Evaluating tax reforms in the presence of externalities *

Transcription

1 Publishe in: Oxfor Eonomi Papers , pp Evaluating tax reforms in the presene of externalities * by Ronnie Shöb University of Essex an University of Munih Abstrat Aoring to the ouble-ivien hypothesis, revenue-neutral green tax reforms are expete both to improve the quality of the environment an to reue existing tax istortions. This paper evelops welfare measures whih are use to estimate these iviens separately. It is shown that the existing tax system an the hoie of the tax rate uts whih aompany an inrease in green taxes have onsierable impat on the magnitue of the environmental ivien. Even a negative impat annot be rule out. Furthermore, the welfare measures allow us to analyse the trae-off between the two iviens an to ientify welfare improving tax reforms. JEL lassifiation: H21, Q28 Corresponene Aress Ronnie Shöb Department of Eonomis University of Munih Shakstrasse 4 D Munih Germany tel.: ++49/89/ fax: ++49/89/ ronnie.shoeb@es.vwl.uni-munhen.e

2 1 "We shall eal with our eonomi system as it is an as it may be moifie, not as it might be if we ha a lean sheet of paper to write upon; an step by step we shall make it what it shoul be." Woorow Wilson 1. Introution In reent years, green taxes have beome very attrative both as an instrument for environmental poliy an as a soure of publi revenues. Following the seminal paper of Sanmo (1975), whih links optimal taxation analysis to environmental issues, a growing literature has emerge on the so-alle ouble-ivien hypothesis. This hypothesis laims that a green tax reform, where existing taxes on non-polluting ('lean') goos are (partly) replae by taxes on polluting ('irty') goos, will both improve the environment an reue the istortion of the existing tax system. To examine these two iviens in etail the paper evelops a set of welfare measures whih allows us to analyse the two iviens separately. Thereby, it follows Felstein (1976) an Ahma an Stern (1984) in fousing on welfare improving tax reforms instea of looking for welfare maximizing tax esign. It seems to be taken for grante that the environmental ivien of suh a green tax reform is always positive (f. Gouler 1995 or Repetto 1994). Obviously, inreasing a tax on a polluting goo will improve the environment. To etermine the environmental ivien from a revenue-neutral green tax reform, however, the effets the aompanying tax rate uts may have on the environment have also to be taken into aount. Due to the omplementarity/substitutability relationships between taxe lean goos an irty goos, environmental quality is affete when the pries of the lean goos hange. Hene, to efine properly the environmental ivien from a revenue-neutral green tax reform, these effets have to be aequately inorporate into the analysis. The first purpose of this paper therefore is to erive neessary onitions for the environmental ivien to be positive. It turns out that the sign an magnitue of the environmental ivien are ritially epenent on the existing tax system from whih the green tax reform starts an on the hoie of the aompanying tax rate uts.

3 2 The seon ivien uner the ouble-ivien hypothesis onerns the effet of a green tax reform on the effiieny of the tax system. Aoring to Gouler (1995) we an istinguish several efinitions of the seon ivien. A seon ivien in its 'weak' efinition ours if tax revenues from a green tax an be use to reue other istortionary taxes an hene improve the alloative effiieny, relative to the ase where tax revenues are returne to taxpayers as a lump-sum transfer (f. Nihols 1984 an Lee an Misiolek 1986). The stronger form efines the seon ivien as the effet a revenue-neutral green tax reform has on the non-environmental welfare ost of the whole tax system. Bovenberg an e Mooij (1994) have shown that, interprete in this stronger form, the seon ivien may not be positive. The seon purpose of the paper is to larify the irumstanes in whih the ouble-ivien hypothesis is vali an shows how to ientify welfare improving tax reforms if the hypothesis fails. Setion 2 evelops a set of welfare measures whih allows the analysis of the two iviens separately. These welfare measures an be use to ientify welfare improving green tax reforms starting from an existing an normally non-optimal tax system (Setion 3). The appliability of these measures for estimating the welfare effets of tax reforms in the presene of externalities is emonstrate in Setion 4 by estimating both iviens an the welfare effet of ifferent tax reforms for the U.K. Equity onsierations follow in Setion 5. Setion 6 onlues. 2. Welfare measures to evaluate tax reforms Consier a small open eonomy. Ignoring istributional issues we assume that there are H iential househols all treate equally by the government. Eah househol onsumes N+2 private goos. The quantities are enote by x, x,..., x, x The first N+1 goos are lean goos, i.e. goos whose onsumption reates no externality. The aggregate onsumption of 0 1 goo, alle the irty goo, reates a negative externality E: E N H x. (1)

4 3 The preferenes of eah househol are esribe by a twie ontinuously ifferentiable, stritly quasi-onave utility funtion u( x0, x1,..., xn, x, E). The marginal utilities u i, i 0,..., N,, are positive; the marginal utility of emissions u E is negative. Positive quantities enote the eman for goos, negative quantities enote the supply of fators. For mathematial onveniene, all initial enowments are normalize at zero. To analyse tax reforms it is onvenient to use the iniret utility funtion v in the soial welfare funtion. In a small open eonomy, prouer pries are equal to worl market pries an hene remain onstant when onsumer pries hange. Normalizing all prouer pries at unity an hoosing goo 0 as numéraire, whih is assume to be untaxe, the utilitarian soial welfare funtion is given by: W Hv( t1,... t N, t, T, E), (2) with t i enoting the tax rate on the lean goo i, with i 1,...,N, an t enoting the tax rate on the irty goo. T is a lump-sum transfer from the government to eah househol. The welfare hange of a tax rate hange, normalize by the marginal utility of the numéraire u 0 (i.e. the marginal utility of lump-sum inome), is given by ~ W W u H xk + u u E 0 0 E t k, (3) t with k 1,...,N,. The first term in brakets represents the iret utility loss of a househol aoring to Roy s ientity. The seon term enotes the iniret effet of a tax rate hange ue to the hange in the environmental quality. Assuming that the onsumption of the irty goo is inepenent of the environment, we an use E t H x t. 1 Beause of the k k k own-prie effet (k ) or the ross-prie effet (k 1,...,N), a hange in the onsumer prie hanges the onsumption of the irty goo an therefore hanges the emissions E. Total tax revenues R are given by N R H tnxn + t x H T. (4) n 1 The first an seon term of the right-han sie over the revenues resulting from ommoity taxation, the thir term enotes the expenitures for lump-sum transfers to the househol.

5 4 Assuming separability between emissions an the onsumption of all private goos, x k 0, k, we obtain the hange of tax revenues resulting from a hange of tax rate k: E R x i Rk tk H xk + ti tk, (5) t t with i k 1,..., N,. The term in brakets enotes the marginal tax revenue (per apita) of the tax on goo k. A revenue-neutral green tax reform 2 whih inreases the green tax t an reues the tax on a lean goo so that publi revenues remain onstant is esribe by: i k R R > 0. (6) Positive revenues ue to an inrease of t ( R > 0 ) are equal to the amount to be refune by ereasing t ( R < 0 ) The marginal iret ost of publi funs To evaluate the welfare effets of a tax reform it is neessary to separate the osts an the benefits of partiular tax rate hanges. In a first step, we therefore erive a measure whih iniates the iret ost of inreasing a partiular tax rate, assuming environmental quality is onstant. Normalizing the utility hange with the marginal utility of the numéraire, u~ u / u 0 [.f., equation (3)], an using Roy's ientity, the iret utility loss of a single househol ue to a marginal inrease of e.g. t k, is %u x t. Aggregating over all E k k househols an relating the total utility loss (in units of the numéraire) to atual marginal tax revenues, we obtain a measure of the Marginal Cost of Publi Funs (MCF) MCF k H u ~ tk R t k E. (7) 2.2 The marginal environmental impat of publi funs This MCF measure oes not take into aount the hange of the environmental quality with respet to the hange in the tax rate on goo k. If the ross-prie effet between any goo k an the irty goo is non-zero, there will be a hange in the eman for the irty goo

6 5 resulting from the tax rate hange. Hene, there will be a hange in the environmental quality, too. To erive this iniret effet on welfare we have to introue a measure whih relates this iniret loss or benefit to the hange in tax revenues in the same way as the MCF-measure oes with the iret ost. The marginal environmental amage of the onsumption of the irty goo is equal to the sum of the marginal rate of substitution between pollution an the numéraire Hu / E u, i.e. 0 it is measure in units of the numéraire (like the MCF-measure). To measure the iniret welfare effet of a tax rate hange, however, the marginal environmental amage has to be multiplie by the hange of pollution ue to the hange of t k. Relating this iniret welfare hange to the marginal tax revenues we obtain MEI k H u E E u0 tk R t k, (8) whih will be alle the Marginal Environmental Impat of a tax rate hange. Aoring to equation (1), an making use of the separability assumption, the numerator an be reformulate: H u E H u H x E E. The term H u is equal to the marginal u0 tk u0 tk ue 0 environmental amage of onsuming the irty goo, while H x is the hange in tk onsumption of the irty goo. Hene, the numerator iniates the iniret marginal welfare hange resulting from inreasing the tax on goo k. Note that eah tax rate hange may have an impat on the environment. Therefore, this impat has to be onsiere whenever analysing tax rate hanges. Subtrating the iniret benefit from the iret ost of taxation we obtain the Marginal Soial Cost of Publi Funs (MSCF): MSCFk MCFk MEI k. (9) This eomposition of the soial osts into iret osts an its environmental impat allows the welfare effets of tax reforms to be analyse with respet to both the ineffiieny of the tax system an the environmental amage. For revenue-neutral green tax reforms the welfare hange is given by [f. equation (3)]:

7 ~ ue E ue E W H x + t H x t u t + + u t > 0. (10) < Solving equation (5) for k, with respet to t an t, using the separability onition, an applying the revenue-neutrality onition (6), omparison of equations (7), (8) an (9) shows that ~ > > W MSCF MSCF R < 0. (11) < Hene, the hange in welfare is orretly measure using the MSCF-measures The evaluation of revenue-neutral tax reforms Using equation (9) to eompose the MSCF into its iret an iniret effets, equation (11) an be rearrange to analyse the ouble-ivien hypothesis for green tax reforms: ~ > > W 0 ( MEI MEI) + ( MCF MCF ) 0. (12) R < < The first braket term enotes the environmental ivien. Beause of an inrease in the green tax, the environment improves (MEI > 0; provie that is not a Giffen goo). This is often the only effet onsiere as the environmental ivien (f. Repetto 1994, p. 3). However, we have to take into aount the effets of the aompanying measures the government takes. If, e.g., the marginal environmental effet of the lean goo, MEI, is positive (the irty goo is a omplement to the lean goo), a tax ut for the lean goo et. par. leas to a worsening of the environment. The environmental ivien of the whole tax reform is smaller than the marginal environmental impat of the green tax. The seon ivien is equal to the reue istortion of taxing the lean goo, MCF, minus the inrease istortion of taxing the green goo, MCF. This ifferene measures the impat the revenue-neutral green tax reform has on the alloative effiieny of the whole tax system. The 'strong' form of the ouble-ivien hypothesis, as efine by Gouler (1995, p.

8 7 159f) hols if both braket terms are positive, i.e. MEI MEI > 0 an MCF MCF > 0, respetively. 5 It is often argue that the environmental ivien of green tax reforms is positive (f. Gouler 1995). However, this nee not be the ase. To see this, we first analyse a revenueneutral tax reform starting from a Ramsey-optimum, i.e. a situation in whih taxes have been set optimally to raise revenues, but environmental onsierations have not been taken into aount. This is haraterize by the ientity of all iret marginal ost of publi funs measures (MCF) exept for the measure of lump-sum transfers. Attention an thus be fouse solely on the environmental onsequenes of tax reforms. Then, in Setion 3.2, the analysis is extene to tax reforms starting from an arbitrary, i.e. non-optimal tax system. Here the iret MCF-measures iffer an it is neessary to onsier both environmental an istortionary onsequenes of tax reforms. 3.1 The environmental ivien of a revenue-neutral green tax reform Starting from the Ramsey-optimum the seon braket term of onition (12) is ientially zero for all lean goos. Using the efinitions (8) an (5) an applying the revenue-neutrality onition (6) yiels: ( ) MEI MEI x t x t R t R t E t R R > < < > < > (13) As total ifferentiation of (1) shows, a positive (negative) marginal environmental impat is equivalent to a reution (an inrease) in emissions. Hene, rearranging (13) yiels: E t x t x t R t R t R R < > < > 0. (14) Emissions fall if, an only if, the ratio of the ross-prie effet on the irty goo to the ownprie effet of the irty goo is less than the ratio of the marginal tax revenues. However, if the irty goo is a substitute for the lean goo, i.e. x t > 0, the left-han sie will be

9 8 negative an emissions will be reue both by inreasing the tax on the irty goo an by reuing the tax on the substitute. 6 In the ase of a omplementarity relationship between the two taxe goos, i.e. x t < 0, the hange in emissions beomes ambiguous. The environment improves if, an only if, the reution in the onsumption of the irty goo ue to its own-prie inrease is higher than the inrease ue to the prie reution of the omplement. To see why emissions may atually inrease, assume that the government inreases the tax on the irty goo by one unit. Other things being equal, inreasing the tax t lowers the onsumption of the irty goo, while reuing the tax on a omplement tens to raise its onsumption. The question is what etermines the net effet of these two ountervailing effets. If the marginal revenue R/###t is very high, the aitional funs the government raises are large. If the marginal tax revenue from taxing the lean goo R/###t is relatively low ompare to R /, the tax on the lean goo an, therefore, be reue at a relatively t high rate. As the ratio of marginal tax revenues R / t / R / t equals the inverse of the ratio of the tax rate hange [f. equation (5)], it etermines the weight of the ross-prie effet x t in equation (13). If the weighte ross-prie effet beomes large ompare to the own-prie effet, it might happen that, even for a low ross prie-effet, relative to the ownprie effet, the inrease onsumption of the irty goo resulting from a reution in t outweighs the reution in onsumption resulting from an inrease in t. Hene, it is the existing tax system whih etermines the effet a revenue-neutral green tax reform has on the environment. PROPOSITION 1 (Green tax reform): In a worl with istortionary taxation, a revenue-neutral marginal green tax reform reues (inreases) emissions from the onsumption of the irty goo, if an only if, either (i) the irty goo is a substitute for, or is unrelate to, the lean goo whose tax rate is reue or (ii) the irty goo is a omplement to the lean goo whose tax rate is reue an the ratio of the ross-prie effet on the irty goo to the own-prie effet of the irty goo is smaller (larger) than the ratio of the assoiate marginal tax revenues.

10 9 For tax reforms starting from the Ramsey-optimum, we an a the following orollary: COROLLARY 1 (Green tax reform): Starting from the Ramsey-optimum, a marginal revenue-neutral green tax reform is welfare inreasing (ereasing) if, an only if, the environmental ivien is positive (negative). Proposition 1 an Corollary 1 are relate to the analysis of Ng (1980). He looks at labour taxation an states that welfare will inrease, "provie that an inrease of the (onsumer) prie of the externality-prouing goo is more effetive in reuing its onsumption proportionately than is an inrease in the (onsumer) prie of labor in inreasing it, proportionately to labor" (Ng 1980, p. 745). Thereby, he oes not reognize that the effetiveness of prie hanges epens on the marginal tax revenues (see his equation (15) an the sueeing isussion). Instea, Ng abstrats "from the ompliations of a positive revenue requirement." (Ng 1980, p. 747). Conition (14), however, shows that beause of the revenue neutrality onition, the marginal tax revenues atually etermine the relative magnitues of the tax rate hanges an thus the 'relative effetiveness' of the prie hanges. If the irty goo is untaxe initially, the question then arises whether there exists at least one revenue-neutral green tax reform whih improves welfare. This will be the ase if Proposition 1 hols for at least one lean goo. Though this seems to be a rather weak onition, this annot be guarantee without imposing some restritions on househol's preferenes. 7 In general, we an reognize benefiial inentives of all taxes on goos to whih pollution is a omplement. Conversely, we also have to be aware of the aitional buren of all taxes on goos for whih pollution is a substitute. Fousing on the environmental ivien only, the best poliy reommenation therefore woul be to avoi tax rate uts for all omplements to the irty goo an to look for strong substitutes. Suggestions for using 'green' tax revenues to exempt publi transportation from VAT point in this iretion. Another wiely isusse green tax reform proposal is to substitute the tax on the irty goo for labour taxes (f. Bovenberg an e Moiij 1994 or Bovenberg an van er Ploeg 1994). Here, poliy reommenations whih fous on the environment only are less

11 10 straightforwar. Assuming that the labour supply urve is upwar sloping, utting labour taxes reues leisure onsumption. If the irty goo is a omplement to leisure, lower labour taxes imply lower emissions. Conversely, if the irty goo is a substitute for leisure, reuing labour taxes inreases emissions. Parry (1995) argues that almost all onsumption goos an be onsiere to be ompensate substitutes for leisure. If this is true for the irty goo an if the irty goo is a normal goo, it is also an unompensate substitute for leisure. In this ase, to etermine the environmental ivien, we have to know the marginal tax revenues. 8 Marginal tax revenues are mainly etermine by the magnitue of the tax base an the own tax rate. Cet. par., marginal tax revenues are inreasing in the tax base an ereasing in the own tax rate. As is pointe out in Bovenberg an e Mooij (1994, p. 1088), substituting the tax on the irty goo for labour taxes implies replaing a broa-base tax by a narrowbase tax. Hene, the ratio of marginal tax revenues in onition (13) tens to be rather low an for a low ross prie-effet, relative to the own-prie effet, it is reasonable to expet emissions to erease. 9 In aition, the ratio of marginal tax revenues tens to erease the 'greener' the tax system beomes. Hene, taxes on substitutes or on labour are goo aniates for green tax reforms as they guarantee the environmental ivien to be positive. However, suh tax reforms might have some unesire istributional onsequenes. If, in the absene of lump-sum transfers, the government wishes to ompensate those who suffer from the green tax, the only way to ensure at least an iniret ompensation is to 'subsiize' omplementary goos. Here, aitional tax revenues from green taxes may be use to reue some narrow-base taxes. The paraoxial ase annot be rule out a priori Revenue-neutral green tax reforms in an arbitrary tax system If we look at an arbitrary tax system, a tax reform analysis whih oes not onsier the environment will reommen a tax reform if the seon ivien in onition (12) is positive. A tax reform analysis whih onsiers environmental onsequenes will onfirm this reommenation if the environmental ivien is positive, i.e. if the ouble ivien ours.

12 11 The ouble-ivien literature emphasizes that in general we annot expet a ouble ivien in its strong form to our. There is a trae off between the effiieny of the tax system an the environmental quality. Therefore, welfare analysis requires measuring both iviens properly. If the true marginal environmental amage is known, the measures erive above allow us to o so. If, however, there is unertainty about the magnitue of the marginal environmental amage, we an alulate at least a minimum marginal environmental amage neessary to guarantee that a green tax reform is welfare improving. Assuming that the environmental ivien is positive, a ritial value of the marginal environmental amage MED v exists for whih the environmental ivien exatly outweighs the iret ost of the green tax reform: MED H u u MEI H u v E u E MEI H u u E MCF MCF. (15) If the atual environmental amage is expete to be larger than the ritial value of the marginal environmental amage, than the green tax reform an be expete to be welfare improving, too. Proposition 2 summarizes. PROPOSITION 2 (Critial value of the marginal environmental amage): If the seon ivien of a green tax reform is negative, a marginal revenue-neutral inrease of the green tax is welfare inreasing (ereasing) if the environmental ivien is positive an the atual marginal environmental amage is larger (smaller) than the ritial value of the marginal environmental amage. The onept of the ritial value of the marginal environmental amage permits the ientifiation of welfare improving tax reforms provie that a onsensus about at least a lower boun for the estimates of the marginal environmental amage exists. As the ritial value is ifferent for eah tax reform, the ritial value approah also shows the sensitivity of the welfare sign of ifferent tax reforms with respet to the estimate marginal environmental amage (see Setion 4).

13 Revenue-neutral tax reform with a lump-sum rebate Reently, lump-sum rebates of green tax revenues have been isusse in e.g. Switzerlan an Germany. The proposal of the so-alle 'eo bonus' is to rebate tax revenues from green taxes lump-sum per apita (f., e.g. Teufel et al. 1993). Suh a tax reform proposal an be evaluate using the welfare measures efine in Setion 2. As these measures are relate to aitional tax revenues, a measure for lump-sum transfers per unit of aitional tax revenues is equivalent to the measure of the marginal osts of publi funs from lump-sum taxes: MCF T % H u T R T E 1 i 1 t i. (7') xi T The MCF T measures the onsumer surplus loss per aitional unit of tax revenues from (reuing) lum-sum transfers. In the presene of istortionary taxes, the MCF T normally iffers from unity as inreasing lump-sum transfers hanges tax revenues from other soures. The efinition for the marginal environmental impat of publi transfers is given by: MEI H u E E u T. (8') R T 0 T For normal goos the MEI T -measure is positive. Inreasing tax revenues by reuing lumpsum transfers reues emissions an therefore has a positive impat on the environment. Using these measures, the analysis of a tax reform R R > 0 is ompletely T analogous to the analysis in Setion 3.1. The iea of an 'eo bonus', however, apparently ontraits the results of Dixit (1975) who shows that, even in an arbitrary tax system, the reution of istortionary taxes ombine with a reution in lump-sum transfers is welfare improving. To see this, onsier the Ramsey-optimum, where the MCF-measures are the same for all ommoity taxes. There we have: < 0, (16) sign MCF MCF sign t s T i i i where s i enotes the ompensate pries effets. The seon ivien of the eo bonus, starting from the Ramsey-optimum is always negative. 11 Therefore, a lump-sum rebate of

14 13 green tax revenues an be welfare improving only if the environmental ivien overompensates the negative seon ivien. This an be seen by etermining the ritial value of the marginal environmental amage for this partiular tax reform (see Setion 3.2). Dixit's (1975) results further imply that reuing some istortionary taxes is preferable to inreasing lump-sum transfers. In the presene of externalities, however, this laim hols only for ommoities whose marginal environmental impat is smaller than the marginal environmental impat of lump-sum transfers. This beomes apparent by analysing a sueeing seon tax reform whih reues both lump-sum transfers an some istortionary taxes on lean goos. 4. Theory at work To alulate the MCF- an MEI-measures we have to estimate a omplete eman system. To illustrate how the theory an be applie in pratie we make use of Pashares' (1993) estimates of the eman system for a representative househol in the UK. Using the 'Almost Ieal Deman System' an ata from the British Family Expeniture Survey , Pashares (1993) alulates the unompensate prie an ross-prie elastiities an the expeniture elastiities of seven ommoity groups. To analyse the impat of gasoline taxation, however, it is neessary to isaggregate the ommoity group 'transportation' into 'gasoline' an 'other transportation'. Assuming the same expeniture elastiities for both groups an an own-prie elastiity of 0.7 for gasoline, this an be one by using the onitions of Cournot an Engel aggregation. The elastiities are presente in Table 1.

15 14 Unompensate elastiities expeniture elast. buget shares total tax 1: foo : alohol : fuel : lothing : gasoline : transportation (other) : other : servies Table 1: Unompensate Elastiities (From Pashares (1993) an own alulations) In aition, further information about the British ommoity tax struture is neee. The total tax as a perentage of the onsumer prie (net tax rate) is liste in the last olumn of Table 1. Exept for alohol an gasoline, where we onsier both speifi average exise taxes an VAT, we onsier only the VAT at the stanar rate of 17.5%. (Note that there is no VAT on foo.) 12 Normalizing total expenitures at unity, tax revenues are equal to the buget share times the net tax rate. From the ata given in Table 1 it is possible to alulate the MCF-measures. Assuming the atual marginal environmental amage of gasoline onsumption to be 35 pene/l in ase a) an 70 pene/l in ase b) we an also alulate the MEI-measures an hene the MSCFmeasure - epening on the atual marginal environmental amage. The results are shown in table 2 (see the appenix).

16 15 a) atual marginal environmental amage 35 Pene/l MCF MEI MSCF net welfare gain b) atual marginal environmental amage 70 Pene/l MEI MSCF net welfare gain ritial value Pene/l 1: foo (2) (5) : alohol (10) (10) : fuel (1) (1) : lothing (3) (4) : gasoline (5) xxx (2) xxx xxx 6: transportation (6) (3) : other (7) (7) : servies (8) (8) : VAT-reution (9) (9) : lump-sum rebate (4) (6) Table 2: Marginal Soial Cost of Publi Funs In ase a) the net welfare gain of a marginal green tax reform is given in olumn 5. If, e.g., we inrease taxes on gasoline an reue VAT on servies, the net welfare gain of that reform is 6.7 pene per poun of aitional tax revenues from gasoline taxation (MSCF 8 - MSCF ). The environmental ivien is MEI5 MEI ( ) , the seon ivien is MCF8 MCF [f. equation (12)]. Table 2 shows that none of the possible green tax reforms yiels a negative environmental ivien. However, the variane of the MEI-measures iniates that the hoie of the aompanying tax rate uts has onsierable impat on the total magnitue of the environmental ivien. A ranking of the MSCFs (olumn 4) shows whih ommoities are the best aniates for the government for raising aitional publi funs. The smaller the MSCF the fewer aitional soial osts arue. As gasoline taxation has a relatively high marginal ost of publi funs (Ranking no. 5), only an aompanying reution in VAT of 'transportation', 'other goos', 'servies' or 'alohol' yiels a net welfare gain to soiety. Note that alohol taxation has a very high MCF ( 3.576). It is argue that alohol onsumption itself reates a large negative externality, whih is not onsiere here. In the

17 16 presene of more than one externality, however, the marginal soial ost of publi funs has to be reefine for all goos. Equation (9) has to be rewritten as MSCFk MCFk MEIk, k, (9') with MEI k being the marginal environmental impat the tax on goo k has on the onsumption of the irty goo, with 1,...D an D N The ata allows us to onsier the effets of two 'broa-base' taxes, a lump-sum rebate an a uniform VAT-reution. With a fixe labour supply, a lump-sum rebate is equivalent to a tax ut on labour inome. This iffers from a uniform VAT-reution beause there are positive exise taxes an there is a zero-rate of VAT on foo. Disregaring other externalities, a uniform VAT-reution yiels a high net welfare gain of 24.7% although the seon ivien is negative. A lump-sum rebate of green tax revenues has to be rejete as the negative seon ivien outweighs the positive environmental ivien (see Setion 3.3). In both ases, the ouble-ivien hypothesis in its strong form fails. The empirial results are similar in spirit to the analysis of Bovenberg an e Mooij (1994) who onsier the istortion taxes on labour have on the labour-leisure eision. They argue that the narrow-base green tax has a higher MCF than a broa-base tax on labour inome as the green tax 'istorts' the omposition of the onsumption basket (f. Bovenberg an e Mooij 1994, p.1088). Here, we assume fixe labour supply. Hene, the reason for a negative seon ivien must be ifferent. The MCF of a uniform VAT-reution is a weighte average of the istortions of all the narrow-base taxes involve (see the appenix). The larger the MCF of the green tax, relative to the MCFs of all other ommoity taxes, the more likely it is that the seon ivien beomes negative an - in the ase of a lump-sum rebate - it outweighs the positive environmental ivien. If the atual marginal environmental amage is 70 pene/l [ase b)], the results hange rastially. Even a subsiy on foo is welfare inreasing on pure effiieny grouns an only a VAT reution for energy still implies a welfare loss. However, any partiular VATreution - exept for alohol - is an inferior solution ompare to a uniform VAT reution.

18 17 The ritial value of the marginal environmental amage an be erive from the eman system without knowlege of the atual environmental amage. This permits ifferent tax reforms to be istinguishe even if all that is known is a lower boun on the value of the marginal environmental amage. For example, a green tax reform whih ereases VAT on 'lothes' only is welfare ereasing in ase a), but welfare improving in ase b). While most ritial values are in the range between 30 pene/l an 40 pene/l the ritial value for e.g. fuel suggests that tax rate uts for fuel onsumption shoul not be onsiere unless the atual marginal environmental amage is expete to be larger than 80 pene/l. Note that a negative ritial value iniates a 'free lunh', i.e. the tax reform is welfare inreasing even without onsiering the environment. 5. Distributional onsierations So far, we have ignore istributional onsierations. However, the welfare measures erive for iential househols an be aequately efine for heterogeneous househols using a welfare funtion of the Bergson-Samuelson-type. In this ase, the iniviual measures have to be erive first. Then, these measures have to be aggregate, weighte with the iniviuals' soial welfare weights, to ahieve the MCF-, MEI- an MSCF-measures. In the Ramsey-optimum, every possible tax reform is neutral with respet to iret ost. Hene, only if the environmental quality hanges, oes welfare also hange. If every househol onsiers pollution as a non-positive externality ( u h 0, h), an improvement of the environment makes every househol better off - regarless of their soial welfare weights. Therefore proposition 1 hols. 14 Starting from an arbitrary tax system, we have to apply the onept of the ritial value of the marginal environmental amage. In this respet proposition 2 also hols. However, the marginal environmental amage an therefore the ritial value now epen on both the marginal willingness to pay of eah househol an its soial weight. E

19 18 6. Conlusions Deomposing the welfare effets of tax rate hanges shows that every tax rate hange may have an impat on both the effiieny of the tax system an the environmental quality. Thus, to evaluate a green tax reform properly, we have to onsier an environmental ivien whih omprises the marginal environmental impats of both the green tax an the aompanying measure the government takes to guarantee revenue neutrality. If a tax reform analysis whih oes not take aount of environmental onsequenes reommens inreasing a green tax, a tax reform analysis whih oes take aount of the environment will o so, too, if the environmental ivien of the reform is guarantee to be positive. This is the ase if the aompanying tax rate ut applies to a goo for whih the irty goo is a substitute. It will also be guarantee in the ase of a omplementarity relationship if one aitional onition is met. The effiieny of a partiular green tax reform in reuing emissions is etermine by the starting point of the tax reform, i.e. the existing tax system. This result is inepenent of the atual marginal environmental amage of pollution. If the ouble-ivien hypothesis fails, the onept of the ritial value of the marginal environmental amage an be use to eie whether tax reform analysis whih oes take aount of the environment will onfirm or rejet the traitional reommenations. The measures evelope for the analysis of green tax reforms have to be applie to lean tax reforms as well. The omplementarity/substitutability relationships between taxe goos an the irty goo requires that environmental onsequenes have to be onsiere for all tax reforms. We are use to talking about the benefiial inentives of green taxes. Taking the eologial perspetive on analysing tax reforms seriously, we an also reognize benefiial inentives of all taxes on goos to whih pollution is a omplement. Conversely, we also have to be aware of the aitional buren of all taxes on goos for whih pollution is a substitute. Appenix To alulate the measures in Setion 4 we nee expliit formulations of the measures suggeste. The expliit form of the MCF-measure is given by

20 MCF j x 19 j x j. 8 xi + t i t i 1 p Using the efinitions Ri ti xi, wi pi xi, an εij x The MEI-measure is given by: MCF j w j 8 i j i 1 j xi, this an be rewritten as: t j R ε MEI MCF H u R t j j u w For a uniform VAT-reution, the MCF is given by: MCF VAT i ij. E 0 Ri Ri. MCF i i j i ε. j

21 20 Referenes AHMAD, E. an STERN, N. (1984): "The Theory of Tax Reform an Inian Iniret Taxes," Journal of Publi Eonomis 25, BOVENBERG, A. L. an VAN DER PLOEG, F. (1994): "Environmental Poliy, Publi Finane an the Labour Market in a Seon-Best Worl," Journal of Publi Eonomis 55, BOVENBERG, A. L. an DE MOOIJ, R. A. (1994): "Environmental Levies an Distortionary Taxation," Amerian Eonomi Review 84, DIXIT, A. K. (1975): "Welfare Effets of Tax an Prie Changes," Journal of Publi Eonomis 4, FELDSTEIN, M. S. (1976): "On the Theory of Tax Reform," Journal of Publi Eonomis 6, GOULDER, L. H. (1995): "Environmental Taxation an the "Double Divien:" A Reaer's Guie," International Tax an Publi Finane 2, GUESNERIE, R. (1977): "On the Diretion of Tax Reform," Journal of Publi Eonomis 7, LEE, D. R. an MISIOLEK, W. S. (1986): "Substituting Pollution Taxation for General Taxation: Some Impliations for Effiieny in Pollution Taxation," Journal of Environmental Eonomis an Management 13, MAYSHAR, J. (1990): "On Measures of Exess Buren an Their Appliation," Journal of Publi Eonomis 43, MAYERES, I. an PROOST, S. (1994): Optimal Tax an Tax Reform Rules with Congestion Type of Externalities, Paper prepare for the EAERE ongress, Dublin, June. NG, Y.-K. (1980): "Optimal Corretive Taxes or Subsiies when Revenue Raising Imposes an Exess Buren," Amerian Eonomi Review 70,

22 21 NICHOLS, A. L. (1984): Targeting Eonomi Inentives for Environmental Protetion, MIT- Press: Cambrige Mass. an Lonon. PARRY, I. W. H. (1995): "Pollution Taxes an Revenue Reyling," Journal of Environmental Eonomis an Management 29, S64-S77. PASHARDES, P. (1993): "Bias in Estimating the Almost Ieal Deman System with the Stone Inex Approximation," Eonomi Journal 103, REPETTO, R. (1994): The Potential Eonomi Gains From a Tax Shift, Paper presente on the 50th Congress of the International Institute of Publi Finane, Cambrige Mass. SANDMO, A. (1975): "Optimal Taxation in the Presene of Externalities," Sweish Journal of Eonomis 77, STERN, N. H. (1987): "Aspets of the General Theory of Tax Reform," in: D. NEWBERY an N. H. STERN: The Theory of Taxation for Developing Countries. New York: Oxfor University Press, TEUFEL, D. et al. (1993): Das Öko-Bonus-Konzept, UPI-Beriht Nr. 27, Heielberg.

23 22 Footnotes * Helpful omments by Lans Bovenberg, Jeremy Ewars, Gaute Torsvik, Mik Keen, Ray Rees, Hans-Werner Sinn, Marel Thum an two anonymous referees are gratefully aknowlege. The usual islaimer applies. A first version of this paper was written while visiting the University of Bergen. Finanial support from the Norwegian Researh Counil (NAV) is gratefully aknowlege. 1 The onsumption of the irty goo might epen on the emissions. In general, the eman for the irty goo is given by Hx ( t1,..., t N, t, T, E). Hene, impliit ifferentiation of (1) yiels: E t ( H x t ) / ( 1 H x E). k k As long as an inrease of emissions by one unit oes not reue the onsumption of the irty goo by more than one unit, i.e. as long as the enominator is positive, the separability assumption oes not hange the results. 2 For tax reform analysis see the seminal papers by Dixit (1975) or Guesnerie (1977) an for a survey, see Stern (1987). Revenue-neutral green tax reforms are onsiere reently by Mayeres an Proost (1994). 3 In equation (6) it is not neessary to assume the tax rate hange to be positive. In the ase of negative marginal tax revenues, equation (6) esribes a tax reform where the reution in the tax on goo inreases the tax revenues whih are to be refune by a reution in the tax on goo. The following measures are not efine for marginal tax revenues equal to zero. 4 This is not neessarily true for all MCF-measures suggeste in the literature. For a survey see Mayshar (1990). 5 The 'weak' form of the ouble-ivien hypothesis efines the seon ivien as MCF - MCF T (f. equation (7') below). For welfare omparisons, the total ivien has to be ompare with the istortion impose by a marginal inrease in the green tax, relative to the marginal inrease of a lump-sum tax, i.e. MCF - MCF T. 6 In what follows all omplementarity/substitutability relationships are unompensate.

24 23 7 A ounter example is given by Ng (1980) for the three-goo ase with zero tax revenues an zero initial tax rates. He shows that emissions unambiguously rise ue to a revenue-neutral green tax reform if the ompensate ross-prie elastiity of the lean goo exees the ompensate own-prie elastiity of the irty goo. Without imposing restritions on preferenes, stanar onsumer theory oes not rule out suh a result. In this ase, however, a revenue-neutral tax reform whih reues the tax on the irty goo woul reue emissions an therefore improve welfare (f. orollary 1). In a non-optimal tax system there is always a whole half-spae of welfare improving iretions of tax rate hanges. 8 To analyse this tax reform within the framework evelope here, we have to onsier leisure as the lean goo. With the time enowment being normalise at zero, labour enters the utility funtion as a negative quantity (x < 0). A labour tax is equivalent to a subsiy of leisure, i.e., a labour tax is esribe by t < 0. If marginal tax revenues of labour taxes are positive, we further have R t < 0. Conition (13) remains vali, although the interpretation has to be slightly moifie. In onition (14), however, the inequality relations are reverse. 9 Bovenberg an e Mooij (1994) assume weak separability between leisure an onsumption, an homogeneity in onsumption. They show analytially that uner these assumptions, emissions unambiguously fall, although the irty goo is a substitute for leisure, x t > Assume that all unompensate ross-prie effets exept those between the lean an irty goo are ientially zero an that tax revenues from taxing the irty goo are twie the tax revenues from taxing the lean goo. Then, plugging into onition (13) the following parameters t 0. 25, t ε 0. 3, ε 0. 9, ε ε (ε ij enotes the unompensate elastiity) generates the paraoxial ase that emissions inrease ue to green tax reform. 11 Aoring to the Ramsey rule, the right-han term in brakets is negative. Conition (16) an also be erive from Dixit's (1975) theorem 1. Note that for arbitrary tax systems the seon ivien might beome positive if the istortion of the tax on the irty goo is alreay very high.

25 24 12 See H.M. Customs an Exise, Annual Report , Lonon: H.M.S.O, Otober Note that in the ase of multiple externalities, orollary 1 an proposition 2 o not apply anymore. 14 However, in onition (14) we have to ompare the ratios of total prie effets, e.g. x h t x h t, with the ratio of marginal tax revenues. H H