Volume Author/Editor: Carlo Carraro and Gilbert E. Metcalf, editors. Volume URL:

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1 Ths PDF s a selecton from an out-of-prnt volume from the Natonal Bureau of Economc Research Volume Ttle: Behavoral and Dstrbutonal Effects of Envronmental Polcy Volume Author/Edtor: Carlo Carraro and Glbert E. Metcalf, edtors Volume Publsher: Unversty of Chcago Press Volume ISBN: Volume URL: Conference Date: June 11â 12, 1999 Publcaton Date: January 2001 Chapter Ttle: Green Taxes and Admnstratve Costs: The Case of Carbon Taxaton Chapter Author: Sjak Smulders, Herman R. J. Vollebergh Chapter URL: Chapter pages n book: (p )

2 3 Green Taxes and Admnstratve Costs The Case of Carbon Taxaton Sjak Smulders and Herman R. J. Vollebergh 3.1 Introducton Implementng envronmental polces through standards, tradable permts, or envronmental taxes alke s far from costless. For nstance, when mplementng an envronmental tax, the tax department has to run a specal unt to enforce and collect taxes and to montor complance. In practce, the costs of mplementng envronmental polces play a sgnfcant role n the choce between polcy optons. The proposals of the European Commsson for a European-wde energy/co 2 tax provde clear examples (Vollebergh 1995). Instead of proposng a totally new tax on CO 2 emssons, the European Commsson employed the close lnkage between CO 2 emssons and the mplct taxaton of carbon by the exstng taxes on energy products (whch are usually ntermedate nputs). Indeed, usng exstng nstruments rather than ntroducng new ones to address new polcy areas may save consderably on admnstratve costs. However, just the mnmzaton of transacton costs mght come at a cost for socety. A strategy based on nput taxes, for example, forgoes the gans that are potentally reaped by a more drect way of taxng the externalty through emssons taxes. Any devaton from the prncple of taxng externaltes at the pont where they arse ntroduces an ncentve to msallocate resources. Thus a trade-off arses between mnmzng transacton costs and drectly nducng ncentve effects. The optmal tax structure has Sjak Smulders s a fellow of the Royal Netherlands Academy of Arts and Scences and s afflated wth CentER, Tlburg Unversty, The Netherlands. Herman R. J. Vollebergh s assstant professor n publc economcs and a research fellow of the Research Centre for Economc Polcy (OCFEB) at Erasmus Unversty Rotterdam. The authors thank conference partcpants as well as Dallas Burtraw, Jan Peters, and especally Don Fullerton for ther detaled comments on an earler draft. 91

3 92 Sjak Smulders and Herman R. J. Vollebergh to balance the burden of complex and expensve-to-run tax systems aganst the ncentves t nduces to nternalze the externalty that t ams to address. Ths paper nvestgates the potental trade-off between admnstratve costs and ncentves of envronmental regulaton, n partcular f the government ams to reduce CO 2 emssons. We analyze how the optmal choce of carbon taxes s affected by the admnstratve costs ncurred by the regulator (government). Usng a smple model, we determne the optmal rates for emssons and nput taxes n the presence of admnstratve costs and whch of these taxes should optmally be ntroduced. Moreover, we explore and nterpret the scarce emprcal evdence on admnstratve costs of taxaton n the lght of optmal carbon taxaton. Because emprcal nformaton on the role of mplementaton costs n the desgn of envronmental polcy s almost entrely lackng, we concentrate on what factors mght be expected to determne those costs, based on studes of admnstratve costs outsde the envronmental polcy area. Although most formal analyss of envronmental regulaton gnores admnstratve costs, complance costs, or transacton costs n general, a growng lterature takes these ssues serously (see the overvew n Krutlla 1999). 1 Several papers recognze that admnstratve costs may be mportant and rule out the use of emssons taxes on these grounds. Typcally nvestgated s whch taxes could best replace or approxmate emssons taxes (Smth 1992). Moreover, under some crcumstances other taxes or tax combnatons are equvalent to perfect emssons taxes (.e., emssons taxes n a world wthout transacton costs). For nstance, Xepapadeas (1999) revews the condtons under whch nput taxes and emssons taxes are equvalent. Eskeland and Devarajan (1996) show how the combnaton of mandated technology and output taxes approaches the deal emssons tax. Fullerton and Wolverton (1997) propose to combne output taxes and subsdes on clean goods, or more general two-part nstrument systems of a depost-refund nature, to replace the emssons tax that nvolves costly montorng. The mplct assumpton n these papers, however, s that emssons taxes are prohbtvely costly to admnster and that other taxes have neglgbly low admnstratve costs. We extend ths approach by more explctly takng nto account the admnstratve costs of all types of taxes, wthout assumng beforehand that emssons taxes are always the most costly type of tax from the admnstratve pont of vew. In partcular we allow dfferent tax nstruments to feature dfferences n admnstratve costs, whch, n addton, are endogenously dependent on the tax rates (cf. Ytzhak 1979). Once other taxes, as well as emssons taxes, are subject to sgnf- 1. The relaton between taxaton n general and transacton costs s more wdely analyzed; see Slemrod and Ytzhak (1998) for an overvew.

4 Green Taxes and Admnstratve Costs: Carbon Taxaton 93 cant admnstratve costs, t becomes unlkely that the frst-best optmum can be reached. Hence, alternatve tax systems should be consdered that are no longer equvalent to perfect emssons taxes. Shortle, Horran, and Abler (1998) research to what extent nput taxes can approach perfect emssons taxes f not all nputs that drectly affect emssons can be taxed. We extend ther analyss by explctly takng nto account admnstratve costs and allowng for the smultaneous use of emssons and nput taxes. We fnd that a mxed tax system mght be (second-best) optmal. Schmutzler and Goulder (1997) arrve at a smlar result usng a model of mxed output and emssons taxaton that ncorporates montorng. We complement ther analyss by nvestgatng nput taxaton and by explorng n more detal how optmal tax rates n the presence of admnstratve costs dffer from Pgouvan taxes. Admnstratve costs n our model manly represent costs stemmng from montorng, and thus our paper s related to the lterature on montorng and enforcement of envronmental polcy (see Cohen 1998 for a survey). Because we are prmarly nterested n optmal taxaton rather than optmal montorng, we do not model montorng n an explct way. The theoretcal part of ths chapter s also closely related to Fullerton, Hong, and Metcalf (chap. 1 n ths volume). The two chapters complement one another n varous respects. Both chapters compare deal emssons taxes wth alternatve taxaton, but they dffer wth respect to the producton structure and the government budget constrant. Frst, Fullerton, Hong, and Metcalf analyze a model n whch there s a one-to-one correspondence between nput use and emssons. Input taxes and emssons taxes are therefore equvalent, but output taxes provde an (mperfect) substtute form of taxaton. In contrast, our model separates nput use from emssons, and consders abatement explctly. Accordngly, we allow for three ways to reduce polluton: output reducton, nput reducton, and abatement. We study nput taxaton as an (mperfect) substtute for emssons taxes. Second, whereas Fullerton, Hong, and Metcalf consder a second-best world wth a dstortonary labor tax for revenue-rasng purposes, the second-best nature of the polces consdered here arses because of admnstratve costs. Thus, the present chapter abstracts from tax-nteracton effects due to recyclng effects. The structure of our paper s as follows. Frst, we explan the nature of the trade-off nvolved f the mplementaton costs of correctve taxes, n partcular admnstratve costs, are consdered explctly. Second, we analyze a stylzed model that ncorporates both emssons and nput taxes to sort out crtcal determnants that shape ths trade-off. Fnally, we evaluate both explct and mplct carbon taxaton n Organzaton for Economc Cooperaton and Development (OECD) countres n terms of the trade-off and suggest some opportuntes for welfare-mprovng carbon tax polces. Note n advance that taxng carbon nputs s not equvalent to taxng CO 2

5 94 Sjak Smulders and Herman R. J. Vollebergh emssons, as s sometmes suggested. Although a close lnkage exsts between the carbon content of energy products and CO 2 emssons, ths s not a fxed chemcotechnologcal relatonshp because several opportuntes for carbon abatement or removal exst (Okken et al. 1992). 3.2 The Trade-off between Incentves and Admnstratve Costs In ths secton we argue that the admnstratve costs argument per se s not suffcent to rule out the mplementaton of emssons taxes. In the presence of admnstratve costs, the costs and benefts assocated wth each specfc type of tax should be compared. Frst, we hypothesze whch factors nfluence the shape of the admnstratve-costs curve. Next, we show why admnstratve costs ntroduce such a general trade-off between the costs and benefts of varous mplementaton strateges. We also develop some useful termnology Admnstratve Costs We defne transacton costs as the costs assocated wth tax assessment, collecton, and enforcement; and all other costs ncurred by any party to enable, facltate, and ensure transactons from taxpayers to tax authortes (Vollebergh 1995). An alternatve term that we use s mplementaton costs. The terms nclude ex ante costs (e.g., costs of excluson) and ex post costs (e.g., montorng costs). It s common to categorze these costs further nto costs for the government (tax recever), or admnstratve costs, to handle forms and enforce complance, and the costs for the tax-lable agent (taxpayer), or complance costs, to carry out the oblgatons of calculatng and payng the tax (see Sandford, Godwn, and Hardwck 1989). In our analyss we concentrate on admnstratve costs. 2 Admnstratve costs of a partcular tax are closely related to the base to whch the tax s appled. The tax base usually vares wth the type of tax. For example, an emssons tax taxes the physcal volumes of hazardous substances, whle an nput tax taxes such substances ndrectly, for nstance through ther use as (ntermedate) nputs. In turn, these dfferences nduce both tax authortes and taxpayers to set up and mantan varous systems for collectng and processng nformaton about the tax, that s, to record how much s emtted or how much nput s used, n order to be able to calculate the total tax payments due. One mportant characterstc of the tax base that determnes (dfferences n) admnstratve costs s the number of agents lable for the tax. A large number of taxable legal unts mples a large mplementaton cost for the 2. Secton 3.4.2, however, shows that admnstratve and complance costs turn out to move together n practce; that s, taxes for whch complance costs are relatvely mportant are also assocated wth relatvely hgh admnstratve costs.

6 Green Taxes and Admnstratve Costs: Carbon Taxaton 95 tax agency, snce each unt requres separate treatment. Taxng a partcular pollutant that s emtted by many producers may be assocated wth large admnstratve costs. Taxng the nputs from whch the pollutant arses as a by-product may be assocated wth sgnfcantly lower admnstratve costs. For nstance, nputs need no longer be taxed at the ponts of consumpton, but can also be taxed at the pont of delvery, such as gas statons or dstrbutors of electrcty. Hence, swtchng from emssons to nputs as the tax base could change admnstratve costs. Note that the dfference n admnstratve costs s ndependent of the nduced regulatory effect. It s a dfference n the fxed-cost component of admnstratve costs, that s, the setup cost and part of the cost to run the nformaton system. Each lable unt submts ts own tax form. The cost of processng forms depends on the number of forms rather than the tax amount due. Nevertheless, ths stll leaves the possblty of economes of scale for a gven type of tax. If the tax base can be broadened across a larger number of taxpayers, the overall admnstratve costs per taxpayer can be reduced. A second mportant determnant of admnstratve costs s measurablty of the base. In most cases emssons levels are lkely to be more dffcult to measure, report, and record than nput or output levels. Heterogenety across ndustres and ther technologes compounds the complexty of a tax system. For nstance, a tax base n terms of weghted unts of measurement, rather than n terms of a sngle unt, may be expected to create hgher admnstratve costs f frms use hghly frm-specfc technologes. One well-known example s NO X emssons from road transportaton, whch depend on vehcle type, equpment, fuel type, drvng patterns, and so forth (see also Hoel 1998, 89). Admnstratve costs are also lkely to vary wth the tax rates and the revenue rased. The possblty of evason by taxpayers requres montorng expendtures by regulators. The remark by Fullerton (1996, 7) that many of the admnstratve costs are fxed costs of calculatng the tax base, not margnal costs of collectng more revenue by rasng the rate of tax on a gven tax base seems to call for a qualfcaton n ths respect. The larger the tax bll, the larger are the ncentves to evade tax payment and the more attractve t s for the regulator to spend resources to reduce tax evason. Regulators usually have varous strateges for montorng and need to sort out the effcent choce of montorng levels and technques. A large lterature on montorng and enforcement studes ths polcy n detal (Cohen 1998). Here, we do not need ths level of detal. Wth respect to envronmental montorng, we can safely assume that when the optmal mx of montorng nstruments s chosen, total cost of montorng ncreases wth the number of polluters, the varety of producton and abatement technques used, the mportance of stochastc nfluences on actual polluton, and the dffculty of measurng emssons. To sum up, no general shape can be assumed ex ante for dfferent types

7 96 Sjak Smulders and Herman R. J. Vollebergh of taxes. However, t seems frutful to assume that both fxed and varable costs (varyng wth the tax rate) play a sgnfcant role. Both n theory and practce, we need a case-by-case approach to study the nature and mplcatons of admnstratve costs The Role of Lnkage The effcency of nstruments to reach a certan polcy goal s usually defned n terms of the extent to whch the nstrument ncreases socal welfare. The most effcent nstrument to ht a gven target has the smallest gross welfare cost, where gross welfare cost 3 refers to the change n welfare apart from that arsng from the reducton n the externalty. 4 In a frst-best world wthout transacton costs, dfferent nstruments can be ranked n terms of effcency by nvestgatng ther effect onprvate welfare. Thngs become more complcated n a world wth transacton costs because both admnstratve costs and the lnkage between regulatory am, emssons reducton, and the type of regulatory tax used play a role (Smth 1992). 5 Frst of all, dfferent types of taxes usually dffer wth respect to the drectness of the ncentve they provde to reduce emssons (assumng emssons reducton reflects the goal of the government). Lessdrect taxaton of the margnal damages caused by an ndvdual polluter causes an effcency loss, but may lower admnstratve costs. Furthermore, dfferent nstruments dstort prvate welfare not only drectly, but also ndrectly through ther mplcatons for transacton costs. The usual gross welfare cost of taxaton has to be supplemented by the transacton costs of the tax. Before turnng to how welfare analyss of envronmental taxaton s nfluenced by transacton costs, t s useful to clarfy our termnology and make t precse. We explctly separate the transacton costs from the total change n welfare assocated wth the use of a certan (tax) nstrument. Hence, n our case of envronmental taxaton, we dstngush (1) admnstratve (transacton) costs, (2) the welfare gan from an mprovement n the envronment, (3) the resdual welfare change, that s the gross welfare cost gnorng transacton costs. The thrd component s called here prvate gross welfare cost. An nstrument that has relatvely low prvate gross welfare 3. The term gross welfare cost s from Goulder (1995). 4. Ths defnton apples to correctve taxes. The gross welfare cost n the case of revenue rasng can be smlarly defned as the change n welfare apart from that arsng from relaxng the government budget constrant. 5. There s an nterestng analogue between the current paper and the long-standng ssue n envronmental economcs of selectng nstruments to mprove ambent qualty drectly or ndrectly through the reducton of emssons. It s well known that the lnkage between emssons and ambent qualty s often ndrect, but the cost of ambent-qualty regulaton can be prohbtve. Thus an nterestng trade-off exsts between the utlty loss n terms of the drectness of lnkage, on the one hand, and the cost of regulaton, on the other hand. We owe ths pont to Dallas Burtraw.

8 Green Taxes and Admnstratve Costs: Carbon Taxaton 97 costs s called relatvely prvately effcent. Of course, n a world wthout transacton costs, effcency just concdes wth ths noton of prvate effcency, snce gross welfare costs do not contan transacton costs. 6 Thus, the relatve effcency of dfferent types of taxes can be measured wth the followng formula: (1) U = Y T D( E), where U s socal welfare of the representatve agent, Y s gross prvate welfare, T s the welfare loss due to transacton (admnstratve) costs, and D s the damage from polluton. Let t 1 and t 2 be two dstnct tax regmes that yeld the same aggregate emssons: E(t 1 ) E(t 2 ). The prvate costs of t 1 are lower than those of t 2 f Y(t 1 ) Y(t 2 ). We do not need to dscuss extensvely the determnants of prvate effcency here, snce they are well known from analyses wthout transacton costs. For example, the effcency of a tax to nternalze polluton externaltes s larger f the ndvdual s tax bll s more drectly lnked to the externalty. Hence, emssons taxes are more (prvately) effcent than nput taxes. Also, effcency requres that the effectve tax rate on margnal contrbutons to damage (D) s equal across polluters. Hence, an emssons tax that apples to all polluters s (prvately) more effcent than an emssons tax wth exemptons or a nonunform emssons tax. As noted n secton 3.1, t s often argued that emssons taxes are too costly to mplement and that admnstratve costs provde a basc motvaton for other (tax) solutons. 7 However, nstead of smply assumng that such a shft away from emssons taxes s optmal, we am at explctly dervng such a concluson wthn a comprehensve welfare framework. A frst step n ths drecton has been taken by McKay, Pearson, and Smth (1990), who hypothesze that a clear trade-off exsts between shfts n the tax system to save on transacton costs, on the one hand, and tax reforms that harness ncentves and promote (prvate) effcency, on the other hand. They assume that regulaton that s lnked less drectly to the externalty does ndeed save on admnstratve costs, but that t comes at a cost to socety by dstortng prvate decsons more. Fgure 3.1 llustrates ths. The horzontal axs measures varous tax systems wth respect to the drectness wth whch they address ncentves to reduce damage; for example, an emssons tax ranks hgh and an nput tax 6. We realze that ths term mght be msleadng, snce transacton costs also affect (ultmately) prvate welfare. However, the term captures the fact that we focus on admnstratve costs that frst affect the tax authorty (and not prvate agents drectly). Indeed, of the three terms n equaton (1), only the frst (Y) captures drect changes n prvate welfare. The thrd term, the envronmental gan, s a publc component of the welfare change f the envronment s assumed to be a publc good. Alternatvely, we could have used the terms frctonless gross welfare cost and frctonless effcency. 7. In fact, Smth (1992) shows that the basc dea can be traced back to the semnal paper of Damond (1973).

9 98 Sjak Smulders and Herman R. J. Vollebergh Fg. 3.1 The basc trade-off between transacton costs and the effcency of nternalzaton of tax systems ranks low. Taxes on dfferent nputs rank dfferently, dependng on the closeness of the lnkage between nput use and emssons subject to regulaton. The vertcal axs measures two components of utlty. The fgure compares a contnuum of tax systems. It s assumed that all of them yeld the same level of damage D by approprate choce of tax rates. The two curves represent the other two components of overall utlty, transacton costs T and prvate utlty Y, for each of the tax systems. Admnstratve costs T ncrease when taxaton s better lnked to emssons. The dea behnd ths s that more-drect taxaton mples fewer lnks to already exstng procedures of the exstng tax system. Gross prvate welfare Y also ncreases wth the lnkage of taxaton to emssons. The more drect the taxaton, the larger the (prvate) utlty s for a gven level of emssons. The optmal tax system balances transacton costs and effcency. In the fgure, welfare s maxmzed by an ndrect tax that corresponds to ponts A and B. The complete swtch to emssons taxes s too costly: The assocated ncrease n admnstratve costs would outwegh the gans from havng a moredrect tax wth better ncentves. Fgure 3.1 s hypothetcal and suggestve. As noted before, we have to assess tax proposals case by case. For example, f margnal admnstratve costs ncrease only slowly, emssons taxes may be optmal despte the presence of admnstratve costs. Moreover, t s not at all guaranteed that the curves T and Y have nce convex and concave shapes, respectvely. Smulders and Vollebergh (1998), for nstance, represent the lnkage to polluton by the fracton of (symmetrcal) sectors that s lable to an emssons tax and fnd that n a very smple settng the Y curve frst declnes and then ncreases. In general, admnstratve costs ntroduce nonconvextes because of ther fxed-cost nature, and the conventonal margnal approach to optmal taxaton has to be extended. Admnstratve costs have many dmensons. The government may affect

10 Green Taxes and Admnstratve Costs: Carbon Taxaton 99 admnstratve costs by varyng the number of frms or sectors subject to the tax, the tax rates chosen for nput and emssons taxes, the accuracy of measurablty amed for, the enforcement spendng to reduce the (probablty of) tax evason, and so on. Each of these dmensons can be measured along the horzontal axs n a fgure smlar to fgure 3.1. Needless to say, each of these factors drectly nfluences the overall welfare effect of mplementng envronmental taxes. It s not only the multdmensonalty of admnstratve costs that makes the smple dagram n fgure 3.1 problematc. As Feldsten (1976) ponted out long ago, a dstncton should be made between the desgn of a tax system de novo and the reform of an exstng tax system. Ths s true for ts assocated admnstratve system as well. Indeed, n practce every tax reform starts from a gven tax and admnstratve system nherted from the past. Ths system determnes the (short-run) scope of welfare-mprovng tax reform at low admnstratve cost (Smth 1992; Vollebergh 1995). For nstance, ncreasng exstng taxes rather than ntroducng new taxes mght save on the fxed costs of admnstraton and therefore on total admnstratve costs. It s also attractve to explot such economes of scale and scope when desgnng envronmental taxes. Levyng envronmentally motvated taxes on a base that s already taxed for other purposes, rather than ntroducng an entrely new emssons tax, would certanly save on admnstratve costs. Furthermore, economes of scope wth the admnstratve system used for other regulatory nstruments may also arse. When mplementng envronmental taxes, the regulator could beneft from experence n related admnstratve procedures for operatons already undertaken. As does Smth (1992), we label ths use of exstng admnstratve procedures and experence for new purposes pggybackng. 3.3 Crtcal Determnants Shapng the Trade-Off Ths secton develops a smple model along the lnes of Kaplow (1990) and Shortle, Horan, and Abler (1998) to compare emssons taxes and nput taxes n the presence of admnstratve costs. The am of the regulator s to correct externaltes from polluton. The presence of admnstratve costs mples that the regulator should devate from the frst-best Pgouvan tax. Hence, admnstratve costs n themselves cause polces to be second best. We abstract from other second-best ssues. In partcular, we assume that lump-sum taxes and transfers are avalable to the government, so that there s no revenue requrement that affects tax rates and we can gnore labor taxes We also abstract from output taxes and abatement subsdes. See Smulders and Vollebergh (1999) for the nteracton between these nstruments and admnstratve costs.

11 100 Sjak Smulders and Herman R. J. Vollebergh The Model We assume a gven number of heterogenous sectors, ndexed. The producton of one unt of fnal output q requres labor l and a sngle homogenous ntermedate nput x (n amount x ). Moreover, frms can spend labor servces on abatement a, whch reduces emssons per unt of output e. The mnmum labor requrement per unt of output equals l (x ). Labor and nputs are substtutes: l l / x 0. Emssons per unt of output depend negatvely on abatement effort and postvely on nputs: e (a,x ) wth e a e / a 0ande x e / x 0. 9 Fnal-good producers face a (sector-specfc) emssons tax and a (perunt) nput tax (t x ). Perfect competton prevals, and frms take the output prce p as gven. They maxmze profts by choosng output, abatement, and nput levels. We normalze the wage to unty. The frst-order condtons can be wrtten as (2) p = l + a + e + ( p + t ) x, x x (3) 1 ( e ) wth equalty f a > 0, a (4) p + t + e l wth equalty f x > 0. x x x Equaton (2) says that prce equals cost, whch n turn equals labor cost for producton, labor cost for abatement, and taxes due per unt of output. Condton (3) states that wth postve abatement levels, the margnal cost of abatement (on the left-hand sde) equals the margnal benefts n the form of a reducton of emssons tax payments (on the rght-hand sde). Condton (4) equates the margnal cost to the margnal benefts of nput use. Margnal nput costs consst of the prce of the nput p x, the sectorspecfc nput tax t x, and the nduced addtonal emssons tax payments. Margnal benefts consst of the labor savng n producton. The ntermedate good s produced wth labor only and subject to constant returns to scale. We choose unts such that one unt of labor produces one unt of the ntermedate good. For smplcty we assume that the producton of the ntermedate nput s nonpollutng (but ths can be easly modfed n a way that s completely analogous to polluton n the fnalgoods sector). Intermedate-good producers face a prce p x, whch they take as gven. Hence, ther frst-order condton for proft maxmzaton smply states that the prce equals the wage, whch s normalzed to 1: (5) p x = Furthermore, e xx 0, e aa 0, and l 0. We ensure concavty by assumng [l ( e a ) e xx ]e aa ( e a )(e ax ) 2 0.

12 Green Taxes and Admnstratve Costs: Carbon Taxaton 101 Equlbrum n the market for the nput requres 10 X = xq, where X s total supply of the ntermedate good. We mpose a very smple demand structure by choosng a quas-lnear utlty functon wth no cross-demand effects, and where the opportunty cost of labor s constant (and normalzed to 1). The utlty functon s (6) u = u( q) + l D( E), where l 0 s lesure, D s damage from emssons, and E s aggregate emssons defned as (7) E = eq. Consumers take prces and emssons as gven and maxmze utlty, subject to ther budget constrant p q L l 0 Z, where Z are transfers from the government. The frst-order condtons read (8) u = p 0. The government collects tax revenue, pays cvl servants for the tax admnstraton (T ), and rebates the remander of tax revenue to households n a lump-sum fashon (Z ). The tax admnstraton employs T unts of labor at wage w 1. The requred admnstratve costs are sector specfc and depend on sectoral taxes and output levels. 11 (9) T = F( I, I ) + V(, t, q), tx x where F represents the fxed costs of the tax system, and V represents the admnstratve costs varyng wth the sze of the rates and bases of the tax system. Fxed costs are determned only by certan taxes beng mplemented or not. Ths s modeled by the dependence of F on ndcator functons I tˆ, each of whch takes the value 1 f tax tˆ (e.g., ) s postve and the value 0 f the tax s 0. The natural restrctons we mpose are sgn V t sgn tˆ for any tax tˆ, that s, both taxes and subsdes are costly to mplement; and V (0, 0, q ) 0, that s, all fxed costs are excluded from V( ). The labor market clears. Labor endowment s fxed and gven by L. Hence, we wrte (10) L = l0 + ( l + a + x) q + T. 10. To smplfy notaton, all summaton sgns refer to summaton over all fnal goods sectors, unless stated otherwse. 11. Note that by assumng lnear sectoral separablty we gnore economes of scope as dscussed n secton 3.2.

13 102 Sjak Smulders and Herman R. J. Vollebergh Substtutng equatons (7) and (10) nto (6), we may wrte utlty as (11) U u( q) L ( l a x ) q T D eq. = ( ) Totally dfferentatng utlty, and substtutng the frst-order condtons for frms and households maxmzaton problems (2), (3), (4), (5), and (8), we obtan (12) du = t dx dt ( D ) de, x where E e q s total emssons n sector and X x q s total nput use n sector. Equaton (12) shows the welfare effects assocated wth changes n nput demands, transacton costs, and envronmental qualty. The frst term on the rght-hand sde of (12) stands for the dstortonary effect of excses on the goods market assocated wth nput taxes. The last term reveals that a reducton n emssons ceters parbus mproves utlty as long as the margnal damage s larger than the emssons tax Optmal Taxaton We can rewrte equaton (12) to separate the three components of welfare, as n equaton (1): (13) du = [ de + t dx ] dt D de. x Equaton (13) categorzes the welfare effect of any polcy n the three components mentoned n secton The bracketed term on the rght-hand sde s the prvate gross welfare effect of the polcy, denoted by dy, n lne wth equaton (1); dt s the transacton costs of the polcy; and D de dd s the envronmental welfare gan. Note that the prvate gross welfare cost s a tax-base effect; the change n each tax base tmes the tax rate correspondng to that tax base together determne ths effect. 12 In the presence of admnstratve costs, a necessary condton for optmalty of the tax system s that the expresson n (13) be 0. The government maxmzes welfare, takng as gven the reactons of households and frms to changes n taxes. It faces a two-stage decson problem: (1) decdng whch taxes to use (tax-base decson), and (2) settng the approprate tax level (tax-rate decson). Concernng the tax-rate decson, we fnd condtons for optmal taxaton by rewrtng equaton (12) n terms of the total dervatves wth respect to each of the taxes and settng these expressons equal to For any tax tˆ ths condton reads 12. See the analyss n Bovenberg and Goulder (1998, sec. 3.1). 13. Note that equatons (2), (3), (4), (5), and (8) allow us to determne how a, x, q, p, and p x and hence also l (x ), e (a, x ), E, X, T, andu depend on the tax rates.

14 Green Taxes and Admnstratve Costs: Carbon Taxaton 103 (14) du dtˆ dx de dt = t x ( D ). dtˆ dtˆ dtˆ = 0 Ths equaton bnds only f the tax s mplemented; that s, equaton (14) gudes the tax decson, condtonal on the tax beng mplemented. Concernng the tax-base decson, the regulator should compare utlty levels assocated wth any combnaton of taxes mplemented at the rate mpled by equaton (14). The optmal tax system may nclude nonzero taxes, set at the level mpled by equaton (14), as well as zero taxes, that s, taxes that are not mplemented. For the latter taxes, equaton (14) may be volated, that s, utlty may margnally ncrease n ths tax. Yet t s optmal not to mplement these taxes. The reason s that, by constructon, n an optmally desgned tax system settng any zero tax at the level mpled by (14) and adjustng all nonzero tax rates such that they satsfy (14) decreases welfare (nonmargnally) because of fxed admnstratve costs. Smlarly, n an optmally desgned tax system, swtchng the rate of any nonzero tax from the rate mpled by (14) to a zero rate and adjustng all other nonzero taxes such that they satsfy (14) decreases welfare (nonmargnally). Snce fxed admnstratve costs play a role, the tax-base decson s subject to nonconvextes and no smple smooth optmalty condton can be wrtten. Instead of optmzng the overall tax system, a more practcal ssue s to fnd a welfare mprovng tax reform. Such an approach takes nto account the fact that actual changes to the tax system are usually slow and pecemeal due to the role of the exstng tax system (Feldsten 1976) and, as we lke to add, ts assocated admnstratve costs. A change n an exstng tax system s worth pursung f ths change entals an ncrease n welfare even f the maxmum level of welfare s not reached. In partcular, we are nterested n the welfare effects of the ntroducton of a new tax, f some taxes already exst (as well as ther assocated tax admnstraton). The obvous rule for a welfare-mprovng ntroducton of a new tax s that the net welfare gan from explotng the newly ntroduced tax should exceed the fxed costs of ntroducng the tax. For any tax tˆ, ths condton can be wrtten as 14 (15) ˆ* ˆo t = t f 0 tˆ o du ˆ, dtˆ dt F t where tˆ o s the level of the tax that corresponds to equaton (14) (.e., the soluton to du/dtˆ 0, or the corner soluton 0), F t dt/di(tˆ) s the fxed cost (admnstratve setup cost) assocated wth ntroducng tax tˆ, tˆ* s the 14. Ths condton can be called the entry condton, analogous to ndustral organzaton models where frms enter f the operatng profts (cf. welfare), measured at the optmal prce (cf. tax), exceed the entry cost (cf. tax ntroducton/setup cost).

15 104 Sjak Smulders and Herman R. J. Vollebergh (second-best) optmal tax rate, 15 and we evaluate all total dervatves, takng nto account changes n other taxes so as to satsfy (14) for all other taxes. As a benchmark, consder the (frst-best) case wthout transacton costs, that s, T dt 0. As s well known, the optmal emssons tax then equals the margnal damage D n each sector and all other taxes should be Ths can be mmedately seen from equaton (12). Indeed, equaton (14) s satsfed for these tax rates. Under the usual condtons on utlty and producton functons, the tax-base optmalty condton s automatcally met snce fxed costs do not play a role and the maxmzaton problem s convex. Startng from a stuaton wthout any taxes, ntroducng the emssons tax mproves welfare. 17 The frst-best outcome may be realzed n some specal cases even f transacton costs play a role. Obvously, f transacton costs are assocated wth other taxes, but not wth emssons taxes, the Pgouvan tax should stll be mplemented. The other way around, f transacton costs apply to emssons taxes only and other taxes can be mplemented wthout such costs, a frst-best outcome may arse provded that other taxes (or tax combnatons) are equvalent to emssons taxes wth respect to ther ncentve effects (prvate effcency). For example, f the emssons-nput rato s fxed, an nput tax can brng about the frst-best outcome. 18 A second-best stuaton arses when other taxes also nvolve transacton costs or when other nstruments are prvately less effcent than emssons taxes. Once transacton costs play a role, t s no longer guaranteed that emssons taxes should be unform, nor that output or nput taxes should be excluded. Most of the lterature on second-best optmal envronmental taxaton concentrates on cases n whch other taxes (taxes on outputs or nputs) can replace emssons taxes wthout loss of ncentves and wthout admnstratve costs (e.g., see the double dvdend lterature; de Mooj 2000). If admnstratve costs are mentoned as a reason not to use emssons 15. To be precse, tˆ* s the tax that maxmzes welfare gven the set of taxes employed; tˆ* 0 f equaton (15) s volated. 16. Solvng the socal-planner problem for the case wthout transacton costs, we fnd the followng optmalty condtons: (1) u l a x e D, (2) 1 e a D wth equalty f a s postve, (3) 1 l e x D wth equalty f x s postve. Comparng these condtons to equatons (2), (3), (4), (5), and (8), we fnd that D, t x 0 mplements the frst-best outcome. As a specal case, f e a 0ande x e /x, any combnaton of taxes that satsfes (x /e )t x D also mplements the frst-best socal optmum (nput taxes and emssons taxes are equvalent, cf. sec ). 17. For ths case du/d reduces to ( D )de /d, whch s postve for D. Hence, the left-hand sde of the nequalty n (15) s postve whle the rght-hand sde s 0, and (15) s satsfed. 18. Smlarly, two-part nstruments may do the job. If only one pollutant causes an externalty and f all other outputs and nputs can be taxed at zero transacton costs, the frst-best outcome can be reached (see Fullerton and Wolverton 1997). In the present model, ths would requre (sector-specfc) taxes on output and nput use and a (sector-specfc) subsdy on abatement. Note, however, that optmalty breaks down when more pollutants play a role.

16 Green Taxes and Admnstratve Costs: Carbon Taxaton 105 taxes, the most common case n the lterature s the one n whch emssons taxes are too costly to mplement because of the transacton costs assocated wth emssons taxes but not wth other taxes (the most dscussed case s nonpont polluton; see Xepapadeas 1999). Our model allows for more subtle mpacts of admnstratve costs by consderng admnstratve costs throughout the entre tax system and takng nto account that admnstratve costs may endogenously vary wth tax rates. To nvestgate these n more detal, we consder some specal cases Pure Emssons Taxes Let us frst focus on emssons taxes by consderng the case n whch all other taxes are ruled out. Note that we cannot smply suppose that only emssons taxes are used; we have to explan wthn the model why ths s so. We gve ths explanaton n subsecton and concentrate here on the optmalty condtons for emssons taxes only. Evaluatng equaton (14) for an emssons tax n sector, we fnd that the followng optmalty condtons should hold: du dt de (16) = ( D ) 0 wth equalty f > 0. d d d Hence, f mplemented, the optmal emssons tax reads (17) o dt/ d = max 0, D. de / d Ths tax should be mplemented f the total welfare gan exceeds the fxed admnstratve costs; see equaton (15). We approxmate the welfare gan by a second-order Taylor expanson, evaluated at o. The optmal tax * s gven by o 1 de o dt (18) * f 2 o = ( ) + ( E + T ) F, 2 d d * = 0 otherwse, where E and T are the postvely defned elastctes of de/d and dt/d wth respect to. Condtons (17) and (18) reveal two cases n whch t s optmal not to use emssons taxes n a partcular sector because of admnstratve costs. The frst case s the case n whch the fxed costs of admnsterng the tax are large relatve to the total potental gans; see equaton (18). The gans are small ndeed f emssons are nsenstve to the emssons tax, that s, f abatement and changes n the nput mx are expensve (de /d small), f the margnal damage (D ) s small, and f margnal admnstratve costs (dt/

17 106 Sjak Smulders and Herman R. J. Vollebergh Fg. 3.2 The optmal second-best tax rate for an emssons tax wth (A) low and (B) hgh transacton costs d ) are large. 19 A second case n whch a sector should be optmally exempted from an emssons tax s the case n whch margnal admnstratve costs for the sector are relatvely large, such that, for any small ncrease n the sector-specfc emssons tax, hgher admnstratve costs more than offset gans from the nduced emssons reducton (du/d 0 for any so that o 0). Fgure 3.2 llustrates the case of emssons taxes n terms of the tradeoff between effcency and admnstratve costs (see secton 3.2). Prvate gross welfare, Y, s maxmzed for zero emssons taxes, snce, loosely speakng, emssons taxes mpede free-market forces. However, they reduce damage D and hence mprove socal welfare. In a frst-best world wthout admnstratve costs, the Pgouvan tax ** maxmzes welfare Y D. In the presence of admnstratve costs T, the gross welfare cost of emssons taxaton (.e., the effect on U D) s hgher and rses more steeply wth tax rates. The (second-best) optmal tax maxmzes Y T D, and t can be easly seen that ths tax s below the frst-best tax. In panel B of fgure 3.2, transacton costs rse steeply wth the tax rate, and the fxed-cost component s large. As a result, the second-best optmal emsson tax s 0. How emsson taxes should be optmally dfferentated across sectors s also revealed by condton (17), condtonal on beng mplemented. Note that the optmal tax equals margnal damage mnus a correcton term that s proportonal to margnal admnstratve costs. The optmal tax equals the Pgouvan tax f margnal admnstratve costs are 0 (dt/d 0). The gap between optmal taxes and the Pgouvan tax wdens f admnstratve costs rse steeply wth tax levels and f emssons are not very senstve to emssons taxaton. The second may arse because of a low elastcty of demand (t s hard to accomplsh emssons reductons by cuttng demand) or because the emssons ntensty s not very senstve to emssons-tax changes (steeply rsng abatement and nput substtuton costs). To clarfy 19. To see ths, substtute equaton (17) nto (18).

18 Green Taxes and Admnstratve Costs: Carbon Taxaton 107 ths, we decompose the emssons-reducton effect of the tax, whch appears as the denomnator n (17), nto these three effects: de (19) = ε + + ξ, d where (20) ε dq d e = dq dp ee, (21) = qe da, d a (22) ξ = q e x dx d, exx (23) =. e That s, ε represents the effect of emssons taxes on emssons through changes n demand, measures the drect effect of emssons taxaton on emssons through abatement, and measures the analogous effect through nput reducton (the reason to separate and becomes clear n subsecton 3.3.4). So far, we have assumed that admnstratve costs rse wth tax rates because ncentves to evade ncrease wth the tax rate, thus rasng the cost for the tax authorty to admnster the tax. The opposte, however, s possble as well. Usng a partal equlbrum model, Polnsky and Shavell (1982) fnd that the optmal emssons tax n the presence of admnstratve costs may be larger than the Pgouvan tax. The argument s that a hgher emssons tax saves on transacton costs f admnstratve costs depend on the number of taxpayng frms and f an ncrease n the emssons tax reduces market demand and the number of frms. In our setup, the number of frms s ndetermnate because of the constant-returns-to-scale producton functons, but the equaton mmedately shows that Polnsky and Shavell s result also apples here f admnstratve costs decrease wth the tax rate, that s, f dt/d Input Taxes: The Role of Lnkage To nvestgate the trade-off between emssons taxes and nput taxes, we frst consder sector-specfc taxes on emssons ( ) and on the use of nput x (t x ). Evaluatng equaton (14) for these taxes, we fnd Note that (x /e ) 2 (ε ) dx /dt x and (x /e )(ε ) de /dt x dx /d.

19 108 Sjak Smulders and Herman R. J. Vollebergh o (24) (25) t where = D dt/ d ε + ξ x x e t max 0,, ε ξ ε ξ o x (26) e + dt dtx = D x + ( ε ξ / ) ε ξ ( x/ e)( ε + ξ ), 1 e dx/ dt e x a x = = + eax x dx d e aa e. / Note that measures the drect effect of nput taxaton on emssons, 21 measures the elastcty of the emssons functon wth respect to nput use, and measures how much nput use s more senstve to nput taxaton than to emssons taxes. Accordng to equaton (24), nput taxes can serve as envronmental taxes and reduce the need for explct emssons taxes. Note that the frst two terms are the same as n equaton (17) after the substtuton of equaton (19). The smaller the drect emssons-tax effect ε de/ d, the larger s not only the effect of margnal admnstratve costs on optmal emssons taxes, but also the scope for nput taxes to replace emssons taxes, as s clear from the thrd term n equaton (24). Indeed, wth hgh margnal admnstratve costs of emssons taxes, nput taxes only should be used as envronmental taxes and should be set accordng to equaton (25), wth 0, whch can be wrtten as (27) t x de dtx = / D dx dt / x dt/ dt x. dx / dt Note that nputs should then be taxed accordng to ther margnal emssons content de /dx tmes margnal damage D corrected for admnstratve costs as a result of changes n nput use. (Of course, we must make the provson that n the presence of large fxed admnstratve costs, such that equaton [15] s volated for t x, the nput tax should not be mplemented.) Replacng emssons taxes by nput taxes reduces effcency. Input taxes dstort the nput mx and fal to provde drect ncentves for abatement. Only f the nput-to-emssons rato s constant and there are no abatement possbltes are the nput taxaton and emssons taxaton equvalent n the absence of transacton costs. Ths corresponds to e /x constant, 1, and 0. Wth an nteror soluton, condtons (24) and (25) can then be rewrtten as x 21. It can be derved, from equatons (3) and (4), that dx/d e a (da /dt x ) e x (dx /dt x ).

20 Green Taxes and Admnstratve Costs: Carbon Taxaton 109 (28) D txx/ e = ε 1 dt 1 + = ξ d ε + dt ξ dtx ( / e). x Wth a fxed emssons-nput rato, nput and emssons taxes would be equvalent n the absence of admnstratve costs (as s well known; see, e.g., Xepapadeas 1999). Indeed, accordng to condton (25), wthout margnal admnstratve costs, any combnaton of taxes such that t x x / e D would acheve the frst-best optmum. Ths mples that the two taxes are equally effcent n terms of the sum of gross prvate welfare and the envronmental beneft (see secton 3.2). Hence, transacton costs consderatons entrely determne the choce between the two taxes. Dfferences n (fxed and/or varable) admnstratve costs across tax nstruments remove the ndetermnacy n the optmal tax choce. Frst, f fxed admnstratve costs dffer across the two taxes, but admnstratve costs are not affected by tax-rate levels, to satsfy the entry condton only the tax wth lowest fxed admnstratve costs should be ntroduced, ether D or t x x /e D. Note that the effectve tax on polluton equals margnal damage (the Pgouvan tax). Second, when both tax rates ncrease admnstratve costs, the effectve tax on polluton ( t x x /e ) should be smaller than margnal damage D. When, n addton, the sum of fxed admnstratve costs for the two taxes are suffcently small to justfy the ntroducton of both taxes, the taxes should be set so as to mnmze varable admnstratve costs, as appears n the second equalty n (28). In the general case of varable and sector-specfc emssons per unt of nput, nput taxes are less effcent than emssons taxes. Hence, f at the same tme admnstratve costs for emssons taxes are hgher, effcency and admnstratve costs may be optmally traded off by choosng a mxed system of nput and emssons taxes. Solvng equatons (24) and (25) for an nteror soluton, and for smplcty assumng that abatement and nput use separately affect emssons (e ax 0 so that 1/ ), we obtan (29) o 1 1 dt dt = D + d , ξ ε ξ ε dtx (30) t o x e 1 1 dt dt = x + d 1 + +, ξ ε ξ ε ξε dt x where (31) = ( ) + + ε ξ > 0.

21 110 Sjak Smulders and Herman R. J. Vollebergh In the above expressons, measures the effcency edge of emssons taxes over nput taxes. Indeed wth a constant emssons nput rato ( 0and 1), we have 0, and equatons (29) (30) collapse to equaton (28). The effcency edge of emssons taxes ncreases n abatement possbltes andn 1. We call ths latter expresson the extent of lnkage between emssons and nputs. The closer to unty the elastcty of emssons s wth respect to nputs ( ), the closer s the correspondence between nputs and emssons, and the more effcently nput taxes mmc emssons taxes. Equatons (29) and (30) reveal that margnal admnstratve costs are less mportant n determnng the optmal tax rates f the effcency of emssons taxes relatve to nput taxes ( ) s larger, that s, f more abatement possbltes abound ( s larger) and emssons are more closely lnked to nputs ( s closer to 1) Lessons from the Model To nternalze envronmental externaltes n the presence of admnstratve costs, pure emssons taxes are optmal only under specfc condtons. These condtons nclude (1) low fxed admnstratve costs, (2) not-toosteeply-rsng admnstratve costs (as a result of ncreases n emssons taxes) relatve to margnal damage and drect emssons-reducton effect of emssons taxes, and (3) relatvely low ncentve effects from alternatve envronmental taxes (taxes on pollutng nputs) to reduce emssons. The optmal second-best rate of emssons taxes falls short of margnal damage. Input taxes may ndeed serve as (optmal) envronmental taxes. Wth the close lnkage between nput use and emssons, and f abatement of emssons (as an alternatve means of reducng the polluton ntensty of producton, rather than changng the nput mx) s relatvely costly, taxes on pollutng nputs may supplement emssons taxes that fall short of margnal damage to nternalze polluton externaltes more fully. In ths case a mxed system of emssons taxes and nput taxes s optmal, essentally because t saves on admnstratve costs whle only moderately affectng ncentves to reduce emssons. If lnkage s close and abatement expensve, and f admnstratve costs assocated wth nput taxaton are suffcently low relatve to admnstratve costs assocated wth emssons taxaton, nput taxes should fully replace emssons taxes. 3.4 Carbon Taxaton and Admnstratve Costs In ths secton we assess exstng and potental envronmental taxes relevant for clmate change polcy, n partcular through carbon taxaton. We argue that current polcy (proposals) can be substantally mproved f the trade-off between ncentve regulaton and admnstratve costs s explctly taken nto account. We concentrate on the explct carbon taxes ntroduced n a number of European countres snce the begnnng of the 1990s.

22 Green Taxes and Admnstratve Costs: Carbon Taxaton 111 Table 3.1 Characterstcs of Man Fossl Fuels Normalzed Energy Carbon Tons of Ol Carbon Content Content Equvalent Content Fuel (GJ) (ton) (TOE) (ton/toe) Coal (metrc ton) Crude ol (barrel) Natural gas (1,000 m 3 ) a Source: OECD/IEA (1993). a Average for Gronngs gas, based on the upper bound of and lower bound of We frst revew relevant facts on exstng carbon taxes, then present evdence on admnstratve costs, next assess current carbon taxes, and fnally dscuss the scope for mprovement Carbon Taxes n Practce Snce the early 1990s, taxes have been serously consdered to combat clmate change, n partcular carbon taxes to curb CO 2 emssons (e.g., Pearce 1991; Cnossen and Vollebergh 1992; Poterba 1992). The debate n Europe was strongly nfluenced by a proposal of the European Commsson, COM(92) 226 (European Commsson 1992), for a hybrd European Unon (EU) tax on energy/co 2 to be mplemented at the European level. The basc dea behnd ths proposal s to brng the (mnmum) rate structure more n accordance wth the carbon content across currently taxed energy products, manly hydrocarbon fuels, as well as to extend the carbon tax base to energy products that are not yet subject to an excse. The same dea s also behnd the carbon taxes actually mplemented n several European countres. Thus the am s to rase the mplct taxaton of carbon at the margn. As s well known, the amount of CO 2 emtted per knd of fuel dffers consderably (see table 3.1). Clearly, ol emts less carbon than coal does. Natural gas, n turn, s cleaner than ol. The obvous mplcaton s that emssons ntenstes also can be reduced by nternalzng the respectve carbon contents n the prce of each knd of fossl fuel. By dfferentatng the fossl fuel excse by the carbon emssons coeffcent nstead of energy content coeffcent, or even a hybrd coeffcent, the consumpton of carbon s put at a dsadvantage at the margn. Thus, users would be nduced to substtute ol for coal and natural gas for coal and ol, and, further, nonfossl fuels for fossl fuels. However, the EU proposal was never mplemented due to consderable resstance from ndustry and specfc countres such as the Unted Kngdom. Despte ths falure to mplement an EU-wde carbon tax, several