The Global Economy, Trade, Environment and the Climate System (GETEC) Model and a Reference Case for Climate Policy Analysis

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1 The Global Economy, Tade, Envionment and the Climate System (GETEC) Model and a Refeence Case fo Climate Policy Analysis Hom M. Pant, Liangyue Cao and Bian S. Fishe Austalian Bueau of Agicultual and Resouce Economics 8 th Annual Confeence on Global Economic Analysis Radisson SAS Senato Hotel, Lübeck, Gemany, 9 11 June 2005 This pape descibes the new featues added to the fowad-looking vesion of the Global Tade and Envionment Model (GTEMLR) to aive at a peliminay vesion of an integated assessment model of climate change the Global Economy, Tade, Envionment and Climate (GETEC) model. New additions include a climate module, a damage function, cleane powe geneation technologies and new aggegation ules fo all enegy uses to stylize the adoption and evolution of cabon-fee enegy technology in the economic module. GETEC is then simulated unde much debated intenational eal income convegence assumption to geneate the A1 scenaio of the IPCC s SRES with and without the damage function tuned on. These simulations povide altenative efeence cases against which a possible climate policy of emissions estiction could be compaed. The esults show that in geneal with the damage function tuned on the eal pe peson income level is lowe eveywhee and income convegence attained by pooe egions is also lowe than without the damage function. This implies that economic costs of climate policies ae likely to be lowe in integated models compaed with the ones that do not have the feedbacks. ABARE poject ISSN

2 1 Intoduction 1 Climate change is now one of the most widely studied and debated topics. One of the easons fo that is the scope of possible consequences of the climate change and anothe is that we, human beings, ae esponsible fo this. Many scientists now believe that human induced emissions of geenhouse gases (GHGs) ae causing the global climate to change aveage suface ai tempeatues will incease, sea levels will ise, ainfall patten will change and thei vaiability will also incease. These climatic changes may cause losses of human lives, popety and othe natual envionments. To avoid possible damages, theefoe, a foegone conclusion is that eduction in GHG emissions is a necessity. Undestanding and esponding to the climate change poblem poses seveal challenges, not least of which includes vaious uncetainties. Fist thee ae significant uncetainties suounding the scientific undestanding of climate change. Second, pojections of human induced emissions ae also uncetain. This is not to say that thee is uncetainty egading whethe o not inceased concentations of GHGs will bing about climatic change this is egaded as a given athe that thee ae diffeences in opinions egading the magnitude, timing and vaious spatial effects that will aise fom a given futue emissions tajectoy. Leaving the esolution of vaious uncetainties of scientific models to climate scientists, we, who wok on social sciences and policy aeas, can take what in geneal has been ageed by climate scientists as given and wok towad a ational esponse to the climate change poblem conditional upon the cuent scientific knowledge. Howeve, as it is impossible to pedict coectly the futue path the global economy will take, a easonable appoach is equied to deal with the esultant uncetainty of the tajectoy of human induced emissions. Commonly used appoaches ae scenaio-based. Scenaios could be designed based on some sot of convegence hypothesis as in Nakićenović et al. (2000) and/o possible gids of pojected county-specific deteminants of technological pogess and economic gowth. Whicheve appoach is taken to poject economic and emissions gowth, if the famewok does not account fo any feedback between the climate system and the economy while making its pojections it is likely that such a famewok will incoectly foecasting futue income/poductivity levels and/o the level of oveall emissions. In geneal, as the climate-economy feedback is likely to esult in losses to most economies (paticulaly unde pojections of a cabon intensive global economy) it would be expected that famewoks without these feedbacks ae likely to ovestate the likely level of climatic change that will occu in the absence of climate policies. Similaly, famewoks that do not account fo climate-economy feedbacks would also be likely to ovestate the cost of a given climate change esponse policy as they ignoe the damage costs that may aise in the absence of such policies. 1 We wish to thank Don Gunasekea, Helal Ahammad, Benjamin Buete and Guy Jakeman fo constuctive comments, without implicating them fo any emaining eos. 2

3 A ational esponse to climate change poblem theefoe equies a bette undestanding of the intedependence between the climate system and the economic system. In paticula, given the esponses of the climate system to inceased concentation of geenhouse gasses in the atmosphee, we need to know the consequences of the pojected climate change. This is a big question and we, as a pofession, ae not yet eady to be able to povide a definite quantitative answe to this all-encompassing question. We can, howeve, ephase the question in tems of measuable economic impacts and maket esponses to these impacts of climate changes. If pojected climate change is damaging the economic system then it would also imply lowe ates of economic gowth and lowe level of global emissions as factos of poductions would be lost o damaged and economic activities would be scaled down. Hence, we can ask: what ae the economic impacts of pojected climate change that esults fom a steam of emissions of GHGs? What ae the emission and the climatic consequences of the economic damages in tun? Answeing both questions simultaneously is not an easy task. This means basically assessing the full consequences of cuent actions including the effects of climate change and possibly affecting individual choices accodingly. It needs an analytical famewok that integates economic systems and climate system togethe with full feedback. Clealy, a consistent answe, even speculative, deived fom the integated famewok to these ephased questions povides a efeence case without active climate policy against which the outcomes of climate change esponse policies can be compaed. This will povide a basis to pefom meaningful cost-benefit analysis of altenative climate change esponse policies and thus help find the optimal couse of human actions. In this pape we descibe a peliminay vesion of an integated assessment model being developed at ABARE. It is deived by including a simplified climate module and a stylised damage assessment module, to the intetempoal vesion of the Global Tade and Envionment Model (GTEMLR) ABARE s geneal equilibium model of the global economy. We call this integated assessment model the Global Economy, Tade, Envionment and Climate (GETEC) model. The climate module of GETEC is simila to the one used by IPCC in its SAR (Houghton 1997). It can poject changes in the global aveage suface tempeatue in esponse to changes in global anthopogenic emissions of geenhouse gases. The damage module employs a hockey-stick function, which diffeentiates egions with espective to thei vulneabilities to climate changes, to stylize the economic damages that might be inflicted upon the economic system by global tempeatue changes. Economic damages ae epesented by facto and secto neutal poductivity losses, which could be viewed as losses in facto supplies at constant poductivity levels o simply factos being less poductive at highe tempeatues o a combination of both. In addition to this the powe geneation secto has been e-modelled and enegy aggegation functions of all enegy uses ae e-specified to stylize the adoption and evolution of cabon-fee enegy technology in the economic module. 3

4 The model is then simulated unde altenative scenaios to investigate whethe inclusion of climatic feedback via damage assessment modeling impoves the quality of climate change policy assessment. In paticula, using this stylised model we investigate whethe the path of eal income, emissions, tempeatue changes, etc. ae significantly diffeent in models containing damage functions fom models that do not take the economic feedbacks fom climatic changes. The emainde of the pape is divided into six sections. In section two, we descibe components of GETEC and in section thee we descibe the climate module. The damage function is descibed in section fou. Section five descibes ou appoach in compaing eal incomes acoss nations and modeling of income convegence, and section six epots the esults of simulating GETEC unde eal income convegence simila to that of SRES A1 scenaio with and without the damage function. In section seven we conclude the pape. 2 The conceptual stuctue of GETEC As a pototype vesion of an integated assessment model, GETEC consists of a combination of a dynamic model of the economic system with an envionmental accounting system, called GTEMLR, a simple climate model and a damage assessment module. Each of these modules ae descibed in the following subsections. 2.1 An oveview of GTEMLR GTEMLR is the intetempoal vesion of The Global Tade and Envionment Model (GTEM), which is a multisectoal and multiegional dynamic model of the global economy developed at ABARE (Pant, 2002). The ecusive vesion of GTEM was oiginally deived fom the fist vesion of GTAP model (Hetel 1997) and so at its coe GTEM looks vey much like the GTAP model; many of the coefficient and vaiable names and data heades ae the same and it is solved using the same softwae, GEMPACK (Haison and Peason 2000) 2. GTEM, howeve, added the following featues to the oiginal GTAP model: a technology-bundle appoach to model enegyintensive industies; a population module that geneates endogenous changes in population and labo supply; a geenhouse module that tacks emissions fom the poduction of vaious commodities and fom the use of fossil fuels; and accumulation elationships fo capital stock, debt and population that made GTEM dynamic. The intetempoal vesion of GTEM (Pant, Tulpulé and Fishe, 2002), which is called GTEMLR, allows GTEM agents to be fowad-looking. Because of this paticula featue, GTEMLR is well suited to study poblems with long time hoizons, such as climate change. 2 We solve GETEC using GEMPACK on a fully 64-bit envionment and hence memoy poblem fo easonable simulation poblems and aggegations ae now a thing of the past. We thank Ken Peason and Jill Haison fo making GEMPACK 64-bit compliant on PCs. 4

5 Biefly, the main featues of the model can be descibed as follows. It contains five basic types of agents: a epesentative consume, egional poduction sectos, impotes, an intenational tanspotation secto, and a global financial cente. All agents behave competitively and take pices as given. Supply of natual esouces, land, govenment policies, technology and tastes ae exogenous. All factos in each egion ae owned by the egional household, which eceives all facto incomes, all tax evenues and makes and eceives tansfe payments to and fom the est of the wold. A epesentative consume decides on the allocation of income of the egional household. The cuent goss national income of each egion is allocated to savings (units of global bonds) and to the consumption of commodities poduced eveywhee to maximise the utility of the epesentative consume. This is done in thee stages: fist, a Cobb- Douglas utility function, defined ove the pivate consumption of goods, govenment consumption of goods and eal savings is maximised. This implies that a fixed shae of goss national income is allocated to each of the thee categoies. The budget allocated to pivate and govenment consumption is futhe allocated to individual commodity composites maximizing a Cobb-Douglas utility function fo govenment consumption and a CDE function fo pivate consumption. In the thid stage, using the Amington assumption of impefect substitution between souces of a commodity and assuming ationality both govenment and pivate demand of each composite commodity is met fom domestic and foeign souces so that the cost of each commodity composite is minimized. Poduction sectos use a CES composite of the fou types of factos of poduction, capital, labo, land and the natual esouce, and combine it with othe enegy and nonenegy mateial inputs to poduce thei output. Poduction technologies contain nests that allow inta-enegy commodity, inta-facto and enegy-facto substitution in esponse to elative pice changes and ae chaacteised by constant etuns to scale. Each secto minimises cost by choosing inputs optimally; and industy output levels ae chosen to maximise pofit, given pices. Thee ae two poduction sectos in GTEM electicity and ion and steel whose poduction functions ae diffeent fom othes. Instead of a single nested poduction function, each of these sectos has a technology bundle. Electicity is poduced by six technologies coal fied, oil fied, gas fied, hydo, nuclea and enewables; and ion and steel is poduced by two diffeent technologies blast funace and electic ac. Each technology employs a diffeent Leontief poduction function. The technology-bundle industies buy CES aggegates of the outputs of coesponding technologies as inputs into thei poduction, which is then sold to the end uses. The allocation of output to diffeent technologies is chosen to minimise the aveage cost of input to the espective technology-bundle industy. Unlike technologies of the ion and steel secto, which can be consideed to poduce outputs that ae impefect substitutes, technologies in the electicity secto poduce nea homogenous output. The CES aggegation of the technologies, which teat them as impefect substitutes, is indeed an impefect epesentation of the capacity constaints faced by each technology in the shot un, lumpiness of investment, and diffeent needs of buyes, such as emote location, etc. that suppot the existence of niche technologies. 5

6 Competitive conditions imply pice-taking behavio on the pat of all agents and satisfaction of zeo pofit conditions in equilibium when all makets clea. Input demands fo commodities ae met fom domestic as well as fom foeign souces. The Amington assumption of impefect substitution between souces and the pocess of cost minimisation again detemine the allocation of input demand between souces of supplies. Aggegation of input and final demand fo each commodity identified by souce detemine a egion s impots by commodity and by egion. This aggegation also yields a egion s expot of a commodity by destination and thus bilateal tade. Shipping of commodities fom a souce to its destination egion is done by an intenational tanspot secto, which has a Leontief poduction technology. This secto buys inputs of tanspots (magin commodities) fom vaious egions minimising the unit cost of the tanspot aggegate. Impotes buy the tanspot sevices and the cost of tanspot ceates the wedge between the fob and cif pices of commodities. Both the tanspot secto and impotes satisfy zeo pofit conditions in equilibium because of competition. The savings of the egional households ae pooled by the global financial cente and then lent to investos esiding in all egions. The allocation esponds to the diffeential of the expected ate of etun with the global ate of etun that cleas the maket. The maket cleaing ate is used to sevice the debt o pay the saves, which guaantees that the global financial cente satisfies its zeo-pofit condition. Regions may diffe in thei isk chaacteistics and policy egimes, theefoe it is maintained that diffeent egions may have diffeent expected ates of etun in equilibium. The equilibium condition simply equies that changes in the expected ate of etun be the same acoss all egions, which equals the changes in the global ate of etun. In this sense, the allocation of investment in GTEM is inefficient. Thee is scope fo anothe allocation of investment (and hence the global capital stock), fom a low etun egion to a high etun egion, which may aise global income and welfae. Howeve, despite the mobility of investible funds, it is maintained in GTEM that the global capital maket does not equalise the expected ates of etun on investment. GTEM is built in the Walasian tadition. Theefoe fo each commodity and facto thee is a competitive maket. It is maintained that with fully flexible pices, makets fo all goods and factos clea in each peiod. Commodities ae distinguished by souce and sold globally. Thus, they have a global maket cleaing condition. Capital and labo ae egion specific, but feely mobile acoss activities in seach of a highe etun; land is mobile within agicultual industies and natual esouces ae specific to each esouce based industy such as coal, oil, gas, foesty and fishing. Factos ae inelastically supplied and thei pices ae detemined by the espective maket demand conditions. The savings of a egional household does not bea any elationship with the amount of egional investment; it is possible fo each egion to have its capital account in imbalance. A suplus leads to an accumulation of foeign debt, which needs sevicing fom the next peiod. This mechanism sets the dynamics of accumulation of net debt in GTEM. As thee is a estiction on the amount of investment that a egion can undetake 6

7 in any peiod which is set by the inteactions of investment demand functions and thei competition fo limited global savings and a egion cannot boow fo consumption, thee is no Ponzi game poblem in GTEM. Capital at the stat of a peiod is given by the depeciated stock of the pevious peiod and the goss investment undetaken ove the pevious peiod. As long as the amount of goss investment is diffeent fom the depeciation equiement, the capital stock of a egion continues to change. GTEM has a population module that links fetility and motality with eal income changes. Togethe with a given net migation ates GTEM pojects population changes by 100-age cohots and gende by egion. With a default assumption that paticipation ates ae constant, using the population of yeas of age, changes in labo supply is endogenously detemined. In its geenhouse module, GTEM accounts fo thee gases: cabon dioxide, methane and nitous oxide. In calculating CO 2 emissions GTEM accounts fo combustion, fugitive emissions and industial pocesses. In the case of methane and nitous oxide, it accounts fo emissions fom livestock and faming activities, fugitive emissions, tanspot, and chemical industies. The main assumption used in the estimation is that the combustion emissions ae popotional to the use of fossil fuels and othe emissions ae popotional to activity level. The constant of popotionality, the emission intensity is taken as a technological paamete and teated exogenously. 2.2 Modeling evolution and adoption of cabon fee enegy technology: some modifications in GTEMLR Using leaning-by-doing as the pinciple mechanism fo educing costs of new technologies in GTEMLR, Pant and Fishe(2004b) examined whethe cabon-fee souce based hydogen can compete with fossil fuels and become the dominant fom of enegy and enegy caie in this centuy. Some of the modeling innovations made in that pape ae adapted in this pape to epesent the development and diffusion of clean enegy technologies. In paticula, the functions epesenting the inceasing cost of natual esouce extaction in the fossil fuel sectos and leaning by doing in newe enegy poduction technologies as thei scale of opeation expands ove time have been evised. These modifications ae descibed in the following sub-sections Modeling inceasing cost of fossil fuels Although thee ae counte aguments (Odell 1999) that cannot be easily ejected, it is geneally agued that as continued use of fossil fuels will deplete the existing eseve, the cost of extacting these esouces will eventually ise (Gelagh and Lise 2003). To model this pocess, we associate the poductivity of the natual esouce facto in the fossil fuel poduction sectos (coal, oil and gas) negatively with the cumulative quantity of the natual esouce used by the industy. Let be the quantity of natual X N, j, t esouce used by the extaction secto j, (we have suppessed the county/egion index), A its poductivity index (it equals 1 in the base yea), P the vecto of pices faced N, j, t jt 7

8 by the secto and Q jt, the output poduced by the secto at time t, then its cost minimizing input demand function can be witten as A X = F ( P, Q, A ) (1) N, jt, N, jt, jt, jt, jt, N, jt, and the poductivity index is given by α N, j, t j N, j, t j j (2) A = [1 β ][ Z / Z N, j, t] + β whee ZN, j, t= XN, j, τ and Z N, j, t= t* XN, j,0 which also implies A N, j, t= 1 if Z = Z. N, j, t N, j, t τ t α in the above equation is a paamete to measue the speed of decline in poductivity with the incease of cumulative natual esouce extaction, and β is the asymptotic teminal value of the poductivity when the cumulative extaction tends to infinity. The values of α and β we used ae shown in table 1. The consequence of modeling the poductivity facto as given in (2) is that continued use of natual esouce at a ate highe than used in the base yea makes the facto less poductive, o expensive in elation to othe factos. Theefoe, to poduce the same quantity of output, moe and moe labo and capital will have to be employed, with a given quantity of natual esouce depending on the size of the elasticity of facto substitution, which we have maintained slightly geate than unity in GETEC, as time goes by. This inceases the cost of fossil fuel slowly to the uses of fossil fuels including the powe geneation secto. As a esult, ceteis paibus, enewable technologies will become elatively moe attactive compaed to fossil fuel technologies Modeling leaning-by-doing in enewable secto As mentioned ealie, leaning by doing is believed to be a pimay eason fo the decline in cost of infant technologies, such as hydogen poduction and distibution. The leaning by doing pocess is intoduced in GETEC as an endogenous impovement in input-neutal poductivity in the enewable technology of the powe geneation secto. Recall that the input output elation in each technology is chaacteised by a Leontief poduction function. Let (3) A, X, it it t = Q fo each input i and time t 8

9 be the input demand function of the enewable, cabon fee technology (note that each technology of the technology-bundle industies has a Leontief poduction function in GTEM). A it, in equation (3) epesents the poductivity facto of the input i, which in othe wods is the invese of the input output coefficient. An incease in the value of A it, implies inceased poductivity as this means that less X it, is needed, without being substituted fo by any othe input, to poduce a given Q t. Assume that one souce of poductivity gowth is via leaning-by-doing, meaning that the cost of poduction declines with accumulated expeience, measued by the cumulative change in the poductive capacity (Aow 1962; Wight 1936). It is commonly believed that a doubling of the cumulative capacity leads to about a 20 pe cent fall in the cost of poduction. In this pape we make the explicit assumption that doubling cumulative capacity, measued by output level, implies a 20 pe cent fall in the equiements of all inputs, which means A i will be about 20 pe cent highe as a esult of doubling of cumulative capacity. 3 This pocess can be modeled as (4) A, it = η 1 Z Z γ i + [1 ηi][ i, t / it, ] i whee Zit, is the cumulative expeience, measued by the cumulative output of the new technology i, Z it, is the cumulative expeience of technology i had its output emained unchanged fom the base yea up to yea t, γ is a paamete that epesents the speed at which the leaning ate eaches the limit with the accumulation of expeience, and 0 η 1 is a leaning paamete such that 1/η is the uppe limit of endogenous poductivity gain though the leaning pocess. The values of γ and η we used ae shown in table 1. Clealy in equation (4) A it, = 1 if Zit, = Z it, which means that if a powe geneation technology simply epoduces its histoy it does not lean; in ode to lean it must be gowing Modeling vaiable elasticity of substitution between altenative enegy souces Even in studies based on simplified models of the economy with two souces of enegy supply and a single use thee is a poblem in modeling the substitution possibility between altenative souces of enegy supply. Should the cabon fee and cabon-ich souces be teated as pefect substitutes, impefect substitutes o complements have emained an unesolved question. Fo example, Peck and Teisbeg (1992) teat the two as pefect substitutes but impose a capacity constaint and highe costs fo the cabon fee technology. Goulde and Schneide (1999) teat them as poo substitutes and set the 3 In GETEC/GTEM enewables technology use only labo and capital as inputs. 9

10 elasticity of substitution vey low, as is done in standad GTEM in which the default value is Li et al. (2003) have set the values of the CRESH paametes diffeently fo diffeent technologies between 0.1 and 1.5. Similaly, van de Zwaan et al. (2002) assume the value to be 3. An inteesting appoach has been followed in Kvendokk et al. (2004), howeve. They have assumed the elasticity of substitution between existing fossil fuel and cabon fee technology to be unity and between thei aggegates and the backstop technology to be infinity. No matte what value we choose fo the elasticity of substitution between the technologies, the size of the estimate eally mattes. Gelagh et al. (2004) ague that since unde a CES aggegation ule, the atio of cost N F minimizing demand fo cabon fee enegy,, to fossil-fuel,, is elated to the atio P t N F of espective pices and accoding to P t Y t Y t F N N F (5) ( Y / Y ) ( P / P ) σ t t t t whee σ is the elasticity of substitution between the two enegy souces, the choice of base yea pices, quantities and the elasticity of substitution should agee and satisfy (5). This means, we must have (6) σ = log( Y F / Y N ) / log( P N / P F ). t t t t When the liteatue based value of Y and P fo both fossil fuel and cabon-fee technologies fo the base yea wee used to calibate the value of the elasticity of substitution, σ, they found that the value is nealy 3. In an ealie pape by Gelagh and Lise (2003) they used a diffeent appoach to tackle the calibation poblem. They agued that the elasticity of substitution depends on the maket shae of the technology. In the case with two technologies, the elasticity of substitution will be low if one technology dominates and highest when both technologies have equal maket shaes. To model this they adopted the vaiable elasticity of substitution (VES) aggegato function poposed in Kadiyala (1972) and teated both technologies symmetically. They calibated the VES function in such a way that the esulting elasticity of substitution fell between 1 and 4. In Gelagh et al. (2004) it is shown (via simulations) that the equied cabon tax to attain a given emission tajectoy o taget citically depends on the elasticity of substitution between altenative souces of enegy supply. If the elasticity of substitution between the conventional cabon-ich and new cabon-fee souces of enegy supply is sufficiently lage then the equied cabon tax that can delive the same outcome could be substantially lowe compaed to the case with low o no possibility of such substitution. It is also demonstated in Gelagh et al. (2004) that, unde the assumptions of thei pape, that is, with a sufficiently high elasticity of substitution, cabon fee souces will almost dominate within this centuy as the sole povide of enegy. In this case the citical question is whethe the atmospheic load of the GHG poduced ove this centuy is within the toleance limit of the climatic system. If not, 10

11 then cabon taxes could be used to bing it unde contol. Theefoe, the size of the elasticity of substitution and the pecise mechanism suppoting the popagation of cabon fee technologies in these models emain the subject fo futhe examination Substitution between powe geneation technologies GTEMLR contains multiple technologies of powe geneation one of them is othe enewables (which excludes hydo). 4 The base yea shae of this technology to total powe geneation is vey small in all egions and has been chosen to epesent all foms of cabon-fee, including clean hydogen, enegy technologies in this pape. It is a common pactice to teat these technologies as impefect substitutes in modeling the simultaneous existence of many technologies with vaying cost stuctues. If we use a CES function to aggegate these powe geneation technologies, as is done in many othe studies and we assign a single value fo the elasticity of substitution between all possible pais, then fo a easonable change in elative pices it is quite clea that the output of the enewables can not ise to any significant numbe. This is simply because even if the elative pice of enewables falls by say 10 pe cent, keeping eveything else constant, with a elasticity of substitution of 3, the output of enewables will ise nealy by a 30 pe cent. Since 30 pe cent of a small numbe is still small, thee would be an extemely long time needed fo this technology to captue a substantial maket shae. On the othe hand, a small incement in the existing capacity of enewables may mean a lage pecentage incease because of the small base. Fo example, an addition of two sola panels when thee was one is a 200 pe cent incease in the poduction capacity and output. Hence, in ode to epesent the behavio of technologies with vey small shaes coectly, use of a CRESH function with diffeent CRESH paametes appeas moe suitable than a CES function. A cost minimizing input demand fo the output of technology k, in pecentage change fom, subject to a CRESH aggegato can be witten as 5 (7) x = q ρ ( p pˆ ) k k k whee q is the pecentage change in the output (o aggegate input of the technology bundle) of the technology-bundle industy, x k is the pecentage change in the output allocated to technology k, p k is the pecentage change in the pice of technology k, ˆp is the modified shae weighted (see equation (8) below) aveage pice of all technologies and ρ k is the CRESH paamete associated with the technology k. The aveage pice, ˆp, is given by 4 Hydoelectic technology is consideed as a matue technology with sevee limitations to gow. 5 See Dixon et al. (1982, pp ) fo the deivation. 11

12 ρksk (8) pˆ = pk whee both and k ange ove the set of technologies. ρ S k The paiwise Allen-Uzawa patial elasticity of substitution is given by ρiρk (9) σ ik = with i k. ρ S The special featue of the CRESH function is shown by equation (9). The atio of pai wise elasticity of substitution paametes, ( σ / σ ) = ( ρ / ρ fo all i k, j and thus ik ij k j ) the atio emains constant fo any pai k, j and hence the name. If, howeve, ρ = ρ, fo all k and j, then the CRESH function becomes identical to a CES function with ρ = ρ = σ. k j Fo a niche technology, we can see fom equation (8) that changes in its pice will not affect the aveage pice in a significant way even if the pice change was lage. Fom equation (7) we can see that the pecentage change in demand fo its output will not be damatically high unless the coesponding CRESH paamete is vey lage. But, we know that in the beginning, when the base quantity is small, a small absolute incease means a vey lage change in pecentage tems. Hence a easonably lage value fo the CRESH paamete of the niche technology is waanted. But as its maket shae gows to a significant numbe, maintaining a lage value fo the CRESH paamete would give undue sensitivity to this technology. The elasticity of substitution between the cabon fee technology vis-a-vis any othe technology will emain high while that between othe fossil fuel technologies will emain low. This is especially impotant in models with leaning by doing, as the aveage cost of the niche technology would be falling with the incease in cumulative capacity, othe things being kept the same, and the demand fo the output of the niche technology will be gowing dispopotionately. Theefoe the CRESH paametes associated with the niche technology should have highe values in the beginning and decline subsequently. This also means that the CRESH paametes should be modelled as time dependent quantities. To addess this poblem we specify the time path of CRESH paametes as k j ρ = ρ + ξ ρ [ s s ][1 2s, ] (10) kt, k,0 k k,0 kt, k,0 kt whee s = Q Q, and ξ k is an adjustment paamete (see table 1 fo the value of kt, kt, / jt, j this paamete). The initial value fo ρ kt,, i.e. ρ k,0, is 2 fo all conventional (fossil fuel 12

13 as well as hydo and nuclea) technologies, and 4.2, 4, 3.5 and 3.5 fo the new cabonfee technology in OCED90, REF, ASIA and ALM egions, espectively. 6 Fo conventional technologies, ξ k is negative, which means ρkt, goes up when thei output shaes fall below thei initial shaes and the initial shaes ae less than 50 pe cent. Incease in these CRESH paametes allows the conventional technologies to be easily substituted with the othe enewables technology as they gow and become competitive. Fo the othe enewables technology, ξkis positive, which means ρkt, goes up when its output shae becomes highe than its initial shae. Incease in the CRESH paamete fo the new cabon-fee technology allows it to captue inceasing maket shae as it becomes cheape. When the shae of the othe enewables technology exceeds 50 pe cent, the substitution paamete declines slightly which is to allow this technology not to be too sensitive to pice changes Use of enegy commodities by fims It was mentioned in section 2, poduction technologies contain nests that allow intaenegy commodity, inta-facto and enegy-facto substitution in esponse to elative pice changes and ae chaacteised by constant etuns to scale CES aggegato functions in each stage. The default elasticity of substitution between enegy commodities in standad GTEM fo shot un simulations is 0.2. In GETEC, which typically coves moe than a centuy, it is set to 2. This is well within the ange used by pevious studies. This incease also pesupposes, at the same time, that machines and equipments that opeate on fuel cells/electicity ae available to compete with the ones that opeate on coal, oil o gas (fo example gas heating system vesus fuel cell/hydogen heating). In paticula, it assumes that FCVs ae available if thee is a demand in the maket to eplace intenal combustion engines Use of enegy commodities by households The othe impotant use of enegy commodities is the household secto. In standad GTEM, household consumption demand is modelled by minimising a CDE expenditue function as in GTAP (Hetel 1997). It does allow substitution between the enegy commodities, but the size of the substitution within the enegy goup may not be compaable to the level of substitution possibilities equied in modeling a tansition to a cabon-fee enegy system, fo example tansition fom gasoline diven cas to electic o fuel cell vehicles. This poblem can be tanslated as the poblem in household demand system of inceasing the substitutability between electicity and othe fuel commodities and allow households to fully substitute fossil fuels by electicity. This is so because household consumption becomes emission fee if it switches fom pimay 6 The egions have been taken to match the aggegate egions used to epot in the Special Repot on Emission Scenaios of IPCC (Nakicenovic 2000). 13

14 enegy commodities to electicity, which may be poduced inceasingly by zeo o nea zeo emissions technologies. Hence, the key poblem is how to allow households to be able to substitute apidly between conventional enegy commodities and electicity to model the adoption of FCVs, should they become cost competitive. To this end, the consume demand system in GETEC has been modified slightly and one moe nest has been added to the optimizing pocess. Using a CRESH aggegato an enegy composite is fomed out of the individual enegy commodities in a sepaate nest. Default values fo the CRESH paametes within the enegy nest ae all set at 2. Demand fo all othe commodities and fo the enegy composite ae deived by minimizing the CDE expenditue function. Given the demand fo enegy composite thus detemined, demand fo individual enegy commodities ae obtained by minimizing the cost of the enegy composite. Once the demand fo each enegy commodity has been woked out fom this nest, the standad GTEM allocation of demand fo each commodity to the souces of supply using an Amington pocess has been maintained. 3 The climate module The climate module is adopted fom 5-box model of Maie-Reime and Hasselman (1987). This model has also been used by othe integated assessment models of climate change such as MERGE (Manne, Mendelsohn and Richels 1995; Manne and Richels 2004) and FUND (Tol 2004). Only thee of the most impotant geenhouse gases ae consideed in the climate module, which ae cabon dioxide (CO 2 ), methane (CH 4 ) and nitous oxide (N 2 O). 3.1 Geenhouse gas stock and concentation (i) Atmospheic Stock of CO 2 Cabon emissions ae divided into five classes (i.e. five boxes), each with diffeent atmospheic lifetimes. The following equation estimates the CO 2 stock fo each class at the beginning of yea t+1, given the stock at the beginning of yea t: (11) S_ CO2( b, t+ 1) = κ( b) S_ CO2( b, t) + ω( b) E_ CO2 ( t), whee S_CO 2 (b, t) is the stock of CO 2 in box b at the beginning of yea t, E_CO 2 (t) is the total emission of CO 2 in yea t, κ( b) is the yealy decay paamete (o the annual etention facto) of the stock of CO 2 in box b, and ω( b) is the faction of total CO 2 emission which belongs to box b. The paamete values we used ae shown in table 1. In each yea, the total CO 2 stock is the sum of CO 2 stock in all classes, that is, (12) S( CO2, t+ 1) = S_ CO2( b, t+ 1). 5 b= 1 14

15 (ii) Atmospheic Stock of CH 4 and N 2 O The following equation estimates the stock of nonco 2 gases (i.e. fo CH 4 and N 2 O) at the beginning of yea t + 1, given the stock at the beginning of yea t: (13) S( g, t+ 1) = ς ( g)* S( g, t) + E( g, t), whee S(g, t) is the stock of nonco 2 gas g at the beginning of yea t, E(g, t) is the total emission of the nonco 2 gas g in yea t, ς is the yealy decay paamete (annual etention facto) fo the nonco 2 gas g. See table 1 fo the paamete values of ς. (ii) Atmospheic concentation of geenhouse gases Fo each of the above geenhouse gases, the concentation is linealy popotional to the stock, that is, (14) CONC( g, t) = θ ( g)* S( g, t), whee g GHG epesents CO2, CH 4 o N 2 O, CONC(g, t) is the concentation of gas g at the beginning of yea t, and θ is the appopiate convesion paamete to convet stock to concentation ppmv fo CO 2, ppbv fo othe gases (see table 1 fo its value used). Note that S, the stock of gases is in commensuable units as well. Base yea concentation (1997) ae estimated at 364 ppmv fo CO 2, 1690 fo CH 4 and 311 fo N 2 O. 3.2 Radiative focing The equations below estimating the adiative focing of geenhouse gases emitted ae also adopted fom the Houghton et al. (1997) and ae simila to the equations used in the MERGE model. (i) Radiative focing due to inceased atmospheic concentation of CO 2 is given by (15) RF( CO, t) = 6.3ln[ CONC( CO, t)/ CONC( CO2,0)], 2 2 whee RF(CO 2, t) epesents the impacts on adiative focing by the concentation of CO 2 at the beginning of yea t, and CONC(CO 2,0) is the 1990 level of CO 2 concentation. (ii) Radiative focing due to inceased atmospheic concentation of CH 4 is given by 15

16 (16) ( 4, ) = 0.036{[ ( 4, )] [ ( 4,0)] } RF CH t CONC CH t CONC CH f ( CONC( CH, t), CONC( N O,0)) f( CONC( CH,0), CONC( N O,0)). 4 2 (iii) Radiative focing due to inceased atmospheic concentation of N 2 O is given by (17) RF( NOt, ) = 0.14{[ CONCNOt (, )] [ CONCNO (,0)] } f( CONC( CH,0), CONC( N O, t)) f ( CONC( CH,0), CONC( N O,0)), 4 2 whee CONC(CH 4,0) and CONC(N 2 O,0) ae the 1990 levels of CH 4 and N 2 O concentations, espectively, and f is a function defined below: (18) f ( xy, ) 0.47 ln[ ( xy) xxy ( ) = Tempeatue change The potential tempeatue change is linealy popotional to the impacts on adiative focing, that is, (19) PT() t = d [ RF( CO,) t + RF( CH,) t + RF( N O,)] t Cool() t, whee PT(t) is the potential tempeatue change in yea t, d is the paamete fo conveting adiative focing to potential tempeatue change (see table 1 fo its value), and Cool(t) is the cooling effect of aeosols which is estimated below as: (20) Cool() t = c1sem () t + c2ln[1 + SEM ()/ t c3], whee SEM(t) is the wold SOx emissions (million tons of sulfu), c 1 is a paamete to measue the diect cooling effect of sulfu emissions, c 2 is a paamete to measue the indiect cooling effect of sulfu emissions, and c 3 is the natual sulfu emissions (million tons pe yea). These paamete values ae listed in table 1. SEM fo the base yea is set at 69 and is assumed to emain constant ove time. 7 7 The poduct of the paamete d with 6.3*ln(2) fom the adiative focing equation fo CO 2 yields the value of climate sensitivity paamete used in this model. Hence the value of the sensitivity paamete is about 2.5, which measues the change in tempeatue fo doubling of the atmospheic concentation of CO 2. Climate sensitivity can be alteed by changing the value of the paamete d o the coefficient in the adiative focing equation fo CO 2. 16

17 The actual tempeatue change lags behind the potential tempeatue change because oceans take a long time to wam up. The lag pocess is modelled as follows: (21) AT( t+ 1) ATt () = τ [ PTt () ATt ()], whee AT(t) is the actual tempeatue change in yea t fom the base yea, and τ, see table 1 fo its value, is a paamete to measue the time of lag between the potential and actual tempeatue changes (fo example, τ = epesents a 40 yea lag). 4 A stylised damage assessment module A simple Hockey Stick function is used to estimate the damages caused by global tempeatue changes. The function is deived by modifying the willingness-to-pay estimation fo non-maket damage in the MERGE5.1 model (Manne and Richels 2004). The damage with the Hockey Stick function is estimated below: δ µ () (22) () {1 [ ()/ ]} t Λ t = AT t Ω, whee Λ () t is the egion specific climate change induced economic loss facto (ELF) in yea t which measues the damage, AT(t) is the global aveage suface tempeatue change in yea t fom the base yea; Ω is the catastophic change in global aveage suface tempeatue fom the efeence yea; δ and µ () t ae paametes to measue the seveity of damage fo a given tempeatue change. We have used the value of the paamete δ and Ω to detemine the shape of the ELF function, Λ () t at µ () t =2. Fo any positive value of µ () t we have Λ () t 0as δ 0 and Λ () t 1as δ and AT(t) < Ω. As AT () t Ω, catastophe esults. Similaly, fo a given finite positive value fo δ, Λ () t 1as µ () t 0 and Λ () t 0as µ () t. So lage values of µ () t and smalle values ofδ, both imply highe damages fom a given tempeatue change. Convesely, lage values fo δ and smalle values fo µ () t imply smalle o no damages fom tempeatue changes that ae less than Ω. The way equation (22) is specified implies that incease in global aveage tempeatue is globally damaging. It can, howeve, be modified to allow some benefits to some egions at small inceases in aveage tempeatue. To keep the mateial simple we have ignoed this possibility in this pape. Following MERGE5.1 calibation, we have set Ω =17 degee Celsius. We have chosen, fo the pupose of this pape, δ =2. By default settings it is implied that the whole economic system would collapse if the actual tempeatue ises by 17 degees Celsius above the base yea level. Fo all tempeatue inceases below that numbe, thee will be some economic activities going on how much of the economic activity will be destoyed by climate change depends on the value ofδ. A lage value of δ implies highe esilience that economic activity will dop only nea the catastophic value of 17

18 the tempeatue change, hence the shape Hockey stick. A value of 2 fo both paametes implies that fo a 2 degee ise in tempeatue above the base yea means about 4 pe cent loss in economic activities and at 9 degees, 50 pe cent of the economy will be wiped out. The time vaiant paamete µ () t =2 fo all time only fo the efeence (o the ichest) egion. Fo othe egions µ () t is futhe defined as below to captue the vulneability of a given county/egion to climate change by linking the egion s eal pe capita income to that of the efeence egion as: (23) µ () t = σ1+ σ2ln[ I ef / I], whee I ef is the efeence pe capita eal income, I is the pe capita eal income of the county/egion consideed in commensuable units, and σ s ae an adjustable paametes to measue the effect of diffeence in eal income affecting the vulneability to tempeatue changes. This diffeentiation is motivated by the obsevations put out by Tol et al. (2000) and Tol (2003) who ague that pooe county/egion have highe vulneability to climate change elative to iche egions. Cuently σ 1 =2 and σ 2 = 1, and OECD90 is taken as the efeence egion. That means all othe egion s vulneability is measued elative to that of the OECD90 egion. It follows that µ () t σ fo each egion. 1 This is whee we deviate fom Manne and Richel s appoach to modeling damages fom climate change. Manne and Richel use the hockey stick function to estimate the willingness to pay by counties to avoid non-maket damages of climate change. The willingness to pay ises with income implies that µ () t 1fo all egions and its value is unity only fo the ichest egion. A value of zeo means that the county would be willing to pay nothing. Fo maket damages they assume that A 2.5 degees tempeatue ise would lead to GDP losses of 0.25 pe cent in the high income counties and 0.5 pe cent in the low income counties. At highe o lowe tempeatue levels than 2.5 degees, we assume that maket losses would be popotional to the change in mean global tempeatue fom its level in 2000 (Manne and Richels 2004, p. 2). Moeove, thei setting of the hockey-stick function implies that non-maket damage would be about 2 pe cent of GDP in ich nations at a 2.5 degee Celsius incease in the global aveage tempeatue. In ou appoach, we do not explicitly model non-maket damages in this pape. We, howeve, ecognise this by assuming that loss of non-maket envionmental entities would contibute towad eduction in facto supplies and/o facto poductivities. At ou default settings OECD90 will lose about 4 pe cent of its GDP in 2100 if the global 18

19 aveage suface tempeatue ises by 2.5 degees Celsius. 8 Loses of pooe egions will be, depending on thei income elative to that of OECD90, slightly highe. The egion specific ELF, Λ () t, in GETEC is cuently linked to the index of total facto poductivity. The diffeence between unity and the value of Λ () t at time t indicates the loss in poductive capacity of the egion by a facto of (1 Λ () t ). This can also be viewed as damages in facto supplies as well o a combination of both. So in the cuent implementation GETEC, a ise in global aveage tempeatue means a loss in economic well-being though a decline in facto poductivities. A positive value of σ 2 in equation (23) means the losses ae highe fo pooe egions compaed to iche egions. The advantage of linking economic damages to pimay deteminants of economic activities, such as facto poductivity, is that it allows us to keep tack of all economic accounts and peseves the popeties of the social accounting matix. 5 Modeling intenational eal income convegence Compaing eal incomes o eal quantities acoss nations is a poblem that comes quite often. One such case is when one ties to model convegence of poductivity o pe capita eal incomes acoss a goup of nations ove a long peiod of time. Neoclassical gowth model pedicts that capital poo counties will gow moe apidly than capital ich counties povided they have identical steady states. In the case of diffeing steady states, thee is conditional convegence. In eithe case of convegence, compaison of eal quantities is unavoidable. One may avoid this poblem, howeve, by not using convegence hypothesis which, of couse, may be desiable fom both theoetical as well as empiical point of view. The use of convegence hypothesis, nevetheless, helps in economising on infomation. Although we can exogenously poject the futue path of natually exogenous vaiables in GETEC to geneate a efeence case, the assumption of convegence, like the ones used in IPCC s SRES, povides us with a compaable execise. Fo the pupose of this pape we maintain intenational convegence in eal pe capita income of the ode of SRES A1 family. As descibed in Pant and Fishe (2004a), we use eal exchange ates to make eal income compaison. In a nutshell the appoach can be descibed as follows. Real exchange ate, elative to the eal quantity being compaed, is defined as: 8 Tol et al. (2000) have povided a table of estimates made by vaious models of likely damages of climate change to vaious egions, in which some egions ae expected to actually gain fom modeate tempeatue inceases. It must, howeve, be undestood that they ae vey peliminay estimates. Ou numbes ae, of couse, fo illustations. 19

20 f R N P h f h f h (24) E / = E / N P whee E h/ f is the geneal equilibium maket exchange ate, defined as numbe of home cuency units pe unit of foeign cuency unit, h f P is the pice of foeign-bundle in foeign cuency units and P is the home pice of the home-bundle in home cuency unit of the eal quantities being compaed. The eal quantities being compaed between the counties may o may not have the same name o chaacteistics that is not impotant hee, take fo example the GDP-bundles. Hence, homogeneity of the commodity bundles acoss nations is not a equied assumption. Goods can diffe by souces o by destination. The question is how can we convet a given bundle of one county into units of the bundle of anothe county? The appoach adopted in GETEC is to find the implied equilibium bate-tems of tade using equilibium commodity pices and exchange ates. It is clea that the equilibium eal exchange ate, E h/ f, measues the bate tems of tade between home and foeign quantities. It is the numbe of home bundle pe unit of the foeign bundle being cuently taded in the maket. It uses the pices of the espective bundles that ae being compaed. This is the ate that is used in GTEC to make eal income compaison. It theefoe follows that fo given units of home bundle say pe capita eal GDP in home units, a convesion into some commensuable units, say into foeign bundle, is equied to make the compaison meaningful. Such a convesion can be made using eal exchange ate. It follows fom the definition of eal exchange ate that R (25) 1 h f Q R h = Qh h E f whee Qh is the expession of home pe capita eal GDP into units of foeign GDPbundle. Real income convegence stipulates that at time T f h f f (26) Q ( T ) = ω Q ( T ), h 20