Environmental Tax Reform, Economic Growth, and Unemployment in an OLG Economy

Environmental Tax Reform, Economic Growth, and Unemployment in an OLG EconomyAuthor(s): Tetsuo OnoSource: FinanzArchiv / Public Finance Analysis, Vol. 63, No. 1 (March 2007), pp. 133-161Published by: Mohr Siebeck GmbH & Co. KGStable URL: http://www.jstor.org/stable/40913142 .

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FinanzArchiv/ Public Finance Analysis vol.63 no. 1 133

Environmental Tax Reform, Economic Growth, and Unemployment in an OLG Economy Tetsuo Ono*

Received 17 January 2006; in revised form 2 August 2006; accepted 16 October 2006

This paper develops an overlapping-generations model characterized by endogenous growth, unemployment and pollution. The paper focuses on the replacement ratio, which measures the proportion of after-tax work earnings replaced by unemployment benefits, and considers a replacement-ratio-neutral reform in which the environmental tax is devoted to cutting the employees' rate of contribution to unemployment insurance. Under this reform, (i) the growth rate is increased, the unemployment rate is

unchanged, and pollution is decreased; (ii) there is a trade-off of nonenvironmental

utility between current and future generations; and (¡ii) when the reform is associated with an ¡ntergenerational transfer from the young to the old, the nonenvironmental utility of every generation can be improved.

Keywords: economic growth, environmental tax reform, overlapping generations, replacement ratio, unemployment

JEL classification: D 60, E 60, H 55, J 21, J 51, J 65, Q 38

1. Introduction

As concern about the environment increases, environmentally motivated taxes either have been introduced or are seriously being contemplated in many OECD countries (OECD, 2001). However, three objections are often raised against environmental taxes. First, the environmental tax burden may crowd out private investment, thereby harming capital accumu- lation and economic growth. Second, the environmental tax burden may create a trade-off between generations. The costs of the environmental

* This paper was formerly circulated under the title "Environmental tax-financed unemployment insurance: its effects on growth, employment, pollution and welfare." The author would like to thank two anonymous referees for their useful comments and sug- gestions, and Masako Ikefuji and Hiroaki Yamagami for their research assistance. Fi- nancial support from the Global Environment Research Fund, the Japan Society for the Promotion of Science (JSPS) through a Grant-in-Aid for Young Scientists (B) (No. 17730131), the Asahi Glass Foundation, the Japan Economic Research Foundation, and the 21st Century COE Program (Osaka University) is gratefully acknowledged. All remaining errors are mine.

FinanzArchiv 63(2007), 133-161 doi: 10.1628/001522107X186755 ISSN 0015-2218 ©2007 Mohr Siebeck



1 34 Tetsuo Ono

tax are borne by the current generations, whereas the benefits in cleaner environmental quality accrue mainly to future generations who are not yet born at the time the environmental tax is introduced. Third, the environmental tax burden establishes an incentive for firms to reduce their labor demand, which results in the possibility of a higher unemployment rate.

This paper explores these three issues within the overlapping-generations model of Diamond (1965). Diamond's model is extended in the present paper by including a productive externality as an engine of endogenous growth (Romer, 1986; Lucas, 1988), pollution as an input into production (Brock, 1973; Nielsen, Pedersen, and S0rensen, 1995; Wagner, 1998), and imperfect labor markets with union wage setting (Layard and Nick- ell, 1990; Nielsen, Pedersen, and S0rensen, 1995; Bye, 2002). Within this framework, the paper considers environmental tax-financed unemployment insurance, and analyzes how the growth, unemployment, environmental quality, and welfare of all generations are influenced by the environmental tax.

In undertaking the analysis, we focus on the replacement ratio, which measures the proportion of after-tax work earnings replaced by unemployment benefits. Because of an increased burden of unemployment benefits, many OECD countries have cut the replacement ratio, resulting in a negative income effect on the unemployed.1 In order to remedy this situation of a de- clining replacement ratio, this paper proposes a replacement-ratio-neutral reform where the environmental tax is devoted to financing unemployment insurance.

Under this type of reform, we obtain the following results. First, the growth rate is increased, the unemployment rate is unchanged, and the aggregate level of pollution is decreased. Second, the reform leads to a trade-off between current and future generations with respect to nonenvironmental utility. Third, when the reform is associated with an intergenerational transfer from the young to the old, the nonenvironmental utility benefits of the reform could be shared between current and future generations: there is a way of improving growth, employment, environmental quality, and the nonenvironmental utility of every generation.

The analysis and the results of this paper differ from those of previous studies in the following three respects. First, this paper analyzes an environmental tax reform. Most existing studies on growth and the environment focus on the design of optimal tax schemes that internalize environmental externalities across generations (John et al., 1995; Ono, 1996; Fisher and van

1 For example, Nickel and Quintini (2002) showed that the replacement ratio has declined

rapidly in the UK from the 1970s. Among the Scandinavian countries, Denmark and Swe- den cut their ratios in the early 1980s and 1990s, respectively (Iversen, 1998).



Environmental Tax Reform, Economic Growth, and Unemployment in an OLG Economy 135

Marrewijk, 1998; Jouvet, Michel, and Pestieau, 2000; Jouvet, Michel, and Vidal, 2000; Wendner, 2003, 2005; Jouvet, Michel, and Rotillon, 2005a). In contrast, we consider environmental tax reform where the revenue from the environmental tax is devoted to cutting an existing tax, namely, the contribution rate to the unemployment insurance.

Second, we provide a sufficient condition for an improvement in the nonenvironmental utility of every generation. John and Pecchenino (1994), Bovenberg and Heijdra (1998, 2002), and Ono and Maeda (2002) considered the intergenerational distributional effects of environmental policy. They focused on total welfare, that is, the sum of the nonenvironmental and the environmental utilities, and proposed tax reforms where the nonenvironmental utility loss was offset by the environmental utility benefit. This paper differs from their analysis in that we provide a method of environmental tax reform that realizes improvements in both the nonenvironmental and the environmental utilities. Thus, this paper contributes to the policy debate on the double dividend, that is, on the improvements in both the nonenvironmental and the environmental utilities (Goulder, 1995; Bovenberg, 1999).

Third, a decrease in unemployment boosts production, and thereby increases emissions as a byproduct of production. We focus on such an unemployment-production-environment effect, which has been ignored by most existing studies. Although Chiroleu-Assouline and Fodha (2005) focused on such an effect, their analysis was limited to the case of no endogenous growth. In addition, their welfare evaluation was limited to the steady-state generations. This paper differs from their analysis in that we examine the effects of environmental taxation on the growth and welfare of every generation.

The paper is organized as follows. Section 2 develops the model. Section 3 describes the equilibrium properties. Section 4 demonstrates the main results. Section 5 considers how extending the model might affect the results shown in section 4. Section 6 provides concluding remarks.

2. The Model

Consider an overlapping-generations economy composed of a competitive firm, individuals who live for two periods, a trade union, and a government. Time is discrete and indicated as t = 1, 2, ... A new generation is born in each period t = 1, 2, ..., and individuals in each generation live for two periods, youth and old age. In period 1, there is an initial old generation that lives for only one period. It is assumed that there is no population growth, and the size of each generation is normalized as N > 0. Figure 1 briefly illustrates the structure of the model.



136 Tetsuo Ono

Figure 1 The Structure of the Model

Trade Union |

Wage Setting i 1 ♦ Environment

Labor Supply^^^- - -

^^'^^ ♦

yy^^ Wage ^^^ Pollution P

Individuals * I Capital Market I ' ' *

^_^'rm I * ' Y - Y 'K, L, P)

The Employees' Contribution Environmental Tax to Unemployment Insurance

Government *

i Unemployment Insurance

2.1. Firms

A representative firm is assumed. The firm is a perfectly competitive profit maximizer that produces the final good Yt using a constant-returns-to-scale Cobb-Douglas production function in the following form:

Yt = At(Kty«(Lt)aL(ptyr, where At is a productivity parameter, Kt is the aggregate capital, Lt is the aggregate labor, Pt is the aggregate level of pollution, and a¿(i = K, L, P) is a constant parameter satisfying a¿ g (0, 1) and aK + aL + aP = 1. Our treat- ment of pollution as an input reflects the idea that the services provided by the natural environment enable the firm to increase its level of output for any input of other factors (see, for example, Brock, 1973; Nielsen, Pedersen, and S0rensen, 1995; Wagner, 1998).

In each period i, the firm chooses capital, labor, and pollution in order to maximize its profit:

77, = At(Kt)a*(Ltr<(Pty' - rtKt - wtLt - (if + qt)Pt , where rt is the rental price of capital, wt is the wage, rf is an environmental tax levied by the government in period t, and qt > 0 is the private cost of pollution in period t. The pollution generated in the production process produces not only public costs (rf ), but also private costs (qt > 0). If qt = 0, the economy without an environmental tax experiences unbounded levels of wages, interest rates, and pollution in every period; in other words, the




economy without an environmental tax is not well defined if qt = 0 (see Jouvet, Michel, and Rotillon, 2005b, for a discussion of this point). Therefore, the assumption of qt > 0 simulates a realistic situation in which the level of pollution is high but remains limited in an economy without environmental taxation. Capital fully depreciates in the process of production.

The firm chooses its inputs of labor, capital, and emissions in order to maximize the profit (77,), taking prices and policy parameters as given. The first-order conditions for profit maximization are

wt = aLAt(ktr(ptr, (d rt = aKAt(kty«-l(ptyr, (2)

^ + qt = apAt(kt)aK(pt)ap-' (3) where kt = Kt/Lt is capital per labor unit, pt = Pt/Lt is emissions per labor unit, and wt is the wage. The firm chooses capital, labor, and pollution following the marginal productivity rules (1), (2), and q(3).

The present paper makes the following two assumptions with respect to the firm's technology.

Assumption 1 (i) At = A(Kt/Lty-aK, where A is a positive constant, and (ii) rf =

ytT? and qt = ytq, where y, = Yt/Lt, and if and q are positive constants.

The first assumption means that there is an external effect of capital per labor unit on productivity, as discussed in the context of endogenous growth theory (see, for example, Romer, 1986; Lucas, 1988). The productive capital stock per labor unit, K/L, enters the technology as a constant parameter from the perspective of current producers. Under this assumption, the aggregate production is given by Yt = A[aP/(rp + q)]apKt, which shows that the aggregate output is independent of unemployment (Corneo and Marquardt, 2000). The role of this assumption will be discussed in detail in section 5.

The second assumption implies that the total cost of emissions, rf + qt, evolves with the aggregate output per labor unit (Bovenberg and Smulders, 1995; Nielsen, Pedersen, and S0rensen, 1995). The government adjusts the environmental tax in accordance with the evolution of the aggregate production per labor unit, and the private cost of pollution also evolves with the aggregate production. If rf + qt remains constant over time, then the amount of emissions becomes infinite as time progresses. We can eliminate this unrealistic case by assuming increasing public and private costs of emissions.2

2 Alternatively, we can eliminate the unrealistic case by assuming rf = rp for all t and qt = qyt. This assumption implies that the environmental tax rate is constant over time, whereas the private cost of pollution evolves with the aggregate output per labor unit, yt. The author would like to thank one of the referees for pointing this out. The alternative assumption is in fact more realistic, because the government can control the environmental tax without relying on the level of yt. However, the assumption pro-



138 Tetsuo Ono

Based on the above assumptions, the first-order conditions for profit maximization, (1), (2), and (3), are respectively reduced to3

Wt = w(ki;TP)âLA^^-JPkt, (4)

Pi=P(TP)^^k' (6) 2.2. Individuals

Each individual has one unit of labor in youth, and none in old age. In- dividuals are organized in a trade union, which monopolizes the supply of labor. Because of this monopolized supply of labor, each individual experiences involuntary unemployment in the sense that he/she is restricted by a union to supplying only his/her proportional share of the total number of working hours. The government compensates the individuals by paying unemployment insurance.

Individual preferences regarding consumption and pollution are represented by the utility function lncj - z(Pt) + ß{'ncf+1 - z(Pt+i)}, where c1 and c2 are the consumption levels in the first and the second periods of the life cycle, respectively.4 The function z : SH+ -► 2t, which represents the disutility of pollution, is assumed to be strictly increasing and strictly con- vex in P. The parameter ß e (0, 1) is a discount factor. The utility function is composed of two factors: the utility from consumption is denoted as V? = lncj + /?lnc2+1, and the disutility from the aggregate level of pollution is denoted as z(Pt)+ßz(Pt+i), where the superscript N in V" signifies "nonenvironmental." In section 4, we will examine the effects of policy reforms on the aggregate level of pollution as well as the nonenvironmental utility of every generation.

Each individual maximizes his/her lifetime utility under the following budget constraints:

C) +St = (l- T")/,W, + bt(l - /,) , (7)

C?+1=Ä,+iS,, (8)

duces the problem that the model fails to attain a closed form of solution; we cannot an- alytically evaluate the effects of taxes on growth, unemployment, pollution, and welfare. In order to avoid this problem, the current paper adopts assumption l(ii), which yields a closed form of solution.

3 With assumption l(ii), (3) is rewritten as yt(iP + q) = apAt(kt)aK(pt)ap/pt. This is reduced to yt(iP +q) = apyt/pt or pt = ap/(if + q), which is equivalent to (6). Equations (4) and (5) are derived by substituting At = A{Kt/Lty~aK [assumption l(i)] and (6) into (1) and (2), respectively.

4 The role of this specification of the utility function will be discussed in section 5.




where st is savings, r" e [0, 1) is the employee's contribution rate to the unemployment insurance, /, is the actual number of hours worked by an individual, bt is the hourly rate of unemployment insurance, 1 - /, is the actual amount of hours spent unemployed, and Rt+i is the gross rate of return on savings. An individual born in period t works lt hours and receives the hourly rate of wages wt and unemployment insurance bt(l - /,). He/she contributes i^ltWt units to unemployment insurance. He/she divides the rest of his/her total income into consumption in youth (cj) and saving for consumption in old age (st). In old age, he/she receives a return on savings (Rt+'st) and consumes this return.

Under the budget constraints, an individual solves the following utility maximization problem:

max lncj - z(P,)+ß[ lnc*+1 - z(Pt+i)} s.t. (7) and (8) given Pt9 Pt+U (1 - r")/,n>, + 6,(1 - /,) and Rt+1 .

The aggregate level of pollution is exogenously given for an individual. The supply of labor, /,, is also given for an individual because it is determined by union wage setting (explained below).

The optimal consumption-saving decision of an individual leads to the first-order condition, c^+1 = ßRt+ic}, which gives

s< = Y^{(1-'f)lM

+ W-lt)}- (9)

By using the budget constraints (7) and (8), we obtain the following indirect nonenvironmental utility function of an individual in generation i, V? (see appendix 7.1 for derivation):

V? = (1 +¿8)ln{(l - i?)ltwt + bt(l - /,)} +jBlnÄ,+1 , (1O) which implies that V" depends on the total income in youth, (1 - t")/^, + bt{' - /,), and the interest rate, Rt+i.

The utility of an individual in the initial old generation is

V0 = ln<*-z(Pi). Each individual in the initial old generation has capital ki as an initial asset, and each of these individuals obtains the return from capital Rikx and consumes that return.

2.3. Union Wage Setting

The wage is set by a monopolistic trade union. The union is large enough to negotiate over the wage but small enough to take fiscal policy variables as given. Under this assumption, the trade union operates at the representative



140 Tetsuo Ono

firm level. The union can affect the welfare of the young members only through their lifetime income (see, for example, Layard and Nickell, 1990; Nielsen, Pedersen, and S0rensen, 1995; Daveri and Tabellini, 2000; and Bye, 2002). Thus, the union's objective function is the expected lifetime income of their young members:

0t = Ltwt(l-ru) + (N-Lt)bt. The problem of the union is to maximize <Pt subject to the labor demand function (1), taking fiscal policy variables as given.

The demand function for labor, (1), is rewritten as

L, = (^-1/(1^{a^(^(P^}1/(1^ .

We substitute this demand function into the objective function <Pt to obtain the unconstrained maximization problem:

max^

given Xa and bt ,

where <Pt is defined by

+ Nbt.

The first-order condition for maximization is5 bt

Wt= TT-

7- <11> «l(1

TT- - r«) The union sets the wage as a markup l/aL of the unemployment benefit bt, corrected for the contribution rate r".

2.4. Government

The unemployment insurance is an intragenerational transfer from the employed to the unemployed. This transfer system is balanced in each period, thereby yielding the following equality:

(N - Lt)bt = r"w,L, + zfPt , (12)

5 The second derivative of <Pt with respect to wt is given by

x (Wf)-aL/(1"aL)"2(l - aL)aL(l - r") < 0,

which establishes the sufficiency of the first-order condition.




where the LHS is total expenditure and the RHS is total revenue. The first term on the RHS is the revenue from taxation on the employed, and the second term is the revenue from environmental taxation of firms.

3. Properties of Equilibrium

Given the initial condition K' > 0, an equilibrium sequence of prices and allocations, {cj, <f , st, /„ Lt, Kt, P,, wt, rt, Rt, 6,}£i> is characterized by the following conditions: the conditions of profit maximization, (4)-(6); the conditions of utility maximization, (9), with the budget constraints (7) and (8); the condition of union wage setting, (11); the government budget constraint, (12); the labor-market-clearing condition, Lt = Nlt' an arbitrage condition under the assumption of full depreciation of capital, rt = Rt' the capital- market-clearing condition, Kt+i = Afa,; and the goods-market-clearing condition, Y, = c)N + cfN + [Kt+1 - (1 - ô)Kt]. In what follows, we will derive the growth rate, the unemployment rate, and the aggregate level of pollution by considering these conditions. We will analyze how these variables are affected by taxes.

3.1. The Growth Rate

Under the assumption that rf = xpyt [assumption l(ii)] and given that Pt = ptLt and pt = aP/(rp + q) from (6), the environmental tax revenue in period i, rfPt, is rewritten as

ft=5x^5x^' (13) fpt y,L,

Based on (4), (12), and (13), we can write the total income of an individual in generation t, /, = (1 - ru)ltwt + bt{' - /,), as follows (see appendix 7.2 for derivation):

We should note that i(rp), representing the aggregate total income of an individual per unit aggregate amount of capital, is composed of the following three factors. The first factor, aL, corresponds to the after-tax wage income, (1 - r")/,w,, plus the revenue from taxation on the employed, rultwt. The second factor, clptp/(tp + q), indicates the revenue from environmental taxation on firms. The third factor, A [aP/(rp + q)]ap, shows the aggregate output per unit aggregate capital, Y/K = A[p(rp)]ap. Proposition 1 will reveal how taxes affect the growth rate via these factors.



142 Tetsuo Ono

Under a full depreciation of capital, the aggregate capital in period t + 1 is determined by the aggregate saving in period t: Kt+i = Nst. Because an individual saves a constant proportion of his/her total income, st = ßhl (1 + /?), the growth rate of aggregate capital becomes

Given the initial condition K' > 0, an equilibrium sequence of capital {Kt} is characterized by (15). Thus, the economy grows at a constant growth rate, ßi(rp)/(i+ß).

Proposition 1 (Growth effects) Consider a change in r" or rp associated with an

appropriate change in the benefit, bt.

(i) The employee's contribution to unemployment insurance is neutral with respect to the growth rate: dG/dr" = 0.

(ii) Raising the environmental tax increases (decreases) the growth rate if and only 'ÌT?<(>)TP* = (l-aL)q/(l-aK):

dG/drP | 0 ^ t? = if* .

Proof. See appendix 7.3. ■

When the employees' contribution rate is increased, their wage is decreased and they save less. On the other hand, there is an increase in unemployment benefits, which completely offsets the reduction of the employees' wage; the net wage of a household remains unchanged. Thus, aggregate saving is also unchanged, and no growth effect occurs.

When the environmental tax rate is increased, there are two effects on the growth rate, shown as follows:

dG ß Al / ap '1+ap 1 „ , if(l _„ , - = Al - - I x q(' „ - aL) , - if(l _„ - aK) , .

I UI effect production effect

The first is the unemployment insurance (UI) effect, which implies a positive income effect on economic growth. Given the output per labor unit, y, and the aggregate amount of emissions, P, raising the environmental tax rate xp leads to an increase in the environmental tax revenue transferred to the unemployed. The second effect on the growth rate is the production effect, which implies a negative income effect on economic growth. Rais- ing the environmental tax rate xp increases the tax burden of firms, thereby reducing production (Y, = A'p(rp)]apKt). Owing to this negative effect on production, firms can pay lower wages to the employed and a lower amount of environmental tax to the government. In equilibrium, the increase in the




growth rate generated by the UI effect is greater (less) than the decrease generated by the production effect if and only if q(' - aL) > (<)rp(l - aK), or if and only if the environmental tax rate is below (above) the critical level, Tf* EE (1 - aL)q/(l - aK).

3.2. The Unemployment Rate

The unemployment rate in period i, ut, is defined by N-Lt

where the numerator on the RHS is the number of unemployed persons, and the denominator is the aggregate amount of labor. The equilibrium rate of unemployment is determined as follows (see appendix 7.4 for derivation):

r" -I apf__ Ul = u = y**> (16) Mi-^ + l^ + sfe)

We utilize the reciprocal of the unemployment rate in the following analysis, calculated as

after-tax wage income effect

1 azXl-r") u= 1

^ azXl-r")

aJ +1- (17)

unemployment insurance effect

Equation (17) indicates that the equilibrium unemployment rate is affected by the following two factors: aL(l -r"), representing the after-tax wage income effect; and Ia + aPrp/aL(rp + q), representing the unemployment insurance effect. The following proposition shows how the employees' rate of contribution to the unemployment insurance and the environmental tax affect the unemployment rate through these two factors.

Proposition 2 (Unemployment effects) Consider a change in r" or rp associated with an appropriate change in the benefit, bt. (i) Raising the employees' contribution to unemployment insurance increases the unemployment rate: du/dr" > 0. (ii) Raising the environmental tax increases the unemployment rate: du/dzp > 0.

Proof. The proof follows directly from (17). ■

Raising the employees' contribution rate to the unemployment insurance has the following two effects. First, it reduces the after-tax wage income, implying a lower return from employment: This is observed in the numerator in (17). Second, it increases the unemployment insurance benefits, implying a higher return from unemployment: This effect is observed in the



144 Tetsuo Ono

denominator in (17). These two effects give unions an incentive to reduce employment, so as to expand the share of unemployment benefits in the total income of the union members, thus maximizing their utility. For this reason, a monopolizing union sets the wage higher, which results in a higher unemployment rate. Raising the environmental tax increases the amount of unemployment insurance benefits. The same logic applies in this case as well: a monopolizing union sets the wage higher, resulting in a higher unemployment rate.

3.3. The Aggregate Level of Pollution

Given (6) and (16), the aggregate level of pollution in period t, Pt, is rewritten as:

Pt=PtLt = -^--N= -^- x['-u{?,t?)}N for allí. ^ v ^ number of employed

pollution/labor

(18)

This equation indicates that the aggregate level of pollution is affected by the following two factors: aP/(rp + q), representing pollution per labor unit, pt' and [1 - u(ru, rp)]N, representing the number of employed workers. The following proposition addresses how government policy affects the aggregate level of pollution via these two factors.

Proposition 3 (Environmental effects) Consider a change in r" or rp associated with an appropriate change in the benefit, bt. (i) Raising the employees' contribution to unemployment insurance reduces the aggregate level of pollution: dP/dr" < 0. (ii) Raising the environmental tax reduces the aggregate level of pollution: dP/dif < 0.

Proof. The proof follows from (18) and the results in proposition 2. ■

Raising the employees' contribution rate to unemployment insurance increases the unemployment rate. Owing to this negative effect on employment, the aggregate level of pollution is decreased. When the environmental tax is increased, there are two effects that reduce the aggregate level of pollution. First, raising the environmental tax decreases pollution per labor unit. Second, it increases the unemployment rate, which in turn affects pollution through the employment effect. Because of these two effects, the environmental tax reduces the aggregate level of pollution.




4. Effects of Replacement-Ratio-Neutral Reforms

This section considers a situation in which there is initially no environmental tax, and the only source of unemployment insurance is the revenue from the tax on the employed: r" > 0 and rp = 0. We consider a policy reform in which the government introduces the environmental tax as an additional means of financing its expenditure (unemployment insurance in this context).

We focus on the replacement ratio, which measures the proportion of after-tax work earnings replaced by unemployment benefits:

_ unemployment benefits bt(l - /,) bt(N - Lt) after-tax work earnings (1 - ru)ltwt (1 - ru)Ltwt

'

Based on the motivation described in the introduction, we consider a replacement-ratio-neutral reform in which the introduced environmental tax is devoted to cutting the employees' rate of contribution to unemployment insurance, keeping the replacement ratio unchanged.6

The replacement ratio defined above is rewritten as follows:

bt(N-Lt) = r"w,L, + rfP, = *" + ¿$+4) 9

(l-r»)Ltwt =

(l-T")Ltwt =

1-T" '

where the second equality is derived from the government budget constraint, (12), and the third equality is derived from (4), (6), and assumption l(ii).7 Equation (19) indicates that when the replacement ratio is fixed, raising the environmental tax requires that r" must be lowered. The government determines the amount of unemployment benefits, ft,, in order to balance its budget in each period. Under the constraint of the fixed replacement ratio, we can determine the effects of different methods of financing unemployment insurance on growth, unemployment, the aggregate level of pollution, and welfare.

4.1. Growth, Employment and Environmental Effects

First, we consider the effects of the replacement-ratio-neutral reform on growth, unemployment, and the aggregate level of pollution.

Proposition 4 Suppose that initially there is a contribution to unemployment insurance, but no environmental tax burden: r" > 0 and zf = 0. Under the replacement-

6 An alternative definition is given by the proportion of before-tax earnings replaced by unemployment benefits: 0 = bt(' - lt)/ltwt = t* + tfap/aL^ + <?). Because 0 is increasing in t" and i?, we can implement the replacement-ratio-neutral reform composed of cutting the contribution rate and introducing the environmental tax under this alternative definition. The choice of the definition does not affect the possibility of implementing the reform.

7 The term rf Pt is rewritten as rf Pt = xPytPtLt = iP{wt/aL)[ap/(xP + q)]Lt.



146 Tetsuo Ono

ratio-neutral reform, (i) the growth rate is increased, (ii) the unemployment rate is

unchanged, and (iii) the aggregate level of pollution is reduced.


The intuition behind the results in proposition 4 is as follows. First, the tax reform involves an increase in the pollution tax rp and, at the same time, a reduction in the contribution rate ru. The contribution to unemployment insurance is paid by the young generation in i, while the environmental tax is paid by both generations in t. Thus, the tax reform involves a shift of the tax burden from the young generation to the old generation in every period. As the savings rate of the young generation [= ß/(l + ß)] exceeds that of the old generation (= 0), this tax reform raises the growth rate of the economy.8

Second, although a cut of r" reduces the unemployment rate, the introduction of an environmental tax raises the unemployment rate (proposition 2). When a cut of ru and the introduction of rp are implemented in a replacement- ratio-neutral manner, the former effect offsets the latter effect. Hence, the replacement-ratio-neutral reform has no unemployment effect. This neutral result is confirmed by observing the replacement ratio, which is rewritten as 0 = aLu/(l - u) (see appendix 7.5 for the derivation of this equation). This equation shows that u is unaffected by changes in tax rates when 0 is fixed.

Finally, in order to consider the environmental effect of the reform, re- call (18), which shows that the aggregate level of pollution is affected by the pollution per labor unit and the unemployment rate. Given that the unemployment rate remains constant and the pollution per labor unit is reduced under the replacement-ratio-neutral constraint, the reform leads to a decrease in the aggregate level of pollution.

The results in proposition 4 are counter to the arguments made by employers, who often oppose environmental taxation. They argue that introducing an environmental tax is harmful to economic activity and thus to economic growth. In addition, they argue that the increased burden of the environmental tax gives them an incentive to reduce their demand for labor, which leads to the possibility of a higher unemployment rate. Based on these arguments, the Japan Business Federation opposes the environmental tax, although the Ministry of the Environment plans to introduce it in order to comply with the Kyoto Protocol.

Proposition 4 indicates that the employers' arguments are not necessar- ily valid. In the presence of a labor-market distortion, the introduction of an environmental tax is beneficial for economic growth when the revenue from the environmental tax is used for financing unemployment insurance. In addition, the employment rate remains unchanged when environmental

8 The author would like to thank one of the referees for suggesting this interpretation.




taxation is associated with lowering the employees' contribution rate to the unemployment insurance. Therefore, there is a means of implementing an environmental tax reform that is not harmful to growth and employment.

4.2. The Nonenvironmental Utility Effect

We have addressed the effects of the replacement-ratio-neutral reform on growth, employment, and pollution. However, we have not yet determined how such a reform affects the nonenvironmental utility of each generation. Therefore, we consider next whether the replacement-ratio-neutral reform improves the nonenvironmental utility of every generation, and, if possible, under what conditions such an improvement is realized. First, we obtain the following result.

Proposition 5 Suppose that initially there is a contribution to unemployment insurance, but no environmental tax burden: r" > 0 and t? = 0. The replacement-ratio- neutral reform fails to improve the nonenvironmental utility of every generation.

Proof. We will demonstrate the validity of this proposition by noting that the nonenvironmental utility of the initial old generation is worsened by the replacement-ratio-neutral reform. The nonenvironmental utility of the initial old generation is measured by its consumption: c' = r(rp)so, where s0 = K'/N is initially given. Given equation (5), r(rp) is decreasing in xp and neutral with respect to r". Thus, the replacement-ratio-neutral reform reduces the nonenvironmental utility of the initial old generation. ■

The replacement-ratio-neutral reform reduces the nonenvironmental utility of the initial old generation because its consumption level cj = r(Tp)s0 decreases when the environmental tax rp is applied, but is neutral with respect to the contribution rate to the unemployment insurance, r". When future generations benefit from environmental taxation in terms of nonenvironmental utility, such an improvement is realized at the expense of the initial old generation's nonenvironmental utility.

This trade-off is peculiar to a framework of overlapping generations, and is not observed in the framework of an infinite-lived agent. Under the latter framework, the weighted sum of the nonenvironmental utilities across periods is increased by the reform if the future positive effect outweighs the current negative effect. This improvement is derived from the fact that any individual suffering from the current loss will also benefit from the future gain. On the other hand, in the framework of overlapping generations, such an improvement never occurs, as shown in proposition 5. Those enjoying the improvement in one period are different individuals to those suffering from the utility deterioration in another period. There is a need to implement



148 Tetsuo Ono

some additional device in order to share the benefit of the environmental tax between these two individuals (i.e., generations).

4.3. A Reform with an Intergenerational Transfer

Based on the consideration outlined above, we will now examine a replacement-ratio-neutral reform that includes an intergenerational transfer from the young in generation 1 to the initial old generation. The government levies a tax on the total income of the young in generation 1 at a rate of 6rp e (0, 1) and transfers the revenue to the initial old generation, where 6 > 0 remains constant. Such a transfer occurs only during period 1; there is no intergenerational transfer in period t > 2.9

Under this alternative reform, we derive the conditions for which (i) the initial old generation is compensated for its nonenvironmental utility loss; (ii) the nonenvironmental utility of generation t > 1 is improved; and (iii) the aggregate level of pollution is decreased in each period. The following proposition shows sufficient conditions under which improvements in both nonenvironmental utility and environmental quality are realized.

Proposition 6 Suppose that initially there is a contribution to unemployment insurance, but no environmental tax burden: r" > 0 and if = 0. Consider an intergenerational transfer in which the government levies a tax on the total income of the

young in generation 1 at a rate of Qt? e (0, 1) and transfers the revenue to the initial old generation. Under a replacement-ratio-neutral reform associated with the

proposed intergenerational transfer, (i) the nonenvironmental utility of every generation is improved; (ii) the unemployment rate is unchanged; and (iii) the aggregate level of pollution is reduced, if the following conditions hold:

ap ( clk' „ ap('-aL ß ' , ß . [cip l-aL' - ap I )<0<- „ I ---r-si and , 7-^<minl . - ' [• -

q 'aL) q' I aL ---r-si 1+ß) 1+ß 'aL ' aL J


The formal proof is given in appendix 7.6. Here, we provide a sketch of the main steps. The first inequality, (aP/q)(aK/aL) < 0, is the condition under which the nonenvironmental utility of the initial old generation is improved, whereas the second inequality, 6 < (aP/q){(l - aL)/aL - ß/(l +ß)}, is the condition under which the nonenvironmental utility of generation t > 1 is

9 We assume that the tax rate on the total income, Or?, is proportional to the environmental tax, tP . Under this assumption, we can simultaneously evaluate both the marginal nonenvironmental utility effect of the replacement-ratio-neutral reform and that of im-

plementing an intergenerational transfer.




improved. The third inequality, ß/(l +ß) < min {aP/aL, (1 - aL)/aL] , guar- antees the existence of 6 (> 0) satisfying the first and second inequalities.10

In order to interpret these inequality conditions, we first consider the nonenvironmental utility of the initial old generation, which is measured by its consumption level:

c' = Rs0 + 01*71 = {R^) + Oifii^K./N , where the second equality is derived by using I' = i{rp)K'/N. The term Rs0 is the return from savings, and the term Orpli is the transfer from generation 1. Because c{ is independent of r", we can observe the marginal effect of a replacement-ratio-neutral reform associated with an intergenerational transfer by differentiating c^ with respect to rp and evaluating the derivative at rp = 0 :

/ '

-± dc¡ faP'1+ap 0aL^- „ q AK1 -± fop dc¡

=( - I -aK + 0aL^- „ q

A-j. AK1 N (20) fop tp=o '9 / ^ ^-JÌL N

V (») / Here term (i), which shows a negative effect, measures the decrease in consumption resulting from the change in the interest rate. Term (ii), which shows a positive effect, measures an increase in the transfer from generation 1. The inequality condition,

dp ( CLk' e>- dp (- ( CLk'

, (21)

ensures that the positive effect overcomes the negative effect. Next, we consider the nonenvironmental utility function of generation 1,

given by V? = (1 +ß)ln(l - 0tp)Ix +ß'nR(rp), from equation (10). This can be rewritten as

V" = (1 -i- ß) ln(l - to?) + (1 + ß) In i(T?) +ß'n R(f) (i) (ii) (iii)

+ (l+ß)in(K1/N). (22)

(iv)

Here term (i) shows a negative effect of the tax levied on the total income; term (ii) shows a positive effect of the environmental tax on the total income [proposition l(ii)], term (iii) shows a negative effect of the environmental tax through the interest rate; and term (iv) is related to an initial condition. Because V^ is independent of r", we can observe the effect of the reform on

10 When the third inequality holds, the upper limit of 6 given by (ap/q){(l - a^/aL - ß/(l +ß)} is (i) greater than the lower bound of 0 given by (ap/q)(aK/aL), and (ii) positive.



150 Tetsuo Ono

V" by differentiating V" with respect to iP and evaluating the derivative at

(ii) (iii) .

where terms (i), (ii), and (iii) correspond to the derivatives of (i), (ii), and (iii) in (22), respectively. The positive effect represented by (ii) overcomes the sum of the two negative effects, (i) and (iii), provided the following inequality holds true:

aP('-aL ß ' „ - aP('-aL I --TT^)>e- ß „ (24) q V aL 1+ßJ

Therefore, both the nonenvironmental utility of the initial old generation and that of generation 1 are improved if (21) and (24) hold.

The remaining task is to determine under what conditions the nonenvironmental utility of generation t > 2 is improved. For this purpose, consider the nonenvironmental utility function of generation t > 2, given by V? = (l+ß)'nlt+ß In R{rp), from (10). This can be rewritten as follows:

V? = (t - 1)(1 + ß) In G + (1 + ß) In i(f) +ß'n R{?) (ii) (iii)

+ (l+ß)ln(K1/N)i, (25)

(iv)

where the first term, (t - 1)(1 + ß) In G, shows the effect of the reform on the growth rate, and terms (ii), (iii), and (iv) correspond to those in (22) for Vf, respectively. Under the condition (24), which ensures an improvement in V?, the sum of terms (ii) and (iii) is increased by the reform. The first term, (t - 1)(1 4- ß) In G, is also increased by the reform (proposition 4). Thus, the nonenvironmental utility of generation í > 2 is improved by the reform if (24) holds. Taking the two conditions (21) and (24) together leads to the sufficient condition mentioned in proposition 6.

That sufficient condition indicates that the marginal rate of tax on the total income of generation 1, 6, should be set within a moderate range. When 6 is too low, the amount transferred from generation 1 to the initial old generation is reduced. Such a transfer is not sufficient to compensate for the nonenvironmental utility loss of the initial old generation. On the other hand, when the marginal rate is too high, each individual in generation 1 must pay a greater amount of the tax transferred to the initial old generation; thus, each individual in generation 1 is made worse off due to this greater tax burden.




The introduction of an environmental tax leads to an increase in the total income of each generation and thus to an increase in the growth rate [proposition l(ii)]. As described in the sketch of the proof, this approach is the key to implementing an intergenerational transfer for the nonenvironmental utility improvement of all generations. The major result is derived from the labor-market distortion caused by monopolized union wage setting. In fact, environmental taxation reduces the activity of firms and thus lowers the wages paid to the employed: this is the production effect, which results in a negative effect on economic growth. However, the unemployed benefit from the increased environmental tax revenue paid out as unemployment insurance: this is the UI effect, which results in a positive effect on economic growth. The positive effect overcomes the negative effect when the environmental tax is introduced [proposition l(ii)].

5. Discussion

Thus far, the analysis has involved two limitations: there is no growth effect of unemployment owing to the specification of the productive externality given by assumption l(i), and the interest rate has no effect on saving owing to the specification of the utility function. The question may arise whether the nonenvironmental utility improvement (that is, the positive growth effect of the environmental tax) holds when these limitations are relaxed. In order to answer this question, section 5.1 considers the case of a productive externality including the growth effect of unemployment. Section 5.2 considers the case of a utility function including the effect of the interest rate on saving; in addition, it considers the case including both effects.

5.1. The Growth Effect of Unemployment

We maintain the assumption of the log-linear utility function given in section 2, but adopt an alternative form of productive externality, including a growth effect of unemployment given by At = A(Kt/N)l~aK . Under this extended framework, the aggregate production function is given by Y, = Ap(T?)apKt(' - uty-aK, which shows that Y, is influenced by unemployment (Bräuninger, 2005).

The growth rate of aggregate capital is determined by

which shows that unemployment reduces economic growth. We consider how the introduction of an environmental tax affects the growth rate through



1 52 Tetsuo Ono

unemployment under the replacement-ratio-neutral constraint. Appen- dix 7.7 provides the details of the calculations.

For the purpose of analysis, we determine the relation between unemployment and the replacement ratio. The replacement ratio is given by

which shows that the unemployment rate is unchanged under a replacement- ratio-neutral constraint. This is the same result as that in section 4. The choice of assumptions about the productive externality does not affect the relation between unemployment and the replacement ratio.

Given that the unemployment rate is unchanged under a fixed replacement ratio, the growth rate is increased by the replacement-ratio-neutral reform, because ¿(if) is increased by the reform (see proposition 4). Therefore, it can be concluded that the growth-enhancing mechanism of the environmental tax holds under the assumption of a productive externality including the growth effect of unemployment.

5.2. Effects of the Interest Rate on Saving

We consider the case where assumption l(i) holds and where the utility function is generalized by adopting the following function with a constant intertemporal elasticity of substitution:

ye(0,oo), y#l, where 1/y is the intertemporal elasticity of substitution.11 When y = 1, the utility function of consumption becomes logarithmic, as presented in section 2.

Under the utility function above, the saving function is now given by ŒR)1/y

S, = 0(Äi+l){(l - T")/,HV + Ml - h)) , <P(R) = R + QJHyty '

where </)(R) is increasing (decreasing) in R if y < (>) 1. The corresponding growth rate is G = 0(í?(tí?))/(tp), which leads to the following result (see appendix 7.8 for the proof):

- > 0 if y > aL .

11 For the utility function of consumption, v(c), the intertemporal elasticity of substitution is defined by -v'(c)/cv"(c). When the function is specified by v(c) = (c1^ - 1)/(1 - y), then the elasticity becomes 1/y.




Therefore, the key result for obtaining nonenvironmental utility improvements holds as long as the absolute value of the elasticity of the marginal utility of consumption (y) is greater than or equal to the share of income earned by labor (aL).

Next, we consider the case including both the growth effect of unemployment and the effect of the interest rate on saving. In this case, the growth rate is given by G = 0(/?(r/7))/(rp)(l - ut)l-aK. Under the replacement-ratio- neutrality constraint, the unemployment rate remains unchanged, as shown in section 5.1. The growth effect of the reform is demonstrated by the factor </>(R(Tf))i(Tf). Thus, we can conclude that the growth rate is increased by the reform if y > aL.

6. Concluding Remarks

This paper has developed an overlapping-generations model of growth, unemployment, and pollution, and demonstrated the potential importance of intergenerational considerations for the choice of an environmental-tax- financed unemployment insurance scheme. The main results and their policy implications can be summarized as follows. First, we focused on a replacement ratio that measures the proportion of the after-tax work earnings replaced by unemployment benefits. We showed that under a replacement- ratio-neutral reform, in which the environmental tax is devoted to cutting the contribution rate to the unemployment insurance, the growth rate is increased, the unemployment rate remains unchanged, and the aggregate level of pollution is decreased (proposition 4).

Second, the initial old generation is consistently made worse off by implementing a replacement-ratio-neutral reform. Such a reform lowers the return on saving, and thus it also lowers the consumption level of the initial old generation (proposition 5). When future generations benefit, in terms of nonenvironmental utility, from the introduction of the environmental tax, such an improvement is realized at the cost of the initial old generation's nonenvironmental utility loss. Thus, a trade-off exists between current and future generations with respect to nonenvironmental utility.

Third, an intergenerational transfer from the young in generation 1 to the initial old generation is a means of sharing the benefits between generations (proposition 6). Because the total income of the young in generation 1 is increased by the environmental tax, they can afford to transfer some of their income to the initial old generation. Proposition 6 provides a sufficient condition under which the initial old generation is made better off by the intergenerational transfer, while individuals in generation 1 are also better off than they would be in the case of no environmental taxation. In addition,



1 54 Tetsuo Ono

it was shown that under this sufficient condition, all successive generations are made better off with respect to their nonenvironmental utility.

The results established in this paper are based on the specification of the model. In particular, the results presented in section 4 are limited to the case where there is initially no environmental tax burden. However, the current paper provides a framework for understanding the effects of environmental taxation on growth, unemployment, pollution, and welfare. It also offers a policy proposal for countries that plan to introduce environmental taxes.

7. Appendix

7.1. Derivation of (10)

Hie nonenvironmental utility of an individual i in generation t is calculated as follows:

ine] +ßlnci+1 = ine] + ßln ßRt+1c] = (1 + ß)lnc] +ßinRt+1 +ßlnß = {1 + ß) ln{(l - t")/,w, + 6,(1 - It) - st] + ß In Rt+1

where the equality in the first line is derived from the first-order condition, c*+1 = ßRt+1c], and the equality in the third line is derived from (7). Substi- tution of the saving fonction into the above equation leads to

Incj +/31nc?+1 = (1 + j8)ln{(l - t")/,w, + 6,(1 - /,)} + ßinRM +/31ni3 - (1 + ß) ln(l + ß) .

Given that the third and fourth terms on the RHS are constant, we can write the nonenvironmental utility function as (10).


We can rewrite It = (1 - i?)ltWt + bt(l - /,) as follows:

/, = (1 - T»)ltwt + tJ<iy^ +

^(1 _ it) given that (12) holds

= (1 - t»)llWl + tUw'L' + r'P' given that ±=± = I holds

= 0v,L, + TfP()/./V

= LaÍ^-Tk, L + ̂-aÍ-^-YkIn I

L 'tP+q) tP+q 'TP+qJ }'

given that (4) and (13) hold




where the definition of i(zp) is given in (14).

7.3. Proof of Proposition 1

Proof, (i): The proof follows from the fact that G in (15) is independent ofr".

(ii): The first derivative of G with respect to rp is given by dG = _ß_ di^l = ß / aP 'l+ap drp

= l+ß* dxP

= 1+ß 'TP + q)

which implies that dG/drp = 0 holds if rp = rp* = (1 - aL)q/(l - aK). The second derivative of G evaluated at rp = rp* is given by

p. drp2 =Tl_j4f-^)'4"x<-')"-^)<o, l+ß 'Tp*+qJ zp* + drp2 ^^ l+ß 'Tp*+qJ zp* + q which implies that G is maximized at rp = rp*. ■


Substituting the wage rate determined by the union wage setting (11) into the government budget constraint (12), we have

(N - Lt)aL(l - j?)wt = T»wtLt + if Pt .

The RHS of the above government budget constraint is rewritten as follows:

r"w,L, + xpPt = t"h>,L, + rPytPt given that rf = i?yt from assumption l(ii)

Tp dp = ruwtLt+-wt--Lt aL rp + q

given that yt = - and Pt = ptLt = - - Lt aL rp + q

Thus, we obtain

(N-Lîl-^^^ +

^^îN + L.-N).

Dividing both sides by w, and rearranging the terms, we obtain (16).



156 TetsuoOno


Proof, (i) From the result in proposition 1, we obtain BG/drf^^ = 0 and dG/drp'rP=0>0, which implies that the growth rate is increased by the replacement-ratio-neutral reform.

(ii) We can rewrite the replacement ratio given by (19) as a function of the unemployment rate:

^ bt{N-Lt) aL(l-i»)wt{N-Lt) u 0 ^ =

(1 - r«)L,w, =

(1 - r«)L,w, = "L x

T~u ' (26)

where the second equality is derived from the union-wage-setting condition (11) and the third equality is derived from (N - Lt)/Lt - u/{' - u). Hence, we obtain

« = -*-.

This shows that, given a fixed 0, the unemployment rate u is neutral with respect to r" and xp .

(iii) Given that the unemployment rate remains unchanged under the replacement-ratio-neutral reform, (18) shows that P is decreasing in rp and is independent of r". ■


Proof. Under a replacement-ratio-neutral reform, the unemployment rate remains unchanged [proposition 4(ii)]. The aggregate level of pollution is reduced because, given the replacement ratio, the aggregate level of pollution is decreasing in rp [proposition 4(iii)]. Thus, the focus hereafter is on the nonenvironmental utility of every generation.

The proof proceeds according to the following three steps. In step 1, we derive the condition under which the nonenvironmental utility of the initial old generation is improved by implementing a replacement-ratio-neutral reform associated with an intergenerational transfer from generation 1. In step 2, we derive the condition under which the lifetime income of each individual in generation t > 1 is increased in the presence of the intergenerational transfer. In step 3, we show that under the condition derived in step 2, the nonenvironmental utility of generation t > 1 is improved.

Step 1 In the presence of the intergenerational transfer from generation 1, the consumption of the initial old generation is

c? = too + Oifh = R(f)Kx/N + Wi^Kr/N from (14) ,

where the first term on the RHS is the return from savings, and the second term is the transfer from generation 1. Because c^ is independent of r",




we can observe the effect of the replacement-ratio-neutral reform on c^ by differentiating c^ with respect to rp and by evaluating the derivative at rp = 0 :

Therefore,

M >o * 0>^. (27)

Step 2 (1 - 6tp)I' is the lifetime income of each individual in generation 1 under the intergenerational transfer. Because (1 - Orp)I' is independent of t", we can evaluate the effect of the reform on (1 - 6if)I' by differentiating (1 - OTf)^ with respect to rp and evaluating the derivative at if = 0 :

9(1 - 6if)h _ 3(1 - Bxî^Kx/N d? TP=0

" d7p TP=0

which leads to

9(1 -*"* >o * ^(l^V*. (28) We should note that under (28), the aggregate capital in period 2, K2 = Nsu is increased by the reform because the savings are linearly related to the lifetime income: sx = ß(l - 6Tf)h/{l + /?).

Next, we consider the lifetime income of each individual in generation 2. As there is no intergenerational transfer in period 2, the lifetime income is I2 = i(rp)K2/N, which is independent of r". In order to evaluate the effect of the reform on 72, we differentiate I2 with respect to if and evaluate the derivative at rp = 0. Then, we obtain

g aT rP=0 -UW,

L + /(0)H ÖTF tP=0A

1/N. aT rP=0 L ÖTF tP=0A

The first term in the brackets, i'(0)K2, is positive (proposition 4), whereas the second term, i(0){dK2/drp'rP=0}1 is positive if (28) holds. Thus, the total income of each individual in generation 2 is increased by the reform if (28) holds. As saving is linearly related to the total income, the aggregate capital in period 3, K3 = Ns2, is increased by the reform if (28) holds. By employing the same procedure for t = 3, 4, ..., we find that the total income of each individual in generation t > 1 and the rate of aggregate capital growth are increased by the reform if (28) holds.



158 Tetsuo Ono

Step 3 The nonenvironmental utility of generation 1 under the current reform is

V» = (1 + fl) ln(l - <W) /(t")§ + ß In J?(z") .

Because V? is independent of r", we can observe the effect of the reform by differentiating V? with respect to rp and evaluating the derivative at rp = 0 :

Thus, we obtain

-L dV" n aP('-aL ß ' n -L >0 n o - £__£l_)>ô. n (29)

By comparing (29) with (28), we find that (29) =► (28). The nonenvironmental utility of generation t > 2 is represented as follows:

Vf = (1 + ß) In /, + ß In Ä(i*) = (1 + ß) In í(t") G'"1 ̂ + jS In R(?) .

Because V^ is independent of r", we can observe the effect of the reform by differentiating U? with respect to if and evaluating the derivative at

d-YL =n i m^°) i (t-l)(l+fl)(dG ' R'(0) ih? ,=0

=n K+P)m+

i i G 'dTP«J+PR(0)

„ , „ap'l-aL ß | , (t-l)(l+ß){dG '

The first term on the RHS of the second line is positive if (29) holds, whereas the second term is positive, as derived from proposition 4. Thus, we have dVy/drP lô > 0 if (29) holds.

In sum, we can conclude that the nonenvironmental utility of every generation is improved by a replacement-ratio-neutral reform associated with an intergenerational transfer from generation 1 to the initial old generation if (27) and (29) hold. There exists a condition 0 > 0 satisfying these two conditions if (i) the upper limit of 0 in (29), (aP/q) [(1 - aL)/aL - ß/(l +ß)] , is positive, and (ii) the upper limit of 0 in (29) is greater than the lower limit of 0 in (27), aKaP/qaL: that is, if (1 - aL)/aL > ß/(l + ß) and aP/aL > ß/(l + /}). These two inequalities are summarized as follows: ß/(l + ß) < min{aP/aL, (1 - aL)/aL}. ■




7.7. Supplementary Explanation for Section 5.1

Consider the case where the productive externality is given by At = A(Kt/N)l~aK. Under this assumption, the first-order conditions for profit maximization are

r'=a^(^)aP(i-M')i"aÄ'

By using these conditions, the revenue from environmental tax, rfP,, is rewritten as

Thus, the total income of an individual in generation t is given by It = i(rP)Kt(l-uty-a«/N.

Under the assumption of the log-linear utility function, the saving function is given by st = /?/,/(l + ß). With the capital-market-clearing condition, Kt+i = Nst, the growth rate is now determined by

By using the union-wage-setting condition and the government budget constraint, the replacement ratio, defined by <p = bt(l - /,)/(l - r")/,H>,, is rewritten as

showing that the replacement-ratio-neutral reform has no effect on unemployment. Given this, we can determine the growth effect of the reform by focusing on the factor i(rp). Therefore, the growth effect in this case is identical to that shown in proposition 1.

7.8. Supplementary Explanation for Section 5.2

Differentiating the growth rate G = (p(R(rp))i(rp) with respect to rp and rearranging terms, we obtain

Y TP+qy '' dtP 1 + ßVr[R(TP)]Vr-i

| q{' - aL) - (1 - aK)TP

(1 - aK)xP + aLq



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Tetsuo Ono Graduate School of Economics Osaka University 1-7, Machikaneyama, Toyonaka Osaka 560-0043

Japan [email protected]



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Environmental Tax Reform, Economic Growth, and Unemployment in an OLG Economy

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