Level versus Equivalent Intensity Carbon Mitigation Commitments

Transcription

1 Western Unversty Economc Polcy Research Insttute. EPRI Workng Papers Economcs Workng Papers Archve Level versus Equvalent Intensty Carbon Mtgaton Commtments Hufang Tan John Whalley Follow ths and addtonal works at: Part of the Economcs Commons Ctaton of ths paper: Tan, Hufang, John Whalley. " Level versus Equvalent Intensty Carbon Mtgaton Commtments." Economc Polcy Research Insttute. EPRI Workng Papers, London, ON: Department of Economcs, Unversty of Western Ontaro (2009).

2 Level versus Equvalent Intensty Carbon Mtgaton Commtments by Hufang Tan and John Whalley Workng Paper # December 2009 Economc Polcy Research Insttute EPRI Workng Paper Seres Department of Economcs Department of Poltcal Scence Socal Scence Centre The Unversty of Western Ontaro London, Ontaro, N6A 5C2 Canada Ths workng paper s avalable as a downloadable pdf fle on our webste

3 Level versus Equvalent Intensty Carbon Mtgaton Commtments 1 Hufang Tan Chnese Academy of Socal Scence Unversty of Western Ontaro John Whalley Unversty of Western Ontaro Centre for Internatonal Governance Innovaton (CIGI ) and N.B.E.R. Abstract Large populaton / rapdly growng economes such as Chna and Inda have argued that n the upcomng UNFCCC negotatons n Copenhagen, any emsson reducton targets they take on should be based on ther ntensty of emssons (emssons/$gdp) on a target date not the level of emssons. They argue that ths wll allow room for ther contnued hgh growth, and level commtments n the presence of sharply dfferental growth between OECD and non-oecd economes represent asymmetrc and unacceptable arrangements. Much of the polcy lterature agrees wth ths poston, also argung that whle there s equvalence between commtments f growth rates are certan, where growth rates are uncertan equvalence breaks down. However, no explct models or expermental desgn are used to support ths clam. Here we use a modelng framework n whch countres face a busness as usual (BAU) growth profle under no mtgaton, and can mtgate (reduce consumpton) and lower temperature change but wth a utlty loss. Internatonal trade enters through trade n country dfferentated goods, and the mpact of mtgaton on country welfare depends crtcally on the assumed severty of clmate related damage. We then consder cases where country growth rates are uncertan, and compare the mpacts of levels versus ntensty commtments, wth the latter made equvalent n the sense that expected emssons are the same. There are dfferent senses of ths equvalence; global equvalence wth dfferng country mpacts, or strct country by country equvalence. Under ntensty commtments there s more varaton n both consumpton and emssons than s the case wth level commtments, and we show cases where level commtments are preferred to ntensty commtments by all countres. Whether ths s the case also depends upon how growth rate uncertanty s specfed. We are also able to consder packages of mxed level and ntensty commtments by country whch mght be the outcome of UNFCCC negotatons. Outcomes can thus be opposte to prevalng opnon, but t depends on how the equvalent targets are specfed. August 09 1 We are grateful to the Academc Development Fund(ADF) of the Unversty of Western Ontaro, the Ontaro Research Fund (ORF-R3), and the Centre for Internatonal Governance Innovaton for fnancal support, and to Yan Dong for dscusson and comment. Hufang Tan s also grateful to the Academc Fund of the Insttute of World Economcs & Poltcs, Chnese Academy of Socal Scence. 1

4 1. Introducton A central dfference n the form of commtment whch has been debated for upcomng global negotatons on clmate change n Copenhagen n December 2007 s between absolute commtments to reduced annual levels of emssons (on a flow bass such as per year) as measured on an agreed commtment date, and relatve commtments to reduced levels of emssons per unt of GDP, agan as measured on an agreed commtment date. Developng countres argue that such forms of commtment are necessary for them gven ther hgh growth, and also commtments of ths form wll encourage them to become more energy and emsson effcent more quckly. In ths paper, we take up the ssue of level versus ntensty commtments n a formal analytcal structure. It s wdely agreed that n the certanty case there s an equvalence between the two commtment forms. For any level target an ntensty target exsts whose mpacts wll be dentcal. The crtcal dfferences arse wth uncertanty over growth rates, autonomous reductons n energy converson effcency, techncal progress, and other consderatons. Whle much of the polcy based lterature (see Pzer (2005)) argues n favor of ntensty commtments on the grounds t leaves more emsson room for hgh growth countres, lttle of t explctly compares the two commtment forms n well specfed experments. In the presence of uncertanty as to growth performance, ntensty commtments wll typcally generate more varance n both output and emssons for equvalent level commtments wth the same expected emssons reducton across the two commtment forms, but at the same tme there are dfferng senses of equvalence. For nstance, equvalence may hold only globally so that expected global emssons are the same, whle country emssons on an expectatons bass vary, or equvalence may hold more strctly on a country by country bass. We use a general equlbrum model appled to a mult decade busness as usual (BAU) scenaro n whch global output determnes emsson levels, and countres trade country specfc goods wth both goods and temperature change enterng preferences. Countres can forgo use of ther own good to meet targets, reducng 2

5 emssons wth a welfare gan from temperature change and welfare loss from reduced consumpton. We use an eght regon structure (Chna, Inda, Russa, Brazl, US, EU, Japan, Rest of the World) whch we calbrate to a Busness as Usual (BAU) scenaro over 50 years. We are able to compare ntensty to level targets beng used by all countres, beng used by a subset of countres (Chna, Inda, Russa, Brazl) whle others use level targets, or only by ndvdual countres (Chna, for nstance). The hgher varance of output and emssons can make ntensty commtments unattractve for countres compared to levels commtments when strct country equvalence holds, although ndvdual country mpacts also reflect terms of trade effects. Sgnfcant dfferences across countres apply when looser global equvalence s used. What stands out s the dfference n perspectve relatve to the polcy based dscusson n that detals of equvalence assumed n the experment and how growth rate uncertanty s specfed matter for country mpacts. Numercal results are also senstve to the assumed damage from clmate change and model parameters used. 3

6 2. Level versus ntensty commtments In December 1997, more than 150 countres concluded negotatons on the Kyoto Protocol, a landmark agreement on global clmate change. Sgned by 84 countres, ncludng the Unted States, the treaty commtted ndustralzed countres to legally bndng lmts on ther emssons of greenhouse gases that are lnked to global clmate change. These lmts were expressed as reductons (or, n a few cases, ncreases) n absolute emssons levels relatve to a 1990 baselne. Developng countres took on no commtments under Kyoto and countres were dvded nto two groups; Annex A wth commtments and Annex B wth no commtments. Ths was seen at the tme as an nterpretaton of the prncple of Common but Dfferentated Responsbltes applyng to developng countres and adopted as part of the earler 1994 UN Framework Conventon on Clmate Change. Kyoto commtments termnate n 2012 and wth the end of the Kyoto mplementaton perod, the focus has now shfted to arrangements for a post Kyoto world and further negotatons under UNFCCC whch are to conclude n Copenhagen n December In these negotatons the partcpaton of large populaton rapdly growng developng countres (Chna, Inda, Brazl, Russa) s seen as key as ther emssons wll progressvely come to domnate global emssons f ther (pre crss) hgh growth rates contnue. These countres, n turn, cte not only common but dfferentated responsbltes, but also ther need for growth and development as the bass for them takng on dfferent forms of commtment compared to developed countres. Level (or absolute) emssons targets typcally specfy a percentage reducton n the amount of carbon doxde and other greenhouse gases (Kg of carbon Doxde equvalent) to be released on a flow bass on a specfed date. Intensty (or relatve) emssons target reductons nvolve a percentage reducton n the amount of emssons relatve to some measure of output (such as GDP) usually stated n dollar or local currency terms, on a specfed date. The commtment n both cases s to percentage reducton by some specfed date relatve to an earler base date. Level commtments were the mechansm used n the 1997 Kyoto Protocol and 4

7 are also wdely used n other treaty arrangements (such as the Montreal Protocol on CFC s). Intensty commtments have attracted growng attenton n global negotatons on greenhouse gas (GHG) emssons due to arguments from rapdly growng large populaton economes (Chna, Inda, Russa, Brazl) that they need room to accommodate hgh growth and that ths ponts to emssons ntensty targets. Intensty-based lmts whch restrct emssons to some pre-specfed rato relatve to nput or output are much more wdely used n domestc envronmental regulaton. Intensty targets can be nterpreted as performance standards. For a company, the standard maybe relatve to company total sales or relatve to unts of a good produced. For a country, the standard s typcally specfed as tons of carbon doxde equvalent relatve to country GDP. If emssons ntenstes are used the choce of exchange rate n calculatng US$ domnated GDP becomes a crtcal ssue. Ths s especally mportant for Chna and Inda due to large dfferences n the dollar measure of GDP dependng upon whether or not purchasng power party or market exchange rates are used. Both the form of commtment and the target date for any commtments n the second round of global emssons reducton negotatons to conclude n Copenhagen n December 2009 are at ths pont unresolved. The Bal 2007 UNFCCC documents contaned language suggestng ndcatve targets of a 25-40% reducton by Developng countres have rased the ssue of the form of commtment not only n terms of levels versus ntensty but also as t relates to other ssues such as the treatment of emssons embedded n exports. In the G8, there has been dscusson of 50% cuts by Chancellor Merkel has also been assocated wth proposals for targets for maxmum temperature change (2) by targets mght also be accompaned by ntermedate targets, say a 30% cut by 2030, and a 20% cut by Avalable lterature on the ntensty / level ssue stresses that n the presence of certanty the two commtment forms are equvalent, n the sense that for any level commtment, an equvalent ntensty commtment can be found wth the same mpacts. It s where growth and any autonomous reductons n energy converson effcency are uncertan that dfferences rse. 5

8 Pzer (2005) argues that absolute emssons targets are too constranng n face of unexpectedly hgh growth and too lax n face of unexpectedly low growth, and that ntensty targets better accommodate unexpected growth and favor developng countres. Hs arguments reflect four key clams: that greenhouse gas emssons wll contnue to rse over the near term, that absolute targets emphasze zero or declnng emssons growth whle ntensty targets do not, that developng countres economc development s ntegrally ted to emssons growth for the foreseeable future, and that ntensty targets are not any more complcated to admnster than levels targets. Ellerman and Wng (2003) also dscuss the dfferences between these two forms of emsson targets, argung lke others that the two forms have dentcal effects n a world where future emssons and economc output (.e. GDP) are known wth certanty. They show that outcomes for emssons and welfare only dverge when the varance of GDP dverges from ts forecast expectaton. They then argue that ntensty targets reduce the mportance of what s the most mportant unknown for any country consderng the cost of meetng emsson targets; future economc performance. Ther concluson s that f uncertanty about the effects of absolute targets mpedes agreement or causes exstng agreements to unravel, then some form of ndexaton of targets to economc growth seems both desrable and necessary to enable agreements to be made. Jacoby et al. (1998) also argue that ntensty targets are more compatble wth the overall archtecture of envronmental agreements. They argue that an absolute cap s only a lmtng form of emsson targets n whch the degree of ndexaton to GDP growth s a choce varable. They suggest that the wdespread use of ntensty targets n envronmental regulaton, ncludng some use as an nstrument to reach Kyoto targets by partes adherng to the Protocol, suggests that more attenton should be pad to ths than n the past. Our pont of departure relatve to ths lterature s to argue that n any comparson of the economy wde performance of level versus ntensty targets, a bass for the comparson s needed n clearer analytcal terms. Precedents for such comparsons le n the tax lterature where the effcency and dstrbutonal mpacts of alternatve tax 6

9 structures are compared on an equal yeld bass. Here, the natural experment would seem to be to consder uncertanty n, say, the growth rate of countres comparng a busness as usual scenaro (wth uncertanty n emssons levels) to outcomes under emssons targets n level (absolute) and equvalent ntensty form, calbrated such that expected emssons levels are the same across the two forms of lmtaton. We also argue that there are dfferng forms of equvalence. One mght be where the expected global emssons ntensty reducton s the same but wth the same absolute reducton n ntensty country dfferences apply n proportonal reductons, and another mght be where equvalence of expected proportonal emssons ntensty apples on a country by country bass. Whle emsson ntensty targets may be argued as nconsstent wth arrangements under the Kyoto Protocol, there s no reason why the form that targets take cannot change from one envronmental negotaton to another. 2 For more than a decade, nternatonal clmate negotatons have focused on absolute emssons targets and tmetables. The result has been a system that s based toward haltng and reversng emssons growth, even as evdence suggests that emssons wll contnue to grow for decades n ndustralzed countres and much longer n the developng world. Ths bas arses because progress vewed n terms of emssons nevtably means emssons reductons not slowng growth of emssons. Shftng the focus of the negotaton towards ntensty targets can thus be defended as openng the door to more nclusve negotatons where a range of approaches ncludng slowng, stoppng, or even reversng emssons growth can be dscussed. Intensty targets can then be nterpreted as performance standards for the whole economy. The queston remans whether ntensty-based emssons targets offer a preferable alternatve to level emssons targets both globally and for ndvdual countres. Do ntensty targets better accommodate growth and make targets for developng countres more lkely to be acceptable than absolute emssons lmts? Or do ntensty targets nstead ncrease the expected varance of both emssons and output and ncrease 2 Some would even abandon entrely the targets-and tmetables archtecture of the Kyoto Protocol and replace t wth agreements on R&D expendtures and technology transfer (Barrett, 2001) or wth a global carbon tax (Cooper, 1998). 7

10 uncertanty relatve to level targets? What s needed s expermental analyss to nvestgate, wth the same expected reducton n emssons whether the expected utlty under ntensty lmts wll be hgher or lower than that n the certanty case. 8

11 3. Model Structure and Experment Specfcaton We use an extended verson of a mult country modelng framework recently developed by Tan, Whalley & Ca (2009) n whch the effects of alternatve clmate change polces relatve to a BAU scenaro can be assessed over many years consdered as a sngle perod. Into ths, we ntroduce uncertanty of country growth rates and compare the expected welfare dfferences nvolved usng comparable level and ntensty targets as counterfactual model experments. We specfy the ntensty equvalent experments n dfferent ways, wth varyng forms of uncertanty of country growth rates as well as expected global equvalence n terms of expected emsson. In one case there are equal absolute reductons n ntensty wth country dfferences n expected proportonal reductons, and n the other equal proportonal ntensty reductons and country by country equvalence n proportonal expected reductons. We are also able to compute the dstrbutonal mplcatons of usng one form of ntensty target over another. The model consders multple regons (Chna, Inda, Brazl, Russa, US, EU, Japan, Rest of the World). Each regon s endowed wth a sngle good and goods are heterogeneous across countres (the Armngton (1969) assumpton). Countres export ther own good, and mport the other country goods. Country utlty s defned over consumpton of goods and temperature change. In the model countres can reduce global emssons by forgong consumpton snce emssons are lnked to the total value of consumpton world wde. In ths way, countres can nduce lowered world temperature change whch benefts all, but at a cost to themselves n terms of foregone consumpton. We use data on consumpton and trade for the eght economes, along wth country growth rate data for We forward project BAU scenaros alternatvely to 2036 and 2056, usng varous damage and temperature change assumptons as our BAU case. Ths base data s thus for a sngle 30 or 50 year perod wth assumed yearly growth rates over the perod. We calbrate the model to a temperature change functon for prospectve changes n temperature under the three growth scenaros out to In these we use varyng estmates of assocated damage reported by Stern (2006) and Mendelsohn (2006). In the model, we ntroduce uncertanty n the form of three dfferent growth scenaros: BAU growth and a hgher and lower growth scenaro for each regon. Our BAU growth rates reflect average annual country growth rates over the perod 9

12 projected forward. We consder one case where hgh and low growth rates reflect the same percentage devaton n country growth rates across all countres. We consder an alternatve case where growth rates for hgh and low growth scenaros reflect averages of above and below mean growth rates for the perod For smplcty, we assume that the hgh and low growth scenaros occur n each case wth equal probabltes. We then use these to assess the mpacts of dfferent emsson reducton targets: comparng the BAU outcome wthout any emssons reducton to a 20% level target reducton n country emssons; and to alternatve ntensty targets that are equvalent to the absolute target n terms of expected mpacts on emsson levels specfed both globally and by country. We compute the welfare level under the BAU scenaro and under the hgh and low growth scenaros n each case for both absolute and ntensty targets. Ths allows us to assess whether the expected welfare of the two weghted average cases n the level target case s hgher or lower than n the ntensty target case. 3.1 Temperature change and top level country utlty functons We analyze a sngle perod of a number of years durng whch each of the economes we analyze grows at a compoundng constant rate. Each country s assumed to have one heterogeneous good whose avalablty also grows at ths rate n the base case (BAU). We assume that consumpton of the good by the country drectly generates emssons of carbon whch, n turn, rases global temperature. Countres generate postve utlty from consumpton of goods, but negatve utlty from temperature change. Countres have an upper bound on ther own use of ther good (consumpton plus export) reflectng the BAU scenaro. If they use less than the upper bound they experence less temperature change, as do all other countres. If they are small, ther own actons have lttle or no effect on temperature change. We analyze the mpacts of emssons reductons over a gven perod of tme whch we consder as a sngle perod whch covers ether 30 or 50 years. There are no explct dynamcs. For ths perod, we focus on changes n consumpton (of both own and foregn goods va nternatonal trade) and utlty, and measure changes n these varables relatve to the outcome of zero growth over the perod. The utlty functon s thus defned over 30 or 50 year changes n consumpton and temperature change. The potental use of the own good by an economy can thus be thought to reflect changes n potental output from the economy over 30 or 50 years. We frst analyze a 10

13 busness as usual (BAU) scenaro whch reflects current observed growth rates remanng unchanged over 30 or 50 years, and wth no global or sngle country emssons lmtaton ntatves n place, and then consder alternatve hgh and low growth cases. We then compute model solutons under alternatve emssons reductons for each scenaro. The utlty of each country n all cases s reflected n a utlty change functon wth argumentsgven by the country s own change n composte consumpton as well as the temperature change of the world. We assume the utlty change functon for each country has a Cobb-Douglas form gven by (1). H ΔT β Δ U =ΔU( ΔRC, Δ T) =Δ RC*( ) (1) H In ths specfcaton, ΔRC represents the change n consumpton for each country (=1,,N). Δ RC s, n turn, a composte of ther own good and other country s goods whch they acqure by exportng ther own good and mportng other country s goods. Ths structure can thus be used to also analyze lnks between trade penaltes (tarffs) and fnancal transfers and partcpaton n emsson reducton ntatves. H can be thought of the global temperature change at whch all economc actvty ceases (say 20 ). As Δ T approaches C utlty goes to zero, and as ΔT goes to zero there s no welfare mpact from temperature change. Utlty change over the model perod ( or ) ncreases as temperature change falls. The share parameter β reflects the severty of damage (n utlty terms) from any gven temperature change. We calbrate the model to varous damage estmates from busness as usual global temperature change reported by Stern (2006) and Mendelsohn (2006), and ths procedure determnes β. Global temperature change, n turn, s determned by the change n carbon emssons over the perod across all countres n the model. We adopt a smple temperature change functon and assume that emssons by each country equal the change n consumpton tmes country emssons ntensty (emssons/gdp) so as to allow for dfferng emssons ntenstes by country. Defnng the emssons ntensty of regon as e, we use a smple power functon (2) for global temperature change due to changes n emssons by all countres over the model perod. 11

14 where (2) Δ T = g( eδ RS ) = a( eδ RS ) b + c ΔRS represents the change n the use ( consumpton plus export) of the own good for each country. We treat the e as exogenous and constant over the perod, but the structure can be extended to also ncorporate an exogenous mprovement n emssons ntensty overtme reflectng ncreased effcency of energy converson. Consumpton across all regons of each country own good s less than of nternatonal trade. Δ RS because Δ RS n turn s less than or equal to the upper bound Δ RS assocated wth the base case scenaro as countres lower use of ther own good to meet emssons targets. 3.2 Composte consumpton goods by country In ths structure, a carbon reducton commtment by a sngle country mples a reducton n consumpton, and ths has both negatve and postve effects on utlty change for countres over the model perod. On the one hand, a reducton n consumpton lowers utlty for the country, but on the other hand, country consumpton reductons lower global emssons and hence world temperature change, and ncreases the utlty both of the country reducng the emssons and all other countres. The composte consumpton good RC s a CES functon of domestc and mported consumpton goods, smlar to the nested CES Armngton functons n trade models (see Whalley (1985)). The model effectvely becomes an Armngton N good N country pure trade economy n whch the endowment of each regon s varable and temperature change enters utlty. The demands for consumpton goods reflect the outcome of sub utlty maxmzaton. Max 1 σ 1 1 σ 1 σ σ σ σ σ σ 1 (, ) (( λ1) ( λ2) ) RC = RC D M = D + M (=1 N) (3) s.t. pd w + pm m I= prs w (=1 N) (4) where D and M represent consumpton of the domestc and a composte mported good respectvely wth p w and m p as ther prces, λ 1 and λ 2 as the consumpton shares, and σ as the substtuton elastcty. The composton of M s determned 12

15 by a thrd level of nestng n the model, and m p s a prce ndex of seller s prces w p j (see equaton (9)). I s country ncome and s gven by sales of own good at the world prce w p. Demands for domestc consumpton goods and a composte of mported consumpton goods are: M λ I ( ) ( ( ) ( ) ) 2 = m w (1 ) m (1 ) P σ 1 p σ λ + λ2 P σ (=1 N) (5) RS D λ I ( ) ( ( ) ( ) ) 1 = w w (1 ) m (1 ) p σ 1 p σ λ + λ2 P σ (=1 N) (6) 3.3 Compostes of Imported Goods and Trade Equlbrum The CES mported composte commodtes are n turn compostes of mported goods from each supplyng country. Gven that each country has one good t can sell, but N-1 goods t mports, the CES composte of other goods defnes an mport composte. Ths s also the outcome of a sub-utlty maxmzaton exercse Max 1 σm 1 σm σm σm σm 1 ( 1, 2,..., 1, + 1,..., N) ( ( κ j) ( j) ) j M = H R R R R R = R (7) (8) w m m s.t. p Rj I = p M j where R j s the mported good by regon j, m p s the composte mport prce for regon, k j s the consumpton share and elastcty. σ m s the second level substtuton m I s the ncome devoted to expendtures on mports from (6). These CES sub-utlty maxmzatons gve: p 1 m w 1 σ 1 σ m m [ κ j( p ) ] j = (=1 N) (9) R κ p M κ ( p ) M m m σ m j j j = = w σm w 1 σm w σm ( p ) κ j( p ) ( p ) j (=1 N) (10) A trade equlbrum n the model s gven by world prces country goods for whch make clear globally,.e w* p for each of the D + R = RS, ( = 1,... N) (11) j j 13

16 Clmate change polces that affect RS change equlbrum prces, as do trade measures (tarffs) or transfers between countres used as mechansms to generate partcpaton n such agreements. 3.4 Hgh, Low and BAU growth scenaros and Model Experments The model captures uncertanty n a smple way by analyzng three alternatve growth scenaros: hgh growth, low growth and BAU growth. For each scenaro we compute utlty and consumpton of goods by regon. We consder two dfferent specfcatons of hgh and low growth rates. In one there s equal percentage varaton n growth rates across hgh and low growth states by country. In the other, we consder hgh growth rates as average growth rates above mean growth rates for , and low growth as average growth rates below the mean. For the hgh and low growth scenaros we consder each wll occur wth probablty one half, and we compute expected utlty and expected emssons. We then ntroduce dfferent emsson targets for the varous growth scenaros by usng alternatve forms of level and ntensty target equvalence. In one case we use equvalence n expected emssons by country, n the other the target s loser n the form of equal expected emssons globally. In the frst case, the global target mples an equ proportonal reducton n ntenstes by country. In the second case, the emsson level target as a common reducton n emssons ntensty subject to a lower bound on emssons ntensty. We then compute the mpacts of equvalent emsson ntensty reductons whch gve the same expected emsson reducton to be acheved as under emsson level targets gven the BAU output of the regon. We thus compute the model utlty change under hgh, low and BAU growth scenaros respectvely for each of the emssons targets, and then compare expected utlty for hgh and low growth scenaros across the two targets. We measure the mpacts of use of one target relatve to another usng a Hcksan money metrc equvalent varaton of the utlty dfference expressed n $ trllon. These amounts can then be compared to the value of GDP (dscounted where dscountng earler) over the model perod (30 or 50 years) 14

17 4 Model Calbratons We calbrate our model to a base case busness as usual (BAU) scenaros for two dfferent model perods and We use an 8 country groupng, of Brazl, Russa, Inda, Chna, US, EU, Japan, and the Rest of the World (ROW). We construct a BAU growth profle usng forward projectons of 2006 data, and model calbraton to ths profle determnes key model parameters. 4.1 Data Descrpton We use GDP growth as the measure of potental change n consumpton by each country over the perod. We use averaged data between 2006 and 2000 to calculated growth rates. We frst assume that under the dfferent (BAU, hgh, low) growth scenaros, country growth rates n the perod reman unchanged over the whole perod of 50 years between 2006 and All the data for each tme perod are forward projected based on the data for We have three components n our data for each growth scenaros: base case data n 2006, cumulatve data for 2056 gven hgh, BAU and low growth, and cumulatve data over the perod relatve to the base year for the same three growth scenaros. Base year output, emssons and growth rates are reported n Table 1. Chna, Inda, Russa, Brazl, USA, EU, Japan and the Rest of the World (Row) have BAU growth rates of 0.09, 0.07, 0.07, , 0.020, 0.17, and 0.30 respectvely, gven by average growth rates of 2000 to 2006 (data from World Bank webste). We use two dfferent specfcatons of hgh and low growth rate scenaros snce these serve to llustrate how the specfcaton of growth scenaro affects the comparson between level and ntensty targets. For the frst specfcaton, hgh growth scenaros use averages of country growth rates for years between 2000 and 2006 wth above mean growth, whle low growth scenaros use averages of growth rates for years between 2000 and 2006 wth below mean growth. Ths yelds hgh growth rates for Chna, Inda, Russa, Brazl, USA, EU, Japan and Row of: 0.105, 0.089, 0.080, 0.042, 0.033, 0.030, 0.025, respectvely and low growth rates of 0.086, 0.043, 0.054, 0.017, 0.016, 0.013, and respectvely. In the second specfcaton, we use hgh and low growth rate data n whch we assume that hgh growth rates are a 50% hgher than n the relevant BAU rate n all countres, and low growth rates a 50% lower than n the relevant BAU rate n all countres. Ths gves hgh growth rates for Chna, Inda, Russa, Brazl, USA, EU, Japan and Row of 0.135, 0.105, 0.105, 0.048, 0.039, 0.030, 15

18 0.025 and 0.045, and low growth rates of 0.05, 0.04, 0.04, 0.02, 0.013, 0.01, and respectvely. The larger the varance of BAU growth rates, then typcally the larger the dfference between hgh and low growth rates for eght countres. In the second specfcaton of hgh and low growth rates, Chna, Inda, Russa and Brazl have more varaton n growth rates than the developed countres. We use BAU growth rates to calbrate the temperature change functon usng BAU temperature change over the two perods drawng on key lterature sources, ncludng Stern (2006) and Mendelsohn (2007). Ths mples that n hgh growth scenaros emssons are larger and also temperature change s hgher. Preferences towards goods and temperature change are determned for each country usng alternatve damage estmates from the same sources. Table 1 Output, Emsson Intensty data n 2006 and Growth Rates out to 2036 and 2056 Chna Inda Russa Brazl U.S E.U. Japan ROW Output n 2006, trll$ Emsson n 2006, ktonc Emsson ntensty BAU growth rate Hgh growth rate (1) Low growth rate (1) Hgh growth rate (2) Low growth rate (2) Note: (1) s the growth specfcaton 1 where all rates are average of country growth rates above/below BAU growth for (2) s the growth specfcaton 2 where growth rates are a 50% hgher / lower n all BAU country growth rates for Calbraton of preference parameters We frst turn to the calbraton of preference parameters. Accordng to the Stern Revew (2006), Mendelsohn (2006) and other lterature, the damage cost of emssons wth BAU paths ranges from 1 to 20% of GDP out to We treat damage from clmate change n the model as a utlty change of the same proporton over the same tme and use t to calbrate the preference parameters n the model. Wthout temperature change, the utlty functon s: 16

19 U * = RC (12) And wth damage we have : H ΔT * β U / U = ( ) (13) H Wth temperature change, there wll be a loss from damage. We can thus calbrate β usng equaton (13) above for gven dfferent values of H. A tme perod of 50 years as the base case yelds the β values reported n Table 2. In our smulaton analyss, we use H=10 as the base case, and perform senstvty analyss wth H=20 and H=30. We next turn to the temperature change functon. The temperature change functon s wrtten as a functon of emsson changes. We treat t as a power functon of total emsson (not output) change for the world: Δ T = a( ΔE ) b (14) Based on the results from Stern Revew (2006), the BAU path of emssons wll lead to about 3 degree temperature ncreases around the year 2035, and near 5 degree C by around For smplcty, we assume that zero growth n the global economy wll lead to no temperature change. Wth the data on growth rates and emsson ntenstes for each country under the BAU growth scenaros, we can calbrate the parameters a and b. We have data for year 2006 and projectons emsson and output data for 2036 and For smplcty, we choose 2006 as the base year, and assume that 30 years later, that s by 2036, the global average temperature wll ncrease by 3 degrees, and 5 degrees by We assume that the BAU path mples output growth for each country comparable to that of , whle emsson ntenstes are unchanged from We are able to relax ths assumpton to allow for autonomous (exogenous) mprovements n energy effcency (ntensty) overtme. Table 2 also reports the calbrated values of a and b. 17

20 Table 2 Calbraton Model Parameters for 50 Year Tme Horzon H β n preferences BAU Damage cost assumed β 10% % % % % % % % a, b n temperature change functon assumng Δ T = 3 Δ T = 5 a=0.304 b=

21 5. Results of Model Experments Usng the 2 alternatve specfcatons of hgh and low country growth rates, and the two dfferent specfcatons of equvalence between level and ntensty targets, we can make 4 calculatons of country welfare under alternatve emsson reducton targets. We can then compute expected utlty under level and ntensty targets for each country for each of 4 specfcatons (wth dfferences n the sense of equvalence of the ntensty target, and the settng of hgh and low growth rates). We can also compare the dstrbutonal mplcatons across countres n the sense of ntensty equvalence (absolute or proportonal). We can also compare how other model features, such as tmeframe, commtment level, and assumed BAU damage from clmate change mpact the choce of emsson target both by country and globally. Table 3 reports the reductons n emsson ntensty over the model perod mpled by alternatve level equvalent experments. Ths ntensty reducton s an equ proportonal reducton of 20% n emssons ntensty mplemented over the whole of the model perod of ether 30 or 50 years, equvalent n expectatons form to a 20% level reducton. The second reducton s an equal absolute reducton n emssons ntensty calculated to gve the same expected global reducton as both the level commtment and the other ntensty commtment. We use a lower bound of an 80% absolute emsson ntensty reducton to preclude country cases (EU & Japan) where emsson ntensty reductons would otherwse be negatve. Table 3 Percentage Changes n Base Year (2006) Intensty by Country Under Alternatve 20% Level Equvalent Reducton 3 Country Reducton 1 Reducton 2 BAU Emsson ntensty over model Emsson ntensty over model perod Emsson perod after proportonal reducton after absolute reducton (subject to 80% ntensty equvalent to lower bound) n equvalent ntensty In % level reducton n emsson target to 20% level reducton n emsson Chna % 15% Inda % 16% Russa % 13% Brazl % 65% US % 62% 3 The reductons n ntensty by country n each case are calculated so as to generate equal expected reductons n emssons. 19

22 EU % 80% Japan % 80% Row % 33% In Table 4 we report welfare mpacts by country of emsson reductons n the certanty case for two alternatve reductons of 20% and 30% as ths provdes a bass for comparson of the alternatve ntensty commtments n the growth uncertanty cases. It has been acknowledged n lterature for some tme that only wth large BAU damage costs from clmate change countres ndvdually beneft n narrow self nterest terms from clmate change reducton. Here we assume a 10% damage estmate n calbratng the model and n both 20% and 30% reducton cases all countres lose. Proportonal to sze Chna loses the most reflectng both ts sze and hgh emsson ntensty. The ssue wth levels versus ntensty targets n ths case s thus under whch nstrument are expected losses larger or smaller, and for whch country. Table 4 Incremental Utlty from Goods Consumpton and Clmate Change wth and Wthout Emsson Reductons Targets n the Certanty Case ( ) 4 BAU scenaro No target 20% level reducton for all countres 30% level reducton for all countres Chna Inda Russa Brazl US EU Japan Row In Table 5, we report welfare comparsons n money metrc terms for the use of level and the two ntensty equvalent commtments for the perod as well as the dfferences between the two ntensty equvalent commtment forms. Welfare 4 Assumng 10% damage from clmate change n the BAU case. 20

23 measures are n Hcksan money metrc form over the whole model perod of 50 years. We use the two dfferent specfcatons of equvalence (equal proportonal, equal absolute) dscussed earler. We also use the two dfferent growth rates scenaros set out above. These results ndcate how both for ndvdual countres and globally these comparsons can produce ether level or ntensty preference. Globally, under hgh/low growth specfcaton (1) proportonal ntensty targets are preferred to level targets but ths result s reversed under hgh/low growth specfcaton (2). Under growth specfcaton (2) all countres gan from the use of a level target relatve to an equvalent ntensty target, reflectng the added uncertanty created by ntensty targets. All countres except Chna gan from ntensty targets wth the alternatve specfcaton of hgh and low growth rates. Results for the comparson of proportonal and absolute ntensty commtment by country show sgnfcant dstrbutonal varaton by country. Countres wth hgh BAU ntenstes (Chna, Inda) are consderably worse off wth proportonal ntensty targets and the US and the EU are much better off. 21

24 Table 5 Welfare Dfferences n Level and Equvalent Intensty Reducton Commtments by All Countres under Dfferent Growth Rate and Equvalence Specfcaton ( ) 5 Hcksan CV measure ($trll) Country Dfference between level and equvalent proportonal ntensty commtment Growth Specfcaton (1) Growth Specfcaton (2) Dfference between level and equvalent absolute ntensty commtment Dfference between equvalent proportonal and equvalent absolute ntensty commtment Dfference between level and equvalent proportonal ntensty commtment Dfference between level and equvalent absolute ntensty commtment Dfference between equvalent proportonal and equvalent absolute ntensty commtment Chna Inda Russa Brazl US EU Japan Row Growth rate specfcaton (1) uses average growth rates above and below mean for Growth rate specfcaton (2) uses growth rates 50% hgher and 50% lower than BAU growth rates. 22

25 Table 6 reports results for the same comparson as n Table 5, but where the tmeframe s vared to run from nstead of These welfare comparsons report lower numbers n $ trllon for the shorter tmeframe snce the economy s smaller n sze, but under growth rate specfcaton (2) the gans from usng proportonal ntensty targets whle stll all postve, are proportonal to GDP lower. For growth rate specfcaton (1), these are 4 results of change n sgn n the comparson, and 4 cases where loses ncrease n sze. Under absolute equvalence a smlar pcture of change emerges, emphaszng the senstvty of these comparsons to specfcaton. 23

26 Table 6 Varyng the Tmeframe Used to Compare Level and Equvalent Intensty Commtments Gven Dfferent Growth Scenaros and Forms of Intensty/Level Equvalence 6 Hcksan CV measure ($trll) Growth Specfcaton (1) Growth Specfcaton (2) Country Chna Inda Russa Brazl US EU Japan Row year Dfference between level and equvalent proportonal ntensty commtment Dfference between level and equvalent absolute ntensty commtment Dfference between equvalent proportonal and equvalent absolute ntensty commtment Dfference between level and equvalent proportonal ntensty commtment Dfference between level and equvalent absolute ntensty commtment Dfference between equvalent proportonal and equvalent absolute ntensty commtment Growth rate specfcaton (1) uses average growth rates above and below mean for Growth rate specfcaton (2) uses growth rates 50% hgher and 50% lower than BAU growth rates. 24

27 In Table 7 we report results for varatons n the depth of commtment n comparsons between level and level equvalent ntensty targets for the same 2 growth rate specfcatons and the two cases of absolute and proportonal equvalence. In these cases, for growth rate specfcaton (2), the welfare gan accrung to countres n level equvalent ntensty target specfcaton from usng proportonal ntensty equvalence ncreases sharply for all countres wth deeper commtments, except the US. For growth rate specfcaton (1) for 7 of 8 losses become gans; Chna s the excepton. Smlar changes occur for absolute rather than proportonal senses of equvalence, and for the US relatve loses from absolute equvalent targets ncrease. 25

28 Country Chna Inda Russa Brazl US EU Japan Row Table 7 Varyng the Commtment Reducton Level n Comparson of Level and Equvalent Intensty Commtments Gven Dfferent Growth Scenaros 7 Reducton level Dfference between level and equvalent proportonal ntensty commtment and Forms of Level Equvalence n Intensty targets Hcksan CV measure ($trll) Growth Specfcaton (1) Growth Specfcaton (2) Dfference between level and equvalent absolute ntensty commtment Dfference between equvalent proportonal and equvalent absolute ntensty commtment Dfference between level and equvalent proportonal ntensty commtment Dfference between level and equvalent absolute ntensty commtment Dfference between equvalent proportonal and equvalent absolute ntensty commtment 20% % % % % % % % % % % % % % % % Growth rate specfcaton (1) uses average growth rates above and below mean for growth rate specfcaton (2) uses growth rates a 50% hgher and 50% lower than BAU growth rates. 26

29 In Table 8, we report results where we nstead compare the welfare mpacts of mxed packages of level and ntensty commtments to the outcome under common 20% level reducton commtments. As ths s a potental outcome from the Copenhagen negotatons, these results are of specal nterest. For proportonal equvalence under both growth scenaros (1) & (2) we show loses to the BRIC countres (Brazl, Russa, Inda, Chna) and gans to the large OECD (EU, US, Japan). Under growth scenaro (2) these effects are large. Under absolute equvalence, the losses to BRIC are smaller and under growth scenaro (1) for absolute equvalence gans occur. If ntensty targets are restrcted n ther use to Chna, under growth scenaro (1) gans accrue to Chna and losses to all others for both absolute and proportonal equvalence. Results reverse for growth scenaro (2). 27

30 Table 8 Welfare Impacts of Mxed Commtments of Level and Equvalent Intensty Commtments Relatve to Common Level Commtments by Country for Dfferent Growth Scenaros 8 and Senses of Equvalence Hcksan CV measure ($trll) BRIC take on ntensty, others level commtments (Proportonal Equvalence) (1) BRIC take on ntensty, others level commtments (Absolute Equvalence) (1) Chna takes on ntensty, others level commtments (Proportonal Equvalent) (1) Chna takes on ntensty, others level commtments (Absolute Equvalent) (1) BRIC take on ntensty, others level commtments (Proportonal Equvalent) (2) BRIC take on ntensty, others level commtments (Absolute Equvalent) (2) Chna takes on ntensty, others level commtments (Proportonal Equvalent) (2) Chna takes on ntensty, others level commtments (Absolute Equvalent) (2) Chna Inda Russa Brazl US EU Japan Row Growth rate specfcaton (1) uses average growth rates above and below mean for Growth rate specfcaton (2) uses growth rates 50% hgher and 50% lower than BAU growth rates. 28

31 In Table 9 we report results from cases n whch the BAU damage cost assumpton used to calbrate preferences n the model s vared pror to comparsons of level and level equvalent ntensty commtments. These cases are computed once agan for the two dfferent growth scenaros and under dfferng senses of equvalence. For growth scenaro (1), ncreasng the damage cost ncreases gans and reduces losses for all countres for proportonal equvalence. For growth scenaro (2) results go unformly n the opposte drecton for proportonal equvalence. Dfferent results are obtaned for absolute equvalence. 29

32 Country Chna Inda Russa Brazl US EU Japan Row Table 9 Varyng Assumed Damage Cost Used to Compare Level and Equvalent Intensty Commtments for Dfferent Growth Scenaros and Senses of Equvalence Hcksan CV measure ($trll) Growth Specfcaton (1) Growth Specfcaton (2) Damage cost Dfference between level and equvalent proportonal ntensty commtment Dfference between level and equvalent absolute ntensty commtment Dfference between equvalent proportonal and equvalent absolute ntensty commtment Dfference between level and equvalent proportonal ntensty commtment Dfference between level and equvalent absolute ntensty commtment Dfference between equvalent proportonal and equvalent absolute ntensty commtment 10% % % % % % % % % % % % % % % % % % % % % % % %

33 Fnally n Table 10, we report results where we vary elastcty parameters n the model. For space reasons, we lmt ths to results for growth specfcaton (1) and for proportonal equvalence. These results ndcate lmted senstvty of fndngs n ths dmenson. 31

34 Table 10 Varyng the Trade Elastcty used to Compare Level and Equvalent Intensty Commtments for Low Growth Varance Hcksan CV measure ($trll) Base case Elastcty between domestc and foregn goods Elastcty between domestc and foregn goods Elastcty across foregn goods Elastcty across foregn goods (Proportonal Equvalent) (1) 50% ncrease (Proportonal Equvalent) (1) 50% decrease (Proportonal Equvalent) (1) 50% ncrease (Proportonal Equvalent) (1) 50% decrease (Proportonal Equvalent) (1) Chna 1.093* Inda * Russa * Brazl * US * EU * Japan * Row *