Public pollution abatement, regional capital mobility, and tax competition.

Hadjiyiannis, Costas ; Hatzipanayotou, Panos ; Michael, Michael S. 等

1. Introduction

In response to growing environmental concerns, governments and international organizations have designed policies of pollution abatement and control (PAC). In a 2003 report the Organisation for Economic Co-operation and Development (OECD) defines PAC activities as

   ... the purposeful activities aimed directly at the preservation,
   reduction, and elimination of pollution nuisances arising as a
   residual of production processes or the consumption of goods and
   services .... In total, PAC expenditure comprises the flow of
   investment, internal current expenditure, subsidies and fees that
   is directly aimed at pollution abatement and control, and which is
   incurred by the public sector, the business sector, private
   households and specialized producers of PAC services.... (Linster
   and Zegel 2003, p. 9)

In the same report, PAC expenditures in OECD countries vary from 0.7% (Portugal, 1994) to 2.6% (Austria, 1998) of Gross Domestic Product (GDP) per annum in the period extending from 1990 to 2000. A revealing stylized fact of this report is that a significant part of these expenditures are undertaken by the public sector. For most countries, public expenditures account for about 40-60% of total PAC. These statistics reveal two important stylized facts. First, PAC expenditures as a percentage of GDP are sizeable, and second, a significant part of these expenditures are incurred by the public sector. (1)

Thus, it is important that both the private and the public sectors' abatement are taken into consideration in analyzing environmental policies, especially in light of the fact that emission tax revenue is often earmarked for pollution abatement activities by governments. For example, Brett and Keen (2000) note that in the United States it is quite customary for environmental taxes to be earmarked for specific environment-related public expenditure. In particular, such tax proceeds are commonly paid into trust funds that finance various clean-up activities or are spent on road and public transport networks. Yet by and large, the literature on pollution abatement has assumed that pollution abatement is entirely undertaken by the private sector in response to emission taxes on private producers (see, for example, Copeland and Taylor 1995; Copeland 1996; Ludema and Wooton 1997; Silva and Caplan 1997). (2)

Hatzipanayotou, Lahiri, and Michael (2002, 2005) and Chao and Yu (1999) provide some of the very few studies that explicitly consider the simultaneous provision of pollution abatement by the private and public sectors. Chao and Yu (1999) examine the welfare implications of international transfers when public pollution abatement is financed by foreign aid and emission tax revenue. Hatzipanayotou, Lahiri, and Michael (2002) examine optimal policies for the donor and recipient countries in a similar framework but also incorporate cross-border pollution. Hatzipanayotou, Lahiri, and Michael (2005) examine the optimal policy implications of a number of multilateral reforms in a two-country model with cross-border pollution, in which public sector abatement is financed through a fraction of environmental tax revenue. These studies, however, ignore an important feature of open economies--that of international capital mobility. On the other hand, there is a large body of literature examining various aspects, including optimal environmental policies, of the interaction between international capital mobility and the environment but without accounting for the simultaneous abatement of pollution by the private and public sectors (e.g., Copeland 1994; Copeland and Taylor 1997; Rauscher 1997).

The present paper bridges the gap in the literature by incorporating both capital mobility and public pollution abatement. To this end, we construct a general equilibrium model of a regional block (RB) with two non-identical countries and free commodity and capital flows. We assume that pollution, a by-product of production, is generated in each country, is transmitted across borders, and is abated partly by the private producers, in response to an emissions tax, and partly by the local governments. Governments finance their public pollution abatement activities using lump-sum and pollution tax revenue. We derive the cooperative and Nash optimal pollution taxes and relate them to the marginal cost of public pollution abatement.

This paper offers two innovations. The first is the generalization of the existing models, which incorporate simultaneous provision of public and private pollution abatement. In this more general model, we incorporate all the features that different papers have stressed as important features in studying environmental policies, such as cross-border pollution and asymmetries between countries. The second innovation is the analysis of these policies in the presence of capital mobility. Changes in environmental policies in the presence of public pollution abatement create externalities between neighboring countries because of cross-border pollution. At the same time, such changes affect tax revenue and therefore public pollution abatement. On the other hand, environmental policies affect capital mobility, which in turn affects emissions.

This generalized model allows us to identify interactions between these features that have been ignored by the literature thus far. Capital mobility affects the optimal choice of pollution taxes in the two countries since higher taxes lower the return to capital and drive capital out of the country. That restricts the ability of governments to finance public pollution abatement. We show that the coexistence of all these features affects optimal pollution taxes by comparing the general results to the special cases in which (i) there is no cross-border pollution; (ii) countries are identical; (iii) there is no capital mobility; and (iv) there is no public pollution abatement.

2. The Analytical Framework

The Model

We develop a general equilibrium model of a RB comprising two small open economies, Home and Foreign, which trade freely with each other and the rest of the world. (3) As a result, commodity prices in the two countries are constant and equal to the world commodity prices. In both countries pollution of the eyesore type is generated as a by-product of production and is transmitted across national borders. Identical residents, inhabiting each country, are adversely affected and suffer disutility from locally generated pollution and from pollution emitted by foreign producers and transmitted across borders. With respect to the flows of factors of production, it is assumed that capital is freely mobile within the RB but immobile between the region and the rest of the world. Other factors of production, such as labor, are intra-regionally and internationally immobile. (4)

Without loss of generality, we call the capital-importing country Home; the model of Foreign, the capital-exporting country, follows analogously. Home's maximum value of production of private goods is denoted by the revenue function R(p, v, t, K), defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

where p is the vector of exogenously given world commodity prices, [phi] (v, K) is the country's aggregate technology set denoting private production and abatement technologies, v is the endowment vector of the immobile factors, [bar.K] is Home's capital endowment, [k.sup.f] the amount of foreign capital operating in Home (and thus K is the domestic supply of capital), x is the vector of net outputs, and z is the amount of pollution emission by the private sector, net of the amount abated by the private sector. (5) In the present analysis, since (v) and (p) are invariant, for notational simplification the revenue function is written as R(t, K). By the envelop theorem, the partial derivative of the revenue function with respect to K (i.e., [R.sub.K]) is the marginal revenue product of capital, and by the same theorem, the level of pollution, z, generated by the private sector is given by (6)

z = -[R.sub.t](t, K). (2)

We assume that the R(t, K) function is strictly concave in K (RKK < 0) and strictly convex in t ([R.sub.u] > 0). The latter assumption implies that a higher emission tax level lowers the amount of pollution emissions by the private sector. We also assume that the polluting activity is capital intensive, that is, [R.sub.tK] < 0 and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Accounting for both private and public sector pollution abatement, the overall net pollution, r, affecting the home country residents is

r = z - g + [THETA]([z.sup.*] - [g.sup.*]), (3)

where the parameter [THETA][member of] [0, 1] is the rate of cross-border pollution or the spillover parameter, g is the level of public pollution abatement in the home country, and [z.sup.*] and [g.sup.*] denote the levels of pollution net of private abatement and the level of public pollution abatement, respectively, in the foreign country. (7) We also assume that private firms can only abate pollution by reducing production, and that they do not have access to the imported abatement good. This is because in some cases, it is in the best interest of the government to forbid its use by private firms. Allowing firms access to this good restricts the government's ability to use pollution taxes to capture terms of trade effects in the capital market. For example, if pollution taxes are higher than the cost of the abatement good, firms abate all pollution using the abatement good, avoiding pollution taxes altogether. That makes pollution taxes completely ineffective in capturing the terms of trade effect in the capital market.

As for the country's public sector, we assume that it imports from the rest of the world, at a constant price [P.sub.g], a commodity used to provide public pollution abatement at the level g. The assumption of the constant world price [P.sub.g] for the public abatement good implies constant marginal abatement cost (MAC). The cost of the imported good (i.e., [P.sub.g]g), used for public pollution abatement, is financed through the emission tax revenue [i.e., -t[R.sub.t](t, K)] and lump-sum taxes (7). Thus, the government's budget constraint is written as

[P.sub.g]g = -t[R.sub.t](t, K) q- T. (4)

This formulation reflects the requirement in many countries that pollution tax revenues are earmarked for environmental clean-up. We also allow governments to use lump-sum taxes to finance public pollution abatement. (8) We abstract from all other activities of the government in an effort to isolate the effects that relate to optimal environmental policies.

Turning to the demand side of the economy, we assume that each country comprises identical individuals. Utility is adversely affected by both local and foreign pollution transmitted across borders. Let E(u, r) denote the minimum expenditure required to achieve a level of utility, u, at constant prices, p, omitted from the expenditure function for reasons noted earlier and at the given level of net pollution, r. The partial derivative of the expenditure function with respect to u, [E.sub.u], denotes the reciprocal of the marginal utility of income. Since pollution adversely affects household utility, the partial derivative of the expenditure function with respect to r, [E.sub.r], is positive, denoting the households' marginal willingness to pay for a reduction in pollution (see Chao and Yu 1999), which is the same as the marginal damage of pollution (MD). (9) That is, a higher level of net pollution requires a higher level of spending on private goods to mitigate its detrimental effects so that a constant level of utility is maintained.

Home's budget constraint requires that expenditures by the private [E(u, r)] and the public sector (Peg) and payments to foreign capital [[k.sup.f][R.sub.K](t, K)] equal total revenue from production [R(t, K)] and pollution tax revenues [-t[R.sub.t](t, K)]. Thus, the economy's income expenditure identity is

E(u, r) + [P.sub.g]g + [k.sup.f] [R.sub.K](t, K) = R(t, K) - t[R.sub.t](t, K). (5)

Using Equation 4 in Equation 5 reduces the income expenditure identity to

E(u, r) = R(t, K) - [k.sup.f] [R.sub.K](t, K) - T. (6)

The model of Foreign, the capital-exporting country, is similarly developed. The corresponding equations for Foreign are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)

[r.sup.*] = [z.sup.*] - [g.sup.*] + [[THETA].sup.*] (z - g), (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (9)

[E.sup.*] ([u.sup.*], [r.sup.*]) = [R.sup.*] ([t.sup.*], [K.sup.*]) + [k.sup.F] [R.sub.K] (t, K) - [T.sup.*], (10)

where [r.sup.*] is the level of total net pollution for Foreign, [[THETA].sup.*] is the rate of cross-border pollution in that country, and [K.sup.*] is the supply of capital. By the assumptions of the model, dK = [dk.sup.f] = - [dK.sup.*]. (10)

Finally, international capital mobility, though non-existent between the RB and the rest of the world, is perfect within the RB (i.e., between Home and Foreign). Since it is assumed that capital earnings are untaxed by both countries, perfect regional capital mobility equalizes the

factor's reward in the two countries. That is, equilibrium in the RB's capital market requires that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (11)

Appendix A of the paper lays out the complete comparative statics of the system.

Pollution Taxes, Public Abatement, and Net Pollution

In this section, we derive and briefly discuss the effects of raising pollution taxes (t and [t.sup.*]) on net pollution (r and [r.sup.*]). These preliminary results are of use in the analysis to follow and highlight the effects that other studies ignore by omitting either public pollution abatement or capital mobility from the analysis. In Home, the effect of a higher pollution tax (t) on domestic net pollution (r) can be derived as follows: Using Equations 2 and 3 and Appendix A we obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (12)

where H = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [mathematical and are negative. Intuitively, Equation 12 shows that a higher tax (t) affects domestic net pollution (r) in three ways. First, it affects r directly by reducing the level of pollution taxed (i.e., - [R.sub.tt] < 0). The second effect is through its impact on public abatement in Home and Foreign, since additional tax revenues are earmarked for public abatement. This effect is not captured by the literature that does not account for public pollution abatement. (11) Third, it affects r through a pollution-haven effect. That is, a higher t induces a capital outflow from Home (i.e., dK/dt < 0), which reduces production-generated pollution z, and net pollution. (12) On the other hand, the higher t raises the stock of capital in Foreign, which raises production-generated pollution [z.sup.*], which in the presence of cross-border pollution also raises net pollution in Home. (13) Moreover, the combination of the last two effects also highlights the importance of including both capital mobility and public pollution abatement in the model.

Equivalently, the effect of the higher pollution tax (t) on Foreign's net pollution ([r.sup.*]) is shown to be

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (13)

The reduced form of Equation 13 is given in Appendix A. Analogous results are inferred for an increase in Foreign's pollution tax ([t.sup.*]) on the Home and Foreign countries' levels of net pollution.

Public pollution abatement and cross-border pollution are important determinants of the impact of emission taxes on pollution in each country. Note that in the absence of public sector pollution abatement and of cross-border pollution in both countries (i.e., [THETA] = [[THETA].sup.*] = 0), we unambiguously obtain that dr/dt(= dz/dt) < 0 and d[r.sup.*]/dt(= [dz.sup.*]/dt) > 0. In the absence of public sector abatement but in the presence of cross-border pollution, we obtain dr/dt < 0 and [dr.sup.*]/dt < 0 if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Therefore, a model that fails to account for public pollution abatement and cross-border pollution would give biased results on the impact of emission taxes.

3. Taxes and Welfare

In this section, we examine the effect of a higher domestic pollution tax (t) on levels of national welfare, (u) and ([u.sup.*]). Analogous results are stated for the effects of a higher tax ([t.sip.*]) on the aforementioned variables. We also examine the effects of higher lump-sum taxes, T and [T.sup.*], for each country's level of national welfare.

We first analyze the welfare effects of small changes in policy variables and show how the coexistence of public pollution abatement and capital mobility alters the existing results. Differentiating Equation 6 gives

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

Lump-Sum Taxes and Welfare

Using Appendix A, the effect of an increase in the domestic (foreign) lump-sum taxes on domestic (foreign) welfare is given by (14)

du / dT = [S.sub.g] / [E.sub.u][P.sub.g] (15)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (16)

where [S.sub.g] [equivalent to] ([E.sub.r] - [P.sub.g])= (MD - MAC)and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Public pollution abatement is locally optimally provided in Home (Foreign) if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]--that is, if MD = MAC ([MD.sup.*] = [MAC.sup.*]). This is the Samuelson rule for optimal public good provision within each country. Given this, we say that the public pollution abatement is locally under(over)-provided in Home if [S.sub.g] > 0 (< 0) and in Foreign if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Therefore, raising lump-sum taxes is unambiguously welfare improving (deteriorating) if the public pollution abatement is locally under(over)-provided. (15)

Pollution Taxes and Welfare

Using Equations 14 and 12, the welfare effect of an increase in Home's pollution tax (t) on its own welfare is given by

du/dt = 1/[E.sub.u] {[R.sub.t] - [E.sub.r] dr/dt - [k.sup.f] ([R.sub.Kt] + [R.sub.KK] dK/dt)}. (17)

The reduced form of Equation 17 is given in Appendix A. Equation 17 shows that the increase in (t) affects Home's level of welfare in three ways. First, the higher (t) induces a transfer of additional resources from production of goods to pollution abatement by private producers. As a result, real income, and therefore welfare, is reduced (i.e., [E.sup.-1.sub.u][R.sub.t] < 0). Second, it affects (u) through changes in domestic net pollution [i.e., - [E.sup.-1.sub.u][E.sub.r] (dr/dt)]. Namely, since [E.sub.r] captures the MD of pollution to households, then -[E.sup.-1.sub.u][E.sub.r](dr/dt) is a measure of the marginal benefit/damage of changes in (r) due to the increase in (t) on households' utility. Through this term, the increase in (t) increases (u) if dr/dt < 0. Third, the term -[E.sup.-1.sub.u] [k.sup.f] ([R.sub.Kt] + [R.sub.KK](dK/dt)) captures the effect of (t) on (u) through changes in payments to foreign capital operating at home. This change in payments to [k.sup.f] is due to changes in the domestic marginal revenue product of capital, [R.sub.K], induced by the higher (t). Namely, by assumption, a higher (t) reduces [R.sub.K] and thus payments to [k.sup.f] In addition, as previously discussed, dK/dt < 0 causes an increase in the marginal revenue product of capital and thus an increase in payments to [k.sup.f] It can be shown, however, that the positive direct effect (-[E.sup.-1.sub.u][k.sup.f][R.sub.Kt]) always dominates the negative indirect effect [-[E.sup.-1.sub.u][k.sup.f] [R.sub.KK](dK/dt)]. Thus, the overall impact of (t) on (u) through changes in payments to [k.sup.f] is positive. (16)

The effect of an increase in (t) on Foreign's level of welfare is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (18)

The reduced form of Equation 18 is given in Appendix A. Equation 18 shows that an increase in (t) affects ([u.sup.*]) through its effect on net pollution, ([r.sup.*]), and its effect on repatriated payments of its capital operating in the home country. The discussion of the first effect follows the discussion of Equation 13, and the discussion of the second effect follows that of Equation 17. Analogously, using Appendix A, we get the reduced-form expressions of an increase in ([t.sup.*]) on welfare in Foreign ([u.sup.*]) and in Home (u).

4. Optimal Lump-Sum and Pollution Taxes

In this section, we turn to the derivation of the optimal pollution taxes, (t) and ([t.sup.*]), and lump-sum taxes, T and [T.sup.*], in the presence of all these interactions generated by the coexistence of public pollution abatement, capital mobility, and cross-border pollution. We first derive the optimal tax rates under the assumption of policy cooperation between the two countries and then under the assumption of lack of such a cooperation.

Cooperative Taxes

A standard result in the literature of environmental economics is that in the presence of cross-border pollution externalities, the optimal policy requires either the adoption of cooperative policies among regions or the mandate of policies by a central (e.g., federal) authority. Here, we begin our analysis of tax policy choices by presenting the first-best policy choices of the RB. This regime entails the simultaneous cooperative choice of lump-sum and pollution taxes that maximize the two countries' joint welfare. This regime constitutes a benchmark solution to which the Nash equilibrium results to follow are compared.

Cooperative Lump-Sum Taxes

The maximization of the countries' joint welfare requires setting du/dT + [du.sup.*]/dT = 0 and du/[dT.sup.*] + [du.sup.*]/[dT.sup.*] = 0, where [du.sup.*]/[dT.sup.*] and [du.sup.*]/[dT.sup.*] are given by Equations 15 and 16, respectively.

Moreover, using Appendix A we obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (20)

From Equations 15, 16, 19, and 20, we determine that the cooperative first-best policy choice for provision of public abatement requires that (17)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (22)

where [lambda] = ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) denotes the ratio of Foreign's marginal utility of income to that of Home. (18) It should be noted that allowing transfers between the two countries would equalize their marginal utility of income, leading to [lambda] = 1. This is reasonable to assume in a perfectly cooperative environment. However, transfers between countries may not always be feasible. For example, it is a lot more difficult for a government to persuade its citizens to embrace monetary transfers to another country than it is to secure cooperation in taxation. Therefore, we present the more general formulation that allows for [lambda] [not equal to] 1.

With this in mind, the economic interpretation of Equations 21 and 22 is as follows. A unit of pollution generated by Home causes Er damage domestically and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] damage in Foreign. Thus [[bar.E].sub.r] is the global MD caused by a unit of locally generated pollution weighted by the relative marginal utilities of income, ([lambda]). Similarly [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the weighted global MD caused by a unit of pollution generated in Foreign. Therefore, [[bar.E].sub.r] ([[bar.E].sup.*.sub.r]) is the weighted global MD of the Home-generated (Foreign-generated) pollution. When [[bar.E].sub.r] = [P.sub.g], we say that the public pollution abatement by Home is globally optimally provided, and when [[bar.E].sub.r] - [P.sub.g] > 0 (< 0), public pollution abatement in Home is globally under-provided (over-provided). Similar definitions apply to Foreign.

Equations 21 and 22 indicate that maximizing joint welfare requires that lump-sum taxes in each country are set at a level at which the weighted global MD of pollution generated in each country equals the MAC of providing it (i.e., [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]). Note that these two equations represent the relevant Samuelson rule for optimal provision of regional public (pollution abatement) goods. Moreover, because of the existence of cross-border pollution, the relevant Samuelson rule accounts not only for the marginal willingness to pay for pollution abatement within the emitting country, but also for the marginal willingness to pay for it in the other country, weighted by the relative marginal utilities of income.

Note that in the absence of cross-border pollution (i.e., [THETA] = [[THETA].sup.*] = 0), changes in one country's lump-sum taxes have no effect on the other country's welfare level and that the first-best cooperative choice for public good provision reduces to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. This result is achieved without cooperation between the two countries.

Cooperative Pollution Taxes

Deriving the cooperative first-best choice of pollution taxes requires setting du/dt + [du.sup.*]/dt = 0 and du/[dt.sup.*] + [du.sup.*]/[dt.sup*] = 0, where the expressions for du/dt, [du.sup.*]/dt, [du.sup.*]/[dt.sup.*], and du/[dt.sup.*] are given in Appendix A. In general, the cooperative pollution taxes, [t.sup.c] for Home and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for Foreign, assuming that the two countries also cooperate in lump-sum taxes, are given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (24)

From Equations 23 and 24, note that in a perfectly cooperative environment with international transfers (i.e., [lambda] = 1), we get that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. In this case, the cooperative optimal policies require that [t.sup.c] = [P.sub.g] = [[bar.E].sub.r] and are independent of capital mobility. If international transfers are not feasible (i.e., [lambda] [not equal to] 1), capital mobility affects the cooperative pollution taxes. (19) This is because payments to Foreign's capital operating in Home constitute a direct income transfer from the latter to the former. Since the marginal utility of income differs in the two countries, the transfer of repatriated capital income affects global welfare. In other words, despite the fact that the income lost by Home is exactly the same as that gained by Foreign, the utilities that correspond to that income are different, and therefore they affect the maximization of their joint welfare. The sign of the coefficient of (1 - [lambda]) in the right-hand side of Equations 23 and 24 is assumed to be positive. (20) Thus, from Equation 23 for [lambda] > 1 we get that [t.sup.c] > [P.sub.g] and from Equation 24 that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], For [lambda] > 1, Home's marginal utility of income is lower than Foreign's, which means that Home is relatively richer, which calls for a higher pollution tax in Home and a lower pollution tax in Foreign. The intuition is as follows: Pollution taxes allow countries to redistribute income between them through their effect on repatriated income of Foreign's capital in Home. As [t.sup.c] increases and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] decreases the return to capital in Home decreases, while that in Foreign increases, causing capital outflow from Home to Foreign. This increases the return to capital and thus increases the repatriated capital income going from Home to Foreign. If [lambda] > 1, the marginal utility of income is higher in Foreign. This means that joint welfare can increase if income is transferred from Home to Foreign. The following proposition summarizes the result.

PROPOSITION l. If the marginal utilities of income across countries are the same ([lambda] = 1) and both countries cooperate in the choice of both policy instruments, the first-best policy choice is achieved when [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If, however, [lambda] > 1, the first-best is achieved when [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If [lambda] < 1, the first-best is achieved when [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Nash Equilibrium Lump-Sum and Pollution Taxes

We now derive the optimal Nash equilibrium lump-sum and pollution taxes for Home and Foreign and compare them to the benchmark cooperative case. The two countries choose these taxes simultaneously.

Nash Equilibrium Lump-Sum Taxes

Setting Equations 15 and 16 equal to 0, we derive the Nash equilibrium lump-sum taxes. The emerging Nash equilibrium conditions require that lump-sum taxes are chosen such that MD = MAC for Home and [MD.sup.*] = [MAC.sup.*] for Foreign.

Nash Pollution Taxes

Setting (du/dt) = 0 and ([du.sup.*]/[dt.dup.*]) = 0, we derive the following reaction functions:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (25)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (26)

Given that the structure of the game is such that lump-sum taxes are locally optimally chosen (i.e., [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), solving simultaneously Equations 25 and 26 gives the following expressions for each country's Nash equilibrium pollution taxes: (21)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (28)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and is positive. From Equations 27 and 28 we note that when lump-sum taxes are locally optimally chosen, the effect of pollution taxes on payments to Foreign's capital operating in Home constitutes the only difference between the Nash and cooperative tax rates derived when [lambda] = 1. Note that the Nash pollution taxes are independent of the marginal utilities of income since in the Nash equilibrium each country is only concerned about its own welfare.

Observing the above expressions, we note that in general the Nash pollution taxes can be greater or smaller than the unit cost of the public pollution abatement, as opposed to the benchmark case of cooperative choice of both instruments and [lambda] = 1. We resolve some of this ambiguity by considering some special cases, as stated in the following proposition:

PROPOSITION 2. Under the conditions of the model and when each country chooses all taxes to maximize its own welfare, leading to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = 0,

1. If [THETA] = 0 and [lambda] = 1, then [t.sup.N] > [t.sup.c] = [P.sub.g]. (22,23)

2. If [[THETA].sup.*] 0 and [lambda] 1, then [[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]].

3. If the two countries are symmetric in the sense that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

4. If [lambda] = 1 and the two countries have identical factor endowments and production technologies, leading to [k.sup.f] = 0, then the Nash and cooperative pollution taxes are the same and equal to the marginal cost of public pollution abatement (i.e., [t.sup.N] = [t.sup.c] = [P.sub.g] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]).

5. If [lambda] < 1 and [THETA] [approximately equal to] 0, then [t.sup.N] > [P.sub.g] > [t.sup.c]. Similarly if [lambda] < 1 and [[THETA].sup.*] [approximately equal to] 0, then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

6. If [lambda] > 1 and [THETA] [approximately equal to] 0, then [t.sup.N] > [P.sub.g] and [t.sup.c] > [P.sub.g]. Similarly, if [lambda] > 1 and [[THETA].sup.*] [approximately equal to] 0, then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The proof of Proposition 2 follows from Equations 27 and 28. Note that cases 1-4 assume that the marginal utilities of income between the two countries are the same. Intuitively, the first three cases of Proposition 2 capture terms of trade effects in capital markets and are directly derived from the assumption that Home is the capital-importing country and Foreign is the capital-exporting country and from the assumption that pollution is capital intensive in both countries. That is, a higher t reduces the payment of foreign capital, leading to a higher domestic Nash pollution tax level. The reverse holds for Foreign, the capital-exporting country.

Case 4 of Proposition 2 highlights a counter-intuitive result. When countries are identical in the above sense, Nash pollution taxes are efficient ([t.sup.N] = [t.sup.c], and [t.sup.*N] = [t.sup.*c]), while Nash lumpsum taxes are not. Nash lump-sum taxes are too low and lead to too little abatement since countries fail to take into account the damage their pollution causes to the other country. Cases 5 and 6 show that the relationship between the Nash and cooperative pollution taxes depends on the relative marginal utilities of income in the two countries. (24) Two key features of our model highlight the contribution of this paper to the literature.

First, contrary to most of the literature, we allow countries to be non-identical. Second, we introduce public pollution abatement in addition to private pollution abatement. The remainder of this section examines the role of country differences, while in the section to follow we examine the role of public pollution abatement in detail.

To show how differences between the two countries affect optimal taxes, we first consider the case in which the two countries are identical. If countries are identical, the return on capital is identical and [k.sup.f] = 0. In that case, if both taxes are chosen optimally [t.sup.N] = [t.sup.c] = [P.sub.g] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. However, from Equations 21 and 22, [T.sup.N] [not equal to] [T.sup.c] and [T.sup.*N] [not equal to] [T.sup.*c]. Therefore, if countries are identical and both taxes are chosen optimally, there is no need for cooperation in pollution taxes since Nash taxes are efficient. On the other hand, there is scope for cooperation in lump-sum taxes. If, however, the two countries are non-identical and choose both taxes optimally, Nash pollution taxes are not efficient. From Equations 21 and 22 we still get that [T.sup.N] [not equal to] [T.sup.c] and [T.sup.*N] [not equal to] [T.sup.*c]. Proposition 2 summarizes the sufficient conditions for [t.sup.N] > [t.sup.c] and [t.sup.*N] < [T.sup.*c]. (25)

5. The Role of Public Pollution Abatement

To highlight the role of public pollution abatement, consider the case in which all pollution abatement is undertaken by the private producers, in response to the emissions tax, and in which pollution tax revenue is lump-sum distributed to local households in each country. Moreover, for simplicity we only consider the case in which [lambda] = 1.

The level of production-generated pollution by the private sector in the two countries is again given by Equations 2 and 7, and overall net pollution affecting Home and Foreign, respectively, are defined as

r = z + [theta][z.sup.*] and [r.sup.*] = [z.sup.*] + [theta]z. (29)

The income-expenditure identities for the two countries are given by

E(u, r) = R(t, K) - t[R.sub.t](t, K) - [k.sup.f][R.sub.K](t, K), (30)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (31)

Equilibrium in the RB's capital market is given by Equation 10. Appendix B presents the comparative statics of this system.

The cooperative first-best choice of pollution taxes is [t.sup.c] = [[bar.E].sub.r] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]]. Note that this cooperative policy choice is different from the solution with public pollution abatement, in which [t.sup.c] = [P.sub.g] = [[bar.E].sub.r] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], since in the latter [P.sub.g] and [[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the cost of public sector abatement in each country is exogenous, and it is to this specific value that the pollution tax and the global damage of a unit of pollution are equated. Also, since dr/dT < 0, when g > 0 we have less r for the same t; thus [t.sup.c](g = 0) > [t.sup.c](g > 0). That is, the higher g and [g.sup.*], the lower the optimal cooperative tax; hence, public abatement substitutes for private abatement. This is one of the ways in which public pollution abatement affects optimal taxes.

Using Appendix B, we get that the Nash equilibrium pollution tax for Home is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (32)

To highlight the differences between the two cases consider the following special case. Let the two countries have identical factor endowments and technologies, leading to [k.sup.f] = 0, and let [THETA] > 0; [THETA].sup.*] > 0 (two-way cross-border pollution). From Equation 32, observe that Nash pollution taxes are inefficient; that is, [t.sup.N] < [E.sub.r] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. On the other hand, and in direct contrast to this result, case 4 of Proposition 2 indicates that in the presence of public pollution abatement, Nash pollution taxes are efficient, while lump-sum taxes are not. This is because Home knows that Foreign has public pollution abatement at its disposal, and that it will use it optimally, thus decreasing the amount of cross-border pollution back into Home. Thus, it can afford to increase pollution taxes to their efficient level. The intuition is as follows: A higher t induces capital outflow from Home, increasing the stock of capital and pollution in Foreign. In the absence of public pollution abatement this increases cross-border pollution and net pollution in Home. This increased cross-border pollution mitigates the benefit from increasing pollution taxes, leading to lower equilibrium taxes. On the other hand, in the presence of public sector abatement, Foreign increases [g.sup.*] and ends up with the same level of net pollution. Thus, there is no extra cross-border pollution into Home. This is because optimal behavior requires the MD ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],) of Foreign to be equal to the exogenous MAC ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), which is constant. Therefore, the benefits of an increase in pollution tax are higher in the presence of public pollution abatement, leading to higher pollution taxes. (26)

These results are summarized in the following proposition:

PROPOSITION 3. If the two countries have identical factor endowments and production technologies, leading to [k.sup.f] = 0 and [lambda] = 1, then

1. In the presence of public pollution abatement, Nash equilibrium lump-sum taxes require that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and are inefficient, while Nash pollution taxes are efficient (i.e., [t.sup.N] = [t.sup.c] = [P.sub.g] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]).

2. In the absence of public pollution abatement, Nash equilibrium pollution taxes are inefficient (i.e., [t.sup.N] < [E.sub.r] < [t.sup.c] = [[bar.E.sub.r] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Proposition 3 has important policy implications. When countries are identical, there is no need for cooperation in emission taxes. On the other hand, even identical countries need to cooperate in lump-sum taxes. To see that, recall that cooperative lump-sum taxes require that ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], while Nash lump-sum taxes require that [E.sub.r] = [P.sub.g] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Proposition 3 demonstrates that the existence of public pollution abatement drives this result. It provides an additional policy tool, making it easier to achieve the first-best emission taxes. The other important policy implication of this section is that cooperation in both emission and lump-sum taxes is very important when countries are different.

6. Conclusion

There is ample real-world evidence that the public sector is a key player in pollution abatement activities. Despite this stylized fact, the literature has paid little attention to it. On the other hand, the few attempts at modeling public pollution abatement ignore another important feature of open economies, that of international capital mobility. This paper extends the existing literature in two ways: (i) It offers a generalized model of simultaneous private and public pollution abatement, which includes asymmetric countries and cross-border pollution; and (ii) It considers public pollution abatement in the presence of international capital mobility. Within this framework, we examine the cooperative and Nash pollution taxes of the countries involved.

To address these issues, the paper presents a model of a RB with two non-identical countries with cross-border pollution, free trade in goods, and perfect capital mobility within the region. Pollution, a by-product of production, adversely affects welfare and is abated by the private and public sectors in both countries. The government uses revenue collected from pollution and lump-sum taxes to finance public pollution abatement.

The major results of the paper are summarized in the various propositions, and to avoid repetition, we do not cite them here. A few general remarks, however, are worth emphasizing, since they highlight effects the literature has ignored so far. First, the cooperative lump-sum taxes need to account for the existence of cross-border pollution and the relative marginal utilities of income between the two countries. Second, the Nash equilibrium pollution taxes depend on whether the country is a net capital importer or capital exporter, on the factor intensity of the polluting activity, and on the degree of cross-border pollution. Contrary to the cooperative taxes, Nash pollution taxes are independent of the relative marginal utilities of income. Third, when countries are symmetric, and in the presence of public pollution abatement, the Nash equilibrium taxes are efficient, while in the absence of public pollution abatement they are not, as a result of the effects of cross-border pollution.

The key policy implication of these results is that cooperation is more important when countries are different. However, there is still scope for cooperation in lump-sum taxes when countries are identical but not in emission taxes.

Appendix A: Comparative Statics

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Appendix B: The Model without Public Pollution Abatement

Differentiating Equation 30 using Equations 30 and 11, we obtain the following matrix system:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the determinant of the matrix of the unknowns.

Received March 2007; accepted January 2008.

References

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Chao, Chi-Chur, and Eden S. H. Yu. 1999. Foreign aid, the environment, and welfare. Journal of Development Economies 59:553-64.

Copeland, Brian R. 1994. International trade and the environment: Policy reform in a polluted small economy. Journal of Environmental Economies and Management 26:44-65.

Copeland, Brian R. 1996. Pollution content tariffs, environmental rent shifting, and the control of cross-border pollution. Journal of International Economics 40:459-76.

Copeland, Brian R., and M. Scott Taylor. 1995. Trade and transboundary pollution. American Economic Review 85:716-37.

Copeland, Brian R., and M. Scott Taylor. 1997. A simple model of trade, capital mobility and the environment. NBER Working Paper No. 5898.

Hatzipanayotou, Panos, Sajal Lahiri, and Michael S. Michael. 2002. Can cross-border pollution reduce pollution? Canadian Journal of Economics 35:805-18.

Hatzipanayotou, Panos, Sajal Lahiri, and Michael S. Michael. 2005. Reforms of environmental policies in the presence of cross-border pollution and public-private clean-up. Scandinavian Journal of Economics 107:315-33.

Linster, Myriam, and Frederique Zegel. 2003. Pollution abatement and control expenditure in OECD countries. Discussion paper, OECD.

Ludema, Rodney D., and Ian Wooton. 1997. International trade rules and environmental cooperation under asymmetric information. International Economic Review 38:605-25.

Rauscher, Michael. 1991. National environmental policies and the effects of economic integration. European Journal of Political Economy 7:313-29.

Rauscher, Michael. 1997. International trade, factor movements, and the environment. New York: Clarendon Press.

Silva, Emilson C. D., and Arthur J. Caplan. 1997. Transboundary pollution control in federal systems. Journal of Environmental Economics and Management 34:173-86.

Turunen-Red, Arja H., and Alan D. Woodland. 2004. Multilateral reforms of trade and environmental policy. Review of International Economics 12:321-36.

Costas Hadjiyiannis, * Panos Hatzipanayotou, ([dagger]) and Michael S. Michael ([double dagger])

* Department of Economics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus; E-mail costah@ucy.ac.cy; corresponding author.

([dagger]) DIEES, Athens University of Economics and Business 76 Patission str., Athens 104 34, Greece; E-mail hatzip@aueb.gr.

([double dagger]) Department of Economics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus; E-mail m.s.michael@ucy.ac.cy.

(1) In particular, table 3b of the same report provides evidence that in many countries a significant part of the financing of cross-border pollution abatement is undertaken by the government. For example, in 1994 the U.S. government spent 0.3% of the GDP on abating air pollution, which accounted for 33% of the total expenditure on air pollution abatement. In the period ranging from 1990 to 2000, punic PAC expenditures as a percentage of total PAC expenditures averaged 55% in Canada, Finland, France, and Korea; 77% in Germany; 35% in Japan; and 40% in the United States.

(2) The OECD, in a 2003 workshop report, provides evidence that many countries impose emission taxes. For example, most European Union (EU) countries, including the United Kingdom, Germany, France, and Italy, impose energy and C[O.sub.2] taxes (see Bygrave and Ellis 2003).

(3) Following the standard convention, we denote all the variables of the foreign country with an asterisk.

(4) The model may resemble the case of a region---either with all its members developed (e.g., EU), some developed, and some developing (e.g., NAFTA), or two regions in a federal state vis-a-vis the rest of the world. In such a context, there is free commodity trade within the region and nearly free commodity trade between the region and the rest of the world.

(5) For simplicity, we assume only one type of pollution emission is generated in one sector. A prime (') denotes a transposed vector or matrix, and p'x - tz is the value of factor income. Finally, [PHI](v, K) includes production technologies and abatement technologies in various private sectors, as they carry out some pollution abatement in response to the emission tax (t).

(6) Copeland (1994) and Turunen-Red and Woodland (2004), among others, define pollution in the same way.

(7) This formulation of additive level of net pollution, r, implies that the two countries emit the same pollutant. Generalizing the present specification to one in which the two countries emit different types of pollutants only results to unwarranted algebraic complications without providing substantive analytical insight.

(8) Lump-sum taxes can be positive or negative depending on whether pollution tax revenues cover abatement costs. This means that the government has two policy instruments. One can think of the government choosing t and T, with g being residually determined, or choosing t and g, with T determined residually to balance the budget. The two formulations are equivalent.

(9) In Copeland's (1994) terminology, [E.sub.r] is a measure of the marginal damage to consumers from pollution.

(10) The cost of the public pollution abatement good may be different in the two countries for country-specific reasons, such as transportation or transaction costs. The case of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a special case of the more general specification presented in this paper.

(11) The effects of environmental policies on pollution, without public sector abatement, in the presence of capital mobility are examined in other studies, such as that of Rauscher (1991) and Copeland and Taylor (1997).

(12) The third effect is a "leakage effect," by which higher domestic emission taxes raise production in Foreign and so raise pollution in Foreign; hence, lower domestic pollution "leaks" into Foreign production.

(13) Hatzipanayotou, Lahiri, and Michael (2002) examine the effect of a higher t on r in a model with [THETA] = 0 and no capital mobility.

(14) All derivatives presented in the paper assume that all other instruments are given.

(15) Recall that in this model, lump-sum taxes are exclusively used to finance public abatement. Thus, with t fixed, dT [P.sub.g]dg, and, hence, for welfare considerations what really matters is du/dg. That is, [p.sub.g](du/dT) = (du/dg) = [S.sub.g]/[E.sub.u] [??] 0.

(16) In Appendix A, this is shown by the last term (i.e., [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) of the reduced form of Equation (17).

(17) Throughout the analysis, we assume interior solutions for the policy instruments and for interior allocations of capital and pollution levels.

(18) If g and t are used as the policy instruments and T is determined residually, the corresponding optimality conditions are [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Therefore, the cooperative first-best rules are again given by Equations 21 and 22.

(19) The Samuelson rule for [lambda] [not equal to] 1 is a modified one in which international transfers are not feasible. The inclusion of public abatement leads to non-trivial results compared to the case in which g = [g.sup.*] = 0, as shown in the last section of the paper.

(20) Combining the first two terms in brackets in the numerator of Equation 23 we obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which is positive if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (sufficient but not necessary condition). That is, the total effect of an increase in capital on its return, direct and indirect through changes in pollution, is negative.

(21) The general expressions for the Nash pollution taxes when lump-sum taxes are not chosen optimally are given in Appendix A.

(22) This is the well-known NIMBY (Not In My Back Yard) effect. That is, in the absence of cross-border pollution, shifting capital away reduces pollution and raises welfare.

(23) In this case, [t.sup.N] > [P.sub.g] to capture terms of trade gains in the capital market. That is, the payments to foreign capital are reduced as a result of the higher t. This is one of the cases that the government wants to restrict access of firms to the pollution abatement good.

(24) Case 5 states sufficient conditions for [t.sup.N] > [P.sub.g] > [t.sup.c], while in case 6 if k is large enough, then [t.sup.c] > [t.sup.N] > [P.sub.g].

(25) Note that when the two countries are identical [t.sup.N] = [tsup.c] = [P.sub.g] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. In this case the government can allow private firms to use the imported pollution abatement good since the private benefit is equal to the social benefit. In all other cases, the government is better off by restricting access to this good to capture terms of trade gains.

(26) An interesting extension to this paper is to consider the strategic adoption of pollution abatement technologies before deciding on taxes.