INTERNATIONAL AND INTERGENERATIONAL DIMENSIONS OF CLIMATE CHANGE: NORTH-SOUTH COOPERATION IN AN OVERLAPPING GENERATIONS FRAMEWORK

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1 INTERNATIONAL AND INTERGENERATIONAL DIMENSIONS OF CLIMATE CHANGE: NORTH-SOUTH COOPERATION IN AN OVERLAPPING GENERATIONS FRAMEWORK by Alberto Ansuateg, Marta Escapa and Azucena Pérez 2003 Workng Paper Seres: IL. 06/03 Departamento de Fundamentos del Análss Económco I Ekonom Analsaren Onarrak I Sala Unversty of the Basque Country

2 Internatonal and Intergeneratonal Dmensons of Clmate Change: North-South Cooperaton n an Overlappng Generatons Framework. Alberto ANSUATEGI Marta Escapa Azucena Pérez Unversty of the Basque Country (SPAIN) December 2003 Abstract Global envronmental problems such as clmate change have both an nternatonal and an ntertemporal dmenson. Recently, some papers have used an overlappng generatons framework to analyze the clmate change problem takng nto account jontly the ssues of ntergeneratonal equty and ntertemporal effcency but wthout consderng the nternatonal aspect of the problem. In ths paper, we extend such approach by consderng an overlappng generatons model of clmate-economy nteractons where the world s splt nto two regons: North and South. We resort to numercal smulatons of the calbrated model to analyze the effect of cooperaton over economc and clmate varables under two dfferent scenaros: long-lved and short-lved governments. The man am of our analyss s to test numercally whether John and Pecchenno s (1997) theoretcal result, whch states that nternatonal agreements wth transfers that lack an ntergeneratonal perspectve could actually harm the envronment, apples to the problem of clmate change or not. Numercal results obtaned allow us to conclude that when we consder short lved governments: (1) the lack of cooperaton always leads to hgher envronmental degradaton, (2) the hgher the welfare weght attached to the North under cooperaton, the lower the envronmental degradaton n the long run, and (3) some cooperatve scenaros may lead n the short run to hgher envronmental degradaton than what t would arse n the non cooperatve scenaro. JEL classfcaton: C70, D62, Q2 Keywords: Clmate Change, Internatonal Envronmental Agreements, Intergeneratonal Externaltes Contact address: Dpto. Fundamentos del Análss Económco I, Unversdad del País Vasco-EHU, Lehendakar Agrre, 83, Blbao, SPAIN. E-mal: jepancoa@bs.ehu.es 1

3 1 Introducton In the last decade the nternatonal communty has become ncreasngly concerned wth the fact that the ncreased concentraton of greenhouse gases (GHG hereafter) n the atmosphere wll cause a global clmate change whch mght have serous effects on socety n the future. In fact, the queston s not whether the Earth s clmate wll change, but rather how much clmatc condtons wll change, how fast t wll occur and how the effects of ths change wll be dstrbuted across dfferent regons n the world. Most scentsts, whlst recognzng that uncertantes exst, beleve that human-nduced clmate change s already occurrng and that future change s nevtable 1. It has been wdely recognzed that cooperaton among countres to reduce GHG emssons s necessary to avod or to mtgate global clmate change. Nevertheless, and n spte of the potental welfare gans that countres can obtan from cooperaton, a bndng nternatonal agreement on clmate change has not been reached yet. The 1997 Kyoto Protocol represents the only agreement reached on clmate change so far and t has not entered nto force because t s stll awatng ratfcaton by many of the 159 countres that adopted t 2. In Kyoto, countres agreed to emssons reductons targets and methods, but t was left to subsequent meetngs to decde on most of the rules and operatonal detals that wll determne how these cuts wll be acheved and how countres efforts wll be measured and assessed. Although many countres sgned the Protocol, the majorty were watng for these operatonal detals to be negotated before decdng whether or not to ratfy the Protocol. Currently, the Protocol only needs ratfcaton by the Russan Federaton to enter nto force. Each Conference of the Partes (COP), where decsons are taken about the mplementaton of the Protocol, has faced a lot of dffcultes 3. It s 1 As t s stated n the IPCC reports to the UNFCCC, t s undsputed that the two last decades have been the warmest for the last 1000 years, sea level s rsng, precptatons patterns are changng, Arctc sea ce s thnnng and the frequency and ntensty of El-Nño events appear to be ncreasng. Moreover, n ts Thrd Assesment Report (2001), the IPCC estmated that globally average surface temperature would ncrease n the range of 1.4 to 5.8 o C between 1990 and Only eght years ago, the IPCC predcted that average temperatures would, at worst, rse by 3 o C. 2 The Kyoto Protocol commts 39 advanced ndustralzed states to cut emssons of fossl fuel gases by an average of 5.2% of 1990 levels by the perod To enter nto force, ths Protocol must be ratfed by 55 Partes to the UN clmate change treaty, ncludng Annex I Partes representng at least 55% of the total carbon doxde emssons for The latest nformaton concernng negotatons and the status of ratfcaton of the Kyoto Protocol can be found n 3 At the World Summt for Sustanable Development held n Johannesburg n 2002 the Executve Secretary of the UNFCCC noted that: In the Conventon s frst decade, the centrepece of global negotatons was to agree on rules for mplementaton. Our challenge now s to apply those rules and move clmate change to the centre of natonal polcy-makng and acton by busness and cvl socety. 2

4 evdent that some of the dffcultes are due to both the nternatonal and the ntergeneratonal dmenson of the problem. Clmate change s an nternatonal problem because t wll affect all countres of the world, wth developng countres (specally the poor n developng countres) beng most vulnerable. But t s also an ntergeneratonal problem because damage due to clmate change wll occur over tme affectng not only to present generatons but also to future generatons. The economc lterature on clmate change has typcally adopted the nfntely-lved agent (ILA) framework to analyze the nternatonal and ntertemporal dmenson of the problem. However, these models do not always allow to take nto account n a proper way the ntergeneratonal dmenson of the problem. As Schellng (1995) ponts t out, ILA models rest on strong assumptons regardng the aggregaton of welfare between generatons and world regons 4. Some recent studes of clmate change have made use of overlappng generatons (OLG) models to study jontly ntertemporal effcency and ntergeneratonal dstrbuton ssues. Examples nclude Ansuateg and Escapa (2002), Gerlagh and Zwaan (2001b), Gerlagh (2000), Howarth (1996 and 1998) and Marn and Scaramozzno (1995). There are also several papers that compare the results derved from ILA and OLG models used to analyze clmate change. On the one hand, Howarth (2000) and Stephan et al. (1997) show that, under certan assumptons and parameter values, both types of models do not dffer n ther mplcaton for greenhouse polcy. On the other hand, Gerlagh and Zwaan (2001a) show that polcy recommendatons derved from OLGmodelscanproveratherdfferent from those resultng from conventonal ILA models dependng on varous assumptons on demographc change and publc nsttutons desgned for the protecton of the envronment. To be exact, ther model ncludes demographc change that represents ncreasng lfe expectancy 5, specfes envronmental damages as a loss of an envronmental amenty assocated to an envronmental resource and consders a transfer mechansm that dstrbutes the value of ths resource to consumers. In the studes mentoned above, the world s descrbed as a sngle regon. However, n real lfe, the world s dvded nto a set of heterogenous countres each of whom can decde about ts own envronmental polcy. As we have just mentoned, nternatonal cooperaton to coordnate those envronmental polces s crucal to tackle the global warmng problem. To our knowledge, there s only one paper (John and Pecchenno 1997) where an nternatonal externalty s analyzed takng nto account explctly the ntergeneratonal dmenson of such external effect. In John and Pecchenno s paper a successve generaton model 6 s consdered and t s assumed that each regon s government can be ether a longlved or a short-lved government, dependng on the tme horzon the government 4 An mportant ssue of dscusson n these models refers to the dscount rate to be used. A descrpton of the two major approaches used to determne the dscount rate for clmate change analyss can be found n IPCC (1995). 5 It s modeled as a transton from a lfecycle of two perods to one of three perods. 6 Itsassumedthatanewgeneratonsbornateachdatetn each country and lves for one perod. 3

5 uses to select ts optmal polcy. They conclude that, although transfers may be necessary to compensate the developng world, nternatonal agreements wth transfers that lack an ntergeneratonal perspectve could actually harm the envronment. In ths paper, we use the OLG model wth clmate-economy nteractons descrbed n Howarth (1998). Snce we are nterested n the nternatonal dmenson of the problem, we have dvded the world nto two regons, whch wll be referred to as North and South. As n John and Pecchenno (1997), we consder that each regon s government can be ether a long-lved or a short-lved government. Dstngushng long lved governments from short lved governments makes t possble to study the effect of takng nto account the ntergeneratonal dmenson of clmate change n nternatonal agreements. We assume that taxes are used to nternalze all types of externaltes and that both, short-lved and long-lved governments, are able to mplement ntergeneratonal transfers, whch are chosen smultaneously wth optmal taxes when the socal welfare functon s maxmzed. Besdes, we consder the possblty that each regon s wllng to make unlateral monetary transfers 7 to the other regon. The scenaro where long-lved governments act cooperatvely allows us to obtan the ntertemporally and nternatonally effcent taxes on GHG emssons whch are such that margnal cost of GHG emssons abatement s set equal to the dscounted sum of every future beneft. The man am of the paper s to check whether nternatonal agreements wth transfers that lack an ntergeneratonal perspectve could actually ncrease global GHG emssons wth respect to the non cooperatve soluton, as John and Pecchenno (1997) predcted n a theoretcal settng. A pror, ths result may occur n our model because when short-lved governments decde the transfers from North to South, they do not take nto account the effects of these transfers on future generatons. Gven that the emsson-output rato s hgher n the South and that transfers mply an ncrease n the producton growth rate of the South n relaton to the non cooperatve soluton, cooperaton wth transfers could mply a level of GHG emssons hgher than that of the non cooperatve soluton. Smulaton exercses are used to compare numercally the evoluton of economc and clmate varables on the dfferent scenaros consdered. The calbraton of the model s based on the scentfc and technologcal assumptons of RICE (Nordhaus and Yang 1996) and the specfc parameters for North and South regons have been taken from Yang (1999). The paper s organzed as follows. After ths ntroducton, secton 2 presents 7 German, Tont and Tulkens (1997), German, Tont, Tulkens and Zeeuw (2003) and Eyckmans and Tulkens (2003) show how nternatonal transfers may be used to facltate cooperaton as they allow to compensate those countres whch are worse off wth the agreement. However, these studes do not consder an overlappng generatons framework. Yang (1999) also analyzes the effects of unlateral transfers from North to South but n an envronmental-economc optmal growth model. In contrast to Yang s paper, where government recevng the transfer must use t to purchase technology to reduce GHG emssons, we assume that the government recevng the monetary transfers uses them to make transfers to consumers. 4

6 the model. Secton 3 descrbes the command optmum. Secton 4 obtans the market equlbrum. Secton 5 combnes the results obtan n the prevous two sectons to show the requred polcy nterventon n dfferent nsttutonal settngs. The model s calbrated n secton 6 and numercal results are contaned n secton 7. 2 The model In our model of global clmate-economy nteractons the world s dvded nto two regons: North and South. Each regon s assumed to produce a sngle commodty whch can be used for ether consumpton or nvestment. Populaton growth and technologcal change are exogenous, whereas captal accumulaton s determned through optmzaton of lfe-cycle savng by ndvduals. The model does not consder nter-regonal trade n goods or captal nor nter-regonal moblty of labor, but unlateral transfers of output between the North and the South (θ t ) are allowed. The approach taken n the model vews the economy n the smplest overlappng generatons framework that assumes that each generaton lves only for two perods. At each date t =0, 1,..., T and n each regon = North, South a new generaton of n t dentcal ndvduals s born who lves at dates t and t +1. Indvduals of generaton t wll be young n t and old n t +1. A typcal person born at date t n regon enjoys the consumpton levels c yt n youth and c ot+1n old age. It s assumed that ndvduals do not get utlty from lesure and so supply ther unt of labor nelastcally to the producton sector at each stage of lfe, earnng a real wage of wt n youth and wt+1n old age. Besdes, each ndvdual receves net ncome transfers π yt and π ot+1 from the regonal government at dates t and t Indvdual preferences are represented by an addtve separable utlty functon defned over per capta consumpton n youth and n old age: u t = u(c yt)+ 1 1+ρ u(c ot+1) ρ = 0,u 0 (.) > 0,u 00 (.) < 0 (1) where ρ represents ndvduals pure tme preference n regon 9. Agentsarebornwthnoassetsandchoosetoendupwthzeroassetswhen they de. The aggregated savng of the young n regon at tme t (St n ts t) generates the aggregated captal stock (Kt+1 n tkt+1) thatsusednregon at tme t +1 to produce output n combnaton wth the aggregated labor supply (Nt+1 n t+1 + n t ) and the resdual emssons of GHGs (E t+1 )nregon at tme t +1. The nvestment n captal of the young n regon at tme 8 Regonal governments use these ntergeneratonal ncome transfers to release the revenues rased by a pgovan tax on greenhouse gas emssons and to acheve a desred dstrbuton of welfare between generatons. 9 The hgher s ρ the hgher s the weght attached to ncrements of consumpton n youth relatve to ncrements of consumpton n old age. 5

7 t (kt+1) s rented out at an nterest rate rt+1to the producton sector to help fnancng consumpton n old age. Thus, the followng equatons represent a typcal person s budget restrctons n regon : c yt + s t = w t + π yt (2) c ot+1 = w t+1 +(1+r t+1)k t+1 + π ot+1 (3) Producton at tme t n regon s organzed by compettve frms that use constant returns technology: Y t = f t (K t,n t,e t,t t ) (4) We assume that f t (.) s ncreasng n captal (K t), labor (N t )andghg emssons (E t) and decreasng n the change of mean global temperature relatve to the prendustral norm (T t ). The tme subscrpt on the producton functon allows for exogenous technologcal change. The change of mean global temperature relatve to the prendustral norm (T t ) s a global publc bad that wll be determned by the tme path of GHG emssons n the past: T t = T t µ P E 0,..., P E t 1 (5) Thus, current emssons wll mply ncreased future envronmental degradaton and hence reduced future output. We wll therefore assume that each regonal government taxes GHG emssons at a rate vt to account for ther negatve mpact on producton. Before proceedng wth the analyss we requre explct assumptons regardng governments scope and dstrbutonal justce crtera. These are dscussed n the next secton. 3 The command optmum 3.1 Non cooperatve short lved governments We wll frst consder the case of short lved regonal governments (NCSL governments hereafter) that do not behave cooperatvely. We wll consder that the non cooperatve stuaton s represented by the open loop Nash soluton whch mples that governments commt themselves to an optmal polcy and cannot react to any devatons from that optmal polcy. Therefore, NCSL government at tme t n regon optmzes resource allocaton and consumpton 6

8 decsons at tme t n regon n order to maxmze utlty of those agents lvng at tme t n regon and assumng that the government at tme t n regon j as well as governments at tme l>tn both regons wll also follow the same strategy. The non cooperatve nature of the government mples that pgovan taxes wll be desgned n order to yeld a wthn regonal effcent allocaton of resources. In other words, GHG emssons wll be locally prced accordng to ther margnal mpact on the local economy and gnorng ther margnal mpact on the rest of the world economy. Note also that, as non cooperatve governments wll thnk regonal nstead of global, no nter regonal transfers of output wll take place (θ t =0). The short lved nature of the government mples that pgovan taxes wll be desgned n such a way that they wll only pursue an effcent allocaton of resources from an ntergeneratonally lmted perspectve. Ths means that, when determnng the optmal prce of GHG emssons, all those effects that outlve the two generatons represented by the government wll be gnored. As t has been mentoned n the prevous secton, the government uses net ncome transfers to release the revenues rased by the tax on GHG emssons and to acheve a desred dstrbuton of welfare between generatons. We assume that taxes and transfers are chosen to obey the balanced budget condton: n tπ yt + n t 1π ot = v te t (6) The desred dstrbuton of welfare between young people and old people wll depend on socal preferences, whch are captured by the followng socal welfare functon: Wt = 1 1+ρ u(c ot)+ 1 1+R u(c yt)+ 1 1+ρ u(c ot+1) (7) where 1+R 1 represents the weght the government n regon attaches to the lfe cycle utlty of a typcal young person relatve to the lfe cycle utlty of a typcal old person. The NCSL regonal government s decsons are subject to ndvduals budget constrants (equatons (2) and (3)) and the followng three constrants: f t (K t,n t,e t,t t )=n tc yt + n t 1c ot + K t+1 K t (8) f t+1 (K t+1,n t+1,e t+1,t t+1 )=n t+1c yt+1 + n tc ot+1 + K t+2 K t+1 (9) T t+1 = T t+1 µ P E 0,..., P E t (10) 7

9 Equatons (8) and (9) characterze consumpton possbltes of the economy n regon at tmes t and t+1 respectvely. Equaton (10) establshes the mpact of current emssons on future envronmental qualty. At each pont n tme, t, the NCSL government maxmzes (7) subject to dfferent budget constrants. Ths maxmzaton problem yelds the condtons: 1+R n t (1 + ρ ) n t 1 = u0 (c yt) u 0 (c ot) (11) (1 + ρ )u 0 (c µ yt) u 0 (c ot+1 ) = 1+ f t+1 Kt+1 (12) ft Et µ = 1+ f t+1 1 f t+1 T t+1 Kt+1 T t+1 Et (13) Equaton (11) establshes that aggregated consumpton at each date must be dstrbuted between ndvduals as to equate the margnal contrbuton of each generaton s consumpton to perceved socal welfare. Equaton (12) establshes that each ndvdual s margnal rate of ntertemporal substtuton must be set equal to the gross return on captal nvestment. Equaton (13) establshes that the margnal cost of GHG emsson abatement must be set equal to the margnal present value damage that current emssons mpose locally n the next perod. 3.2 Cooperatve short lved governments Next we wll consder the case of short lved regonal governments that do behave cooperatvely (CSL governments hereafter). The CSL government at tme t optmzes resource allocaton and consumpton decsons at tme t n order to maxmze aggregated utlty of those agents lvng at tme t n both regons and assumng that governments at tme l>twll also follow the same strategy. The cooperatve nature of the government mples that pgovan taxes wll be desgned n order to yeld a cross regonal effcent allocaton of resources. In other words, GHG emssons wll be locally prced accordng to ther margnal mpact on the global economy. Note also that, as cooperatve governments wll thnk global we wll relax the assumpton that no nter regonal transfers of output wll take place. The short lved nature of the government stll mples that pgovan taxes wll be desgned n such a way that they wll only pursue an effcent allocaton of resources from an ntergeneratonally lmted perspectve. Thus, as n the prevous scenaro, when determnng the optmal prce of GHG emssons, all those effects that outlve the two generatons represented by the short lved governments wll be gnored. 8

10 Havng specfed two types of transfers, ntergeneratonal transfers and nter regonal transfers, we need to re specfy regonal governments balanced budget condtons. In what follows we wll represent varables referrng to the South wth an astersk to dstngush them from varables referrng to the North. The balanced budget condtons of CSL governments are thus the followng: n t π yt + n t 1 π ot = v t E t θ t (14) n t π yt + n t 1 π ot = v t E t + θ t (15) We assume that when θ t s postve (negatve), the South (North) uses net ncome transfers to release the revenues rased by both the tax on GHG emssons and the transfers receved from the North (South) and the North (South) uses the revenues rased by the tax on GHG emssons to make transfers to ndvduals n ts regon and to make transfers to the South (North). The desred dstrbuton of welfare between young people and old people n both the North and the South wll depend on socal preferences agreed by the two cooperatve governments. These socal preferences wll be captured by the followng socal welfare functon: 1 W t = α 1+ρ u(c ot)+ 1 1+R +(1 α) u(c yt ) ρ u(c ot)+ 1 1+R 1+ρ u(c ot+1) + (16) u(c yt)+ 1 1+ρ u(c ot+1) where α and (1 α) represent the weght attached to the local welfare of the North and the South, respectvely. At each pont n tme, t, CSL governments maxmze (16) subject to dfferent budget constrants. Ths maxmzaton problem yelds the condtons: (1 + R) n t = u (c yt ) (1 + ρ) n t 1 u 0 (c ot ) 0 (17) (1 + R ) n t (1 + ρ ) n = u0 (c yt) t 1 u 0 (c ot) (1 + ρ)u 0 (c yt ) u 0 (c ot+1 ) = µ 1+ f t+1 K t+1 (1 + ρ )u 0 (c µ yt) u 0 (c ot+1 ) = 1+ f t+1 Kt+1 (18) (19) (20) 9

11 u 0 (c ot ) u 0 (c ot) = n t 1(1 α)(1 + ρ) n t 1 α(1 + ρ ) (21) f t+1 K t+1 = f t+1 K t+1 (22) f t E t = f t E t µ = 1+ f 1 t+1 ft+1 + f t+1 Tt+1 (23) K t+1 T t+1 T t+1 E t Equatons (17) and (18) establsh that aggregated consumpton n each regon at each date must be dstrbuted between ndvduals as to equate the margnal contrbuton of each generaton s consumpton to perceved socal welfare. Equatons (19) and (20) establsh that n each regon each ndvdual s margnal rate of ntertemporal substtuton must be set equal to the gross return on captal nvestment. Equaton (21) establshes that aggregate consumpton n the world economy at each date must be dstrbuted between ndvduals n dfferent regons as to equate the margnal contrbuton of ndvduals of dfferent regons to perceved socal welfare. Equaton (22) establshes that productve captal must be redstrbuted nternatonally as to equate the margnal productvty of captal across regons. Equaton (23) establshes that the margnal cost of GHG emsson abatement n each regon must be set equal to the margnal present value damages that current emssons mpose globally n the next perod. 3.3 Cooperatve long lved governments Fnally we wll consder the case of long lved regonal governments that do behave cooperatvely (CLL governments hereafter). The CLL government at tme 0 n regon optmzes resource allocaton and consumpton decsons at tme t [0,T] n regon n order to maxmze aggregated utlty of those agents lvng at tme t [0,T] n both regons and assumng that the government n regon j 6= wll also follow the same strategy. The cooperatve nature of the government mples that pgovan taxes wll be desgned n order to yeld a cross regonal effcent allocaton of resources and that nter regonal transfer of output may take place. The long lved nature of the government stll mples that pgovan taxes wll be desgned n such a way that they wll pursue a fully effcent allocaton of resources from an ntergeneratonal perspectve. When determnng the optmal prce of GHG emssons every future mpact of emssons wll be taken nto account. We assume that at each pont n tme the CLL governments face the same balanced budget condtons that were assumed for CSL governments. Wth 10

12 regard to socal preferences, these preferences wll be captured by the followng socal welfare functon: " T # X X T W 0 = α (1 + R) t 1 u(c yt )+(1+ρ) 1 (1 + R) t u(c ot ) + (24) t=0 " T # X X T (1 α) (1 + R ) t 1 u(c yt)+(1+ρ ) 1 (1 + R ) t u(c ot) t=0 At tme 0, CLL governments maxmze (24) subject to dfferent budget constrants. Ths maxmzaton problem yelds the same frst order condtons as those of the short lved governments except for equaton (23), that now t has to be re wrtten as: t=0 t=0 f t E t = f t E t = TX h=t+1 Ã sy l=t+1 µ 1+ f! 1 l fh + f h Th (25) K l T h T h E t Equaton (25) establshes that the margnal cost of GHG emsson abatement n each regon must be set equal to the present value of future margnal damage that current emssons mpose globally. 4 The market equlbrum The prevous secton provded the socal governments soluton to the optmal resource allocaton problem. In ths secton we consder the decsons of consumers and frms. The consumers problem: The representatve consumer s optmzaton problem can be wrtten as follows: max c yt,c ot+1 u(c yt)+ 1 1+ρ u(c ot+1) (26) subject to the followng budget constrants: c yt + s t = w t + π yt (27) c ot+1 = w t+1 +(1+r t+1)s t + π ot+1 (28) Solvng the frst order condtons gves us 11

13 (1 + ρ ) = u 0 (c yt) u 0 (c ot+1 ) (29) 1+r t+1 The frms problem: The frms optmzaton problem can be wrtten as follows: max K t,e t f t (K t,n t,e t,t t ) w tn t r tk t v te t (30) The frst order condtons wll be: ft Kt = r t (31) ft Et = v t (32) >From the zero proft condton, we note that f t (K t,n t,e t,,t t ) r tk t v te t N t = w t (33) The compettve equlbrum for ths economy s completed wth the goods market clearng condton that establshes that the captal stock at tme t +1 s fully determned by savng decsons made at tme t: K t+1 = n ts t (34) 5 GHG emsson taxes and ntergeneratonal transfers In ths secton we combne the results obtaned n sectons 3 and 4 to show the requred polcy nterventons n dfferent nsttutonal settngs. After comparng the condtons obtaned n the prevous two sectons, t s clear that the compettve equlbrum does not n general support an optmal dstrbuton of welfare. Two types of nterventons are requred n order to acheve an optmal dstrbuton of welfare. Frst, emssons must be properly prced (emsson taxes). Second, ncome transfers (π yt and π ot) have to be selected wth the ntenton of maxmzng socal welfare. Emsson taxes wll vary dependng on the nternatonal and ntertemporal scope of the regulatory body. NCSL governments wll choose emsson taxes to 12

14 equate the margnal present value damage that current emssons mpose locally n the next perod: µ vt = 1+ f t+1 1 f t+1 T t+1 Kt+1 T t+1 Et (35) Ths wll ensure the equvalence between equatons (13) and (32). CSL governments wll choose emsson taxes to equate margnal cost of GHG emssons abatement and the margnal present value damage that current emssons mpose globally on generaton t when old: µ v t = vt = 1+ f 1 t+1 ft+1 + f t+1 Tt+1 (36) K t+1 T t+1 T t+1 E t Ths wll ensure the equvalence between equatons (23) and (32). CLL governments wll choose emsson taxes to equate margnal cost of GHG emssons abatement and the margnal present value future damage that current emssons mpose n every regon at any pont n tme: v t = v t = TX h=t+1 Ã sy l=t+1 µ 1+ f! 1 l fh + f h Th (37) K l T h T h E t Ths wll ensure the equvalence between equatons (25) and (32). 6 Model calbraton To proceed wth the analyss we must mpose specfc assumptons regardng the model s functonal forms and parameter values. We calbrate the model based on the techncal constrants of Yang s (1999) two regon verson of the RICE model developed by Nordhaus and Yang (1996). Both models smulate economy envronment nteractons usng an ILA framework. The man dfference s that n Nordhaus and Yang s RICE model the global economy s dvded nto sx regons, whereas n Yang s modfed RICE model these sx regons are merged nto two regons: the North and the South. More precsely, n the modfed RICE model the North represents the USA, Japan and the European Unon, whle the South ncludes the Former Sovet Unon, Chna and the rest of the world n the orgnal RICE model. We take the year 2000 as the startng pont for our analyss wth an ntal global populaton of bllon people, wth bllon people lvng n the North and lvng n the South. Accordng to data taken from the U.S. Bureau of the Census ( people under the age of thrty fve account for some 50% n the North and 65% n the South. Based 13

15 on these observatons, the number of young people lvng at each date n each regon can be parameterzed n the followng manner 10 : n yt = ( ) t (38) n yt = ( ) t (39) Equaton (38) mples an ntal populaton growth rate of 0.3%/year n the North wth convergence over the long run to a populaton of bllon people. Equaton (39) mples an ntal populaton growth rate of 1.04%/year n the South wth convergence over the long run to a populaton of bllon people. These patterns closely match the aggregate demographc assumptons contaned n Yang s modfed RICE model. Followng Yang, utlty s logarthmc n consumpton and we assume that n each regon gross regonal output (Yt ) s gven by a Cobb Douglas producton functon defned over captal (Kt)andlabor(N t ): Yt = A tkt 0.25 Nt 0.75 where A t s an ndex of total factor productvty. The nput output elastctes are based on the assumpton that wage ncome accounts for 75% of gross output n the global economy. Based on Yang s baselne model s estmates for the year 2000, the ntal captal stock s set equal to trllon dollars n the North and trllon dollars n the South. The level of GHG emssons that would arse n the absence of polluton abatement (E ot), measured n bllon tons of carbon equvalent per perod, are assumed to be lnearly proportonal to gross output: E ot = ³ (0.4661) t Y t (40) E ot = ³ (0.6484) t Y t (41) Equaton (40) mples that the emssons output coeffcent falls at an annual rate of 1.03% n the North n the year 2000, wth convergence to a 49% reducton of the emssons output coeffcent n the long run. Equaton (41) mples that the emssons output coeffcent falls at an annual rate of 1.14% n the South n the year 2000, wth convergence to a 476% reducton of the emssons output coeffcent n the long run. These patterns of energy-savng technologcal change closely match the numercal content of the modfed RICE model. 10 Havng assumed that each generaton lves for two perods, each perod should represent half of human lfe span (' 35 years). 14

16 Total factor productvty n each regon s determned by the nteracton of three terms: A t = Ã (0.7748) t µ!ã 1.5 µ Tt E! 2.89 t 2.5 E ot (42) A t = Ã (0.8139) t µ!ã 1.5 µ Tt E! 2.89 t 2.5 E ot (43) The frst term n equaton (42) mples an ntal rate of exogenous technologcal progress of 1.38%/year n the North. Ths rate falls steadly over tme wth a long run productvty ncrease of 263% relatve to the present. The frst term n equaton (43) mples an ntal rate of exogenous technologcal progress of 3.19%/year n the South. Ths rate falls steadly over tme wth a long run productvty ncrease of 1507% relatve to the present. The patterns of exogenous technologcal change closely match the numercal content of the modfed RICE model. Followng the modfed RICE model, our model assumes that clmate change damages ncrease wth the square root of the cubc change n mean global temperature relatve to the pre ndustral norm. A temperature ncrease of 2.5 o C causes a 1.155% reducton n gross output n the North and 1.6% reducton of gross output n the South. Ths effect s captured n the second term of equatons (42) and (43). The thrd term n these equatons measures the cost that GHG emssons abatement mposes on economc actvty. It can easly be seen that reducng emssons n the South costs twce as much share of gross output as reducng emssons n the North. Wth regard to the relatonshp between gross and net output, we keep the assumpton that captal deprecates at 10%/year. Thsmeansthat, over generatonal tme spans, gross captal nvestment (It) wll be represented usng: I t = K t+1 (1 0.1) 35 K t (44) The functonal relatonshp between GHG emssons and envronmental qualty s the same that t s used by Howarth (1998) n hs OLG model of economy clmate nteractons: T t = µ µ Qt 5.92 ln + F t /1.41 (45) 590 In equaton (45) Q t measures the effectve stock of carbon doxde and CFCs n the atmosphere (measured n bllon tons of carbon equvalent) and F t 15

17 captures the radatve forcng caused by trace concentratons of methane, ntrous oxde and water vapor (measured n watts/m 2 ). Ths varable s exogenously determned accordng to a path Howarth approxmates usng: F t = (0.523) t (46) The atmospherc stock of carbon doxde and CFCs s governed by the followng dfference equaton: Q t = 0.64 Ã X E t! +( ) 35 (Q t 590) (47) Equaton (47) mples that (1) 64% of GHG emssons reman n the atmosphere at the end of one perod and (2) that, over the long run, the stock of GHGs n excess of the pre ndustral norm (590 bllon tons of carbon equvalent) s naturally removed from the atmosphere at a rate of 0.833%/year. The ntal GHG stock s set at the level reported by Howarth: 784 bllon tons of carbon equvalent. Before presentng the results, t s necessary to address four fnal techncal consderatons concernng (1) the choce of the pure rates of tme preference (ρ and ρ ), (2) the choce of the nternatonal welfare weghts (α), (3) the choce of the ntergeneratonal dscount rates (R and R )and(4)thechoceofthetme horzon T. Wth regard to the pure rates of tme preference, we have chosen them to equate the rates of captal accumulaton n the NCSL scenaro and the modfed RICE model. Ths has led us to consder a pure rate of tme preference of 0.5%/year both n the North and n the South. Wth regard to the nternatonal welfare weght attached to the North, we have consdered several values (rangng from α =0.2 to α =0.8) norderto analyze how they affect to the cooperatve soluton. These dfferent welfare weghts may reflect dfferent degrees of ether barganng power or nterregonal altrusm of cooperatve short lved governments. Wth regard to ntergeneratonal dscount rates, for the sake of smplcty, we have decded to start assumng that t s nsttutonally nfeasble to mplement an ntergeneratonal transfers scheme. Ths mples that, ndependently on the rate of ntergeneratonal dscount rate chosen by socety n each regon, governments wll lack the necessary nstruments to pursue the desred dstrbuton of welfare between generatons. Thus, not beng able to re-allocate ntal endowments, there wll be a sngle effcent allocaton of resources wthn each regon. Intergeneratonal transfers wll be consdered n future development of the analyss. Fnally, wth regard to the tme horzon, computatonal dffcultes have forced us to consder year 2490 (T = 15) as the fnal year n the analyss. 16

18 7 Prelmnary results and conclusons In ths sesson we present the numercal results obtaned usng both GAMS and the solver routne of Excel. Fgures 1a and 1b show how clmate change and total emssons evolve under the CSL and NCSL scenaros 11. The number n brackets represents the value of α. 12 ºC NCSL CSL (0,2) CSL (0,3) CSL (0,4) CSL (0,5) CSL (0,6) CSL (0,7) YEAR Fgure 1a: Temperature Change TONS/YR NCSL CSL (0,2) CSL (0,3) CSL (0,4) CSL (0,5) CSL (0,6) CSL (0,7) YEAR Fgure 1b: GHG Emssons 11 So far our analyss focuses on decsons by short-lved governments, snce t s n the case of short-lved governments where we can expect cooperaton to harm the envronment. 17

19 Several prelmnary results follow: 1. The NCSL scenaro leads to hgher envronmental degradaton n the long run than any CSL scenaro. 2. The hgher the welfare weght attached to the North under cooperaton, the lower envronmental degradaton n the long run. 3. It may happen that some CSL scenaros lead to hgher envronmental degradaton n the short-run than the NCSL scenaro. In fact, ths seems to be happenng when the welfare weght attached to the North s 20%. Result no 3 s n lne wth the cautonary note of John and Pecchenno (1997): nternatonal agreements wth transfers that lack an ntergeneratonal perspectve could actually harm the envronment. Ths result s more clearly lustrated n Fgures 2a and 2b. The ntuton behnd our result s the followng: When α =0.2, gven that (1) nternatonal agreements capture that the South s socal welfare has to be weghted four tmes as much as the socal welfare of the North and (2) the North s ntally rcher than the South, there are mportant transfers of ncome from North to South. Ths mples that some growng potental s transferred from North to South. These transfers mply an ncrease n total emssons of GHGs, due to the fact that the South produces usng a technology that t s less envronmentally frendly TONS/YR NCSL CSL (0,2) YEAR Fgure 2a: GHG Emssons n the Short Run 18

20 ºC YEAR NCSL CSL (0,2) Fgure 2b: Temperature Change n the Short Run 0,6 0,5 Tons/1000$ 0,4 0,3 0,2 0,1 E0/Y North E0/Y South generatons Fgure 3: Energy-savng technologcal change Thus, the exogenous nature of energy-savng technologcal change s an mportant drvng force behnd our result (see Fgure 3). Energy-savng technologcal change cannot be estmulated wth growth. Consequently, acceleratng the growth n the South may result n greater envronmental degradaton unless t s accompaned wth hgher abatement effort. The ncentves to mplement hgher abatement effort are clearly weakened by the short-lved nature of the government. Acknowledgements Ths paper has benefted from comments by partcpants at the followng conferences: 4th Semnar on Envronmental and Resource Economcs, (June 2001, Unverstat de Grona, Span), 11th Annual Conference of EAERE (June 2001, Southampton) and EuroConference on the Internatonal Dmenson of Envronmental Polcy (Acquafredda d Maratea, Italy, October 2001). Fnancal support from grants 9/UPV 00I01.I /2002 and SEC s gratefully acknowledged. 19

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