When Can Carbon Abatement Policies Increase Welfare? The Fundamental Role of Distorted Factor Markets

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1 When Can Carbon Abaemen Poliies Inrease Welfare? The undamenal Role of Disored aor Markes Ian W. H. Parry Roberon C. Williams III awrene H. Goulder Disussion Paper REV Revised June P Sree, W Washingon, DC Telephone ax Resoures for he uure. All righs reserved. o porion of his paper may be reprodued wihou permission of he auhors. Disussion papers are researh maerials irulaed by heir auhors for purposes of informaion and disussion. They have no undergone formal peer review or he ediorial reamen aorded R books and oher publiaions.

2 When Can Carbon Abaemen Poliies Inrease Welfare? The undamenal Role of Disored aor Markes Ian W. H. Parry, Roberon C. Williams III, and awrene H. Goulder Absra This paper employs analyial and numerial general equilibrium models o assess he effiieny impas of wo poliies o redue U.S. arbon emissions a revenue-neural arbon ax and a non-auioned arbon quoa aking ino aoun he ineraions beween hese poliies and pre-exising ax disorions in faor markes. We show ha ax ineraions signifianly raise he oss of boh poliies relaive o wha hey would be in a firs-bes seing. In addiion, we show ha hese ineraions pu he arbon quoa a a signifian effiieny disadvanage relaive o he arbon ax: for example, he oss of reduing emissions by 10 peren are more han hree imes as high under he arbon quoa as under he arbon ax. This disadvanage refles he inabiliy of he quoa poliy o generae revenue ha an be used o redue pre-exising disorionary axes. Indeed, seond-bes onsideraions an limi he poenial of a arbon quoa o generae overall effiieny gains. Under our enral values for parameers, a non-auioned arbon quoa (or se of grandfahered arbon emissions permis) anno inrease effiieny unless he marginal benefis from avoided fuure limae hange are a leas $17.8 per on of arbon abaemen. Mos esimaes of marginal environmenal benefis are below his level. Thus, our analysis suggess ha any arbon abaemen by way of a non-auioned quoa will redue effiieny. In onras, our analysis indiaes ha a revenue-neural arbon ax an be effiieny-improving so long as marginal environmenal benefis are posiive. Key Words: arbon ax, arbon quoa, pre-exising axes, welfare effes JE Classifiaion os.: 51, H23, D52 ii

3 Table of Conens I. Inroduion...1 II. The Analyial Model...4 A. Model Assumpions...4 B. Carbon Tax...6 C. Carbon Quoa...9 III. The umerial Model...10 A. Model Sruure...11 i. irm Behavior...11 ii. Household Behavior...12 iii. Governmen Poliy...13 iv. Equilibrium Condiions...13 B. Calibraion of he Model...13 C. Poliy Proposals and Carbon Damage Senarios...15 IV. umerial Resuls...16 A. Marginal Coss of Emissions Reduion...16 B. Average Coss of Emissions Reduion...17 C. Effiieny Impas under Seond-Bes Opimal Emissions Reduion...18 D. Effiieny Impas under he Pigouvian Rule...18 V. Sensiiviy Analysis...19 VI. Conlusions and Caveas...21 Appendix A: Analyial Derivaions...24 Appendix B: he umerial Model...27 Referenes...32 is of Tables and igures Table 1. Benhmark Daa for he umerial Model...15 Table 2. Marginal Abaemen Coss under Alernaive Parameer Values and Model Speifiaions...20 igure 1. Marginal Cos of Emissions Reduion...35 igure 2. Raio of Seond-Bes o irs-bes Coss...36 igure 3. e Welfare Gain from he Opimal evel of Regulaion...37 igure 4. e Welfare Gain Under he Pigouvian Rule...38 iii

4 WHE CA CARBO ABATEMET POICIES ICREASE WEARE? THE UDAMETA ROE O DISTORTED ACTOR MARKETS Ian W. H. Parry, Roberon C. Williams III, and awrene H. Goulder * I. ITRODUCTIO The prospe of global limae hange from he oninued amospheri aumulaion of arbon dioxide (CO 2 ) and oher greenhouse gases has promped analyss o onsider a number of poliy opions for miigaing emissions of CO 2. The issue has aained heighened imporane sine he signing of he Kyoo Proool in Deember 1997, when 160 naions resolved o redue emissions of CO 2 and oher greenhouse gases. This paper fouses on alernaive ways ha he U.S. migh ahieve signifian reduions in CO 2 emissions. The ruial poin of deparure from previous sudies of CO 2 abaemen poliies 1 is he presen paper's fous on onneions beween he effiieny impas of CO 2 abaemen poliies and pre-exising ax disorions. The moivaion for his fous sems from reen sudies of environmenal regulaion in a seond-bes seing. These papers have shown ha he oss of environmenal regulaions are higher in a world wih pre-exising faor marke disorions han hey would be in he absene of suh disorions. 2 The higher oss refle wo effes. irs, by raising he oss of produion in he affeed indusry, environmenal regulaions give rise o higher pries of oupu in ha indusry and hus a higher prie of onsumpion goods in general. This, in urn, implies a lower real wage and a reduion in labor supply. If here are pre-exising axes on labor, he reduion in labor supply has a firs-order ha is, non-inremenal effiieny os, whih has been ermed he ax-ineraion effe. Seond, under some environmenal poliies, anoher effe an parially offse he axineraion effe. Polluion axes and oher environmenal poliies ha raise revenue allow ha revenue o be reyled hrough us in he marginal raes of pre-exising disorionary * Ian W. H. Parry, Energy and aural Resoures Division, Resoures for he uure; Roberon C. Williams III, Sanford Universiy; awrene H. Goulder, Sanford Universiy, Resoures for he uure, and BER. Please address orrespondene o Dr. Ian Parry, Resoures for he uure, 1616 P Sree W, Washingon DC 20036; phone (202) ; fax (202) ; The auhors graefully aknowledge he helpful ommens and suggesions of Gary Beker, Dallas Burraw, Jenny ighar, wo referees and an assoiae edior. We also hank he aional Siene oundaion (gran number SBR ) for finanial suppor. 1 See for example ordhaus (1994) and Manne and Rihels (1992). 2 See for example Bovenberg and de Mooij (1994), Bovenberg and van der Ploeg (1994), Goulder (1995), Goulder e al. (1997), Parry (1995, 1997), and (in a somewha differen onex) Browning (1997). Earlier papers by Terkla (1984), ee and Misiolek (1986), and Ballard and Medema (1993) examine poliies in whih revenues from environmenal axes finane reduions in disorionary axes, alhough hese papers do no expliily address he ways ha pre-exising disorionary axes raise he oss of new environmenal axes. 1

5 R REV axes. The lower marginal raes redue he disorionary oss assoiaed wih hese axes, hus providing an effiieny gain. This is he revenue-reyling effe. These onsideraions are highly relevan o he hoie among alernaive insrumens for reduing emissions of CO 2. The mos frequenly ied insrumens for dealing wih CO 2 emissions are arbon axes, arbon quoas (or "arbon aps"), and markeable arbon emissions permis. 3 All of hese poliies generae a (osly) ax-ineraion effe, bu only some of hem an exploi he offseing revenue-reyling effe. Carbon axes, as well as arbon quoas or radable permis ha are auioned by he governmen, enjoy he revenue-reyling effe so long as he revenues obained are used o finane us in marginal ax raes of disorionary axes suh as he inome ax. In onras, grandfahered (non-auioned) arbon quoas and permis fail o raise revenues and hus anno exploi he revenue-reyling effe. Carbon axes whose revenues are reurned hrough lump-sum ransfers o households also fail o enjoy his effe. This paper shows ha he inabiliy o make use of he revenue-reyling effe an pu he laer poliies a a subsanial effiieny disadvanage relaive o he former poliies. 4 Indeed, he absene of he revenue-reyling effe may make i impossible for he laer poliies o generae overall effiieny gains, despie he benefis from avoided fuure limae hange! 5 These resuls bear direly on urren CO 2 -abaemen poliy disussions in he U.S. and Europe, where grandfahered radable arbon permis are gaining serious onsideraion. In his paper we use analyial and numerially solved general equilibrium models o onras he effes of wo sors of poliies, where he ruial differene beween he wo poliies is he presene or absene of he revenue-reyling effe. These poliies are a arbon ax wih revenues devoed o us in marginal ax raes, and a non-auioned arbon emissions quoa. To our knowledge, his is he firs sudy o ompare hese CO 2 -abaemen poliies in he presene of pre-exising disorionary axes. As menioned, he firs poliy explois he revenue-reyling effe, while he seond does no. or simpliiy, we apply he 3 See for example Tieenberg (1991), Poerba (1993), Hoel (1991), Oaes and Porney (1992). 4 Some earlier analyses of arbon axes have reognized he poenial imporane of he revenue-reyling effe. Repeo e al. (1992) and ordhaus (1993a) indiae ha he oss of a arbon ax are muh lower when revenues are reurned hrough us in marginal ax raes han when revenues are reurned lump-sum. These sudies make a valid poin abou he relaive oss of poliies ha do or do no exploi he revenue-reyling effe. However, he absolue oss of arbon ax poliies are no fully apured in hese sudies beause hey do no inegrae pre-exising axes in he analysis and hus hey anno aoun for he ax-ineraion effe. The presene or absene of he revenue-reyling effe an be linked o wheher poliy-generaed rens are apured by he governmen and reurned o axpayers (as in he ase of a polluion ax) or insead lef in produers' hands (as in he ase of polluion quoas or freely offered polluion permis). On his see ulleron and Mealf (1997). 5 The impossibiliy of effiieny gains was demonsraed hrough numerial simulaions performed by Bovenberg and Goulder (1996a). They found ha any arbon abaemen hrough a arbon ax poliy ha reyles he revenues in lump-sum fashion (and hus does no exploi he revenue-reyling effe) will be effiieny-reduing, if he marginal environmenal benefis from arbon abaemen do no exeed a srily posiive hreshold value. This resriion on environmenal benefis does no apply o arbon ax poliies involving reyling hrough us in marginal raes. The presen sudy differs from he Bovenberg-Goulder sudy in deomposing he ax-ineraion and revenue-reyling effes and in examining quoa poliies (and he reamen of quoa rens) in some deail. 2

6 R REV labels "arbon ax" and "arbon quoa" o hese poliies, sine i is umbersome o refer repeaedly o he presene or absene of he revenue-reyling effe. I should be kep in mind ha, as indiaed above, some poliies involving quoas or radable permis would share effiieny properies of our former aegory, while some poliies involving axes or radable permis would share effiieny properies of our laer aegory. We begin by deriving analyial formulas indiaing ha he effiieny oss assoiaed wih he ax-ineraion effe an be quie large relaive o he dire oss of arbon abaemen onsidered in ypial poliy models. We hen perform numerial simulaions ha show ha he absene of he revenue-reyling effe makes he arbon quoa poliy signifianly more osly han he arbon ax. Under enral values for parameers, he marginal oss of emissions abaemen begin a approximaely $18 per on under he quoa, as ompared wih $0 per on under he revenue-neural arbon ax. The quoa's minimal marginal os of $18 per on has some powerful impliaions for poliy. Esimaed marginal benefis from arbon abaemen are ypially below $18 per on (see in pariular ordhaus 1991a, 1994). If marginal benefis are indeed below his value, hen only he arbon ax an produe an effiieny improvemen in our model; a arbon quoa (or se of grandfahered radable permis) neessarily redues effiieny, and poenially by a large amoun. Clearly, here is enormous unerainy as o he poenial gains from reduing arbon emissions; as disussed below, under more exreme senarios for limae hange, benefi esimaes an easily exeed $18 per on. Ye even in his ase, here is sill a very srong effiieny argumen for preferring a arbon ax over a (non-auioned) quoa. Our numerial resuls indiae, for example, ha a five peren reduion in arbon emissions is almos six imes as osly under a quoa han a arbon ax. We would emphasize ha he absolue oss of he arbon quoa, and is os relaive o ha of he arbon ax, are sensiive o differen assumpions abou labor supply elasiiies, whih are diffiul o pin down auraely. oneheless, even under exremely onservaive values for labor supply elasiiies he marginal os of he quoa a zero abaemen sill signifianly exeeds he enral esimae of $5 per on for marginal environmenal benefis in ordhaus (1994). Our analysis also absras from a number of poenially signifian onsideraions, suh as apial aumulaion and pre-exising soures of disorion in he eonomy due o non-ax faors. However, as we disuss a he end of he paper, generalizing he analysis may well srenghen raher han weaken our empirial resuls. Our resuls are onsisen wih bu in some ways more sriking han he resuls obained by Goulder e. al (1997) in a sudy of he sulfur dioxide (SO 2 ) permi program under he 1990 Clean Air A Amendmens. Goulder e al. found ha, under enral esimaes for marginal environmenal benefis from SO 2 reduions, a sysem of grandfahered (freelyalloaed) SO 2 permis allows for an improvemen in effiieny relaive o he unregulaed saus quo. The presen sudy indiaes ha he prospes for effiieny gains hrough quoas or non-auioned permis are muh dimmer in he CO 2 onex. Quoas or non-auioned permis have a greaer hane a yielding effiieny gains in he SO 2 ase beause he enral esimaes for marginal environmenal benefis are relaively high (ompared wih marginal 3

7 R REV abaemen oss) in his ase. In onras, enral esimaes for marginal environmenal benefis from CO 2 reduions are fairly low relaive o marginal abaemen os. 6 The res of he paper is organized as follows. Seion II develops and applies our analyial model. This model is fairly simple, onaining wo final goods, a lean and diry inermediae inpu, and one primary faor labor. In Seion III, we desribe an exended version of he original model ha disinguishes differen fossil fuels and idenifies differen non-fuel inermediae goods. Seion IV applies he exended model, whih is solved numerially. The numerial soluion mehod enables us o onsider large (non-inremenal) poliy hanges, and his urns ou o be relevan o he relaive oss of he differen poliies. Seion V disusses he sensiiviy of he resuls o alernaive values for imporan parameers. Seion VI onludes and disusses some limiaions of he analysis. II. THE AAYTICA MODE Here we presen an analyially raable model ha reveals he effiieny impas of arbon axes and non-auioned arbon quoas in a seond-bes seing. This model shares some feaures of analyial models developed by Parry (1995, 1997) and Goulder e al. (1997). However, he presen model is disin from Parry's in deriving resuls expliily from uiliy maximizaion. In addiion, i differs from he model in Goulder e al. in inorporaing a more flexible relaionship beween he levels of polluion emissions and he level of oupu produed by he regulaed indusry. A. Model Assumpions A represenaive household alloaes is ime endowmen ( ) beween labor supply () and leisure, or non-marke ime ( l = ). I also purhases wo onsumpion goods, C and C. C represens an aggregae of final oupu from indusries ha use fossil fuels () inensively, and C is an aggregae of all oher onsumpion goods. We ignore apial aumulaion in he eonomy, whih means ha we jus fous on behavior in one period, raher han solving a dynami problem (see Seion IV). The household uiliy funion is given by: u( C, C, l) φ ( ) (II.1) where u(.), uiliy from non-environmenal goods, is oninuous and quasi-onave. φ is disuiliy from urren, anhropogenially aused addiions o he sok of CO 2 in he amosphere, aused by (ombusion of) fossil fuels. These damages represen he presen 6 Anoher opion for reduing arbon emissions is o mandae erain ehnologies ha require less fossil fuel inpu and hus enail lower emissions. A reen paper by ulleron and Mealf (1997) analyzes he effiieny impas of a pariular ehnology resriion, along wih emissions axes and quoa, in a seond-bes seing. The paper shows ha inremenal abaemen hrough a ehnology resriion need no be any more osly han inremenal abaemen under a polluion ax. Our analysis differs from ha in ulleron and Mealf by onenraing speifially on CO2 emissions reduions and in examining no only inremenal emissions abaemen bu also large amouns of abaemen. As emphasized below, he relaive oss of quoas and axes depend imporanly on he exen of emissions abaemen. 4

8 R REV disouned value of he expeed uiliy losses due o indued hanges in fuure global limae. 7 The separabiliy in (II.1) implies ha fuure limai hange does no affe he relaive araiveness of leisure and he wo ypes of onsumpion. 8 C and C are produed under onsan reurns o sale. The produion funions are given by: = (,, ) ; C C( ) C C =,, ; (II.2) where is a "lean" (non-polluing) inermediae good. abor is he only inpu used o produe he inermediae goods and, and he marginal produ of labor in eah of hese wo indusries is aken o be onsan. We assume ha produion in all four indusries is ompeiive. The use of fossil fuels in he C and C indusries leads o a proporional amoun of arbon emissions. This is a sandard assumpion in energy models: unlike he ase of SO 2, here are no eonomially viable srubber ehnologies o redue CO 2 emissions per uni of fuel inpu. Aggregae fossil fuel use is: = + (II.3) We hoose unis o imply one on of arbon per uni of. We do no onsider heerogeneiy in he oss of emissions abaemen among produers wihin a given indusry. If regulaors have imperfe informaion abou hese oss, in general hey will be unable o ahieve produion effiieny in he alloaion of quoas: marginal oss of abaemen are likely o differ aross produers. Under hese irumsanes a arbon ax or a sysem of radable arbon permis would have an effiieny advanage over fixed arbon quoas, apar from he advanages assoiaed wih revenue-reyling, whih are he fous of our analysis. 9 inally, we assume ha he governmen has an exogenous spending requiremen of G, whih is reurned o households as a lump sum ransfer. The governmen also levies a proporional ax of on labor inome, and regulaes arbon emissions using eiher a ax or a non-auioned quoa. The governmen budge is assumed o balane, and herefore any revenue onsequenes from regulaion are neuralized by adjusing he rae of. Denoing he demand pries of C and C by p and p, and normalizing he gross wage o uniy, he household budge onsrain is given by: 7 Alhough we fous on he oss o he U.S. of arbon abaemen poliies, we use environmenal benefi esimaes for he world eonomy. This seems appropriae sine we are dealing wih a globally dispersed polluan. 8 If polluion were o aler he radeoff (marginal rae of subsiuion) beween onsumpion and leisure (as would be he ase if polluion affes onsumer healh or labor produiviy) hen he benefis of redued polluion ould be magnified or diminished by ax ineraions. or more deails on his poin see Bovenberg and van der Ploeg (1994) and Williams (1997). 9 Poliy analyss have paid onsiderable aenion o his heerogeneiy issue and he assoiaed poenial gains from rades. Perhaps as a resul, radable arbon permis seem o enjoy more poliial suppor han non-radable quoas. 5

9 R REV p C + p C = ( 1 ) + G (II.4) Households hoose C, C and o maximize uiliy (II.1) subje o (II.4) and he ime endowmen. rom he resuling firs-order ondiions and he household budge onsrain, we obain he (implii) unompensaed demand and labor supply funions: C ( p, p, ); C ( p, p, ); ( p, p, ) (II.5) Subsiuing (II.5) ino (II.1) gives he indire uiliy funion: V = v( p, p, ) φ ( ) (II.6) rom Roy's Ideniy: v p = λc ; v p = λc ; v = λ (II.7) where he agrange muliplier λ is he marginal uiliy of inome. Consider a poliy eiher a arbon ax or quoa ha reaes a wedge of τ per uni beween he demand and supply prie of fossil fuels. Under onsan reurns o sale and ompeiion, he general equilibrium inrease in final produ pries 10 ha resuls from an inremenal inrease in τ is (see Appendix A): dp dτ = ; C dp dτ = (II.8) C ha is, he raio of fossil fuel inpu o final oupu. inally, he equilibrium quaniy of fossil fuels an be expressed as a funion of he poliy variables (see Appendix A): ( τ, ) = ( τ, ) + ( τ, ) (II.9) where d dτ < 0. These funions summarize he effe of hanges in τ on fossil fuel use hrough: (a) he subsiuion effe, ha is, he replaemen of labor and for fossil fuels in produion of C and C ; (b) he oupu effe, ha is, he hange in derived demand for fossil fuels from hanges in he quaniies of C and C aused by he effe of τ on final produ pries. Changes in affe fossil fuels hrough heir effe on he quaniy of final onsumpion goods, in response o a hange in he relaive prie of leisure. B. Carbon Tax Suppose τ represens a ax per uni paid by firms purhasing fossil fuels. Given he fixed proporions beween fuel use and emissions, his is equivalen o a ax of τ per on on arbon emissions. In his ase, he governmen budge onsrain is: τ + = G (II.10) 10 Tha is, he inrease ha applies when all pries and quaniies are reaed as variable. 6

10 R REV ha is, he sum of arbon ax revenues and labor ax revenues equals governmen spending. Consider a balaned-budge poliy hange involving an inremenal hange in τ and. Toally differeniaing (II.10) holding G onsan and using (II.5) and (II.9) we an express he hange in as: where d dτ d dτ We define: Z d + τ + dτ = + = + τ = + d dτ τ (II.11) (II.12) This is he parial equilibrium effiieny os from raising an addiional dollar of labor ax revenue, or marginal exess burden of labor axaion. The numeraor is he welfare loss from an inremenal inrease in ; i is he wedge beween he gross wage (equal o he value marginal produ of labor) and ne wage (equal o he marginal soial os of labor in erms of foregone leisure), muliplied by he reduion in labor supply. The denominaor is marginal labor ax revenue (from differeniaing ). The welfare effe of he poliy hange is obained by differeniaing he uiliy funion (II.6) wih respe o τ, allowing o vary. This gives: dv dτ v dp v dp v d d = + + φ ( ) p dτ p dτ dτ dτ Subsiuing (II.3), (II.7), (II.8), (II.11) and (II.12) gives: 1 dv λ dτ φ d d = τ Z τ 1 Z + λ + + ( ) (II.13) dτ dτ τ P dw R I W W Thus, he welfare effe (in dollars) an be separaed ino hree erms. The firs, dw P, is he effe wihin he fossil fuel marke, or primary welfare gain. This is he overall inremenal reduion in fossil fuel muliplied by he gap beween he marginal soial os ( q + φ λ ), and marginal soial benefi or demand prie ( q + τ ) of fossil fuel (where q is he supply 7

11 R REV prie of ). The seond, W R, is he (marginal) revenue-reyling effe, or effiieny gain from using addiional arbon ax revenues o redue he labor ax. This equals marginal arbon ax revenue muliplied by he marginal exess burden of axaion. The hird, W I, is he (marginal) ax-ineraion effe. This onsiss of: (i) ( τ ), he welfare loss from he reduion in labor supply, aused by he effe of τ on inreasing final goods pries and hereby reduing he real household wage; plus (ii) Z ( τ ), he resuling reduion in labor ax revenue muliplied by he marginal exess burden of axaion. The ax-ineraion effe an be expressed as (see Appendix A): I hηl + hηl η W = µ Z ; µ = s η + s η η l l I I (II.14) where η l and η l are he ompensaed elasiiy of demand for C and C wih respe o he prie of leisure; η I is he inome elasiiy of labor supply; h and h are he shares of fossil fuels in he C and C seors (h + h = 1); and s and s are he shares of C and C in he value of oal oupu ( s + s = 1 ). µ is a measure of he degree of subsiuion beween fossil-fuel-inensive onsumpion and leisure, relaive o ha beween aggregae onsumpion and leisure. In general, boh η l and η l are posiive, beause from he household budge onsrain (II.4), aggregae onsumpion and leisure are inversely relaed. If C and C are equal subsiues for leisure (ha is, η l = η l ) hen µ = 1. In his ase (omparing W I ha is, µz wih W R ), he ax-ineraion effe equals he revenue-reyling effe when τ = 0, bu exeeds i when τ > 0 (sine d dτ < 0 ). Therefore, aking ino aoun he pre-exising labor ax raises he slope, bu does no affe he inerep (equal o zero), of he marginal os of arbon emissions reduion. 11 Sine C is arbon-inensive, he share of fossil fuels used in he C seor exeeds he share of C in oal produion ( h > s ). Therefore, if C were a sronger (weaker) subsiue for leisure han Y (ha is η l is greaer (less) han η l ), hen µ would be greaer (less) han 1, and he marginal os of emissions reduion would have a posiive (negaive) inerep This is he same qualiaive resul as ha for a revenue-neural polluion ax on a final good (Goulder e al. 1997). oe ha, despie subsiuion of labor for fossil fuels in produion of final goods, he aggregae effe on labor supply is sill negaive. This ours beause, given our assumpions of onsan reurns o sale and ha labor is he only primary faor inpu, he aggregae demand for labor is perfely elasi and hanges in he quaniy of labor are deermined purely by hanges in he real household wage (he non-subsiuion heorem is saisfied (Varian 1992, pp. 354). Any poliy whih auses final goods pries o inrease, and hene he real wage o fall, will herefore redue labor supply. 12 or more disussion abou how he oss of emissions axes depend on he relaive degree of subsiuion beween oupu from he polluing seor and leisure see Bovenberg and van der Ploeg (1994), and Parry (1995). 8

12 R REV C. Carbon Quoa Suppose insead ha arbon emissions are redued by a quoa (or non-auioned permis). We define his quoa by τ q, he wedge i reaes beween he demand and supply q q prie of fossil fuels (τ an also be regarded as a "virual ax"). τ produes quoa rens of π = τ q q (sine he prie exeeds marginal privae os by τ for eah uni of ), whih arue o households, who own firms (in heir role as shareholders). We will generally assume ha his ren inome is axed a he same rae as labor inome. (In he sensiiviy analysis of Seion V, we will onsider he ase where quoa rens are no axed.) In general, he governmen budge onsrain is: ( π + ) = G (II.10 ) If insead, ren inome were axed a 100 peren, or he quoas were sold by he governmen a a prie of τ q, hen he arbon quoa would be equivalen o he arbon ax in his model. ollowing he analogous proedure o before, we an express he welfare hange from a marginal ighening of he quoa (ha is an inrease in τ q ) as (see Appendix): where 1 dv q λ dτ φ q d q d = τ Z τ 1 Z q + q q λ + + ( ) (II.13 ) dτ dτ τ P dw R I W W Z = (II.12 ) + + π Comparing (II.13 ) wih (II.13), one will observe ha he quoa auses he same primary welfare effe as he ax. I also indues he analogous ax-ineraion effe, sine i inreases he prie of onsumpion goods in he same way as he arbon ax. The key differene is ha i only produes an indire revenue-reyling effe, hrough he axaion of quoa rens, and his is equal o fraion of he revenue-reyling effe under he arbon ax. Therefore when C and C are equal subsiues for leisure, he revenue-reyling effe will only parially offse he ax-ineraion effe for he firs uni reduion in arbon; hene he marginal os of emissions reduion will now have a posiive inerep. If he environmenal benefis from arbon abaemen are below his inerep, hen a arbon quoa anno inrease welfare in expression W R in (II.13 ) represens he fraion of quoa rens ha he governmen obains hrough inome axaion and uses o u oher axes. In he ase of a revenue-neural auioned quoa would be uniy in his expression (as in equaion (II.13)). Alernaively, in he ase of arbon ax where he revenues are reurned as lump sum ransfers raher han used o u disorionary axes, =0. oe ha he marginal exess burden of axaion in (II.12 ) is slighly differen han in (II.12), beause inreasing now affes ax revenues from ren as well as labor inome. 9

13 R REV When C and C are equal subsiues for leisure, his hreshold benefi level ( B ) an be expressed as (see he Appendix): where B dτ d q 0 = Z ( 1 ) (II.15) ε 1 Z = 1 ε 1 u (II.12 ) u and ε and ε are he ompensaed and unompensaed labor supply elasiiy respeively. Z is an alernaive, empirially useful expression for he marginal exess burden of labor axaion, ha akes ino aoun general equilibrium inome effes. 14 In he numerial u model below, he benhmark parameer values we use for, ε, ε are 0.4, 0.3, and 0.15, implying Z = In addiion, dτ q / d = $0.085 per million ons, and iniial emissions are 1423 million ons. Subsiuing hese values in (II.12 ), he analyial model predis ha he quoa anno inrease welfare unless environmenal benefis exeed $16 per on. III. THE UMERICA MODE The simpliiy of he model in Seion II lends o ranspareny of resuls, bu i also limis he model's abiliy o gauge he empirial imporane of he seond-bes issues of ineres. In his seion we inrodue some exensions o he original analysis o gain a beer sense of he signifiane of hese issues. We exend he analysis in wo main ways. irs, we onsider he effes of "large" poliy hanges, ha is, poliy hanges ha produe greaer han inremenal reduions in emissions. As will be shown below, he relaive (as well as absolue) oss of arbon axes and quoas depend imporanly on he exen of arbon abaemen ahieved hrough hese poliies. In order o onsider large hanges, we mus speify funional forms for he uiliy and produion funions and solve he model numerially. The seond exension is o disaggregae furher he inermediae goods in produion. We disaggregae fossil fuels ino oil, oal, and naural gas o allow for emissions reduions no only hrough subsiuion of non-fuel inpus for fossil fuels (olleively), bu also hrough subsiuion of low-arbon fuels (suh as naural gas) for high-arbon fuels (suh as oal). We also disinguish beween energy-inensive and non-energy-inensive non-fuel inpus. This disaggregaion allows us o perform a rih sensiiviy analysis, whih is no possible in he analyial model. 14 Tha is, when he dollar of revenue raised is reurned o households as a lump sum ransfer. (The formulas in (II.12) and II.(12 ) are parial equilibrium and do no ake ino aoun his inome effe, and herefore depend only on unompensaed oeffiiens.) or a omprehensive disussion of he formula in (II.12 ) see Browning (1987). 10

14 R REV Subseion A desribes he behavioral assumpions for households, firms, and he governmen, and he equilibrium ondiions of he exended model. The omplee se of equaions for he model is presened in Appendix B. Subseion B desribes he alibraion of he model. A. Model Sruure There are six inermediae goods. ossil fuels are divided ino oal ( C ), peroleum ( P ) and naural gas ( ). Coal is he mos arbon-inensive fuel per uni of energy and naural gas he leas. The remaining inermediae goods are eleriiy (E), an aggregae of oher energy-inensive inermediae goods (I), and an aggregae of non-energy-inensive inermediae goods (). 15 As in he analyial model, here are wo onsumpion goods: C represens final oupu from indusries ha use inensively, and C I represens final oupu from indusries ha use he oher five inermediae goods (noably energy) inensively. abor ime is he sole primary faor of produion, and equals he household ime endowmen ne of leisure. All of he inermediae goods and labor are used as inpus in produion of inermediae goods. inal goods are produed using only inermediae goods as inpus. As before, labor is axed a a proporional rae of. The ax revenue is used o provide a fixed level of lump-sum ransfers o households. Carbon emissions 16 are proporional o he use of eah of he hree fossil fuels, wih a differen arbon onen for eah. Again, we onsider wo insrumens: a ax and a quoa on arbon emissions. i. irm Behavior We assume ompeiive produers ha ake inpu and oupu pries as given. Produion funions in all indusries have he following nesed onsan-elasiiy-ofsubsiuion (CES) form: X ρ j ρ ρ jm jm j = α i, j X i, j + i m i g α i, j X ρ jg i, j ρ j ρ jg + α, j X ρ j, j 1 ρ j (III.1) m = { I, }, g = {, C, P, E}, j = {, C, P, E, I,, C I, C } where he ρ's and he α i,j 's are parameers; ρ = ( σ 1 ) / σ and σ is he elasiiy of subsiuion beween faors in produion. This funion divides inpus ino hree groups: energy (fossil fuels and eleriiy), maerials (he wo remaining inermediae goods) and labor, wih differen elasiiies of subsiuion beween inpus in he same group han beween inpus in differen 15 Energy-inensive inermediae goods are hose for whih a relaively large proporion of energy goods (fossil fuels and eleriiy) are used as inpus, suh as meals proessing and ransporaion. on-energy-inensive inermediae goods are hose wih a relaively low proporion of energy inpus, suh as servies and agriulure. 16 This sudy measures emissions in erms of arbon onen. One on of arbon emissions is equivalen o 3.67 ons of arbon dioxide. 11

15 R REV groups. Beause his produion funion possesses onsan reurns o sale, supply urves in all indusries are perfely elasi for given inpu pries. Produers hoose inpu quaniies in order o maximize profis. In he ase of he arbon quoa, his is subje o he onsrain on emissions. Profis equal he value of oupu minus expendiures on labor and inermediae goods used in produion, less any harges per uni of arbon emissions (τ ). 17 Thus, profi for indusry j (π j ) is given by: ( j β jτ C ) X j π = p X (III.2) j p i i, j I where p i and p j are he pries of inpus and oupus, respeively, and β j represens he arbon emissions per uni of good j. β j is zero for all goods exep, C, and P. oe ha beause his produion funion exhibis onsan reurns o sale, profis will equal zero under he arbon ax, bu will equal he quoa rens under he emissions quoa. Toal arbon emissions are: e = β X + β X + β X (III.3) C C P P ii. Household Behavior We assume he following nesed CES uiliy funion: ρ u ρu (,,, ) u ( α α ρ ) φ( ) U = U l C C e = l + C + e I l 1 (III.4) where C C ( α C I α C ) I C = C + C ρ ρ ρ 1 C (III.5) l is leisure ime and he α's and ρ's are parameers. ρ U and ρ C are relaed o he elasiiies of subsiuion beween aggregae onsumpion and leisure and beween he wo onsumpion goods, respeively, in he same manner as in he produion funion. e denoes arbon emissions. 18 The household maximizes uiliy subje o he budge onsrain: ( 1 ) ( 1 ) p C + p C = p + π + p G (III.6) CI I C R C where is he ax rae on labor inome, R is he ax rae on ren inome, = l is labor supply, π is he oal ren generaed by a quoa poliy, G is real governmen spending in he 17 We assume here ha arbon axes are levied on he produers of fossil fuels imposed a soure, in keeping wih mos arbon ax proposals. 18 As in he analyial model, he damages from limae hange are assumed o be separable in uiliy from goods and leisure. Weak separabiliy beween goods and leisure and homohei preferenes over onsumpion goods ogeher imply ha C I and C are equal subsiues for leisure (see Deaon, 1981). Sine here is no obvious reason or empirial evidene o sugges ha energy-inensive goods are relaively srong or relaively weak subsiues for leisure, we regard his as a reasonable simplifiaion. 12

16 R REV form of ransfers o households, and p C is he omposie prie of onsumpion. This onsrain requires ha expendiure on onsumpion equal afer-ax inome in he form of wages, rens, and governmen ransfers. Exep in he sensiiviy analysis in Seion V, we assume ha he ax raes on labor inome and ren inome are he same: =. 19 iii. Governmen Poliy The numerial model onsiders he same wo ypes of emissions regulaion onsidered in he analyial model: a ax of τ on arbon emissions, and an emissions quoa yielding a virual ax of τ q. As shown in Appendix B and in he analyial model, firms behave idenially under he arbon ax as under he quoa for a given level of abaemen. The ruial differene beween he wo poliies is ha he ax direly raises revenue for he governmen and uses hose revenues o finane reduions in pre-exising ax raes. The governmen's budge onsrain is given by: p G = + π + τ e (III.7) C R Under a arbon ax, π is equal o zero, while under a arbon quoa, τ equals zero. As before, any revenue onsequenes of arbon regulaion are neuralized by adjusing he ax raes and (if appliable) R so as o mainain a fixed level of real ransfers, G. iv. Equilibrium Condiions The requiremens of general equilibrium are ha he demand for labor and for eah good equal supply, ha he governmen's revenue requiremen be saisfied, and ha arbon emissions equal a speified arge (if appliable). We an redue he se of equilibrium ondiions o hree equaions: aggregae labor demand equals aggregae supply, governmen revenue equals expendiures, and arbon emissions equal he arge level. 20 The model is solved by adjusing he primary pries: he pre-ax wage (p,); he ax rae on labor inome ( ); and he ax rae on arbon emissions (τ ), or virual ax rae (τ q ), suh ha hese hree ondiions hold. B. Calibraion of he Model The benhmark daa se, summarized in Table 1, approximaes he Unied Saes eonomy in he year 1995, he mos reen year for whih he relevan energy daa were R 19 The effeive ax on labor earnings (primarily personal inome and payroll axes) and non-labor earnings (personal and orporae inome axes) are roughly he same. or example, uas (1990) esimaes hem o be 40 peren and 36 peren respeively. 20 Our assumpions of ompeiion and onsan reurns o sale imply produ pries equal marginal os and ha supply urves are perfely elasi. The ompuaional algorihm used o solve he model only uses he governmen budge and arbon emissions ondiions. By Walras's law, if hese wo ondiions are saisfied, hen he aggregae exess demand for labor mus also equal zero. As a hek on he ompuaion, we verify ha he hird equilibrium ondiion holds, and also ha he resul is onsisen wih he appropriae homogeneiy ondiions in pries and quaniies. 13

17 R REV available. We developed his daa se by aggregaing 1987 daa from he Survey of Curren Business on inpu uses, oupu levels, and onsumpion paerns ino he six inermediae and wo final goods indusries in he model. We hen saled he daa up o he year 1995, using daa from he Survey of Curren Business on growh raes in he differen indusries modeled, and informaion on 1995 eleriiy and fossil fuel use from he 1997 Annual Energy Updae. 21 In he model, he sensiiviy of labor supply o he afer-ax wage is onrolled by he parameer σ U. Based on he exising lieraure, we se σ U = 1.20, whih implies an unompensaed and ompensaed labor supply elasiiy of 0.15 and 0.3 respeively. 22 The baseline labor ax rae is aken o be 40 peren, whih is mean o aoun for axes a boh he ederal and sae levels. 23 The elasiiies of subsiuion in produion of inermediae and final goods are aggregaed from hose esimaed by MKibbin and Wiloxen (1995). We adjused he ouernes elasiiies (elasiiy of subsiuion beween labor, maerials, and energy) so as o produe, in he absene of pre-exising labor axes, a shedule of marginal oss of arbon emissions abaemen ha losely mahes he urve derived by ordhaus (1991b) from a survey of exising sudies. The resuling elasiiies are given in Table 1B. The arbon onen for eah of he hree fossil fuel inermediae goods (β ) is alulaed by dividing he 1995 emissions of arbon from he burning of eah fuel, as repored in he 1997 Annual Energy Oulook, by he quaniy of eah fuel burned. The α disribuion parameers were alibraed based on he assumed elasiiies of subsiuion and he idenifying resriion ha eah indusry uilized he os-minimizing mix of inpus, or, equivalenly, he resriion ha in he absene of an emissions-onrol poliy, he model will repliae he benhmark daa We saled up non-energy-indusry daa o 1993 using indusry-speifi growh raes, and hen saled he daa up o 1995 levels using he rae of GDP growh from , hus impliily assuming ha boh non-energy indusries grew a he same rae from Energy-indusry daa were saled up based on 1995 use of eah fuel and of eleriiy. We used Kuroda's mehod o ensure ha he resuling daa se me he neessary adding-up ondiions. As shown in Seion V, our resuls are largely insensiive o he relaive size of differen indusries. 22 These elasiiies also refle he assumpion ha, in he iniial daa se, non-sleep leisure ime equals 0.3 imes hours worked. The labor supply elasiiies are median esimaes from he eonomeri lieraure (see he survey in Russek, 1996). They represen he effes of hanges in ne wages on he pariipaion rae and average hours per worker. We regard hese values as onservaive, sine hey do no apure he effe of hanges in ne wages on effor per hour. Oher ax-simulaion models ofen assume somewha higher values. or example Bhaarai and Whalley (1997) assume an unompensaed elasiiy of Oher sudies use omparable values. See, for example, uas (1990) and Browning (1987). The sum of ederal inome, sae inome, payroll, and onsumpion axes amouns o around 36 peren of ne naional produ. This average rae is relevan for he pariipaion deision. The marginal ax rae, whih affes effor level and hours worked per employee, is higher beause of various ax deduions. Our values for ax raes and labor supply elasiiies imply a marginal exess burden of labor axaion equal o 0.22 (when addiional spending is reurned as a lump sum ransfer). 24 or a disussion of alibraion mehods for general equilibrium models, see Shoven and Whalley (1992). 14

18 R REV Table 1. Benhmark Daa for he umerial Model A. Inpu-Oupu lows (in millions of 1995 dollars exep arbon emissions in millions of ons) C P E I C I C l Toal Inpu Value C P E I Toal Oupu Value e Elasiiy of Subsiuion Among Energy, abor, and Maerials B. Parameer Values σ E Elasiiy of Subsiuion in Energy (fuels and eleriiy) nes σ M Elasiiy of Subsiuion in Maerials nes C P E I C I C σ C =0.5, σ U =1.2 (elasiiies of subsiuion beween final goods and beween onsumpion and leisure, respeively) In he simulaion experimens below we ompare ouomes in a seond-bes seing (wih he labor ax) o hose in a firs-bes seing (when he labor ax is se o zero). The iniial quaniies of emissions and gross domesi produ are eah approximaely 12 peren higher in he firs-bes ase. 25 This means ha, for a given proporionae reduion in emissions, he absolue gross os in he firs-bes ase is somewha higher han he primary os in he seond-bes seing. 26 C. Poliy Proposals and Carbon Damage Senarios The Kyoo Proool alls for indusrialized naions (he so-alled Annex I ounries) o ahieve signifian reduions in a baske of greenhouse gases (inluding CO 2 ) by Eliminaing he labor ax inreases he afer-ax wage, so individuals supply more labor and hus GDP is higher. This has a roughly equal effe aross all indusries, so emissions rise by he same proporion. 26 Tha is, environmenal benefis minus he primary welfare gain. 15

19 R REV The U.S., in pariular, mus ahieve a level of emissions abou seven peren below 1990 levels. Under business-as-usual ondiions, emissions are projeed o grow signifianly from he presen ime unil ; hene meeing he Kyoo arges would ompel he U.S. o redue is emissions by onsiderably more han seven peren. In our numerial simulaions, we onsider emissions reduions ranging from 0 o 25 peren, a range ha seems relevan o he reduions required from he Kyoo Proool. We onsider a range of esimaes for benefis from arbon abaemen. Cenral esimaes in he lieraure are ypially below $20 per on (for example, $5 per on in ordhaus 1994). 27 The "low" values for he enral esimaes refle he noion ha oninued aumulaion of greenhouse gases will no produe exreme hanges in limae over he nex enury, and he idea ha mos eonomi aiviies are no exepionally sensiive o modes limae hange. In addiion, disouning over long periods of ime subsanially redues he benefi esimaes, whih are presen values. However under exreme values for limae hange, sensiiviy of he eonomy o suh hange, or disoun raes, muh higher benefi esimaes arise. Under an exreme senario, ordhaus (1991a), for example, esimaes benefis o be $66 per on. 28 The simulaions below aim o span a wide range of benefi senarios, onsidering a range from 0 o 100 dollars per on. In all ases, we assume marginal benefis are onsan over he range of emissions reduions. 29 IV. UMERICA RESUTS A. Marginal Coss of Emissions Reduion igure 1 (see page 35) shows how he pre-exising labor ax affes he marginal os of reduions in arbon emissions. The boom urve is he marginal os when here is no disorionary labor ax. This urve is roughly he same in real erms as ha in ordhaus (1991b). The urve is upward sloping, refleing he inreasing diffiuly of subsiuing fossil fuels for oher inpus in produion. In a firs-bes world, he same urve applies no maer wheher he reduion is ahieved by a ax or quoa. In a seond-bes world, in onras, he marginal os urves differ signifianly. In our enral ase senario, whih assumes a pre-exising labor ax ( 0 ) of 40 peren, he quoa poliy shifs up he marginal os urve, giving i a posiive inerep. This upward shif refles he ax-ineraion effe. Under he arbon ax, he marginal os urve pivos upward bu reains he zero inerep ha applies in he firs-bes ase. The middle urve in igure 1 represens marginal oss under he arbon ax. The zero inerep refles he fa ha he revenue-reyling effe exaly 27 The firs benefi esimae was $7 per on, by ordhaus (1991a). Oher esimaes inlude $12 (Pek and Teisberg, 1993) and $20 (ankhauser, 1994). 28 The esimaes have also been riiized for negleing some eosysem impas, poenially adverse effes on he disribuion of world inome, and he possibiliy of non-lineariies wihin he limae sysem. ordhaus (1993b) provides insighful ommenary on hese issues. 29 This seems a reasonable approximaion (see Pizer, 1997). 16

20 R REV offses he ax-ineraion effe a he firs inremen of abaemen. The zero inerep implies ha he arbon ax an inrease welfare so long as marginal benefis from emissions reduion are posiive. In onras, under he quoa marginal benefis mus exeed a srily posiive value ($17.8 per on under enral-ase values for parameers) in order o inrease welfare. These qualiaive resuls were aniipaed by he analyial model. The value of he inerep of he marginal os under he quoa is almos idenial in boh analyial and numerial models. 30 B. Average Coss of Emissions Reduion igure 2 (see page 36) shows he average oal os of reduing arbon emissions under he ax and quoa, expressed relaive o he average oal os of he same emissions reduion in a firs-bes seing wih no pre-exising labor ax. 31 or boh poliies, pre-exising axes imply higher oss a all levels of abaemen han would our if he labor ax were zero. A all levels of abaemen, he os of he arbon ax is abou 22 peren higher when he pre-exising labor ax is 0.4 han when here is no pre-exising labor ax. 32 Under he quoa poliy, preexising axes have a muh greaer impa. The average oal os of a 5 peren emissions reduion, for example, is six imes as high wih pre-exising axes han wihou; he average os of a 15 peren emissions reduion is 2.6 imes as high. The very high raios refle he fa ha he marginal oss of abaemen begin a a srily posiive level in a seond-bes seing, whereas hey sar a zero in he absene of prior axes, as shown in igure 1. igure 2 shows ha, on effiieny grounds, pre-exising axes pu he quoa poliy a a onsiderable disadvanage relaive o he ax poliy. or all levels of emissions reduion up o 25 peren, he os of he quoa is more han double ha of he ax. Whaever he benefis from reduing arbon emissions, here is a srong effiieny ase for preferring he arbon ax o he arbon quoa. oe ha he relaive disrepany beween he ax and quoa delines wih he level of abaemen. The marginal ax-ineraion effe is approximaely onsan, bu marginal ax revenue and hene he marginal revenue-reyling effe is delining. This ours beause he arbon ax base ( in (II.13)) delines wih abaemen. Evenually, 30 The inerep of he quoa urve is somewha lower han ha implii in he numerial model of Bovenberg and Goulder (1996a), whih inorporaes a muh more deailed reamen of he ax sysem. In heir model, a arbon ax wih revenues reyled hrough lump-sum ransfers is effiieny-reduing unless marginal benefis from emissions reduion exeed $55 per on. This poliy would be equivalen o he above quoa poliy if here were no axaion of quoa rens. When we assume no axes on quoa rens in he presen model, he inerep of he marginal os urve rises o $29.4 per on (see Seion V). The bulk of he differene resuls beause we assume a lower (ompensaed) labor supply elasiiy han in heir model (we assume 0.3 for his elasiiy while Bovenberg and Goulder assume 0.6). In addiion Bovenberg and Goulder (1996a) inorporae pre-exising axes on gasoline, whih inreases marginal abaemen oss. 31 We ompare average oss, raher han oal oss, beause baseline (unregulaed) emissions are higher in he absene of a labor ax. As noed earlier, eliminaing he labor ax enourages labor supply 32 The raio of average oss beween he firs- and seond-bes seing is onsan wih respe o he amoun of emissions reduion, in he arbon ax ase. This is beause he marginal ne loss from he ax-ineraion and revenue-reyling effes hanges in proporion o he slope of he primary marginal os of emissions reduion. 17

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