvely low ). We use (,..., n ) to denote the vector of countres technologcal neffcency parameters and normalze 9 For convenence, we use the word country to refer to both a country and ts poltcal leader. 5

7 them, np j =. j= Note that the economc beneft functon b (x ) s strctly ncreasng, concave, and b () =. The cost of polluton p (x,...,x n ) s strctly ncreasng n all terms, p (,...,) =, and has the followng two for j 6=, and () p (x,...,x n ) >p j (x,...,x n ) f < j. Property () mples that a margnal ncrease n domestc emssons s more damagng than the same margnal ncrease n another country. Ths means that ether the emsson has addtonal local effects besde the global effects, or n addton to the real effects, t has psychologcal effects, such as people feelng gulty about ther own country s emssons. Property () mples that, regardless of sources, people n developed countres are more envronmentally aware and perceve more of envronmental damage than people do n developng countres. The target utlty t x,b R captures a country beng averse to losng ts economc benefts relatve to ts economc target b R. We can consder ths to be country s economc reference level. In other words, f the economc beneft reaches ths level, b (.), then the country s satsfed by the postve dfference, whch t perceves as a gan. b R On the other hand, f the economc beneft does not reach the target, b (.) <b R, then the country s dsapponted by ths negatve dfference, whch t perceves t as a loss. Moreover, countres tend to strongly prefer avodng economc losses to acqurng gans, relatve to the economc target. The loss-averson parameter > measures how country values losses versus gans. The functon t (.) s ncreasng n ts emsson level, decreasng n ts economc target, and ndependent of how much other countres emt. The net-beneft functon of country wth an economc target smplfes to the followng: 8 < B x,...,x n,,b R = : x x + x P j6= x j P + x j6= x j b R, f bg (.) b R b R, otherwse, (5) where = < captures the economc target concerns of country n the loss doman. Country, wth an economc target, ntally maxmzes the objectve functon n the frst row, B G (.). If the economc beneft reaches the target, b G (.) b R, then country s n the gan doman and ts net beneft s determned. However, f the economc beneft does not reach ts target, b G (.) apple b R, then country s n the loss doman and maxmzes the objectve functon n the second row, B L (.). For a standard country, there s no target utlty n (). Any country belongs one of the three types {L, G, S}: that fals to reach ts economc target (L); that reaches ts economc target (G); and wth no economc target (S). We use (,..., n ) to denote the vector of countres types. In order to study the mpact of dfferent types of countres, we solve the model for the case n whch all countres fal to reach ther economc targets. The results for the other types of countres can be found by smply applyng = for any country reachng ts economc target Neumayer () shows that democraces exhbt stronger nternatonal envronmental commtment than non-democraces. Ths supports property () f one accepts that democraces are also more developed. For some parameter values, countres can fal to reach ther economc target when maxmzng B G (.) and then reach ther economc target when maxmzng B L (.). Ths maxmzaton procedure s to elmnate potental loops. 6

8 (G), and =for any standard country (S). Note that ncreases as a country s type changes n the drecton of S! G! L. 3 Statc Game The am of ths secton s to characterze the non-cooperatve Nash equlbrum of n technologcally asymmetrc countres wth economc targets. The Nash equlbrum serves as a credble punshment or threat to support nternatonal envronmental cooperaton n the repeated settng examned n the followng secton. In the non-cooperatve Nash soluton, each country sets ts emsson level where the margnal beneft s equal to the margnal cost. We fnd the best response functon BR and Nash emsson for country x N usng the standard frst-order L (.) /@x =, as well as some addtonal L (.) X = j6= x j A x =, (6) The frst-order condton shows that economc target concerns ncreases the margnal beneft of emssons. Multplyng the frst-order condton by x > nx j= and determnes the best response functon for country : x j BR (x )= A x =for =,,...,n, (7)! P + x j j6= +, (8) where x (x,...,x,x +,...,x n ). Note that country s emsson level when t best responds to other countres emssons ncreases n ts economc target concerns,.e., hgher, and as t becomes technologcal less effcent,.e., hgher. Summng n equatons n (7) and solvng for the total emsson level gves: where x N j nx x N j = j= np P j + n j j j= j= P + n, (9) j j= P s country j s Nash emsson level. Substtutng (9) nto (7) and usng n j =gves the Nash emsson level below: The statc Nash equlbrum would be the unque equlbrum for the dynamc game as well f an IEA were not feasble (e.g., owng to exogenous, poltcal reasons, or because countres are mpatent and do not value the future.) j= 7

9 x N ( ) X j j A. () j6= Equaton () shows that stronger country s economc target concern, that s, an ncrease n, mply a hgher Nash emsson level for country. In other words, Nash emsson level of a country wth an economc target places more value on the economc benefts than a standard type country does, and even more so f t s a type L than G. On the other hand, a hgher j for any other country j mples a lower Nash emsson level for country. Ths s due to the envronmental concern of country about the hgher envronmental polluton caused by country j. Note also that country s Nash emsson level ncreases as the country becomes technologcally less effcent,.e., hgher, and as the other countres becomes technologcally more effcent,.e., lower j s. 3 For any gven types, the Nash emsson levels are neffcently hgh (.e., x O <x N for all ), where the optmum level of emssons x O x O P,...,xO n maxmzes the countres jont net-benefts n B. Ths s because emssons are transboundary and the negatve spllover effects are not nternalzed when the countres act non-cooperatvely. 4 = 4 Dynamc Game In ths secton we study the repeated nteracton between countres. More precsely, the statc game analyzed n the prevous secton s repeated nfntely many tmes n the dynamc game, and countres dscount the future perod by a dscount factor (, ). We focus on self-enforcng IEAs. Thus, countres cannot make bndng commtments. In such a settng, countres can sustan nternatonal envronmental cooperaton, the degree of whch depends on how severely they can credbly punsh a devator. Our am n ths secton s to examne the consequences of economc targets and loss-averson for the sustanablty of a cooperatve emsson equlbrum n the framework of an IEA wth full partcpaton. Thus, our framework s n lne wth the U.N. Clmate Summts, n whch partcpaton has been almost unversal. Countres employ nfnte Nash reverson strateges to enforce envronmental cooperaton. 5 We focus on cooperatve subgame-perfect equlbra n whch the followng hold: () along the equlbrum path, the countres mplement cooperatve emsson levels n each perod; and () f at any pont n the game a defecton occurs, all countres revert to non-cooperatve Nash emsson levels from the followng perod onwards. Each country wll prefer to emt at the cooperatve emsson levels f ts net beneft from 3 See the appendx for calculatons. 4 Usng the frst order n P (+ ) n(+ ) = B L /@x =, the optmum level of emssons under full symmetry becomes: x O =. There are no closed-form solutons for optmum emssons n the case of asymmetry. Nevertheless, they are not needed for the sustanablty of IEAs. 5 We employ nfnte Nash reverson strateges for smplcty, but they have well-known credblty ssues. Instead, we could consder other strateges, such allowng renegotaton (Barrett, 994; Ashem and Holtsmark, 9). In these cases, the degree of cooperaton that any type of countres could sustan would be quanttatvely dfferent. Nevertheless, all the forces leadng to the qualtatve results would reman the same. 8

10 cooperatng s no less than ts payoff from defecton. The latter payoff conssts of a one-perod gan from devaton and the dscounted net beneft of playng Nash reverson forever; that s: B x C,,,b R B BR x C,x C,,,b R + B x N,,,b R, () where (,..., n ) s the vector of economc target concerns, ndcatng also the country types, x C x C,...,xC n s the vector of cooperatve emsson levels, and BR x C s the best response functon of country when other countres emt at the agreed cooperatve emsson levels. From Fredman (97), we know that for a suffcently hgh dscount factor and any gven economc target concerns, there s a subgame-perfect Nash equlbrum at a vector of cooperatve emsson levels x C, such that x C x C,xN, where x C s the most cooperatve emsson level country can sustan. Substtutng cooperatve emssons x C, the best response functon n (8), and Nash emsson n () nto B L (.) gve the net beneft functons when all countres cooperate, when country unlaterally devates whle others contnue to cooperate, and at the Nash emssons, respectvely: 6 B L x C,,,b R = x C + x C X j6= xc j b R, () B L BR x C,x C,,,b R = + + Xj6= + xc j b R, (3) B L + ( ) x NL,...,x NL n,,,b R = P j j j6= C A + b R. (4) Smlar to publc goods game, we have B BR x C,x C,,,bR >B x C,,,b R >B x N,,,b R. We take the terms on the RHS over to the LHS n () and call ths country s sustanablty functon S x C,,,. Substtutng (), (3), and (4) nto () gve the sustanablty functon, S (.) = x C + x C X j6= xc j P + (+ j6= xc j ) + + ( ) P j j j6= C A +. Gven the parameters of the model, the sustanablty functon gves non-negatve values for sustanable cooperatve emsson levels, and gves negatve values for unsustanable cooperatve emsson levels. In ths paper, our man concern s how the economc target concerns affect the sustanablty of an agreed cooperatve emssons. An ncrease n country s economcs target concerns does only ncrease the mpact of the target utlty. It means that the mpact of ths ncrease depends on the levels of the economc beneft b (.) and the economc target b R. Note that the economc target parameters n S (.) cancel each other out b R =. Thus, the country s economc target only determnes ts type, but has no other effect on sustanablty. Therefore, gven the types, the mpact of an ncrease n economc 6 More detaled calculatons are provded n the appendx. (5) 9

11 target concerns on sustanablty depends on the economc beneft levels when country cooperates b C b x C, when t unlaterally devates whle others contnue to cooperate b D b BR x C, and at the Nash emssons b N b x N. Our frst proposton descrbes the mpact on sustanng a cooperatve emsson level f country s more concerned about ts economc target. Ths ncrease n economc target concerns can be due country s type changng n the drecton of S! G! L. Proposton Gven any cooperatve emsson levels x C, technologcal neffcences wth j =, economc target concerns, and a common dscount factor target,.e., hgher, then n P j=, f country s more concerned about ts economc () t s more dffcult to sustan cooperaton at the agreed cooperatve emsson x C for /@ <, and () t s easer for any country j to sustan cooperaton at x j /@ >. An ncrease n country s economc target concerns ncreases ts margnal beneft from emsson. Snce x C <x N <BR (x C ) for any, the economc benefts at these emsson levels are ordered as follows: b C <b N <b D. Furthermore, whle country s cooperatve emsson level does not change, ts Nash emsson level and emsson level when t unlaterally devates from the cooperatve emsson level ncreases n. These mply a stronger ncentve to devate and, thus, a decrease n S (.). Sustanng cooperaton at x C becomes more dffcult for country. On the other hand, an ncrease n for any other country j only decreases country j s Nash emsson level because of the strategc substtutablty of countres emsson levels, thus lowerng ts ncentve to devate from the agreed cooperatve emssons. Therefore, sustanng cooperaton at x C becomes easer for country j. Next, we dscuss the mpact on sustanng a cooperatve emsson level f all countres are more concerned about ther economc targets. To ths end, we ncrease the economc target concerns unformly, whle stll allowng these concerns to be dfferent from each other. Proposton Gven any cooperatve emsson levels x C, technologcal neffcences wth j =, economc target concerns, and a common dscount factor n P j=, an equal ncrease n all countres economc target concerns, d = d j 8j, mpedes country sustanng cooperaton at x C f d + j d j < b C ( ) b D + ( + ) (n 3 (n )) b N <. (6) () If apple n 3 n, whch requres n 4, then bn enters non-negatvely and the nequalty (6) does not hold for suffcently large. Otherwse, b N enters negatvely and the nequalty (6) or the opposte can hold. () It s easer for the nequalty (6) to hold for a lower x C and hgher x C j s. Whle Proposton examnes the mpact of one country beng more concerned about ts economc targets, Proposton examnes the mpact of all countres havng stronger concerns about ther economc targets. Thus, for each of n countres, there are two effects, as dscussed n Proposton : () an ncrease

12 n hnders sustanng cooperaton for country, but () facltates cooperaton for any other country j. If the nequalty (6) holds, Proposton s () domnates () when all countres have stronger economc target concerns. If the opposte of nequalty (6) holds strctly, then () domnates (). The frst pont n Proposton states that f there are suffcently many and patent countres, () domnates () for a technologcally not very neffcent country. If any of these condtons fal to hold, then dependng on the specfc parameter values () or () domnates the other. To gan more nsght nto ths, frst note that the number of countres and countres technologcal neffcences are lnked due to np the normalzaton, j =. An ncrease n the number of countres requres at least some countres to j= become technologcally more effcent. For any gven number of countres, a country beng suffcently technologcally effcent and, thus suffcently envronmentally aware, mply the other countres to be suffcently technologcally neffcent and envronmentally unaware. For such a developed country, the effect () would become stronger, snce ncrease n Nash emsson levels owng to the ncrease n economc target concerns would be smaller; and, the effect () would be weaker, snce ncrease n Nash emsson levels and emsson levels when country unlaterally devates from the cooperatve emsson level owng to the ncrease n economc target concerns would be smaller. Note that f () domnates () for some countres and they cannot sustan cooperaton at x C anymore, then IEA would breaks down. note that for countres to contnue sustanng cooperaton at the agreed cooperatve emsson levels anymore, then that x C The second pont n Proposton states that f country agrees on a more cooperatve emsson level or some other countres j s agree on a less cooperatve emsson levels x C j s, then t s easer for the nequalty (6) to hold. The ntuton s straghtforward: a more cooperatve (lower) emsson level x C would reduce country s economc beneft at cooperatve emsson level and a less cooperatve emsson levels x C j s would ncrease country s economc beneft when t unlaterally devates from the cooperatve emssons. 4. Sustanablty, the Crtcal Dscount Factor, and the Most Cooperatve Emssons In all the propostons, we study how changes n economc target concerns, ether country s or any other country j s or all countres, affect the sustanablty a cooperatve emsson level, gven the agreed upon cooperatve emsson levels x C and a common dscount factor. Alternatvely, we could study the mpact of economc target concerns on the crtcal dscount factor above whch x C can be sustaned by country or on the most cooperatve (mnmum) cooperatve emsson levels x C for a gven. To ths end, frst we solve the no-defecton condton () for and obtan the crtcal dscount factor above whch x C can be sustaned by country : 7 7 See the appendx for more detaled calculatons. (x C,, )= BD B D B C B N, (7)

13 where B C, BD, and BN are abbrevatons of the net beneft functon when all countres cooperate, when country unlaterally devates whle others contnue to cooperate, and at the Nash emssons, respectvely. At ts crtcal dscount factor (x C,, ), country can just sustan the agreed cooperatve emssons x C, thus, ts sustanablty functon equals to zero, S x C,,, =. So far, we have studed how changes n economc target concerns affect countres sustanng cooperaton at a x C. Next, we study the relatonshp between country s ablty to sustan cooperaton at a x C and ts crtcal dscount factor. Ths allows us to nterpret our prevous results from the perspectve of countres patence levels. Lemma Gven any cooperatve emsson levels x C, technologcal neffcences wth n P j= j =, economc target concerns, f country s ablty to sustan cooperaton at x C ncreases (decreases) for some reason other than dscount factor and cooperatve emsson levels x C, S (xc, ) > (<)S (x C, ), then the crtcal (mnmum) dscount factor above whch x C can be sustaned by country decreases (ncreases), (x C ) < (>) (x C ). If country s ablty to sustan cooperaton at x C has ncreased for whatever reason other than and x C, then the crtcal dscount factor before the ncrease does not bnd for sustanng cooperaton at x C. Ths means that country can sustan agreed cooperatve emsson x C wth some dscount factors lower than the crtcal dscount factor before the ncrease. Thus, the crtcal dscount factor decreases after the ncrease n country s ablty to sustan cooperaton at x C. A decrease n crtcal dscount factor (x C ) means even some other relatvely mpatent country s can start sustanng cooperaton at x C. Smlarly, a decrease n country s ablty to sustan cooperaton at x C requres (.) to ncrease and, thus, only suffcently patent country s can contnue sustanng cooperaton at x C. Next, we study the relatonshp between country s ablty to sustan cooperaton at x C and the most cooperatve emsson level t can sustan. Ths allows us to nterpret our prevous results from the perspectve of lowest emssons countres can sustan. Proposton 3 Gven any technologcal neffcences wth suffcently hgh dscount factor of country, n P j= j =, economc target concerns, and a () If country s ablty to sustan cooperaton at x C ncreases (decreases) for some reason other than dscount factor and cooperatve emsson levels x C,.e., S (xc, ) > (<)S (x C, ), then country s most cooperatve emsson decreases (ncreases), x C < (>)x C. () If all countres abltes to sustan cooperaton at x C ncrease (decrease) for some reason other than dscount factor and cooperatve emsson levels, x C,.e., S (xc, ) > (<)S (x C, ) for all, then the most cooperatve emsson levels countres can sustan decrease (ncrease), x C < (>)x C n all dmensons. The ntuton behnd the Proposton 3 s smlar to the one underlyng Lemma. Bascally, after any country s ablty to sustan cooperaton at x C ncreases for whatever reason other than ts dscount factor and cooperatve emsson, the crtcal dscount factor before the ncrease does not bnd for sustanng

14 cooperaton at x C. Ths means that countres wth hgher ablty to sustan cooperaton at x C can support greater degree of nternatonal envronmental cooperaton. An nterestng pont s that a country j s ablty to sustan cooperaton at x C ncreases as x C decreases f b C j >b D j ( ).8 Ths means that country becomng more cooperatve n ts emsson level allows some suffcently patent countres to also emt more cooperatvely. 5 Extensons 5. Symmetrc Countres In ths subsecton, we assume countres to be symmetrc. More specfcally, we assume countres to be dentcal n ther technologcal neffcences, =/n for any, economc target concerns, = j, and agreed cooperatve emsson levels, x C = x C j 8 j. As n proposton, we study the mpact of all countres beng more concerned about ther economc targets. Proposton 4 Gven technologcal neffcences =/n for any, a common dscount factor, and dentcal economc target concerns = j 8j, the most cooperatve emsson level country can sustan x C ncreases n economc target concerns <, n + b C < ( ) b D + b N. (8) n Bascally, the condton (6) smplfes to the condton (8) under symmetry. To nvestgate further ths scenaro, we also resort a numercal analyss. We assume that there are two countres and j, dentcal n ther technologcal neffcences = j =/, n ther types = j, n ther dscount factor = j =.99, and agree to cooperate by emttng the same amount x C = x C j. Moreover, we assume that economc target concerns are L = L j =.3for loss, G = G j =.5 for gan, and S = S =for standard types. We summarze the fndngs n Fgure. It shows how sustanablty functons changes aganst emssons wth any country s type {L, G, S}. The red dotted, blue dashed, and contnuous black curves represent countres beng loss (L), gan (G), and standard (S) types, respectvely. Each curve ntersect the zero value lne twce: the smaller emsson level s the most cooperatve emsson level countres can sustan and the hgher emsson level s the Nash emsson level. For suffcently hgh, we fnd that for some relatvely hgh (less) cooperatve emsson levels the condton (8) does not hold, meanng that a jont ncrease n economc target concerns can ncrease the sustanablty for such relatvely hgh (less) cooperatve emssons. On the other hand, f the countres agree on a low (more) cooperatve emsson level, then a jont ncrease n economc target concerns decreases the sustanablty functons and, thus, the most cooperatve emsson levels of loss, gan, and standard types of countres are ordered as follows: x CL 8 See the appendx for detaled calculatons. > x CG > x CS, for any. Therefore, economc 3

15 Value Emsson Sustanablty functons Loss Gan Standard -4-5 Fgure : The most cooperatve emssons target concerns could be another reason preventng countres to support a greater degree of nternatonal envronmental agreements. 5. Asymmetry n Technology Next, we examne the mpact of countres becomng more or less asymmetrc n ther technologes, n addton to ther possbly asymmetrc economc target concerns. Ths analyss allows us to study a North South relatons model as well as a North North model. To ths end, we employ a numercal analyss wth two countres to ncorporate how technologcal neffcences and j, wth + j =, and dfferent types =(, j ) affect countres ablty to sustan cooperaton. Fgure contans two subfgures. Each shows how the sustanablty of a symmetrc cooperatve emsson, set to x C =(.,.) here, aganst country s technologcal neffcency changes wth country s type {L, G, S}. The two subfgures dffer by the other country j s type j {L, S}. Bold sustanablty functons belong to country and lght sustanablty functons belong country j. The red dotted, blue dashed, and contnuous black curves represent country beng n a loss (L), gan (G), and standard (S) doman, respectvely. In both subfgures, the symmetry n technologes helps to sustan cooperaton. The developng country fals to sustan cooperaton f countres are suffcently asymmetrc n ther technologes. For nstance, n Subfgure a, where j = L, cooperaton can be sustaned by both countres at approxmately (.5;.6), (.46;.58), and (.44;.56) for = S, G, and L, respectvely. Country can sustan cooperaton for values of below the upper lmt and country j can do so for values of above the lower lmt. As ncreases, n other words, as the country s type changes n the drecton of S! G! L, the upper lmt decreases, and sustanng cooperaton becomes more dffcult for country. At the same tme, the lower lmt ncreases, makng t easer for country j to sustan cooperaton, as shown n Proposton. 4

16 (a) Type (L, G, S) and type j = L Value a Sustanablty of Types at q=hlll at q=hgll at q=hsll j at q=hlll j at q=hgll j at q=hsll (b) Type (L, G, S) and type j = S Value a Sustanablty of Types at q=hlsl at q=hgsl at q=hssl j at q=hlsl j at q=hgsl j at q=hssl Fgure : The net beneft of sustanng cooperaton at x C =(.,.) for country type par =(, j ), when the loss-averson parameter =.5and the scalng factor =., for all, and technologcal neffcency, when + j =, at dscount factor =.99. Countres sustan cooperaton for non-negatve values. Bold sustanablty functons represent country and lght sustanablty functons represent country j. The red dotted, blue dashed, and contnuous black lnes represent country s type beng L, G, and S, respectvely. 5

17 In the case of technologcal asymmetres, an ncrease n economc target concerns mght help or hnder sustanng a cooperatve emsson. Fgure shows that the more developed country can sustan cooperaton at the agreed upon emsson level regardless of the economc target concerns. However, economc target concerns do matter for the sustanablty of the less developed country. f country s less developed (.e., s >.5), regardless of economc target concerns of the other country j, havng stronger economc target concerns hnders ts ablty to sustan cooperaton at the agreed upon emsson level. On the other hand, the more developed county j havng stronger economc target concerns facltate sustanng cooperaton for the less developed country. Thus, the best scenaro for the countres to sustan cooperaton s the developng country has weaker and the developed country j has stronger economc target concerns. However, f one consders that developed countres have more establshed poltcal and economc nsttutons and would have weaker economc target concerns than developng countres, then economc target concerns enter as another dffculty for supportng substantal nternatonal envronmental cooperaton. 5.3 Comparatve analyss wth Economc Targets In all our propostons, we focus on the mpact of countres beng more concerned about ther economc targets. Alternatvely, we could examne the mpact of countres havng more ambtous economc targets b R. Ths may lead to two possble scenaros. Frst, f a country contnues to be n a gan or loss after an ncrease n ts economc target b R, then ts objectve functon does not change. In ths case, ts emsson level and sustanablty functons reman the same. Second, f a country starts falng to reach ts economc beneft after an ncrease n ts economc target, then t wll start maxmzng B L (.). In ths case, t wll have stronger concerns about ts economc targets. Therefore, the second scenaro leads to dentcal mplcatons dscussed n the propostons. 6 Concluson Motvated by the fact that many polcy decsons are often nfluenced by poltcal partes ncentves to be elected, we examne the mplcatons for IEAs on transboundary emssons of countres beng motvated to reach ther economc targets and beng averse to falng to acheve ther economc targets. More specfcally, we examne whether countres havng stronger economc target concerns help or hnder the sustanablty of agreed upon cooperatve emssons n the context of self-enforcng IEAs, that s, nvolvng full partcpaton. We fnd that the stronger the concern of a country about ts economc targets, the more dffcult t s for the country to sustan cooperaton, but the easer t s for other countres to do so. If all countres have stronger economc target concerns and are suffcently patent, then t can facltate sustanng cooperaton for a suffcently developed countres n the presence of developng countres, but the effect t ambguous for a developng country. If the countres are symmetrc n all dmensons, then countres havng stronger economc target concerns hnders sustanng cooperaton. Ths means that countres needs to be much more patent to contnue sustanng the agreed cooperatve emsson levels or the most cooperatve 6

18 emsson levels countres can sustan ncrease for the same patence level. The real IEAs, such as clmate change, are much more complex than the smple model utlzed here. They requre nternatonal coordnaton to agree on the cooperatve emsson levels, n whch countres often fal to keep ther promses. We show that even n a world n whch sustanng the most cooperatve emssons s effortless, ambtous economc targets owng to an ncentve to be elected lead to IEAs wth less cooperatve emsson levels than could be acheved wthout such concerns. Thaler and Sunsten (8), n ther hghly nfluental book, suggest nudges. It s a desgn of a choce envronment usng frames and defaults, among others, that alters people s behavor n a predctable way, wthout mandatng a partcular acton or changng economc ncentves, n order to overcome behavoral falures. However, the mpact of nudges s lmted f polcymakers suffer from such behavoral falures, ether drectly or through voters, as dscussed n the ntroducton. Whle a poltcal party can frame the clmate change problem to alter behavor to promote greener polces (e.g., Al Gore), another can frame t to favor nacton (e.g., the Bush admnstraton). 9 It appears that correctng the ncentves leadng to ambtous economc targets and an averson to economc losses requre a strong call for acton at the sub-natonal level. As ctzens of the earth, we should talk more about the envronmental problems and rase publc awareness to ncentvze poltcal partes to pursue greener polces. Appendx: Calculatons and Proofs Calculatons: Technologcal neffcency and Nash = It s straghtforward to N /@ j ( ) + ( ) X j j A j6= X j j A > j6= (9) Net beneft functons: It s straghtforward to see that substtutng cooperatve emssons nto B L (.) gves (). Let s substtute the best response functon n (8) nto B L (.) to fnd the net beneft functon when country unlater- 9 See Gsottbauer and van den Bergh (3) for the detals of these frames. Communcaton and rasng publc awareness s one of the four strategc prortes of the U.N. Envronmental Programme s clmate change programme. 7

19 ally devates whle others contnue to cooperate, B L X ( + x C j ) A + j6= X ( + x C j ) A + j6= = + + Xj6= xc X BR x C j,x C j,br = j6= xc X ( + x C j ) A + + b R j6= X ( + + b R j6= x C j ) A b R () We substtute Nash emsson n () nto B L (.). Usng the (9) and some algebra gve the net beneft at the Nash emssons, B L x NL,...,x NL n,b R = = x NL = = = + nx ( ) + ( ) x NL! b R X j j AA j6= X j j AA j6= X j j AA j6= P j j j6= C A + + P + n j j j= C A + j j A b R j= + ( ) b R b R Xj6= j j b R () Crtcal Dscount Factor The condtons () and (7) are equvalent. For notatonal smplcty, let us use B C, BBR, and B N for net beneft functons when all countres cooperate, when country unlaterally devates whle others contnue to cooperate, and at the Nash emssons, respectvely. B C B BR + B N, B C ( )B BR + B N, B BR B N B BR B C, B BR B BR B C B N () 8

20 Interdependence of Countres Most Cooperatve C = (xc j ) j = b C j j + + j + j X6=j xc + b D j j, (3) C <, we should have: b C j >bd j ( ). Proofs: Proof of Proposton. We take the dervatve wth respect to () = x C {z } b C + Pj6= xc j! + {z } b BR ( )(+ ) ( P +( ) j6= j j ). {z } b NL (4) For country s sustanablty to decrease n ts economc <, b C < ( )(+ ) b NL +( {z } ) b BR. (5) > Snce x NL >x C and BR x C >x C, we have bnl >b C and b BR >b C. Then, any pont n convex combnaton of b NL and b BR s also hgher than b C, whch completes part () of the proof. Let us now take the dervatve of S j wth respect to () = =(+ j ) P j +( j ) j 6=j j j {z } b NL j P 6=j > (6) Ths condton always holds because t s the same condton requred for the Nash emssons to be postve n (), completng the proof of part (). Proof of Proposton. Total dervaton of the sustanablty functon wth respect to countres economc target concerns, ds = b C d + j d j : b BR ( )(+ ) ( ) b NL d + X ( + ) j6= P j6= j ( ) b NL d j (7) Note that P j6= j =. The sustanablty of country ncreases by an equal ncrease n all 9

21 countres economc target concerns (d = d 8) f ds >, b C ( ) b BR ( )(+ ) b NL b C ( ) b BR + ( + ) b C ( ) b BR + ( + ) +(n ) ( + ) ( ) b NL >, b NL ((n ) ( ) + ) >, b NL (n 3 (n )) > (8) () The last parenthess becomes postve f apple n 3 n, whch also requres n 4. In ths case, the condton (6) does not hold for suffcently large. Otherwse, we need to know specfc parameter values n order to determne whether the condton (6) holds or not. () It s easer for the condton (6) to hold for a lower x C, snce the only term that depends on t n the condton (6) s b C, whch decreases for a lower xc. On the other hand, It s easer for the condton (6) to hold for hgher x C j s, snce the only term that depends on them n the condton (6) s bd, whch ncreases for hgher x C j s. Proof of Lemma. Gven the parameters of the model, let (x C ) be the crtcal dscount factor so that S (x C, ) =. Suppose, for some reason other than dscount factor and cooperatve emssons x C, country s sustanablty ncreases, S (xc, ) >S (x C, ) =. Therefore, there exsts another such that S (xc, )=and (.) < (.). Proof of Proposton 3. () Suppose country s sustanablty ncreases for some reason other than ts dscount factor and cooperatve emssons x C. We know by lemma that f S (xc, ) >S (x C, ) for any cooperatve emssons x C, then (x C ) < (x C ). Furthermore, from (7), we have B D B D B C = (x C ) B D B N B C = (x C ) B D B N (9) Snce (x C ) < (x C ): B D (x C ) B D B C < (x C ) B D <B C (x C )B N, B N, (3) meanng that the no-defecton condton (7) does not bnd for country at the x C, (x C ) par. Note that B N does not depend on the cooperatve emssons. Moreover, B D does not depend on country s cooperatve emssons. Thus, country can sustan cooperaton at ˆx C such that ˆx C < x C and ˆx C j = xc j for any j. Snce these arguments apply to any x C, (x C ) par for any (x C ) that countres can mantan some cooperaton, we have that for any such, x C < x C. () Let all countres sustanablty functons ncreases for some reason other than ts dscount factors and cooperatve emssons. For any country, the condton (3) does hold. For any cooperatve emssons

22 x C lower than x C n all dmensons, net beneft under defecton s hgher at x C than at x C : B BR x C,x C,,b R >B BR x C, x C,,b R (3) Furthermore, for such a x C < x C, net beneft under cooperaton s also hgher at x C than at x C : B x C,,,b R >B x C,,,b R (3) By the contnuty of B (.), there exst a cooperatve emssons vector x C < x C such that for any country the condton (3) stll holds. Snce these arguments apply to any x C, (x C ) par for any (x C ) that countres can mantan some cooperaton, we have that for any such, x C < x C. Proof of Proposton 4. Country s sustanablty functon under symmetry: S = = xc /n + nx C n n + + (n )x C n+ n (/n) /n + n+ n. (33) We take the dervatve wth respect to n order to capture the mpact of havng dfferent degrees of economc target concerns or types changng n the drecton of S! G! = = /n n + + (n )x C /n n + n ( ) (/n)/n /n + (34) Any country s sustanablty decreases as ts economc target <, x C /n {z } b C < ( ) /n n + + (n )x C {z } b D + n + n ( + ) /n. (35) n {z } b N By proposton, we know that f all countres sustanablty functons decrease, then the most cooperatve emssons countres can sustan ncreases, completng the proof. References Alesna, A. and Passarell, F. (4). Loss averson n poltcs. Ashem, G. and Holtsmark, B. (9). Renegotaton-proof clmate agreements wth full partcpaton: Condtons for pareto-effcency. Envronmental and Resource Economcs, 43(4): Barrett, S. (994). Self-enforcng nternatonal envronmental agreements. Oxford Economc Papers, 46: