Environmental Regulation of a Global Pollution Externality in a Bilateral Trade Framework: The Case of Global Warming, China and the US

Bilateral trade and capital flows have increased substantially between the United States and China yielding economic gains to both countries. However, these beneficial bilateral relations also bring about global environmental consequences including greenhouse gas emissions. We develop a footloose capital model of international trade between the North (United States) and the South (China) in the presence of a global pollution externality. Each country's share of global pollution depends on its share of world capital. We show that, if the disutility of pollution in the United States is high, there will be pressure on the US to raise environmental regulations on industry. Capital will move to China. Because the increased pollution in China has global effects, the US may not benefit from the environmental restrictions and a joint regulation of pollution by both parties may be a preferred outcome. We also show that the implementation of differential control policies by the parties may also be optimal. JEL D43 Q54 F18


Introduction
One of the few bright spots in recent international negotiations to replace the expiring Kyoto Protocol on curbing global greenhouse gas (GHG) emissions has been the framework agreement concluded at the 17 th Conference of the Parties (COP17) that took place in Durban, South Africa in December 2011. In addition to extending the Kyoto Protocol, COP17 produced the Durban Platform for Enhanced Action as the foundation for a prospective and comprehensive climate change agreement in 2015. However, the Durban Platform is most notable for securing the tentative inclusion of the United States and Chinathe world's two biggest GHG emitterswho were not signatories to the Kyoto Protocol (Ewing 2012). The signing of the Durban Platform by United States and China accords with the view expressed by some scholars that closer bilateral trade and economic ties between the two countries would foster their cooperation on a number of global issues, including combating climate change (Antholis 2009;Foot 2010;Foot and Walter 2012;Lieberthal and Sandalow 2009). As argued by Foot and Walter (2012, p.20), "…globalization…has greatly raised the importance of the bilateral China-US relationship. Both countries have increasingly assessed the merits of behavioural convergence with a range of global norms." The purpose of the following paper is to explore how bilateral trade and capital relationships might provide the incentives for increased cooperation over a global pollution problem. We consider the United States and China to be the prime examples of this bilateral framework, and greenhouse gas emissions and global warming to be the transboundary pollution problem.

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International trade and capital flows between countries can function as important drivers to improve efficiency and economic development by improving the allocation of resources (Krugman 2008). Industrialized countries such as the United States (US) are increasingly trading with developing countries such as China. US exports accounted for 8.42% of its GDP in 2007, with around 17% of its imports (US$323 billion) originating from its largest trading partner China (Xu et al. 2009). The bilateral trade between the US and China continues to grow substantially, as has capital flows between the two countries (Broda and Weinstein 2006). US foreign direct investment in Chinese stocks was estimated at $49.4 billion in 2009, and Chinese investment in the US was US$791 million (USTR 1995).
The United States and China benefit enormously from these bilateral trade and capital flows. However, international trade also brings considerable environmental consequences in both the country of origin and destination (Xu et al 2009, Peters and Hertwich 2008, Shui and Harriss 2006. The US and China dominate global greenhouse gas (GHG) emissions from carbon dioxide and similar pollutants. In the past century, the US emitted more GHGs than any other country (Lieberthal and Sandalow 2009).The US has been responsible for approximately 29% of energy-related carbon dioxide emissions since 1950, and China for about 8% over the same period (Foot 2010). However, by 2007 China surpassed the US as the world's top annual emitter of carbon dioxide (Antholis 2009). The two countries are responsible for 40% of the GHGs released to the atmosphere each year.
Some scholars have suggested that the growing economic ties between the United States and China may be the key to resolving global environmental problems, such as ~3~ controlling GHGs to mitigate climate change. For example, Lieberthal and Sandalow (2009) argue that the increasing bilateral trade between the US and China will eventually foster their mutual interest to engage in bilateral negotiation and cooperation on the regulation of GHGs. Lieberthal and Sandalow (2009) suggest that this incentive to cooperate will also contribute to the success of multilateral climatic negotiations, given that China and the United States account for a large share of global GHG emissions.
Similar arguments, that the close economic relations between the US and China will lead to greater cooperation on global environmental issues, have been put forth by Antholis (2009), Foot (2010 and Foot and Walter (2012). Antholis (2009) suggests that the US and China need to focus on concrete partnerships as a way of demonstrating progress and cooperation between the two nations. (Foot 2010) argues that cooperation between China and the US is vital for addressing global economic crisis and global challenges such as climatic change. Foot and Walter (2012) state the US and China are two important countries that are central to the global economy and climatic protection.
The two states are very pivotal to the evolution of the global climatic control policy Our paper seeks to analyze how the increasing bilateral trade and capital relationships between the US and China might influence their policy coordination over a global pollution externality, such as climate change. With global pollution, and international mobility of factors, environmental policies by an individual region will have an effect on its competitiveness, ability to attract capital to its jurisdiction, and positive external benefits that accrue to other region. Therefore the important question that we seek to analyze is what are the implications of unilateral and bilateral coordinated policy ~4~ approaches to control of a global pollution externality in the context of a bilateral trade and capital investment relationship?
The interaction between trade and global pollution externalities has been considered by a number of studies. These include, an analysis of the effect of global pollution on trade and welfare (Benarroch and Thille 2001), the design of international schemes to control global pollution externalities (Caplan and Silva 2007), an analysis of the effect of global pollution on trade (Suga 2007;Benarroch and Weder 2006) and an analysis of non-cooperative and cooperative policy approaches to control global pollution (Duval and Hamilton 2002;Zheng and Zhao 2009;Rieber and Tran 2009). Rieber and Tran (2009) show that the unilateral action by a developed country drives industrial firms out of the region and lowers real incomes. Duval and Hamilton (2002) find that inefficient high environmental taxes may be optimal for a net exporting region in noncooperative circumstances, as the motive to shift rents by selecting an inefficiently low tax rate is countervailed by incentives to shift the burden of the tax to foreign consumers. Zheng and Zhao (2009) show that a pollution haven may arise if environmental regulation is slightly more stringent in the larger region compared to the smaller region.
A number of studies have also explored the conditions under which international environmental cooperation is possible. For example, de Zeeuw (2008) shows that, in a dynamic game, cooperation depends on the relative costs of emission abatement of the negotiating parties. Rubio and Ulph (2007) find that cooperation between parties decreases as the steady-state pollution stock and the cost of damages rise. Carraro and Siniscalco (1998) find that partial coalitions and multiple arrangements tend to prevail ~5~ among a sub-set of negotiating parties, whereas agreement among all parties is unlikely to exist.
Our paper contributes to this literature on global policy by developing a theoretical model to explore how bilateral trade and capital relationships might provide incentives for increased cooperation to control a global pollution externality, GHG emissions. We incorporate three features of US-China relations in our model: bilateral trade, capital flows and the presence of a global pollution externality between the regions.
The two-region economy produces an indigenous set of goods supplied by imperfectly competitive firms. We allow for transaction costs in international trade, which raise the cost of imported goods and induce home bias in consumption. We incorporate structural differences between a relatively rich (United States) and a poor region (China) in terms of differential factor endowments and technology.
Our paper incorporates a framework on differential factor endowments, lack of factor price equalisation and cross-country technological differences following the work of Kikuchi and Shinomura (2007) and Behrens et al. 2009. The paper applies a general equilibrium analysis approach to compare the unilateral and the coordinated bilateral equilibria's shares of manufacturing firms and tax levels. We examine the resulting welfare effects from a comparison of the unilateral and bilateral coordinated policy approaches to control a global pollution externality.
Our main results are as follows: when the disutility of pollution in the US is high, there is pressure in the US for tighter environmental regulations on industry. Capital flows to China, and pollution there increases. If the pollution in China has global effects, as the case with GHG emissions and climate change, then the US may not be better off ~6~ from unilaterally imposing environmental measures that limit domestic pollution only.
Instead, joint regulation of the pollution generated by both regions may be a preferred outcome. This joint regulation can be achieved by two countries taking on differential levels of investments to reduce global pollution, and thus supporting the principle of common but differentiated responsibility in global policy. The implication of the study is that it is beneficial for the US and China to engage in bilateral arrangements to control a global pollution externality, as it promotes trade and development while protecting the environment.
The modelling approach we take in this paper is different from the main tax competition literature such as Markusen et al. (1995), in that we include agglomeration and regional asymmetry to the model. Nevertheless, the results of our paper complement the main tax competition results in the literature as we find that the principle of common but differentiated responsibilities is one of the optimal policies to tackling global pollution externalities.
The paper is outlined as follows; the next section presents the economic model, section three discusses unilateral and coordinated policy choices and section four concludes.

The economic model
The model developed is a variant of the footloose capital model (Martin and Rogers 1995;Baldwin 1999;Baldwin et al 2003). The footloose capital model is relevant given the relative free flow of capital between our two representative regions, the US and China (Blinder 2009;MacCauley 2003). We develop a linear economic geography model ~7~ with mobile capital and without income effects. This choice is due to low mobility of labour between these countries. In this footloose capital model, location of mobile capital is determined by an arbitrage condition that equalises profits across countries, and we analyse the case of perfect capital mobility. The stock of capital is exogenous, and the value of capital is given by its profit.
Consider an international economy consisting of two regions, each having two sectors and two factors of production, capital and labour. Physical capital, K , is fully mobile between the two regions, but the owners of capital do not migrate. Labour, L , however, is immobile. We treat the two regions as separate nations (US and China). We will therefore refer to the two regions as "North" and "South", and we assume that the two regions have identical preferences but differ in terms of the disutility of pollution, factor endowments and technology. In this model we will treat the North as relatively abundant in capital endowments (high / KL ratio) compared to the South. The South is abundant in labour resources compared to the North. We adopt the conventional notation of distinguishing Northern from Southern variables by denoting the latter by an asterisk.
Each economy consists of two sectors, the composite goods sector, and the differentiated manufacturing goods sector. Production of the homogenous goods occur using labour only as an input. In each region, each firm produces a differentiated manufactured variety using labour and capital as inputs. Production of differentiated manufactured varieties produces a global pollution externality that negatively affects the global citizens. A global pollution externality is defined as an externality in which consumers will bear the cost regardless of where production occurs. In each region, each firm is charged a per unit tax on emissions that is distributed as a lump sum to local ~8~ consumers. The consumers own the capital and supply labour for production. They derive utility from consumption of the composite and differentiated manufacturing goods.

The consumers
Consumers in each region are identical and factor ownership is equally distributed across households. We assume that a Northern consumer own In addition, we model a tax transfer from producers to consumers. Let us assume that each industrial firm is taxed at the rate of t on the global pollution externality, and that the tax revenue is redistributed lump sum to all households in a region. A representative Northern consumer's budget constraint is; where the right hand side is income and left hand side is expenditure. c C is the consumption of composite numeraire good, i c is the consumption of Northern domestic 1 Given that physical capital is fully mobile between regions, K , K  are endogenously determined. The initial factor endowments assumption plays no role in the determination of the capital analysis; it plays a role in the wealth consumers in the two regions. , ~9~ differentiated manufactured good, j c denotes the imported and consumed quantity of a Southern differentiated good, and is the Samuelson iceberg transport cost mark-up. If trade costs are high then a large portion of the goods produced will melt in transit, thus will not actually be consumed by the consumer. Thus i p and j p  are the price of Northern and Southern goods, respectively, and K and K  is the level of capital. The total amount of capital varieties is given by w K K K   . An analogous budget function holds for the Southern consumer, which is denoted by an asterisk.
In each region a representative consumer has preferences given by the following quasi-linear utility function (Neary 2006).
as a measure substitutability of manufactured product varieties, such that goods. We assume that pollution is a pure public bad with global effects, and consumers in each region are negatively affected by total current emissions from world production, W E . 2 We assume that the disutility from emission is linear, implying a constant marginal disutility from emissions, This is a standard assumption to improve tractability of the model that has been used in literature, for example Pfluger 2001.

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A representative consumer maximises utility by choosing to consume a continuum of the differentiated manufactured products, yielding the following inverse demand functions; By symmetry, the inverse demand functions for a representative Southern consumer are analogous.
Given the identical technology and factor endowment assumptions within a particular region, the prices for these varieties are identical and therefore the arguments The aggregate demand for manufactured varieties produced in the North consists of domestic demand and demand from the South. Manufactured products produced in the North are traded costless within the region, but when manufactured products are imported, a trade cost of  is charged and the consumer price increases. The demand for the manufactured commodity produced in the North and the South equals 3 A region's income is composed of the wage income from labour within that region, and return to capital augmented with the lump sum redistribution of pollution 3 The local consumption c is composed of total foreign and domestic demand.
The aggregate incomes for the North and South are respectively The income of the representative household is greater in the North than in the South given that On average the aggregate incomes for the North should be larger compared to that of the South. However the incomes in the South may be larger than that of the North if a larger share of manufacturing firms locates in the former region. In this case the Southern consumers' augment their incomes from lump sum tax redistribution.
Substituting the inverse demand functions (3a, b) into utility equation (2) gives the Northern and Southern consumers' indirect utility functions 5 ; 4 The incomes in the northern region are higher compared to the southern region iff From the Northern consumer's utility function: Finally we provide an aggregate welfare in both regions as given by; Total welfare consists of total utility derived from consumer commodities and the expected damages from global pollution externality. Welfare from manufactured good consumption increases when the capital varieties increase. However, the consumers are negatively affected by the global pollution generated by both local capital and capital located in the foreign region. There is no trade-off between firm location and global pollution externality. Increasing the capital varieties in a region increases welfare to its consumers but does not alter the magnitude of expected damages from global pollution.
The welfare loss from the expected damages may be larger in the South where there is a larger population compared to the North.

The composite goods sector
The supply side of the composite goods sector is assumed to produce a homogenous good using only labour as an input, under Walrasian conditions of constant returns to scale technology and perfect competition. The composite goods sector is extremely simple in that there is no increasing returns, perfect competition and the good is traded costlessly between the two regions. The cost function for production of the good is C wa , where w is the labour wage rate and C a is the unit input coefficient. We assume that the two regions have differing technologies such that /1 CC aa   , in which compared to the South, the North exhibits an absolute advantage in the homogenous goods sector.
This provides a simple way to account for international factor price differences driven by Ricardian variations in labour productivity Behrens et al (2009). From equation (1), given that the composite good is a numeraire good, we have * 1 cc pp  Perfect competition means that equilibrium is achieved where marginal cost is equal to the marginal revenue or price, we have 1 . Costless trade will equalize the Northern and Southern prices; and wages 1/ C wa  and * / CC w p a   must hold for all regions provided some numeraire production takes place everywhere. The North's wage w is greater than the South's wage w  due to a higher labour productivity. The Northern consumers are richer than their Southern counterparts.

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The differentiated goods manufacturing sector The manufacturing sector is monopolistically competitive and faces increasing returns in production of differentiated varieties. The production of a typical variety of manufactured goods includes the services of one capital input 6 , which is the fixed cost, and D a units of labour for each unit of output produced. We assume variations in labour productivity across regions, allowing for cross regional technological differences such , then no region has a comparative advantage over the other in the manufacturing goods sector.
We assume that production of differentiated varieties brings about a pollution externality that negatively affects all the global citizens. The pollution is a negative externality associated with production at the firm level. Following an approach by Elbers

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and Withagen (2004)   is the level of regional investment in pollution reduction, x is the total output produced by a firm in the Northern region. High values of  indicate stronger investments in pollution reduction effort. This may include regulations and investments in alternative sources that limit the pollution. Under this scenario, the pollution function represents or exhibits constant returns to scale with respect to the level of capital (Benarroch and Thille 2001). We assume that investments in pollution reduction increase the costs of the capital input.
In each region, the assumption that firms produce differentiated varieties using the same technology allows us to consider production and supply only by a representative firm (i.e., the indices i and j can be dropped to distinguish different firms).

The short-run
The number of manufacturing firms in both regions is assumed to be relatively large, which allows us to assume that each firm ignores the actions of other firms in choosing its outputs. Although in the long run, profits for each firm are eventually driven to zero by free entry and exit, in the short run each manufacturing firm is a monopolist in its own market segment. Each firm has in effect two markets, a domestic and a foreign market. Denoting each firm's total revenue from sales to both markets as The first order conditions are given by From the first-order conditions, the firm's sale prices in the local and export market are; The Southern firms have analogous price functions that are given by The firm charges a mark-up greater than its marginal cost of supply to the market.
The marginal cost for each firm involves the wage rate paid to the immobile labour and the per unit tax on emissions. As a result of free trade, the producer prices are equalised in the manufacturing sector. Therefore the manufacturing firm charges the same price for local and Southern markets. We assume that the iceberg tax is incorporated via the consumer budget constraint.

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The long run In the long run, free entry and exit will mean that a firm will produce at an equilibrium level of output where profits are zero, implying that operating profit will be sufficient to cover its fixed costs. Given that producer price is a constant mark-up over marginal cost, the operating profit earned on each unit produced is also constant. The For equilibrium to hold in which the labour market and the goods market clears the magnitude of the difference between ratio of labour productivity in the manufacturing sector and composite good sectors between the regions has to equal the difference in marginal tax payments. We agree that this might be a rather restrictive assumption which could hold by chance. 11 We have A representative Southern firm has an analogous equilibrium output function. As the North enjoys an absolute advantage in differentiated goods production, it is possible that the equilibrium output for a representative firm in the North is greater or equal to that of a representative firm in the South.
From equation (11) . Although the Northern region has absolute advantage in manufacturing, in this case the Southern region has comparative advantage. All the capital will locate in the Southern region.

Costs from Global Emissions
The costs occur as a result of the current and past accumulation of GHGs into the atmosphere, which last for a long period of time (IPCC 2007;USGCRP 2009). We assume that emissions in the next period are equal to emissions from the last period, since the total capital is fixed in the model. The emission level is damaging but it is also costly to abate. Following de Zeeuw (2008)

Equilibrium Analysis
Taking into account equations (12a, b), and equations ( The share of capital in a region is a decreasing function of the trade costs as To show the existence of the equilibria, we follow an approach outlined in Kikuchi and Shimomura (2007). If the firms exist in both regions, then firm profits must be identical in the two regions. Substituting the demand functions (3a, b) into equation Substituting for the mill pricing rule (10a,b) into *    , and simplifying yields; marginal labour costs adjusted for the differential rental rates of capital, weighted by the differential marginal labour cost between the two regions, net the rental rate of capital in the North.

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Using these results one sufficient condition for the co-existence of firms in both regions is that 0  , in which we have Defining an index as In the free trade equilibrium the profits must be zero. The equations are satisfied if the index 1  .
Therefore this implies the co-existence of capital in both regions. Manufacturing takes place in both regions despite the cross regional technology difference in the monopolistic competitive sector. If the index is 1  , then a core periphery equilibrium exists in which all the capital is located in the North.

Unilateral and bilateral coordinated policy approaches
We attempt to provide an answer to the important question: what are the welfare implications between a unilateral and a bilateral coordinated policy approach in a North-South international trade model with a global pollution externality? A unilateral approach is when an individual region reinforces its own environmental regulations by constraining the capital located in its jurisdiction. A coordinated approach is a bilateral agreement between the US and China, which we consider to be similar to joint welfare maximisation by a global planner who takes into account the needs of both regions to reinforce global ~25~ environmental regulations and the pollution externality. Thus, the global planner is assumed to be a proxy for bilateral coordination between the US and Chinaon the location of capital and the level of investments in pollution reduction between their respective regions. We compare the unilateral and bilateral coordinated equilibria in terms of the share of capital and pollution control investments between two regions. 15

Unilateral Optimization Equilibrium
We consider that the US and China unilaterally maximize the aggregate welfare within their regions by selecting the optimal level of capital , without taking into account the effect on global pollution on the other region. The aggregate welfare functions of the North and South are respectively Therefore the simplified welfare functions 16 can be written as The general approach used is similar to one used in tax competition literature by Oates and Schwab (1998) and Kunce and Shogren (2005). 16 Hence the welfare function is quadratic in level of capital ; therefore a region maximizes welfare by directly solving for the endogenous number of firms, for a given level of tax rate and pollution investment levels.
The optimal level of capital that maximizes a region's welfare is given by; Solving the first order conditions yields the optimal level of capital in the North and South as respectively 17 We can find the unilateral optimization equilibrium without finding a Nash Equilibrium because the welfare function is additively separable in domestic and foreign firms.
We carry out comparative static analysis on equation (  A core-periphery equilibrium also occurs under two contrasting conditions. The first is that both regions have identical investments in pollution control, the Northern region has a higher tax rate compared to the Southern region, and the ratios of the consumer disutility of pollution is greater than the inverse labour ratio, ie The second is that both regions have identical tax rates, the North region has a lower 20 For a symmetric equilibrium to occur, we The first term of F represents the benefits to consumers from importing manufactured goods variety. The second term represents the marginal contribution of a local firm to foreign expected damages. The last term denotes the shadow value of having an additional unit of capital in a jurisdiction. The magnitude of the three terms determines the magnitude of divergence between the unilateral and the coordinated optimal equilibria.
The unilateral and the coordinated optima are equal if 0 F  .This implies that the marginal benefits of importing Southern manufacturing varieties adjusted for the marginal social cost of pollution to Southern consumers from Northern production activities and the shadow value of having an additional firm is zero. Under the unilateral approach, a region is indifferent between having capital locate within or outside its jurisdiction, and its objectives coincide with that of the coordinated optimum. For policy, this implies that the unilateral optimal share of capital, taxes and the level of investments in pollution reduction coincide with that of the coordinated optimum. The unilateral equilibrium efficiently internalizes the externalities.
If 0 F  , then the unilateral optimal share of capital is less than the coordinated optimum. This implies that the marginal benefits of local Northern consumers from ~35~ importing the manufacturing varieties from abroad adjusted for the marginal social costs imposed on foreign consumers is greater than the shadow value of capital locating in a jurisdiction. Thus, from a policy perspective the unilateral equilibrium over-shoots the coordinated equilibrium by mandating higher taxes and investments in pollution reduction, and having a lower share of capital.
If 0 F  , then the unilateral share of capital is greater than that dictated by the coordinated optimum. This means that the marginal benefits of importation adjusted for spillover costs to foreign region from the local pollution activities, is less than the shadow value of having an additional unit of capital locate in a jurisdiction. Thus the unilateral equilibrium under-shoots the coordinated equilibrium in which firms mandate lower taxes and investments in pollution reduction so as to attract a larger share of capital compared to the coordinated optimum.
It is more likely that then the unilateral share of capital is greater than the coordinated optimum. We expect the unilateral decisions by regions to make less investment in pollution control efforts compared to the coordinated optimum, regions do not take into account the global externalities and the spill-over effects from pollution reduction investments, ie F . Each individual region would unilaterally mandate lower environmental standards, than those dictated by the coordinated optimal solution. This is a source of inefficiency, and regions are better off in coordinated equilibrium that internalizes the global pollution externalities and the positive spill-over benefits from pollution control efforts.
The key outcome of the model is that in a bilateral arrangement, regions can collaborate and implement differential commitments in environmental policy initiatives ~36~ and investment mechanisms to reduce a global pollution externality. The bilateral arrangement is more efficient and leads to the improvement in the global environment, compared to unilateral decisions. The implication of the study is therefore that except for a rare case discussed above, there are efficiency gains to be obtained if the US and China engage in bilateral agreements to control a global pollution externality , while promoting trade and development.

Conclusion
Bilateral trade and capital flows between the US and China increase the varieties of manufactured goods available to their consumer and promotes development. However this economic cooperation has environmental consequences, such as the emission of greenhouse gases (GHGs) that are a global pollution problem. If the disutility of pollution in the United States is higher, there will be pressure on the US government to impose more environmental regulations. This causes capital to migrate to China, and pollution increases there. However given the global nature of the emissions, the US may not be better-off unilaterally mandating environmental regulations because of the spill-over externality arising from a global pollutant such as GHGs. Thus a bilateral coordinated approach is more efficient in the regulation of the global pollution externality. The efficient coordinated solution can be attained between the US and China, allowing that the countries differ in pollution control investment levels, tax rates, quantities of labour employed in the manufacturing sector and the share of manufacturing. Consequently, a key contribution of our paper is to demonstrate that economic trade and capital flows between relatively rich and poor economies is not an obstacle to but possibly an incentive ~37~ for global cooperation on environmental regulation. To our knowledge, our analysis is the first to show explicitly that an important source of the efficiency gains from the US and China agreeing jointly to control a global pollution externality is the blilateral trade and capital flows that promote mutual development of both economies.
The policy implication of the study is that there is scope for bilateral coordination between the developed US and developing China on efforts to effectively control global pollution. This is a win-win situation for both countries in which development and trade, The paper also supports the idea that efficiency in regulating the global pollution externality can be achieved within the framework of common but differentiated responsibilities between the richer US and poorer China. Areas for further research may include a study of different policy approaches to protect the environment under common pool resources or resources or insecure property rights under international trade between the developing and the developed world.