Artículos

 

Climate policy and border tax adjustments: Might industrial organization matter?

 

Ian Sheldon,¹ Steve McCorriston²

 

¹ Professor of International Trade, Department of Agricultural, Environmental, and Development Economics, Ohio State University, e-mail: sheldon.1@osu.edu.

² Professor, Department of Economics, University of Exeter Business School, e-mail: S.McCorriston@exeter.ac.uk.

 

Recepción: 12/08/2011
Aceptación: 26/04/2012

 

 Abstract

In this paper, analysis is presented relating to the impact of border tax adjustments for climate policy on the problem of carbon leakage, and the related issue of competitiveness of energy-intensive industries. Compared to the current literature, these policies are set in the context of a vertically-related market characterized by successive oligopoly. Specifically, it is shown that an appropriate border tax adjustment depends on the incidence of domestic climate policy, the nature of competition in upstream and downstream sectors, as well as the basis for assessing the trade neutrality of any border tax adjustment. If trade neutrality is defined in terms of market volume, even though carbon leakage is reduced, domestic firm competitiveness cannot be maintained. This compares to defining trade neutrality in terms of market share, which results in domestic competitiveness being maintained and global carbon emissions being reduced. In either case, consumers incur deadweight losses.

Keywords: climate policy, carbon leakage, border tax adjustments, industrial organization.

Clasificación JEL: H87, Q38.

 

Resumen

En este artículo se analiza el impacto de los ajustes de impuestos fronterizos sobre políticas públicas ambientales orientadas a las emisiones de carbón. Asimismo, se abordan temas de competitividad e industrias intensivas en energía. En comparación con la literatura relevante este trabajo se sitúa en un marco de un mercado integrado verticalmente bajo una estructura de oligopolio sucesivo. En particular, se muestra que un ajuste óptimo de impuestos fronterizos depende de las políticas ambientales locales, la naturaleza de la competencia entre las empresas proveedoras y compradores y de la forma cómo se defina la neutralidad de dicho ajuste. Los principales resultados de los ajustes de impuestos fronterizos son dos. Por un lado, si la neutralidad del comercio se define en términos de volumen de mercado, entonces la competitividad de las empresas domésticas no se puede mantener aunque las emisiones de carbón se reduzcan. Por el otro, si la neutralidad se define como la participación de mercado, entonces la competitividad se mantiene y las emisiones de carbón se reducen. En ambos casos se incurre en pérdidas sociales.

 

Introduction

In the past decade, it has become increasingly obvious that even though negotiation of the Kyoto Protocol on Global Climate Change in 1997 was a useful first step, further efforts to develop a comprehensive multilateral agreement for reducing carbon emissions will be necessary if global climate change is to be properly addressed (Frankel, 2009). However, irrespective of the logic supporting a multilateral approach to dealing with a global public bad, many countries such as the United States and the European Union (EU) have been actively pursuing national efforts to reduce carbon emissions through tougher climate policy.

Much of the recent discussion as well as actual application of climate policy has focused on the use of market-based instruments such as carbon taxes and tradable emissions permits rather than command-and-control instruments such as regulatory standards. This follows from the economic argument that a properly designed tax or system of tradable permits will face economic agents such as electricity producers with the social cost of emitting carbon, minimize the aggregate cost of abating carbon emissions, and provide incentives for the adoption of efficient abatement technologies (Stavins, 2003). Carbon taxes have been proposed in many countries, including China, and are also currently applied in several countries, most notably Australia. In the case of the current European Emissions Trading Scheme (ETS), and also proposed US climate policy legislation, the choice of instrument is a system of tradable permits or what is usually referred to as cap-and-trade, i.e., a cap is placed on aggregate carbon emissions in conjunction with the sale of tradable emission permits.³,⁴ The system resolves the externality problem because agents can only emit carbon up to the extent of the permits they hold, and with permits being tradable they are purchased by those agents who value them most at the margin.⁵

Whether a carbon tax or cap-and-trade system is used, the expectation is that energy-intensive industries downstream from electricity production will face increased costs of production. As a consequence, much of the proposed climate legislation also includes some type of border measure to be targeted at energy-intensive imports (Frankel, 2009). The inclusion of border measures in climate change legislation is predicated on two concerns: first, there will be carbon leakage, i.e., production by energy-intensive industries will be shifted to countries with less restrictive climate policies; second, there will be a reduction in competitiveness of firms in industries most affected by domestic climate policies (WTO/UNEP, 2009).

As Karp (2010) has recently pointed out, these two related concerns have their basis in the economics of pollution havens, which are defined as:

"...a region or country with a concentration of pollution-intensive activity that has been induced by pollution policy that is weak relative to its trading partners..." (Copeland and Taylor, 2003, p.143).

Through its effect on relative prices, unilateral application of tougher climate policy by one country/region reduces the international competitiveness of energy-intensive industries in that country/region relative to another country/region that has weaker climate policy, the latter becoming a pollution haven (Burniaux, Martin and Oliviera-Martins, 1992; Pezzey, 1992).⁶ The increased concentration of pollution-intensive activity in a country/region with weaker climate policy is the basis for the now widely used concept of carbon leakage, i.e., the increase in carbon emissions in locations where climate policy is weak as a proportion of the reduction in carbon emissions in locations that have stringent climate policy (Perroni and Rutherford, 1993).

Detailed analysis of how countries might cooperate over climate policy has been conducted by several authors, including, inter alia, Hoel (1992; 1994), Carraro and Siniscalo (1993), and Barrett (1994a). In the context of the current paper, there has also been a specific focus on how trade policy instruments might be used to prevent carbon leakage when one group of countries commits to cooperation over climate policy, while a second group free-rides by not implementing climate policy (Hoel, 1996; Maestad, 1998). Hoel (1996), for example, shows that a social optimum can be obtained if cooperating countries set common carbon taxes, and at the same time use import tariffs (export subsidies) on all energy-intensive traded goods, the objective being to shift the terms of trade against free-riding countries, thereby reducing carbon leakage.⁷

A concern raised by Hoel (1996) is that the use of tariffs and subsidies could be constrained by WTO/GATT rules. However, if such trade policy instruments are treated as border tax adjustments (BTAs) rather than border taxes (subsidies), the view of economists is that the principle for their use in the presence of a domestically imposed excise tax is well-founded in the literature on the impact of origin vs. destination-based taxation systems (Lockwood and Whalley, 2010). A synthesis of the analysis of this issue by Lockwood, de Meza and Myles (1994) shows that as long as a domestic tax is applied uniformly across all goods, and BTAs are set no higher than the domestic tax, if either prices or exchange rates are flexible, movement between an origin and a destination base for taxation has no real effects on trade, production and consumption.

Essentially, this principle is captured in the WTO/GATT rules: GATT Article II: 2(a) allows members of the WTO to place on the imports of any good, a BTA equivalent to an internal tax on the like good. However, under GATT Article III: 2, the BTA cannot be applied in excess of that applied directly or indirectly to the like domestic good; i.e., they have to be neutral in terms of their impact on trade, their objective being to preserve competitive equality between domestic and imported goods (WTO, 1997). In addition, with respect to exported goods, WTO/GATT rules allow rebate of the domestic tax on the exported good, as long as the border adjustment does not exceed the level of the domestic tax, it is not regarded as an export subsidy under the GATT Subsidies Code (WTO, 1997).

While there has been considerable discussion about the legal permissibility of BTAs for domestic climate policy, from the standpoint of this paper, two key aspects of the debate remain unresolved.⁸ First, it is unclear whether a BTA will be allowed on imports of a final energy-intensive good, such as steel, when the domestic carbon tax directly affects an input into steel production such as electricity, which is not physically present in the final good. Pauwelyn (2007) argues convincingly that if an objective of a carbon tax on electricity production is to ensure that the price domestic consumers pay for an energy-intensive product such as steel reflects the social cost of producing steel, then a BTA on imported steel should be permitted.

Second, it is also unclear whether WTO rules on BTAs would apply in the case where domestic climate policy consists of a cap-and-trade system. Here Pauwelyn (2007) argues that if emission credits command a market price, then the obligation of electricity producers to hold emission credits up to the actual level of their carbon emissions qualifies as an internal tax. Assuming this internal tax is passed forward to domestic steel producers/consumers, an appropriate BTA can be implemented on imports of steel. In light of this discussion, this paper proceeds upon the assumption that a BTA for either a domestic carbon tax or cap-and-trade system will be considered legal.⁹

While the use of BTAs is not a particularly new regulatory issue, there are additional analytical challenges when examining a domestic climate policy that has the potential to affect several stages of a vertical production system characterized by successive oligopoly -neither being accounted for in extant analysis of BTAs and carbon leakage. In this context, the focus of this paper is on modeling climate policy targeted at upstream energy production, and its associated incidence on downstream production of energy-intensive goods, paying attention to both upstream carbon leakage effects and downstream competitiveness effects. In analyzing this problem, the current paper is organized as follows: in section 1, a brief discussion of competitiveness is presented along with some stylized facts about the type of vertically-related production system most likely to be affected by developed country climate policy; this is followed in section 2 by description of a model of successive oligopoly, which is then used in section 3 to analyze BTAs for domestic climate policy; finally, a summary of the paper and some conclusions are presented.

In previewing the results, the paper makes three key contributions. First, by assuming a vertical market structure, the incidence of climate policy is properly accounted for. Specifically, it is shown that under reasonable assumptions about demand, carbon pricing targeted at upstream producers of energy will not be fully passed through to downstream import-competing firms, which has implications for the level at which BTAs are imposed on downstream imports. Second, characterizing downstream firm behavior as oligopolistic captures the link between carbon leakage and competitiveness, and how that link is sensitive to the nature of competition between downstream firms. Importantly, it is shown that the extent to which climate policy results in carbon leakage and a loss of competitiveness by energy-intensive import-competing firms depends on how aggressively foreign downstream firms respond to the former's output changes. Third, the results illustrate a classic regulatory problem: the difficulty of achieving several policy objectives (ensuring no carbon leakage/maintaining competitiveness) with a limited set of policy instruments (climate policy, BTAs), in a situation where there is a binding external constraint (WTO/GATT rules) on the use of one of those instruments (BTAs). Specifically, the results show that the ability of a policymaker to prevent carbon leakage as well as maintain the competitiveness of import-competing firms is very sensitive to how one interprets the WTO/GATT rules on BTAs. In addition, absent a production subsidy targeted at domestic firms, consumers incur deadweight losses from these policy choices as aggregate output downstream is reduced by oligopolistic firms.

 

Competitiveness, climate policy and energy-intensive industries

While the issues of carbon leakage and competitiveness are closely connected in the climate policy debate, the latter is a rather more difficult concept to define. Typically, it would be thought of in terms of market share and/or the profit of firms, which in turn are a function of the specific characteristics of an industry subject to domestic climate policy, including factors such as market structure, industry technology and the nature of competition between firms (WTO/UNEP, 2009). In the case of perfectly competitive firms, atomistic firms make zero economic profits in long-run equilibrium. Consequently, if firms and policymakers are concerned about the effect of unilateral implementation of climate policy on competitiveness as defined above, markets would have to be imperfectly competitive with firms having non-trivial market shares and earning positive economic profits in equilibrium. This suggests that climate policy and BTAs are perhaps best analyzed in the context of the literature on trade and environmental policy pioneered by, inter alia, Barrett (1994b), Conrad (1993), and Kennedy (1994).

The key point of this previous literature is that if firms earn positive economic profits, implementation of climate policy and/or a BTA may have the effect of shifting profits between domestic and foreign firms, thereby affecting the former's competitiveness.

In analyzing this issue, therefore, it matters what type of industries are most likely to be affected by the unilateral implementation of climate policy. In the case of the US, Houser et al. (2009) identify five energy-intensive industries most likely to be affected by domestic climate policy: steel, aluminum, chemicals, paper and cement, where energy accounts for between 10 and 20 percent of total costs. A similar set of industries have been discussed with respect to EU concerns about carbon leakage (Monjon and Quirion, 2010). If both upstream energy and downstream energy-intensive final goods markets are perfectly competitive, then the appropriate treatment of imports of an energy-intensive good such as steel is relatively straightforward: an import tax on imported steel, equal to the level of say a carbon tax times the extent to which energy enters the cost function for domestically produced steel, would raise marginal costs for the importer of steel by the same amount, and consequently will have a neutral effect on imports of steel, and thereby be WTO/GATT-consistent (see Poterba and Rotemberg, 1995).

It may be more appropriate, however, to assume that both the intermediate energy and energy-intensive final goods markets are oligopolistic. In the case of electricity production markets, with increased deregulation it is now quite commonplace to characterize generating firms in terms of their oligopolistic interaction (Ventosa et al., 2005). For example, Borenstein and Bushnell (1999), and Fowlie (2009) both model the Californian electricity market as a Cournot game, while Bolle (1992), Green and Newberry (1992), and Green (1996) all model the UK electricity market as a supply function equilibrium, the upper bound to which is the static Cournot outcome. With respect to the set of downstream energy-intensive industries, several authors analyzing the carbon leakage/competitiveness issue have already modeled firm behavior as oligopolistic, e.g., steel (Demailly and Quirion, 2008; Ritz, 2009) and cement (Ponssard and Walker, 2008), and there is also empirical evidence that firms in these industries may behave less than competitively, e.g., steel (Gallett, 1996); aluminum (Yang, 2001); paper (Mei and Sun, 2008); and cement (Azzam and Rosenbaum, 2001).

Consequently, if the vertical market structure of these industries is best described as one of successive oligopoly, then taxing imports of downstream energy-intensive goods at the same level as the internal tax imposed on upstream energy production may not have a neutral impact. In order to analyze this possibility, the remainder of the paper consists of the adaptation and use of a vertical-market model developed in earlier papers by McCorriston and Sheldon (2005a; 2005b).

 

A Model of Successive Oligopoly

Assumptions

The model introduced here is one of successive oligopoly, i.e., both the upstream (intermediate) and downstream (final) sectors are imperfectly competitive, and one that is standard when dealing with policy issues in vertically-related markets (for example, Sleuwaegen et al., 1998; Ishikawa and Spencer, 1999). In the downstream sector, the domestic firm competes with a foreign exporter of the energy-intensive final good. In both domestic and foreign upstream sectors, two firms produce a non-traded intermediate input, electricity, which is homogenous once generated and supplied to the electricity transmission system (see figure 1). Production of electricity generates carbon emissions e via the function e_j = f(x^U_j), where x^U_j is total upstream electricity production in countries j =1, 2, U denotes the upstream sector and 1 refers to the home country and 2 the foreign country. Also, f' (x^U_j) > 0, and we can allow for f' (x^U₂)(x") > f' (x^U₁), capturing the idea that the foreign country's electricity production could generate more carbon emissions e_j for a given level of output. It is assumed that domestic climate policy, be it a carbon tax or cap-and-trade system, will raise domestic intermediate firms' costs, subsequently raising the domestic downstream firm's costs due to the increased price of electricity. The technology linking each sector is one of fixed proportions. Formally, x_j = Φ x^U_j, j = 1, 2, where X_j and x^U_j represent output in both the domestic and foreign downstream and upstream sectors respectively, and where Φ is the constant coefficient of production. To ease the exposition, Φ is set equal to one in the framework outlined below. Like much of the previous literature on vertical markets, arm's length pricing between the downstream and upstream sectors is also assumed, i.e., the downstream sector takes electricity prices as given (Abiru, 1988; Salinger, 1988).¹⁰

Following Ishikawa and Spencer (1999), the model consists of a three-stage game. At the first stage, the domestic government commits to climate policy and a BTA, while the second and third stages consist of Nash equilibria in the upstream and downstream sectors. The timing of the firm's strategy choice goes from upstream to downstream. Specifically, given costs and the derived demand curve facing the upstream sector, each domestic upstream firm simultaneously chooses output to maximize their profits, given the output choice of the other upstream firm, which generates Nash equilibrium in the upstream sector.¹¹ The intermediate input prices are taken as given by the domestic downstream firm which, simultaneously with their foreign competitor, chooses output to maximize profits, given the output choice of the other downstream firm, thus giving Nash equilibrium in the downstream sector. In terms of solving the model, equilibrium in the downstream sector is derived first and then the upstream sector.

Equilibrium in the Energy-Intensive Sector

Let x₁ equal the output choice of the domestic downstream firm and x₂ the output choice of its foreign competitor. The revenue functions can be written as:

We assume downward sloping demands and substitute final goods.

Given (1) and (2), the relevant profit functions downstream are given as:

where c₁ and c₂ are the domestic and foreign firms' respective costs. Firms' costs relate to the purchase of the intermediate input electricity, other production costs being omitted as arguments.

The first-order conditions for profit maximization are given as:

Equilibrium in the downstream sector can be derived by totally differentiating the first-order conditions (5) and (6):

The slopes of the reaction functions are found by implicitly differentiating the firms' first-order conditions:

With this set-up, we can deal with both strategic substitutes and strategic complements, where the variable of interest is the cross-partial effect on marginal profitability, i.e., the sign of r_i = sign of R_i,ij. The distinction between strategic substitutes/complements relates to the "aggressiveness" of firms' strategies (Bulow et al., 1985). With strategic substitutes, firms' strategies are less aggressive than those associated with strategic complements, i.e., with strategic substitutes (complements), an increase in the output of firm 1 would be met by a decrease (increase) in that of firm 2.¹² Consequently, with reference to equation (8) and (9), if R_i,ij < 0, then r_i< 0. In this case, we have the case of strategic substitutes, and the reaction functions are downward sloping. However, if R_i,ij > 0,, the reaction functions are upward sloping and we have strategic complements.

Given (7), the solution to the system is found by re-arranging in terms of dx_i and inverting where Δ is the determinant of the left-hand side of (7):

To simplify the notation re-write (10) as:

where: α₁ = R_1,11α₂ = R_2,22, and b₁ = R_1,12 b₁ = R_2,21.

For stability of the duopoly equilibrium, the diagonal of the matrix has to be negative, i.e., α_i< 0, and the determinant positive, i.e., Δ = α₁α₂-b₁b₂ > 0., i.e., own effects on marginal revenue outweigh the cross effects. Given these conditions, further comments can be made about the reaction functions. r_i= -(b₁)/α_i- from (8) and (9). Hence, if α_i< 0, then for strategic substitutes, b₁ > 0, in order to satisfy r_i< 0, and b₁ > 0 in order to satisfy r_i< 0 for strategic complements. The expression for r_i can be substituted into (11) in order to make the comparative statics easier to follow:

Equilibrium in the electricity generating sector

Given the fixed proportions technology and Φ= 1, total output in either the domestic or foreign electricity generating sectors is given by x^U_j(= x_j). The latter also implies that upstream emissions can be written directly as function of the downstream firm's output, i.e., e_j= f(x^U_j) / f(x_j). It is assumed that in each country there are two upstream firms (A and B) whose combined output of electricity equals x^U_j, i.e., x_j^A + x_j^B= x^U_j. Due to the intermediate good electricity being assumed homogeneous once supplied to the transmission system, the downstream firms are therefore indifferent about the relative proportions of x_j^A and x_j^B used in their production process. Assuming that the downstream firms face no costs other than the price paid for electricity, the inverse derived demand function facing firms in the upstream sector can be found by substituting p_i^U for d in (5) and (6) respectively. In countries j = 1, 2, firms' profits in the upstream sector are, therefore, given by:

where c_j^A and c_j^B are the upstream firms' costs respectively in country j.

Given this, following the outline above, equilibrium in the upstream market, j = 1, 2, is:

where α_j^A, α_j^B 1 0 and (Δ^U_j)^-1 > 0 for stability.

 

Climate policy and border tax adjustments

Climate policy and leakage

Assume initially that BTAs are not available, so that the domestic government can only target climate policy at its electricity producers. To keep the exposition simple, the price associated with emitting carbon or any other greenhouse gas (GHG), is denoted as g^e, which is based on either a carbon tax t^e, or the market price of an emissions permit m^e, and it is assumed g^e = t^e = m^e. The imposition of g^e on domestic electricity producers raises both c^A₁ and c^B₁. In turn, this raises the price of electricity p^U_j, i.e., the costs to the domestic downstream firm ci. The cost increase to the domestic downstream firm also affects imports of the energy-intensive final good, given by dx₂/dc_i. Following Ritz's (2009) technical specification of carbon leakage, which draws on the earlier definition of Perroni and Rutherford (1993), and assuming that domestic electricity producers do not respond to g^e by reducing their intensity of carbon emissions via cleaner technology, carbon leakage l is given as:

i.e., even if intensity of carbon emissions is the same in the domestic and foreign upstream sectors, f' (x^U₁) = f' (x^U₂) there will be positive carbon leakage, l > 0, if there is positive output leakage, dx^U₂-dx^U₁> 0. Given that x^U_j (= x_j), (12) can be used to re-write (16) as:

If l > 0, there is positive carbon leakage, and if l < 0, there is negative carbon leakage in the sense that foreign carbon emissions actually decrease after implementation of the policy. Given Δ^-1 > 0 and α₂< 0, such that dx₁= Δ^-1 α₂dc₁ < 0, the direction of carbon leakage is given by the sign of r₂, and the extent by the size of f' (x^U₂) relative to f' (x^U₁): if f'(x^U₂) = f' (x^U₁) and r₂ < 0 (> 0), then dx₂ = Δ^-1 α₂r₂dc₁> 0 (< 0) and l > 0 (< 0), i.e., there is positive (negative) carbon leakage if final goods are strategic substitutes (complements), i.e., in response to the domestic downstream firm cutting output, the foreign downstream firm either raises its output (strategic substitutes), causing positive carbon leakage, or it reduces its output (strategic complements) causing negative carbon leakage; and if f'(x^U₂) > f' (x^U₁), given | r₂ | < 1, the extent of positive (negative) carbon leakage depends on the intensity of foreign relative to domestic carbon emissions.

Lemma 1: With strategic substitutes, pricing carbon emissions causes positive carbon leakage. With strategic complements, pricing carbon emissions causes negative carbon leakage. The extent of positive or negative carbon leakage is determined by the relative intensity of foreign to domestic carbon emissions.

Border tax adjustments and neutrality

Now assume a BTA, t^b, can be targeted at imports of the energy-intensive final good, thereby raising the costs of the downstream firm's foreign competitor which, in turn, affects the level of imports. This is given by dx₂/dc₂, which, given the assumption of fixed proportions, also feeds back into foreign electricity production, dx₂/dc₂ = dx^U₂ / dc₂ = d(x^A₂ + x^B₂)/dc₂, which in turn affects foreign carbon emissions e₂, and thereby carbon leakage l. Since the WTO/GATT guidelines are not specific in defining 'competitive equality', we consider the cases where the neutral BTA (neutral BTA) is defined as either the change in c₂ that keeps the volume of final good imports constant given a carbon price g^e, or as the change in c₂ that keeps the domestic market share of final good imports constant given g^e.

Import-Volume Neutrality. If neutrality is defined in terms of import volume, the appropriate BTA is given as:

When markets are competitive, then |dx₂ / dc₂| = |dx₂ / dc₁|, the net effect being such that dx₂ = 0, there being no carbon leakage, i.e., the appropriate BTA should be set equal to the domestic carbon price of g^e. Specifically, with a carbon price of g^e, the BTA is effectively based on the carbon embodied in the domestically produced final good. This rules out the domestic policymaker setting t^b > g^e when f'(x^U₂) > f' (x^U₁), i.e., given binding WTO/GATT rules, the appropriate BTA cannot be based on the carbon embodied in the foreign produced final good.¹³

In contrast, when markets are imperfectly competitive, setting the BTA equal to the price of carbon will lead to a non-neutral outcome, dx₂≠0.

Lemma 2: With strategic substitutes, the appropriate import policy to ensure neutrality is an import tax. With strategic complements, import volume neutrality requires an import subsidy.

Consider first of all the effect of the import tax on the imports of the final good. Using (12), dx₂= Δ^-1 α₁dc₂, since Δ^-1> 0 and α₂< 0, the border tax (as expected) reduces the level of final good imports, i.e., dx₂ < 0. From the previous section, the effect of the domestic climate policy on final good imports dx₂= Δ^-1 α₂r₂dc₁ depends on the sign of r₂. In the case of strategic substitutes, r₂< 0, which results in dx₂ / dc₁ > 0, i.e., import volume neutrality requires an import tax, as the foreign downstream firm is aggressive in raising its output. Necessarily, if dx₂= 0 there will be no carbon leakage.

In the case of strategic complements r₂> 0, so that dx₂ / dc₁ < 0, suggesting that domestic climate policy has a non-neutral impact on imports of the final good, the foreign downstream firm acting less aggressively by reducing its output. Specifically, the carbon price imposed on domestic electricity production reduces domestic output in the downstream sector and imports of the final good. From (18) this implies that with strategic complements, since dx₂ / dc₁ < 0, to restore neutrality, the appropriate policy is an import subsidy rather than an import tax. However, this outcome, while in principle satisfying WTO/GATT rules, is not actually necessary to reduce carbon leakage. This is due to the fact that a domestic carbon price, by causing the foreign downstream firm to reduce its output, actually results in negative carbon leakage.

The appropriate border tax adjustment for domestic climate policy that ensures import volume neutrality is summarized in the following proposition:

Proposition 1: The BTA required to ensure import volume neutrality depends on (a) whether the nature of competition is strategic substitutes or complements; (b) the effect of a change in costs in the final market; and (c) the extent to which the domestic carbon price, g^e, is transmitted into an increase in domestic downstream firm's costs.

Part (a) of Proposition 1 follows directly from Lemma 2. Relating to parts (b) and (c), whether the expansion of imports due to domestic pricing of carbon matches the contraction due to the BTA depends on two factors: the effect of the change in input costs on the downstream sector, and the extent to which the domestic carbon price, g^e, is transmitted into an increase in the downstream firm's costs, dc₁. Focusing, first of all, on the former, even if dc₁ = dc₂, the impact of domestic climate policy will likely be less than the BTA. For example, if α₁ ≈ α₂, as, | r₂ | < 1, then α₂r₂r < α₁. Second, consider the likelihood of dc₁ = dc₂. This depends on the incidence of the upstream carbon tax on the downstream firm's cost function, i.e. dp^U_1,1/(dc₁^A + dc₁^B), the extent to which the price of domestic energy rises as a result of the domestic price of carbon. Since electricity is homogenous at the point of consumption downstream, then:

Using (15):

where p^U_1,1 < 0, and D = (Δ^U)^-1 [α₁^B(1 + r₁^B) + a₁^A(l + r₁^A)] < 0. Therefore, domestic downstream costs will increase with imposition of a carbon price upstream, i.e., dc₁ = dp^U₁ > 0. For reasonable characterizations of the demand function, there will be under-shifting of climate policy {p^U_1,1D} g^e < 1.¹⁴

Using (12), and (18)-(20), the appropriate BTA implied by Proposition 1 can generally be given as (assuming α₁≈ α₂):

It is clear that the form of the BTA, i.e., whether it is an import tax or subsidy, depends on the nature of competition in the downstream sector.¹⁵ Further, the size of the appropriate BTA depends on the nature of competition in both the downstream and upstream sectors. Also, note that if the appropriate BTA is set, i.e., dx₂ = 0, there will be no carbon leakage. As with the case of perfect competition noted earlier, the BTA cannot be used to target foreign final good production when f'(x^U₂) > f' (x^U₁) as this would violate the import-volume neutrality constraint. Given this, the following corollary can be stated:

Corollary 1: To be WTO-consistent, a border tax adjustment cannot be based on the level of carbon embodied in the foreign produced final good, implying that t^b≤ g^e, even if foreign production of the final good is more carbon-intensive f'(x^U₂) > f' (x^U₁).

Import-Share Neutrality. In the case of import-share neutrality, the appropriate BTA is defined as one where the net effect of the carbon price g^e on x₁ and x₂ must equal the net effect of the BTA on x₁ and x₂. In this case, the neutral BTA is defined as:

Proposition 2: Defining competitive equality in terms of market share leads to a policy that does not depend on the existence of strategic substitutes or complements However, the BTA required will be lower in the case of strategic complements compared to that required for the case of strategic substitutes.

Using (22) and assuming α₁≈ α₂, the neutral BTA can be re-written as:

It is clear from (23) that defining "competitive equality" in terms of market shares does not lead to the "sign" of the policy. However, the magnitude of the BTA is still dependent on the nature of competition between the downstream firms. Specifically, in the case of strategic substitutes, r_i < 0, and given that | r₁ | > | r₂ |, the appropriate BTA exceeds that for the case of import-volume neutrality as given in (21).¹⁶ For strategic complements, r_i < 0, and given that | r₁ | > | r₂ |, the neutral BTA is lower than in the strategic substitutes case. However, whether final goods are strategic substitutes or complements, the domestic price of carbon combined with the BTA "facilitates" collusion, a result similar to that when import restrictions are defined in terms of market share (Denicolo and Garella, 1999). As a result, even though the BTA is not set above the domestic carbon price in order to be WTO-compliant, global carbon emissions are actually reduced below that prior to implementation of domestic climate policy, i.e., there is negative carbon leakage.

Border Tax Adjustemets and Competitiveneses

While appropriate BTAs satisfying the constraint of neutrality can be defined in the presence of imperfect competition, thereby ensuring no carbon leakage, the downstream competitiveness effects of the two definitions of neutrality are quite different. This is important since even though the appropriate BTA will keep imports of the final good at the same level, re-distribution of profits between domestic and foreign downstream firms can still occur. This can be summarized in the following proposition.

Proposition 3: With import volume neutrality, an appropriate BTA for domestic pricing of carbon reduces profits of the domestic downstream firm, thereby reducing its competitiveness, while increasing the profits of the foreign downstream firm. With the import share rule, the domestic downstream firm improves its competitiveness, both domestic and foreign downstream firms gaining additional profits.

Specifically, under import-volume neutrality, and for either strategic substitutes or complements, the combination of a domestic carbon price and BTA reduces output and profits of the domestic downstream firm, and raises profits of the foreign downstream firm. Under the rule that dx₂ = 0, the change in output of the domestic downstream firm is derived from (12), and assuming α= α₁≈ α₂:

Given Δ^-1 > 0,α < 0,dc₁> dc₂, and | r_x|< 1, then dx₁ < 0 for both r₁ < 0 and r₂> 0, i.e., even if the BTA is trade neutral, the domestic firm still reduces its output with a positive carbon price. In the case of profits, totally differentiate (3) and (4):

Again, based on the rule that dx₂= 0, and π_1,c1 dc₁ = - x₁ dc₁ from (3), it is easy to see that, dπ₁< 0, i.e., domestic downstream firm profits fall. For the foreign downstream firm, and assuming, α= α₁≈ α₂, (26) can be re-written as:

Given Δ^-1 > 0, p_2,1< 0, α< 0, and r₁> 0, as long as [.] > 0, then dπ₂ > 0, i.e., foreign downstream firm profits increase. The reason for this is that the BTA has been set appropriately and is less than the domestic carbon price. If r₁ > 0, and an import subsidy is used, as can be seen from (25), dπ₁ > 0, i.e., the domestic downstream firm's profits still decline. In the case of the foreign downstream firm, from (27), as long as dc₁> |r₁dc₂|, and [...] > 0, then dπ₂ > 0, i.e., the downstream foreign firm's profits increase. In other words, even with an appropriately set BTA, which results in no carbon leakage, the domestic downstream firm still suffers a loss of competitiveness.

For import-volume neutrality, the competitiveness effect is illustrated in figure 2 for the case of strategic substitutes. The initial Nash equilibrium is N is where downward-sloping reaction functions for the domestic downstreamand F₁ and foreign downstream firms F₂ cross each other, their equilibrium outputs being x₁ and x₂ respectively, with associated profits of π₁ and π₂. If only a domestic carbon tax is imposed upstream, we assume this is passed through to the domestic downstream firm as a change in its costs dc₁, which shifts its reaction function to F'₁ the new Nash equilibrium being at N*. The net result is that the foreign downstream firm aggressively increases its output as well as profits which comes at the expense of the domestic downstream firm, i.e., there is a loss in the latter's competitiveness as well as positive carbon leakage in the foreign country.

If a BTA is allowed for, the pass-through of the domestic carbon price still shifts the domestic downstream firm's reaction function to F'₁while the BTA shifts the foreign downstream firm's reaction function from F2 to F2 the new Nash equilibrium being N', such that the foreign downstream firm's output remains at x₂ = x₂, resulting in no foreign carbon leakage. However, even with a trade neutral BTA, the domestic downstream firm reduces its output to x₁, its profits falling to π'₁, while the foreign downstream firm's profits increase to π'₂. Consequently, while the carbon leakage problem can be solved, competitiveness of the domestic downstream firm cannot be maintained.

Under import-share neutrality, the combination of the carbon price and BTA increases the profits of both the domestic and foreign downstream firms in both the strategic substitutes and complements cases. In order to see this, first derive dx, and dx₂ from (12), assuming α = α₁ ≈ α₂, and substituting in for dc₂ from (23):

As Δ^-1> 0, α < 0, dc₁ > 0 and for strategic substitutes, r_i < 0, then dx₁ < 0 and dx₂ < 0. For strategic complements, r_i > 0, so again, dx₁ < 0 and dx₂ < 0. Substituting (28) and (29) into (25) and (26):

For strategic substitutes, r_i< 0, and in addition, in (30), p _1,2 < 0, Δ^-1> 0, a < 0, and [.] 2 0 while in (31), p_2,1< 0, Δ^-1> 0,α<0 and [.] > 0. Therefore, as long as p_1,2 Δ^-1α[.]> 1 in (30), and also that p_1,2Δ^-1αdc₁[.]>dc₂ in (31), then it follows that dπ₁ >0, and dπ₂ >0. The same holds for strategic complements.

For import-share neutrality, the competitiveness effect is illustrated in figure 3 for the case of strategic substitutes. The initial Nash equilibrium is again at N, equilibrium outputs being x₁ and x₂ respectively, with associated profits of π₁ and π₂. Note that this equilibrium lies on the line denoted k = {x₂/( x₂ + x₁)}. This line represents constant market share for the foreign firm, where in figure 2 it is drawn to show a symmetric equilibrium of k = 0.5, i.e., the foreign downstream firm has a fifty percent market share. Pass-through of the domestic carbon price shifts the domestic downstream firm's reaction function to Fl, the new Nash equilibrium again being at N*. The net result is that the foreign downstream firm aggressively increases its market share as well as profits which comes at the expense of the domestic downstream firm, i.e., there is a loss in the latter's competitiveness as well as positive carbon leakage in the foreign country.

If a BTA is allowed for, the pass-through of the domestic carbon price still shifts the domestic downstream firm's reaction function to F'₁, while the BTA shifts the foreign downstream firm's reaction function from F₂ to F'₂ the new Nash equilibrium being N'. The net result is that domestic and foreign downstream firms decrease their output to x'₁ and x'₂ respectively, the foreign downstream firm's market share remaining constant at k. Importantly, reduction in the foreign firm's output not only generates negative carbon leakage, but profits of the domestic downstream firm also increase to π'₁ as collusion between the domestic and foreign downstream firm is facilitated, i.e., competitiveness of the former is more than maintained through use of the BTA.

While there is no explicit political economy set-up in this model, one would expect the domestic downstream firm to lobby for trade neutrality to be defined in terms of market-share as it improves its competitiveness by moving into the Pareto-superior profit set bounded by the iso-profit contours π₁ and π₂. In contrast, its foreign competitor would prefer trade neutrality to be defined in terms of market-volume where it maintains its exports, and earns higher profits, moving the domestic downstream firm outside of the Pareto-superior profit set. Of course, in either case, even though trade neutrality and no carbon leakage are ensured, the aggregate reduction in output of the final good generates a deadweight loss to consumers. Minimizing the costs of the latter distortion would necessarily have to be taken into account if the carbon tax were being set optimally.¹⁷

 

Summary and Conclusions

The analysis presented in this paper is motivated by the fact that proposed climate legislation often includes some type of border measure to be targeted at energy-intensive imports. The argument for including such measures is not only the possibility that import-competing firms will become less competitive following unilateral implementation of domestic climate policy, but that there will be carbon leakage as market share shifts to foreign firms. In this context, the main contribution of this paper is analysis of the impact of climate policy and border measures in a setting that reasonably characterizes the industrial organization of the import-competing energy-intensive sectors, such as steel and aluminium production. Once oligopoly in the latter sectors is allowed for, competitiveness can be defined in terms of rent-shifting between domestic and foreign firms. Importantly, the extent of carbon leakage and reduction in competitiveness are both shown to be very dependent on how downstream firms interact with each other in the presence of policies that affect their costs of production. Specifically, it matters whether firms compete more or less aggressively with each other in response to each other's output changes, i.e., whether their strategies are modelled as strategic substitutes or complements, captured in the model by the slope of firms' reaction functions.

Assuming that the WTO/GATT rules on border tax adjustments apply in the context of carbon pricing initially borne by producers of an intermediate good but passed on to producers of a final good, the key consideration in the paper is whether such adjustments will jointly resolve the issues of carbon leakage and loss of competitiveness by domestic downstream firms. Using a model of successive oligopoly where an intermediate good, electricity, is used in the energy-intensive production of a final good such as steel, it has been shown that the level of any downstream border tax adjustment is dependent on the nature of oligopolistic competition at both upstream and downstream stages, vertical incidence of the carbon price, and how competitive equality between domestic and foreign downstream firms is defined.

Importantly, if the WTO/GATT rules on border tax adjustments are based on maintaining the volume of final good imports, and firms' output strategies are strategic substitutes, there will be no carbon leakage, domestic firm(s) incurring a reduction in output and lost profits and hence their competitiveness. In addition, this rule would rule out setting border tax adjustments targeted at the emissions level of foreign electricity producers. Alternatively, if the WTO/GATT rules on border tax adjustments are interpreted in terms of maintaining the share of final good imports, global carbon emissions are actually reduced for both strategic substitutes and complements, and the competitiveness of domestic firm(s) is improved due to the combination of policy instruments acting to facilitate downstream collusion. It should also be noted that in both interpretations of the WTO/GATT rules on border tax adjustments, consumers actually suffer a deadweight loss due to aggregate output of final goods being reduced in an oligopolistic setting.

As noted in the introduction, a key issue in implementation of measures at the border for domestic climate policy is the extent to which an internal tax on carbon affects the costs of downstream energy-intensive sectors. The main conclusion to draw from this paper is that failure to account for the extent to which climate policy is passed through a vertical market system, and the response of downstream oligopolistic firms to changes in their costs has important implications for the implementation of WTO/ GATT consistent border tax adjustments. Consequently, industrial organization does matter to the analysis of climate policy and border tax adjustments -something that other studies of this issue, such as Mattoo et al. (2009), do not explicitly account for in their analysis.

 

References

Abiru, M. (1988). "Vertical Integration, Variable Proportions and Successive Oligopolies," Journal of Industrial Economics 36 (3):315-325.         [ Links ]

Azzam, A., Rosenbaum, D. (2001). "Differential Efficiency, Market Structure, and Price," Applied Economics 33 (10): 1351-1357.         [ Links ]

Barrett, S. (1994a). "Self-Enforcing International Environmental Agreements," Oxford Economic Papers 46 (October): 878-894.         [ Links ]

Barrett, S. (1994b). "Strategic Environmental Policy and International Trade," Journal of Public Economics 54 (3): 325-338.         [ Links ]

Bolle, F. (1992). "Supply Function Equilibria and the Danger of Collusion," Energy Economics, 14 (2): 94-102.         [ Links ]

Borenstein, S., Bushnell, J. (1999). "An Empirical Analysis of the Potential for Market Power in California's Electricity Industry," Journal of Industrial Economics 47 (3):285-323.         [ Links ]

Bulow, J. I.; Geanakopolos, J. D., Klemperer, P. D. (1985). "Multi-Market Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy 93 (3): 488-511.         [ Links ]

Burniaux, J-M.; Martin, J. P., Oliveira-Martins, J. (1992). "Trade and the Effectiveness of Unilateral CO₂ Abatement Policies: Evidence from GREEN," OECD Economic Studies 19 (December):123-140.         [ Links ]

Carraro, C., Siniscalco, D. (1993). "Strategies for the International Protection of the Environment," Journal of Public Economics 52 (3): 309-328.         [ Links ]

Conrad, K. (1993). "Taxes and Subsidies for Pollution-Intensive Industries as Trade Policy," Journal of Environmental Economics and Management 25 (2): 121-135.         [ Links ]

Conrad, K. (1996). "Optimal Environmental Policy for Oligopolistic Industries under Intra-Industry Trade," in Carraro, C.; Katsoulacos, Y, Xepapadeas, A. (eds.), Environmental Policy and Market Structure, Dordrecht: Kluwer Academic Publishers: 65-83.         [ Links ]

Copeland, B. R., Taylor, M. S. (2003). Trade and the Environment: Theory and Evidence, Princeton, NJ: Princeton University Press.         [ Links ]

Copeland, B. R., Taylor, M. S. (2004). "Trade Growth and the Environment," Journal of Economic Literature 42 (1): 7-71.         [ Links ]

Demailly, P., Quirion, P. (2008). "European Emission Trading Scheme and Competitiveness: A Case Study on the Iron and Steel Industry," Energy Economics 30 (4): 2009-2027.         [ Links ]

Denicolo, V., Garella, P. G. (1999). "Market-Share Import Restraints in Oligopoly," Review of International Economics 7 (4): 732-743.         [ Links ]

Fowlie, M. (2009). "Incomplete Environmental Regulation, Imperfect Competition, and Emissions Leakage," American Economic Journal: Economic Policy 1(2): 72-112.         [ Links ]

Frankel, J. (2009). "Environmental Effects of International Trade," A Report for the Swedish Globalization Council, Government of Sweden, mimeo, Boston, MA: Harvard University.         [ Links ]

Gallet, C. A. (1996). "Mergers and Market Power in the US Steel Industry," Applied Economics Letters 3 (4): 221-223.         [ Links ]

Green, R. (1996). "Increasing Competition in the British Electricity Spot Market," Journal of Industrial Economics 44 (2): 205-16.         [ Links ]

Green, R., Newberry, D. (1992). "Competition in the British Electricity Spot Market," Journal of Political Economy 100 (5): 929-953.         [ Links ]

Hoel, M. (1992). "International Environment Conventions: The Case of Uniform Reductions of Emissions," Environmental and Resource Economics 2 (2): 141-159.         [ Links ]

Hoel, M. (1994). "Efficient Climate Policy in the Presence of Free Riders," Journal of Environmental Economics and Management 27 (3): 259-274.         [ Links ]

Hoel, M. (1996) "Should a Carbon Tax be differentiated Across Sectors," Journal of Public Economics 59 (2): 17-32.         [ Links ]

Horn, H., Mavroidis, P. C. (2010). "Border Carbon Adjustments and the WTO," Working Paper, London: Centre for Economic Policy Research.         [ Links ]

Houser, T.; Bradley, R.; Childs, B.; Werksman, J., Heilmayr, R. (2008). Leveling the Carbon Playing Field, Washington DC: Peterson Institute for International Economics, and World Resources Institute.         [ Links ]

Ishikawa, J., Spencer, B. J. (1999). "Rent-Shifting Export Subsidies with an Imported Intermediate Product," Journal of International Economics 48 (2): 199-232.         [ Links ]

Karp, L. (2010). "Reflections on Carbon Leakage," Working Paper, Berkeley, CA: Department of Agricultural and Resource Economics, University of California.         [ Links ]

Kennedy, P. W. (1994). "Equilibrium Pollution Taxes in Open Economies with Imperfect Competition," Journal of Environmental Economics and Management 27 (1): 49-63.         [ Links ]

Leahy, D., Neary, J. P. (2001). "Robust Rules for Industrial Policy in Open Economies," Journal of International Trade and Economic Development 10 (4): 393-409.         [ Links ]

Lockwood, B.; de Meza, D., Myles. G. (1994). "When Are Origin and Destination Regimes Equivalent?" International Tax and Public Finance 1 (1): 5-24.         [ Links ]

Lockwood, B.; Whalley, J. (2010) "Carbon-Motivated Border Tax Adjustments: Old Wine in Green Bottles?" The World Economy 33(6):810-819.         [ Links ]

Maestad, O. (1998). "On the Efficiency of Green Trade Policy," Environmental and Resource Economics 11 (1): 1-18.         [ Links ]

Markusen, J. R. (1975). "International Externalities and Optimal Tax Structures," Journal of International Economics 5 (1) 15-29.         [ Links ]

Mattoo, A.; Subramanian, A.; van der Mensbrugghe, D., He, J. (2009). "Reconciling Climate Change and Trade Policy." CGD Working Paper, 189, Washington, D.C.: Center for Global Development.         [ Links ]

McCorriston, S., Sheldon, I. M. (2005a). "Market Access and WTO Border Tax Adjustments for Environmental Excise Taxes under Imperfect Competition," Journal of Public Economic Theory 7 (4): 579-592.         [ Links ]

McCorriston, S., Sheldon, I. M. (2005b). "Export Competition and the Remission of Domestic Environmental Taxes," International Tax and Public Finance 12 (5): 627-637.         [ Links ]

Mei, B., Sun, C. (2008). "Assessing Time-Varying Oligopoly and Oligopsony Power in the U.S. Paper Industry," Journal of Agricultural and Applied Economics 40 (3): 929-939.         [ Links ]

Messerlin, P. A. (2012). "Climate and Trade Policies: From Mutual Destruction to Mutual Support," World Trade Review 11 (1): 53-80.         [ Links ]

Monjon, S., Quirion, P. (2010). "How to Design a Border Adjustment for the European Union Emissions Trading System?" Energy Policy 38 (9): 5199-5207.         [ Links ]

Pauwelyn, J. (2007). "U.S. Federal Climate Policy and Competitiveness Concerns: The Limits and Options of International Trade Law," Working Paper, 07-02, Durham, NC: Nicholas Institute for Environmental Policy Solutions, Duke University.         [ Links ]

Perroni, C., Rutherford, T. F. (1993). "International Trade in Carbon Emission Rights and Basic Materials: General Equilibrium Calculations for 2020," Scandinavian Journal of Economics 95 (3): 257-278.         [ Links ]

Pezzey, J. (1992). "Analysis of Unilateral CO2 Control in the European Community and OECD," The Energy Journal 13 (3): 159-171.         [ Links ]

Ponssard, J. P., Walker, N. (2008). "EU Emissions and the Cement Sector: A Spatial Competition Analysis," Climate Policy 8 (5): 467-493.         [ Links ]

Poterba, J. M., Rotemberg, J. M. (1995). "Environmental Taxes on Intermediate and Final Goods When Both Can Be Imported," International Tax and Public Finance 2 (2): 221-228.         [ Links ]

Ritz, R. A. (2009). "Carbon Leakage under Incomplete Environmental Regulation: An Industry-Level Approach," Discussion Paper Series, No. 461, Oxford: Department of Economics, University of Oxford.         [ Links ]

Salinger, M. A. (1988). "Vertical Mergers and Market Foreclosure," Quarterly Journal of Economics 103 (2): 345-356.         [ Links ]

Sleuwaegen, L.; Belderbos, R., Jie-A-Joen, C. (1998). "Cascading Contingent Protection and Vertical Market Structure," International Journal of Industrial Organization 16 (6): 697-718.         [ Links ]

Stavins, R. N. (1998). "What Can We Learn from the Grand Policy Experiment? Lessons from SO2 Allowance Trading," Journal of Economic Perspectives 12 (3): 6988.         [ Links ]

Stavins, R. N. (2003). "Experience with Market-Based Environmental Policy Instruments," in Mäler, K. G.; Vincent, J. R. (eds.), Handbook of Environmental Economics Volume 1, Amsterdam: North Holland: 355-435.         [ Links ]

Taylor, M. S. (2004). "Unbundling the Pollution Haven Hypothesis," Advances in Economic Policy and Analysis 4 (2): Article 8.         [ Links ]

Ventosa, M.; Baillo, A.; Ramos, A., Rivier, M. (2005). "Electricity Market Modeling Trends," Energy Policy 33 (7): 897-913.         [ Links ]

Weitzman, M. L. (1974). "Prices vs. Quantities," Review of Economic Studies 41 (4):477-491.         [ Links ]

WTO. (1997) "Taxes and Charges for Environmental Purposes-Border Tax Adjustments, Committee on Trade and the Environment," WT/CTE/W/47, Geneva: World Trade Organization.         [ Links ]

WTO/UNEP (2009). Trade and Climate Change, Geneva: WTO Secretariat.         [ Links ]

Yang, S-P. (2001). "Measuring Market Power in the U.S. Aluminum Industry: A Residual Demand Approach," Review of Industrial Organization 19 (3): 365-380.         [ Links ]

 

Notas

* The authors would like to thank anonymous reviewers for their comments on an earlier version of this paper, as well as participants in seminars at North Carolina State University, the Economic Research Service, USDA, the University of Guadalajara, the University of Guanajuato, and the University of Monterrey.

³ In the 111th US Congress, a climate bill sponsored by Representatives Waxman and Markey and passed by the US House of Representatives would have established a cap-and-trade system similar to that being operated in the EU.

⁴ The US implemented a cap-and-trade system for sulfur dioxide emissions in 1990, which subsequently proved very successful in controlling acid rain pollution from coal-burning electricity generating plants (Stavins, 1998).

⁵ Weitzman (1974) has shown the conditions under which a quantity-based instrument, such as tradable permits, will be more efficient compared to a price instrument such as a carbon tax.

⁶ This idea is often expressed in terms of the 'pollution haven hypothesis', which is a rather strong theoretical result, for which there is rather weak empirical support (Copeland and Taylor, 2004). This follows from the fact that trade specialization will be affected by other determinants of comparative advantage. However, there is more empirical support for the related 'pollution haven effect' whereby implementation of tougher environmental policy in one country deters its exports (encourage its imports) of goods that embody a public bad (s) (Taylor, 2004).

⁷ A similar result was derived in an earlier paper by Markusen (1975).

⁸ For example, see Pauwelyn (2007), Horn and Mavroidis (2010), and Messerlin (2012).

⁹ In the case of a domestic regulation on carbon emissions, Pauwelyn (2007) argues that imposition at the border of a similar regulation on imports of energy-intensive products is less likely to withstand WTO scrutiny.

¹⁰ It should be noted that we assume that there is no bargaining over upstream prices. This is a common assumption in models of successive oligopoly. Adapting a rationale for this provided by Ishikawa and Spencer (1999), it is assumed that the upstream electricity-producing firms sell to a large number of different downstream sectors, reducing any monopsony power one individual downstream sector may have.

¹¹ Nash equilibrium here is based on the idea that no firm can do better than its equilibrium output choice, given the output choice of its rival(s).

¹² Whether we have strategic substitutes or complements in quantity space depends on the second derivatives of the demand function (see Ishikawa and Spencer, 1999; and Leahy and Neary, 2001).

¹³ In recent empirical analysis, Mattoo et al. (2009) find significantly different trade effects of BTAs depending on whether they are based on the carbon content embodied in final goods produced in the importing country or the carbon content embodied in the imported goods.

¹⁴ For example, a linear, or more generally a weakly convex demand function will generate under-shifting.

¹⁵ Note that including the upstream sector generalizes the impact of the domestic carbon price and hence what the appropriate BTA should be. If the upstream sector were perfectly competitive, then the incidence of the carbon price in the upstream sector would not matter. In this case dc₁=1 the neutral BTA being equal tor₂.

¹⁶ This assumption relates to the relative slopes of the reaction functions, implying that firm 1's reaction function is steeper, in absolute terms than that of firm 1, which is necessary to ensure stability of equilibrium.

¹⁷ While the domestic carbon price is treated as exogenous in this paper, it could be derived explicitly from maximizing a social welfare function that takes into account consumer surplus, profits of downstream domestic firm(s) as well as the externality due to carbon emissions (see Conrad, 1996).