Ecological Tax Reforms and the. Environment: A Note

Publishe in: Bulletin of Eonomi Researh 50.1997, pp. 83-89 Eologial Tax Reforms an the Environment: A Note Ronnie Shöb University of Munih JEL lassifiation: H21, Q28 Aress: Ronnie Shöb Department of Eonomis University of Munih Shakstrasse 4 D-80539 Munih Germany tel. ++49/89/21806261 fax ++49/89/397303 email: ronnie.shoeb@es.vwl.uni-muenhen.e

1 ECOLOGICAL TAX REFORMS AND THE ENVIRONMENT: A NOTE * R. Shöb ABSTRACT There is wiesprea agreement on the ability of eologial tax reforms to improve the environmental quality. This paper, however, points out that a negative marginal impat on the environment annot be rule out for revenue-neutral eologial tax reforms in both first-best an seon-best frameworks. Therefore, suffiient onitions are erive whih ensure the improvement of the environmental quality. I. INTRODUCTION In reent years the ouble-ivien hypothesis has beome very popular in both publi finane an environmental eonomis. Eologial tax reforms that inrease taxes on polluting goos, are expete to both improve the quality of the environment an to reue the istortions of the existing tax system. While there is a ontroversy about the existene of the seon ivien (f., Bovenberg an e Mooij 1994, an Repetto 1994), there is wiesprea aggreement on the positive environmental impat of eologial tax reforms (f., Gouler 1995). 1 * Helpful omments by Jürgen Eihberger, Roger Guesnerie an Ray Rees are gratefully aknowlege. However, the usual islaimer applies. A first version was written while visiting the University of Bergen. Finanial support from the Norwegian Researh Counil (NAV) is gratefully aknowlege. 1 In the literature on the ouble ivien hypothesis, the environmental ivien is efine as the gross benefit arising from an improvement in the environmental quality (f. Shöb 1996). Hene, although this paper oes not

2 This note, however, points out that a negative impat on the environment annot be rule out for eologial taxes in general. Setion II presents the moel. Setion III then shows that even in a first-best worl an inrease of the eologial tax, aompanie by a lump-sum rebate of tax revenues, oes not neessarily improve the environment. In a seon-best worl the ounterintuitive ase of an eolgial tax reform whih eteriorates the environmental quality is even more likely to our (Setion IV). The paper, therefore, erives onitions whih guarantee that the environmental impat of eologial tax reforms beomes positive. II. THE MODEL We ignore istributional issues by assuming that there are H iential househols all treate equally by the government. Eah househol onsumes three private goos 0,,. Goo 0 (i.e. leisure) is hosen as numéraire an is assume to be untaxe. The preferenes of eah househol are esribe by a twie ontinously ifferentiable, stritly quasi-onave utility funtion. Assuming a small open eonomy, prouer pries are equal to worl market pries an remain onstant when onsumer pries hange. This allows us to erive the eman funtions for all goo from the househol's maximization behaviour: xi( t, t, T), (1) with i = 0,,. t enotes the tax rate on the lean goo, an t enotes the tax rate on the goo, alle the irty goo. T is a lump-sum transfer from the government to the househol. The transfer might be negative, in whih ase it is onsiere to be a lump-sum tax. The onsumption of the irty goo reates a negative externality E. The externality (emissions) epens on the aggregate onsumption of the irty goo: E = e Hx( t, t, T), (2) with e x > 0. Note that in this framework we assume that the onsumption of all goos is inepenent of the level of emissions. provie a welfare analysis but fouses on hanges in emissions, it shoul be note that a reution (inrease) in emissions is always assoiate with a positive (negative) environmental ivien.

3 When analysing tax reforms we have to onsier the buget onstraint for the government. Defining R as the given tax requirement to provie a fixe amount of publi goos, the buget onstraint is given by R = H t x HT. (3) k k=, k The first term overs the tax revenues ue to ommoity taxation, the seon term enotes the lump-sum transfers to the househols. In what follows we fous on revenue-neutral tax reforms. 3. FIRST-BEST ANALYSIS If there are no externalities an if the government an impose lump-sum taxes, any given publi goo provision is finane by lump-sum taxes only. In the presene of externalities, however, the government might use tax revenues from taxing the irty goo as well. Hene, the buget onstraint in a first-best framework is given by R = H( t x T). (3') Now onsier a marginal eologial tax reform. Revenue neutrality requires: x x R = H x + t t + 1 + t T = 0. (4) T The hange in emissions an be erive from total ifferentiation of equation (2). Foussing on the hange in emissions, we obtain the following onition: x E = 0 t x + T T = 0. 2 (5) 2 The onsumption of the irty goo might epen on the emissions. In general, the eman funtion for the irty h h goo is given by x = x ( t, t, T, E). Impliit ifferentiation of (1) using (2) yiels: E E H x E x x H x k = 1. However, as long as an inrease of emissions by one unit oes not k E 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.

4 Solving equation (4) for T an substituting in onition (5), we finally obtain: E t s = 0 x 1 t T = 0, (6) where s = x + x x T enotes the ompensate own-prie effet whih is negative. The enominator enotes the marginal revenue of lump-sum taxes. Hene, from onition (6) we an erive the following proposition: Proposition 1 (First-best eologial tax reform): In a non-istorte tax system, a revenue-neutral eologial tax reform reues (inreases) emissions if marginal tax revenues from lump-sum taxes are positive (negative). For being a normal goo ( x T > 0 ), it turns out that a very high tax on might lea to the ase that even in the first-best worl with lump-sum rebate of eologial tax revenues, an inrease of the eologial tax might lea to an inrease in emissions. Figure 1 illustrates this extreme ase. Assuming separability between private goo onsumption an emissions an an alreay very high tax on the polluting goo, the househols initial onsumption bunle is given by P 0 whih yiels the househol a sub-utility level of u 0. Now assume that a further inrease of t reues tax revenues, R < 0. Without hanging other tax rates, the househol woul en up in P' (points above the iso-revenue line R = 0 iniate a tax revenue shortfall). To meet the tax requirement (R = 0), the government has to raise aitional tax revenues. If, as a result of the high tax on the irty goo, the marginal tax revenues from lump-sum taxes are negative, R T > 0, the government atually has to lower the lump-sum tax. This implies a shift of the (otte) buget line to the right. As the new line is steeper, a solution tangent to the original inifferene urve u 0 woul still lea to a tax revenue shortfall. Therefore, the buget line has to shift further to the right, going beyon P 0, resulting in a higher onsumption of the irty goo an higher emissions, respetively. Note that, in this ase, the lean goo is an inferior goo.

5 Figure 1 Private utility inreases from u 0 to u 1 while the sub-utility from emissions ereases. If we ontinue to inrease the tax on the irty goo, we will en up with an optimal tax whih is * equal to the marginal environmental amage, t = H( u u0) ( E x ) (f. Baumol an E Oates 1988). For the ase where, emissions atually inrease, the Pigovian taxes exaly offset marginal losses in environmental quality by inreasing private utility. This ompensation sheme is the exat opposite of what is expete when looking at Pigovian taxes. IV. SECOND-BEST ANALYSIS As long as the government is not restrite in hoosing the appropriate instruments, we an proee in a first-best framework. However, the government normally oes fae some restritions in using lump-sum taxes. 3 Assume that the government is not allowe to use lump-sum transfers. Instea, the government is fore to pay bak the revenues from inreasing the tax on the irty goo by reuing the tax rate on the lean goo. In this ase, the revenue-neutrality onition is given by 3 This is a stanar assumption in optimal taxation theory.

6 R R t t R xk xk = + t = H( x + tk t + H x + tk t = ) ( ) 0. (7) The hange in emission now beomes: k=, k=, E x x E = H t + t. (8) x Again, we are intereste in the sign of the hange in emissions. Assuming that both marginal tax revenues are positive, R k > 0, it implies that for a revenue-neutral tax reform if t > 0 then t < 0. Using the revenue-neutrality onition (7), substitute for t (8), we obtain E t R= 0 x = 0 x t into equation R =. (9) R 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 > 0, the left-han sie will be negative an emissions will be reue by both inreasing the tax on the irty goo an reuing the tax on the substitute. 4 In the ase of a omplementary relationship between the two taxe goos, i.e. x < 0, the hange in emissions beomes ambigious. 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. If the marginal tax revenue R/ is very high, the aitional funs the government raises are large. These have to be refune by reuing the tax on the lean goo, t < 0. If the marginal tax revenue of the lean goo R/ is relatively low ompare to R/, the lean goo will be reue at a high rate. As an be seen from (8), the ratio of 4 In what follows all omplementarity/substitutability relationships are unompensate.

7 marginal tax revenues, R/ / R/, is just the weight of the ross-prie effet x. If the weight is large ompare to the weight of the own-prie effet (= 1), it might happen that, even in the ase of a low ross prie-effet, relative to the own-prie 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, the existing tax system etermines the effet a revenue-neutral eologial tax reform has on the environment. Proposition 2 summarises: Proposition 2 (Seon-best eologial tax reform): In a worl with istortionary taxation, a revenue-neutral marginal eologial tax reform is reuing emissions, (i) if the aompanying tax reution applies to a substitute for the irty goo or (ii) if it applies to a omplement for the irty goo an the ratio of the ross-prie effet on the irty goo to the own-prie effet of the irty goo is smaller than the ratio of the assoiate marginal tax revenues. Proposition 2 is relate to the analysis of Ng (1980). 5 He looks at a revenue-neutral tax reform where the tax on the irty goo is inrease an the tax on labour is erease aoringly. He onlues 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" (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 following isussion of his results.) Instea, Ng abstrats "from the ompliation of a positive revenue requirement" (p. 747) when interpreting his result. Conition (9), 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. It is the existing tax system the tax reform starts from, an the hoie of the aompanying tax instruments, whih etermines the effiieny of eologial tax reforms to reue emissions. 5 See also Shöb (1996).

8 V. CONCLUSION When looking at eologial tax reform proposals it turns out that the hange in the environmental quality epens on both the eologial tax an the aompanying measures the government takes to guarantee revenue neutrality. It is, therefore, the existing tax system an eologial tax reform starts from, whih atually etermines the effiieny of eologial tax reforms in ahieving environmental targets. REFERENCES Baumol, W. J. an Oates, W. E. (1988): "The Theory of Environmental Poliy" Cambrige University Press: Cambrige, Mass., 2n eition. Bovenberg, A. L. an e Mooij, R. A. (1994): 'Environmental Levies an Distortionary Taxation', Amerian Eonomi Review vol. 84, pp. 1085-89. Gouler, L. H. (1995): 'Environmental Taxation an the Double Divien: A Reaer's Guie', International Tax an Publi Finane vol. 2, pp. 157-84. Ng, Y.-K. (1980): 'Optimal Corretive Taxes or Subsiies when Revenue Raising Imposes an Exess Buren', Amerian Eonomi Review vol. 70, pp. 744-51. Repetto, R. (1994): The Potential Eonomi Gains From a Tax Shift, Paper presente at the 50th Congress of the International Institute of Publi Finane, Cambrige, Mass. Shöb, R. (1996): 'Evaluating Tax Reforms in the Presene of Externalities', Oxfor Eonomi Papers vol 48.1996, pp. 537-55.