Trade policy, cross-border externalities and lobbies: do linked agreements enforce more cooperative outcomes?

Journal of International Economics 67 (2005) 175 – 199 www.elsevier.com/locate/econbase

Trade policy, cross-border externalities and lobbies: do linked agreements enforce more cooperative outcomes? Nuno Lima˜o* Economics Department, University of Maryland, College Park MD 20742, U.S.A. Received 16 January 2003; received in revised form 17 April 2004; accepted 30 August 2004

Abstract We analyze whether linking international cooperation in trade policy to environmental policy (or other issues with nonpecuniary externalities) promotes more cooperation in both policies, or whether cooperation in one is strengthened at the expense of the other. In the context of self-enforcing agreements, we show that if the policies are independent in the government’s objective function, then linkage promotes cooperation in one policy at the expense of the policy that is easier to enforce under no-linkage. However, if the linked policies are not independent and if these policies are strategic complements, then linkage can sustain more cooperation in both issues than no-linkage. The policies are strategic complements only if (i) the production externality has cross-border effects; (ii) the weight on the externality cost is high; (iii) import competing lobbies are not bpowerfulQ. D 2004 Elsevier B.V. All rights reserved. Keywords: Trade; Linkage; Environment; Labor; Cross-border externality, repeated games JEL classification: F13; F18; F42; H23; H77

1. Introduction In trade policy agreements, trade concessions are increasingly made conditional on cooperation in nontrade issues, what is known as blinkageQ. This trend is clear in * Tel.: +1 301 405 7842; fax: +1 301 405 3542. E-mail address: [email protected]. 0022-1996/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jinteco.2004.08.009

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multilateral, bilateral, and regional trade agreements. Multilaterally, compliance with intellectual property rights is now enforced through the threat of import barriers, sanctioned by the World Trade Organization (WTO).1 Moreover, the trend to link will surely intensify. At the end of the last multilateral trade liberalization round, a long list of issues was proposed for similar treatment by the WTO including investment and competition policy, as well as labor and environmental standards. Therefore, linkage has become one of the most important and contentious issues in trade policy.2 Perhaps the most obvious role of linkage in agreements is not as an enforcement tool but rather as a side payment. If cooperation on an individual issue benefits country A but hurts B, then the agreement requires either a transfer to B or cooperation in a different issue that benefits B. The use of linkage as a side payment when there are asymmetric benefits across countries is important in the case of regional trade agreements between large and small countries (Abrego et al., 2001 and Lima˜o, 2002b), and it has also been analyzed in the context of environmental agreements (Cesar and de Zewe, 1996).3 Despite the prominence of linkage in policy debates, there is little theoretical support for it in terms of its impact on enforcement. The majority of work in the trade literature focuses on static standard trade models to examine what is the impact of harmonizing labor or environmental standards on factor and goods prices or welfare for different countries and economic agents.4 In this context, one of the most frequent objections to linkage, arising from the optimal policy targeting literature, is that btrade policy measures are usually not the best instruments for achieving social objectivesQ (Anderson, 1998, p. 244). However, we argue that the important policy question behind linkage is whether the threat of tariffs is effective in enforcing more cooperation in another agreement and vice versa. This question cannot be addressed by the targeting literature, which has no basic predictions regarding enforcement. To explain the motivation and consequences of linkage from an enforcement perspective, we must first understand two key features of international cooperative agreements. First, one of their main objectives is to internalize the costs of countries’ actions. When countries impose tariffs, they do not internalize any costs this may have 1

Bilaterally, the United States and the EU attach investment, environmental and labor clauses to trade preferences given to developing countries via the Generalized System of Preferences. Regionally, NAFTA includes an environmental and a labor agreement. 2 Including nontrade clauses in trade agreements is not an entirely new phenomenon (Charnovitz, 1998). The main difference is the willingness to enforce those clauses and the availability of effective mechanisms to do so such as the dispute settlement system of the WTO. Certain multilateral environmental agreements such as the Montreal Protocol on CFCs include the threat of trade restrictions in response to noncompliance. However, some of these measures are inconsistent with GATT rules and therefore according to the European Commission b...problems could arise if a country imposed a trade measure for environmental purposes on another WTO member which had not signed the multilateral environmental agreement. The EU wants WTO members to agree that this should not be allowed to happenQbhttp://trade.info.cec.int/europa/2001newroundN. 3 See also Horstmann et al. (2001) for the effects of linkage in the context of Nash bargaining. Conconi and Perroni (2000) use a cooperative approach to study the effect of linkage on blocking coalitions in a three-country model. For an early analysis of linkage in the political science literature, see Sebenius (1983). 4 See, for example, Esty (1994) and the volumes edited by Bhagwati and Hudec (1996) and Anderson and Blackhurst (1992).

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on foreigners, such as lower export prices. Reciprocal trade liberalization agreements allow countries to internalize these terms-of-trade effects (TOT; Bagwell and Staiger 1999). Similarly, cooperative agreements on issues with nonpecuniary negative externalities are required if that externality has a cross-border effect. Second, international cooperative agreements must be self-enforcing given the absence of a supranational authority to punish violators. That is, these agreements are subject to incentive constraints (IC) which balance the gains of deviating from the agreement against the ensuing losses from retaliation. If countries are not sufficiently patient, then the cooperative first-best is not feasible since the IC bind. Now, since the relevant set of IC for an agreement depends on which policies are available for retaliation, then so must the degree of cooperation. Given the nature of the agreements considered for linkage, it is clear that understanding its impact on enforcement is crucial. In this regard, one of the central objections put forward by opponents of linkage in trade agreements—that it will lower cooperation in trade policy—is very relevant.5 Therefore, the central question we ask is the following. Must linkage of trade and nontrade policies cause a reallocation of enforcement or can it actually create enforcement? That is, if in an international agreement we allow for retaliation across two policies, must cooperation in one always be strengthened at the expense of less cooperation in the other, or can linkage sustain more cooperation in both? To answer this, we focus on a two-country model where the traded goods generate a negative production externality which can have a cross-border effect. The noncooperative equilibrium features inefficiently high tariffs and low externality taxes (e-taxes henceforth) from a global perspective; governments overcome this through cooperative agreements. We assume a status quo of no-linkage, that is retaliation occurs policy-by-policy; hence, for example, noncooperation in e-taxes leads to a punishment in e-taxes but not in tariffs. We then contrast the set of subgame perfect equilibrium policies under no-linkage with those achieved under a linkage regime where noncooperation in either policy can trigger punishment in either or both policies.6 Under linkage, the only relevant IC is the one requiring that the gains from deviating in both policies are no higher than the gain from cooperating in both, since if a country decides to deviate in any, it is punished in both, hence it would not be optimal to deviate in only one. Under no-linkage, there are additional IC because of the possibility of deviation in each individual policy. Thus, at a no-linkage solution, the sum of the gains from deviating in each policy cannot exceed the sum of the gains from cooperating in them. Therefore, the joint IC does not bind and linkage creates enforcement if, at the no-linkage solution, the following holds. First, the joint gain from deviation is lower than the sum of

5

In summarizing the objections to linkage Anderson (1998, p. 244) states that bthis activity can lead to an escalation in trade disputes...undermining the global trading system.Q. 6 The TRIPs agreement in the WTO allows for the removal of trade concessions if there is an infringement of intellectual property. But the reverse is also explicitly allowed as shown by the WTO’s authorization for Ecuador to ignore its TRIPs obligations towards the EU as a retaliation against the EU’s trade policy on bananas (WTO Doc. WT/DS27/ARB/ECU on bhttp://www.wto.orgN).

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gains from individual deviations, and second, the joint gain from cooperation is higher than the sum of the individual gains from cooperation. To determine when linkage creates enforcement, we show that if the linked tariffs and e-taxes are strategic complements, so that an increase in tariffs raises the marginal benefit of e-taxes, then the gain from a simultaneous deviation to higher tariffs and lower e-taxes, which occurs under linkage, is lower than the sum of the gains from deviations in each individual policy. Moreover, we also show that for a number of objective functions, including the one in our trade model, strategic complementarity is also sufficient to ensure that the gains from cooperating in both policies exceed the sum of the gains of cooperating in either. Our main result is not specific to this trade model. It can be applied to other economic problems with a similar structure where agents must enter self-enforcing contracts to repeatedly deal with a cooperation problem over multiple issues that are related even before linkage. The focus on issues that are related, in the sense that we cannot write payoffs for each issue as a function of a single policy, distinguishes our linkage result from previous work. Our approach is motivated by the work on multimarket collusion by Bernheim and Whinston (1990; BW), who show that by aggregating incentive constraints from unrelated markets (so that profits in market A depend only on prices in that market), oligopolists can always achieve at least as much collusion in each market but never more in both.7 Spagnolo (1999a) extends BW by allowing oligopolists to value the profits from the unrelated markets using a concave function and shows linkage will then enforce more collusion in both markets. Spagnolo (1999b) maps this last result into an international context by interpreting profits as payoffs to unrelated issues that are valued nonlinearly by governments entering into self-enforcing international agreements. However, the payoffs for governments of various policies considered for linkage in international agreements are actually related. Since such cases are particularly important in the trade setting—for example, tariffs on autos and environmental standards in the auto industry—we had to extend and modify previous results in a nontrivial way. Thus, in our model, where issues are related, linkage can create enforcement and if the new feasible set includes the global optimum, then the equilibrium features more cooperation in both policies. However, if the global optimum is not self-enforcing under linkage, then, even if more cooperation in both policies is feasible, the equilibrium may still entail a reallocation of enforcement. To clearly characterize when reallocation occurs and which policy it benefits, we analyze a limit case of our model where, although the e-issue is still trade-related, the policies are independent because the different components of their cross-effect on the government’s objective function offset each other. We show that in this case, no creation is possible and linkage always leads to reallocation when there is sufficient asymmetry in the enforceability of each issue under no-linkage. Moreover, if under no-linkage tariffs are easier to enforce than e-taxes, i.e., relatively closer to their cooperative optimum, then linkage leads to more cooperation in e-taxes at the expense of higher tariffs. Although a reallocation of enforcement can occur even if the linked issues are related, this does not imply linkage will have a negative 7

Phillips and Mason (1992) provide experimental evidence in support of BW.

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welfare effect since that reallocation will further cooperate on the issue that is more difficult to enforce.8 In the trade literature our result on the creation of enforcement stands in contrast to Ederington (2002), who analyzes a model where social welfare-maximizing governments have access to a tariff and a production tax that addresses an externality with no cross-border effect. He shows that linkage does not enforce more cooperation, because the tariff is the most effective instrument to address the TOT effect. Bagwell and Staiger (2001) also conclude that when the only cross-border externality is due to the TOT, governments simply need to negotiate a market access commitment and should then be free to independently set any policy addressing domestic externalities provided this does not erode the market access negotiated in the WTO, which they argue is ensured by current rules.9 Independently from our work, Ederington (2001) incorporates a cross-border externality into a parametrized version of his earlier model. He shows that linkage sustains the first best solution at the same discount factor as no-linkage when only import sector policies are available. In contrast, our result implies that linkage can sustain more cooperation. In addition to differences in the setup, e.g., our government is not necessarily a welfare maximizer, one important assumption generating the difference in results is that we allow governments to reoptimize after a deviation under no-linkage—a natural assumption since when policies are interdependent, their cooperative levels depend on the actual value of the other policy. Moreover, our analysis applies even if countries can never sustain the first-best. This is crucial because if no-linkage already sustains the firstbest, then countries have no incentive to switch to linkage and because it allows us to address the concerns of policymakers as to whether linkage necessarily causes a reallocation of enforcement. In addition to deriving the general conditions for creation and reallocation of enforcement, our other main goal is to show when they are satisfied by this trade model. We find that for the foreign policies to be strategic complements in the home government’s objective, the nontrade issue must have cross-border spillovers and be sufficiently valued. This implies that for a pair of poor countries, which may place a low weight on the production externality, linkage is unlikely to create enforcement. We also find that import-competing lobbies cannot be too bpowerfulQ; that is, they cannot have too much weight in the objective function, otherwise the domestic tariffs and e-taxes become strategic substitutes. This last result occurs because when a sector’s supply increases due to tariff protection, the marginal benefit of lowering the production tax is higher because it affects a higher volume of production. When import lobbies are given sufficient weight in the objective function, this cross-effect is the dominant one. The structure of the paper is as follows. In Section 2, we introduce the model and derive the noncooperative and cooperative equilibria; in Section 3, we derive the conditions under which linkage reallocates and creates enforcement; in Section 4, we 8

A similar result applies to cases where the issues are both unrelated and valued additively, as shown by BW for the case of oligopolies, since such cases imply that the policies are independent. However, independence of policies does not imply the issues are unrelated as is clear from the limit case of our model. 9 Bagwell and Staiger (2001) abstract from enforcement issues.

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analyze when these conditions hold in the trade model; and in Section 5, we summarize and discuss the results. All proofs are in the Appendix.

2. Model 2.1. Setup Each of the two countries produces two homogeneous goods, i=x,y, where x denotes home’s import. When countries trade, the consumer and producer prices at home are, respectively, q i =pwi +s i and p i =pwi +s i
e i , where pwi is the bworldQ price, s is a specific import tariff, and e i a unit production tax. Home’s excess demand is then M i uD i ( q i )
S i ( p i ).10 Denoting the foreign variables with b*Q, pwi is determined by the usual market clearing condition and is therefore a function of the policy variables:
 
4 w 4 4 ð1Þ M i pw i ; s i ; e i þ M i pi ; s i ; e i ¼ 0 We assume that countries have market power, and export taxes are unavailable.11 The world price is decreasing in tariffs and increasing in production taxes since tariffs depress imports and e lowers world supply. Tariffs raise domestic prices for consumers and producers. Production taxes raise domestic consumer prices but lower producer prices since the direct producer tax effect dominates the rise in pwi . w Bpw i =Bsi b0; Bqi =Bsi ¼ Bpi =Bsi N0; Bpi =Bei N0; Bqi =Bei N0; Bpi =Bei b0

ð2Þ

One important aspect of import lobbies not yet fully examined in the literature is their impact on the enforcement of trade agreements when nontrade policies are under negotiation. Thus, the first step is to ask if lobbies are relevant at all in the choice of enforcement regime, and to address it, we leave the lobbying mechanism implicit and focus directly on a reduced form objective function for the government, W=W x +Wy, that allows an extra weight to be placed on producer surplus in the import sector relative to consumer surplus and tax revenue. In the expression below, we have k i z1 in the import sector and k i =1 in the export sector.12 The government’s objective also accounts for the nontrade issue, which we model as a negative production externality. Throughout, we also refer to the government’s objective function as aggregate welfare, although we must bear in mind that the government does not necessarily weight all agents’ welfare equally. Z pi Z l Wi u ð3Þ Di ðqi Þdqi þ ki Si ðpi Þdpi þ si Mi þ ei Si
wi Wi ðSi þ ai S4i Þ qi

0

In the absence of production externalities, w i =0, this objective function represents the reduced form of a political contributions model, such as Grossman and Helpman 10 11 12

We assume these functions are linear in own prices. For evidence of market power in trade, see Knetter (1993) and Chang and Winters (2002). It is straightforward to extend the model to include export lobbies.

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(1994).13 We assume that W is twice differentiable and convex and W i (0)=0. The nonnegative weights, w i , may differ across countries or sectors thus reflecting different strengths of environmental lobbies or the different valuation by each country of the externality. The geographical scope of the externality is captured by a-positive if the externality has a cross-border effect, zero otherwise. This parameter may be interpreted more broadly as the relative weight placed on the foreign source of the externality.14 To focus on one important motivation for linkage, the asymmetry in enforceability between trade and nontrade policies, we rule out other potential motivations for linking agreements. More specifically, we assume symmetry across countries, such that home and foreign import (and export) sectors are mirror images of each other, that is, Wi =W j* for ipj.15 Moreover, for ease of exposition, we initially assume that domestic production in the export sector produces no externality, but foreign production does, hence W y =W y (aS y*) and, by symmetry, Wx =Wx (S x ). This allows us to initially abstract from e-taxes in the export sectors. In the Appendix, we show that this assumption is not essential for the main results. One crucial point to note is that it is impossible to write any subcomponents of the governments’ objective, e.g., producer surplus or the production externality cost, in terms of only the tariff or the e-tax. The nontrade issue is inherently trade-related, because changes in the tariffs change prices and therefore equilibrium supply levels. 2.2. Noncooperative vs. fully cooperative equilibrium In our model, in addition to the cooperation problem in trade generated by the TOT externality, governments also face a cooperation problem due to the presence of the negative production externality. Governments overcome these cooperation problems through repeated interaction, and we now characterize the Nash equilibrium of the stage game that is repeated. Home chooses taxes in the import sector to maximize Eq. (3), taking foreign policies as given.16 We drop the subscript, x, and unless otherwise stated, the policies refer to home’s

13

¯ +c, where W ¯ is Staiger (1995). In Grossman and Helpman (1994), the government’s objective is W GH=aW social welfare, c is political contributions and a is the marginal rate of substitution between the two. In W x the term k
1 can be directly interpreted as the inverse of a when factor ownership is extremely concentrated. Thus, underlying our model is the basic general equilibrium structure used in Grossman and Helpman (1994). We augment this by modelling a production externality that enters additively in utility and assuming that the revenues from the e-tax are distributed lump-sum to obtain Eq. (3). 14 For instance, the existence of slave or child labor anywhere in the world may generate per se a bpsychological costQ; a can then represent the weight placed on the such conditions abroad relative to home. The weight and scope of the production externality are likely to change over time as scientific knowledge about the externality evolves or as we become aware of foreign practices that induce bpsychological costsQ. 15 Lima˜o (2002b) analyzes the gains from linkage in an enforcement context when countries forming regional integration agreements are asymmetric and have different bargaining powers. 16 The necessary first-order conditions are given in Appendix A.2.

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import sector. Given the symmetry, the following noncooperative equilibrium also applies to the foreign import sector policies.17 sN ¼ pw =e ;

eN ¼ wWV
ðk
1ÞS=SV

ð4Þ

In the absence of import lobbies, the optimal e-tax is equal to the marginal cost of the externality, otherwise the e-tax is lower than wWV. The Nash tariff is inversely related to the elasticity of the foreign excess demand, eup wM*V/M*; it does not reflect the extra weight placed on producers directly since the producer tax is the most efficient instrument to transfer surplus to those producers.18 Neither policy reflects the cross-border scope of the externality, because home ignores this effect on foreign, and foreign does not create an externality in home’s import sector. Finally, note that because the nontrade issue is traderelated, the policies are generally jointly determined even before any strategic relation through linkage is present. The fully cooperative policies for these governments are found by choosing the cooperative tariffs and e-taxes, s c and e c that maximize their joint objective. This c is equivalent to maximizing Eq. (3) after imposing symmetry, W c=W x (s c,e c)+Wy (s*=s , y c e*=e ). The first-order conditions (in Appendix A.2) yield: y sg ¼ 0

;

eg ¼ wWV þ aw4W4V
ðk
1ÞS=SV

ð5Þ

The difference between the Nash and global cooperative policies confirms that the externalities which countries must resolve arise due to market power in trade and the crossborder effect of the production externality. Therefore, the underlying motivation for cooperative agreements is independent of the existence of import lobbies. However, we will show that lobbies can alter the benefits of cooperation in an agreement and will therefore be important in the comparison of the linkage and no-linkage enforcement regimes.19

3. Effects of linking trade to nontrade agreements 3.1. Two enforcement regimes: linkage and no-linkage The absence of a supranational authority to punish violators implies that international agreements must be self-enforcing. Therefore, the outcome of such agreements depends on the enforcement regime, i.e., on which policies are available to enforce cooperation. We now analyze the effects of two important enforcement regimes: linkage and no-linkage. Our central question is whether a switch to linkage must result in a reallocation of enforcement across issues or if this trade-off can ever be avoided through the creation of enforcement. As we note in the Introduction, a reallocation of enforcement occurs if greater cooperation on 17 In the general equilibrium model implicit in the analysis there is a numeraire good, which maintains the balance of payments equilibrium. This allows us to focus on individual sectors in isolation. 18 The equilibrium value of s N is indirectly affected by k through the impact of e on the world price. 19 A cooperative agreement on e-taxes may be necessary even if the production externality is purely domestic because the production tax affects world prices. The WTO’s agreement on subsidies deals precisely with domestic policies and tries to prevent market access concessions from being eroded through the use of secondary trade barriers. See Copeland (1990) and Bagwell and Staiger (2001) on this issue.

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nontrade issues occurs at the expense of higher tariffs or vice versa. A creation of enforcement occurs if under linkage more cooperation in both policies becomes feasible. Cooperative self-enforcing agreements are well characterized by certain repeated games.20 The indefinitely repeated stage game is the Nash game described, and we assume that each government observes the other governments actions at the end of each period. We focus on symmetric, subgame perfect, stationary Nash equilibria and adopt the simplest trigger strategies that maintain such equilibria-infinite Nash reversion—the exact trigger depends on whether the policies are linked or not. The payoffs are given by W discounted at the rate d=d¯qb1, where d¯ reflects a proper discount factor, and q the probability that the game continues for one more period. Under a linkage regime, noncooperation in either issue can be met with punishment in either or both issues.21 That is, a government implements the cooperative level of a particular policy in period t as long as, in all previous periods, the history of play for all players in that policy was one of cooperation. Otherwise, the government reverts to the Nash levels in either or both linked policies. In the most cooperative linkage agreement, if a government decides to deviate in any policy, it finds it optimal to deviate in all linked policies (Abreu, 1988). The reason for this is that the most cooperative policies will be sustained by the most painful punishment which entails punishment in both policies.22 In sum, although under linkage, governments can deviate and punish using any combination of tariffs and e-taxes, it is not optimal for them to pursue deviations in individual policies. Thus, we need only consider cooperation, deviation, or Nash in all policies. Since symmetry allows us to express everything in terms of the home country variables, the period payoffs are:       W Cse scx ; ecx uWx scx ; ecx þ Wy s4y c ¼ scx ; e4y c ¼ ecx       W Dse scx ; ecx uWx sNx ; eNx þ Wy s4y c ¼ scx ; e4y c ¼ ecx     W N se uWx sNx ; eNx þ Wy s4y N ¼ sNx ; e4y N ¼ eNx

ð6Þ

In these expressions, (s xc,e xc) denotes the policy values during a period of cooperation in both policies and (s xN ,e xN ) the Nash values. The period gain from cooperation, x se (s xc,e xc)uW Cse
W Nse , represents the difference between the cooperative and the Nash payoffs. The period gain from deviation, X se (s xc,e xc)uW Dse
W Cse , is given by the

20 See Dixit (1987) and Bagwell and Staiger (1990) for trade applications and Barret (1994) for environmental ones. 21 As the GATT’s former director of legal affairs makes clear in Roessler (1998, p. 226). 22 The one period gain from deviating in either policy cannot exceed the gain to deviating in both by the definition of a Nash best response. Stating that a government knows it will be punished in both policies implicitly assumes that the threat of punishment in both policies is a credible one. This threat achieves the most cooperative policies. However, ex post the threat may not be realized. To deal with this issue we could model renegotiationproof strategies (Farrell and Maskin, 1989) and verify whether they affect our results by checking if it reduces the feasible degree of cooperation under linkage differently from no-linkage.

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difference between the deviation and cooperation payoffs. In choosing the cooperative policies, the following incentive constraint must be satisfied each period: Xse ðscx ; ecx ÞV

d xse ðscx ; ecx Þ 1
d

ð7Þ

This condition, henceforth ICse , states that for each country, the net gain from deviating in any one period must not exceed the discounted value of the net benefit from future cooperation. If governments are sufficiently patient, ICse does not bind at the global maximum. We assume that the discount factor is small enough that this constraint binds at the global optimal policies in Eq. (5), but large enough that cooperation improves on the Nash values. This is the empirically relevant case, since we do not observe full cooperation in either trade or e-issues.23 In a no-linkage regime, governments retaliate policy-by-policy; hence, for instance, their response to a deviation in e-taxes is to revert to Nash in e-taxes but not in tariffs. If a deviation occurs in several policies, then the response is to revert to Nash in each of the policies deviated in. This corresponds to the current regime for environmental and labor standards in relation to the trade agreements in the WTO. The payoffs under cooperation, deviation, and punishment in all policies are defined by Eq. (6), as before. When the deviation and punishment occur only in the trade policy, we have the following payoffs: 


W Ds scx ; ecx uWx srx ; ecx þ Wy scx ; ecx  
ns
 
ns
þ Wy srx ens W N s uWx srx ens x ; ex x ; ex We can define analogous payoffs for a deviation and punishment in the e-tax by interchanging the variables. Fig. 1 clarifies at which points the payoffs are being evaluated. Start at a cooperative point, such as NL. From NL, a deviation in tariffs places home at D xs with domestic tariffs given by the Nash reaction, s r, evaluated at the original cooperative etax and foreign policies at (s xc,e xc).24 Partial cooperation follows a deviation in tariffs. That is, countries stop cooperating in tariffs but continue to cooperate in e-taxes so that in the period following a deviation in tariffs, the new equilibrium value for the e-taxes is found at N s , where countries choose e c to maximize cooperative welfare given tariffs are set at s r. 23

The severity of this constraint depends importantly on how long it takes to start a punishment after a deviation occurs, which in turn depends on two factors. First, the speed of detection of the deviation, which is not long for transparent trade policies, e.g., tariffs, but may be long when it applies to the enforcement of certain domestic policies such as environmental standards. Second, the initiation of punishment can be delayed by bureaucratic delays in implementing new legislation or by consultations between the countries to ascertain if a deviation did occur. For example, while the WTO was ruling on the legality of the U.S. steel tariffs of 2002 other countries were unable to retaliate. Thus, the United States enjoyed the bbenefitsQ of that deviation for several months. 24 Since the equilibrium values of the tariffs and e-policies are not independent a deviation in one policy must eventually lead to a change in the equilibrium value of the other. We assume that if this adjustment were to happen simultaneously with the deviation then foreign would consider that home deviated in the two policies. Therefore, in the period that home deviates in tariffs (e-taxes) it does not simultaneously adjust the level of its e-tax (tariff), unless it wishes to deviate in all policies.

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Fig. 1. Cooperation and deviation strategies under no-linkage.

Graphically this corresponds to the tangency point of W c and the Nash FOC, s r(e), if the IC for the e-tax does not bind.25 The period gains from joint cooperation and deviation are unchanged, hence the relevant incentive constraint is the one in Eq. (7). The gains from cooperation and deviation in tariffs, assuming cooperation in e-taxes, are, respectively, x s uW Cse
W Ns and X s u W Ds
W Cse . The gains from cooperation and deviation in e-taxes are defined analogously. Under no-linkage governments are subject to three incentive constraints, which now reflect the possibility of deviation in the tariff or e-tax individually, or in both simultaneously. In both enforcement regimes, the governments’ problem is to choose the cooperative levels of tariffs and e-taxes that maximize their joint objective function subject to the relevant set of incentive constraints. Given the symmetry of the model, it is sufficient to focus on one country, and, since the problem is stationary, it is equal each period. Thus, the solution set under linkage and no-linkage is, respectively:  se  c c
 ð8Þ Ul uarg max x sx ; ex : ICse c c sx ;ex

 se  c c
 Unl uarg max x sx ; ex : ICse ; ICs ; ICe c c sx ;ex

ð9Þ

Since the objective function is the same and under no-linkage an extra two incentive constraints must be met, we can see immediately that all cooperative tariff and e-tax vectors feasible under no-linkage are also feasible under linkage. Thus, in a symmetric equilibrium, aggregate welfare under linkage is never lower than under no-linkage for either country. The key to this result is that in a no-linkage regime, a government can deviate in either or all policies, hence there are unconstrained deviation possibilities but constrained punishment possibilities since only the policies deviated in are subject to punishment. By contrast, under linkage, there are unconstrained deviation possibilities and unconstrained punishment If it does bind, then N s is given by the intersection of the e-tax iso-incentive constraint and s r. Assuming that, when there is only partial cooperation in policy k, countries first choose k cooperatively and then set the other policy is reasonable here because countries can always change the policy that is being set noncooperatively. See Copeland (1990) on a similar point. 25

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possibilities. Therefore, under linkage, we can always find punishments at least as painful as under no-linkage. This was the basic intuition underlying the results in BW in the context of multimarket collusion when markets are unrelated. The previous result does not tell us if a regime switch to linkage can create enforcement or if it must lead to a reallocation of enforcement, and consequently whether linkage will lead to lower cooperation in tariffs or e-taxes. Moreover, it does not ensure that aggregate welfare under linkage is strictly higher than under no-linkage. We now turn to these questions. 3.2. Reallocation of enforcement To isolate the reallocation effect of linkage, we consider a benchmark case where tariffs and e-taxes are independent, i.e., B2W/Bs x Be x =B2W/Bs*Be *=0. As we show in y y Section 4, this is a special case of our model where the pecuniary and nonpecuniary effects are exactly offsetting. Therefore, although the e-tax can be independent of the tariff, according to the definition above, the e-issue can still be trade-related, since changes in tariffs continue to affect supply and thus the level of the externality directly. The following definitions are useful in establishing the first proposition. The slope of the linkage incentive frontier in s c
e c space represents the marginal change in tariffs required to maintain incentive compatibility given a marginal change in e-taxes, hence we refer to it as the marginal rate of substitution in enforcement. We say that tariffs are easier to enforce than e-taxes if, under no-linkage, the discount factor required to sustain the global optimum in tariffs, d s , is lower than d e . Thus, d s is defined by the tariff IC evaluated at the global ds optimum for tariffs, Xs ðsg ; :Þ ¼ 1
d xs ðsg ; :Þ; de is similarly defined. s Propositon 1. (Reallocation of enforcement). (a) If tariffs and e-taxes are independent and their MRS in cooperative welfare and enforcement are not equalized under no-linkage, then a switch to linkage leads to a reallocation of enforcement. (b) If tariffs are easier to enforce than e-taxes under no-linkage, then linkage lowers cooperation in tariffs and raises cooperation in e-taxes for all da(d s ,d e ) and some dbd s . The opposite is true if e-taxes are easier to enforce. The intuition for part (a) is that if the discount factor is low enough, i.e., if dVmin (d s ,d e ), then both of the individual IC bind at the no-linkage solution, NL. The FOCs for the linkage problem defined in Eq. (8) require that the MRS of the policies in welfare and enforcement be equalized. Thus, if at NL the cooperative isowelfare curve is not tangent to the incentive frontier, then linkage leads to an aggregate welfare improvement by eliminating the individual IC. The switch to linkage entails a reallocation of enforcement, because at NL, the linkage IC must also bind when the policies are independent. Therefore, starting at NL, an increase in e c, for example, implies that the gain to deviating in the e-tax now exceeds the gain to cooperating, violating the linkage IC. But if at the higher e-tax both countries increase s c towards its Nash level, the incentive to deviate in the e-tax remains unchanged, due to

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independence, but the incentive to deviate in tariffs and therefore the overall incentive to deviate is lowered. To understand part (b), suppose that tariffs are easier to enforce and that free trade is just feasible under no-linkage. At NL, a small increase in cooperative tariffs has no firstorder effect (from the FOC for s g) and creates slack in the overall IC, which can be reallocated towards increasing e-taxes under linkage. Since the increase in e-taxes creates a first-order gain, this reallocation leaves governments strictly better off. By continuity of the functions, there also exists some d lower than d s for which this is true. If tariffs are easier to enforce than e-taxes, then the analysis above provides a formal justification in terms of enforcement for the reallocation concerns put forth by opponents of linkage within the WTO.26 However, this analysis applies to the linkage of independent policies, which is a limit case when the e-issue is trade-related, as in our model. Thus, we now analyze the case when the linked policies are not independent. 3.3. Creation of enforcement If the policies are not independent, can the linkage IC hold with slack at the no-linkage solution, that is can linkage create enforcement? We now derive the conditions to answer this question in the affirmative so that linkage can always yield a strictly higher aggregate welfare than no-linkage. Moreover, we show this can occur without any trade-off in cooperation across the issues. Suppose we find the optimal (and feasible) cooperative tariffs and e-taxes under nolinkage, U nl . Then, linkage can sustain more cooperation in both policies if the linkage IC does not bind at U nl . A sufficient condition for this is that the following holds at U nl :27 Xse VXs þ Xe

ð10Þ

xse zxs þ xe

ð11Þ

with at least one inequality being strict. These are sufficient since they imply that: Xse VXs þ Xe V

d d ðxs þ xe ÞV xse 1
d 1
d

ð12Þ

with the middle inequality resulting from the fact that U nl is implemented and therefore self-enforcing. The proposition stating the conditions for the creation of enforcement relies 26 Since we model the nontrade issue as inherently trade related there is no simple condition characterizing which policy is easier to enforce. In a simpler model where the issue is not trade-related, so the payoffs for cooperation in each policy can be written independently, there is a simple argument why tariffs are easier to enforce: the effective discount factor for trade agreements may be higher, d¯q s Nd¯q e . The probability of continuing a trade agreement may be higher than for certain environmental problems because technological progress can eliminate the environmental problem, e.g., moving from coal to solar powered plants eliminates emissions. Alternatively, a more realistic model with several countries may generate differential motives for free-riding in the different individual agreements and generate predictions about which policy is easier to enforce. On this issue, see Barret (1994) and the WTO report on the environment (1999, p.7). 27 This condition follows the approach in Spagnolo (1999a) who focuses on the case of independent stage game payoffs.

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on two lemmas establishing the conditions for Eqs. (10) and (11) to hold. To do so, we recall the definition of supermodularity. Definition 1. (Supermodularity). A function W(s) R n YR is (strictly) supermodular in saS if: W ðsÞ þ W ðs˜ ÞðbÞ ¼ W ðmaxðs; s˜ ÞÞ þ W ðminðs; s˜ ÞÞ8ðs; s˜ ÞaS Intuitively supermodularity states that pairing the lowest strategies (e.g., low tariffs with low e-taxes) and the highest ones yields a higher payoff than when other combinations of those strategies is played. Therefore, it captures the idea of complementarity between the policies. Lemma 1. (Relative gains from deviation). If the objective function, W, is (strictly) supermodular in the linked domestic policies, then X se (b)=X s +X e . To understand the intuition behind Lemma 1, first note that a continuously differentiable function is strictly supermodular in (s x ,e x ) if and only if B2W/Bs x Be x N0 (Topkis, 1979). Thus, strict supermodularity in the domestic-linked policies reduces to a requirement that those policies are strategic complements. Assume this is the case, then a country incurs an extra cost when it deviates jointly, that is, when it increases tariffs and reduces e-taxes, that is not present if it deviates only in one individual policy. When tariffs are increased, the marginal benefit of deviating in e-taxes, i.e., decreasing them, falls. Thus, linking, by bforcingQ deviation in both policies, lowers the temptation to deviate in any given policy.28,29 To establish the conditions for Eq. (11), note that we can use the definitions of the gains from cooperation to rewrite it as W Cse +W Nse VW Ns +W Ne . That is the sum of home’s objective (jointly in the import and export sectors) under cooperation (NL in Fig. 1) and no-cooperation (N) must not exceed the sum of the objective evaluated when there is partial cooperation (N s and N e ). If W is supermodular in the linked domestic and foreign policies, then we can see from the definition of supermodularity and Fig. 1 that we can establish W Cse +W Nse VW Is +W Ie . Thus, we must also verify whether supermodularity ensures the following partial cooperation condition: W Is +W Ie VW Ns +W Ne . The issue that arises when the linked issues are intrinsically related is that the Nash phase in tariffs occurs 28

The gain from deviating under linkage is always at least as large as either of the gains from deviating in tariffs or e-taxes individually. This occurs because deviation under linkage requires countries to play their best response in both policies. 29 Lemma 1 builds upon a result in Spagnolo (1999a) but differs in two respects. He considers two issues each with an independent prisoner’s dilemma structure and material payoffs C1 and C2 which take different values depending on whether agents cooperate or not. These payoffs are evaluated according to U(C 1,C 2) and it is shown that the gains from deviation under linkage are lower than the sum of the gains from deviation if U is submodular in (C1,C 2). The first, trivial, difference occurs because, in our model, the deviations in the linked policies occur in opposite directions (higher tariffs, lower e-taxes); therefore, we require supermodularity as opposed to submodularity. The second, and more substantive, difference occurs because an important set of issues linked are intrinsically related and therefore we cannot write C1 and C 2 separately. Because in our model the linked issues are intrinsically related, lemma 1 also shows that the bmovementQ from I s (I e ) to D s (D e ), in Fig. 1, improves aggregate welfare. Such a movement would not take place if the issues were unrelated and the policies set independently during the stage game.

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at N s not at I s , and for e-taxes, it occurs at N e not at I e .30 This raises the question of whether supermodularity is sufficient to establish the relative gains from cooperation. We now show that supermodularity is in fact sufficient for establishing the relative gains from cooperation for a nontrivial set of objective functions. Lemma 2. (Relative gains from cooperation). If the objective function, W, is supermodular in the linked domestic policies and strictly supermodular in the linked foreign policies, then x se Nx s +x e . Moreover, there exist objective functions, W, strictly supermodular in both the linked domestic and foreign policies such that x se Nx s +x e . The intuition is the following. When W is supermodular in domestic policies and strictly supermodular in the linked foreign policies, the simultaneous increase in foreign tariffs and decrease in e-taxes that occurs during a punishment under linkage carries an extra cost which is not present if each of the punishments was carried out individually at points I s and I e . This complementarity increases the severity of the Nash punishment under linkage and explains why W Cse +W Nse bW Is +W Ie . Let’s now turn to the partial cooperation condition. When W is supermodular in domestic policies, then the deviation and Nash levels of a given policy coincide. Hence, for example, in Fig. 1 the individual best-response functions would be perpendicular and intersect at N. However, if W is also strictly supermodular in the linked foreign policies then, when foreign increases its tariff, home would like foreign to increase its e-tax as well. This implies that in Fig. 1 the tariff under partial cooperation would be s N , but the optimal level of the cooperative e-tax for that tariff differs from e c (the level at which I s is evaluated) and therefore W Is bW Ns . Similarly, W Ie bW Ne so that the partial cooperation condition is satisfied. Given that the condition for the gains from cooperation holds strictly when W is strictly supermodular in foreign policies and supermodular in domestic policies, it also holds for some positive levels of complementarity between the domestic policies, as we state in the second part of the lemma and prove in the Appendix. With Lemmas 1 and 2 and the following definition, we state the main proposition of this section. d Definition 2. (Creation of enforcement). Linkage creates enforcement if Xse b 1
d xse at Unl , that is, if it can enforce both lower tariffs and higher e-taxes than no-linkage.

Proposition 2. (Creation of enforcement). If the objective function, W, is supermodular in the domestic policies and strictly supermodular in the foreign policies, then linkage creates enforcement. Moreover, there exist objective functions, W, strictly supermodular in both domestic and foreign policies such that linkage creates enforcement. Proof. Follows directly from Eq. (12) and Lemmas 1 and 2. The conditions above are sufficient for linkage to yield a strictly higher aggregate welfare than no-linkage, such that no trade-off in cooperation across the issues is 30

We also discuss this issue in page 13. This constitutes another important difference relative to earlier work. In the case of independent payoffs, studied by Spagnolo (1999a), the readjustment of policies after a deviation does not arise because the policies on different issues are not related during the stage game. In that case I s and I e exactly coincide with N s and N e in Fig. 1 and the partial cooperation condition is trivially satisfied with equality.

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necessary. This proposition does not rule out the possibility that the optimal linkage solution entails a reallocation of enforcement, which may happen if there is a strong asymmetry in the enforceability of the policies. However, the key point is that the creation of enforcement allows for a strictly higher aggregate welfare level without a need for the reallocation of enforcement, since the direction of change for the cooperative policies is (locally) unrestricted.

4. Structural conditions for the creation of enforcement We now show when the supermodularity conditions that are sufficient for the creation of enforcement hold in our trade model. The objective is to give guidelines as to what btypesQ of e-issues (i.e., with a national or a cross-border scope; highly valued or not) and countries (developed or developing; with powerful import lobbies or not) satisfy the complementarity conditions. We analyze these dimensions because of their importance in policy debates of linkage in the context of the WTO.31 4.1. Strategic complementarity of domestic tariffs and e-taxes To determine whether own tariffs and e-taxes are strategic complements in the import sector (x), we first differentiate W, which yields: W s =(1+p sw)(sMV+(e
wWV)SV)
p swM+(k
1)(1+p sw)S. The subscripts now denote partial derivatives unless the function has only one argument in which case a prime is used. The first term, (1+p sw), represents the positive effect of the tariff on domestic prices; sMV represents the fall in tariff revenue due to lower imports; eSV represents the increase in e-tax revenue due to higher production; wWVSV the increase in externality cost and
p swM refers to the positive change in the TOT. The final term reflects the presence of import lobbies. If governments place additional weight on producer surplus in the import sector, then an increase in tariffs has an added benefit in the form of increased producer surplus. The cross-derivative is then:32     
w w Wse ¼ 1 þ ps SV þ
ps Me þ
wWse þ ðk
1Þ pw
1 1 þ Psw SV e þ

þ

þ




ð13Þ The first term represents a strategic revenue effect; when domestic supply expands due to higher tariffs, the marginal benefit of increasing e-taxes increases, so this effect is positive. The second one represents a strategic TOT effect, and it is positive; higher e-taxes expand home imports, which is more valuable at the lower world prices delivered by the increased domestic tariff. The strategic externality effect,
wWse , can be decomposed into two factors, the change in the marginal cost of the externality due to higher e-taxes,
( p ew
1)SVwWW, and the domestic tariff effect on the externality, (1+p sw)SV. The latter 31

Lima˜o (2002a) analyzes the actual adoption of linkage by different governments in more detail. Recall that we assume linear demand and supply functions, which is standard in similar analysis of strategic effects of trade policies and implies that the cross derivative of world prices with respect to tariffs and e-taxes is zero. 32

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factor is positive since higher tariffs increase the domestic supply and thus the level of the externality. The domestic e-tax effect on the externality ( p ew
1)SV is negative. Thus, the strategic externality effect is positive since the loss function is convex. The last term in Eq. (13) is the strategic lobby effect, which is negative. It captures a basic intuition, likely to be present in other models with import-competing lobbies, that when production expands due to tariff protection, the marginal benefit of increasing direct taxes on the producers is lower because it affects a higher volume of production. With the following definition, we can summarize the conditions for complementarity between domestic tariffs and e-taxes. We say that a country has powerful import lobbies if kzk¯ , where k¯ is defined by W se (k¯ ,.)=0. That is a country has powerful import lobbies if the weight placed on producer surplus is at least as high as the critical value at which domestic tariffs and e-taxes are independent. We show that such a weight exists and is nontrivial, in the sense that it requires governments to actually give extra weight to import producers. Proposition 3. Domestic tariffs and e-taxes are strategic complements in the domestic objective function, W, if and only if a country does not have powerful import lobbies. The existence of a threshold point, k¯ , is simple to show, since the extra weight on import producers affects only the strategic lobby effect and all of the other strategic terms depend only on exogenous parameters.33 Thus, if the weight equals one, the lobby effect disappears, but, if it is sufficiently large, this effect dominates all others and domestic tariffs and e-taxes become strategic substitutes. As we show in Lemma 1 the condition in Proposition 3 is sufficient to compare the incentives to deviate under linkage and no-linkage. Therefore, by determining when the domestic policies are complementary, import lobbies affect whether linkage creates enforcement. To compare the cooperation gains, we must also analyze the interaction of the foreign policies in W. 4.2. Strategic complementarity of foreign tariffs and e-taxes Once again we drop the subscripts, all conditions and variables now refer to home’s export sector, y. Differentiating W, we find two negative effects of a foreign tariff increase on domestic welfare: W s*=
pws* M+(
wWV(1+pws*)aS*V). The first term is the cost due to a reduction in home’s export prices, i.e., the usual TOT effect. The second term is the extra externality cost when there is a cross-border effect, since higher foreign tariffs lead to an expansion in foreign production. The cross-derivative is given by:   w Ws4e4 ¼
ps4 Me4 þ
wWs4e4 ð14Þ þ





pws* M e*,

is negative. An increase in foreign tariff reduces world The strategic TOT effect, prices for domestic’s exports, thus an increase in foreign e-taxes becomes less valuable since it expands domestic exports at a reduced world price. The strategic externality effect 33

Assuming that Wj=0, which is the case if W is quadratic for example.

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is now
wW s*e*=
( pwe*
1)aS*VwWW(1+pws* )aS*V. It consists of the change in marginal cost of the externality due to changes in the e-tax,
( pwe*
1)aS*VwWW, weighted by the positive foreign tariff effect on the externality level, (1+pws* )aS*V.34 Consider the critical value w¯ such that the policies are independent, i.e., W s*e*(w¯ ,.)=0. We say that the externality is sufficiently valued if wNw¯ . Proposition 4. Foreign tariffs and e-taxes are strategic complements in the domestic objective function, W, if and only if the production externality is sufficiently valued and is not purely domestic. The key to this result is that when we focus on the pecuniary effects alone, the foreign policies are strategic substitutes, which require the externality effect in the export sector to be positive. This is the case because when the loss function is convex the marginal benefit from reducing the externality level is greater at higher levels of the externality. Since an increase in foreign tariffs increases the level of the externality, it also increases home’s marginal benefit from a foreign increase in e*, because the latter reduces S*. When the externality is sufficiently valued, this effect dominates the pecuniary one. More importantly, the proposition rules out purely domestic production externalities, since in that case no externality effect exists and therefore foreign policies are strategic substitutes. The conditions for supermodularity in the last two propositions can be exactly satisfied by a range of parameter combinations in our trade model. Since we can also find combinations such that the policies are independent these propositions also confirm that the analysis in Section 3.1 does apply to a special case of our trade model, although the production externality is trade-related.

5. Conclusions We started by asking if linking trade policy to other cooperative agreements can ever result in the creation of enforcement rather than always leading to the reallocation of enforcement. We show that the fear of reallocation of enforcement pervasive in the trade literature on linkage is justified if the linked policies are independent because it is quite likely that the trade and nontrade policies are asymmetric in their enforceability. Moreover, if under no-linkage it is relatively easier to cooperate on tariffs than on e-taxes, the reallocation entails more cooperation on nontrade issues at the expense of higher tariffs. Thus, the model helps explain both the recent demands for linkages with trade policy by lobbies for different e-issues and the respective opposition. If the main goal of the WTO remains multilateral trade liberalization, then our result also lends support to this institution’s current practice which, except in the area of intellectual property, avoids retaliation across unrelated issues that are typically characterized by independent policies. However, in switching to a linkage regime, reallocation is not inevitable if policies are not independent to begin with. We show that linkage creates enforcement if the objective function is supermodular in linked policies. This result can be applied to a number of 34

If we had also allowed for export lobbies then Eq. (14) would include an additional negative term: (k
1)pws* pwe* SV.

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economic problems where agents must enter self-enforcing contracts to repeatedly deal with a cooperation problem over multiple issues that are related even before linkage. Obvious candidates are other international cooperative agreements, e.g., on health issues, transport infrastructure. Other applications include firm collusive behavior across interdependent markets (e.g., due to economies of scope or vertical integration) or when there is more than one instrument of collusion in the same market (e.g., price and advertising). Self-enforcing contracts are also pervasive in developing countries where the lack of rule of law often renders binding legal contracts too costly. We show that the issues for which linkage creates enforcement must have cross-border effects and be sufficiently valued to offset strategic pecuniary effects. These conditions are sufficient when import lobbies are not bpowerfulQ. We believe that both the increase in the weight placed on environmental (and other nontrade issues) and the broader interpretation of the scope of their externalities are changing the strategic relation between policies. This can partially explain the increasing demand for linkage, as well as its origin in developed countries. If the externality weight rises with income, that is, if clean air is a normal good, our result suggests that this phenomenon will intensify. Our analysis is also quite relevant for regional integration agreements. First, one of our basic assumptions—a country’s market power in trade—is most plausible at the regional level since transport costs segment markets. Second, more issues have regional rather than global cross-border effects. Thus, there is more scope for the creation of enforcement through linkage regionally. This may explain why linkage in regional integration agreements has been more frequent and less contentious than in the WTO. Enforcement is not the only factor in the decision to link agreements, but it is certainly an important one. By analyzing linkage from an enforcement perspective, we show that it need not necessarily reduce cooperation in trade policy. One practical concern in implementing linkages is that institutions, such as the WTO, are not equipped to decide on certain nontrade issues. However, in our model, linkage would require only that WTO rules allow the threat to use trade sanctions to enforce certain specific agreements and vice versa. This is compatible with a world order where there exist functional clubs to deal with each specific issue, e.g., the environment, with one or more global coordinating clubs to deal with linkages among issues.35 Potential drawbacks from linkage may arise from redistribution problems due to within and across country asymmetries and from different degrees of imperfect monitoring of compliance that can potentially cause an escalation in trade disputes.36 Both of these issues should be fully addressed in the enforcement context used in this paper. It is clear that demands for linkage will not soon fade. Thus, rather than allow the unilateral abuse of trade sanctions, we must understand how to use multilateral threats of noncooperation, in both trade and other issues, to promote more cooperative outcomes.37 35

As suggested, for example, by Lawrence et al. (1996, p. 107). According to our calculations based on data from Reinhardt (2000).the number of WTO disputes involving nontrade issues tripled from 1994–1999 relative to the previous four years largely due to the inclusion of intellectual property issues in the WTO. However, it is too early to determine if the disputes will reduce cooperation in trade policy or if their number will fall once countries adapt their levels of cooperation in intellectual property. 37 See Hufbauer et al. (1990) for a thorough review of the U.S.’s use of trade sanctions. 36

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Acknowledgement I thank two anonymous referees, Stephanie Aaronson, Jagdish Bhagwati, Alessandra Casella, Gernot Doppelhoffer, Josh Ederington, Helen Milner, Rohini Pande, Eric Reinhardt, Mike Riordan, Xavier Sala-I-Martin, Giancarlo Spagnolo, Robert Staiger, David Weinstein, and Gerald Willmann. I am also grateful for comments and suggestions from participants in seminars at the Econometric Society meeting (Atlanta), Georgetown, NYU (Inter-university Conference), Penn State, Stanford University, University of British Columbia, University of Maryland, World Bank, and Yale University. I am particularly indebted to Kyle Bagwell and Don Davis for their support. The usual disclaimer applies.

Appendix A A.1. Proofs Proof of Proposition 1. (a) If dVmin (d s ,d e ), then the necessary FOC for the interior linkage solution, U l, are  se c c Ws þWs Ws þdWs d s ; e Þ ¼ 1
d xse ðsc ; ec Þ. Thus, if the MRS are not We þWe ¼ We þdWe and X equalized at the no-linkage point, it is not a linkage solution. Reallocation must d then occur because at the no-linkage solution (NL), we have Xse ¼ 1
d xse and se se Bec d d se se at NL note that when policies are Bsc jX ¼ 1
d x N0. To show X ¼ 1
d x independent we have X se (s c,e c)=X s (s c,e c)+X e (s c,e c) and x se (s c,e c)=x s (s c,e c)+ x e (s c,e c) (independence corresponds to the case when W is not strictly supermodular, and so these equalities are proved precisely in Lemmas 1 and 2 d below). Thus, Xse ¼ 1
d xse , because the individual incentive constraints bind at se se Ws þdWs Bec d d se c NL. To show ¼ 1
d xse N0 note that Be c jX Bsc jX ¼ 1
d x ¼
We þdWe ¼ d BðXs
1
d xs Þ=Bsc Bs
B Xe
d xe =Bec , where the first equality employs the definitions of X se and ð 1
d Þ x se , and the second the definitions of X s , x s , Xe , and x e .
At NL the d individual incentive constraints bind therefore B Xs
1
d xs =Bsc b0 and
 e se d e c Bec d se B X
1
d x =Be N0, hence Bsc jX ¼ 1
d x N0. s þdWs (b) If d=d s then s c=0 and W s +W s*=0 whereas
W We þdWe N0 and an increase in s and e Ws þWs Ws þdWs until We þWe ¼ We þdWe is optimal. By continuity of W and of the incentive frontier a dbd s , such that the reallocation still occurs from tariffs to e-taxes. The same argument holds if at NL there is slack in ICs , i.e., d s bdbd e . 5 Proof of Lemma 1. X se VX s +X e fW xCse +W xDse VW xDs +W xDe where Cse, Dse, Ds, De are defined at points NL, N, D s , and D e in Fig. 1. Adding and subtracting both W x (s N ,e c) and W x (s c,e N ) to the RHS of the equivalence relation above, we have s x +a x V0, where:  
 

 ðA1:1Þ sx uWx sc ; ec Þ þ Wx sN ; eN
Wx sN ; ec þ Wx sc ; eN

    ax uWx sN ; ec
Wx sr ; ec Þ þ Wx sc ; eN
Wx ðsc ; er Þg ðA1:2Þ

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As we show in Section 2.2, s cbs N and e cNe N . Thus, max [(s c,e c),(s N ,e N )]=(s N ,e c) and min [(s c,e c),(s N ,e N )]=(s c,e N ). Therefore, if W is (strictly) supermodular in s,e (or, what is equivalent, W xse (N)=0), then s x (b)=0. Moreover, a x V0, since s r is the best response to e c and similarly for e r relative to s c. 5 Proof of Lemma 2. Claim 1. If W is supermodular in (s x ,e x ) and (s*,e y *) y and the partial cooperation condition, W Is +W Ie VW Ns +W Ne , holds then x se zx s +x e . Proof of Claim 1. x se zx s +x e fW Cse +W Nse VW Ns +W Ne . Rewriting this expression as s+aV0 where:  
 

 suW sc ; ec Þ þ W sN ; eN
W sN ; ec þ W sc ; eN ðA1:3Þ auW ðsc ; eN Þ þ W ðsN ; ec Þ
fW ðsne ; er ðsne ÞÞ þ W ðsr ðens Þ; ens Þg ¼ W Ie þ W I s
ðW Ne þ W N s Þ

ðA1:4Þ

(Strict) supermodularity ensures s(b)=0, and the partial cooperation condition states that aV0 so s+aV0. 5 Claim 2. If the objective function, W, is supermodular in the linked domestic policies and strictly supermodular in the linked foreign policies then x se Nx s +x e . Moreover, there exist objective functions, W, strictly supermodular in both the linked domestic and foreign policies such that x se Nx s +x e . Proof of Claim 2. W is supermodular in (s x ,e x ) iff W xse =0 (given that W is continuous and twice differentiable). If W xse =0 then, in Fig. 1, s r and e r are, respectively, vertical and horizontal and therefore s r(e ns )=s N and e r(s ne )=e N . This implies that I s and N s (I e and N e ) share the same tariff, s N , (e-tax, e N ). Now, if the individual IC for the e-tax (tariff) holds at I s (I e ), which we show below is true, then I s (I e ) is feasible when countries choose N s (N e ). Therefore, W Is +W Ie VW Ns +W Ne , moreover this inequality is strict if W is strictly supermodular in (s*,e since then the optimal cooperative e-tax y *), y (tariff) at I s (I e ) differs from that at NL. Therefore, x se Nx s +x e since, from Claim 1, sb0 if W is supermodular in (s x ,e x ) and strictly supermodular in (s*,e y *). y To show the existence of W with W xs *e *N0 and W xse a(0,e], i.e., strictly se s e r ne N supermodular in (s*,e y *) y and (s x ,e x ), such that x Nx +x note that limeY0+e (s )=e r ns N and limeY0+s (e )=s . Given that W is continuous, a eN0 exists such that W Is +W Ie VW Ns +W Ne and therefore, from Claim 1, x se Nx s +x e follows. To conclude, we show that ICs and ICe are satisfied at I e and I s , respectively. First, note that when there is partial cooperation in one policy, the other policy’s IC becomes irrelevant. Intuitively, ICs holds at I e because it held at NL and, since e N be c, we have that at NL the gains from deviation are at least as high and the gains from cooperation lower than at I e . We show this for the two cases in the lemma. Case 1. W is supermodular in domestic policies and strictly supermodular in foreign policies. X s (s c,e c)=X s (s c,e N ). By expanding and rearranging, we have X s (s c,e c)
X s (s c,e N )=
s x =0 where s x is defined in (A1.1), and the last equality is proved in Lemma 1.

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x s (s c,e c )bx s (s c,e N ). By expanding and rearranging, we have x s (s c,e c )
x s (s c,e N )=sb0, where the inequality is proved in Claim 1. Thus, under Case 1, ICs does not bind at I e and therefore W Ie bW Ne , since at N e the countries have chosen the optimal cooperative tariff given e=e N . A similar proof applies to show that ICe does not bind at I s and therefore W Is bW Ns . Case 2. W is strictly supermodular in both domestic and foreign policies. X s (s c ,e c )NX s (s c ,e N ). By expanding and rearranging, we have X s (s c ,e c )
X s (s ,e N )=
{s x +W x (s N ,e c)
W x (s r,e c)}N0. As we show in Lemma 1, strict supermodularity in domestic policies ensures that s x b0, moreover W x (s N ,e c)
W x (s r,e c)b0 since s r is the best-response to e c. x s (s c,e c)bx s (s c,e N ) also holds for some W strictly supermodular in both domestic and foreign policies. By expanding and rearranging, we have x s (s c,e c)
x s (s c,e N )=s+ W Is
W Ns b0, where sb0, from Claim 1. Moreover, as we show for Case 1, if Wys *e *N0 and W xse =0 then W Is bW Ns , therefore we must have that limW xseY0+(W Is
W Ns )V0. Thus, under Case 2, ICs does not bind at I e for Wys*e*N0 and W xse a (0,e¯ ]. Therefore, Ie W bW Ne , since at N e the countries have chosen the optimal cooperative tariff given e=e N . A similar proof applies to show that ICe does not bind at I s and therefore W Is bW Ns . 5 c

Proof of Proposition 3. BW se /Bk=( p ew
1)(1+p sw)SV as long as Wj=0, thus, using the results in Eq. (2), BW se /Bkb0 for all k. From the definition of powerful import lobbies if ¯ k=k¯ , then W se =0 thus if such a k N1 exists then we have W se N0 for k¯ Nkz1. As we describe ¯ above, W se (k=1)N0 which implies that a k N1 exists and is unique, for given values of the other exogenous parameters, because BW se /Bk is linear in k. 5 Proof of Proposition 4. BW s*e*/Bw=
( pwe*
1)(aS*V)2(1+pws* )WW as long as Cj=0. Thus, since we assume CWN0, if aN0 then BW s*e*/BwN0 for all w, by using the results in ¯ Eq. (2). By definition W s*e*(w¯)=0, thus if such a w exists then we have W s*e*(wNw¯ ) N0. ¯ As we describe above, W s*e*(w=0)b0 which implies that a w N0 exists and is unique, for given values of the other exogenous parameters, since BW s*e*/Bw is linear in w. 5 A.2. Analytical details A.2.1. Necessary conditions for Nash and global optimal policies. The expressions below represent the FOC for the Nash policies.
 Ws ¼ 0 : 1 þ Psw ½ sMV þ ðe
wWV þ ðk
1ÞS=SVÞSV
pw sM ¼0

ðA2:1Þ


w W e ¼ 0 : pw e
1 ½e
wWV þ ðk
1ÞS=SV SV þ sSV þ pe ð sM V
M Þ ¼ 0

ðA2:2Þ

The expressions below represent the FOC for the global optimal policies. 
Wsc ¼ 0 : 1 þ pw s ½ sM V þ ðe
ðwWV þ a4w4W4VÞ þ ðk
1ÞS=SVÞSV ¼ 0

ðA2:3Þ


w Wec ¼ 0 : pw e
1 ½ðe
ðwWV þ a4w4W4VÞ þ ðk
1ÞS=SVÞSV þ sSV þ pe sM V ¼ 0 ðA2:4Þ

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197

A.2.2. Supermodularity conditions Impact of domestic e-taxes on domestic imports (sector x): w Me ¼ ð D V
SVÞpw e þ SV ¼ M Vpe þ SV ¼

SVM 4V N0 ð M V þ M 4VÞ

ðA2:5Þ

where p ew=
SV/(MV+M*V) by applying the implicit function theorem to (1). Impact of foreign e-taxes on domestic exports (sector y): Me4 ¼ pw e4 M V

ðA2:6Þ

A.3. General model A common concern surrounding import lobbies in debates over linkage is that btraditional protectionist groups will manipulate environmental concerns in order to reduce competition from importsQ (Anderson and Blackhurst, 1992, p.20). This issue does not arise in the simpler version of our model because the foreign country’s production externality occurs only in home’s export sector. Therefore, a producer in the import competing sector does not benefit from a higher foreign e-tax, e*, y since it does not affect the price of home’s imported good. We briefly discuss the extension of our model that covers such cases by allowing the externality and spillovers to occur in all sectors. For details and proofs of the main results, see Lima˜o (2002a). The basic change is to allow for production externalities in both sectors in each country. Given the existence of externalities in the export sectors e y and ˜ , is obtained e*x become relevant instruments. The government’s objective function, W by not restricting the use of e-taxes in the export sector in the original expression in Eq. (3). Lemma 1 extends with no changes to the general model because the objective function is additive in the different production sectors. The main change in Lemma 2 is to augment the strategy space in the supermodularity definition to include e y and ˜ e*. x Once we do this, it is possible to show that if the objective function, W, is supermodular in (s x ,e x ),(s x ,e*),(s *,e x y y ) and strictly supermodular in (s*,e y *) y then linkage ˜ , strictly supercreates enforcement. Moreover, there exist objective functions, W modular in (s x ,e x ),(s x ,e*),(s *,e x y y ), and (s*,e y *) y such that linkage creates enforcement. Thus, the basic result on the creation of enforcement holds in this more realistic setting. In addition to the two complementarity conditions examined in the simpler model, we must also ensure that both (s x ,e*) x and (s*,e y y ) are strategic complements with ˜ . Moreover, the strategic externality terms in the original conditions in respect to W (13–14) now account for the effect of the policy changes on the total supply of that externality, e.g., S x +a x S*x in home’s import sector. The key point is that there still exist parameters such that the objective function is strictly supermodular in the linked policies. Thus, the sufficient conditions for linkage to create enforcement hold even if we allow for externalities and production taxes in both the import and export sectors provided that the government does not place too much weight on import producers.

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