Environmental Levies and Distortionary Taxation: Pigou, Taxation, and Pollution

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1 Tufts University From the SelectedWorks of Gilbert E. Metcalf 2002 Environmental Levies and Distortionary Taxation: Pigou, Taxation, and Pollution Gilbert E. Metcalf, Tufts University Available at:

2 Journal of Public Economics 87 (2003) locate/ econbase Environmental levies and distortionary taxation: Pigou, taxation and pollution Gilbert E. Metcalf and NBER Tufts University, Department of Economics, Medford, MA 02155, USA and NBER Received 10 September 2000; received in revised form 15 February 2001; accepted 28 March 2001 Abstract I note an important distinction between the optimal price of environmental quality in a second-best world and the optimal level of environmental quality. Using an analytical general equilibrium model, I show that for reasonable parameter values, an increase in tax distortions (arising from an increase in required tax revenues) leads to a fall in the optimal Pigouvian tax rate even while environmental quality improves. In general, knowledge of the direction of changes in optimal environmental tax rates due to changes in the economy is not sufficient for understanding the impact on environmental quality Elsevier Science B.V. All rights reserved. JEL classification: H21; H23; Q28 1. Introduction The double dividend hypothesis suggests that a tax on pollution can both improve the environment and reduce distortions in the tax system. In an important article, Bovenberg and de Mooij (1994) reframed the hypothesis as a question of whether the optimal tax on pollution in a second best world is higher or lower than the social marginal damages of pollution. In that paper, they demonstrate that, in the presence of pre-existing distorting taxes, the optimal pollution tax typically lies address: gilbert.metcalf@tufts.edu (G.E. Metcalf) /03/$ see front matter 2003 Elsevier Science B.V. All rights reserved. PII: S (01)

3 314 G.E. Metcalf / Journal of Public Economics 87 (2003) below the Pigovian tax, which fully internalizes the marginal social damage from pollution (p. 1085). In this note, I point out an important distinction between the optimal price of environmental quality in a second-best world and the optimal level of environmen- 1 tal quality. While the focus on optimal tax rates is important, equally important is the relation between the level of tax distortions in the economy and the amount of environmental quality. Moreover, knowing that the optimal pollution tax falls below social marginal damages does not imply that environmental quality falls in the presence of pre-existing tax distortions. In effect, we should distinguish between price questions and quantity questions. The price question refers to tax rates while the quantity question refers to the amount of environmental quality. Framed this way, this note evokes Atkinson and Stern (1974) and their analysis of public good provision in a second best world. Atkinson and Stern first showed how the Samuelson ondition for pure public goods is affected by the presence of distortionary taxes (a price question). They then showed how the optimal provision of the pure public good is affected by distorting taxes (a quantity question). A key message in their paper is that answering the question of how the Samuelson ondition changes tells us nothing about the optimal provision of the public good. This note gives a similar message in the environmental policy arena (hence the sub-title of the note which plays off the title of Atkinson and Stern s paper). Specifically, I show that the optimal environmental tax component of a commodity tax on a polluting good falls short of social marginal damages and that this environmental tax component falls as revenue needs (and hence tax distortions) rise. The fact that the environmental tax falls might lead one to believe that environmental quality would also fall as revenue needs rise. Instead, I show that the response of environmental quality to an increase in the revenue requirement depends on two effects: (1) a commodity substitution effect, as consumers substitute from clean to dirty goods as the environmental tax component falls and (2) a leisure substitution effect, as consumers substitute from purchased commodities to leisure (here assumed to be a clean good). For reasonable parameter values, I find that the leisure substitution effect dominates the commodity substitution effect so that an increase in required revenues improves the environment while simultaneously reducing the optimal Pigouvian tax increment. The relationship between environmental quality in a second-best versus a first-best world has been examined before, albeit typically in a partial equilibrium setting. Lee and Misiolek (1986), for example, carry out a partial equilibrium analysis in which revenues from pollution taxes are used to lower other distorting taxes. They argue that the second-best pollution tax rate is less (greater) than social marginal damages as the elasticity of tax revenue with respect to pollution demand 1 The emphasis on tax rates can also be found in a number of papers that followed Bovenberg and de Mooij, including Fullerton (1997), Schob (1997), and Jaeger (1999).

4 G.E. Metcalf / Journal of Public Economics 87 (2003) is greater (less) than 1. When the optimal tax rate is less than social marginal damages in their model, the level of pollution is greater than the level that would hold if the Pigouvian prescription were applied. Partial equilibrium results such as these drive the commonly held view that a second-best tax on pollution below social marginal damages will be associated with higher levels of pollution. Where this argument breaks down is in ignoring the efficiency costs of the pollution tax itself, a cost that can only be properly identified in a general equilibrium model. The efficiency costs arise because an environmental tax affects prices in other markets which are already subject to distortions arising from taxation. There is a small general equilibrium literature that has previously noted the distinction between the price and level of environmental quality in a second-best world. Bovenberg and van der Ploeg (1994) construct an analytic general equilibrium model and study the impact of changes in preferences (via changes in weights in a social welfare function). They carry out a similar exercise to the one I do (by increasing the weight on public consumption in their social welfare function) and derive an equation similar to the key equation in this paper [Eq. (12)]. The analysis in this note differs from that of Bovenberg and van der Ploeg by sharpening the focus on the price versus level question. In particular, this analysis abstracts from any demand side effects and as a result of this and other simplifications, the formula showing how environmental quality changes in response to a demand for increased government spending is considerably more transparent. In addition, I provide some numerical results to show the relative magnitude of the two effects highlighted in the note. Another paper in the spirit of this note is one by Gaube (1998). Gaube compares environmental quality in a first-best relative to a second-best optimum and finds that environmental quality is higher in the second-best optimum. To obtain this result, he restricts utility to be quasi-linear in private consumption, leisure, the government good, and the environment. This restriction is stronger than the restrictions on preferences in this model. I also carry out a slightly different experiment. Instead of looking at two disparate points, I carry out a comparative statics analysis to address the issue of the impact of increased tax distortions on environmental quality. 2. The model In this section, I first present the model and then solve for optimal tax rates on the clean and dirty good taking into account the environmental externality. In the next section, I carry out comparative statics on these optimum prices and 2 The role of the tax elasticity (e) indicates the importance of revenue raising in Lee and Misiolek s model. If additional pollution (from the amount prescribed by the Pigouvian rule) increases tax revenue (e.1), then a lower tax should be implemented to bring about a greater amounts of pollution (and tax revenue).

5 316 G.E. Metcalf / Journal of Public Economics 87 (2003) quantities to examine how increases in required government revenue affect both the optimal Pigouvian tax increment as well as the optimal amount of environmental quality. Following Bovenberg and de Mooij, I employ a linear production technology in which labor (L) is used to produce a clean good (), a dirty good (D), and government services (G). Government services can be either clean or dirty, and I assume that the fraction of these services that contribute to pollution is constant and equal to g. The economy has N identical individuals and labor productivity equals h. Since each good is produced using one unit of labor, the technology is NhL 5 N 1 ND 1 G. (1) Utility is a function of the two goods and government services as well as leisure (V ) and environmental quality (E): U 5 u(,d,v;g,e) (2) where environmental quality is a function of the aggregate production of the dirty good and the government good: E 5 e(nd 1 gg), with e9,0. The parameter g measures the proportion of G that contributes to pollution. Individuals maximize utility subject to a time constraint (V 1 L 5 1) and a budget constraint: hl 5 (1 1 t ) 1 (1 1 t D)D (3) where t is a tax on and td a tax on D. The social marginal damage of pollution in dollar terms (t) is the marginal damage divided by the private marginal utility of income (l): U t 52] e9n/l (4) E Following the approach taken by previous authors, I assume a subutility function for and D that is homothetic and weakly separable from leisure. Let this function be Q(,D). With this assumption, I can characterize the preference for and D in terms of the elasticity of substitution in consumption (s): ˆ 2 Dˆ 5 s(tˆ 2 t ˆ ) (5) D where the hats indicate proportional changes ˆ 5 d/ and in the case of the tax variables, tˆ5 dt/(11 t). In other words, tˆ is the change in tax as a percentage of the consumer price. The consumer price for ( p ˆ ) equals 1 1 t,sot5pˆ (similarly for p D). Labor earns a fixed gross wage of h and a real wage of w 5 h/p Q, where pq is a price index on the consumption bundle Q(,D). Labor supply is related to the real wage by the uncompensated labor supply elasticity (e): s d Lˆ 5 ewˆ (6)

6 G.E. Metcalf / Journal of Public Economics 87 (2003) onditional on some level of required government services, the model is easily 3 solved for the optimal relationship between the optimal tax rates on and D: t* 5 t* 1 (1 2 et* )t (7) D I next turn to an experiment in comparative statics and consider the effect of an increase in government expenditures (G) on the level of the second-best optimal tax rates as well as on the amount of environmental quality in equilibrium. Before turning to this experiment, however, I note a few points about the optimal tax rates in Eq. (7). First, suppose that environmental tax revenues are sufficient to cover government expenses without a tax on the clean good (t* 5 0). In this case, the tax on D (as well as the difference, td2 t ) exactly equals t. This is the Pigouvian rule in a first-best situation. Second, even if a tax on is required, the first-best rule still holds so long as e equals zero. Third, if neither of these conditions hold, then the Pigouvian tax increment st* D2 t* d falls short of t so long as et is positive. 3. The impact on the environment of increasing government revenue Given the optimizing behavior described in the last section, I now consider the following policy experiment. Imagine that the government needs to raise addition- 4 al distortionary tax revenues to finance an expansion of government services. I investigate how the increase in required distortionary taxes to finance the increase in G changes (1) the Pigouvian tax increment (t* D2 t* ) and (2) the optimal amount of environmental quality (E). Let me first consider the question of the impact of an increase in G on the Pigouvian tax increment. From Eq. (7) we see that d(t 2 t ) 52et dt (8) D and the Pigouvian tax increment will fall if the tax rate on rises as G increases. Rewrite Eq. (7) as t* D5 t 1 (1 2 et)t* and note that the sign of dtd equals the sign of dt if 1 2 et.0. With a high range estimate of e equal to 0.5, the expression 12et will be positive so long as t,2, or that the social marginal damages of pollution do not exceed twice the production cost of the dirty good. I 5 will assume that this condition holds. If we rule out any Laffer tax effects, then 3 Eq. (7) and the government budget constraint will pin down both tax rates. I am only concerned here with the Pigouvian tax increment td2 t. 4 I treat G as an exogenous parameter while the tax rates are set in an optimal fashion. In other words, some political process leads to a choice of G and, conditional on that choice, tax authorities set tax rates to minimize deadweight loss. 5 This condition also ensures that t D. t (see Schob (1997) for an argument that this will hold).

7 318 G.E. Metcalf / Journal of Public Economics 87 (2003) sgn (dt D)5sgn (dt )5sgn (dg).0. With dt.0, Eq. (8) indicates that the Pigouvian tax increment falls as G rises (so long as e.0). An increase in required distortionary tax revenues does not favor increased taxation of the dirty good relative to the clean good. The intuition underlying this result is quite simple. Sandmo (1975) showed that the optimal tax on a polluting good is a weighted average of a Ramsey component and marginal environmental damages (MED). As government revenue needs increase, the weight on the Ramsey component rises and the weight on the environmental component falls. With separability between leisure and consumption goods, the optimal Ramsey components on the two goods are equal. Thus an increase in the Ramsey weight leads to a decrease in the difference between the two tax rates (i.e., the Pigouvian tax increment). Having answered the price question, I now turn to the quantity question. Note that the diversion of resources from the private to the public sector directly affects the environment to the extent that public services themselves may pollute more than the mix of private goods reduced. For example, if public services are entirely clean, the expansion of the government sector will likely lead to a cleaner environment since the increased government output has no impact on the environment. To avoid this demand side effect, I assume that government spends 6 its revenue on the same mix of clean and dirty goods as does the private economy. In other words, dirty government output is a fraction of G equal to p D gg ;]]] G (9) p 1 p D where g is the fraction of G that is dirty and p (p D) is the share of (D) in total production. Environmental quality will increase if ND 1 gg decreases. Differentiating this expression, environmental quality will increase if (1 2 p )Dˆ 1 p G ˆ, 0 (10) G G where pg5 G/NhL and p1 pd1 pg5 1. We can rewrite Eq. (10) in a more instructive form using Eq. (5) and a log linearization of the overall resource constraint: Lˆ 5 p ˆ 1 p Dˆ 1 p G ˆ D G (11) Eqs. (5) and (11) can be substituted into Eq. (10) to obtain (1 2 p )Dˆ 1 p Gˆ 5 ps(tˆ 2 t ˆ ) 1 L ˆ (12) G G D Thus, de. 0 p s(tˆ 2 t ˆ ) 1 L ˆ, 0. The first term on the right hand side of Eq. D 6 This is the approach taken in Harberger (1962) to rule out demand side effects in his classic analysis of the incidence of the corporate income tax. I thank Don Fullerton for suggesting this approach.

8 G.E. Metcalf / Journal of Public Economics 87 (2003) (12) is positive, since the Pigouvian tax increment falls. Regarding the second term, labor supply will fall as the real wage (w) falls so long as labor supply is not completely inelastic. The change in the real wage is given by: ŵ 52ftˆ 2 (1 2 f)t ˆ (13) D where f is the share of consumer spending on the clean good. The real wage (and labor supply) falls since the optimal taxes on both and D increase. The first term in Eq. (12) is a commodity substitution effect. As the Pigouvian tax increment falls, consumers will substitute from to D. The strength of this effect depends on the elasticity of substitution in consumption (s). This substitution effect will work towards reducing environmental quality. The second term is a leisure substitution effect and reflects the fact that the increase in taxation will lead to a substitution away from both produced goods towards leisure. Since leisure is a clean commodity, this effect serves to improve environmental quality. Whether an increase in government spending financed by increased taxes leads to a fall or rise in environmental quality depends on the relative size of the two substitution effects. While the model in this note is quite simple, the basic point is more general. Decreases in the Pigouvian tax increment as public revenue needs rise will affect environmental quality through the commodity substitution channel. But additional channels also affect the supply of environmental quality. In this model, the second channel is a leisure demand channel. A more realistic model would include other factor markets as well as additional commodity markets. Additional realism and complexity does not affect the central point of the note that knowledge of the direction of changes in optimal environmental tax rates due to changes in the economy is not sufficient for understanding the impact on environmental quality. To get a feel for the relative importance of the two offsetting effects in this model, consider the following numerical example where I assume an economy 8 with the characteristics listed in Table 1. With these parameter values, the optimal tax rates are t* , t* D5 0.55, and the Pigouvian tax increment is 0.28,t. Now consider a 10% increase in required government revenue. The Pigouvian tax increment falls by This induces a commodity substitution effect equal to Meanwhile, the leisure substitution effect equals , so the total effect is Multiplying this total effect by p /(p 1 p ) yields the change in ND 1 gg as a fraction of total D D output. With our assumed production shares, the change equals In other 7ˆ t 5 (1 2 et) (11 t )/(11t ) ˆt ; Vt ˆ where V, 1 since t. t and 1 2 et, 1. Thus ˆ D s D d D td2 ˆt 5 (V 2 1)t ˆ, 0. 8 See Fullerton and Metcalf (2001) for a justification for these assumptions. To carry out the comparative statics, we need six equations to measure the general equilibrium effects of an increase in G on, D, L, t, t D, and w. Eqs. (5), (6), (11), and (13) provide four of the six equations. The remaining two come from differentiating the household budget constraint and Eq. (7).

9 320 G.E. Metcalf / Journal of Public Economics 87 (2003) Table 1 Parameter assumptions Parameter Value e 0.30 t 0.30 p 0.30 p 0.40 D p 0.30 G s 1.00 Table 2 Impact of increased revenue requirement on Pigouvian tax increment e s This Table shows d(td2 t ) for a 10% increase in G. words, the 1.5% fall in labor supply will more than offset the commodity 9 substitution effect and pollution falls by 0.6%. Table 2 presents a range of estimates of the impact of a 10% increase in the required revenue on the Pigouvian tax increment while Table 3 shows the impact on the amount of pollution, for differing values of s and e. The Pigouvian tax increment falls in every case while environmental quality Table 3 Impact of increased revenue requirement on dirty production e s This table shows d(nd 1 gg) as a fraction of total output for a 10% increase in G. 9 The improvement in environmental quality depends importantly on the relationship between leisure and pollution. I have made the extreme assumption that leisure is an entirely clean activity. This is clearly not entirely accurate. hanging this assumption does not alter my main message: no conclusion can be drawn as to changes in the amount of environmental quality given a particular change in the Pigouvian tax increment.

10 G.E. Metcalf / Journal of Public Economics 87 (2003) nearly always rises. Only in the case of an elasticity of substitution equal to 2 combined with a low labor supply elasticity (0.15) does the increased revenue requirement fail to reduce pollution. In all other cases, pollution falls between and 1.2%. 4. onclusion I have shown that an increase in government revenue needs has two offsetting impacts on the environmental quality. For reasonable parameter values, environmental quality improves despite the decrease in the Pigouvian tax increment. This result evokes Atkinson and Stern s analysis of public good provision in a second-best world. The first part of their paper focused on how the Samuelson ondition for pure public goods is altered in the presence of distortionary taxation. That question is analogous to the current focus on the relationship between the environmental tax increment (td2 t ) and social marginal damages (t). Atkinson and Stern then pointed out that answering the question of how the Samuelson ondition changes (a price question) tells us nothing about the optimal provision of the public good (a quantity question). Similarly, here learning that the optimal tax increment falls increasingly short of social marginal damages as the need for distortionary taxes rises does not imply that environmental quality must fall as revenue needs increase. On the contrary, a quite plausible result is a cleaner environment. In short, while the focus on tax rates is important for determining optimal second-best levels of environmental taxation (and for adjusting those rates in the face of increased revenue needs), attention should also be paid directly to how pollution itself is altered by changes in the need for distorting taxes. Acknowledgements I appreciate comments from A. Lans Bovenberg and Don Fullerton on an earlier version of this note. I am also grateful for support from the Joint Program on the Science and Policy of Global hange at M.I.T. and a National Science Foundation grant (SBR ) through the National Bureau of Economic Research. 10 The result that environmental quality tends to rise as the Pigouvian tax increment falls in response to an increase in public spending is not particularly sensitive to the distribution of private consumption between the clean and dirty goods. For example, reducing pd to 0.1 and increasing p to 0.6 does not affect the result that pollution falls for the central estimates of e equal to 0.30 and s equal to 1.0. Only in the case where s equals 2.0 and e equals 0.15 does pollution increase with government spending and then only by 0.1%.

11 322 G.E. Metcalf / Journal of Public Economics 87 (2003) References Atkinson, A., Stern, N., Pigou, taxation, and public goods. Review of Economic Studies 41, Bovenberg, A.L., de Mooij, R., Environmental levies and distortionary taxation. American Economic Review 94, Bovenberg, A.L., van der Ploeg, F., Environmental policy, public finance and the labour market in a second-best world. Journal of Public Economics 55 (3), Fullerton, D., Environmental levies and distortionary taxation. American Economic Review 87 (1), , omment. Fullerton, D., Metcalf, G.E., Environmental controls, scarcity rents, and pre-existing distortions. Journal of Public Economics 80 (2), Gaube, T., Distortionary Taxes Preserve the Environment. Department of Economics, University of Bonn, Bonn, Discussion Paper No. A-579. Harberger, A.., The incidence of the corporation income tax. Journal of Political Economy 70 (3), Jaeger, W., Double Dividend Reconsidered. Williams ollege, Williamstown, MA. Lee, D.R., Misiolek, W.S., Substituting pollution taxation for general taxation: some implications for efficiency in pollution taxation. Journal of Environmental Economics and Management 13 (3), Sandmo, A., Optimal taxation in the presence of externalities. Swedish Journal of Economics 77, Schob, R., Environmental taxes and pre-existing distortions: the normalization trap. International Tax and Public Finance 4 (2),