Environmental Externalities of International Trade and Transport

Environmental Externalities of International Trade and Transport January 31, 2010 Abstract While the production-related pollution effects of international trade have been well studied, the direct environmental impacts of transport in a global general equilibrium framework have received less attention. We extend a standard Heckscher-Ohlin model of international trade to include environmental impacts generated by the movement of goods and analyze the effect of policy to mitigate this pollution. Generalizing existing trade and pollution models, we describe a unified framework for analyzing two types of transport externalites. In the case of shared global public bads like greenhouse gases, exports generate damages for both the exporter and importer. The second type of externality we consider is one in which damages are incurred by the importer alone, as in the context of invasive species introduced through contaminated exports. Our aim is to provide a framework for understanding and ultimately assessing the effects of global multi-lateral agreements such as the existing International Standard for Phytosanitary Measure (ISPM)-15 which aims to mitigate the transfer of invasive species. We decompose the effect of an abatement policy into technique, composition and scale effects, where the latter two are further differentiated into consumer and producer effects, a novel extension driven by the trade-externalities setting. 1

1 Introduction International trade has at least four types of impacts on the environment, including product, scale, structural and direct effects (UNEP 2005). While the first three categories in this list have received significant attention from economists, direct impacts in a global framework have received far less attention. Growing international trade is an important direct source of environmental change due to externalities of transportation services, for example from the emission of greenhouse gases (GHGs) and the transfer of invasive species (UNEP 2005). While a handful of international agreements targeting direct environment effects from trade have been adopted, economic evaluation of such regulations is hampered by the lack of a well-understood analytic framework. In this paper we extend a standard Heckscher-Ohlin (H-O) model of international trade to include environmental impacts generated by the movement of goods and analyze the effect of policy designed to mitigate this pollution. To our knowledge there have been two theoretical examinations of the transport-externalities problem in a general equilibrium framework. Batra et al. (1998) focus on pollution from the energy necessary for international transport while Kohn and Capen (2002) ground their theoretical analysis in the context of invading species hitch-hiking on international trade. Batra et al. (1998) observed that while economists have considered the effect of production-related pollution on gains from trade and on the ideal tariff, no pre-existing study had considered trade itself a major source of pollution (p. 175). Both analyses are based on a 2x2 model two goods produced using two factors of production. Batra et al. (1998) focus on a small open economy (SOE) model while Kohn and Capen (2002) use a two country H-O approach. For policy analysis, both papers consider a Pigovian tariff on the polluting imported good to internalize the social damages from transportrelated pollution. Neither study considers the option for abatement in the form of reducing the intensity of pollution per unit trade, which is assumed fixed. The theoretical economic literature has paid more attention to the transport externality stemming from invasive species than from GHGs. Olson (2006) reviews the economics of terrestrial invasives in general and the economics of international trade and invasive species in particular, including studies that have taken a partial equilibrium approach to the optimal design of domestic policy for imports potentially contaminated with invasive species. For example, Costello and 2

McAusland (2003) examine how one country s regulation of imports for invasive species risk affects both invasion risk and vulnerability to invasion as domestic industry adjusts to the restriction. McAusland and Costello (2004) examine how one country s optimal mix of tariffs and inspections of imports depend on the attributes of the exporter, including the infestation rate, damage per introduction and marginal production cost. Margolis et al. (2005) introduce a political economy model of tariff setting in the invasive species context and observe that, in addition to smuggling and ship pollution, (i)nvasive species are among a relatively small group of market failures the source of which is trade itself. We develop a framework to capture two main types of environmental externatilities from trade. In the first, pollution is a global public bad, inflicting damages on both exporter and importer alike, as in the case of GHG emissions. While such emissions are not currently covered under a multilateral agreement e.g. the Kyoto Protocol included emissions from domestic but not international flights there is interest in bringing international transport emissions at least partially under existing regulatory regimes within the next few years (Levinson et al. 2008). In the second type of externality we consider, the impact of pollution is incurred by the importer alone, such as in the case of the introduction of invasive species from an exporter to an importing region via contaminated transport. One example of a recent multilateral agreement to reduce this type of event is International Standard for Phytosanitary Measure (ISPM)-15, implemented in 2006 to codify a standard for abating invasive species contamination of trade, in particular, treatment of pallets and wood packaging material to reduce the incidence of wood-infesting insects (e.g. Cerambycidae and Scolytidae) (FAO 2009). While there is interest in assessing the economic and environmental impacts of ISPM-15 in advance of additional phytosanitary policy under discussion 1, a comprehensive conceptual framework for transportation-related pollution and abatement has yet to be developed. For ease of comparison, we construct and analyze our model in a similar fashion as the wellknown approach to trade and environment developed by Copeland and Taylor (2003). Our main departure from the framework of Copeland and Taylor is in the nature of the pollution-generating process. Whereas in the standard model pollution is generated from production of the capitalintensive good, we are concerned with pollution generated from the international exchange of goods. Thus, for a fixed pollution intensity and quantity of output produced, the level of pollution will be 1 For example USDA APHIS recently published a proposal to regulate plant imports (APHIS 2009). 3

determined in equilibrium by the proportion of goods that are exported, versus domestic production. Pollution policy is implemented as a requirement on the stringency of pollution abatement, for example to reduce the intensity of invasive species or GHGs per unit of transportation services demanded. Our approach then is a synthesis of the abatement approach from Copeland and Taylor with the transport externalities focus of Batra et al. (1998) and Kohn and Capen (2002). We argue that an explicit focus on an abatement policy (versus a Pigovian tariff) is pragmatic in that it is consistent with approaches to control invasive species, both existing (e.g. ISPM-15) and proposed (e.g. APHIS (2009)). As in Copeland and Taylor any mitigation of pollution comes at the expense of diverting primary factors to provide abatement. This can be conceptualized visually by a contraction of the production possibility frontier to a net production frontier (NPF) that accounts for the diversion of primary factors. However, in our setting this demand for abatement is not tied to each unit of a dirty good produced but rather to each unit exported a quantity only determined given consumer demand. Thus the NPF is not a fixed curve but is also determined in the general equilibrium. Environmental quality is a normal good which implies that optimal mitigation policy stringency will increase with income. But when transport-related pollution impacts the importing country, as in the case of invasive species, globally the socially optimal level of mitigation by the exporter depends on the income of the importer. We describe interesting differences from the Copeland and Taylor results when examining the effects of a change in pollution policy. The standard analysis includes a decomposition of the change in pollution levels into a scale, composition and technique effect. The main difference in our results reside in the scale effect for which we must generalize to incorporate trade-related pollution. In the standard model, pollution can be shown to fall given a decrease in the scale of the economy by considering production decisions alone. However in the transport externalities setting, a change in the scale of the economy effects both the efficient production and consumption decision. Because the level of the polluting activity in our setting depends not just on domestic production but also domestic consumption (since the residual is exported), we characterize both a production scale and a consumption scale effect. We find that these are opposing effects and their sign depends on a particular parameterization of the problem. Finally, for the case of invasive species, we consider the context of endogenous pollution policy 4

where stringency is chosen in a social welfare framework to optimally balance the supply of and demand for pollution. We examine the way in which the incentives of a global social decision maker and the two countries differ, both under the constraint that any standard must be uniform and symmetric between countries (as in the case of ISPM-15) and under the case of no policy-symmetry constraint. 1.1 A general equilibrium model of transport externalities The general equilibrium model we employ is initially similar to the workhorse model of Copeland and Taylor (2003). Capital (K) and labor (L) are the two primary factors used to produce two goods one capital intensive (x) and the other labor-intensive (y) both with constant returns to scale technology. The factors K and L are supplied inelastically. Pollution is assumed to harm consumers but not the productivity of industry. Utility of the two consumption goods is increasing, concave, homothetic and separable from pollution damages, D. Environmental quality is a normal good which implies that optimal abatement policy stringency will increase with income Copeland and Taylor (2003, p. 37). Applied to our setting, where transportrelated pollution effects the importer, optimal mitigation by the exporter will depend, in part, on the income of the importer. A significant departure from the basic model of Copeland and Taylor involves the pollutiongeneration process. In the Copeland and Taylor model, pollution is associated with the production of goods, specifically as a necessary input. We focus rather on pollution generated by the international exchange of goods. Thus for a fixed quantity of production the level of pollution will be determined in equilibrium by the proportion of goods that are exported versus consumed domestically. Another key difference is a departure from the assumption that pollution generated impacts consumers in the producing region. Here in the trade externalities setting, either pollution harms the importer of the goods, as in the case of invading species, or it harms both the importer and exporter, as in the case of GHGs. We adopt an H-O model with two countries, Home and Foreign, because we are interested in capturing the response to a global change in transport pollution mitigation policy (e.g. ISPM-15) for which the assumption of constant world prices is insufficient. 2 Notationally, variables for Foreign 2 Under certain conditions (i.e. holding the emissions per unit output in the polluting sector constant across 5

are denoted using a tilde, e.g. x. We let subscripts s and m represent levels of domestic supply and net imports, respectively. When levels of the goods are presented without a subscript they represent domestic demand. We will assume that Home has a capital-intensive factor endowment relative to Foreign: K/L > K/ L. In an equilibrium with international exchange, Home will export the capital-intensive good (x m < 0, x m > 0) and Foreign will export the labor-intensive good (y m > 0, ỹ m < 0). In Copeland and Taylor (2003) the pollution-intensive sector is the capital intensive industry. In our analysis the analogous differential in pollution intensity is given by two parameters. First, β j represents the units of polluting activity per unit of trade, for j {x, y}. For example, this could represent the units of wood packaging material (WPM) required or the energy necessary to move a unit of the goods being traded. Then γ j represents the baseline units of pollution per unit of polluting activity associated with transport from j (e.g. invasives per unit WPM or GHGs emitted per unit energy). The total units of pollution associated with exports from Home and Foreign in the absence of any abatement are given by v = γ x β x x m, ṽ = γ y β y ỹ m. (1) In order to fully characterize production we must first specify the nature of the abatement good z. Let α represent the pollution policy, specifically the required level of abatement per unit of polluting activity v. When we consider a differentiated policy, the required pollution abatement intensity in Foreign will be given by α. When we focus on a uniform policy where the same intensity of abatement is required in Home and Foreign, the standard α will to Foreign as well ( α = α). Conditional on export levels, the necessary production of the abatement good is given by z = αβ y ( y m ) and z = αβ x ( x m ). We assume that the same technology is employed in Home and Foreign. The technological possibilities set for Home is {x, y, z} F (K, L), and similarly for Foreign { x, ỹ, z} F ( K, L). Given an abatement policy, the effective level of pollution from imports to Home and Foreign countries) the small open economy model of Copeland and Taylor (2003) takes on all of the comparative statics properties of the H-O framework (p. 14, 32). 6

is given by h = vg( α) = γ x β x x m g( α) h = ṽg(α) = γy β y ỹ m g(α), (2) where g( ) [0, 1] is a decreasing function of the policy level of abatement. 3 Note that for Homes imports (x m ) the resulting pollution (h) is a function of the abatement policy that applies in Foreign ( α). Let transport-related damages per unit of pollution h be given by d. Total damages to consumers for Home and Foreign are D(h) = dh = dγβ x g( α)x m (3) D( h) = d h = dγβ y g(α)ỹ m. As in Copeland and Taylor (2003), social welfare in Home and Foreign is given by the utility of consumption less damages from pollution: U(x, y, h) = u(x, y) D(h) (4) Ũ( x, ỹ, h) = ũ( x, ỹ) D( h). The price of good j is given by p j in Home and p j in Foreign. 2 Equilibrium conditions To solve the equilibrium model we make several assumptions. Utility is Cobb-Douglas with θ j representing the parameter determining the relative share of income devoted to good j. To simplify notation, we define θ = θx θ y and p = px p y for Home and similarly for Foreign. We normalize prices by p y = 1. As described by Copeland and Taylor (2003), constant returns to scale in production allows us to focus on solving the unit cost minimization problem since the factor intensity will be constant for each unit produced. Let a i,j (w, r) represent unit factor demand, that is the cost minimizing 3 E.g. g(α) = exp( δα) for α 0, or g(α) = 1 α for α [0, 1]. 7

level of i to produce one unit of j given labor price w and capital price r, which may be found using Shephard s lemma. Since abatement z is produced with the same capital-labor intensity as the capital-intensive good in both countries, we account for factors devoted to and production of z within y (and similarly for z within ỹ). An assumption of free entry provides the first equilibrium condition corresponding to zero profits: a Lx w + a Kx r = p x (5) a Ly w + a Ky r = p y ã Lx w + ã Kx r = p x ã Ly w + ã Ky r = p y. Solving the system of equations in (5) yields factor prices as a function of output prices and hence a i,j (p). Full employment implies the equilibrium conditions a Lx x s + a Ly y s = L (6) a Kx x s + a Ky y s = K ã Lx x s + ã Ly ỹ s = L ã Kx x s + ã Ky ỹ s = K. Substituting unit factor demand as a function of output prices from (5), the system of equations (6) can be solved for output supplies in Home as a function of p, L and K, denoted x s (p ; L, K) and y s (p ; L, K), and similarly for Foreign. Since we assume abatement, z, is produced using a technology with same capital-labor intensity 8

as y, the market clearing conditions within each country are given by x d = x s + x m (7) x d = x s + x m y d = y s + y m z = y s + y m + αβ y y m ỹ d = ỹ s + ỹ m z = ỹ s + ỹ m + αβ x x m, and globally by x m = x m (8) y m = ỹ m. The balanced account account conditions are p x x + p y y = p x x s + p y y s (9) p x x + p y ỹ = p x x s + p y ỹ s. Equilibrium prices, assuming home imports x and exports y, are p x = p x + αβ x p y (10) p y = p y (1 + αβ y ). The final equilibrium condition is derived from the first-order condition (FOC) for utility maximization, which sets the marginal rate of substitution equal to the price ratio: θ x y θ y x = θ y x = p (11) θx ỹ θy x = θ ỹ x = p. Next we turn to a graphical examination of the equilibrium defined by the system of equations in (5) through (11), taking the level of a uniform abatement policy ( α = α) as given. 9

3 Results 3.1 Graphical analysis As an intermediate step to our goal of understanding how abatement of the transportation externality affects pollution levels in general equilibrium, we first describe what happens to production and consumption. In Figure 1 we depict graphically the equilibrium in Home before and after an abatement policy is established. This analysis takes advantage of earlier work in trade theory examining the effect of including transport costs in models of international exchange. Figure 1 draws from a similar graphic presented by Falvey (1976), here modified to correct for an error in the original 4 and to include the idea of a net production frontier (NPF) which is explicitly drawn as a dash-dot line and described further below. The no policy (α = 0) equilibrium is given by levels of production (Q) and consumption (C) which jointly determine imports of the labor-intensive good (x m ) and exports of the capital intensive good ( y m ). When an abatement policy is established, exports from Home must be accompanied by a level of abatement services z determined by the policy variable α. The equilibrium price ratio faced by consumers in Home becomes steeper, shifting from p x /p y to (p x + αβ x p z )/p y. The point Q is the only point on the production possibility frontier (PPF) where capital and labor are fully employed and the price ratio (p x + αβ x p z )/p y holds, determining equilibrium revenue. However, Q does not represent actual equilibrium production since the policy given by α requires factor substitution to the abatement service z in proportion to exports ( y m ). The NPF depicts the production possibility frontier conditional on α, that is, given the decrease in factors available for production of x and y. The equilibrium consumption and production decisions under the binding abatement policy are given by C α and Q α, respectively. This post-policy outcome is determined in equilibrium by one final assumption adopted from Falvey (1976) and Casas (1981) we assume that the terms of trade (TOT) pre- and post-policy are the same, that is, y m /x m = y α m/x α m. 5 In the policy-free setting the domestic price ratio is equal to the terms of trade (both given by the line segment QC). However, under a binding policy treatment costs for exports drive a wedge between 4 Casas (1981, p. 742) points out that the consumption equilibrium after including transportation services in the model is identified incorrectly in Falvey (1976, p. 540). 5 This assumption over TOT is for graphical convenience and will only be the case for a particular parameterization of the problem. 10

consumption C T at the tangency with the utility level set. 5. From here we need one further assumption to pin down production. Falvey (1976) assumes that the pre and post aper policy TOT are identical. Thus Q T is found by identifying the tangency between the NPF and original price ratio p x /p y. By the definition of TOT this line must also pass through C T. domestic price ratio faced by consumers ((p x + αβ x p z )/p y ) and the terms of trade ( ym/x α α m) as depicted by the disjoint line segments Q C α and Q α C α, respectively. Y exportable u α u 0 y s y s 0 y y PPF y m NPF y m Q Q Q α C α C p p x y x m p p p x x z y 0 xs x m x s x x 0 importable X Figure 1: The general equilibrium response in Home to a change from no policy (α = 0) to a binding abatement policy (α > 0). PPF represents the potential production frontier given no factor allocation to abatement services. NPF indicates the net production frontier given a portion of factor endowments devoted to abatement services. Q and C represent equilibrium production (x 0 s, ys) 0 and consumption (x 0, y 0 ), respectively. The variable superscript α indicates equilibrium outcomes given a binding abatement policy. Q represents the hypothetical production equilibrium given a binding policy before the diversion of factors to abatement services is accounted for. Since demand for abatement services z in Home is determined in equilibrium by the demand for exports, the NPV curve itself is determined in equilibrium. Note that the NPV curve deviates from the PPF at and above the level of domestic demand for the exportable good, given by C α. This is in contrast to the setting of Copeland and Taylor (2003) where the NPF curve deviates for any positive production level of the dirty good and is fixed because abatement is directed toward production-related pollution and thus applies to each unit of the polluting good produced, whether exported or consumed domestically. By design the uniform abatement policy given by α leads to a decrease in the pollution generated by the exports of both Home and Foreign. In general equilibrium this involves multiple overlapping effects, which in the trade-externalities setting do not each necessarily change pollution levels in the same direction. To parse out the various effects we will extend a decomposition approach which 11

identifies scale, composition and technique effects, used by Grossman and Krueger (1993) in an examination of the effect of NAFTA on air pollution and further popularized by Copeland and Taylor. After introducing a useful diagram to illustrate this decomposition, we will describe each effect in turn. For a detailed description of these three components see chapter 2 from Copeland and Taylor (2003). In Figure 2 we present each effect graphically, extending the depiction of the equilibrium for Home first presented in Figure 1. The two additional axes in Figure 2 represent increasing pollution from either Home s imports (h) or pollution from Foreign s imports ( h). In Figure 2, pollution in the policy-free state, h 0, is given by the function h 0 (x 0 m), where x 0 m indicates the level of imports. Visually, in the southeast quadrant, h does not increase across consumption of X in general but rather over the range from x 0 s to x 0 which encompasses imports. Summarizing the pollution effects of an abatement policy is complicated by a shift in the range over which pollution is generated, which occurs at both ends. Post-policy pollution is given by h α (x α m) which both begins (at x α s ) and ends (at x α ) at new locus. To aid in decomposing the various effects, we redraw the pollution function under abatement h α (x α m) over the range of policy-free imports x 0 m and label this function h α (x 0 m). The technique effect is identified by holding everything in the economy constant except for the change in pollution intensity per unit of trade due to the abatement policy described by α. For Home s imports, this results in a decrease in the associated pollution from h 0 to h T E. In the standard analysis of Copeland and Taylor (2003), pollution generated from domestic production of a dirty good depends only on production. Identifying the two remaining effects (composition and scale) in our trade-externalities setting is complicated by the fact that pollution is generated from imports therefore the response of both consumers and producers must be accounted for. We will describe a scale and composition effect first for consumers and then for producers. The composition effect involves the change in pollution due to a shift in the share of each good in the economy, holding technique and scale constant. The scale effect captures the change in pollution due to a change in the size of an economy, holding technology and the composition of output fixed. A measure of the scale of the economy before the advent of the abatement policy is given by consumption at point C at prices p x and p y. The consumer-scale effect (C-SE) depicted in Figure 12

Y 0 h ( y 0 m) Q h ( y Q ) m n P-SE: imports increase Q α P-CE: imports fall C α C-CE C C-SE C p p x y p p x x z p y (increasing pollution from Foreign s imports) h h 0 h 0 xs x s x x 0 X h C h TE h P-SE Producer P-CE C-CE Consumer C-SE h ( x m ) h x m 0 ' ( ) 0 h Technique effect h (increasing pollution from Home s imports) 0 0 h ( x m ) Figure 2: The general equilibrium response in Home import-driven pollution h and in Foreign import-driven pollution h to a change from no policy to a binding abatement policy. The northeast quadrant is replicated from Figure 1. The northwest quadrant shows the decrease in pollution from Foreign s imports ( h 0 to h α ) and the southwest quadrant the same for Home (h 0 to h α ). The pollution response in Home is decomposed into a technique effect, scale effect for consumers (C-SE) and producers (P-SE) and a composition effect for consumers (C-CE) and producers (P-CE). 2) is identified by moving down the fixed composition line (which intersects the origin) from C to C. The consumer-composition effect (C-CE) is determined by the shift from C to the post-policy consumption equilibrium, C α. The net consumer effect on pollution is a shift from h T E to h C. On the production side, we find that the producer-scale effect (P-SE) increases Home s imports (from point Q to Q ) and hence pollution as well. The P-SE is dominated, however, by the producercomposition effect (P-CE) as the mix of goods produced shifts from Q to the final abatement policy equilibrium point Q α. Since producer effects in Figure 2 change imports from the supply side visually lying opposite from the demand side consumer effects we use three parallel lines to map changes in production decisions to changes in pollution. While the P-SE leads to an increase in 13

pollution, this effect is more than offset by the P-CE, that is, a shift away from producing goods for export towards producing goods for import. For pollution associated with Foreign s imports (not shown here), we find effects of identical sign the technique, composition and scale effects all lead to a decrease in pollution, except for the producer-scale effect (P-SE) which leads to an increase in pollution, albeit more than overcome by the mitigating effects. In summary, as in the standard analysis of Copeland and Taylor, an increase in the stringency of the environmental policy causes a reduction in pollution due to the technique and composition effects. The technique effect occurs by explicit design of the policy which aims to reduce the pollution intensity of the damaging activity. The composition effect occurs because increased stringency raises the opportunity cost of the polluting activity production of the dirty good in the standard model and transport of any good in our setting. In contrast to the standard analysis, in the trade-externalities setting the scale effect decreases both the supply of and demand for polluting imports. While the net scale effect as drawn in Figure 2 represents a decrease in pollution, in general the sign of this effect (before parameters are determined) is ambiguous. 3.2 Endogenous trade pollution policy: the invasive species case In the graphical analysis above, we considered the effects of an exogenously determined abatement policy. However, given a specification for utility which includes the impacts of pollution, we now turn to a consideration of policies where the stringency of abatement is chosen endogenously to maximize social welfare. We assess endogenous policy here using assumptions consistent with the invasive species case pollution associated with a country s imports damages only the importing country. We consider four settings from the intersection of two binary cases describing the uniformity and the scale at which policy is chosen. We begin with an assumption that the abatement policy is uniform one shared abatement standard applies to both Home and Foreign. Subsequently, we will consider the case in which abatement policy can be differentiated, i.e. set at different levels in Home and Foreign. Within both of these cases we will examine the optimal choice of a global social decision-maker (GSD) versus the optimal choices preferred by Home and by Foreign alone. To facilitate the analysis we adopt a Lagrange multiplier approach to account for the welfare 14

effects of changes in policy stringency. We represent the policy constraints in Home and Foreign by A(α) and Ã( α), respectively: A(α) = z + αβ y y m = 0, (12) Ã( α) = z + αβ x x m = 0. For Home s welfare, let λ α represent the Lagrange multiplier for the policy constraint on α and let λ α represent the multiplier for the policy constraint on α. While this might seem strange at first, note that constraints on the abatement policy in Foreign will have impacts on welfare in Home (outside of the change in damages) since levels of exchange and terms of trade will be affected. Finally, for welfare in Foreign, let λ α represent the Lagrange multiplier for the policy constraint on α and λ α for the constraint on α. 3.2.1 Uniform policy First we consider the optimal uniform policy level given by the constraint α = α, which is consistent with the approach taken to reducing wood-boring exotic insect hitchhikers under ISPM- 15. Using the utility functions specified in the system of equations in (4), the Lagrangians for the constrained utility maximization problems in Home and Foreign are L α = u(x, y) D(h( α = α)) + λ α A(α) + λ α=α Ã( α = α), (13) L α = ũ( x, ỹ) D( h(α)) + λ α A(α) + λ α=α Ã( α = α). The Lagrangian for the GSD, whose objective is to maximize the global net benefits of a policy, is given by V α = L α + L α. (14) For ease of comparison, the first-order conditions (FOCs) for the optimal policy under a GSD (20), and under a unilateral choice by either Home (21) or Foreign (22) are presented next in sequence. 15

Using the envelope theorem for constrained maximization, the FOCs are: 6 D (h) h α + D ( h) h α = λ A α α + Ã λ α α + λ A α α + λ α Ã α, (15) D (h) h A = λ α α α + Ã λ α α, (16) D ( h) h α = A λα α + λ α Ã α. (17) In each expression above the term(s) on the left-hand side represent(s) the marginal benefits (marginal averted damages) and the terms on the right-hand side represent the marginal costs. The Lagrange multipliers capture the change in welfare from a marginal change in the level of abatement services required, which leads to lost purchasing power, either through a loss in revenue from diverting factors from the optimal production of the consumption goods alone and/or due to changes in terms of trade. Let the optimal uniform unilateral policy for Home that satisfies Equation (16) be given by α H. Similarly for Foreign let α F satisfy Equation (17). If Home sets an optimal unilateral uniform policy on its own, it will select the same policy as the GSD if and only if α H = α F. Home will select a uniform policy level on its own that is more stringent than the level preferred by both the GSD (from Equation (15)) and Foreign if, at the point α = α H, the marginal benefit for Foreign is less than its marginal cost, that is when D ( h) h α < λ α A α + λ α Ã α. 3.2.2 Country-differentiated policy For global welfare, the most efficient structure would allow for a differentiated abatement policy by country. The Lagrangians for Home and Foreign in this setting are: L α, α = u(x, y) D(h( α)) + λ α A(α) + λ α Ã( α), (18) L α, α = ũ( x, ỹ) D( h(α)) + λ α A(α) + λ α Ã( α). 6 The envelope theorem implies that derivative of a production or consumption choice variable or a Lagrange multiplier with respect to the parameter α will be equal to zero. 16

Combining the equations above, the Lagrangian for the GSD problem is V α, α = L α, α + L α, α. (19) In this non-uniform policy setting the two FOCs for the GSD are D (h) h α = Ã λ α α + λ α Ã α, (20) D ( h) h α = λ A α α + λ A α α. The FOCs for Home (21) and Foreign (22) determining the policy they would impose on their trading partner are D (h) h α = Ã λ α α, (21) D ( h) h α = + λ α A α. (22) All else equal, countries in a differentiated setting would prefer that their own required level of abatement for pollution from their exports be set to zero. As expected, since each country ignores the marginal cost to their trading partner as described by the additional term on the right-hand side in the system (20) versus equations (21) and (22) they would likely impose a policy of greater stringency than that given by the GSD (or under a uniform policy). However, it is not necessarily the case that infinite abatement would be chosen as the optimal policy to impose on their trading partner. As policy is raised above zero, the marginal cost term on the right-hand side of equation (21) or (22) could be negative, reflecting the enjoyment of improved TOT for the importer. However, unless it is optimal to eliminate imports entirely (here through a cost-prohibitive abatement policy) there will be a point at which the sign flips and ultimately where the lost marginal surplus from imports equate with the declining marginal benefits of reducing pollution, or invasives propagule pressure. 17

4 Conclusion In this paper we describe an approach for considering different types of environmental trade externalities in a unified framework. We generalize previous analyses of trade and the environment to show how, in the current setting, the effect on pollution of an abatement policy necessitates an accounting not only of production decisions but also the consumption decisions that jointly determine trade levels. Decomposing the various effects on trade and pollution, we find that the producer-scale effect works in opposition to the other effects, implying that the net (producer and consumer) scale effect is of ambiguous sign. In the context of invasive species, we consider the endogenous choice of an abatement policy from a social welfare perspective. We demonstrate that if an abatement policy is constrained to be uniformly applied to each country, a single country such as Home could have an incentive to argue for a policy that is either more or less stringent than what would be ideal from a global welfare perspective. For example, Home has an incentive to argue for a more stringent policy if, at Home s ideal policy stringency, marginal averted damages in Foreign have already declined below its marginal welfare cost. Allowing a differentiated policy stringency between countries allows for a more efficient result from an aggregate global welfare perspective but raises equity concerns while generating an incentive for a country to have its own abatement requirement set low and its partner s abatement requirement set high. Future iterations of this paper will extend the analysis of endogenous policy in two ways. First, we will compare the existing invasive species case to that of a non-discriminating pollutant like GHGs where damages from imports affect all countries. We will then unpack the determinants of the Lagrange multipliers or shadow values of the policy constraints. These will be expressed as functions of the model parameters, allowing us to provide greater detail regarding when a particular result would be expected to dominate. 18

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