Capturing Natural Resource Dynamics in Top-Down Energy Economic Equilibrium Models

Transcription

1 Captuing Natual Resouce Dynamics in Top-Down Enegy Economic Equilibium Models Da Zhang, Valeie Kaplus and Sebastian Rausch TSINGHUA - MIT China Enegy & Climate Poject Repot No. 284 Octobe 2015

2 The MIT Joint Pogam on the Science and Policy of Global Change combines cutting-edge scientific eseach with independent policy analysis to povide a solid foundation fo the public and pivate decisions needed to mitigate and adapt to unavoidable global envionmental changes. Being data-diven, the Pogam uses extensive Eath system and economic data and models to poduce quantitative analysis and pedictions of the isks of climate change and the challenges of limiting human influence on the envionment essential knowledge fo the intenational dialogue towad a global esponse to climate change. To this end, the Pogam bings togethe an intedisciplinay goup fom two established MIT eseach centes: the Cente fo Global Change Science (CGCS) and the Cente fo Enegy and Envionmental Policy Reseach (CEEPR). These two centes along with collaboatos fom the Maine Biology aboatoy (MB) at Woods Hole and shot- and longtem visitos povide the united vision needed to solve global challenges. At the heat of much of the Pogam s wok lies MIT s Integated Global System Model. Though this integated model, the Pogam seeks to: discove new inteactions among natual and human climate system components; objectively assess uncetainty in economic and climate pojections; citically and quantitatively analyze envionmental management and policy poposals; undestand complex connections among the many foces that will shape ou futue; and impove methods to model, monito and veify geenhouse gas emissions and climatic impacts. This epint is one of a seies intended to communicate eseach esults and impove public undestanding of global envionment and enegy challenges, theeby contibuting to infomed debate about climate change and the economic and social implications of policy altenatives. Ronald G. Pinn and John M. Reilly, Pogam Co-Diectos Fo moe infomation, contact the Pogam office: MIT Joint Pogam on the Science and Policy of Global Change Postal Addess: Massachusetts Institute of Technology 77 Massachusetts Avenue, E Cambidge, MA (USA) ocation: Building E19, Room Main Steet, Cambidge Access: Tel: (617) Fax: (617) globalchange@mit.edu Website:

3 Captuing Natual Resouce Dynamics in Top-Down Enegy-Economic Equilibium Models Da Zhang *, Valeie Kaplus, and Sebastian Rausch Abstact Top-down enegy-economic modeling appoaches often use delibeately simple techniques to epesent heteogeneous esouce inputs to poduction. We show that fo some policies, such as feed-in taiffs (FIT) fo enewable electicity, detailed epesentation of enewable esouce gades is equied to descibe the technology moe pecisely and identify cost-effective policy designs. We extend a hybid appoach fo modeling heteogeneity in the quality of natual esouce inputs equied fo enewable enegy poduction in a stylized computable geneal equilibium (CGE) famewok. Impotantly, this appoach esolves neaflat o nea-vetical sections of the esouce supply cuve that tanslate into key featues of the maginal cost of wind esouce supply, allowing fo moe ealistic policy simulation. In a second step, we epesent the shape of a esouce supply cuve based on moe detailed data. We show that fo the case of onshoe wind development in China, a diffeentiated FIT design that can only be modeled with the hybid appoach equies less than half of the subsidy budget needed fo a unifom FIT design and poves to be moe cost-effective. Contents 1. INTRODUCTION PREVIOUS WORK A STYIZED GENERA EQUIIBRIUM MODE Hybid Appoach Compaison with the Taditional Appoach NUMERICA EXAMPE OF ONSHORE WIND DEPOYMENT IN CHINA Model Data Static Model The Dynamic Extension of the Model Step-fitting Method Results CONCUSION REFERENCES APPENDIX A: Algebaic Exposition of Equilibium Conditions APPENDIX B: Notations APPENDIX C: Gaphical Repesentations of the Function Foms INTRODUCTION Top-down modeling appoaches specify technology in a delibeately simple manne, even as they offe impotant insights because they account fo endogenous adjustment of pices and quantities in esponse to policy. While this appoach is often justifiable when the question unde investigation does not depend on a pecise epesentation of technology, fo some applications additional technological detail can be citical to the design and evaluation of altenative policy * Joint Pogam of the Science and Policy of Global Change, Massachusetts Institute of Technology, MA, U.S. Institute of Enegy, Envionment, and Economy, Tsinghua Univesity, China. Coesponding autho ( zhangda@mit.edu). Sloan School of Management, Massachusetts Institute of Technology, MA, U.S. Depatment of Management, Technology and Economics, ETH Züich, Züich, Switzeland. 1

4 poposals. Because of the discete natue of engineeing design o esouce quality, the cost cuves associated with the application of many technologies ae known to be kinked. Fo example, a modele may wish to captue the cost of educing emissions as a function of the costs of competing altenatives fo instance, efficiency impovement, end-of-pipe emissions emoval, and a displacement with a non-emitting enewable esouce. Within each of these altenatives, the numbe of distinct technological options and thei popeties can matte significantly to the optimal choice of a solution. Ovesimplifying can intoduce substantial eos when estimating abatement costs of policy. In this pape, we extend an integated (bottom-up in top-down) hybid appoach that is moe flexible and pecise than taditional appoaches used in CGE models, taking as ou stating point the pocedue developed in Kiuila and Ruthefod (2013). This innovation is especially useful if the shape of cost cuve is not egula, fo instance, it has lage steps o is not simply convex o concave. This pocedue is genealizable to any many-step aggegated abatement cost cuve epesenting diffeent abatement technologies o a technology that equies heteogeneous esouces as an input. We detail the application of this hybid appoach by showing its ability to accuately captue the dynamics of technology fo electicity geneation fom wind. The hybid appoach has a distinct advantage in is its capability to eplicate a wind ush phenomenon, in which lage quantities of wind capacity ae cyclically deployed upon eaching a theshold electicity pice (as a function of an implicit o explicit subsidy). Howeve, this effect cannot be captued by the taditional appoach, which elies on smooth cuve fits fo esouce epesentation. As we will show, the hybid appoach also allows fo the simulation of policies tageted at diffeent gades of esouce, e.g. a diffeentiated FIT policy. By explicitly epesenting each gade of esouce, theshold levels fo policy incentives can be assigned, and impacts assessed, moe pecisely. Resouce-diffeentiated policies have been widely applied and dawn moe attention as they equie a smalle subsidy budget. The est of the pape is stuctued as follows. In Section 2, we biefly summeize the pevious wok on epesenting technology in top-down models. Section 3 constucts a simple, stylized top-down economic model and applies it to demonstate the application of this hybid appoach, illustate the wind ush phenomenon and its advantages compaed to taditional appoaches. Section 4 povides a eal-wold example of how the same method can be extended using data fo China s economy and onshoe wind esouces. The final section discusses the esults and policy implications. 2. PREVIOUS WORK Pevious effots have focused on adding technological detail to top-down models. Hee we conside a specific class of top-down models, enegy-economic computable geneal equilibium (CGE) models. Effots to intoduce additional technology detail include models applied in the Enegy Modeling Foum 29 s Bode Cabon Adjustment study (Böhinge et al., 2012), the PET model (O Neill et al., 2010), the PACE model (Hemeling et al., 2013), and the MIT EPPA model (Chen et al., 2015). All of these examples involve intoducing enegy-elated technologies using 2

5 the existing constant elasticity of substitution fomulation, which equies smooth cuve fits fo estimation of key esponse paametes, including esouce equiements. The block decomposition algoithm suggested by Böhinge and Ruthefod (2009) can be used to couple top-down and bottom-up sub-models using an iteative pocedue to solve fo a consistent geneal equilibium esponse in both models. Rausch and Mowes (2014) applied this technique to integate two lage-scale simulation models, the MIT USREP model (Rausch et al., 2010) and NRE s ReEDS model (Shot et al., 2011) to study distibutional and efficiency impacts of clean and enewable enegy standads fo electicity in the United States. Though this method povides a compehensive and consistent modeling famewok, it equies both top-down and bottom-up sub-models that have been well established and calibated to a consistent benchmak point, which is highly demanding fo most modeling cases. Anothe appoach involves diect epesentation of bottom-up technological infomation within a geneal equilibium famewok descibed by Böhinge and Ruthefod (2008). As poposed by Kiuila and Ruthefod (2013), eithe a smooth cuve (taditional appoach, applied by Jogenson et al. (2008), Mois et al. (2010), Boetes and Bollen (2012), Spingmann (2014)) o a eontief technology (hybid appoach, applied by Koopmans and Velde (2001), Fei et al. (2003), Jacoby et al. (2006), aitne and Hanson (2006), Sue Wing (2008)) can be applied to integate of bottom-up abatement costs with top-down models 1. By implementing both appoaches to epesent a bottom-up cost cuve developed in the McKinsey epot (McKinsey epot, 2009) within a top-down static model (Imhof and Ruthefod, 2010) to study the climate policy in Switzeland, Kiuila and Ruthefod (2013) compae the esults of these two appoaches fo the fist time 2. They found both appoaches povide vitually the same esults when the calibation pocess is pecisely executed. In this pape, we fist show that the hybid appoach can moe flexibly handle the nea-flat o nea-vetical sections of the esouce supply cuve that tanslate into key featues of the maginal cost of esouce supply. By demonstating a many-step supply cuve fo China s onshoe wind based on detailed wind esouce data (Zhang et al., 2014a) that can be integated into a ecusive dynamic top-down model, this pape then shows how a complex cost cuve fo abatement o esouce-dependent poduction can be embedded diectly o appoximately using a step fitting method within a CGE model. It futhe demonstates the impotance of this technique fo analysis of technology-specific policy that depends on detailed epesentation of the undelying technology. 1 The taditional appoach is moe commonly used because constant-etun-to-scale (CRTS) functions, e.g. constantelasticity-of-substitution (CES) functions, ae widely employed functional foms in top-down enegy-economic models fo envionmental and climate policy assessment. 2 The McKinsey cuve used by Kiuila and Ruthefod (2013) only has 8 steps. Moeove, the taditional appoach in thei pape will not be ealistic when the policy is vey stingent, because all the abatement technology options should be exhausted and a vey high abatement cost should be given when the hybid appoach is applied, but the taditional appoach in thei case will give stable abatement cost even unde vey high abatement equiement due to its concave shape as calibated. 3

6 3. A STYIZED GENERA EQUIIBRIUM MODE 3.1 Hybid Appoach We stat ou analysis by epesenting a heteogeneous esouce using the hybid appoach in a stylized two-secto (esouce-dependent good Y, fo example, electicity, and othe goods and sevices V ), single-egion geneal equilibium model 3. A backstop electicity technology BY, in this case wind, is distinguished fom othe fossil-based electicity geneation in the benchmak. The stylized epesentation of the closed economy is displayed in Table 1. Table 1. Illustative benchmak social accounting matix (SAM) fo a closed economy. Fossil (FY) Y V W CONS Wind (BY) P Y P V P W P P K P F P E P S Note: P Y electicity secto; P V othe goods and sevices; P W composite consumption good; P labo; P K capital; P F fossil fuel; P E emissions allowance; P S0 wind esouce that entes the geneation mix in the benchmak. We design a supply cuve fo wind electicity geneation using a simple thee-step cuve with a lage step fo this stylized model. This design illustates the potential loss of fidelity that can esult fom the epesentation in such a simple cuve fom. The static cuve (assuming all the pices of vaiable inputs emain unchanged) is shown as below (see Figue 1). We assume wind electicity is a pefect substitute fo fossil-based electicity, and the pice of wind electicity theefoe is equal to the electicity pice. The height and width of each step in the piecewise cuve eflect the gade and potential, espectively, of diffeent wind esouces. Fo example, point (2, 1.04) and (5, 1.04) in Figue 1 mean that the static supply of wind is five times the benchmak wind electicity poduction when the electicity pice is 1.04 times of the benchmak electicity pice holding all the input pices unchanged, and the potential of this gade of wind esouce is thee times the benchmak wind electicity poduction. The basic model stuctue is simila to the static model discussed in Böhinge and Ruthefod (2008), but hee we assume the electicity poduce using fossil fuel beas a significant shae of cost fo emissions allowances. This paamete setting can lead to a lage incease in the electicity pice when the emissions cap constaint becomes moe stingent in ou policy 3 The souce code of this stylized model can be downloaded fom 4

7 P Y BY Figue 1. Supply cuve of wind electicity geneation assuming all the pices of vaiable inputs unchanged (BY supply of wind electicity geneation elative to the benchmak; P Y electicity pice elative to the benchmak). simulations, which will allow moe backstop wind poduction to ente the geneation mix. The model is stuctued in a MCP fomat, and decision vaiables ae denoted as follows. Activity levels: Y is the poduction of electicity, FY is the poduction of electicity based on fossil fuel, BY is the poduction of electicity based on backstop technology (wind), V is the poduction of othe goods and sevices, and W is the composite consumption (utility). Maket pices 4 : P Y P V P W P P K P F P E PS 0 PS 1, PS 2, and PS 3 is the pice of electicity, is the pice of othe goods and sevices, is the pice of composite consumption (utility), is the pice of labo, is the pice of capital, is the pice of fossil fuel, is the pice of emissions allowance is the pice of the esouce facto used in the benchmak wind poduction, and ae pices of the othe thee esouce factos epesented by the thee steps. 4 All the pices ae calibated to 1 o 0 in the benchmak. 5

8 Income levels: M is the income of the epesentative household. The unit-pofit function of V is 5 : Π V = P V P θv P 1 θv K (1) whee θ V is the cost shae of labo in poduction of V. The unit-pofit function of FY is: whee Π FY = P Y { θ FY K ( P θ FY P 1 θfy K ) 1 σ FY F + ( ) ( 1 θk FY θf FY P F + θ FY E P ) 1 σfy F E } 1 1 σ FY F (2) θ FY θ FY θf FY K is the cost shae of the value-added composite in poduction of FY, is the cost shae of labo within the value-added composite in poduction of FY, is the cost shae of fossil fuel within the total cost of fossil fuel and emissions allowances in poduction of FY, is the cost shae of emissions allowances within the total cost of fossil fuel and emissions allowances in poduction of FY, is the elasticity of substitution between the value-added composite and fossil fuel in poduction of FY. θ FY E σ FY F The wind electicity geneation is epesented using the hybid appoach suggested by Kiuila and Ruthefod (2013). Wind electicity geneation technology using capital, labo and diffeent gades of esouces (i.e. diffeent classes of wind) is able to poduce a good that is identical to the output of fossil-based electicity technology. In ou example, we distinguish fou gades of wind esouces by diffeent fixed esouce factos. The pice of the esouce facto used in the benchmak wind poduction is PS 0, and pices of the othe thee epesented by the thee steps ae PS 1, PS 2, and PS 3 espectively. The unit-pofit function of the benchmak wind poduction BY 0 and backstop poductions BY i (i = 1, 2, 3) ae: Π BY 0 = P Y { ( θ BY 0 K P θby 0 ) P 1 θby 0 K + ( } ) 1 θ BY 0 K PS0 (3) 5 The pice with a tilde epesents the elative pice to the benchmak pice. 6

9 { ( Π BY i = P Y µ BY i K espectively, whee P θby i ) } P 1 θby i K + α BY i PS i (4) θ BY 0 K is the cost shae of the value-added composite in poduction of BY 0, θ BY 0 is the cost shae of labo within the value-added composite in poduction of BY 0, θ BY i is the cost shae of labo within the value-added composite in poduction of BY i, µ BY i K is the mak-up paamete fo the cost of poduction of BY i 6, and α BY i is the quantity of fixed esouce facto used in one unit poduction of BY i. In this model, we apply the simplification that the utility good W is identical to the final consumption demand, which can be chaacteized by a composite good of V and Y. The unit-pofit function of W is: whee Π W = P W { θ W V P 1 σw V V + ( 1 θ W V ) P 1 σ W V Y } 1 1 σ W V (5) θv W σv W is the shae of othe goods and sevices V in the final demand, and is the compensated elasticity of substitution between othe goods and sevices V and electicity Y in the final demand. Zeo-pofit conditions that detemine the activity levels of all the above poduction and consumption ae as follows: Π V 0 V 0 (6) Π FY 0 FY 0 (7) Π BY 0 BY 0 (8) Π W 0 W 0. (9) A epesentative household in ou stylized model is endowed with labo, capital, fossil fuel, emissions allowances, and diffeent gades of esouces fo wind electicity poduction. The total 7

10 income of the epesentative household is given as follows: M = P + P K K + P F F + P E E + P S0 S 0 + i P Si S i (10) whee is the aggegate labo endowment, K is the aggegate capital endowment, F is the aggegate fossil fuel endowment, E is the total initial emissions allowances, S 0 is the endowment of wind esouce used in the benchmak wind poduction BS 0, and S i is the endowment of wind esouce used in the backstop wind poduction BS i. Maket cleaance conditions that detemine all the pices ae detemined as follows: V P V + FY P FY + BY 0 P BY 0 + i K V P K V + FY P K FY + BY 0 P K BY 0 + i BY i P BY i P 0 (11) BY i P K BY i P K 0 (12) F FY P F FY P F 0 (13) E FY P E FY P E 0 (14) S 0 BY 0 PS 0 BY 0 PS 0 0 (15) S i BY i PS i BY i PS i 0, i = 1, 2, 3 (16) V W P V W P V 0 (17) FY + BY 0 + i BY i W P Y W P Y 0 (18) W M P W P W 0. (19) We fist show that ou modeling famewok using the hybid appoach can illustate the wind 8

11 Figue 2. Cyclical incease and stagnation of wind installation ( BY, ight vetical axis), electicity pice and emissions allowance pice ( P Y and P E, left vetical axis) with naowing emissions cap (hoizontal axis: atio of emissions cap to the benchmak emissions). ush phenomenon, which usually cannot be epesented in the taditional top-down model as the supply cuve is smooth. Wind ush hee efes to the cyclical apid incease of wind poduction tiggeed by subtle changes of policy stingency. Hee we un 100 policy scenaios and gadually lowe the emissions cap fom 100% to 50% of the benchmak emissions. When simulated, the electicity pice inceases as a function of the inceasing emissions allowance pice, and diffeent classes of wind become economic in tandem, as shown in Figue 2. The wind poduction inceases apidly (within a vey small ange of emissions cap change) until it eaches the potential limit of this level of esouce. Meanwhile, the pice of emissions allowances as well as the electicity pice emains almost constant as the supply of wind inceases without incuing moe than a tivial cost incease, esulting in a decease in the supply of fossil-based electicity. When this level of wind esouce is exhausted, the pice of electicity and emissions allowances stat to ise again while the wind installation stagnates, until the next level of wind esouce becomes economic. The ush and silence cycles ae displayed in Figue 2. The cost of wind electicity geneation emains almost unchanged duing the ush phase because the pices of labo and capital ae elatively stable and the pice of anothe input a cetain gade of wind esouce fo the cuent ush phase is zeo as this gade of esouce is ovesupplied as it is exhausted. The evolution of backstop wind esouce pices is shown in Figue 3. 9

12 PS 1 PS 2 PS 3 Figue 3. Evolution of backstop wind esouce pices of thee gades of wind esouces (PS1, PS2 and PS3, vetical axis) with naowing emissions cap (hoizontal axis: atio of emissions cap to the benchmak emissions). 3.2 Compaison with the Taditional Appoach We then compae simulated supply cuves deived by the taditional appoach using diffeent smooth fitting methods. This taditional appoach is widely applied by the CGE modeles as it uses a standad CES function fom to fit the oiginal piecewise supply cuve. We fist build on the discussion in Boetes and Bollen (2012) to show how a one-level CES poduction function with a fixed facto in calibated shae fom suggested by Ruthefod (2008) can be used fo fitting. In the cost function below, Y denotes the output (enegy); R and V denote natual esouce and aggegate of vaiable inputs, espectively. p Y = ( θ R p 1 σ R ) + (1 θ R ) p 1 σ 1 1 σ (20) V whee θ R is the value shae of the natual esouce, and σ is the elasticity of substitution. As the natual esouce is fixed at its initial value (R 1), and the vaiable factos ae assumed to have stable pices ( p V 1), we can solve fo output 7 : Ỹ = [ 1 (1 θr ) p σ 1 ] σ 1 σ Y. (21) θ R 7 This epoduces the calculation of equation #5 in Boetes and Bollen (2012), except that in Boetes and Bollen the denominato θ R inside the squae backet is not included. 10

13 Thus the elasticity of supply is: η s = σ 1 s R s R (22) whee s R is the vaiable value shae of the natual souce: s R = 1 (1 θ R ) p 1 σ Y. (23) One staight-fowad fitting method hee we call it the naïve smooth fitting method assumes s R θ R, so σ can be diectly calculated using Equation (22) and η s estimated by the odinay least-squaes fitting fo the supply cuve shown in Figue 1 8 as follows. log Y = α + η s log P Y + ɛ (24) whee α is the estimated intecept, and ɛ is an eo tem. A moe pecise fitting is to use Equation (21) diectly as the functional fom when pefoming least-squaes fitting. Hee both of θ R and σ ae fee vaiables. We call this fitting method local smooth as it still uses the local pat of oiginal supply cuve as the above naïve fitting method. Howeve, use of the whole oiginal supply cuve fo fitting is also possible. Fo the one-level CES poduction function with a fixed facto in calibated shae fom, Boetes and Bollen (2012) shows that thee is an uppe bound fo the output pice if σ > 1: p max Y = (1 θ R ) 1 1 σ. (25) Unde this condition, output can be poduced with the vaiable facto alone and has no limit, which is not ealistic fo the enegy poduction that elies on natual esouces. In fact, output usually has an uppe limit simila to the oiginal supply cuve we design, which implies σ < 1. The maximum supply can be deived fom Equation (21) by setting p Y to infinity: Ỹ max = θ σ σ 1 R. (26) By applying the maximum supply constaint by Equation (26), we can again use Equation (21) as the functional fom fo the least-squaes fitting. Howeve, hee only θ R o σ is the fee vaiable. We call this fitting method full-ange smooth as it uses the supply infomation when the pice goes to infinity 9. 8 In the vetical diection, the supply cuve extends to the infinity. Howeve, we have to tuncate the cuve and use pat of it when the least-squaes fitting is applied. Since we have no ex-ante infomation about how high the electicity pice ( P Y ) will each elative to the benchmak level, hee we choose P Y = 1.2 as the highest bound (coveing all the thee hoizontal steps and a significant pat of the last vetical line) fo ou tuncation. 9 The souce code of local smooth and full-ange smooth fitting methods can be downloaded fom enegyda.com/cge.html. 11

14 The θ R and σ values estimated by the above thee smooth fitting methods ae shown in Table 2. Table 2. θ R and σ values estimated by thee smooth fitting methods. θ R σ Smooth fitting naïve (SMTN) Smooth fitting local (SMT) Smooth fitting full-ange (SMTF) Note: θ R appoaches zeo in SMTF, theefoe, we set a lowe bound at a vey small level (1E-5) fo θ R and un the estimation. To epesent the wind electicity geneation by the CES function using the calibated θ R and σ as above, we eplace Equation (3) and (4) by the following equation: whee Π BY = P Y { (1 θ BY R ) ( P θ BY P 1 θby K ) 1 σ BY + θ BY R } 1 1 σ 1 σby P BY S 0 (27) θ BY R θ BY σ BY is the cost shae of esouce in poduction of BY, which is equal to the calibated value θ R in Table 2 fo each smooth fitting method, is the cost shae of labo within the value-added composite in poduction of BY, and is the elasticity of substitution between the value-added composite and esouce in poduction of BY, which is equal to the calibated value σ in Table 2 fo each smooth fitting method. We then un the same 100 policy scenaios to get the simulated supply cuve fo each smooth fitting method. All the simulated supply cuves togethe with the cuve geneated using the hybid appoach (epesented by STP) ae compaed in Figue 4. We find that the cuve using the naïve fitting method has a diffeent concave shape fom all the othes, which implies that this widely-used method can lead to potentially significant eos. The local and global fitting methods both geneate cuves with convex shape, but the cuve by the full-ange fitting method is systematically deviated to the left to the STP cuve, because it is appoaching the last vetical pat of the piecewise cuve at infinity. The local fitting method exhibits much highe accuacy NUMERICA EXAMPE OF ONSHORE WIND DEPOYMENT IN CHINA In this section, we apply the hybid appoach in a eal wold example by integating an estimated multi-step onshoe wind supply cuve fo China into a ecusive dynamic multi-secto open-economy CGE model. Supplies of onshoe wind in China ae estimated in each peiod unde an inceasingly stingent emissions contol policy. We show how a step-fitting method can be applied to educe the complexity of the oiginal piecewise supply cuve without significantly compomising fidelity. Futhemoe, we design additional feed-in-taiff scenaios to incentivize 10 Howeve, the full-ange fitting method may outpefom the local fitting one if a vey stingent policy can significantly incease the electicity pice, which will lead the cuve by local fitting method give unealistic highe supply. 12

15 Figue 4. Compaison of the simulated supply cuve by the hybid appoach and all the cuves by diffeent smooth fitting methods. moe wind deployment and estimate the coesponding total subsidy equied. Ou esults also show that the hybid appoach outweighs the taditional appoach when epesenting enewable esouce infomation with high fidelity, peseving the installed capacity infomation and capacity to apply flexible FIT policies in top-down models. 4.1 Model Data We apply a global enegy-economic data set based on the GTAP 8 data base (GTAP, 2012), which povides consistent global accounts of poduction, consumption and bilateal tade as well as consistent accounts of physical enegy flows, enegy pices and emissions in the yea 2007 (GTAP, 2012). We futhe aggegate 129 counties in the GTAP data base to two egions (China and est of the wold) and 57 commodities to 10 poduction sectos (Agicultue, Coal, Cude oil, Natual gas, Electicity, Enegy intensive industies, Manufactuing and othe seconday industies, Tanspotation, and Othe sevice industies, see Table A1). We integate into the CGE model an onshoe wind supply cuve fo China descibed in Zhang et al. (2014a). This onshoe supply cuve is deived based on NASA s MERRA (Moden-Ea Retospective analysis fo Reseach and Applications) data set (Rienecke et al., 2011). We tuncate this cuve to a 306-step piecewise cuve which coves the geneation cost ange fom the lowest cost (0.32 yuan/kwh) to 0.80 yuan/kwh, as we believe China s feed-in-taiff will not 13

16 exceed 0.80 yuan/kwh (2007 pice) even unde vey stingent policy 11. The supply cuve is then shifted upwad afte accounting fo a constant tansmission and distibution cost (0.26 yuan/kwh) estimated fom the diffeence between GTAP 8 s electicity taiff fo China (0.61 yuan/kwh) and China s aveage geneation taiff fo coal-based powe in 2007 (0.35 yuan/kwh) Static Model The static model famewok and paamete settings ae simila to the CGE model descibed in Zhang et al. (2013) except the teatment of tade, which is simplified as we only include two intenational egions hee. The supply cuve fo electicity geneated fom onshoe wind is assumed to be a pefect substitute fo fossil-based electicity and integated into the model by the hybid appoach. Detailed fomulations of the model can be found in the online appendix The Dynamic Extension of the Model We extend the model fom 2007 to 2029 by updating the facto supply evey two yeas. Fo simplicity, we assume a unifom gowth ate fo all the factos (labo, capital and othe sectoal-specific esouces) in each time peiod. Annual gowth ates of factos fo China and est of the wold in each peiod ae calibated to match expected GDP gowth ates (gadually deceasing fom about 10% in 2007 to 4.5% in 2030 fo China). A 1%/yea impovement in economy-wide enegy efficiency, consistent with othe models (Sue Wing and Eckaus, 2007), is assumed hee. In ou policy simulation, we assume that a cabon pice is levied fom 2009 to 2029 to achieve the emissions eduction path consistent with the Acceleated Effot scenaio descibed in (Zhang et al., 2014b), which is consistent with the tagets poposed in U.S.-China Joint Announcement on Climate Change in late The geneation and installed capacity of onshoe wind ae obseved in each time peiod. In addition to a cabon tax, we develop two feed-in taiff scenaios to achieve onshoe wind deployment tagets. The tagets ae set to be 60 GW fo 2011, 80 GW fo 2013, 100 GW fo 2015 (consistent with the 12th FYP taget) and additional 40 GW fo evey two yeas afte 2015 until 2029 (consistent with the estimated pace of wind deployment; see Zhang et al. (2014a)). The subsidy budget fo FIT is financed by a tax levied on electicity consumption, and the tax level is endogenously detemined in the model to maintain evenue neutality. A unifom FIT is implemented in the model using the SMT and STP methods, and a diffeentiated FIT to achieve the tagets with minimal size of subsidy taget (the FIT level fo each gade of wind is endogenously detemined in the model to squeeze the wind esouce ent to zeo) is implemented in the model using STP as this scenaio can only be implemented with the step-cuve. 11 This is veified in ou policy simulation. The tuncation is actually tivial fo the hybid appoach as the tail of the cuve neve entes poduction and stays edundant. Fo the taditional appoach, howeve, the tuncation is essential fo the accuacy of fitting. The own-pice elasticity of supply will diffe significantly if the cuve is tuncated. 12 The online appendix can be found at 14

17 Stat fitting (m=1) Minimizing the esidual with m points m=m+1 Residual < Toleance? No End Yes Figue 5. Pocess chat of the step-fitting method. 4.2 Step-fitting Method Although the 306-step (let N = 306) piecewise onshoe wind supply cuve in ou example is acceptable in tems of computational complexity, hee we illustate how a step-fitting method could futhe simplify the epesentation of the cuve by using a cuve with many fewe steps that is well fitted to the oiginal one within a given toleance 13. The pocess of the step-fitting method can be summaized in Figue 5. Since a m-step piecewise cuve used to fit the oiginal N-step cuve can be detemined by m points (the ight endpoint of each step), we can find the best-fit m-step cuve by optimizing locations of m points to minimize the aea between the fitted cuve and oiginal cuve. The aea is defined as Residual hee. The optimization poblem can be futhe simplified by finding the vetical coodinates of m points because the hoizontal coodinates ae endogenously detemined. The optimization poblem is shown as follows: min {optinem} Residual = n (onshoecuve n,gen onshoecuve n 1,Gen ) (onshoecuve n,p optine agminm optine m onshoecuve n,p ) s.t. onshoecuve 1,P optine m onshoecuve N,P whee optine m epesents the vetical coodinate of the m th point of the fitted cuve, onshoecuve n,gen is the hoizontal coodinate of the ight endpoint of the oiginal cuve s n th step, and onshoecuve n,p is the vetical coodinate of the ight endpoint of the oiginal cuve s n th step. We can choose a toleance of esidual epesenting the equied goodness of fit, fo example, 1% of the aea of the ectangle taken by the oiginal cuve. Theefoe, Residual should satisfy 13 The souce code of this step-fitting method can be downloaded fom 15

18 Pice (yuan/kwh) Geneation (PWh) Oiginal Cuve Fitted Cuve Figue 6. Oiginal and fitted onshoe wind supply cuve fo China. the following condition: Residual < 0.01 (onshoecuve n,gen onshoecuve 1,Gen ) (onshoecuve n,p onshoecuve 1,P ). If Residual is not smalle than the toleance, we stat a new optimization poblem by intoducing one additional fee point fo the fitted cuve. The optimized locations of points in the last iteation ae inheited in the new optimization as stating points, and the location of the newly intoduced point can be andomly selected. The iteation of optimization stops when Residual is smalle than the toleance. The fitted function is chosen in ode to achieve a 1% level of toleance, and an 41-step cuve is geneated using this optimization outine as shown in Figue 6. Simila to the stylized model, we also epesent the onshoe wind supply cuve using the thee smooth fitting methods that we descibed in Section 2. The θ R and σ values estimated by the above thee smooth fitting methods ae shown in Table 3. Table 3. θ R and σ values estimated by thee smooth fitting methods. θ R σ Smooth fitting naïve (SMTN) Smooth fitting local (SMT) Smooth fitting full-ange (SMTF)

19 Figue 7. Geneation of onshoe wind fo China in each time peiod. 4.3 Results The geneation of onshoe wind fo China in each time peiod without feed-in taiff unde the countefactual cabon-pice only scenaio is shown in Figue 7. We find that the geneation will gadually incease to about 0.12 PWh, oughly 40 GW. The esults ae obust if we use the fitted cuve instead of the oiginal cuve with about 30% savings in computation time with an Intel i7-2.80ghz CPU. Again, the cuve estimated using the taditional appoach deviates fom oiginal and fitted cuves geneated with the hybid appoach. Of the smooth fitted cuves, the local smooth fitting (SMT) has the least deviation, while the full-ange smooth fitting (SMTF) and naïve smooth fitting (SMTN) methods geneate significantly devegent esults. Moeove, all the smooth fitting methods cannot cedibly epesent installed capacity as the capacity facto of electicity poduction cannot be obtained fo the equilibium solution in futue yeas fa fom the benchmak. We implement two FIT scenaios to achieve an exogenous path of wind geneation tagets. The geneation taget path is tanslated fom a capacity taget path stating fom about 60 GW in 2011, inceasing 20 GW evey two yeas befoe 2019 and evey 40 GW afte The capacity taget path is compaable to China s midium-to-long tem wind development taget. An endogenous subsidy is implemented to suppot wind geneation taget achievement, and an endogenous tax on the electicity use is levied to fund the subsidy budget. Fo a unifom FIT design, a unifom subsidy ate is implemented fo all the gades of wind esouce and it can be simulated using both the smooth cuve (STM) and the step cuve (STP). Fo a diffeentiated FIT design, which can only be implemented by step cuves because they distinguish diffeent gades 17

20 Figue 8. Subsidy budget to achieve China s wind deployment tagets. of esouce, diffeentiated subsidy ates that foce the esouce ent of all gades of wind esouce to zeo ae endogenously detemined in ode to find a minimum subsidy budget. The size of the subsidy budget is epoted in the two FIT scenaios shown in Figue 8. Unde a unifom FIT design, about 27.6 billion 2007$ is equied estimated by STP and SMT in If a diffeentiated FIT is applied, less than the half of the oiginal subsidy budget, about 11.8 billion 2007$, is equied to achieve the same taget. We also obseve that the welfae loss compaed to the BAU scenaio is 0.4% (in elative tems) smalle in the diffeentiated FIT scenaio than the unifom FIT scenaio, due to the lowe policy cost. In both of the FIT scenaios, we also obseve that coal consumption inceases by 0.4% (about 15 million tce) compaed to cabon-pice only scenaios. This occus because the cabon pice (which penalizes coal most) falls unde the FIT scenaios as moe enewables educe the stingency of the emissions cap. This esult is also consistent with the geen pomotes the ditiest phenomenon descibed by Böhinge and Rosendahl (2010). 5. CONCUSION In this pape, we develop a hybid method to incopoate technologies that equie heteogeneous esouces as inputs into top-down economic model that is both efficient and flexible. We show how the hybid model can epesent a wind ush phenomenon: as cabon policy stingency inceases slightly, the piecewise shape of the supply cuve dictates that lage quantities of wind capacity will be deployed upon eaching theshold electicity pices almost without aising the CO 2 and enegy pice. This effect, togethe with complex cyclical pice evolution, is typically not captued by taditional top-down models, which ely on smooth cuve 18

21 fits fo esouce epesentation. We futhe show that the supply cuves deived fom policy simulations by the taditional appoach (with diffeent smooth fitting methods) can deviate fom the eal supply cuve obtained via the hybid appoach significantly, especially fo the fitting method that is widely adopted. If the taditional appoach has to be applied, the local smooth fitting method that we intoduce in this pape exhibits the best pefomance (unde the condition that the pice changes in the simulation do not exceed the ange fo local smooth fitting vey much), especially in the welfae analysis. Finally, we demonstate how a piecewise supply cuve based on detailed wind esouce data can be integated into a top-down model that includes heteogeneous esouce pices and multiple sectos focusing on China s onshoe wind electicity as an example. The esults suggest that a diffeentiated FIT design that can only be modeled with the hybid appoach equies less than the half of the subsidy budget and is moe cost-effective compaed to a unifom FIT design. This has impotant policy implications as many counties ae setting moe ambitious tagets fo enewable and othe unconventional foms of enegy, which is poduced by using natual esouces of heteogeneous quality as inputs, and the efficiency of the subsidy budget is of geat concen. The hybid appoach also has the advantage that it peseves the inheent physical coespondence between installed capacity and electicity geneation infomation. Moeove, it can be implemented by applying a flexible and computionally inexpensive fitting method. This hybid appoach has many applications, and can be used to epesent esouce availability in enegy-economy equiliium top-down models in cases whee quality-diffeentiated esouce infomation is available. Extensions could captue impotant dynamics in the deployment of sola o othe low cabon pimay enegy altenatives, as well as scale up of pollution contol technologies and pocesses. These assessments could alet policymakes to potential bottlenecks that may aise when pice signals pompt apid deployment of tageted technologies o in cases whee the featues of the supply cuve ae not amenable to fitting with a smooth functional fom. Acknowledgements This wok was suppoted by Eni S.p.A., ICF Intenational, the Fench Development Agency (AFD), and Shell, founding sponsos of the MIT-Tsinghua China Enegy and Climate Poject. We ae futhe thankful fo suppot povided by the MIT Joint Pogam on the Science and Policy of Global Change though a consotium of industial sponsos and U.S. fedeal gants. In paticula, this wok was suppoted by the DOE Integated Assessment Gant (DE-FG02-94ER61937). 19

22 6. REFERENCES Boetes, S. and J. Bollen, 2012: Fossil Fuel Supply, eakage and the Effectiveness of Bode Measues in Climate Policy. Enegy Economics, 34: S181 S189. Böhinge, C. and K. E. Rosendahl, 2010: Geen pomotes the ditiest: on the inteaction between black and geen quotas in enegy makets. Joounal of Regulatoy Economics, 37: Böhinge, C. and T. F. Ruthefod, 2008: Combining bottom-up and top-down. Enegy Economics, 30: Böhinge, C. and T. F. Ruthefod, 2009: Integated assessment of enegy policies: Decomposing top-down and bottom-up. Jounal of Economic Dynamics and Contol, 33: Böhinge, C., T. F. Ruthefod, E. J. Balistei and J. Weyant, 2012: Intoduction to the EMF 29 special issue on the ole of bode cabon adjustment in unilateal climate policy. Enegy Economics, 34: S95 S96. Caon, J., S. Rausch and N. Wincheste, 2015: eakage fom sub-national climate policy: The case of Califonia. The Enegy Jounal, 36: fothcoming. Chen, Y.-H., S. Paltsev, J. Reilly, J. Mois and M. Babike, 2015: The MIT EPPA6 Model: Economic Gowth, Enegy Use, and Food Consumption. MIT Joint Pogam on the Science and Policy of Global Change Repot 278. Dikse, S. P. and M. C. Feis, 1995: The PATH Solve: a non-monontone stabilization scheme fo mixed complementaity poblems. Optimization Methods and Softwae, 5: Fei, C., P. Haldi and G. Salos, 2003: Dynamic fomulation of a top-down and bottom-up meging enegy policy model. Enegy Policy, 31: GTAP, 2012: Global Tade, Assistance, and Poduction: The GTAP 8 data base. Cente fo Global Tade Analysis, Pudue Univesity. Hemeling, C., A. öschel and T. Mennel, 2013: A new obustness analysis fo climate policy evaluations: A CGE Application fo the EU 2020 Tagets. Enegy Policy, 55: Imhof, J. and T. Ruthefod, 2010: Cabon Taxes in Switzeland: Of Fuel Exemptions and Revenue Recycling. mimeo. Swiss Fedeal Institute of Technology Zuich. Jacoby, H., J. Reilly, J. McFaland and S. Paltsev, 2006: Technology and technical change in the MIT EPPA model. Enegy Economics, 28: Jogenson, D., R. Goettle, P. Wilcoxen and M. Ho, 2008: The economic costs of a maketbased climate policy. White Pape. Pew Cente on Global Climate Change. Kiuila, O. and T. F. Ruthefod, 2013: The cost of educing CO 2 emissions: Integating abatement technologies into economic modeling. Ecological Economics, 87: Koopmans, C. and D. Velde, 2001: Bidging the enegy efficiency gap: Using bottom-up infomation in a top-down enegy demand model. Enegy Economics, 23: aitne, S. and D. Hanson, 2006: Modeling detailed enegy-efficiency technologies and technology policies within a CGE famewok. Enegy Jounal, 27: Mathiesen,., 1985: Computation of economic equilibia by a sequence of linea complementaity poblems. Mathematical Pogamming Study, 23:

23 McKinsey epot, 2009: Swiss geenhouse gas abatement cost cuve. Technical Repot. McKinsey & Company, Zuich. Mois, J. F., J. Reilly and S. Paltsev, 2010: Combining a Renewable Potfolio Standad with a Cap-and-Tade Policy: A Geneal Equilibium Analysis. MIT Joint Pogam on the Science and Policy of Global Change Repot 187. O Neill, B. C., M. Dalton, R. Fuchs,. Jiang, S. Pachaui and K. Zigova, 2010: Global demogaphic tends and futue cabon emissions. Poceedings of the National Academy of Sciences, 107: Paltsev, S., J. Reilly, H. Jacoby, R. Eckaus, J. McFaland, M. Saofim, M. Asadooian and M. Babike, 2005: The MIT Emissions Pediction and Policy Analysis (EPPA) Model: Vesion 4. MIT Joint Pogam on the Science and Policy of Global Change Repot 125. Rausch, S. and M. Mowes, 2014: Distibutional and efficiency impacts of clean and enewable enegy standads fo electicity. Resouce and Enegy Economics, 36: Rausch, S., G. E. Metcalf, J. M. Reilly and S. Paltsev, 2010: Distibutional implications of altenative U.S. geenhouse gas contolmeasues. The B.E. Jounal of Economic Analysis and Policy, 10: Symposium. Rienecke, M. M., M. J. Suaez, R. Gelao and et al, 2011: MERRA: NASA s moden-ea etospective analysis fo eseach and applications. Jounal of Climate, 24: Ruthefod, T. F., 1995: Extension of GAMS fo complementaity poblems aising in applied economics. Jounal of Economic Dynamics and Contol, 19(8): Ruthefod, T. F., 1999: Applied geneal equilibium modeling with MPSGE as a GAMS subsystem: an oveview of the modeling famewok and syntax. Computational Economics, 14: Ruthefod, T. F., 2008: Calibated CES Utility Functions: A Woked Example. Mimeo, ETH Züich. Shot, W., P. Sullivan, T. Mai, M. Mowes, C. Uiate, N. Blai, D. Heimille and A. Matinez, 2011: Regional enegy deployment system (ReEDS). National Reneweable Enegy aboatoy. Technical Repot NRE TP-6A Spingmann, M., 2014: Integating emissions tansfes into policy-making. Natue Climate Change, 4: Sue Wing, I., 2008: The synthesis of bottom-up and top-down appoaches to climate policy modeling: Electic powe technology detail in a social accounting famewok. Enegy Economics, 30: Sue Wing, I. and R. S. Eckaus, 2007: The implications of the histoical decline in US enegy intensity fo long-un CO 2 emission pojections. Enegy Policy, 35: Zhang, D., S. Rausch, V. Kaplus and Z. Xiliang, 2013: Quantifying egional economic impacts of CO 2 intensity tagets in China. Enegy Economics, 40:

24 Zhang, D., M. Davidson, B. Guntuu, X. Zhang and V. Kaplus, 2014a: An integated assessment of China s wind enegy potential. MIT Joint Pogam on the Science and Policy of Global Change Repot 261. Zhang, X., V. Kaplus, T. Qi, D. Zhang and J. He, 2014b: Cabon Emissions in China: How Fa Can New Effots Bend the Cuve? MIT Joint Pogam on the Science and Policy of Global Change Repot

25 Online Appendix Ou algebaic model identifies thee categoies of conditions fo a geneal equilibium using a system of inequalities: (i) zeo-pofit conditions fo all the poduction, (ii) maket cleaance conditions fo all goods and factos and (iii) income balance conditions fo all agents. The fist class of conditions detemine a vecto of activity levels, the second detemines pices and the thid detemines incomes. The model equilibium is fomulated as as a mixed complementaity poblem (MCP) (Mathiesen, 1985; Ruthefod, 1995) using the Geneal Algebaic Modeling System (GAMS) and the Mathematical Pogamming System fo Geneal Equilibium (MPSGE) (Ruthefod, 1999). The PATH solve (Dikse and Feis, 1995) is used to solve fo non-negative pices and quantities. We state the algebaic exposition of equilibium conditions below. In the zeo-pofit conditions, Π Z g denotes the unit pofit function fo the poduction/supply of good g in egion whee Z is the associated activity. The patial deivative of the unit pofit function with espect to input and output pices povides compensated demand and supply coefficients used in maket cleaance conditions. We use g as an index fo all sectos plus a pivate consumption composite, a public good composite and an investment good composite. The index PE epesents the subset of pimay fossil enegy good (coal, cude oil and gas), E epesents the subset of final fossil enegy good (coal, efined oil, gas and electicity), and FE epesents the subset of final fossil enegy good except fo electicity EE. Wind epesents the electicity fom wind poduction, which is teated as a pefect substitute of fossil-based electicity. Fo simplicity, we suppess the time index hee. As customay in applied geneal equilibium analysis, we use the exogenous elasticities as the fee paametes of the functional foms that captue poduction technologies and consume pefeences. The elasticities in poduction and consumption CES functions ae adopted fom the MIT EPPA model (Paltsev et al., 2005) and the value of Amington elasticities ae adopted fom Caon et al. (2015). We ecognize that a obust execise would equie the empiical estimation of these elasticities in a stuctually simila famewok. Such an execise is out of the scope of the pesent study. Table A1 to Table A10 explain the notations fo vaiables and paametes employed within ou algebaic exposition. Figue A1 to Figue A4 povide gaphical epesentations of the function foms. 23

26 APPENDIX A: Algebaic Exposition of Equilibium Conditions Zeo pofit conditions 1. Poduction of agicultue goods (Y g g=agr ): Π Y g = P Y g(1 t Y g) ( θ va g P Y g (( θ g ( P (1 + t g) P g ) 1 σ va ( ( ( P R + (1 θg va ) θg R g (1 + t R g) i/ E P R g ( ) 1 σ ae + (1 θg) E θigp A ig A ) 0 Y g 0 2. Poduction of fossil fuels (Y g g PE ) Π Y g = P ( g(1 Y t Y g) P Y g ( + (1 θg) R i θ R g ( P K + (1 θg) (1 + t K ) g) ) 1 1 σ va 1 σ va ) 1 σ eva ) 1 σ e ( P R g (1 + t R g) P R g θ A igp A ig + θ va g P K g P K g + (1 θg) ( R (θgp E g E 1 σ ae 1 ) ) 1 1 σ ae 1 σ e ( θ g ) 1 σ f ( P (1 + t g) P g 1 σ e ) 1 σ eva ) 1 1 σ eva ) 1 σ va ( P K + (1 θg) (1 + t K ) g) 1 σ va) 1 σ 1 ) ) 1 va 1 σ f 1 σ f 0 Y g 0 3. Poduction of othe goods (Y g g / {AGR,PE} ): Π Y g = P ( g(1 Y t Y g) + θ eva g ( P Y g θ va g ( (θ g i/ E θ A igp A ig ( P (1 + t g) P K g P g ) 1 σ va ( P K + (1 θg) (1 + t K ) g) 1 σ va ) 1 σ 1 ) ) 1 ) va 1 σ eva + (1 θg va )Pg E 1 σ eva 1 σ eva 0 Y g 0 24