Environmental Duties and International Harmonization of Standards.

Josh Ederington [*]

Demands by domestic industries for protection from foreign competition aided by lower standards have led to proposals to set trade barriers conditional on the environmental policies of other countries. This article shows that the threat of such environmental duties can assist in achieving global efficiency when countries cannot commit to a negotiated environmental standard. In addition, this article shows that, in a repeated game framework, the enforcement of a free-trade agreement may require some convergence in environmental standards across countries when trade is driven by differences in such standards. However, it is also shown that it is more efficient to enforce a trade agreement by setting tariffs to partially offset differences in policy standards than to attempt to harmonize standards within environmental side agreements.

1. Introduction

Substantial reductions in tariffs over the past several decades have exposed countries to more international competition, focusing attention on domestic policies such as environmental and labor standards as potential sources of comparative advantage. Consequently, many firms in the United States (and other advanced countries) have demanded protection from foreign competition, arguing that lower environmental standards in foreign countries place them at a disadvantage.

An environmental duty is a trade tax that is set conditional on the environmental policies of one's trading partner. Such environmental duties are seen as a means of insulating domestic producers from the "unfair" competitive effects of differing foreign standards. For example, in the International Pollution Deterrence Act of 1991, former U.S. Senator David Boren proposed that environmental duties be applied to imports of products made abroad by industries that have lower environmental standards than in the United States. However, most trade economists are opposed to such proposals, arguing that tariffs aimed at offsetting differing standards across countries cannot be justified on economic efficiency grounds (e.g., see Bhagwati and Srinivasan 1996). Basically, their argument is that there are legitimate reasons for diversity in environmental regulations across countries (e.g., differences in preferences, natural endowments, or population density) and that differences in competitiveness arising from this dive rsity increase the gains to mutually beneficial trade. Indeed, one of the outcomes of the Uruguay Round of GATT was an explicit definition of a subsidy that rules out the use of countervailing duties based on lax standards in foreign countries. Thus, there appears to be substantial disagreement about the merits of allowing countries to set trade taxes that are conditional on the environmental standards/policies of other countries. This article proposes a theoretical analysis of the conditions under which environmental duties may be justified.

I investigate this question within a standard model of trade in which countries have different preferences over the environment and the differing environmental standards of the two countries lead to mutually beneficial trade. The basis for the analysis is the assumption that a country's policies (both trade policies and domestic policies) affect the world market through their effect on world prices. As a result, countries will unilaterally set their policies with trade concerns in mind, and there will be a role for international negotiation in achieving global efficiency. A sizeable literature has established the theoretical ability of countries to use environmental policy (and other governmental standards) as an instrument of trade policy (e.g., Markusen 1975; Krutilla 1991; Kennedy 1994). In this article, I argue that environmental duties can be justified if countries set their environmental policies with trade concerns in mind.

In section 3 of the article, I show that the threat of environmental duties may be desirable in that it deters countries from distorting their environmental policies away from efficient levels. Specifically, if the environmental duty is set to ensure that the world price remains constant as the foreign country adjusts its environmental tax, it eliminates the terms-of-trade incentives of the foreign country to distort its environmental standards. Thus, an environmental duty results in the foreign country setting the efficient standard. [1] This result suggests that, even when countries cannot commit to a negotiated environmental policy (and thus must set environmental policies unilaterally), they can still achieve the globally efficient outcome if they can commit to a tariff formula that involves environmental duties.

In section 4, I investigate the case where countries cannot commit to either trade or environmental policy and thus must rely on punishment strategies to support the agreement. I follow the growing literature on self-enforcing agreements (e.g., see Dixit 1987; Bagwell and Staiger 1990; Ederington 2001) by modeling an international agreement covering trade and environmental policies as an infinitely repeated game in which countries threaten infinite reversion to the noncooperative equilibrium as punishment for deviations from the agreement. Therefore, when the discount rate is low (and thus countries heavily discount the future losses to triggering the punishment phase), the globally efficient outcome cannot be supported.

I first show that, when the discount rate is low, free trade can only be supported if countries adjust their environmental policies away from the optimal standard. When trade is driven by differing environmental standards (i.e., the country exporting the dirty good has the weaker environmental standard), this adjustment entails partial convergence of standards in order to reduce the temptation to cheat on the agreement. This result provides a novel interpretation of various environmental side agreements that often accompany free trade agreements. [2] Under this interpretation, such side agreements represent a necessary attempt to manipulate environmental standards so that free trade (which is essentially required by the World Trade Organization for the formation of regional free-trade agreements) can be supported.

Second, I show that, when the discount rate is low, an agreement involving efficient environmental policy can be supported by moving tariffs away from free trade. I show that, if trade is driven by differing environmental standards, the most cooperative tariff is, in effect, an environmental duty, as it is set to partially offset the differences in environmental standards across countries so as to mitigate the incentive to deviate from the agreement. I finally show that an implication of Ederington (2001) is that allowing such environmental duties to support a trade agreement is more efficient than trying to support free trade by manipulating environmental standards across countries through side agreements.

In the following analysis, section 2 lays out the basic model and derives noncooperative and globally efficient trade and environmental policies. Section 3 investigates the use of environmental duties as a means of deterring countries from distorting their environmental policies. Section 4 analyzes the use of environmental duties and environmental side agreements as a means of enforcing an international agreement within a repeated game framework. Finally, section 5 concludes.

2. The Model

The analysis is conducted within a partial equilibrium model of trade similar to that used in Krutilla (1991). There are two symmetric countries, a home and foreign country (denoted by *) that have access to two policy instruments: trade and environmental policy. Demand and supply functions are given exogenously, with the home country being the natural importer of a homogenous good. Home country supply is given by the linear function Q([p.sup.s]) = [p.sup.s], where [p.sup.s] is the local producer price. Supply functions within the foreign country are identical and defined in terms of the foreign producer price [p.sup.s*]. Demand in the home (foreign) country is given by the function D([p.sup.d]) = 1 + [alpha] - [p.sup.d] [[D.sup.*]([p.sup.d*]) 1 - [alpha] - [p.sup.d*]], where [p.sup.d] is the local consumer price. [3] To ensure that trade volume is positive and that the good is consumed in each country, it is assumed that [alpha] [epsilon] (0, 1/6).

The home-country production tax is denoted by t, and [tau] is the specific trade tax applied to imports. Likewise, [t.sup.*] and [[tau].sup.*] denote, respectively, the production and trade tax choices of the foreign country. Therefore, in the home country, producer and consumer prices (provided that trade taxes are not prohibitive) are given, respectively, by [p.sup.s]([p.sup.w], t, [tau]) = [p.sup.w] - t + [tau] and [p.sup.d]([p.sup.w], [tau]) = [p.sup.w] + [tau], with [p.sup.w] denoting the world (untaxed) price of the good. Prices in the foreign country are symmetrically defined as [p.sup.s*]([p.sup.w], [t.sup.*], [[tau].sup*]) = [p.sup.w] - [t.sup.*] - [tau].sup.*] and [p.sup.d*]([p.sup.w], [[tau].sup.*] = [p.sup.w] - [tau].sup.*].

Given a positive trade volume, world markets will clear (i.e., world demand will equal world supply). From this market-clearing condition and the demand and supply equations, the market-clearing world price for the good can be derived as [p.sup.w](t, [tau], [t.sup.*], [[tau].sup.*]). [4] Using this world price, local producer and consumer prices for each country can be expressed as functions of trade and environmental policy in that country and the market-clearing trade volume can be calculated. Letting M be the import volume of the home country (M([p.sup.d], [p.sup.s]) = D([p.sup.d] - Q([p.sub.s])), it follows that M(t, [tau] [t.sup.*], [tau.sup.*]) = [2[alpha] - 2([tau] + [[tau].sup.*]) + t - [t.sup.*]]/2. The foreign export ([E.sup.*]) volume follows directly from the market clearing condition that M = [E.sup.*].

I follow Krutilla (1991) by modeling the environmental externality as a distinct linear function of production that enters separably into a country's welfare function, the cost of which is given by the functions S(Q) and [S.SUP.*]([Q.SUP.*]). Specifically, I assume that pollution in the home country is given by S(Q) = s.Q([p.sup.s]). while pollution in the foreign country is defined symmetrically, with [S.SUP.*]([Q.SUP.*]) = [s.sup.*].[Q.SUP.*]([p.sup.[s.sup.*]]). The parameters s and [s.sup.*] reflect the marginal external costs of production and are restricted over the interval [0, 2/3]. To assure that the foreign country is the natural exporter of the good, I assume that [s.sup.*] [less than] 2[alpha] + s.

Finally, governments are assumed to maximize the sum of consumer surplus and producer surplus, net of external costs of production, and trade policy and environmental policy revenue. The welfare for the home country is given by

W(t, [tau], [t.sup.*], [[tau].sup.*]) [equivalent] [[[integral].sup.1].sub.[[p.sup.d].sub.x]] D([p.sup.d]) dp + [[[integral].sup.[[p.sup.s].sub.x]].sub.0] Q([p.sup.s]) dp + [tau]*M([p.sup.s], [p.sup.d]) + [t - s]*Q([p.sup.s]), (1)

while foreign country welfare is given by

[W.sup.*](t, [tau] [t.sup.*], [[tau].sup.*]) [equivalent] [[[integral].sup.1].sub.[[p.sup.d].sub.x]] [[[integral].sup.[[p.sup.s*].sub.x]].sub.0] [Q.sup.*]([p.sup.s*]) dp + [[tau].sup.*]*[E.sup.*]([p.sup.s*], [p.sup.d*]) + [[t.sup.*] - [s.sup.*]].[[Q.sup.*]([p.sup.s*]). (2)

In the absence of an international agreement, each country sets production taxes and trade taxes to maximize national welfare, taking the policy choices of its trading partner as given. Taking the derivatives of Equation 1 with respect to t and [tau] and solving out the first-order conditions, the unilaterally optimal environmental and trade policies for the home country ([t.sup.D], [[tau].sup.D]) are given by [5]

[t.sup.D] ([tau], [t.sup.*], [[tau].sup.*]) = s - [[lambda].sub.t][[tau] -1/[epsilon]] (3)

[[tau].sup.D](t, [t.sup.*], [[tau].sup.*]) = 1/[epsilon] - [[lambda].sub.r][t - s], (4)

where

[epsilon] [equivalent] [partial]M([p.sup.s], [p.sup.d])/[partial][tau] / M([p.sup.s]), [p.sup.d]) * [[partial][p.sup.w]/[partial][tau]] [great than] 0, [[lambda].sub.t] [equivalent] [partial]M([p.sup.s], [p.sup.d])/[partial]t / [partial]Q([p.sup.s])/[partial]t [less than] 0, [[lambda].sub.[tau]] [equivalent] [partial]Q([p.sup.s])/[partial][tau]/[partial]M([p.sup.s], [partial].sup.d])/[partial][tau] [less than] 0.

In both Equation 3 and 4, 1/[epsilon] reflects the typical optimal tariff formula for a large country. Note that the reduction in world price that accompanies a slight increase in import tariffs redistributes income from the exporting country to the importing country. Thus, the home country will impose an import tariff to restrict trade in pursuit of terms-of-trade gains. If [tau]is set equal to 1/[epsilon], then the tariff is fully handling this trade distortion, and Equation 3 implies that t should be set to handle the production distortion. However, if a country were not fully pursuing terms-of-trade advantages with its trade policy ([tau] [not equal to] 1/[epsilon]) there would be a secondary role for environmental policy to play in restricting trade. Similarly, in Equation 4, s reflects the marginal external cost of production. If t is set equal to s (the Pigouvian tax), then the environmental distortion has been fully internalized, and Equation 4 implies that [tau] will be set to handle the trade distortion ([tau] = 1/[epsilon]). However, if t [not equal to] s, then Equation 4 implies that [tau] must be set to handle both the trade and production distortion.

Equations 3 and 4 define reaction functions for import sector policies (t, [tau]) to any choice of export sector policies ([t.sup.*], [[tau].sup.*]) by a country's trading partner. Solving Equations 3 and 4 for these best-response functions yields the standard result of welfare analysis: the first-best policy choice is to pursue international trade distortions with trade policies (set [tau] = 1/[epsilon]) and counter local production distortions with environmental policy (set the Pigouvian tax where t = s). This is due to the fact that trade policy is the most efficient means of affecting the world price (the source of the trade distortion), and environmental policy is the most efficient means of affecting local prices (the source of the environmental distortion). Similarly, there will be a set of foreign reaction functions, and the intersection of the reaction functions defines the Cournot-Nash equilibrium. The Nash equilibrium policies are a set of import and export policies ([t.sup.N], [[tau].sup.N], [[tau].sup.N*] [[tau].sup.N*]) that simultaneously satisfy Equations 3 and 4 and their export-sector analogues. Solving for the Nash equilibrium yields

[t.sup.N] = S, [t.sup.N*] = [s.sup.*], [[tau].sup.N] = 1/4[V.sub.f], [[tau].sup.N*] = 1/4[V.sub.f], (5)

where [V.sub.f] is the volume of imports in the absence of distortionary policy (i.e., when [tau] = [[tau].sup.*] = 0, t = s and [t.sup.*] = [s.sup.*]).

Globally efficient trade and environmental policies will be set to maximize joint welfare (W + [W.sup.*]) and will serve as the natural goals toward which countries strive when they cooperate. Taking derivatives of Equations 1 and 2 with respect to t, [t.sup.*], [tau], and [[tau].sup.*], one finds that globally efficient environmental ([t.sup.c] and [t.sup.c*]) and trade ([[tau].sup.c] and [[tau].sup.c*]) policies satisfy the following first-order conditions:

[partial]W + [W.sup.*]/[partial][tau] = 0 = ([tau] + [[tau].sup.*])[partial]M/[partial][tau] + (t - s)[partial]Q/[partial][tau] + ([t.sup.*] - [s.sup.*])[partial][Q.sup.*]/[partial][tau]

[partial]W + [W.sup.*]/[partial]t = 0 = ([tau] + [[tau].sup.*])[partial]M/[partial]t + (t - s)[partial]Q/[partial]t + ([t.sup.*] - [s.sup.*])[partial][Q.sup.*]/[partial]t

[partial]W + [W.sup.*]/[partial][t.sup.*] = 0 = ([tau] + [[tau].sup.*]) [partial]M/[partial][t.sup.*] + (t - s)[partial]Q/[partial][t.sup.*] + ([t.sup.*] - [s.sup.*])[partial][Q.sup.*]/[partial][t.sup.*]. (6)

In the first term of Equation 6, [tau] + [[tau].sup.*] represents the net trade barrier (the wedge between local prices in the two countries). It is well known that an entire locus of efficient (Pareto optimal) trade tax combinations can be obtained by imposing import tariffs and symmetric export subsidies, as doing so alters the world price (thus redistributing income between the countries) while holding local prices constant (see Mayer 1981). As is apparent from Equation 6, the globally efficient policies are given by free trade ([[tau].sup.c] + [[tau].sup.c*] = 0) and the nondistortionary environmental taxes ([t.sup.c] = s and [t.sup.c*] = [s.sup.*]). Intuitively, there is no reason for policy intervention driven by "beggar-thy-neighbor" trade-restricting motivations in an efficient cooperative arrangement. Thus, the goal of international cooperation is to achieve efficiency by (i) eliminating the terms-of-trade motivations from each country's trade policy decisions and (ii) preventing each country from di storting its environmental policy as a secondary means of protection.

The results of this section are well known in the literature and are summarized by Lemma 1.

LEMMA 1.

(1) In the absence of an international agreement, each country sets the standard optimal import tariffs and export taxes ([[tau].sup.N] = 1/[epsilon] and [[tau].sup.N*] = 1/[epsilon]) to exploit any terms-of-trade power it might have and enacts Pigouvian environmental taxes ([t.sup.N] = s and [t.sup.N*] = [s.sup.*]) to fully counter the environmental distortion.

(2) Globally efficient trade and environmental policies are characterized by free trade (i.e, setting the net trade barrier at zero, [[tau].sup.c] + [[tau].sup.c*] = 0) and Pigouvian environmental taxes ([t.sup.c] = s and [t.sup.c*] = [s.sup.*]).

3. Cooperative Agreements

The previous section established that, while countries have a unilateral incentive to erect barriers to trade, such barriers are globally suboptimal. However, the fully efficient outcome (free-trade and nondistortionary environmental policies) can be achieved with full cooperation over both trade and environmental policies if countries can commit to both the globally efficient trade tax and the globally efficient environmental tax. In this section, I assume that, while each country can commit to a cooperative trade tax, they cannot commit to a cooperative environmental tax. In other words, I investigate the case where countries cooperate over trade policy while setting their environmental policies noncooperatively.

As suggested by Copeland (1990), trade negotiations that constrain the ability of countries to pursue terms-of-trade advantages through trade policies will induce substitution toward nonnegotiable secondary trade barriers (such as environmental policy). As shown in Equation 3, when the home country tariff is lowered below the unilaterally optimal level (i.e., [[tau].sup.c] [less than] 1/[epsilon]), the home country faces a unilateral incentive to relax its environmental tax as a secondary trade barrier (i.e., set [t.sup.D] [less than] s). A corollary of this statement is the proposition that cooperation over trade policy alone will fail to achieve the fully efficient solution.

PROPOSITION 1. If trade policy is set independently of environmental policy, then globally efficient policies cannot be achieved through cooperation over trade policy alone.

PROOF. See the Appendix.

Proposition 1 implies that a fully efficient agreement will require international cooperation over both trade and environmental policy since cooperation over trade policy induces the use of domestic policy as a secondary trade barrier. However, Proposition 1 assumes that countries set trade policy independently of environmental policy. This precludes the possibility that cooperative trade taxes could be set conditional on each country's environmental policy. Indeed, it is readily shown that, when countries are allowed to use environmental duties, the fully efficient outcome can be obtained even if countries set their environmental policies unilaterally.

PROPOSITION 2. Through the use of environmental duties, countries can achieve the fully efficient outcome even if they cannot commit to negotiated environmental policies.

PROOF. Assume that both countries cooperate to set [[tau].sup.c] = 1/2([t.sup.*] - [s.sup.*]) and [[tau].sup.c*] = - 1/2(t - s). Substituting these trade policy structures into Equations 1 and 2 and taking the derivative of W with respect to t (and [W.sup.*] with respect to [t.sup.*]), one derives that the noncooperative equilibrium for environmental policy is given by t = s and [t.sup.*] = [s.sup.*]. Substituting t = s and [t.sup.*] = [s.sup.*] into the above trade policy structure, one derives that each country will set their cooperative trade taxes at zero (i.e., [[tau].sup.c] = [[tau].sup.c*] = 0), resulting in the globally efficient outcome. This completes the proof.

Note that the cooperative tariff formulas in the above proof ([[tau].sup.c] = -1/2([t.sup.*] - [s.sup.*]) and [[tau].sup.c*] = 1/2(t - s)) are environmental duties in which trade policies are set conditional on the environmental policy of one's trading partner. The intuition behind Proposition 2 lies in the terms-of-trade effects of these environmental duties. Specifically, as a result of the environmental duty, [partial][p.sup.w]/[partial]t = 0 and [partial][p.sup.w]/[partial][t.sup.*] = 0 (i.e., the presence of the environmental duty ensures that the world price remains constant as each country adjusts its environmental tax). Since the environmental duty eliminates the terms-of-trade incentives of each country to distort its environmental standards, it results in each country setting the efficient standard. The above result suggests that the globally optimal environmental duty is one that offsets the world price effects of the other country's environmental policy.

As argued in Lemma 1, the same globally efficient outcome could be achieved by full international negotiations over both trade and environmental policy by the two countries. However, if countries cannot commit to (or enforce) cooperation over environmental policy, they can implement the same efficient outcome by agreeing to impose environmental duties that offset the terms-of-trade effects of any deviation in environmental policy. Such environmental duties may also be beneficial for political reasons because they provide greater freedom to each country in the setting of their environmental policy. While it is true that environmental duties indirectly infringe on a country's environmental policy choice, they do allow each country to set environmental policy unilaterally. The only constraint they place on countries is that, after allowing each country to set their environmental policy freely, they compensate the opposing country by removing the terms-of-trade effects of those policy choices. Thus, environmental duties can be structured to achieve the globally efficient outcome while allowing countries greater sovereignty over their domestic policy decisions.

It should be noted that the environmental duty suggested by this section is not intended to offset differences in environmental standards across countries. As should be apparent from the preceding analysis, given that the marginal cost of pollution (s) differs across countries, countries will set differing standards in the cooperative equilibrium. In addition, in the cooperative equilibrium, neither country will set a positive environmental duty (i.e., [[tau].sup.c] = [[tau].sup.c*] = 0 in equilibrium) because it is only the threat of such duties that is needed to deter countries from distorting their environmental policies.

4. Self-Enforcing Agreements

The previous section assumed that countries could commit to a cooperative tariff formula (and thus achieve the globally efficient outcome even when environmental policies were set noncooperatively). In this section, I assume that countries cannot commit to either trade or domestic environmental policy and thus must rely on punishment strategies to enforce cooperation. Dixit (1987), Bagwell and Staiger (1990), and Riezman (1991) show how countries can support low tariffs within a repeated relationship by configuring the tariff agreement so that each country fears that a decision to cheat on the agreement would trigger a costly retaliatory episode in the future. Ederington (2001) extends this work to a self-enforcing agreement covering both trade and domestic policies and provides the basis for the repeated game framework that follows. In this section, I first show that, when the discount rate is sufficiently low, free trade can only be supported if countries adjust their environmental policies away from the Pi gouvian optimum. Specifically, I show that, if the country with weak environmental standards is the exporter of the dirty good, then free trade can only be supported if the two countries agree to some convergence in their environmental policy. Second, I show that, when the discount rate is sufficiently low, an alternative means of supporting the agreement is to allow each country a positive trade tax and that these trade taxes will in effect be environmental duties because they will be a function of the difference in environmental standards across countries. Finally, I employ a result derived in Ederington (2001) to show that, as a means of enforcing the agreement, allowing such environmental duties will be preferable to adjusting environmental standards across countries.

The Repeated Game Framework

Consider then an agreement in which countries cooperate over trade and environmental taxes and credibly threaten infinite reversion to the noncooperative (Nash) equilibrium, characterized by Equation 5, if cooperation is ever violated. [6] In each period, each country chooses a trade and environmental policy pair. An international agreement is defined by a set of cooperative policy pairs ([[tau].sup.c], [t.sup.c], and [[tau].sup.c*] [t.sup.c*]). Thus, the cooperative level of welfare in each period (it is assumed that all periods are identical) is defined by

[W.sup.c] [equivalent] W([tau] = [[tau].sup.c], t = [t.sup.c], [[tau].sup.*] = [[tau].sup.c*], [t.sup.*] = [t.sup.c*]).

It is equivalently defined for the foreign country as [W.sup.c*] [equivalent] [W.sup.*]([tau] = [[tau].sup.c], = [t.sup.c], [[tau].sup.*] = [[tau].sup.c*] [t.sup.*] = [t.sup.c*]). Each country is free to deviate from the agreement at any time. A country that chooses to defect from this agreement does so by selecting a trade and environmental tax pair ([[tau].sup.D], [t.sup.D]) along its best response curves, which are defined by Equations 3 and 4. The level of welfare achieved by deviating from the agreement is given by deviating from the agreement is given by

[W.sup.D] [equivalent] W([tau] = [[tau].sup.D], t = [t.sup.D], [[tau].sup.*] = [[tau].sup.c*], [t.sup.*] [t.sup.c*]).

It is equivalently defined for the foreign country by [W.sup.D*] [equivalent] [W.sup.*]([tau] = [[tau].sup.c], t = [t.sup.c], [[tau].sup.*] = [[tau].sup.D*], [t.sup.*] = [t.sup.D*]). However, once a country defects from the agreement, both countries abandon the agreement and revert to their Nash tariffs and environmental taxes ([[tau].sup.N], [t.sup.N], and [[tau].sup.N*] [t.sup.N*]) in all future periods. Nash welfare for the home country is then given by W([tau] = [[tau].sup.N], t = [t.sup.N], [[tau].sup.*] = [[tau].sup.N*], [t.sup.*] = [t.sup.N*]) [equivalent] [W.sup.N], with Nash welfare for the foreign country symmetrically defined and denoted by [W.sup.N*]. Thus, defining as the discount factor between periods, the discounted value of avoiding a (permanent) breakdown in cooperation for the home country is given by [delta]/(1 - [delta])([W.sup.c] - [W.sup.N]).

An optimal international agreement results in both countries jointly choosing cooperative trade ([T.sup.c],[T.sup.c*]) and environmental policies ([t.sup.c],[t.sup.c*]) to maximize the joint level of cooperative welfare ([W.sup.c] + [W.sup.c*]), subject to the constraint that neither country has an incentive to defect from the agreement,

[(W.sup.D] + [W.sup.D*] - ([W.sup.c] + [W.sup.c*])] - [delta]/1 - [delta] [(W.sup.c] + [W.sup.c*]) - ([W.sup.N] + [W.sup.N*] [less than or equal to]0. (7)

The self-enforcement constraint (Eqn. 7) is satisfied if the discounted value to future cooperation for both countries is greater than the sum of the one-period gains to deviation for both countries. If this condition is satisfied, then the gains to cooperation can be distributed across the two countries so that neither country has an incentive to cheat on the agreement. Thus, the constraint that an agreement be self-enforcing requires the agreement to be configured so as to balance the current gains to deviating from the agreement against the future long-term losses to retaliation.

Note that, when countries place great value on the future (high [delta]), the self-enforcement constraint will not bind (since countries will value highly the future gains to cooperation). Thus, any sufficiently high discount factor will support the efficient symmetric trade and environmental policy pair as a self-enforcing agreement. However, when countries place less importance on the future, an international agreement will be unable to support the efficient outcome and thus will require relaxation of cooperation in either trade or environmental policy. [7]

Given the symmetry of the model, I will focus on a symmetric agreement in which countries set a common cooperative trade barrier (i.e., [tau] = [[tau].sup.*] = [[tau].sup.c]). [8]. In addition, given the symmetry of the model, it can be established that an efficient self-enforcing agreement entails equal and opposite deviations from the Pigouvian tax in domestic policy.

LEMMA 2. Within an efficient self-enforcing agreement, ([t.sup.c] -s] = -([t.sup.c*] - [s.sup.*]).

PROOF. See the Appendix.

Using Lemma 2, the sum of the one-period gains to cooperation for each country [omega] = [W.sup.c]+[W.sup.c*] - [W.sup.N]+[W.sup.N*]) can be calculated from Equations 1 and 2 as

[omega]([[tau].sup.c],[t.sup.c] = -[([t.sup.c] - s).sup.2]-2[([delta].sup.[tau]]).sup.2] + 2[[tau].sup.c]([t.sup.c] - s) + 4([delta].sup.[tau]])[[tau].sup.N], (8)

where [[delta].sup.[tau]] represents the difference between the Nash equilibrium tariff and the cooperative tariff([[delta].sup.[tau]] = [[tau].sup.N] - [[tau].sup.c]. Isogain-to-cooperation loci, labeled d[omega] = 0, are graphed in Figure 1 and describe a cone that descends from the efficient trade and environmental policy pair. Since the gains to cooperation are maximized at [t.sup.c] = S, [t.sup.c*] = s*, and [[tau].sup.c] = [[tau].sup.c*] = 0 (free trade), the efficient symmetric policies are represented at the point labeled E. Isogain-to-cooperation curves (indifference curves) are roughly oval in shape, with movements away from E representing lower cooperative welfare levels.

In Figure 1, as countries move their cooperative policies toward E, the value of the agreement is increasing. However, for an agreement to be viable, it must also be self-enforcing, which requires holding the incentive to deviate from the agreement in check. Welfare calculations from Equations 1 and 2 reveal that the sum of the one-period gains to deviating from cooperative policy levels ([omega] = [W.sup.D] + [W.sup.D*] - [W.sup.c] + [W.sup.c*]) are given by

[omega]([[tau].sup.c], [t.sup.c] = 7/6[([t.sup.c] - s).sup.2] + 8/3[([[delta].sup.[tau]]).sup.2] + 8/3[[delta].sup.[tau]]([t.sup.c] - s). (9)

Isogain-to-deviation loci, labeled d[omega] = 0, are shown graphically in Figure 1 and reflect an elliptic cone rising from the Nash equilibrium. The gains to cheating are minimized at the Nash equilibrium (denoted N, where [[tau].sup.c] = [[tau].sup.N] and [t.sup.c] = s) since neither country has a unilateral incentive to deviate from the Nash equilibrium. The isogain-to-deviation loci are roughly oval in shape, with movements away from N representing larger gains to cheating on the agreement.

The dilemma faced by countries in setting cooperative levels of trade and environmental policy is made clear by Figure 1. When countries do not cooperate, they lie on a relatively low indifference curve (at N) as each is erecting trade barriers with their trade policy. Since such trade barriers are not globally optimal, there are potential gains to cooperation in moving toward the cooperative optimum (E) by reciprocally lowering trade barriers while maintaining environmental taxes at their nondistortionary levels. However, as countries cooperate to move from the Nash point N toward the cooperative optimum E (say along the path NE in Figure 1), the gains to deviation for each country are rising, and thus cooperation between the countries is feasible only up to the point where the self-enforcement constraint binds.

International Harmonization of Standards

In this section, I consider the case where the two countries attempt to implement free trade (set [[tau].sup.c] = 0) when the discount factor is too low to support the globally efficient outcome ([delta] [less than or equal to] 4/7).

Figure 2 demonstrates the relationship between [t.sup.c] and the gains to cooperation ([omega]) and deviation ([omega]) when countries are at free trade ([[tau].sup.c] = 0). As Figure 2 shows, given [delta] [less than or equal to] 4/7, the discounted gains to cooperation ([[delta]/(1 - [delta])][omega]) are less than the current gains to deviation ([omega]) at [t.sup.c] = s (i.e., the globally optimal equilibrium cannot be supported). Thus, countries will have to manipulate environmental standards (i.e., lower [t.sup.c] and symmetrically raise [t.sup.c*]) in order to support free trade as an equilibrium within the agreement. Evaluated at [[tau].sup.c] = 0, the gains to cooperation are maximized and flat at [t.sup.c.] = s and are concave and monotonically decreasing in [t.sup.c]. Likewise, the gains to deviation are also (initially) decreasing in [t.sup.c] and, in the area around = s, the gains to deviation ([omega]) are decreasing faster than the gains to cooperation ([omega]). This is due to the fact that, at [t.sup.c] = s, a small increase in [t.sup.c] has no impact on cooperative welfare (and thus [omega]) by the first-order condition that defines the globally cooperative equilibrium. Therefore, assuming [delta] is sufficiently large, there will exist a range of environmental taxes (given by the interval [[t.sup.c], [t.sup.c]] in Figure 2) under which both the self-enforcement constraint (Eqn. 7) is satisfied and free trade can be supported. [9]

It is straightforward to verify from Equation 8 that, when [[tau].sup.c] = 0, joint cooperative welfare is monotonically increasing as countries move their environmental policies toward the Pigouvian optimum (i.e., as [t.sup.c] [right arrow] s). Therefore, to maximize joint cooperative welfare, countries will choose the smallest deviation from the nondistortionary tax that satisfies the self-enforcement constraint. In Figure 2, the most cooperative environmental tax ([t.sup.c]) is given by

[t.sup.c] = s - 16(1 - [delta]) - [square root][[16(1 - [delta])].sup.2] - 4(7 - [delta])(16 - 28[delta])/2(7 - [delta]) [[tau].sup.N]. (10)

Equation 10 tells us that countries can support progressively smaller deviations from the Pigouvian tax as the discount factor rises. Indeed, as [delta] converges to [[delta].sup.*] = 4/7, [t.sup.c] converges to s (the Pigouvian tax). In addition, it is direct to verify from Equation 10 that, when [delta] [less than] 4/7, the self-enforcement constraint binds and [t.sup.c] [less than] s (i.e., the home country that imports the dirty good will lower its environmental tax below s). Given the symmetry of the model outlined by Lemma 2, it will also be the case that [t.sup.c*] [greater than or equal to] [s.sup.*] (i.e., the foreign [exporting] country will raise its environmental tax above [s.sup.*]).

Assume that trade is partially driven by differing environmental standards, which is the case when the exporter of the dirty good places a lower valuation on the environment (i.e., s [greater than] [s.sup.*]) and thus has the weaker environmental standard (i.e., t [greater than] t* at the Nash equilibrium). In this case, the decrease in [t.sup.c] (and the symmetric increase in [t.sup.c*]) that is necessary to support free trade implies that environmental policies have become more similar across the two countries in the self-enforcing agreement. Thus, I can state Proposition 3.

PROPOSITION 3. When the discount rate is low and the country with weak environmental standards is the exporter of the dirty good, then supporting a free-trade agreement will require some convergence in environmental policy across the two countries.

Proposition 3 is a function of the fact that the underlying reason that countries wish to deviate from the agreement is for the terms-of-trade gains associated with restricting trade. Thus, the gain to deviating from the agreement ([omega]) is a function of the underlying volume of trade since a larger volume of trade implies a greater terms-of-trade incentive to restrict trade. When trade is driven by differing environmental standards (i.e., when the country exporting the dirty good has the weaker environmental standard), then one means of appeasing this temptation to defect is by reducing the diversity in environmental policy across countries to remove some of the motivation for trade. This result is especially relevant to the analysis of regional trade agreements, which are essentially required by the WTO to adopt free trade. The above analysis suggests that, if the discount rate is too low to support the efficient outcome, free trade is only supportable given some convergence in environmental policy acros s the member countries. This provides a novel interpretation of environmental side agreements as a necessary means of manipulating environmental standards to prevent the collapse of the free-trade agreement.

It is interesting to note that convergence in environmental standards will not always assist in supporting lower trade barriers. Assume that the exporter of the dirty good places a higher valuation on the environment (i.e., [s.sup.*] [greater than] s) and thus has the stronger environmental standard (i.e., [t.sup.*] [greater than] t at the Nash equilibrium)). [10] In such a situation, convergence in environmental standards will actually increase the volume of trade since it emphasizes the natural comparative advantage of the exporting country. It is direct to verify that, when [s.sup.*] [greater than] s, enforcing free trade will actually require making the countries' environmental policies less similar. Thus, the above analysis would predict that demands for harmonizing standards would be strongest in those cases where the country exporting the dirty good has the weaker environmental standard.

Environmental Duties

In the previous section, I investigated the case where countries cooperate fully over trade policy (i.e., implement free trade) and then support the agreement by adjusting their environmental policies. In this section, I investigate the case where countries cooperate fully over environmental policy (i.e., set Pigouvian taxes) and then adjust their trade policies to support the agreement. Thus, I analyze the choice of enforceable trade policies to maximize cooperative welfare, given that [t.sup.c] = s and [t.sup.c*] = [s.sup.*].

Figure 3 demonstrates the relationship between [[tau].sup.c] and the gains to cooperation ([omega]) and deviation ([omega]) when [t.sup.c] = s. As Figure 3 shows, the discounted gains to cooperation, [[delta]/(1 - [delta])][omega], are maximized at [[tau].sup.c] = 0 and are concave and monotonically decreasing in [[tau].sup.c] for [[tau].sup.c] [less than][[tau].sup.N] (also note that [omega]([[tau].sup.N],[[tau].sup.c] = s) = 0). Likewise, the gains to deviation are minimized at [[tau].sup.c] = [[tau].sup.N] (note that [omega]([[tau].sup.c], [t.sup.c] = s) is flat and equal to zero at [[tau].sup.c] = [[tau].sup.N]) and are convex and decreasing in [[tau].sup.c] for [[tau].sup.c] [less than] [[tau].sup.N]. Therefore, the range of enforceable tariffs is given by the interval [[[tau].sup.c], [[tau].sup.N]], as pictured in Figure 3, and the most cooperative trade tax ([[tau].sup.c], the lowest tariff barrier that satisfies the self-enforcement constraint) will be determined by where Equation 7 binds. Solving th is constraint, the most cooperative tariff is given by

[[tau].sup.c] = 4 - 7[delta]/6(4 - [delta]) [2[alpha] + s - [s.sup.*]]. (11)

Equation 11 shows that the most cooperative trade tax within a self-enforcing agreement will be a function of the difference in environmental standards in the two countries (i.e., [[tau].sup.c] is an environmental duty). Specifically, when the exporting country has the weaker environmental standard ([s.sup.*] [less than] s), then [[tau].sup.c] will be increasing as the differential in environmental standards across the two countries grows. [11] Therefore, all else equal, higher cooperative trade taxes will be required between countries with the greatest differential in their environmental standards (i.e., an environmental duty). Intuitively, this is because trade is driven by differing standards across countries and, since the gain to deviating from the agreement is increasing in trade volume, an enforceable tariff will be set to partially offset some of the diversity in environmental standards. This result is summarized in Proposition 4.

PROPOSITION 4. When the discount rate is low and the country with weak environmental standards is the exporter of the dirty good, then the most cooperative trade tax will be set to partially offset the difference in environmental standards in the two countries.

This section demonstrated that, when trade is driven by differing environmental standards, cooperation across the two countries can be sustained by either adjusting environmental policy to mute the differences across the two countries or adjusting trade policy to partially offset those differences. This analysis raises the obvious question about which mechanism is a more efficient means of enforcing the agreement. The answer to this question is implicitly provided in Ederington (2001), who showed that, within a self-enforcing agreement covering both trade and production taxes, countries will cooperate to set the nondistortionary Pigouvian tax (i.e., [t.sup.c] = s), regardless of the discount factor. This result reflects a simple logic: It is the temptation to pursue terms-of-trade gains that creates problems with enforcing international agreements over trade and domestic policies, and since domestic policies (like environmental policy) are an inefficient means of pursuing such terms-of-trade gains, cooperatio n over domestic policy should not be relaxed as a means of holding this temptation to defect in check. In the context of this paper, this result suggests that it is more efficient to support a trade agreement through a system of environmental duties (which mute the differences in environmental standards across countries) than through attempting to harmonize environmental standards within environmental side agreements.

5. Conclusion

Demands for harmonization of environmental standards as well as environmental duties on imports of products made abroad by industries with lower environmental standards have increased as countries have become more integrated. Thus, it seems relevant to consider arguments under which such policies may be justified to better understand the strengths and weaknesses of these demands. This article serves that purpose by advancing two arguments for cases where environmental duties can be justified. It should be stressed that this article does not disagree with the main contention of many economists that there are legitimate reasons for diversity in environmental regulation across countries and that comparative advantages arising from such regulatory differences are part of the case for mutually profitable trade between countries. Indeed, it is true that, within the model advanced in this article, the globally optimal outcome is always a combination of free trade and Pigouvian environmental taxes that respect the d iversity of international standards across countries. What this article argues is that environmental duties can be justified in cases where such full cooperation is not feasible.

It should be noted that, while this article considered the case of environmental policies and standards (due to the attention that has been focused on this topic), there is nothing special about environmental policy in this article. Thus, while the most cooperative tariff of section 4 is needed to offset the comparative advantage of the exporting country, such comparative advantage does not arise solely from diversity in environmental standards, and enforceable tariffs will be required to partially offset the source of any comparative advantage (e.g., wage differences or productivity differences). Likewise, there are many domestic policy instruments that can be used to affect the world market, and it is not obvious the environmental policy will necessarily be used as an instrument of trade policy. Thus, while the focus of this article was on environmental policies, the results and analysis of this article can be applied to a wide range of domestic policy instruments that can be used by governments to affect t he world market.

(*.) Department of Economics, University of Miami, P.O. Box 248126, Coral Gables, FL 33124, USA; E-mail [e-mail].

I would like to thank Jenny Minier and two anonymous referees whose valuable comments greatly improved the presentation in the paper.

(1.) A recent paper by Bagwell and Staiger (2001) uses similar reasoning to argue that the market access rules provided in Article XXIII of GATT can achieve global efficiency while allowing countries full sovereignty over their domestic policies.

(2.) For example, the North American Free Trade Agreement (NAFTA) included an environmental side agreement (the North American Agreement on Environmental Cooperation) that was widely viewed as attempting to bring Mexico's environmental policies and enforcement more in line with those in the U.S.

(3.) The partial equilibrium approach can be rationalized in general equilibrium terms by assuming a quasi-linear utility function that is linear in a numeraire good and that production is a function of labor supply, which is infinitely elastic at a unitary wage. Provided that the residual good is always consumed in positive amounts, the marginal utility will be fixed at one and the market for each nonnumeraire good can be analyzed in partial equilibrium fashion. Trade in the numeraire good is then determined by the condition for overall trade balance for each country.

(4.) Solving for these world prices, [p.sup.w](t, [tau], [t.sup.*], [[tau].sup.*]) = [2 - 2([tau] - [[tau].sup.*]) + t + [t.sup.*]]/4.

(5.) Best response functions for the foreign country are defined symmetrically. The assumptions made about the functional forms of the model also ensure that the second-order conditions are satisfied and that a Nash equilibrium (in which Eqns. 3 and 4 and the equivalent conditions for the foreign country hold simultaneously with positive trade volume) exists. Uniqueness is assured by the fact that, within the model, trade and environmental policy are imperfect substitutes (i.e., [[lambda].sub.t] [not equal to] [[lambda].sub.[tau]]).

(6.) I focus on infinite reversion to the Nash equilibrium as the subgame perfect threat that is used to support cooperation. One can consider alternative subgame perfect punishment schemes (as in Abreu 1986, 1988) that generate a more severe welfare level in the punishment phase. However, the severity of the punishment will not affect the basic results of this section, although it will affect the range of polices that can be supported by the agreement.

(7.) In this setting, efficient policies can be sustained in a self-enforcing agreement whenever [delta] [less than or equal to] 4/7,

(8.) The symmetry assumption simplifies the analysis and implies that the countries split the gains to cooperation equally.

(9.) For free trade to be supported, it has to be the case that [delta] [greater than or equal to] [delta] = [square root]97 - 7)/6. However [delta] [less than] 4/7, so relaxing cooperation in environmental policy does increase the range of [delta] over which free trade can be supported.

(10.) This will be the case where the foreign (exporting) country has a separate source of comparative advantage that outweighs the difference in environmental standards across the two countries.

(11.) When the country importing the dirty good has the weaker standard, then trade volume will decrease as the differential grows and lower tariff rates can be supported. Thus, one would expect calls for environmental duties to he strongest in cases where the exporting country has the lower standard.

References

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Ederington, Josh. 2001. International coordination of trade and domestic policies. American Economic Review. In press.

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Riezman, Raymond. 1991. Dynamic tariffs with asymmetric information. Journal of International Economics 30(3-4):267-83.

[Graph omitted]

[Graph omitted]

Appendix

Proof of Proposition I (Proof by Contradiction)

Assume that countries cooperate over trade policy to achieve globally efficient policies while setting environmental policies noncooperatively. Globally efficient policies are given by [[tau].sup.c] + [[tau].sup c*] = 0, t = s, and [t.sup.*] [s.sup.*]. From Equation 3, in order for the domestic country to set t = s, it must be the case that [[tau].sup.c] = 1/[epsilon].

Taking the derivative of Equation 2 with respect to [t.sup.*] and solving out the first-order conditions, one derives that unilaterally optimal environmental policy for the foreign country ([t.sup.D*]) is given by

[t.sup.D*]([tau], t, [[tau].sup.*]) = [s.sup.*] - [[[tau].sup.*] - 1/[epsilon]][partial]M([p.sup.s], [p.sup.d])/[partial][t.sup.*]/[delta][Q.sup.*]([p.sup.s])/[partial][t .sup.*].

Therefore, in order for [t.sup.*] = [s.sup.*], it must be the case that [[tau].sup.c*] = 1/[epsilon]. However, given that [epsilon] [greater than] 0, this contradicts our previous assumption that [[tau].sup.c] + [[tau].sup.c*] = 0. Thus, cooperation over trade policy alone cannot achieve the globally optimal equilibrium.

Proof of Lemma 2

An efficient agreement requires maximization of joint welfare subject to the self-enforcement constraint (Eqn. 7). Solving for the first-order conditions of this maximization with respect to t and [t.sup.*], one derives that

[partial]L/[partial]t = [partial][[W.sup.C] + [W.sup.C*]]/[partial]t - [lambda][partial][[W.sup.D*] - 1/1 - [delta]([W.sup.C] + [W.sup.C*])]/[partial]t [partial]L/[partial][t.sup.*] = [partial][[W.sup.C] + [W.sup.C*]]/[partial][t.sup.*] - [lambda][partial][[W.sup.D] - 1/1 - [delta]([W.sup.C] + [W.sup.C*])]/[delta][t.sup.*].

Solving for the Lagrange multiplier ([lambda]) in each of the above first-order conditions and setting it equal, one can derive that an efficient agreement requires that

[partial][[W.sup.C] + [W.sup.C*]]/[partial]t/[partial][[W.sup.C] + [W.sup.C*]]/[partial][t.sup.*] = [partial][[W.sup.D*]]/[partial]t/[partial][[W.sup.D]]/[partial][t.sup .*].

Substituting the respective partial derivatives into the above equations gives

[partial]M/[partial]t/[partial]M/[partial][t.sup.*] = ([tau] + [[tau].sup.*])[partial]M/[partial]t + (t - s)[partial]Q/[partial]t + ([t.sup.*] - [s.sup.*])[partial][Q.sup.*]/[partial]t/([tau] + [[tau].sup.*])[partial]M/[partial][t.sup.*] + (t - s)[partial]Q/[partial][t.sup.*] + ([t.sup.*] - [s.sup.*])[partial][Q.sup.*]/[partial][t.sup.*].

However, given the symmetry of the model, it is the case that [partial]M/[partial][t.sup.*] = -[partial]M/[partial][t.sup.*], [partial]Q/[partial]t = [partial][Q.sup.*]/[partial][t.sup.*], and [partial][Q.sup.*]/[partial]t = [partial]Q/[partial][t.sup.*]. Therefore, the above equality (which satisfies the first-order conditions for maximizing joint welfare) is satisfied under the condition that ([t.sup.c] - s) = -([t.sup.c*] - [s.sup.*]).