Pollution, Factor Taxation and Unemployment *

Transcription

1 Published in: International Tax and Public Finance Vol. 5, No. 3, pp Pollution, Factor Taxation and Unemployment * Erkki Koskela + University of Helsinki Ronnie Schöb ++ University of Munich Hans-Werner Sinn ++ University of Munich Revised version: February Department of Economics ++ Center for Economic Studies University of Helsinki University of Munich P.O. Box 54 (Unioninkatu 37) Schackstrasse 4 FIN University of Helsinki D Munich Finland Germany tel /9/ tel. ++49/89/ fax ++358/9/ fax ++49/89/ erkki.koskela@helsinki.fi ronnie.schoeb@ces.vl.uni-muenchen.de hans-erner.sinn@ces.vl.uni-muenchen.de * The first author is indebted to the Research Unit on Economic Structures and Groth (RUESG) for financial support and acknoledges ith gratitude the hospitality of the Center for Economic Studies (CES) at the University of Munich. We ould like to thank Bruno de Borger, Jeremy Edards, Toshihiro Ihori, Marcel Thum and to anonymous referees for helpful comments and suggestions. The usual disclaimer applies. HWS_FCPO.DOC

2 1 Abstract When consumers choose beteen clean and dirty goods and the labour market clears, a green tax reform may not bring about a double dividend in the sense of increasing environmental uality and increasing employment. Hoever, hen firms choose beteen clean and dirty factors of production, and hen there is unemployment, such a result is very likely to occur. The paper investigates a model of a monopolistic firm here labour and energy are factors of production and trade unions negotiate the age rate, accepting some unemployment as a result of aggressive age demands. It is shon that, in such a frameork, a green tax reform ill boost employment provided it does not increase the net-of-tax age rate by too much. This is the case hen the elasticity of substitution beteen labour and energy is greater than one, eual to one or not too far belo one. JEL classification: H20, J51 Keyords: factor taxation, green tax reform, unemployment, trade unions.

3 1. Introduction Europe is suffering from persistently high levels of unemployment. In the third uarter of 1997, the average unemployment rate in the European Union as nearly 11%. 1 The high level of unemployment has limited the scope for active environmental policies. Although it is generally agreed that green taxes ill reduce environmental pollution, the fear that these taxes ould exacerbate the problem of unemployment is idespread. Environmental policy is seen as a luxury that should be postponed until better days. This paper uestions the generality of this vie. Focusing on green taxes on the production side, e sho that a green tax reform hich benefits the environment ill boost employment if it results in the trade unions accepting the same, a loer, or a not too much higher net-of-tax age. Thus there is little reason to postpone environmental policy measures in order to fight the ongoing pollution of the environment. But ho can green taxes reduce unemployment? One obvious anser is by rebating tax revenues from green taxes through cuts in labour taxes. The high level of taxes on labour income, combined ith the high level of unemployment benefits, is often made responsible for unemployment since it distorts labour supply and increases age pressure in labour markets (see OECD 1995). A green tax reform may alleviate the tax burden on labour and hence reduce the resulting disincentives. The early literature on the employment effects of green tax reforms as pessimistic ith regard to hether such reforms ould boost employment. Bovenberg and de Mooij (1994) and Bovenberg and van der Ploeg (1994) have argued that labour supply ill normally fall as a result of a green tax reform. Hoever, their arguments are based on models ith market clearing in the labour market and, therefore, full employment. 2 More recent ork has given up the assumption of full employment and concludes that positive employment effects are possible. In a model ith fixed net-of-tax ages, Bovenberg 1 OECD, cf. Main Economic Indicators, December 1997, p See Bovenberg (1995) for a survey of the early literature on the double dividend hypothesis ith particular focus on the employment effects. HWS_FCPO.DOC

4 2 and van der Ploeg (1996) sho that if green taxes are lo initially, employment may increase if substitution beteen labour and resources ithin the production sector is easy. Bovenberg and van der Ploeg (1995) identify ithin a search theoretic frameork positive employment effects for a revenue-neutral green tax reform hich increases the tax on a polluting factor of production and hich succeeds in shifting the tax burden aay from labour income to transfer income. Using an efficiency age model, Schneider (1997) also shos that employment may increase due to an increase in green taxes. Koskela and Schöb (1996) apply a model ith endogenous age negotiations. They sho that, if unemployment benefits are nominally fixed and are taxed at a loer rate than age income, a revenue-neutral green tax reform hich increases green taxes on the consumption of a polluting good alleviates unemployment. Holmlund and Kolm (1997) examine the role of an environmental tax reform for a small open economy ith monopolistic competition. Assuming a Cobb-Douglas technology, they sho for a to sector economy that a revenue-neutral tax reform hich increases the energy tax and reduces the labour tax increases employment if ages in the tradable sector are higher than in the non-traded sector. Finally, Carraro, Galeotti and Gallo (1996), provide numerical simulations of the effects of a carbon tax reform in a bargaining model, hich indicate some evidence in favour of a short-run employment dividend. This paper analyses the effects of green tax reforms on unemployment. Throughout the analysis e assume that full employment has not yet been reached and that the government policy objective is to further reduce unemployment. We therefore apply a model similar to, but more general than, Koskela and Schöb (1996), here the age is endogenously determined in a bargaining process beteen trade unions and firms. Hoever, hile Koskela and Schöb analyse green tax reforms in a model ith consumption externalities, a single factor of production, and exogenous goods prices, e study green tax reforms ith production externalities, to factors of production, and monopolistic firms. The main focus is on the impact the revenue-recycling effect has on the age negotiations and employment. The age negotiations are analysed using a 'right-to-manage' model by alloing non-constant elasticities

5 3 of factor demands. Trade unions and firms bargain over ages and firms then choose the employment level that maximizes profits. Thus, our analysis can be regarded as a partial synthesis of Holmlund and Kolm (1997) on the one hand and Bovenberg and van der Ploeg (1996) on the other hand. The paper is organized as follos. Section 2 presents the basic model. In Section 3 the implications of a revenue-neutral green tax reform are analysed hen the net-of-tax age is kept constant. Section 4 derives conditions hich guarantee positive employment effects for consecutive marginal revenue-neutral green tax reforms. Section 5 extends the analysis to the case here the net-of-tax age is negotiated beteen a trade union and the firm and analyses ho the possible changes in the net-of-tax age modify the picture. Finally, there is a brief conclusion. 2. The model We consider a monopolistic firm hich produces output Y using imported energy R and domestic labour L as inputs. The use of energy in production is dirty in the sense that it produces a negatives externality on households or other sectors of the economy. The technology is linear-homogenous and is represented by a CES production function L NM O QP σ σ 1 σ 1 σ 1 σ σ Y = f ( L, R) = L + R, (1) here σ denotes the elasticity of substitution. The firm faces a donard sloping demand curve hich is assumed to be isoelastic. Denoting the output price ith p and the output demand elasticity ith ε Dp p Y e have: 3 Y = D( p) = p ε. 3 The elasticity of demand depends on the consumer's elasticity of substitution beteen good Y and its substitutes. See Dixit and Stiglitz (1977) for a formal analysis of the relationship beteen substitutability and pricing.

6 4 To guarantee a profit maximum the output demand elasticity must exceed unity. Profit is given by π = py L % R %, here the firm considers the energy price % and the gross age rate % as given. The gross age is the net-of-tax age, hich is negotiated beteen a trade union and the firms, plus the labour tax, modelled as a payroll tax: % = ( 1 + t ). The energy price is the foreign resource price plus a green tax levied on the use of energy in production: % = ( 1 + t ). Profit maximization ith respect to inputs yields the conditional labour and energy demand functions: L = σ 1 σ 1 % % + % σ 1 σ Y σ and σ 1 1 1, R = σ σ % % + % σ σ Y respectively. Substituting the conditional demands into the cost function e obtain 1 C( %, %, Y) = Y % 1 σ + % 1 σ 1 σ Yc ( %, %), (2) here c( %, %) denotes average and marginal cost of production. Profit maximization ith respect to output yields the first-order condition p F1 HG 1 I K J = ε c( %, %), (3) i.e. the domestic firm demands a price hich exceeds the marginal cost by a (constant) markup factor of ε cost, i.e. π = cy / ( ε 1 ). / ( ε 1 ). Due to the iso-elastic output demand, profit is proportional to total The government reuires a fixed amount of tax revenues to finance the public good G. In addition, it has to finance the unemployment benefit b. The only tax instruments available are taxes on labour and energy. In general, the government budget constraint is then given by t L + t R = G + b( N L). In the folloing, hoever, e abstract from changes in the

7 5 government budget due to changes in the unemployment benefit payments and focus on a reduced form of the government budget constraint given by t L + t R = G. (4) The employment effects are not ualitatively affected by this simplification. If employment increases because of the tax reform, feer tax revenues are reuired to meet the budget constraint and vice versa. 3. Labour tax system vs green tax system We start our analysis by asking hether there exists a "green tax system", characterized by relatively high tax rates on energy and relatively lo labour taxes, hich yields the same output as the existing "labour tax system" here the labour tax rate exceeds the energy tax rate, but generates a higher level of employment. For the time being it is assumed that the net-of-tax age is fixed. This assumption ill be relaxed in Section 5. The initial tax system is characterized by a tax on labour income, t, hich is larger than the (ad-valorem) tax on energy input, t. It can be shon that, for given net-of-tax factor prices and, there is an alternative tax system, hich generates the same output and tax revenue but allos for a higher level of employment. There are a fe conditions that must be satisfied for the green and labour tax systems. First, both tax systems produce the same output, f ( L, R) = Y 0, (5) here the output level Y 0 is ceteris paribus determined by the initial tax rates t A and t A. Second, profit maximization reuires that output is produced ith minimum cost. The firstorder condition for cost-minimization can be represented by f % ( L, R) f % ( L, R) = 0, (6) R L

8 6 here f i denotes the partial derivative of f ( L, R) ith respect to i = L, R (e.g. f = R f R ). Third, the marginal cost is eual in the to systems for otherise the firm ould not sell the same output in euilibrium as before. With linear-homogenous technologies this implies constant total cost, L % + R % = C 0. (7) In the special case of a CES production function, this cost could even be explicitly calculated from euations (2) and (3): C = p 1 1 ε Y 0 0 b g. Fourth, the government budget constraint (4) must be met. Euations (4) through (7) provide an euation system hich can be solved ith respect to the optimal inputs and the necessary tax rates, respectively. As the initial labour tax system A A ( t, t ) provides a first solution ith a higher tax rate on labour than on energy, the second solution ill yield an euilibrium ith higher taxes on energy and a higher labour demand. The solution is represented in Figure 1 here point A indicates the initial labour tax A A system ( t, t ) ith t A A > t, hich is given by the tangency of the iso-cost curve and the B B isouant for Y 0. Point B indicates a green tax system ( t, t ) ith t B B > t hich yields the same output at the same total cost. The latter is the case as B lies on the dotted iso-revenue line hich is parallel to the before-tax iso-cost curve (starting in L max ). Moving directly from A to B ill instantaneously increase employment ithout imposing any additional cost on either firm or government. In addition, less energy ill be used, and, conseuently, the environment ill improve. This result is summarized in proposition 1. PROPOSITION 1: With given net-of-tax factor prices and a linear-homogenous production technology, there exists a green tax system ith higher tax rates on energy than on labour hich yields the same output level and same tax revenues as the existing labour tax system here the labour tax rate exceeds the energy tax rate. The green tax system generates both a higher level of employment and a cleaner environment.

9 7 Note that Proposition 1 refers to linear-homogenous production functions in general. The CES production function introduced in (1) has not yet been used in the derivation. Figure 1: Labour tax system versus green tax system 4. Marginal revenue-neutral green tax reforms Section 3 considered a jump from a labour tax system to a green tax system. One may ask, hoever, under hat condition do consecutive revenue-neutral green tax reforms also guarantee positive employment effects. To analyse the employment and output effects of a marginal revenue-neutral green tax reform, e split the tax reform into to separate steps. First, e consider a marginal green tax reform hich increases the energy tax and loers the labour tax so that the output level is kept constant, i.e. dy = 0. This implies a movement along the isouant, hich guarantees that labour input ill increase, hile leaving marginal cost constant as a direct implication of Euler's theorem.

10 8 If such a tax reform generates excess tax revenues, dg > 0, the surplus in tax revenues ill be rebated in a second step by euiproportionally reducing both taxes so that dg = 0. Since an euiproportional change in tax rates reduces marginal cost, this ill increase output and conseuently the demand for both inputs. Hence, such a green tax reform ill unambiguously increase employment hile the effect on energy input remains a priori ambiguous. The output-neutral tax reform can be derived by totally differentiating the production function (1): L N O Q L N 1 1 dy = = ML L + R R P 1 1 dt + ML L + σ σ σ σ 0 % % % R R% Pdt. (8) O Q Solving for dt one gets dt dt dy = 0 ( 1 s)( 1+ t ) =, (9) s( 1+ t ) here s L % cy denotes the cost share of labour and ( 1 s) 1 L % cy = %R cy the cost share of energy. Next, consider the impact such an output-neutral tax reform has on the government budget: dg = L + t L% + tr % dt + R + t L% + tr % dt. (10) Substituting conditions (8) and (9) in (10) yields (after some manipulations) dg 1 = dt s( 1+ t ) dy = 0 sr( σ( 1+ t ) t ) ( 1 s) L( σ ( 1+ t ) t ). Depending on the relationship beteen the to tax rates e obtain dg dt R> S = T U V W R S T U V W > 0 t = < t. dy = 0 < Suppose labour is taxed more heavily than energy, i.e. t tax reform leads to a surplus in tax revenues, i.e. dg dt dy = > 0 > t. In this case, the output-neutral 0. Rebating this budget surplus

11 9 reduces the marginal cost and conseuently increases output and therefore factor demands. Output ill rise more the higher is the output demand elasticity ε. Figure 2: Consecutive marginal green tax reforms Figure 2 shos to conceivable paths of consecutive marginal tax reforms starting in the labour tax system A and ending in the green tax system B. Up to points C or C' here t = t, employment ill definitely increase. A further increase in t, hoever, ill result in output reductions. This output effect countervails the substitution effect of moving along the isouant. If the output demand elasticity is small, the initial rise and subseuent fall in output ill be small and the substitution effect ill dominate the output effect. This case is represented by path I in Figure 2. Moving from C to B further increases employment hile output is falling. If output demand is very elastic, hoever, as represented by path II there ill be an interval on the path II from C' to B here output and employment are falling simultaneously. 4 This result can be summarized in the folloing proposition. 4 For the same reason, moving from A to C' increases energy demand and hence orsens environmental uality.

12 10 PROPOSITION 2: As long as the labour tax rate exceeds the energy tax rate, a marginal revenue-neutral green tax reform, hich leaves the net-of-tax age unaffected, ill increase output and employment. Going beyond C or C', e can add the folloing corollary. COROLLARY 1: If the energy tax rate exceeds the labour tax rate, a marginal revenueneutral green tax reform, hich leaves the net-of-tax age unaffected, ill reduce the level of output. The corollary can be considered as a direct implication of the Diamond and Mirrlees (1971) production efficiency theorem. For given total cost and tax revenue reuirement, an euiproportional factor taxation, hich is euivalent to an output tax, maximizes output Green tax reform and age negotiations It is time no to relax the assumption of exogenously given ages, as promised. We assume that the age level is determined in age negotations hich take place beteen a small trade union and the firm. The objective of the trade union is to maximize the income of its N members. Each member orks one unit of time and receives a age income. Unemployed members are entitled to unemployment benefits. The net-of-tax age is again denoted by. The unemployment benefit is fixed at the level b. The objective function of the trade union can be ritten as 6 * V = L + b( N L). 5 Notice that an euiproportional factor taxation need not be elfare-maximizing in our frameork of imperfectly competitive labour markets, though it is in the Diamond-Mirrlees frameork. 6 A linear objective function is used for analytical convenience. It is often claimed that trade unions do not care about the level of employment if lay-offs follo an inverse seniority rule. In this case the objective function of the trade union ould reduce to V * = (cf. Osald 1993). In the folloing, e abstract from age taxes, taxes on unemployment benefits and different types of tax alloances. The effects these parameters have on trade union's behaviour are elaborated in detail by Koskela and Schöb (1996).

13 11 Wages are usually determined in a bargaining process beteen the trade union and the firm, and the firm then unilaterally determines employment. To model this, e apply a 'right-to manage' model hich represents the outcome of the bargaining by asymmetric Nash bargaining. 7 The fall-back position of the trade union is given by V 0 = bn, i.e. all members receive their reservation age eual to the unemployment benefit. The fall-back position for the firm is given by zero profits, i.e. π 0 = 0. The Nash bargaining maximand can then be ritten as * Ω = ( V V 0 ) β π 1 β, * ith β representing the bargaining poer of the trade union. Using V V V 0, the first-order condition ith respect to the net-of-tax age is V = 0 + ( 1 β) π = 0, (11) V π Ω β here the subscripts denote partial derivatives (e.g. V = V / ). In the folloing e focus on changes in tax rates only. Provided that the second derivative is negative, i.e. Ω < 0, euation (11) defines the negotiated age from Nash bargaining as a function of the tax rates t, t so that = ( t, t ). The next section provides the comparative statics necessary to analyse revenue-neutral green tax reforms affecting the production side. 5.1 Comparative statics The uestion is ho the negotiated age ill react to changes in the tax rates. From implicit differentiation of condition (11) e can infer that t = = Ω Ω, i =,. This i ti ti allos us to sign the net-of-tax age change due to a change in either the labour tax or the energy tax: 7 This approach can be justified either axiomatically (cf. Nash 1950), or strategically (cf. Binmore, Rubinstein and Wolinsky 1986). Alternatively, one could apply an efficient bargaining model here the trade union and the firm negotiate over both ages and employment. Our approach here is in line ith Osald (1993) ho has shon that empirically, in almost all contracts, firms explicitly obtain the right to unilaterally determine employment.

14 12 F HG β sign( ) = sign( ) = sign V VV V V 1 Ω + β ππ π π 2 2 π ti ti ti ti ti ti I K J. (12) To interpret this expression e make use of the explicit form of the folloing factor (cross-) price elasticities, hich can be derived analogously to the case of perfect competition [cf. Allen (1938) or Hamermesh (1993)]. The age elasticity of labour demand η L, % is given by and the cross-price elasticity is L % ηl, % % = σ + s( σ ε), (13) L L ηl, % = ( 1 s)( σ ε). (14) L % % If η L, % > 0 factors are factor price substitutes and they are factor price complements if the reverse is true (cf Hamermesh 1993, p.37). In the folloing e assume that energy and labour are complements in the sense that η L, % < 0. Obviously, this is the case if the output demand elasticity falls short of the elasticity of substitution. Combining euations (13) and (14) allos an interpretation of the labour demand elasticity. First, the labour demand elasticity depends on the substitutability of factors, indicated by σ. The more easily energy can be substituted for labour the more elastic labour demand is. The size of the labour demand elasticity also depends on hether factors are substitutes or complements. If factors are complements, the marginal productivity of labour declines as an increase in ages reduces energy demand. This has a negative effect on labour demand hich becomes stronger the larger the share of labour in total cost is (cf. Hamermesh 1993, p.24). To understand the impact that changes in the labour tax have on the negotiated age, e ill analyse the effects on the trade union's and the firm's objective functions separately. First, a labour tax affects the income of the trade union only to the extent that the labour demand elasticity is not constant but reacts to a change in the labour tax rate: F η sign( VVt V Vt ) = sign H G t L, % I KJ. (15)

15 13 From the partial derivative of the trade union's objective function V = ll + ( b) L it can be seen that a constant labour demand elasticity implies that if the labour tax rate increases and the trade union fights for higher ages, the benefits of a age increase for those employed fall in proportion to the losses hich occur because more orkers are fired. If the labour demand becomes less elastic, hoever, the benefits fall at a loer rate and it becomes profitable to demand higher ages. The partial derivative of the labour demand elasticity ith respect to the labour tax rate is given by η t L, % = ( σ ε), st ith s = s s = > t s = < % = ( + t ) ( 1 )( 1 σ 1 ) 0 σ 1. < > R S T U V W R S T U V W As e assume labour and energy to be complements, i.e. ε sign( VV t VVt ) = signbσ 1g. > σ, condition (15) reduces to If substitutability is lo, i.e. σ < 1, the cost share of labour increases ith the labour tax rate. A larger share s implies that a one percent increase in the age rate induces a larger increase in total cost and, conseuently, a larger fall in output. This ill lead firms to lay off more orkers. Hence, if s increases, labour demand becomes more elastic. This eakens the bargaining position of the trade union since the potential losses in terms of lay-offs that result from a age increase go up. The situation is reversed if s decreases. With respect to the firm's bargaining position, it can be shon that sign( ππt ππt ) = signbσ 1g. If substitutability is lo, the cost share of labour is an increasing function of the age rate. In this case, a rise in the net-of-tax age rate ill induce a fall of profits. Therefore the firm ill become more reluctant to accept age increases and demand loer ages. Hence, if

16 14 substitutability is lo, an increase of the labour tax rate ill eaken the trade union's bargaining position and strengthen that of the firm. As a conseuence, the to effects of an increase in the labour tax rate ork in the same direction. Depending on the elasticity of substitution e can summarize the total effect as: R S T < 0 as σ < 1 t = 0 as σ = 1. (16) > 0 as σ > 1 In hat follos e assume that the total effect on gross ages, d% dt = + ( 1 + t ), is t alays positive, i.e. a labour tax ill not be fully shifted onto the orkers. 8 Next consider a change in the green tax levied on energy input. The rationale for such a tax is to reduce emissions connected ith the use of oil, gas or coal hich damage the environment. Thus, e take it for granted that a reduction in the energy input into production has a positive impact on the environment. Given this assumption, e are then interested in the impact such a green tax has on age negotiations. Analytically, the impact on the trade union's bargaining position is given by here F η sign( VVt V Vt ) = sign H G t L, % I KJ, η t L, % = ( σ ε), st and s t ( 1+ t ) = st. ( 1+ t ) 8 This is also in line ith empirical evidence. See e.g. Lockood and Manning (1993) and Holm, Honkapohja and Koskela (1994).

17 15 The energy tax has the opposite effect on the labour demand elasticity to an increase in the labour tax. If substitutability is lo, an increase in t reduces the cost share of labour. Since factors are complements, a loer share implies that labour demand becomes less elastic. A similar analogy can be made for the effect on firm's profit. In this case e have sign( ππt π πt ) = signb1 σg. With respect to the firm's bargaining position, the energy tax has the opposite effect to the labour tax. Again both effects ork in the same direction. If substitutability is high, the trade union's bargaining position becomes eaker hile the firm's position becomes stronger, and vice versa. Depending on the elasticity of substitution e can summarize the total effect of an increase in t as: R S T > 0 as σ < 1 t = 0 as σ = 1. (17) < 0 as σ > 1 As in the case of labour taxes, the net-of-tax age effect of a green tax rate increase depends solely on the size of the elasticity of substitution, but ith opposite sign. Given the assumption that d% dt > 0, even if t < 0, the firm ill never shift a labour tax increase completely to the trade union. Hence, employment alays falls as a result of an increase in the labour tax. The employment effect in the case of the energy tax rate is given by dl = L d% + L dt, % % ith L % < 0 and L % < 0, respectively. The employment effect is ambiguous for σ > 1 because there are of to opposing effects. As factors are complements, an increase in one factor price alays reduces the demand for the other factor. Hoever, if in addition σ > 1, an increase in the energy price ill also reduce the negotiated age. The total effect is therefore a priori ambiguous. Analogously, e can determine the output effects. As η L, % < 0, a reduction in labour demand due to an increase in the gross age rate is accompanied by a reduction in energy input and hence a reduction in output. As a change in the green tax rate also affects the

18 16 negotiated age, the output effect of this change is ambiguous if substitutability is very high since in this case trade unions ill accept a loer age in the bargaining process. 5.2 Green tax reform ith net-of-tax age reactions In general it is to be expected that net-of-age rates ill not stay constant after a green tax reform. Hoever, there is an interesting special case of a Cobb-Douglas production technology ith σ = 1. In this case, as the conditions (16) and (17) sho, the net-of-tax age rate is not affected from changes in the tax rates and the analysis of Section 3 and 4 applies. Propositions 1 and 2 carry over to the case of a Cobb-Douglas production technology hen ages are negotiated beteen the trade union and the firm. The folloing proposition is readily available from this consideration. PROPOSITION 3: If there are age negotiations beteen the trade union and the firm and the technology is Cobb-Douglas, a marginal revenue-neutral green tax reform ill increase output and employment as long as the labour tax rate exceeds the energy tax rate. Changes in the net-of-tax age rate ill occur if σ 1. The government then has to take into account the effects tax rate changes have on the negotiated age, and conseuently its repercussion on the factor price ratio, the marginal cost and the tax revenue. The change in the net-of-tax age rate due to changes in the tax rates is given by d = dt + dt, t t hich affects total tax revenues (4) by dg = t L + t L ( 1+ t ) + t R ( 1 + t ) d. % % The condition for a revenue-neutral change in the structure of factor taxation is given by dg = * G dt + * G dt = 0, (18) t t ith

19 17 G * t L = ( 1+ t ) L NM F I R 1+ t ( 1+ ηl, % ) + t ηr, % ( 1+ ω t ) (19) H L K O QP and G * t R = ( 1+ t ) L N M F HG L L 1+ t( 1+ η t t t R, % ) + ηl, % + ω t ( 1+ ηl, % ) + η R, %. (20) R R IO KJ Q P The terms ω t = ( 1 + t ) t and ω t = ( 1 + t ) t describe the net-of-tax age elasticities ith respect to t and t, respectively. The asterisks in euations (18) through (20) indicate that the effect on the net-of-tax age rate has been taken into account. Using the definition of the tax revenue elasticity ith respect to the tax rate t i τ t = G * t ( 1 + t i ) / G, reformulation of the revenue-neutrality condition (18) yields i i τ τ t t ( 1+ t ) dt = ( 1+ t ) dt. (21) The change in employment is given by dl = L ( 1 + t ) + L dt + L ( 1 + t ) + L dt, % t % % t % hich can be reritten as L L dl = ηl, % ( 1+ ω t ) dt + ηl t + L dt, % ω η, %. (22) ( 1+ t ) ( 1+ t ) Substituting the condition (21) into (22) and rearranging, yields the folloing general condition for the change in employment: dl dt dg = 0 R> S = T U V < W 0 τ τ t t R> S = T U V < W ηl, % ω t + η L, % η ( L, % 1+ ω ). (23) t If a tax reform increases the gross energy price by one percent, the ratio of the left-hand side indicates the percentage by hich the gross age has to decrease because of a cut in the labour tax in order to keep the public good provision G constant. The ratio of the right-hand side denotes the percentage the gross age has to decline to keep the employment level constant. If the revenue-neutrality reuirement allos the government to cut the age tax at a higher rate

20 18 than is necessary to sustain the employment level, age negotiations ill lead to loer ages and ill increase employment accordingly. No if the elasticity of substitution exceeds unity, the net-of-tax age elasticity ith respect to t, is positive, ω t > 0. Hence, the net-of-tax age is reduced by a cut in the labour tax rate, hich is ceteris paribus good for employment. Hoever, a fall in the net-of-tax age rate also reduces the tax revenues and conseuently the scope for the reduction of labour taxes. It follos from condition (12) that ω t = ω (24) t (see Appendix 1). The partial derivatives of euations (19) and (20) ith respect to the net-oftax age elasticity are given by: G ω * t t L = ( 1+ t ) F H t R ( 1+ η t η, % ) +, % L K < 0 (25) L R I and * * Gt G t R L = = t ( 1+ ηl, % ) + tηr, % 0, (26) ω ω ( 1 + t ) R t t F HG I > KJ here the signs are determined by the assumption of positive marginal tax revenues. Substituting euations (25) and (26) for the definition of the tax elasticities in condition (23), it can easily be shon that the left-hand side of condition (23) is increasing in ω t. Differentiating the right-hand side of condition (23) yields: ω t ηl, % ω t + ηl ηl η, %, % + L, % = < 0. 2 η ( 1+ ω ) η ( 1+ ω ) L, % t L, % t The right-hand side of condition (23) is thus decreasing in ω t. These to facts establish that if employment is increasing hen the net-of-tax age is unaffected hich has been shon to be true for t > t employment ill also increase hen the negotiated age falls due to the revenue-neutral green tax reform. This yields Proposition 4.

21 19 PROPOSITION 4: As long as the labour tax rate exceeds the energy tax rate, a marginal revenue-neutral green tax reform hich induces a reduction in the net-of-tax age rate ill increase both the level of output and employment. If, on the contrary, the elasticity of substitution is less than unity, σ < 1, so that the trade union succeeds in increasing the age rate, a negative effect on employment results. Hoever, such an increase in the net-of-tax age rate also implies a higher tax revenue hich allos for larger tax cuts. It can be shon that the net-of-tax age elasticity is an increasing function of the bargaining poer of the trade union: ω t β σ < 1 < 0. (27) According to condition (27) the stronger the bargaining poer of the trade union the less elastic is the net-of-tax age reaction. Hence, the left-hand side of condition (23) is decreasing hile the right-hand side is increasing in β. This implies that the relative employment effect of a revenue-neutral green tax reform is the larger the stronger the trade union is. Note, hoever, that the level of employment is the loer, the stronger the trade union is. Furthermore, in the case here the trade union exercises monopoly poer and there is no energy tax e kno that a marginal revenue-neutral green tax reform increases employment hen σ = 1. It can be shon that, ith σ = 1, the positive employment effect is increasing ith the elasticity of substitution. 9 This leads to PROPOSITION 5: If the elasticity of substitution is belo a critical value σ * hich is itself less than one, a marginal revenue-neutral green tax reform ill reduce employment. The critical value is a function of the bargaining poer of the trade union, as measured by β. In the folloing e provide some numerical results for the case of a monopoly trade union, remembering that the range for a positive employment effects increases ith the bargaining poer of the firm. In Figure 3 e consider the case here there is no initial energy tax rate, i.e. 9 A proof is available upon reuest.

22 20 t = 0 and the cost share of energy is The bold lines in Figure 3 sho the geometric locus of the combinations of the elasticity of substitution and the initial labour tax, θ = t ( 1 + t ), here the employment effect is zero. The line AA is calculated for the output demand elasticity of ε = 1. 5 and the line BB for ε = In the case of ε = 1. 5, any elasticity of substitution above 0.64 guarantees a positive employment effect for any positive initial labour tax rate. The corresponding critical value σ * for ε = 2. 5 is Hoever, if the initial labour tax is 0.3, any elasticity of substitution above 0.57 (0.49) guarantees a positive employment effect hen ε = 1. 5 (ε = 2. 5). A comparison of the lines AA and BB shos that a positive employment effect becomes more likely, the higher the output demand elasticity, and that the higher the initial labour tax rate, the more likely the employment effect becomes positive. 10 Figure 3: The critical tax rate θ for t = 0 10 Alternatively, one could ask hat happens if an increase in the energy tax is compensated, not by a decrease in the labour tax rate, but by an increase in lump-sum transfers? The anser depends not only on the elasticity of substitution, but also on ho receives the lump-sum transfers. Consider for simplicity the case of the Cobb- Douglas production function. An increase in the energy tax rate compensated by a rise in lump-sum transfers to the firm ould increase the net-of-tax age rate. Hence unemployment ould go up. On the other hand if a lump-sum transfer is given to the members of the trade union, the net-of-tax age rate ould decrease so that the unemployment effect ould remain indeterminate. A complete set of results is available from the authors upon reuest.

23 21 6. Concluding remarks This paper elaborates the employment effect of a revenue-neutral green tax reform hich raises taxes on energy input and reduces the tax rate on labour input accordingly. If such a tax reform does not affect age negotiations beteen trade unions and firms, labour demand ill increase at least as long as the tax rate on energy does not exceed the tax rate on labour. The same result applies to the case here the green tax reform leads the trade union to accept loer age rate hich is the case if the elasticity of substitution beteen labour and energy exceeds unity. No ualitatively unambiguous anser can be given for the case here the elasticity of substitution beteen labour and energy is smaller than unity, for in this case the green tax reform implies an increasing net-of-tax age rate. Hoever, if the elasticity of substitution is not too far belo one, it ill still be true that unemployment is reduced. In addition, our analysis shos that the loer the bargaining poer of the trade union, and the larger the actual labour tax rate, the more likely it is that a green tax reform ill boost employment. In conclusion, our analysis presents conditions under hich green tax reforms on the production side ill reduce rather than increase unemployment. Thus, there seems to be little reason to postpone the implementation of environmental policies. This paper considers the case of a small trade union only. Folloing Calmfors and Driffill (1988), hoever, e can expect that more centralized age negotiations ill lead trade unions to take into account the fact that higher ages increase consumer prices and hence reduce the real income of their members. In economies ith ceteris paribus highly centralized age bargaining, therefore, green tax reforms ill have a more positive effect on employment than in economies ith highly decentralized age bargaining. Assuming centralized bargaining ould therefore strengthen our results.

24 22 Appendix 1: Net-of-tax age elasticities The signs of the net-of-tax age elasticities ω t = t t i for i =, are determined by i i Ω 1 Ω, t = Ω Ω t t = t 1. Furthermore, e have, using condition (12): Ω β = V VV V V ( 1 β) d i + dππ π π i π t 2 t t 2 t t 1 = + 1+ L NM e j e jo t β t t t t Ω t t V VV V V ( β) t + ππ π π 2 2 π 1 t From this, it is straightforard to derive condition (24). 1 QP = 1 + +

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