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Environmental taxes and quotas in the presence of distorting taxes in factor markets
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RESOURCE
and ENERGY .
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ELSEVIER
Resource and Energy Economics 19 (1997) 203-220
Environmental taxes and quotas in the presence of distorting taxes in factor markets Ian W . H . Parry * Resources for the Future, 1616 P Street NW, Washington, DC 20036, USA Accepted 6 June 1996
Abstract
Environmental quotas tend to compound the welfare cost of pre-existing tax distortions in the labor market. Under plausible parameters, this source of welfare loss can easily be large enough to outweigh the entire partial equilibrium welfare gain from the quota. Environmental taxes induce the same interaction effect, however they also raise government revenues. If the revenues are used to reduce distortionary taxes, then most of this interaction effect can be offset. Therefore, revenue-raising can be a necessary condition for environmental policies to increase welfare. © 1997 Elsevier Science B.V. JEL classification: Q28; H21; H23 Keywords: Environmental tax; Environmental quota; Pre-existing labor tax; General equilibrium welfare effect
I. Introduction
An understanding of how environmental policies affect economic efficiency is crucial, both for choosing amongst alternative types of policy instruments, and for judging the appropriate level of policy intervention. Up till very recently, environmental policies have usually been evaluated in partial equilibrium models, or at least in models which do not pay attention to the complications posed by distortions in other markets of the economy. Yet public finance economists have
* Phone: (202)328-5151; e-mail: [email protected]. 0928-7655/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. Pll S 0 9 2 8 - 7 6 5 5 ( 9 6 ) 0 0 0 1 2 - 7
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long emphasized the importance of evaluating regulatory policies in general equilibrium models, which do capture the secondary efficiency effects in other distorted markets (Lipsey and Lancaster, 1956-57; Harberger, 1974a,b). The most important source of 'other distortions' are those caused by the tax system, particularly in the labor and capital markets. Indeed a number of recent contributions have shown that the overall welfare effects and optimal level of environmental taxes in the presence of distorting taxes in factor markets, can differ significantly from those implied by partial equilibrium models. Analytical work by Bovenberg and de Mooij (1994), Bovenberg and van der Ploeg (1994) and Parry (1995a), has shown that the potential welfare gain from a revenue-neutral pollution tax in the presence of a pre-existing tax on labor income is generally less than the partial equilibrium effect. 1 The overall effect of the tax can be decomposed into two effects - the revenue-recycling and tax-interaction effects - in addition to the partial equilibrium (or Pigouvian) effect, described in first-best, textbook analyses. 2 The revenue-recycling effect is the welfare gain from using the pollution tax revenues to reduce the pre-existing distortionary tax (relative to when the revenues are returned as lump sum transfers). However, introducing the tax drives up the relative price of (polluting) consumption goods and induces some substitution out of employment and into leisure. This causes a welfare loss (the tax-interaction effect), since the labor tax creates a wedge between the marginal social benefit and marginal social cost of labor. In general the tax-interaction effect dominates the revenue-recycling effect, and only if the polluting good is a sufficiently weaker than average substitute for leisure could the net effect from interactions with the tax system be positive. The optimal environmental tax in these models is typically around 70% of the Pigouvian tax (or marginal environmental damages). 3 Goulder (1995b), and Bovenberg and Goulder (1996a,b,c) have examined the welfare effects of revenue-neutral environmental taxes in a dynamic general equilibrium model, which incorporates a detailed treatment of the tax system and energy sector. The revenue-recycling and tax-interaction effects are more complex in this type of model. Nevertheless the same conclusion - that the potential welfare gains from environmental taxes are lower when full allowance is made for interactions with the tax system - is generally robust. These analytical and empirical contributions have revealed the fundamental flaw in the widely held view that there was a 'double dividend' from environmental taxes. This hypothesis asserted that environmental taxes could simultaneously correct market failures and reduce the welfare costs of the tax system, when the
l This result is implicit in earlier contributions by Sandmo (1975) and Ng (1980). 2 See Parry (1995a) (who used a slightly different terminology), Goulder (1995a) and Oates (1995). 3 Subsidies for goods with positive externalities have symmetrical effects (Sandmo, 1975; Ng, 1980; Parry, 1995b) that is the optimal subsidy is somewhat below marginal environmental benefits,
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revenues are used to cut other taxes. The crucial problem with this argument is that it ignores the efficiency loss from the tax-interaction effect. This effect is generally large enough so that, despite revenue-recycling, the overall impact of environmental taxes is to compound the welfare costs of the tax system. 4 This paper expands on this literature by comparing the welfare effects of environmental taxes with non-auctioned environmental quotas in the presence of a tax on labor income. For a given amount of environmental improvement, the quota causes the same partial equilibrium and tax-interaction effect as the environmental tax, but no revenue-recycling effect. This is a potentially crucial asymmetry, because we show that the revenue-recycling and tax-interaction effects can easily be large relative to the partial equilibrium effect. Therefore, under plausible parameters, the tax-interaction effect can more than offset the entire Pigouvian gain from the quota, and only the environmental tax is potentially welfare-improving. Thus the analysis suggests that the complications posed by pre-existing tax distortions can be a key consideration in instrument choice. This has important implications for the potential choice between a carbon tax versus a system of (freely allocated) carbon permits as a policy to address the possibility of future global warming. It also suggests that the costs of the existing permit program to abate sulfur dioxide emissions could be greatly reduced if the permits were auctioned rather than grandfathered. The results are also relevant to the choice of instrument to regulate fisheries; traffic congestion; the destruction of natural habitat; and so on. More generally, they suggest that the welfare costs of almost any (non-revenue-raising) government regulation may be substantially greater, when allowance is made for the effect on compounding pre-existing tax distortions. Indeed a parallel result has recently emerged in the context of monopoly pricing. Browning (1995) estimated that the welfare costs from monopoly pricing in the U.S. are several orders of magnitude greater, in a model which incorporates pre-existing taxes in the labor market. The next two sections examine the efficiency effects of an environmental tax and quota on a final consumption good, in the presence of a tax on labor income. Section 4 extends the analysis to incorporate the regulation of a (polluting) intermediate good. Section 5 cautions that the general equilibrium welfare effects of environmental policies are considerably more complex than suggested by the simple analytical model used below. Three ways in which the analysis might be usefully extended are discussed. However the basic point - that, despite environmental benefits, revenue-raising can be a necessary condition for environmental policy to be welfare-improving - is likely to be robust. Section 6 summarizes.
4 The rise and fall of the double dividend hypothesis is discussed in detail by Oates (1995) and Goulder (1995a).
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2. The regulation of consumption goods 2.1. The model 5 A one-period model is assumed in which X t . . . . . X k consumption goods are produced in the economy, using labor and possibly intermediate goods. One of these goods, X~, causes damage to the environment of c per unit which is not internalized by the private sector, while all other goods are environmentally clean. As usual, we assume that (private) marginal production costs are constant (for given producer prices). 6 Also, besides the environmental externality, the only other source of distortion in the economy is assumed to be a (proportional) tax of m on labor income. Therefore, there are no imperfections due to monopoly pricing, regulations, other taxes, etc. The government has an exogenous spending requirement of G, which is just returned to households as a lump sum transfer. 7 Choosing units such that the marginal rate of transformation between all consumption goods and leisure is unity, the aggregate household budget constraint can be expressed as k
Y'~Xi+ (1 - m)N= (1 - m)T+ G
(1)
i=1
where N is leisure and T is the household time endowment ( T - N is labor supply). Thus the labor tax is equivalent to a tax on T (which is not distortionary) plus a subsidy for leisure. We assume that the government budget must balance, and therefore any changes in revenues directly or indirectly caused by the environmental policy are offset by adjusting the rate of the pre-existing tax. This is the conventional approach in the optimal tax literature. An alternative is to assume that revenue changes are just neutralized by lump sum transfers, and therefore have no efficiency consequences. However this approach is problematic because it implies there would be no welfare cost to financing regulatory subsidies, and a whole
5 The model used here is the same as in Parry (1995a), which first decomposed the revenue-recycling and tax-interaction effects. However that paper only looked at environmental taxes, and did not examine the size of these effects relative to the partial equilibrium effect. 6 The above type of model readily generalizes to incorporate upward sloping supply curves (Harberger, 1974b; Stem, 1987). In this case the Slutsky demand coefficients used below would be replaced by an analogous reduced form coefficient, which shows how output in a particular market responds to tax changes, when allowance is made for interdependencies in demand and supply across all commodities. 7 The analysis would be the same if G were a public good, so long as the quantity of government spending is held constant.
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range of c o m m o d i t y subsidies which are inefficient in a partial e q u i l i b r i u m sense might then be justified (Parry, 1995b). 8 E n v i r o n m e n t a l regulation causes no first-order effect on disposable household i n c o m e since aggregate tax revenues are constant, and therefore all the d e m a n d coefficients and elasticities below are (Slutsky) compensated. W e also ignore any efficiency effects from changes in the distribution of income. 9 Finally, to facilitate empirical estimation the d e m a n d for X 1 and N are taken to be linear over the relevant range, and therefore the welfare change formulas below are secondorder approximations. 10
2.2. Pollution taxes Suppose a tax of t < c is n o w introduced on X 1. The resulting welfare effect consists of three components: 11 (i) The Pigouvian effect. This is illustrated in Fig. 1 the d e m a n d , supply and marginal social cost curves and XI* are the free market, regulated and P i g o u v i a n The tax produces a welfare gain equal to the shaded the output of a c o m m o d i t y for which marginal social ~2 benefit - which has area
where D 1, S 1 and S 1 + c are respectively, and X °, Xl(t) levels of output respectively. trapezoid - since it reduces cost exceeds marginal social
(c )/xo
(ii) The revenue-recycling effect. This is the welfare gain from using the pollution tax revenues to reduce the labor tax, relative to w h e n they are returned lump s u m and have no efficiency consequences. Let the efficiency cost of raising an additional dollar of (labor) tax revenue be denoted V (this is defined below). The revenue-recycling effect is the product of V and pollution tax revenue, or
W R = VtXI(t)
(3)
which is the shaded rectangle in Fig. 1.
8 This is because these subsidies reduce the price of consumption relative to leisure, and the tax-interaction effect - which is now a welfare gain - can dominate the partial equilibrium loss. 9 These can occur when households differ in their propensity to consume goods and leisure out of additional income. However, in general these effects are thought to be small, and are usually ignored in empirical analysis. lo The purpose here is just to indicate broad orders of magnitude for interactions with the tax system. In general, more precise estimation requires specification of the household utility function and solving the model by numerical simulation. i~ As in Parry (1995a), a graphical analysis is used below to clarify the intuition on this topic, which has been so poorly understood (Oates, 1995). The formulas used below are a simple application of the 'triangles and rectangles' approach developed by Harberger (1974a,b) and others. A more rigorous derivation from utility and production functions is available from the author on request. 12The formula in Eq. (2) also applies when t > c.
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Prie. D1
l+c
M
Sl+c
l+t l+Vt
I
X l"
X l(t )
X1 °
Quanity
Fig. 1.
(iii) The tax-interaction effect. This is illustrated in Fig. 2, where D °, SN and N O are the initial demand, supply and quantity of leisure respectively. 13 D ° is downward sloping because of declining marginal utility from leisure, and SN is perfectly elastic given our assumption of constant marginal production costs. The leisure subsidy drives a wedge of m between the supply and demand price of leisure, which produces a welfare cost of area abc. Typically goods and leisure are substitutes, in which case the demand for leisure will shift out (slightly) when the price of X 1 is driven up by the environmental tax. 14 In Fig. 2 the post-regulation demand and quantity are D 1 and N ~ respectively. Since there is a wedge of m between the marginal social cost and marginal social benefit of leisure, the increase in leisure leads to a welfare loss of rectangle bedc. This rectangle is also the reduction in labor tax revenue indirectly caused by the environmental tax, since N 1 - N O units are no longer
13 The demand and supply of leisure are just the mirror image of the supply of and demand for labor respectively. 14 From Eq. (1) leisure and aggregate consumption, and hence the average consumption good, must be substitutes. Complementarity with leisure is possible for narrowly-defined (polluting) goods such as a lawn mower, but these cases are not considered here. Another interpretation is that the increase in price of X 1 reduces the real wage and therefore reduces labor supply (Bovenberg and de Mooij, 1994).
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Price
\\ a
e
SM
l-m
NO
N1
Quanity
Fig. 2. paying the tax of m. Therefore the total welfare loss from the tax-interaction effect is bedc multiplied by 1 + V, which is the shaded rectangle. This has area 15 W ' = (1 + V ) m ( N ' - N O)
(4)
Labor tax revenue is initially m ( T - N°), and therefore marginal tax revenue is T - N O- m(dN/dm). Also, the welfare loss from the increase in leisure induced by an incremental increase in m is m(dN/dm). Therefore, the efficiency cost of raising an extra dollar of labor tax revenue, or marginal welfare cost of taxation, is 16
m(dNfdm) V= T - N ° - m ( d N / d m ) " Using the Slutsky symmetry property, the increase in leisure is dX1 N 1- N O t d(1 - m)
(5)
(6)
15 Fig. 2 is not drawn to scale: the shaded rectangle is typically very small relative to triangle abc. However, what matters is its size relative to the trapezoid in Fig. 1. 16 For a comprehensive discussion of the marginal welfare cost of taxation see Browning (1987). V is taken as constant in the current analysis, which is a reasonable approximation when environmental tax revenues are small relative to labor tax revenues (Parry, 1995a).
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where 1 - m is the demand price of leisure. Using Eqs. (4)-(6) the tax-interaction effect can be expressed, after some manipulation 17
WI=
05VtX°'~
05 =
,7°N ~.o
(7)
where ~7°u =
dX 1
1- m
d(1 - m)
X°
is the elasticity of demand for X1°) and EO~.
d ( T - N °) d(1 - m )
X1
with respect to the price of leisure (evaluated at
1-m
T-N °
is the labor supply elasticity (evaluated at T - N°). T - N o equals aggregate consumption, 18 therefore e0 can also be interpreted as the elasticity of demand for aggregate, and hence average, consumption with respect to the price of leisure. If X 1 were an average substitute for leisure, then 05 = 1 and comparing (7) with (3) the tax-interaction effect exceeds the revenuerecycling effect because X ° > Xl(t). Only if X 1 were a relatively weak substitute for leisure (05 < 1) could the revenue-recycling effect dominate, and the overall welfare effect of the tax exceed the Pigouvian effect.
2.3. Environmental quotas Suppose, instead of the tax, that a non-auctioned quota is used to restrict output to Xl(t) in Fig. 1. The Pigouvian welfare gain is the same trapezoid, given by Eq. (2). Also, since the price of X 1 relative to leisure increases by the same amount, the tax-interaction effect is again the shaded rectangle in Fig. 2, or Eq. (7). 19 However - despite the taxation of quota rents - there is no revenue-recycling effect. The rents created by the quota are CXl(t) in Fig. 1. These are ultimately received as profits by households, but only at the expense of real labor earnings. That is for a given labor supply, aggregate real output and hence real gross income paid to households is the same in the tax and quota case. Therefore, so long as all
17 Note that 1 + V = V(T - N ° ) / m ( d N / d m ) from (5) and that d N / d m = d(T - N ) / d ( 1 - m). 18 This follows from Eq. (1), and because the initial government budget constraint is G = m(T - NO). 19 We abstract from transactions costs which may hinder the trading of quotas amongst firms. These would reduce the Pigouvian gain from the quota, but would not affect the increase in price of X 1 (which is determined by Xl(t)), and hence the tax-interaction effect.
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income is taxed at the same rate, income tax revenues are the same, regardless of the respective shares o f rent and labor earnings in total income. 20
3. E m p i r i c a l analysis
3.1. Welfare under the Pigouvian rule First of all, suppose that X 1 is an average substitute for leisure (4) = 1) and that the Pigouvian rule is adopted, therefore t = c and output is X1* in Fig. 1. The Pigouvian welfare gain is now a triangle with area c W P = -~( X ° - X,*)
(2a)
Using Eqs. (2a), (3) and (7), the size of the tax-interaction effect, and tax-interaction effect net of the revenue-recycling effect, expressed relative to the Pigouvian effect, are Wl
2V
w P -
Xl
W 1_
W R
(8)
and
We
2V
(9)
respectively, where xl* = ( X ° - X l * ) / X ° is the proportionate reduction in X 1. To estimate V, Eq. (5) is easily manipulated to give (m/(1 V= 1 - (m/(1
-m))e ° -m))e °
(5a)
which is (essentially) the formula used by Browning (1987). Based on the existing empirical literature, he concluded that the most likely ranges for the (marginal) rate of labor tax and compensated labor supply elasticity are 0 . 3 8 - 0 . 4 8 and 0 . 2 - 0 . 4 respectively. F r o m (5a) this gives a range of (approximately) 0 . 1 5 - 0 . 6 for the marginal welfare cost of taxation, with a central estimate of 0.3. Table 1 compares the welfare loss from interactions with the tax system under
20 In the U.S. non-labor income is taxed at a slightly lower rate than labor income. (Both are subject to income taxes, but the effects of corporate taxation on the former are outweighed by the effects of social security taxation on the latter.) Thus for a given level of real income, a quota which increases the share of non-labor income at the expense of labor income would reduce overall tax revenues and lead to a negative revenue-recycling effect. By ignoring this, the above analysis (slightly) understates the asymmetry between pollution taxes and quotas.
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Table 1 Welfare loss from interactions with the tax system under the Pigouvian rule (relative to the Pigouvian effect) Policy
x1 *
Quota
0.05 0.2 0.6
Tax
V 0.15
0.3
0.6
6 1.5 0.5
12 3 1
24 6 2
0.3
0.6
1.2
quota and tax, expressed relative to the Pigouvian triangle, using Eqs. (8) and (9). The startling result is that the welfare loss from the tax-interaction effect can easily exceed the entire Pigouvian welfare gain from an environmental quota (this occurs when the cell entry exceeds unity). For example when V = 0.3, the tax-interaction effect is 12 times, 3 times and the same size as the Pigouvian effect, when the proportionate reduction in output is 5%, 20% and 60% respectively. Even under a very low estimate for the marginal welfare cost of taxation ( V = 0.15), the tax-interaction effect is still crucial to determining at least the magnitude, if not the sign, of the general equilibrium effect from the quota. In the case of the Pigouvian tax, the net loss from interactions with the tax system is much smaller, but can still offset a large amount of the Pigouvian gain. For example, when V = 0.3 the tax-interaction effect net of the revenue-recycling effect is 60% of the Pigouvian triangle. The intuition behind the quota result is straightforward. Most of the substitution away from X~ will lead to higher demand for other consumption goods rather than leisure - that is, the base of the shaded rectangle in Fig. 2 is small relative to the base of the Pigouvian triangle. However, the welfare cost per additional unit of leisure is large because taxes effectively drive a substantial wedge between the marginal social cost and marginal social benefit of leisure (around 40%) - that is, the height of the rectangle can be large relative to the height of the triangle. 21 3.2. Welfare under the optimal environmental tax The above results may be unduly pessimistic because they calculate welfare effects at the Pigouvian level of regulation, rather than the second-best optimal
21 AS mentioned above, the results are consistent with Browning (1995), who found that the welfare loss in the labor market caused by monopoly pricing is much larger than the Harberger triangles in the product markets. Previous empirical studies in environmental economics emphasized the relative importance of the revenue-recycling effect, but did not take into account the - even more important tax-interaction effect. For example, Nordhaus (1993) estimated that revenue-recycling increased the optimal tax on carbon from $5 per ton to $59 per ton.
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213
level. Therefore this subsection compares taxes and quotas when regulation is equivalent to that of the optimal environmental tax, maintaining the assumption that ~b = 1. Adding Eqs. (2) and (3), subtracting Eq. (7), and differentiating with respect to the reduction in Xl(t), gives the following formula for marginal welfare under the environmental tax:
c--~-Vt+
+V ( X ° - X l ( t ) ) d X , ( t )
Equating this with 0, and noting that dX~ t X ° - Xl(t) = - - - t = -Xl*X ° dt c
(10)
gives the following formula for the optimal environmental tax (Parry, 1995a): t c
1 I+2V
(11)
This lies between 45% and 77% of the Pigouvian tax, given our range for V. Under this level of regulation, the welfare loss from interactions with the tax system under the environmental quota and tax, relative to the Pigouvian effect, are (from Eqs. (2), (3), (7), (10) and (11)) WI
2 V ( l -3t-2 V )
WP
(1 + 4 V ) x ,
,
(8b)
and Wl _
W R
We
2V = - -
(9b)
1 + 4V
respectively. Table 2 shows calculations of Eqs. (8b) and (9b). The welfare loss from interactions with the tax system is now much smaller for the pollution tax,
Table 2 Welfare loss from interactions with the tax system under the second-best optimal tax (relative to the Pigouvian effect) Policy
Quota
Tax
x1 *
0.05 0.2 0.6
v 0.15
0.3
0.6
4.88 1.22 0.41
8.73 2.18 0.73
15.53 3.88 1.29
0.19
0.27
0.35
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Table 3 Sensitivity with respect to ¢ Policy
xI *
~b 0.5
1.5
Quo~
0.05 0.2 0.6
6.0 1.5 0.5
18.0 4.5 1.5
T~
0.05 0.2 0.6
-5.4 -0.9 0.1
6.6 2.1 1.1
between 19% and 35% of the Pigouvian gain. However, the tax-interaction effect is still crucial for the magnitude, and possibly the sign, of the general equilibrium welfare effect from the quota (again a cell entry greater than unity indicates that the overall welfare impact of the policy is negative). 3.3. Degree of substitution with leisure The above calculations assume that the regulated commodity is an average substitute for leisure. In general this may be the best assumption we can make, since it is usually very difficult to estimate the degree of substitution between particular goods and leisure. 2z However, it is useful to examine how sensitive the results are to relaxing this assumption. Returning to the case when the Pigouvian rule t = c is adopted, the relative effect from interactions with the tax system under the environmental quota and tax are (using Eqs. (2a), (3), (7) and (10) when ~b 4: 1) Wl wp =
2thV (8c)
X 1"
and
W'- WR Wr,
2V(~b- 1 + x : ) • x1
(9c)
respectively. Table 3 calculates these formulas when the elasticity of demand for X 1 with respect to the price of leisure is 50% below and 50% above that for the average good, and assuming the central estimate of 0.3 for V. Clearly the results are sensitive to ~b, for example under the Pigouvian tax when x~* = 0.2, there is a net
22 See for example Deaton and Muellbauer (1980, Ch. 3). The numerical models discussed in the introduction restrict utility - by assuming leisure is weakly separable and preferences are homothetic over consumption goods - such that all goods are equal substitutes for leisure.
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215
loss from interactions with the tax system equal to 210% of the Pigouvian effect if ~b = 1.5, and a gain of 90% if ~b = 0.5. However, even in the scenario when X 1 is a relatively weak substitute for leisure, the tax-interaction effect exceeds the Pigouvian effect from an environmental quota when x I = 0.05 and 0.2, and offsets 50% of it when x~ = 0.6.
4. The regulation of intermediate goods This section extends the previous analysis to examine the welfare effect of environmental regulations imposed on an intermediate good (gasoline, coal, pesticides, etc.). We assume this good, denoted Z, is produced competitively with constant marginal cost (normalized to unity), is used in the production of X~, and causes an environmental damage of c per unit. All other assumptions from before are maintained, and there is no regulation of X 1.
4.1. Environmental taxes and quotas Suppose the Pigouvian tax of t = c is imposed on Z, and the revenues are used to reduce the labor tax. Analogous to before, the general equilibrium welfare effect consists of: (i) The Pigouvian welfare gain triangle, given by
wP=
c
*)
(2')
where Z* is the Pigouvian level of output. The reduction in Z consists of the familiar substitution effect (the replacement of Z for other inputs in production) plus the output effect (the fall in demand for Z from the reduction in X 1). (ii) The welfare gain from the revenue-recycling effect, which is w
= VcZ*.
(3')
(iii) The welfare loss from the tax-interaction effect. This occurs because the increase in cost of Z drives up the price of X 1, thereby inducing some substitution into leisure. 23 Denoting the price increase by Apl, then analogous to (7), the tax-interaction effect can be expressed W l = 6VX°Apl.
(7')
To a second-order approximation, the price of X~ increases by the product of c and the average of the ex ante and ex post ratio of Z to X 1 (see Appendix A).
23 Despite possible substitution of labor for Z in the production of X1, the tax-interaction effect is positive, assuming X l and leisure are substitutes. This is because the aggregate quantity of leisure is determined by the price of leisure relative to consumption, and must increase when the price of X 1 increases.
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This ratio falls by tx(Z ° - Z *) / X °, where /x is the fraction of the total reduction in Z due to the substitution effect. Therefore
c( ap, = Xo z ° -
tZ z O _ z . ) 7 ( ) "
(12)
From Eqs. (12) and (7'), the tax-interaction effect is
( 2)
W ~= chVcZ ° 1 -
/xz
(7")
where z* = (Z ° - Z* ) / Z ° is the proportionate reduction in Z. Comparing Eq. (7") with Eq. (3'), we have essentially the same result as before. That is, the tax-interaction effect exceeds the revenue-recycling effect, except possibly in the case when final output from the polluting sector is a relatively weak substitute for leisure (th < 1). 24 Again, a non-auctioned environmental quota which has the equivalent Pigouvian welfare effect in Eq. (2'), causes the same tax-interaction effect (Eq. (7")), but no revenue-recycling effect.
4.2. Empirical comparison Using Eqs. (2'), (3') and (7"), the welfare loss from interactions with the tax system (relative to the Pigouvian effect) under the environmental quota and tax are 2~bV( 1 - / z z */2}
W I
WP
=
(8')
Z*
and
W'-W' WP
2V{qb(1-tzz*/2)-
z*
(l-z*)} (9')
Table 4 shows simulations on Eqs. (8') and (9'), assuming X 1 is an average substitute for leisure and V = 0.3. If Z is used in fixed proportions to output, then all of the reduction in Z is due to the output effect and /z = 0 (third column). In this case, the relative welfare loss from interactions with the tax system is the same as in Table 1.25 The other extreme is when all the reduction in Z is due to the substitution effect, that is /z = 1 (fourth column). This has some impact on reducing the tax-interaction effect, for example the relative welfare cost of
24 Again, it has long been recognized in optimal tax models (which do not decompose the revenue-recycling and tax-interaction effects) that in general the welfare effect from interactions with the tax system is negative for taxes on intermediate goods (Diamond and Mirrlees, 1971). 25 For a given reduction in final output, regulating a factor input is equivalent to regulating final output, when the factor is used in fixed proportions (Wisecarver, 1974).
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Table 4 Intermediate goods Policy
z 0
Quota
0.05 0.2 0.6
Tax
0.05 0.2 0.6
12 3 1 0.6 0.6 0.6
217
/z 1 11.7 2.7 0.7 0.3 0.3 0.3
interactions with the tax system are reduced from 60% to 30% under the Pigouvian tax. However, for the quota it makes little empirical difference to the previous conclusion that the tax-interaction effect can easily dominate the Pigouvian welfare gain. For example, the tax-interaction effect is still 11.7 and 2.7 times as large as the Pigouvian triangle when the proportionate reduction in Z is 5% and 20% respectively.
5. Generalizing the analysis In practice the general equilibrium welfare effects of environmental policies are considerably more complex than suggested by the simple analytical model used above. This section briefly discusses three ways in which the analysis might be extended. However, the basic result - that revenue-raising can be a necessary condition for environmental policy to increase welfare - is likely to be robust in more general models. 5.1. Interactions with the capital market
The other market in the economy which is substantially distorted by taxes is the capital market. To the extent that an environmental policy reduces investment rather than consumption, it will compound the welfare cost of taxes on capital rather than labor (Bovenberg and Goulder, 1996b). Therefore, assuming the marginal welfare cost of taxation is greater for capital than for labor, 26 incorporating capital into the above analysis is likely, if anything, to increase the welfare loss from the tax-interaction effect. On the other hand, if environmental tax revenues are used to reduce taxes on capital, the revenue-recycling effect, and hence the asymmetry between taxes and quotas, will be larger.
26 See for example Lucas (1990).
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5.2. Non-tax distortions
Market imperfections due to non-tax factors such as monopoly pricing, government regulations, imperfect information and externalities, are quite pervasive in the economy. Therefore, a specific environmental regulation could potentially cause efficiency effects in a variety of other markets in addition to the labor and capital markets. However, taken individually these other efficiency effects are likely to be empirically unimportant, unless the market is severely distorted and closely related to that being regulated. In this connection, Oates and Strassmann (1984) suggest that pre-existing distortions in product markets due to monopoly pricing do not substantially affect the overall welfare effect of environmental policies. This is mainly because the price wedges caused by imperfect competition are much smaller than those caused by the tax system. Nevertheless, a recent paper by Browning (1994) suggests that the aggregate impact of non-tax distortions could be significant. He estimated that non-tax distortions effectively increase the overall distortion in the labor market from 43% to around 55%. Therefore, by ignoring these non-tax factors, the above analysis may significantly understate the revenue-recycling and tax-interaction effects. 5.3. Command and control regulations
Command and control regulations are much more prevalent in practice than the pure taxes and quotas analyzed above. Like quotas, they do not raise revenues. They also increase marginal production costs, and hence increase the relative price of consumption goods, and induce a tax-interaction effect similar to that discussed above. However by constraining the method of abatement, they typically lead to production inefficiency and higher (partial equilibrium) abatement costs than the equivalent quota. A useful extension to the analysis would be to consider the contribution of the tax-interaction effect, relative to that from production inefficiency, in the overall abatement costs from command and control regulations.
6. Summary By increasing the relative price of consumption goods, environmental policies typically induce some substitution into leisure, which compounds the welfare cost of tax distortions in the labor market. Under plausible parameters, this effect can dominate the partial equilibrium effect of the policy. Therefore, despite environmental benefits, the overall welfare impact from imposing the Pigouvian quota could be negative. However, an environmental tax raises revenues and if these are used to reduce the labor tax, most of this interaction effect can be offset. Thus in some cases only revenue-raising environmental policies can potentially increase welfare.
1.W.H. Parry~Resource and Energy Economics 19 (1997) 203-220
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Acknowledgements This paper is a revised version of an earlier draft, 'Environmental Policy in a Second Best World'. I am grateful to Larry Goulder, Mark Harrison, Larry Sjaastad, David Starrett, and seminar participants at Chicago, Maryland, NBER and Resources for the Future for very helpful comments.
Appendix A. Deriving Eq. (12) From a second-order Taylor series expansion, the change in total cost (to) of producing X l, following a change of c in the price of input Z is do~ C
dpz
c 2 d2to -I-----
2 dp~
where Pz is the price of Z. Dividing by X ° to convert to marginal production costs and substituting d to/dpz = Z ° (from Shephard's lemma) and c(d2to/dp~) = / z ( Z * - Z°), gives Eq. (12).
References Bovenberg, A.L. and R.A. de Mooij, 1994, Environmental levies and distortionary taxation, American Economic Review 84, 1085-1089. Bovenberg, A.L. and L.H. Goulder, 1996a, Optimal environmental taxation in the presence of other taxes: An applied general equilibrium analysis, American Economic Review, forthcoming. Bovenberg, A.L. and L.H. Goulder, 1996b, Costs of environmentally motivated taxes in the presence of other taxes: General equilibrium analyses (Stanford University, Stanford, CA). Bovenberg, A.L. and L.H. Goulder, 1996c, Integrating environmental and distortionary taxes: General equilibrium analysis (Stanford University, Stanford, CA). Bovenberg, A.L. and F. van der Ploeg, 1994, Environmental policy, public finance and the labor market in a second best world, Journal of Public Economics 55, 349-390. Browning, E.K., 1995, The welfare cost of monopoly and other output distortions (Department of Economics, Texas A&M University, College Station, TX). Browning, E.K., 1994, The non-tax wedge, Journal of Public Economics 53, 419-433. Browning, E.K., 1987, On the marginal welfare cost of taxation, American Economic Review 77, 28-38. Deaton, A. and J. Muellbauer, 1980, Economics and consumer behavior (Cambridge University Press, New York). Diamond, P. and J. Mirrlees, 1971, Optimal taxation and public production II: Tax rules, American Economic Review 61,261-278. Goulder, L.H., 1995a, Environmental taxation and the 'double dividend': A reader's guide, International Tax and Public Finance 2, 157-184. Goulder, L.H., 1995b, Effects of carbon taxes in an economy with prior tax distortions: An intertemporal general equilibrium analysis, Journal of Environmental Economics and Management 29, 271-297.
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Harberger, A.C., 1974a, Taxation, resource allocation and welfare, In: Taxation and welfare (University of Chicago Press, Chicago, IL). Harberger, A.C., 1974b, The measurement of waste, In: Taxation and welfare (University of Chicago Press, Chicago, IL). Lipsey, R.G. and K. Lancaster, 1956-57, The general theory of the second best, Review of Economic Studies 24, 11-32. Lucas, R.E., 1990, Supply-side economics: An analytical review, Oxford Economic Papers 42, 293-316. Ng, Y.K., 1980, Optimal corrective taxes or subsidies when revenue-raising imposes an excess burden, American Economic Review 70, 744-751. Nordhaus, W.D., 1993, Optimal greenhouse gas reductions and tax policy in the 'DICE' model, American Economic Review 83, 313-317. Oates, W.E., 1995, Green taxes: Can we protect the environment and improve the tax system at the same time? (presidential Address), Southern Economics Joumal 915-922. Oates, W.E. and D.L. Strassmann, 1984, Effluent fees and market structure, Journal of Public Economics 24, 29-46. Parry, I.W., 1995a, Pollution taxes and revenue recycling, Journal of Environmental Economics and Management 29, $64-$77. Parry, I.W., 1995b, The effects of environmental subsidies in the presence of distorting taxes (Resources for the Future, Washington, DC). Sandmo, A., 1975, Optimal taxation in the prescence of externalites, Swedish Journal of Economics, 77, 86-98. Stem, N.H., 1987, Aspects of the theory of tax reform, In: D. Newberry and N.H. Stern, eds., The theory of taxation for developing countries (Oxford University Press, New York). Wisecarver, D., 1974, The social costs of input market distortions, American Economic Review 64, 359-372.
r,
RESOURCE
and ENERGY .
ECONOMICS
!
ELSEVIER
Resource and Energy Economics 19 (1997) 203-220
Environmental taxes and quotas in the presence of distorting taxes in factor markets Ian W . H . Parry * Resources for the Future, 1616 P Street NW, Washington, DC 20036, USA Accepted 6 June 1996
Abstract
Environmental quotas tend to compound the welfare cost of pre-existing tax distortions in the labor market. Under plausible parameters, this source of welfare loss can easily be large enough to outweigh the entire partial equilibrium welfare gain from the quota. Environmental taxes induce the same interaction effect, however they also raise government revenues. If the revenues are used to reduce distortionary taxes, then most of this interaction effect can be offset. Therefore, revenue-raising can be a necessary condition for environmental policies to increase welfare. © 1997 Elsevier Science B.V. JEL classification: Q28; H21; H23 Keywords: Environmental tax; Environmental quota; Pre-existing labor tax; General equilibrium welfare effect
I. Introduction
An understanding of how environmental policies affect economic efficiency is crucial, both for choosing amongst alternative types of policy instruments, and for judging the appropriate level of policy intervention. Up till very recently, environmental policies have usually been evaluated in partial equilibrium models, or at least in models which do not pay attention to the complications posed by distortions in other markets of the economy. Yet public finance economists have
* Phone: (202)328-5151; e-mail: [email protected]. 0928-7655/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. Pll S 0 9 2 8 - 7 6 5 5 ( 9 6 ) 0 0 0 1 2 - 7
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long emphasized the importance of evaluating regulatory policies in general equilibrium models, which do capture the secondary efficiency effects in other distorted markets (Lipsey and Lancaster, 1956-57; Harberger, 1974a,b). The most important source of 'other distortions' are those caused by the tax system, particularly in the labor and capital markets. Indeed a number of recent contributions have shown that the overall welfare effects and optimal level of environmental taxes in the presence of distorting taxes in factor markets, can differ significantly from those implied by partial equilibrium models. Analytical work by Bovenberg and de Mooij (1994), Bovenberg and van der Ploeg (1994) and Parry (1995a), has shown that the potential welfare gain from a revenue-neutral pollution tax in the presence of a pre-existing tax on labor income is generally less than the partial equilibrium effect. 1 The overall effect of the tax can be decomposed into two effects - the revenue-recycling and tax-interaction effects - in addition to the partial equilibrium (or Pigouvian) effect, described in first-best, textbook analyses. 2 The revenue-recycling effect is the welfare gain from using the pollution tax revenues to reduce the pre-existing distortionary tax (relative to when the revenues are returned as lump sum transfers). However, introducing the tax drives up the relative price of (polluting) consumption goods and induces some substitution out of employment and into leisure. This causes a welfare loss (the tax-interaction effect), since the labor tax creates a wedge between the marginal social benefit and marginal social cost of labor. In general the tax-interaction effect dominates the revenue-recycling effect, and only if the polluting good is a sufficiently weaker than average substitute for leisure could the net effect from interactions with the tax system be positive. The optimal environmental tax in these models is typically around 70% of the Pigouvian tax (or marginal environmental damages). 3 Goulder (1995b), and Bovenberg and Goulder (1996a,b,c) have examined the welfare effects of revenue-neutral environmental taxes in a dynamic general equilibrium model, which incorporates a detailed treatment of the tax system and energy sector. The revenue-recycling and tax-interaction effects are more complex in this type of model. Nevertheless the same conclusion - that the potential welfare gains from environmental taxes are lower when full allowance is made for interactions with the tax system - is generally robust. These analytical and empirical contributions have revealed the fundamental flaw in the widely held view that there was a 'double dividend' from environmental taxes. This hypothesis asserted that environmental taxes could simultaneously correct market failures and reduce the welfare costs of the tax system, when the
l This result is implicit in earlier contributions by Sandmo (1975) and Ng (1980). 2 See Parry (1995a) (who used a slightly different terminology), Goulder (1995a) and Oates (1995). 3 Subsidies for goods with positive externalities have symmetrical effects (Sandmo, 1975; Ng, 1980; Parry, 1995b) that is the optimal subsidy is somewhat below marginal environmental benefits,
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revenues are used to cut other taxes. The crucial problem with this argument is that it ignores the efficiency loss from the tax-interaction effect. This effect is generally large enough so that, despite revenue-recycling, the overall impact of environmental taxes is to compound the welfare costs of the tax system. 4 This paper expands on this literature by comparing the welfare effects of environmental taxes with non-auctioned environmental quotas in the presence of a tax on labor income. For a given amount of environmental improvement, the quota causes the same partial equilibrium and tax-interaction effect as the environmental tax, but no revenue-recycling effect. This is a potentially crucial asymmetry, because we show that the revenue-recycling and tax-interaction effects can easily be large relative to the partial equilibrium effect. Therefore, under plausible parameters, the tax-interaction effect can more than offset the entire Pigouvian gain from the quota, and only the environmental tax is potentially welfare-improving. Thus the analysis suggests that the complications posed by pre-existing tax distortions can be a key consideration in instrument choice. This has important implications for the potential choice between a carbon tax versus a system of (freely allocated) carbon permits as a policy to address the possibility of future global warming. It also suggests that the costs of the existing permit program to abate sulfur dioxide emissions could be greatly reduced if the permits were auctioned rather than grandfathered. The results are also relevant to the choice of instrument to regulate fisheries; traffic congestion; the destruction of natural habitat; and so on. More generally, they suggest that the welfare costs of almost any (non-revenue-raising) government regulation may be substantially greater, when allowance is made for the effect on compounding pre-existing tax distortions. Indeed a parallel result has recently emerged in the context of monopoly pricing. Browning (1995) estimated that the welfare costs from monopoly pricing in the U.S. are several orders of magnitude greater, in a model which incorporates pre-existing taxes in the labor market. The next two sections examine the efficiency effects of an environmental tax and quota on a final consumption good, in the presence of a tax on labor income. Section 4 extends the analysis to incorporate the regulation of a (polluting) intermediate good. Section 5 cautions that the general equilibrium welfare effects of environmental policies are considerably more complex than suggested by the simple analytical model used below. Three ways in which the analysis might be usefully extended are discussed. However the basic point - that, despite environmental benefits, revenue-raising can be a necessary condition for environmental policy to be welfare-improving - is likely to be robust. Section 6 summarizes.
4 The rise and fall of the double dividend hypothesis is discussed in detail by Oates (1995) and Goulder (1995a).
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2. The regulation of consumption goods 2.1. The model 5 A one-period model is assumed in which X t . . . . . X k consumption goods are produced in the economy, using labor and possibly intermediate goods. One of these goods, X~, causes damage to the environment of c per unit which is not internalized by the private sector, while all other goods are environmentally clean. As usual, we assume that (private) marginal production costs are constant (for given producer prices). 6 Also, besides the environmental externality, the only other source of distortion in the economy is assumed to be a (proportional) tax of m on labor income. Therefore, there are no imperfections due to monopoly pricing, regulations, other taxes, etc. The government has an exogenous spending requirement of G, which is just returned to households as a lump sum transfer. 7 Choosing units such that the marginal rate of transformation between all consumption goods and leisure is unity, the aggregate household budget constraint can be expressed as k
Y'~Xi+ (1 - m)N= (1 - m)T+ G
(1)
i=1
where N is leisure and T is the household time endowment ( T - N is labor supply). Thus the labor tax is equivalent to a tax on T (which is not distortionary) plus a subsidy for leisure. We assume that the government budget must balance, and therefore any changes in revenues directly or indirectly caused by the environmental policy are offset by adjusting the rate of the pre-existing tax. This is the conventional approach in the optimal tax literature. An alternative is to assume that revenue changes are just neutralized by lump sum transfers, and therefore have no efficiency consequences. However this approach is problematic because it implies there would be no welfare cost to financing regulatory subsidies, and a whole
5 The model used here is the same as in Parry (1995a), which first decomposed the revenue-recycling and tax-interaction effects. However that paper only looked at environmental taxes, and did not examine the size of these effects relative to the partial equilibrium effect. 6 The above type of model readily generalizes to incorporate upward sloping supply curves (Harberger, 1974b; Stem, 1987). In this case the Slutsky demand coefficients used below would be replaced by an analogous reduced form coefficient, which shows how output in a particular market responds to tax changes, when allowance is made for interdependencies in demand and supply across all commodities. 7 The analysis would be the same if G were a public good, so long as the quantity of government spending is held constant.
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range of c o m m o d i t y subsidies which are inefficient in a partial e q u i l i b r i u m sense might then be justified (Parry, 1995b). 8 E n v i r o n m e n t a l regulation causes no first-order effect on disposable household i n c o m e since aggregate tax revenues are constant, and therefore all the d e m a n d coefficients and elasticities below are (Slutsky) compensated. W e also ignore any efficiency effects from changes in the distribution of income. 9 Finally, to facilitate empirical estimation the d e m a n d for X 1 and N are taken to be linear over the relevant range, and therefore the welfare change formulas below are secondorder approximations. 10
2.2. Pollution taxes Suppose a tax of t < c is n o w introduced on X 1. The resulting welfare effect consists of three components: 11 (i) The Pigouvian effect. This is illustrated in Fig. 1 the d e m a n d , supply and marginal social cost curves and XI* are the free market, regulated and P i g o u v i a n The tax produces a welfare gain equal to the shaded the output of a c o m m o d i t y for which marginal social ~2 benefit - which has area
where D 1, S 1 and S 1 + c are respectively, and X °, Xl(t) levels of output respectively. trapezoid - since it reduces cost exceeds marginal social
(c )/xo
(ii) The revenue-recycling effect. This is the welfare gain from using the pollution tax revenues to reduce the labor tax, relative to w h e n they are returned lump s u m and have no efficiency consequences. Let the efficiency cost of raising an additional dollar of (labor) tax revenue be denoted V (this is defined below). The revenue-recycling effect is the product of V and pollution tax revenue, or
W R = VtXI(t)
(3)
which is the shaded rectangle in Fig. 1.
8 This is because these subsidies reduce the price of consumption relative to leisure, and the tax-interaction effect - which is now a welfare gain - can dominate the partial equilibrium loss. 9 These can occur when households differ in their propensity to consume goods and leisure out of additional income. However, in general these effects are thought to be small, and are usually ignored in empirical analysis. lo The purpose here is just to indicate broad orders of magnitude for interactions with the tax system. In general, more precise estimation requires specification of the household utility function and solving the model by numerical simulation. i~ As in Parry (1995a), a graphical analysis is used below to clarify the intuition on this topic, which has been so poorly understood (Oates, 1995). The formulas used below are a simple application of the 'triangles and rectangles' approach developed by Harberger (1974a,b) and others. A more rigorous derivation from utility and production functions is available from the author on request. 12The formula in Eq. (2) also applies when t > c.
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208
Prie. D1
l+c
M
Sl+c
l+t l+Vt
I
X l"
X l(t )
X1 °
Quanity
Fig. 1.
(iii) The tax-interaction effect. This is illustrated in Fig. 2, where D °, SN and N O are the initial demand, supply and quantity of leisure respectively. 13 D ° is downward sloping because of declining marginal utility from leisure, and SN is perfectly elastic given our assumption of constant marginal production costs. The leisure subsidy drives a wedge of m between the supply and demand price of leisure, which produces a welfare cost of area abc. Typically goods and leisure are substitutes, in which case the demand for leisure will shift out (slightly) when the price of X 1 is driven up by the environmental tax. 14 In Fig. 2 the post-regulation demand and quantity are D 1 and N ~ respectively. Since there is a wedge of m between the marginal social cost and marginal social benefit of leisure, the increase in leisure leads to a welfare loss of rectangle bedc. This rectangle is also the reduction in labor tax revenue indirectly caused by the environmental tax, since N 1 - N O units are no longer
13 The demand and supply of leisure are just the mirror image of the supply of and demand for labor respectively. 14 From Eq. (1) leisure and aggregate consumption, and hence the average consumption good, must be substitutes. Complementarity with leisure is possible for narrowly-defined (polluting) goods such as a lawn mower, but these cases are not considered here. Another interpretation is that the increase in price of X 1 reduces the real wage and therefore reduces labor supply (Bovenberg and de Mooij, 1994).
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209
Price
\\ a
e
SM
l-m
NO
N1
Quanity
Fig. 2. paying the tax of m. Therefore the total welfare loss from the tax-interaction effect is bedc multiplied by 1 + V, which is the shaded rectangle. This has area 15 W ' = (1 + V ) m ( N ' - N O)
(4)
Labor tax revenue is initially m ( T - N°), and therefore marginal tax revenue is T - N O- m(dN/dm). Also, the welfare loss from the increase in leisure induced by an incremental increase in m is m(dN/dm). Therefore, the efficiency cost of raising an extra dollar of labor tax revenue, or marginal welfare cost of taxation, is 16
m(dNfdm) V= T - N ° - m ( d N / d m ) " Using the Slutsky symmetry property, the increase in leisure is dX1 N 1- N O t d(1 - m)
(5)
(6)
15 Fig. 2 is not drawn to scale: the shaded rectangle is typically very small relative to triangle abc. However, what matters is its size relative to the trapezoid in Fig. 1. 16 For a comprehensive discussion of the marginal welfare cost of taxation see Browning (1987). V is taken as constant in the current analysis, which is a reasonable approximation when environmental tax revenues are small relative to labor tax revenues (Parry, 1995a).
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where 1 - m is the demand price of leisure. Using Eqs. (4)-(6) the tax-interaction effect can be expressed, after some manipulation 17
WI=
05VtX°'~
05 =
,7°N ~.o
(7)
where ~7°u =
dX 1
1- m
d(1 - m)
X°
is the elasticity of demand for X1°) and EO~.
d ( T - N °) d(1 - m )
X1
with respect to the price of leisure (evaluated at
1-m
T-N °
is the labor supply elasticity (evaluated at T - N°). T - N o equals aggregate consumption, 18 therefore e0 can also be interpreted as the elasticity of demand for aggregate, and hence average, consumption with respect to the price of leisure. If X 1 were an average substitute for leisure, then 05 = 1 and comparing (7) with (3) the tax-interaction effect exceeds the revenuerecycling effect because X ° > Xl(t). Only if X 1 were a relatively weak substitute for leisure (05 < 1) could the revenue-recycling effect dominate, and the overall welfare effect of the tax exceed the Pigouvian effect.
2.3. Environmental quotas Suppose, instead of the tax, that a non-auctioned quota is used to restrict output to Xl(t) in Fig. 1. The Pigouvian welfare gain is the same trapezoid, given by Eq. (2). Also, since the price of X 1 relative to leisure increases by the same amount, the tax-interaction effect is again the shaded rectangle in Fig. 2, or Eq. (7). 19 However - despite the taxation of quota rents - there is no revenue-recycling effect. The rents created by the quota are CXl(t) in Fig. 1. These are ultimately received as profits by households, but only at the expense of real labor earnings. That is for a given labor supply, aggregate real output and hence real gross income paid to households is the same in the tax and quota case. Therefore, so long as all
17 Note that 1 + V = V(T - N ° ) / m ( d N / d m ) from (5) and that d N / d m = d(T - N ) / d ( 1 - m). 18 This follows from Eq. (1), and because the initial government budget constraint is G = m(T - NO). 19 We abstract from transactions costs which may hinder the trading of quotas amongst firms. These would reduce the Pigouvian gain from the quota, but would not affect the increase in price of X 1 (which is determined by Xl(t)), and hence the tax-interaction effect.
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211
income is taxed at the same rate, income tax revenues are the same, regardless of the respective shares o f rent and labor earnings in total income. 20
3. E m p i r i c a l analysis
3.1. Welfare under the Pigouvian rule First of all, suppose that X 1 is an average substitute for leisure (4) = 1) and that the Pigouvian rule is adopted, therefore t = c and output is X1* in Fig. 1. The Pigouvian welfare gain is now a triangle with area c W P = -~( X ° - X,*)
(2a)
Using Eqs. (2a), (3) and (7), the size of the tax-interaction effect, and tax-interaction effect net of the revenue-recycling effect, expressed relative to the Pigouvian effect, are Wl
2V
w P -
Xl
W 1_
W R
(8)
and
We
2V
(9)
respectively, where xl* = ( X ° - X l * ) / X ° is the proportionate reduction in X 1. To estimate V, Eq. (5) is easily manipulated to give (m/(1 V= 1 - (m/(1
-m))e ° -m))e °
(5a)
which is (essentially) the formula used by Browning (1987). Based on the existing empirical literature, he concluded that the most likely ranges for the (marginal) rate of labor tax and compensated labor supply elasticity are 0 . 3 8 - 0 . 4 8 and 0 . 2 - 0 . 4 respectively. F r o m (5a) this gives a range of (approximately) 0 . 1 5 - 0 . 6 for the marginal welfare cost of taxation, with a central estimate of 0.3. Table 1 compares the welfare loss from interactions with the tax system under
20 In the U.S. non-labor income is taxed at a slightly lower rate than labor income. (Both are subject to income taxes, but the effects of corporate taxation on the former are outweighed by the effects of social security taxation on the latter.) Thus for a given level of real income, a quota which increases the share of non-labor income at the expense of labor income would reduce overall tax revenues and lead to a negative revenue-recycling effect. By ignoring this, the above analysis (slightly) understates the asymmetry between pollution taxes and quotas.
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Table 1 Welfare loss from interactions with the tax system under the Pigouvian rule (relative to the Pigouvian effect) Policy
x1 *
Quota
0.05 0.2 0.6
Tax
V 0.15
0.3
0.6
6 1.5 0.5
12 3 1
24 6 2
0.3
0.6
1.2
quota and tax, expressed relative to the Pigouvian triangle, using Eqs. (8) and (9). The startling result is that the welfare loss from the tax-interaction effect can easily exceed the entire Pigouvian welfare gain from an environmental quota (this occurs when the cell entry exceeds unity). For example when V = 0.3, the tax-interaction effect is 12 times, 3 times and the same size as the Pigouvian effect, when the proportionate reduction in output is 5%, 20% and 60% respectively. Even under a very low estimate for the marginal welfare cost of taxation ( V = 0.15), the tax-interaction effect is still crucial to determining at least the magnitude, if not the sign, of the general equilibrium effect from the quota. In the case of the Pigouvian tax, the net loss from interactions with the tax system is much smaller, but can still offset a large amount of the Pigouvian gain. For example, when V = 0.3 the tax-interaction effect net of the revenue-recycling effect is 60% of the Pigouvian triangle. The intuition behind the quota result is straightforward. Most of the substitution away from X~ will lead to higher demand for other consumption goods rather than leisure - that is, the base of the shaded rectangle in Fig. 2 is small relative to the base of the Pigouvian triangle. However, the welfare cost per additional unit of leisure is large because taxes effectively drive a substantial wedge between the marginal social cost and marginal social benefit of leisure (around 40%) - that is, the height of the rectangle can be large relative to the height of the triangle. 21 3.2. Welfare under the optimal environmental tax The above results may be unduly pessimistic because they calculate welfare effects at the Pigouvian level of regulation, rather than the second-best optimal
21 AS mentioned above, the results are consistent with Browning (1995), who found that the welfare loss in the labor market caused by monopoly pricing is much larger than the Harberger triangles in the product markets. Previous empirical studies in environmental economics emphasized the relative importance of the revenue-recycling effect, but did not take into account the - even more important tax-interaction effect. For example, Nordhaus (1993) estimated that revenue-recycling increased the optimal tax on carbon from $5 per ton to $59 per ton.
1.W.H. Parry / Resource and Energy Economics 19 (1997) 203-220
213
level. Therefore this subsection compares taxes and quotas when regulation is equivalent to that of the optimal environmental tax, maintaining the assumption that ~b = 1. Adding Eqs. (2) and (3), subtracting Eq. (7), and differentiating with respect to the reduction in Xl(t), gives the following formula for marginal welfare under the environmental tax:
c--~-Vt+
+V ( X ° - X l ( t ) ) d X , ( t )
Equating this with 0, and noting that dX~ t X ° - Xl(t) = - - - t = -Xl*X ° dt c
(10)
gives the following formula for the optimal environmental tax (Parry, 1995a): t c
1 I+2V
(11)
This lies between 45% and 77% of the Pigouvian tax, given our range for V. Under this level of regulation, the welfare loss from interactions with the tax system under the environmental quota and tax, relative to the Pigouvian effect, are (from Eqs. (2), (3), (7), (10) and (11)) WI
2 V ( l -3t-2 V )
WP
(1 + 4 V ) x ,
,
(8b)
and Wl _
W R
We
2V = - -
(9b)
1 + 4V
respectively. Table 2 shows calculations of Eqs. (8b) and (9b). The welfare loss from interactions with the tax system is now much smaller for the pollution tax,
Table 2 Welfare loss from interactions with the tax system under the second-best optimal tax (relative to the Pigouvian effect) Policy
Quota
Tax
x1 *
0.05 0.2 0.6
v 0.15
0.3
0.6
4.88 1.22 0.41
8.73 2.18 0.73
15.53 3.88 1.29
0.19
0.27
0.35
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L W.H. Parry / Resource and Energy. Economics 19 (1997) 203-220
Table 3 Sensitivity with respect to ¢ Policy
xI *
~b 0.5
1.5
Quo~
0.05 0.2 0.6
6.0 1.5 0.5
18.0 4.5 1.5
T~
0.05 0.2 0.6
-5.4 -0.9 0.1
6.6 2.1 1.1
between 19% and 35% of the Pigouvian gain. However, the tax-interaction effect is still crucial for the magnitude, and possibly the sign, of the general equilibrium welfare effect from the quota (again a cell entry greater than unity indicates that the overall welfare impact of the policy is negative). 3.3. Degree of substitution with leisure The above calculations assume that the regulated commodity is an average substitute for leisure. In general this may be the best assumption we can make, since it is usually very difficult to estimate the degree of substitution between particular goods and leisure. 2z However, it is useful to examine how sensitive the results are to relaxing this assumption. Returning to the case when the Pigouvian rule t = c is adopted, the relative effect from interactions with the tax system under the environmental quota and tax are (using Eqs. (2a), (3), (7) and (10) when ~b 4: 1) Wl wp =
2thV (8c)
X 1"
and
W'- WR Wr,
2V(~b- 1 + x : ) • x1
(9c)
respectively. Table 3 calculates these formulas when the elasticity of demand for X 1 with respect to the price of leisure is 50% below and 50% above that for the average good, and assuming the central estimate of 0.3 for V. Clearly the results are sensitive to ~b, for example under the Pigouvian tax when x~* = 0.2, there is a net
22 See for example Deaton and Muellbauer (1980, Ch. 3). The numerical models discussed in the introduction restrict utility - by assuming leisure is weakly separable and preferences are homothetic over consumption goods - such that all goods are equal substitutes for leisure.
LW.H. Parry~Resource and Energy Economics 19 (1997) 203-220
215
loss from interactions with the tax system equal to 210% of the Pigouvian effect if ~b = 1.5, and a gain of 90% if ~b = 0.5. However, even in the scenario when X 1 is a relatively weak substitute for leisure, the tax-interaction effect exceeds the Pigouvian effect from an environmental quota when x I = 0.05 and 0.2, and offsets 50% of it when x~ = 0.6.
4. The regulation of intermediate goods This section extends the previous analysis to examine the welfare effect of environmental regulations imposed on an intermediate good (gasoline, coal, pesticides, etc.). We assume this good, denoted Z, is produced competitively with constant marginal cost (normalized to unity), is used in the production of X~, and causes an environmental damage of c per unit. All other assumptions from before are maintained, and there is no regulation of X 1.
4.1. Environmental taxes and quotas Suppose the Pigouvian tax of t = c is imposed on Z, and the revenues are used to reduce the labor tax. Analogous to before, the general equilibrium welfare effect consists of: (i) The Pigouvian welfare gain triangle, given by
wP=
c
*)
(2')
where Z* is the Pigouvian level of output. The reduction in Z consists of the familiar substitution effect (the replacement of Z for other inputs in production) plus the output effect (the fall in demand for Z from the reduction in X 1). (ii) The welfare gain from the revenue-recycling effect, which is w
= VcZ*.
(3')
(iii) The welfare loss from the tax-interaction effect. This occurs because the increase in cost of Z drives up the price of X 1, thereby inducing some substitution into leisure. 23 Denoting the price increase by Apl, then analogous to (7), the tax-interaction effect can be expressed W l = 6VX°Apl.
(7')
To a second-order approximation, the price of X~ increases by the product of c and the average of the ex ante and ex post ratio of Z to X 1 (see Appendix A).
23 Despite possible substitution of labor for Z in the production of X1, the tax-interaction effect is positive, assuming X l and leisure are substitutes. This is because the aggregate quantity of leisure is determined by the price of leisure relative to consumption, and must increase when the price of X 1 increases.
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This ratio falls by tx(Z ° - Z *) / X °, where /x is the fraction of the total reduction in Z due to the substitution effect. Therefore
c( ap, = Xo z ° -
tZ z O _ z . ) 7 ( ) "
(12)
From Eqs. (12) and (7'), the tax-interaction effect is
( 2)
W ~= chVcZ ° 1 -
/xz
(7")
where z* = (Z ° - Z* ) / Z ° is the proportionate reduction in Z. Comparing Eq. (7") with Eq. (3'), we have essentially the same result as before. That is, the tax-interaction effect exceeds the revenue-recycling effect, except possibly in the case when final output from the polluting sector is a relatively weak substitute for leisure (th < 1). 24 Again, a non-auctioned environmental quota which has the equivalent Pigouvian welfare effect in Eq. (2'), causes the same tax-interaction effect (Eq. (7")), but no revenue-recycling effect.
4.2. Empirical comparison Using Eqs. (2'), (3') and (7"), the welfare loss from interactions with the tax system (relative to the Pigouvian effect) under the environmental quota and tax are 2~bV( 1 - / z z */2}
W I
WP
=
(8')
Z*
and
W'-W' WP
2V{qb(1-tzz*/2)-
z*
(l-z*)} (9')
Table 4 shows simulations on Eqs. (8') and (9'), assuming X 1 is an average substitute for leisure and V = 0.3. If Z is used in fixed proportions to output, then all of the reduction in Z is due to the output effect and /z = 0 (third column). In this case, the relative welfare loss from interactions with the tax system is the same as in Table 1.25 The other extreme is when all the reduction in Z is due to the substitution effect, that is /z = 1 (fourth column). This has some impact on reducing the tax-interaction effect, for example the relative welfare cost of
24 Again, it has long been recognized in optimal tax models (which do not decompose the revenue-recycling and tax-interaction effects) that in general the welfare effect from interactions with the tax system is negative for taxes on intermediate goods (Diamond and Mirrlees, 1971). 25 For a given reduction in final output, regulating a factor input is equivalent to regulating final output, when the factor is used in fixed proportions (Wisecarver, 1974).
L W.H. Parry/Resource and Energy Economics 19 (1997) 203-220
Table 4 Intermediate goods Policy
z 0
Quota
0.05 0.2 0.6
Tax
0.05 0.2 0.6
12 3 1 0.6 0.6 0.6
217
/z 1 11.7 2.7 0.7 0.3 0.3 0.3
interactions with the tax system are reduced from 60% to 30% under the Pigouvian tax. However, for the quota it makes little empirical difference to the previous conclusion that the tax-interaction effect can easily dominate the Pigouvian welfare gain. For example, the tax-interaction effect is still 11.7 and 2.7 times as large as the Pigouvian triangle when the proportionate reduction in Z is 5% and 20% respectively.
5. Generalizing the analysis In practice the general equilibrium welfare effects of environmental policies are considerably more complex than suggested by the simple analytical model used above. This section briefly discusses three ways in which the analysis might be extended. However, the basic result - that revenue-raising can be a necessary condition for environmental policy to increase welfare - is likely to be robust in more general models. 5.1. Interactions with the capital market
The other market in the economy which is substantially distorted by taxes is the capital market. To the extent that an environmental policy reduces investment rather than consumption, it will compound the welfare cost of taxes on capital rather than labor (Bovenberg and Goulder, 1996b). Therefore, assuming the marginal welfare cost of taxation is greater for capital than for labor, 26 incorporating capital into the above analysis is likely, if anything, to increase the welfare loss from the tax-interaction effect. On the other hand, if environmental tax revenues are used to reduce taxes on capital, the revenue-recycling effect, and hence the asymmetry between taxes and quotas, will be larger.
26 See for example Lucas (1990).
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L W.H. Parry~Resource and Energy Economics 19 (1997) 203-220
5.2. Non-tax distortions
Market imperfections due to non-tax factors such as monopoly pricing, government regulations, imperfect information and externalities, are quite pervasive in the economy. Therefore, a specific environmental regulation could potentially cause efficiency effects in a variety of other markets in addition to the labor and capital markets. However, taken individually these other efficiency effects are likely to be empirically unimportant, unless the market is severely distorted and closely related to that being regulated. In this connection, Oates and Strassmann (1984) suggest that pre-existing distortions in product markets due to monopoly pricing do not substantially affect the overall welfare effect of environmental policies. This is mainly because the price wedges caused by imperfect competition are much smaller than those caused by the tax system. Nevertheless, a recent paper by Browning (1994) suggests that the aggregate impact of non-tax distortions could be significant. He estimated that non-tax distortions effectively increase the overall distortion in the labor market from 43% to around 55%. Therefore, by ignoring these non-tax factors, the above analysis may significantly understate the revenue-recycling and tax-interaction effects. 5.3. Command and control regulations
Command and control regulations are much more prevalent in practice than the pure taxes and quotas analyzed above. Like quotas, they do not raise revenues. They also increase marginal production costs, and hence increase the relative price of consumption goods, and induce a tax-interaction effect similar to that discussed above. However by constraining the method of abatement, they typically lead to production inefficiency and higher (partial equilibrium) abatement costs than the equivalent quota. A useful extension to the analysis would be to consider the contribution of the tax-interaction effect, relative to that from production inefficiency, in the overall abatement costs from command and control regulations.
6. Summary By increasing the relative price of consumption goods, environmental policies typically induce some substitution into leisure, which compounds the welfare cost of tax distortions in the labor market. Under plausible parameters, this effect can dominate the partial equilibrium effect of the policy. Therefore, despite environmental benefits, the overall welfare impact from imposing the Pigouvian quota could be negative. However, an environmental tax raises revenues and if these are used to reduce the labor tax, most of this interaction effect can be offset. Thus in some cases only revenue-raising environmental policies can potentially increase welfare.
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219
Acknowledgements This paper is a revised version of an earlier draft, 'Environmental Policy in a Second Best World'. I am grateful to Larry Goulder, Mark Harrison, Larry Sjaastad, David Starrett, and seminar participants at Chicago, Maryland, NBER and Resources for the Future for very helpful comments.
Appendix A. Deriving Eq. (12) From a second-order Taylor series expansion, the change in total cost (to) of producing X l, following a change of c in the price of input Z is do~ C
dpz
c 2 d2to -I-----
2 dp~
where Pz is the price of Z. Dividing by X ° to convert to marginal production costs and substituting d to/dpz = Z ° (from Shephard's lemma) and c(d2to/dp~) = / z ( Z * - Z°), gives Eq. (12).
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