DISCUSSION PAPER. Is There a Rationale for Output-Based Rebating of Environmental Levies? Alain L. Bernard, Carolyn Fischer, and Alan Fox

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1 DISCUSSION PAPER October 00; revsed October 006 RFF DP 0-3 REV Is There a Ratonale for Output-Based Rebatng of Envronmental Leves? Alan L. Bernard, Carolyn Fscher, and Alan Fox 66 P St. NW Washngton, DC

2 Is There a Ratonale for Output-Based Rebatng of Envronmental Leves? Alan L. Bernard, Carolyn Fscher, and Alan Fox Abstract Poltcal pressure often exsts for rebatng envronmental leves, partcularly when ncomplete regulatory coverage allegedly creates an unlevel playng feld wth other, unregulated frms or ndustres. Ths paper assesses the condtons under whch rebatng envronmental leves s justfed for the regulated sector, combnng a theoretcal approach wth numercal smulatons parameterzed to reflect the Regonal Greenhouse Gas Intatve. Rebates are undesred f one can nstead tax the producton of the unregulated sector. Otherwse, rebatng s justfed only when the goods of the competng sectors are close substtutes wth smlar emssons profles. Polcy constrants are costly n terms of welfare and envronmental effectveness. Key Words: envronmental tax, rebate, fscal dstortons, emssons permt allocaton JEL Classfcaton Numbers: Q, Q43, H, D6 006 Resources for the Future. All rghts reserved. No porton of ths paper may be reproduced wthout permsson of the authors. Dscusson papers are research materals crculated by ther authors for purposes of nformaton and dscusson. They have not necessarly undergone formal peer revew.

3 Contents Introducton... Model... 5 Specfcatons... 5 Decentralzed Markets... 6 Planner Problem... 7 Numercal Model... 0 Polcy Scenaros... Model Specfcatons... Calbraton... 3 Results... 5 Concluson... 7 Appendx... Second-Best Optmzaton... Tables... 5 Fgures... 7

4 Is There a Ratonale for Output-Based Rebatng of Envronmental Leves? Alan L. Bernard, Carolyn Fscher, and Alan Fox Introducton Envronmental taxes, lke many tax polces wth a narrow focus, have long been ted to related expendtures. For example, France has used effluent fees to subsdze nvestments n abatement equpment, and the Unted States earmarked a feedstock tax on petroleum and chemcal ndustres for fnancng Superfund cleanup operatons. Today, however, emssons taxes do more than fnance envronmental polces; more often they are the polces themselves. When prce mechansms, such as taxes or tradable permts, are leved on emssons to create ncentves for envronmental protecton, the queston arses of how to dstrbute the accompanyng revenues, or rents. Poltcal pressure exsts for envronmental regulators to desgn self-contaned, revenueneutral polces. The motves and methods for dstrbutng the rents vary, however. Owners of sunk captal argue for grandfathered emssons permts or other lump-sum transfers as compensaton for lost nvestments or forgone profts. Ths model was used n the 990 Clean Ar Act Amendments, whch nsttuted an emssons tradng program for sulfur doxde (SO ) n the Unted States: the permts were predomnantly allocated accordng to the hstorcal emssons of partcpants. However, grandfatherng can transfer rents that far outwegh the actual costs of complance. 3 Economsts concerned about preexstng dstortons n the economy then tend to argue for usng the revenues to reduce ncome and other taxes. Another worry may be the Alan L. Bernard s at the Mnstry of Transportaton and Housng, Tour Pascal B, 9055 Pars La Défense Cedex 04, France, Carolyn Fscher (correspondng author) s a Fellow at Resources for the Future, 66 P St., NW, Washngton, DC , tel: , fax: , e-mal: Alan Fox s an Economst at the U.S. Internatonal Trade Commsson, 500 E Street SW, Washngton, DC 0436; The content heren s the sole responsblty of the authors and does not represent an offcal poston of ther organzatons. Support from U.S. EPA-STAR s gratefully acknowledged. OECD (993). Such revenue earmarkng has been a focus n poltcal economy, where earmarkng can be shown to offer an enforcement mechansm for compromse among dfferent nterest groups (Wagner 99). However, we abstract from the dstrbutonal ssues behnd these motvatons. 3 E.g., Bovenberg and Goulder (00).

5 ncomplete coverage of envronmental regulaton. Regulated sectors argue that to mantan a level, compettve playng feld, the revenues should be used to subsdze ther producton. Envronmental regulators mght also worry that, wthout such subsdes, producton would shft abroad to polluton havens, countres wth less strngent polces. Ths paper focuses on the latter argument: the ratonale that mperfect regulatory coverage creates for subsdzng regulated polluters. The ssue bears some smlartes to and some dstnctons from the well-known lterature on the nteractons of envronmental taxes wth dstortons created by labor ncome taxaton (for a comprehensve collecton, see Goulder 00). The common problem s that some factor escapes taxaton n ths case emssons, n the latter case lesure. As a result, the optmal tax s a second-best result wth general equlbrum effects. In the tax-nteracton models, the polcy constrant s that needed revenue cannot be rased wth lump-sum taxaton; as a result, although the regulator s free to fully tax the externalty, the optmal rate s typcally lower than n the frst-best settng, snce the tax dstorton ncreases the cost of the envronmental polcy. In ths paper, lump-sum taxaton s allowed, thus makng a revenue constrant nonbndng and commodty taxaton undesrable n the frst-best case. Rather, the polcy constrant s that one of the pollutng sectors cannot be fully regulated. As a result, not only s the optmal emssons tax affected, but also the optmal commodty taxes and we focus n partcular on determnng n whch stuatons the optmal tax on the regulated commodty s sgnfcantly negatve, mplyng that an output subsdy s desred. 4 Some polluters may escape regulaton for many reasons techncal, jursdctonal, poltcal, or otherwse. Techncal reasons can arse when frm-level montorng of emssons s nfeasble or prohbtvely costly. For example, although contnuous emssons montorng for ntrogen oxdes (NO x ) may be cost-effectve for large electrcty generators, t may not be for small ones, nor may t be feasble for nonpont sources of polluton, lke automobles. Jursdctonal boundares can mean that some polluters operate outsde the regulator s reach, such as across state or natonal boundares, or outsde the partcular controlled ndustry. For example, n some countres the department of the envronment mght be able to regulate statonary sources but not moble ones, whch are the doman of the transportaton department; alternatvely, the envronmental agency mght be authorzed to regulate specfc ndustres, lke 4 Ths ntal case s a necessary frst step to develop ntuton about regulatory constrants. In the concluson we dscuss how these two approaches mght be combned to analyze the problem wth both a regulatory and a revenue constrant, thus ncorporatng more complex tax nteractons.

6 electrcty generators, but a broad-based polluton tax on energy could requre legslatve approval. Furthermore, nondscrmnaton requrements of trade agreements lke the World Trade Organzaton or the U.S. Commerce Clause can prevent these jursdctons from taxng mports of goods that escape polluton regulaton. 5 Fnally, sectors that are consdered vulnerable or that are otherwse nfluental (steel or agrculture, for example) may be exempted for poltcal reasons. In the case of clmate polcy, there are many reasons why regulaton of carbon doxde (CO ) mght be uneven, both domestcally and nternatonally. Some countres have commtted to emssons caps under the Kyoto Protocol, whle others have not; those that have commtted, lke the European Unon, are mplementng downstream systems that focus emssons permt tradng on a few major sectors; other sectors are ether left alone or face an assortment of polces, ncludng ndrect taxaton of energy products. Energy-ntensve ndustres then argue that wthout output subsdes, a polcy of emssons prces alone wll compromse ther ablty to compete wth companes n nonpartcpatng countres. Partcpatng countres worry that carbon leakage may lmt the effectveness of ther efforts. Smlarly, as some northeastern and neghborng md-atlantc states embark on the Regonal Greenhouse Gas Intatve (RGGI) to curb CO emssons from the electrc power sector, they worry about leakage to nonpartcpatng states. 6 In response, polcymakers have proposed earmarkng mechansms amed at allevatng or cancelng the dstortonary effect of polluton taxaton vs-à-vs unregulated compettors. In partcular, output-based rebatng has emerged as a popular mechansm for ntegratng an offsettng subsdy nto an envronmental polcy that rases producton costs. Essentally, the revenues generated by the envronmental polcy are refunded back to the partcpants n proporton to ther output, thus offerng a producton subsdy. Output-based rebatng can take several forms: emssons taxes wth rebates, output-allocated tradable emssons permts, and tradable performance standards, n whch permts are allocated accordng to a polluton-ntensty standard per unt of output. All these polces are smlar forms of the same scheme: they each smultaneously mpose a margnal cost on emssons and offer a subsdy to producton. 5 Taxes can be leved on mports for polluton physcally emboded n the goods, f domestc products are subject to such a tax. However, mports cannot be taxed based on emssons arsng from the producton process. See Fscher et al. (003). 6 Kruger and Pzer (005). 3

7 Furthermore, the margnal value of that subsdy s not fxed but rather ted to the average value of nframargnal emssons to the affected ndustry. 7 Some ntal studes of rebatng polces have been made, typcally focusng on a specfc type. 8 More attenton has been pad to performance standards, for whch several researchers have compared the effcency effects to tradtonal tax or permt polces. 9 In the presence of preexstng tax dstortons, these mechansms can outperform a system of grandfathered emssons permts. Fscher and Fox (004) consder dfferent rules for output-based allocaton and ther effectveness at combatng carbon leakage, as well as tax dstortons. However, the ssue of optmal second-best subsdes has not receved attenton. The purpose of ths paper s to assess, on theoretcal grounds and through numercal smulatons, the desrablty of such measures for correctng the dstorton between the regulated and unregulated sectors. If an emssons tax can be mposed on one sector but not another, the next recourse s a system of commodty taxaton on all goods. One mght expect that a postve rate of taxaton on the good produced by the unregulated sector, coupled wth a negatve tax (a rebate) n the regulated sector, would prove desrable. Analyss shows that only part of ths ntuton s true: t s (second-best) optmal to tax the unregulated sector, but not generally to rebate n the regulated sector. If the unregulated sector s also untaxable, the ratonale for a rebate n the regulated sector then appears stronger. However, rebatng all the revenues s rarely deal; the optmal rebate depends on the polluton ntensty of the unregulated sector and the degree of substtutablty between the goods. In fact, the desrablty of the output rebate s not guaranteed; t s possble to show examples n whch t s desrable that the regulated sector, though facng competton from an unregulated and nontaxable sector, be postvely taxed. Only when the two sectors are close substtutes wth smlar emssons profles does a 00 percent rebate approach the constraned optmum. The next secton presents the analytcal model and the results for the optmal second-best tax rates. Then, numercal smulatons, parameterzed to reflect the RGGI case, are used to 7 Fscher (00). 8 Sterner and Isaksson (006) focus on the Swedsh NO x program; Jensen and Rasmussen (000) look at permt tradng wth output-based allocaton for CO. 9 See Goulder et al. (999), Parry and Wllams (999), Fullerton and Metcalf (00), and Dssou (005). 4

8 develop ntuton about the effects of substtutablty and damage costs on not only the optmal tax and rebate rates, but also the potental magntude of the welfare losses and emssons, relatve to optmal polcy. The fnal secton offers concludng thoughts. Model The mnmal representaton of the economy necessary to cope wth the ssues at hand nvolves a model wth two sectors (regulated and unregulated), two goods, and two factors of producton (labor and emssons). Labor s consdered the thrd good and (wthout loss of generalty) taken as the numérare and untaxed good (wth ts prce set to unty). The followng lst summarzes our notaton: Specfcatons Quanttes Q = Producton n the regulated sector Q = Producton n the unregulated sector L = Labor demand n the regulated sector L = Labor demand n the unregulated sector L = Labor supply l = Lesure = L C = Demand for good produced n the regulated sector C = Demand for good produced n the unregulated sector E = Emssons of pollutant n the regulated sector E = Emssons of pollutant n the unregulated sector Prces p = Consumer prces n the regulated sector p = Consumer prces n the unregulated sector q = Producer prces n the regulated sector q = Producer prces n the unregulated sector w = Labor wage τ = Tax on emssons n the regulated sector τ = Tax on emssons n the unregulated sector T = Refund of tax revenues (lump-sum transfer) The household sector comprses a representatve consumer, allowng us to avod consderaton of equty n the analyss. Utlty s a functon of consumpton of both goods and lesure: U = U C, C, ). () ( L Gven the absence of labor tax dstortons here, lesure could equvalently represent all clean commodtes, and labor a fxed factor supply. 5

9 Households also suffer dsutlty as a functon of total emssons: 0 D = D( E ) + E. () The welfare functon, then, s the dfference between consumpton utlty and emssons dsutlty, whch we have assumed to be separable: W = U D = U( C, C, L) D( E + E ). (3) Producton n each sector ( =, ) s a functon of labor and emssons: Q = f L, E ). ( Equvalently, labor n each sector can be specfed as a functon of output and emssons: L = L Q, E ). (4) ( Decentralzed Markets It s well understood that f the socal planner could choose quanttes of output and emssons drectly, the margnal damage of all emssons would be equalzed wth the cost of reducng them and the margnal value of a good s consumpton would equal ts socal margnal cost, nclusve of the externalty. In the decentralzed problem, the planner uses taxes to nfluence market prces and acheve ths outcome. The maxmzaton problems of the consumer and producers form the constrants for the planner, along wth any regulatory constrant. Consumer Problem Takng polluton externaltes as gven, the representatve household maxmzes utlty wth respect to consumpton and lesure, subject to a budget constrant: U C, C, ) (5) ( L ( = From the consumer problem, we obtan λ ) p C + p C wl T 0. (6) U U U ( C ) = pλ; ( C ) = p λ; ( L) = λw. (7) C C L 0 An alternatve and equvalent formalzaton would be to mpose a lmt to total damages; the shadow prce of the constrant then represents the value of the margnal damage. Smulatons would then compare results gven an emssons target, as wth a cap-and-trade polcy, rather than gven an emssons tax that equalzes margnal costs and benefts. 6

10 Producer Problems The representatve frm n each sector chooses output and emssons to maxmze profts: π = q Q wl ( Q, E ) τ E, (8) from whch we obtan L L ( Q) q = w ; ( E) w = τ. Q E (9) The frst expresson mples that the output prce equals the margnal cost (or, wth some rearrangng, that the value of the margnal product of labor equals the wage rate). The second means that the labor cost savngs from usng more emssons just equal the tax. Market Equlbrum In equlbrum, we have C = Q; C = Q ; L ( Q, E ) + L ( Q, E ) = L. (0) and q = p t. Wth well-behaved utlty and producton functons, consumpton of each good s decreasng n ts own costs, whch nclude output and emssons taxes, so dc / dt < 0 (and dc / dτ < 0). Let us defne the goods as substtutes f dc / dt > 0 and complements f dc / dt < 0. These cross-prce effects depend not only on the sgns of the cross-partals n the j utlty functon, but also on the general equlbrum. Overall labor supply s ncreasng n the margnal utlty of consumpton. Planner Problem The queston at hand s what happens when the polcymaker cannot regulate polluton n sector. Two polar cases wll be consdered: ) the output of the unregulated sector can be taxed (or subsdzed), as can that of the regulated sector; ) the unregulated sector must also reman untaxed, whle the regulated sector can be taxed or subsdzed as well as regulated. The socal planner maxmzes welfare, W, wth respect to t, t, τ, subject to the aforementoned constrants. The Appendx provdes an alternatve approach for solvng ths j 7

11 second-best optmzaton problem. However, the essence of the optmal tax problem can be seen by totally dfferentatng welfare: U U U D dw = dc + dc dl de + de C C l E ( ). () Usng the frst-order condtons from the consumer problem, ths equaton smplfes to Furthermore, L L dl = dq + de Q E dl = dl+ dl ( ) dw = p λdc + p λdc λ wdl D de + de. () and totally dfferentatng the producton functon, we get. Substtutng, and usng the producer frst-order condtons, we get the margnal welfare mpacts of the dfferent polcy levers (relatve to the margnal utlty of consumpton): Frst Best dw / dt dc / dt dw dc dc D de D de = t + t + τ + τ ; (3) λ dt dt dt { λ dt λ dt { dw dc dc D de D de = t + t + τ + τ ; (4) λ dt dt { dt λ dt { λ dt dw dc dc D de D de = t + t + τ + τ λ dτ dτ { dτ λ dτ { λ dτ. (5) From these equatons, t s easy to see that f τ = τ = D / λ, then t = t = : evaluatng 0 at that pont, margnal welfare s declnng wth any devaton n t from 0, snce t and take opposte sgns. In other words, at the welfare optmum, when the emssons externalty s fully nternalzed wth Pgouvan taxes, no output taxes or subsdes are needed. Unregulated Sector However, when τ = 0, the second-best optmum mples τ D de = ; t = 0; t = τ. (6) λ dc 8

12 These results are also smple to nterpret: emssons n sector are taxed accordng to margnal damages; there s nether tax nor rebate for commodty ; and commodty s taxed accordng to the margnal damages of the assocated emssons. The expresson for t reveals that the tax rate on sector equals the polluton tax appled n sector multpled by the margnal propensty to emt. Thus, f emssons from the exempt sector are nsgnfcant, the optmal commodty tax wll be neglgble. More generally, the optmal commodty tax reflects the average tax payments that would accrue from a polluton tax. However, the rate and level of emtted polluton are hgher than n the frst-best case because the ncentve effect s not at work. As a result, the optmzed unregulated equlbrum exhbts a welfare loss relatve to the frst-best, whch can be measured and wll be calculated n numercal smulatons. Unregulated, Untaxed Sector Now suppose sector cannot be taxed at all nether ts emssons nor ts output. A unlateral tax on sector s emssons rases the relatve prce of good. To allevate the dstorton to competton, t may be desrable to subsdze sector that s, mpose a negatve commodty tax. Such a result s not assured, however. Smplfyng the equatons for the welfare changes, we have dw dc D de D de = t + τ λ dt dt { λ dt { λ dt ; (7) dw dc D de D de = t + τ λ dτ dτ { λ dτ { λ dτ. (8) In ths case, the second-best polcy combnaton mples τ D de = ; t = τ. (9) λ dc The emssons tax n sector affects and E n the same way as an output tax, by C ncreasng margnal costs for that sector. Thus, there s no reason for the emssons tax to devate from the Pgouvan level, snce the output tax can be used to nfluence those varables. Stll, the 9

13 optmal emssons tax n ths case wll dffer from the less constraned cases, snce equlbrum margnal damages and the margnal utlty of consumpton wll dffer. The optmal tax on the regulated sector reflects the margnal value of the change n emssons n sector that t nduces. If the goods are substtutes, then de / dc < 0, and an output subsdy s justfed. The strength of that subsdy depends on both the strength of that substtuton effect dc / dc and the margnal emssons n the other sector de/ dc. Under what crcumstances mght 00 percent rebatng be justfed, as wth a performance standard or output-based rebatng? Ths polcy mples that the total subsdy equals the total revenue from the emssons tax: tc = τ E. Substtutng the optmal tax values and rearrangng, we get de dc E =. (0) C Thus 00 percent rebatng s optmal f the emssons n sector dsplaced by the addtonal output n equal the average emssons rate n sector. Logcally, ths condton s most lkely to hold when the two goods are close substtutes and have smlar emssons profles. In other words, output-based rebatng can be justfed when parts of the same compettve sector cannot be regulated or taxed. However, output-based rebatng s suboptmal when the two sectors are not drect compettors, or the competng sector has relatvely low emssons. For example, f the regulated sector s electrcty generaton, sgnfcant rebatng would not be justfed because the transportaton sector s exempt, or because renewable energy s exempt. On the other hand, f ndustral bolers or out-of-state coal-fred plants n the same arshed and on the same grd are exempt from ar emssons regulaton, rebatng may be a reasonable response. More generally, D de D de t = + τ λ dc λ dc D D de dc τ = + t λ λ dc de () Numercal Model The precedng analytcal results ndcate the optmal tax response to regulatory constrants, but they cannot reveal the magntude of the welfare loss assocated wth those constrants or the optmal tax levels that arse from these equlbra. To develop ntuton about 0

14 those mpacts and ther senstvty to mportant parameters lke margnal damages and substtutablty, we employ a smple numercal model. (A complete specfcaton of the secondbest optmzaton problem, whch s the analytcal foundaton for the numercal model, s lad out n the Appendx.) We then parameterze t to reflect the U.S. economy and electrcty sector. We consder the ratonale for optmal rebatng when some states regulate carbon emssons whle others do not, as wth the Regonal Greenhouse Gas Intatve. Ths program, n whch northeastern and md-atlantc states are jonng together to develop a regonal cap-and-trade program for CO, represents a good case study for the value of polcy optons (and the costs of constrants) n the face of ncomplete partcpaton. In ths case, the emssons prce sets an equvalent polluton tax, whle the allocaton mechansm allows for the possblty of a rebate, n the form of updatng based on output. Polcy Scenaros Table presents the polcy scenaros evaluated wth the parameterzed model. In addton to the frst-best polcy and the two second-best polces analyzed n the prevous secton, we consder the case of a mandatory 00 percent rebate of the polluton tax n sector. Even though we have demonstrated t s not usually optmal, t s frequently advocated, so an mportant queston s the extent of effcency loss wth ths strategy compared wth other polces. Fnally, we also consder the effectveness of taxng only polluton n sector, wth no other taxes or rebates. We compare the effects of these dfferent polcy constrants on welfare, emssons, and the emssons tax rate. We also explore the relatonshp between substtutablty among the goods and the optmal (constraned) polcy parameters. Model Specfcatons Utlty Though t s not the most general specfcaton, a convenent one for the subsequent numercal analyss s the two-level nested CES utlty functon. For three goods, X, X, and X 3, The majorty of allowance allocaton s up to the dscreton of the states, and the updatng opton s one of several allocaton mechansms beng consdered (Burtraw et al. 005).

15 ts formulaton s µ µ U = [ uz + ( u) X ] µ ν ν, wth = [ vx + ( v X ] ν 3 Z. () ) Ths functon s homogeneous of degree one and separable; although t s not the most general specfcaton, t allows us to capture varous possble relatons of substtutablty and complementarty. The elastctes of substtuton are s = n the global functon and + µ s = n the nest. Note that n ths smple, general equlbrum model, substtutablty s +ν determned relatve to the thrd good. Damages We assume lnear damages: D = ( E+ E )δ. Although margnal damage costs are constant, the value of margnal damages depends on the margnal utlty of consumpton as well. Producton By defnton, the unregulated sector receves no drect prce sgnal for emttng polluton; consequently, t sets ts emssons at a level such that the margnal productvty s always zero. Logcally, emssons must be fnte, whatever the expected producton, and we have to represent ths property n the specfcaton of the producton functon. More precsely, the producton functon must be such that when the polluton prce s zero, labor and emssons become smple functons of the level of producton. The ntuton s that, when the margnal productvty of emssons s always zero, any level of output can be acheved only wth a unque amount of labor and emssons: E = ψ ( Q), and L= ϕ( Q). A farly general specfcaton for a sector producton functon wth the necessary L= αq+ g Q/ E, n propertes s (leavng off the sector ndex subscrpts for the moment) [ ] whch α s a constant and g s a monotonc ncreasng functon of the average product of emssons (the nverse of emssons ntensty). Let m = E / Q represent the emssons rate, so x = In a full-scale trade model (GTAP, for example), the substtuton effect would depend not only on the elastcty of substtuton n the nest, the preference for domestc or mported goods (v n our model), and the preferences and elastctes of substtuton n the utlty functon, but also on multsector general equlbrum effects, ncludng cross-sector complementartes that arse through producton nput relatonshps. dc / dc

16 /m. Let n ( ) = β n + n n gx mx x c, where m s the baselne emssons rate, and β and c are constants. An mportant condton s that the margnal productvty of polluton equal zero at n n fnte emssons; for ths functon, the soluton of g ( x) = nx nx = 0 mples x = / m. The parameter c represents a calbraton adjustment to avod postve profts n the baselne scenaro n ( c = βm /( n) ); n other cases, profts are assumed to be transferred to consumers as shareholders n lump-sum fashon. Then, n the case of no emssons tax, the factor functons for sector reduce to E mq L φq = ; =. (3) The correspondng margnal labor requrement (the nverse of the margnal product of labor) s L m m = α + nβ n Q m Q. (4) The parameter α represents the (constant) drect margnal producton costs (n terms of labor unts needed), whle β shfts those margnal costs upward, to the extent that the emssons rate falls below the zero-margnal-product rate of emssons. The margnal labor requrement arsng from addtonal emssons s L m m = nβ n+ E m Q, (5) whch s negatve for any emssons rate lower than the baselne. For most scenaros the value of β s not very mportant, snce n the absence of an emssons charge n that sector, the term functons lke a resdual n the producton functon and does not affect margnal labor costs. It does, however, matter n terms of relatve welfare losses. Rasng β rases abatement costs n sector, meanng less would be done n the presence of a drect emssons tax. Therefore, the relatve welfare loss from polcy restrctons s decreasng n β. Calbraton We calbrate ths model to represent two electrcty sectors and the rest of the economy. We postulate scenaros n whch some states decde to go ahead wth mandatory carbon controls whle others do not. The partcpatng states are assumed to be those partcpatng n RGGI, ts 3

17 observer states, and Calforna. 3 In our smulaton, X s electrcty producton by those states, X s producton n nonpartcpatng states, and X 3 s everythng else. To focus on the roles of the frst two sectors, n lne wth the theoretcal model, we gnore the emssons of the thrd sector and assume t s clean. As s the case n general equlbrum modelng, the frst step s calbraton to a reference scenaro, whch s here the market equlbrum wthout polluton damages (δ = 0). In Table, the ntal values for output are represented n dollar values, mplyng all ntal prces are normalzed to. Output values are for 00 and orgnate from GTAP, 4 and they are apportoned among RGGI and non-rggi states accordng to the Energy Informaton Admnstraton (EIA 004a), whch also provded emssons rate nformaton. 5 As for the man parameters of the producton functons, we use α = α = and calbrate the functon g(.) wth two studes of carbon constrants on the U.S. electrcty sector usng the Natonal Energy Modelng System (NEMS), EIA (998) and EIA (004b). The former study of the Kyoto Protocol evaluated sx scenaros, gvng sx pars of carbon prces and emssons rates for the electrcty sector. From these results, we estmated that n = 3 represented the best ft for our functon. We then used the more recent study of the Clmate Stewardshp Act, even though t evaluated only two scenaros, to calculate the β parameters, usng the average for the scenaros. 6 Note that these estmates are senstve to the ntal values of output and emssons, so n our senstvty analyss, n whch we consder the effects of dfferent relatve emssons rates, the β parameters also change. We note those central and alternatve assumptons n Table 3. Other key parameters for optmal tax values are the elastctes of substtuton between the goods, as llustrated n Table 4. In the central scenaro, we assume that the elastcty wthn the nest (.e., between electrcty n RGGI and non-rggi states) s a relatvely elastc.0, whle 3 Partcpatng states are Connectcut, Delaware, Mane, New Hampshre, New Jersey, New York, and Vermont; Maryland wll jon them n 007. Observng jursdctons are the Dstrct of Columba, Massachusetts, Pennsylvana, and Rhode Island, plus the eastern Canadan provnces, New Brunswck, and Calforna (http://www.rgg.org/states.htm). 4 https://www.gtap.agecon.purdue.edu/databases/v6/default.asp (accessed /7/06). 5 Certan correctons n ths verson had to be made from the ndvdual state reports n EIA (004a). 6 From the frst-order condton, we get those usng the Kyoto study. = /3/( ). These estmates are also largely consstent wth 4 β τmq m m 4

18 electrcty s a relatve complement to the rest of the economy, wth an nelastc substtuton elastcty of 0.5. We also conduct senstvty analyss for, consderng a less elastc case of 0.75, whch mght be the case wth more nterregonal transmsson constrants, for example, and a more elastc case of 5.0, whch could reflect more compettve nterstate markets. Gven these assumptons, u and v are then calbrated to replcate the baselne (no-polcy) scenaro. Results We present the results, generally expressed n relaton to optmal polcy, n the followng sets of fgures. They show the magntude of tax and welfare dfferences as the externalty cost δ ( Damage Rate ) vares from $0 to $50/MtC. They clearly demonstrate the mportance of the substtutablty between the two commodtes and of the relatve emssons ntenstes for optmal tax and rebate polces. 7 Rebate Rate The rebate rate n sector s the rato of subsdes to polluton tax revenues from that sector (.e., t C / τe ). We see that n the central scenaro, the optmal rebate rate exceeds 40 percent, n large part because the unregulated sector s more emssons ntensve. When the baselne emssons rates are assumed to be equal, the optmal rebate falls well under 00 percent, and when the emssons rates are reversed, makng the regulated sector the greater polluter, the optmal rebate rate falls to the percent range. Fgure depcts the optmal rebate rates as a functon of the margnal damages from carbon emssons for the three emssons rate scenaros. However, the elastcty of substtuton also explans the optmal rebate rate. When the two sectors are not as strong substtutes, the rebate rate falls, as depcted n Fgure. More generally, the less substtutable are the two sectors between each other (relatve to the rest of the economy), the less effcent s a prce dfferental for nducng polluton abatement, because t does not change ther relatve demand as much. s 7 The underlyng assumptons regardng the use of emssons n each producton functon are also mportant, as noted regardng the calbraton of β. 5

19 Emssons Tax Rate Regardng the actual level of taxaton, the dfferences are very small n these smulatons because of the overwhelmng sze of the thrd sector and the assumpton of lnear damages, whch lmt varablty n the value of margnal damages. We note that, relatve to the frst-best case, the constraned optmal emssons tax rate s slghtly hgher when the unregulated sector can be taxed and lower when t cannot. The reason s that the commodty tax helps mantan the effectveness of the emssons tax, whle the rebate encourages electrcty consumpton and lmts the ablty of the emssons tax to encourage abatement. Smlarly, consumpton of the thrd good s slghtly hgher wth the tax on sector and lower n the rebate scenaros, snce electrcty prces fall. Emssons We see these effects reflected n the mpacts of the polcy constrants on emssons outcomes, as portrayed n Fgure 3. Wth each addtonal polcy restrcton, total emssons rse. Note that the opportuntes for sector (the nonpartcpatng states) to cost-effectvely reduce emssons determne the sze of the gap between emssons n the frst-best case and the unregulated sector case. However, the dfference between the other scenaros depends not on these opportuntes but rather on each polcy s ablty to crowd out output from the unregulated sector. Welfare The ultmate queston s how the constrants, gven these optmal responses to them, affect welfare. Fgure 4 depcts the welfare gans from each knd of polcy as a share of total gans from frst-best regulaton. Clearly, polcy constrants are very costly n terms of welfare, and the welfare costs ncrease wth the strngency of the restrctons. The welfare costs are also qute senstve to the degree of the emssons leakage problem. In the central scenaro, the unregulated electrcty sector has a hgher emssons rate than the regulated one. We see n ths example that wth the sngle restrcton of no polluton regulaton for one sector, even wth the opton of commodty taxaton, two-thrds or more of the welfare gans from envronmental polcy are forgone. Removng the opton to tax the unregulated sector drectly, even allowng for rebatng, means that only 0 to 5 percent of the potental gans from envronmental polcy can be acheved. The addtonal constrant of mandatory, rather than optmal, rebatng mposes a relatvely small addtonal loss. Fnally, wth no rebate avalable, no gans can be captured at all; an emssons tax on sector actually reduces welfare, snce t causes emssons to rse n the unregulated sector more than t reduces 6

20 emssons n sector. On the other hand, when the baselne emssons rates are reversed, meanng the regulated sector comprses the more ntense polluters, more of the potental welfare gans can be captured, though stll less than half, even wth the commodty tax opton. Optmal rebatng then offers about a thrd of the potental gans, and no rebatng acheves 0 to 5 percent. Implctly, the welfare costs are ncreasng wth not only the emssons of the unregulated sector, but also the ease wth whch those emssons could be abated n the frst-best scenaro. Although substtuton elastctes certanly play a role, they seem to have much less mpact on the relatve welfare effects of the constraned polces than do the relatve baselne emssons rates. These results sgnal the mportance of allocaton program desgn for the success of the RGGI, as well as the lmtatons of such a program whle ts membershp remans ncomplete. Concluson We have consdered the arguments for allocatng envronmental revenues n the form of output subsdes to affected ndustres. The desrablty of such a polcy depends on the crcumstances of the constrant on polcymakng, the emssons ntensty of the exempt producton, and whether the goods of the regulated ndustry are substtutes for or complements of those of the unregulated ndustry. As usual, the frst-best polcy s always to have a full set of polcy tools. Then the emssons of each ndustry are taxed drectly, and the revenues are refunded n a nondstortng manner to consumers. However, f for some reason the emssons of one of the pollutng sectors cannot be regulated drectly, the next-best response s to tax those emssons ndrectly. A tax should be leved on the output of the unregulated sector, reflectng the extent to whch emssons are ncorporated n ts producton. Meanwhle, a drect tax on the regulated sector s emssons remans n place, and the revenues are agan refunded n lump sum; no rebate s justfed. If taxng the unregulated sector s output s not possble ether, then an output-based rebate to the regulated sector s justfed, but only to the extent that () the goods are close substtutes and () the unregulated sector s pollutng. Requrng that the rebate rate equal 00 percent for the regulated sector represents an addtonal polcy constrant and thus reduces welfare compared wth the prevous scenaro. Obvously, such a requrement s least costly when the optmal rebate rate s close to, as when both the goods and ther emssons profles are smlar. In a complements stuaton, a mandatory full rebate s worse than no rebate at all. In any case, the loss n terms of flexblty for settng the 7

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