Trade Agreements and the Nature of Price Determination † 470 Determination by Pol Antràs and Robert W

American Economic Review: Papers & Proceedings 2012, 102(3): 470–476 http://dx.doi.org/10.1257/aer.102.3.470

Contents

† Trade Agreements and the Nature of Price Trade Agreements and the Nature of Price Determination † 470 Determination By Pol Antràs and Robert W. Staiger*

I. Perfect Competition 471 The terms-of-trade theory of trade agree- from subsequently manipulating their domes- ments holds that governments are attracted to tic policy choices to undercut the market access trade agreements as a means of escape from a implications of their tariff commitments, can II. Imperfect Competition 472 terms-of-trade–driven prisoner’s dilemma see bring governments to the efficiency frontier.1 Bagwell and Staiger 1999 . One of the terms-( In this paper, we show that the nature of inter- of-trade theory’s most striking) predictions is national price determination can have important III. Matching 474 about the treatment of behind-the-border pol- effects on this prediction of the terms-of-trade icy measures in trade agreements. According theory. In particular, while the terms-of-trade to this prediction, in the noncooperative Nash theory adopts the view that international prices REFERENCES 476 equilibrium from which countries would begin are fully disciplined by market clearing condi- in the absence of a trade agreement, tariffs are tions, we show here that support for shallow set inefficiently high but behind-the-border poli- integration is overturned, and instead a need for cies are set at efficient levels. Hence, even in the “deep” integration is suggested—wherein direct context of a complex policy environment there negotiations occur over both border and behind- is no need for member governments of a trade the-border policies—if international prices are agreement to negotiate directly over the lev- determined through bargaining. els of their behind-the-border policies. Rather, Our results are most closely related to those according to the terms-of-trade theory, the in Antràs and Staiger forthcoming , where we fundamental problem for a trade agreement to focus on the potential( for offshoring) of spe- solve is to prevent terms-of-trade manipulation cialized inputs to increase the prevalence of and to thereby reduce tariffs and raise trade vol- bargaining as a mechanism for international umes, without introducing distortions into the price determination, and where we argue that unilateral choices of domestic tax subsidy and as such the recent rise in offshoring may pres- regulatory policies as a result of the/ negotiated ent the World Trade Organization (WTO) with constraints on tariffs see Bagwell and Staiger a profound institutional challenge. Here we 2001 . Importantly, this( result holds for a wide abstract from the details of offshoring and con- variety) of government preferences and has also sider instead foreign producers and domestic been shown to hold in imperfectly competitive consumers of a final good that interact under environments. different market structures and under different The terms-of-trade theory of trade agreements mechanisms of price determination. Our main therefore provides strong support for “shallow” result is that when foreign producers and domes- integration as the most direct means to solve the tic consumers must match and bargain over the policy inefficiencies that would arise absent a terms of their exchange, and this bargaining is trade agreement. Simply put, according to the not fully disciplined by market clearing condi- terms-of-trade theory, negotiations over tariffs tions, shallow integration can no longer achieve alone, coupled with an effective “market access internationally efficient policies. Although the preservation rule” that prevents governments

1 At a conceptual level, this resonates with the approach * Antràs: Harvard University, Cambridge, MA e-mail: taken by the General Agreement on Tariffs and Trade (GATT) [email protected] ; Staiger: University of Wisconsin,( and, to a lesser extent, by the WTO to behind-the-border Madison, WI e-mail: [email protected]) . We thank Kyle policies,( wherein negotiations focus )on tariff reductions as Bagwell, Arnaud( Costinot, and Michele )Ruta for helpful a means to expand market access, and where various GATT comments. provisions such as GATT’s “nonviolation” clause are then † To view additional materials, visit the article page at meant to protect( the value of negotiated market access) agree- http://dx.doi.org/10.1257/aer.102.3.470. ments against erosion by behind-the-border policies. 470 VOL. 102 NO. 3 Trade Agreements and Price Determination 471

simple models we develop below are special Welfare levels are given by the sum of con- along several dimensions, in a longer version of sumer and producer surplus and net tax revenues this paper, Antràs and Staiger 2012 , we show in addition to labor income : ( ) ( Λ) that our main results apply in much more general _p environments. We refer the reader to this longer W 1 2 D p dp D p 2; paper for the derivations of our main results. = Λ + ( / ) p ( ) + τ ( )/ ∫ _p I. Perfect Competition W * 1 2 D p dp *s*, p * = Λ + ( / ) p * ( ) + π( ) We consider first a two-country Home/Foreign ∫ partial-equilibrium perfectly competitive trade *D p 2 s* L *s*, p *, + τ ( )/ − ( ) model in which Foreign denoted with a “*” exports a single good to Home.( In particular, we) where we have suppressed the dependence of p assume that there is a measure 1 2 of consumers and p * on s* and * to save space. at Home with demand D p , a /measure 1 2 of We consider (τfirst + τ) the efficient policies, ( ) * / W * consumers in Foreign with demand D p , and which maximize W W W . Letting a measure 1 of firms in Foreign with( produc) - T *, it is straightforward = + to show that tion technology y* F L*, with F L* 0, W≡W is(τ only + τ a) function of the aggregate trade tax F L* 0, and Inada= ( conditions) ′(holding.) > T and the labor subsidy s*. The efficient choice Finally,″( ) < there is a measure of workers in of these instruments must then satisfy the first- each country that are paid a wageΛ of 1 with a order conditions W W T 0 and W W s* numeraire good entering linearly into ( utility 0, which yield ∂ /∂ = ∂ /∂ and closing our partial equilibrium model in the = usual way . T e 0, s*e 0. We suppose) that the Home government has = = an import tariff , while the Foreign government That the efficient policies in this setting corre- has both an exportτ tax * and a labor subsidy s* spond to laissez-faire should come as no sur- applied only to the export τ sector . All policies prise, as there are no frictions in our competitive are( defined in specific terms. Markets) are inte- model. grated and so the wedge between foreign and The noncooperative Nash policies are deter- domestic prices satisfies p p* * for mined by the three first-order conditions nonprohibitive tariffs. Throughout, = + (weτ + assume τ) W * * 0, W * s* 0, and W 0. that governments are social welfare maximizers, Manipulating∂ /∂ τ = the∂ first /∂ two = first-order∂ /conditions,∂ τ = but none of our results depend on this. which determine the Foreign best-response poli- The competitive production sector in Foreign cies to any Home tariff, yields hires labor to maximize profits and thus solves *R *R p M, s 0, L * arg max * p*F L* 1 s* L*, τ = /η = = {π = ( ) − ( − ) } where M is the elasticity of Home import yielding the first-order condition p*F L * demandη defined positively and so *R is the 1 s*, and implying L *s*, p*, and hence′( ) Johnson optimal terms-of-trade–manipulatingτ =y  * s* ,−p * F L *s*, p* . The( )international export tax defined for a specific tariff. Turning market( clearing) ≡ ( condition( )) is then to the Home best-response tariff, the associated first-order condition can be manipulated to yield y *s*, p* D p* * 2 D p* 2, ( ) = ( + (τ + τ))/ + ( )/ R p * * , E determining the market clearing foreign τ = /η * * * * * * price p s , . We then have p  s , where E is the elasticity of foreign export sup- p *s*,( τ +* τ) *. Notice that( τthe + for τ)- ply andη so R is the Johnson optimal import tar- eign≡ (and τ domestic + τ) + local(τ + pricesτ) are functions of iff defined τfor a specific tariff. * * N * * *N the sum of tariffs only, as are L and y . We will Nash policies are p E , p M, use this property shortly when we solve for the and s*N 0 where allτ prices = and/η elasticitiesτ = / ηare efficient tariffs. evaluated = at (the Nash policies . Notice that the ) 472 AEA PAPERS AND PROCEEDINGS MAY 2012 sum of the Nash tariffs is strictly positive, and market-access preservation constraint subse- so Nash tariffs are inefficiently high T N T e, quent to its tariff negotiations with Home, the ( > ) * * but the Foreign Nash subsidy is set at its efficient Foreign choices of and s will then satisfy the level s*N s*e. As a consequence, the funda- following first-orderτ condition: mental( inefficiency = ) for a trade agreement to correct in this setting is the unilateral incentive * * * d p ds* dW W W / 0, for each government to manipulate the terms of _ds* = _∂s* − _∂ * _d p d * = trade with its tariff choice. But Foreign could in ∂ ∂τ / τ * * * principle use both and s to alter its terms of with W evaluated at 0. Straightforward trade. Why, then, isτ s* left undistorted from its manipulations establish τthat = this equation can internationally efficient level in the noncoopera- only hold if s*R 0. Hence, with 0, the tive Nash equilibrium? The simple reason is that market access constraint = will induceτ =Foreign * * the tariff is the first-best instrument for manipu- to select the combination 0 and s 0 to lating the terms of trade in this environment, and meet the market access constraintτ = and deliver= hence with the Foreign Nash tariff set to achieve the efficient trade volume, so that “shallow” this purpose, there is no need for Foreign to dis- negotiations designed in this way will achieve tort any other policy choices to engage in terms- the efficiency frontier. of-trade manipulation. The fact that the Foreign Nash subsidy is set at its efficient level does not mean that the two coun- II. Imperfect Competition tries could achieve the efficiency frontier by simply committing to reduce their tariffs from Nash In this section, we illustrate the robustness levels to free trade, because such an agreement of our main result above to the introduction of would induce Foreign to then alter its subsidy imperfect competition. This will serve as an from the efficient level of zero as a partial substi- intermediate step in isolating the role that price tute for its now-constrained tariff. Hence, while it determination plays in our results, given that is true that s*N is set at the efficient level, this does our matching model below inherently features not imply that a simple agreement to eliminate ex post market power. For that purpose, sup- tariffs can move countries from the inefficient pose( now) that production in Foreign is under- Nash equilibrium to the efficiency frontier. taken by a single monopoly firm, and that the Suppose, though, that the two countries begin Home and Foreign markets are segmented so at the Nash policies and negotiate a tariff agree- that the Foreign monopolist is unconstrained in ment in which Home agrees to eliminate its tar- its ability to set different prices in the Home and iff and Foreign agrees to eliminate its tariff, and Foreign market see Antràs and Staiger 2012 for in addition Foreign agrees to a “market access alternative models( of imperfect competition . preservation” constraint, according to which it The quantity produced by the Foreign monop)- will not make policy adjustments in the future olist for local Foreign sales is denoted by x*, that alter the trade volume implied by the two while that produced( for )export to the Home mar- countries’ tariff commitments and the Foreign ket is denoted by x, with total Foreign produc- subsidy policy in place at the time of their nego- tion given by y* x* x. Market clearing in tiation i.e., the subsidy level s*N 0 . Can the each market determines = + the local price at which efficiency( frontier be achieved with = this) form of the Foreign monopolist’s chosen quantity sells: “shallow” integration? The answer to this question hinges on the x D p 2 p P x , policies Foreign will choose in light of the = ( )/ ⇒ = ( ) market-access preservation constraint. As pre- x* D p* 2 p* P x*. serving p with adjustments in Foreign policies = ( )/ ⇒ = () is necessary and sufficient for preserving equi- The Foreign monopolist production levels are librium trade volume in this environment, the determined by maximizing profits: market-access preservation constraint can be written as changes in s* that are accompanied * P x * x P x* x* * π = [ ( ) − (τ + τ)] ⋅ + () ⋅ by changes in that leave p unchanged, or d * ds* d pτ ds* d p d *. Facing this 1 s* L*x x*, τ/ = − ( / )/( / τ ) − ( − ) ⋅ ( + ) VOL. 102 NO. 3 Trade Agreements and Price Determination 473

* * * * which results in x s , and x *s , . conditions, which determine the Foreign With these in hand,( τ +one τ ) can compute( τ + τthe) best-response policies to any Home tariff. Using monopolist’s labor demand L *s*, * the first-order condition for profit maximization L* x s*, * x *s*, * ,( and τ +equi τ)- and the market clearing conditions, these two librium≡ ( ( domestic τ + τ ) and+ foreign( τ + τlocal)) prices p conditions can be manipulated to yield P x s*, * and p * P x *s*, * . ≡ ( ( τ + τ)) ≡ ( ( τ + τ)) *R * * *R * Welfare levels are given by the sum of con- p D , s 1 D , sumer surplus, profits, and net tax revenues: τ = /η = /η * where recall that D is the Foreign elasticity of _p η demand defined positively. The best-response W 1 2 D p dp x ; tariff of Foreign thus corrects for the Foreign = Λ + ( / ) p ( ) + τ ∫ monopoly distortion faced by consumers in the _p Foreign market reducing the Foreign local price ( * * W * 1 2 D p dp * with an export tax p  D but otherwise leaves p * /η ) = Λ + ( / ) ( ) + π undistorted the Foreign monopoly exporter’s ∫ incentive to exploit its monopoly power in the * x s* L *, Home market. And notice that the formula for + τ − the best-response Foreign subsidy though not necessarily the level of the subsidy( is identi- where we suppress arguments on the right-hand cal to that for the efficient Foreign) subsidy. side of each expression for simplicity. Turning to the Home best-response tariff, using Efficient policies maximize W W W W *, the market clearing conditions and the fact which are again functions of only = the + sum that p 2 D p , the associated first-order of tariffs and the Foreign labor subsidy. condition′ = can/ be′( manipulated) to yield Recalling that T *, the efficient tar- ≡ (τ + τ) W R iffs T must then satisfy W T 0 and x d x d p D , the efficient Foreign subsidy∂ s * /∂must = satisfy τ = − /( / τ) − /η W * W s 0. Together with the first-order where D is the elasticity of Home demand ∂conditions /∂ = for profit maximization and the mar- definedη positively. The best-response Home tar- ket clearing conditions, these two first-order iff serves two roles: first, it extracts rent from conditions can be manipulated to yield T e 0 the Foreign monopolist with a tax x d x d and s*e 1/2 D p * p * L* where primes = on imports; and second, this incentive(− /( to/ taxτ)) denote =derivatives, − ( ) ⋅which ′/ ′ by the first- imports is tempered by the incentive to correct order conditions for profit maximization for the Foreign monopoly distortion of Home implies p p * L*. Hence, under the effi- consumption with an offsetting import subsidy = = ′ cient policies, price in each market is equated p D. As is well known, whether the best- to marginal cost. Finally, using the market clear- response(− /η ) Home tariff is positive or negative ing condition to derive p  * 2 D p * , we may depends on the curvature properties of demand. rewrite the efficient policies′ = as / ′( ) Again, Nash policies are the mutual best- N response policies: x d x d p D, e *e * *N * * *Nτ = −* /( / τ) − /η T 0, s 1 D , p D and s 1 D where all prices, = = /η derivatives,τ = /η and elasticities = /η are evaluated at the * with D the elasticity of Foreign demand defined Nash policies. As with the competitive model positivelyη and evaluated at the efficient policies above, with a Foreign monopoly the sum of the where Foreign and Home demand elastici- Nash tariffs is strictly positive, and so Nash tariffs ties( are equal . Evidently, the efficient Foreign are inefficiently high T N T e. And while the production subsidy) addresses the Foreign level of the Foreign Nash( subsidy> ) will in general monopoly distortion, and there is no role for differ from the efficient subsidy level because * tariffs. the elasticity of Foreign demand D is evaluated The noncooperative Nash policies are deter- at different points on the Foreignη demand curve mined by the three first-order conditions across Nash and efficient policies, the fact that W * * 0, W * s* 0, and W 0. the two expressions are identical implies that the ∂As before, /∂ τ = we begin∂ /with∂ the= first two∂ first-order/∂ τ = Foreign Nash subsidy is efficient conditional on 474 AEA PAPERS AND PROCEEDINGS MAY 2012 the Nash trade volume, a feature which extends of the agents is 0.2 After learning their match, to the Foreign best-response subsidy and which producers produce an amount of x with the we next exploit. production function F L in anticipation of the Suppose then that Home and Foreign begin at payoff they will obtain( from) bargaining. With the Nash policies and negotiate a tariff agreement the cost of producing x sunk at the time of bar- in which Home agrees to eliminate its tariff and gaining, and with utility given by the increas- Foreign agrees to set its tariff at a level _ * such ing and concave function u x , the consumer that x s*N, 0 _ * x s*e, T e, and in additionτ and the producer Nash bargain( ) over the ex Foreign( agrees + τto )a = market-access ( ) preservation post surplus, with producers capturing a share constraint, according to which it will not make 0, 1 of surplus. policy adjustments in the future that alter the α ∈Suppose ( ) that an international match is formed trade volume implied by the two countries’ tariff and then Foreign sellers take their good to the commitments and the Foreign subsidy policy in Home country. In such a case, tariff costs are not place at the time of their negotiation i.e., s*N. sunk at the time of bargaining, and the ex post Is this form of shallow integration sufficient( )to surplus over which the parties negotiate is achieve the efficiency frontier? S L, * u F L * F L . The As before, the answer to this question hinges labor( τ L+ hiredτ) ≡ by( (Foreign)) − (τproducers + τ) ( selling) on the policies that Foreign will choose in light at Home is then determined by maximizing of the market access preservation constraint. S L, * 1 s* L, which optimizing In this environment, the market-access preser- αover( L τ defines+ τ) −L  (s*, − ) * and thus trade vol- vation constraint can be written as changes in ume F L s*, (* τ according+ τ) to s* that are accompanied by changes in * that ( ( τ + τ)) hold x or alternatively, p constant: dτ* ds* 1 u F L * F L 1 s*. d x (ds* d x d *. Facing) this marketτ/ ( ) α[ ′( ( )) − (τ + τ)] ′( ) = − access= − ( constraint,/ )/( /theτ Foreign) choices of * and By contrast, for Foreign producers selling s* will then satisfy the first-order condition:τ locally to consumers in the Foreign country and creating Foreign local pairs, labor demand * * * d x ds* L  *s* is determined by dW W W / 0, () _ds* = _∂s* − _∂ * _d x d * = ∂ ∂τ / τ 2 u F L * F L * 1 s*. with W * evaluated at 0. Straightforward ( ) α ′( ( )) ′( ) = − algebra indicates that thisτ = condition can only Home welfare is composed of the Home share hold if s*R s*e and *R 0. Hence, with nego- of bargaining surplus from the measure 1 2 of tiations setting = τ0 and = * _ *, the mar- international matches, plus the tariff revenue/ ket-access preservationτ = constraintτ = τ will induce associated with these matches: Foreign to select the combination * 0 and s* s*e to meet the market-accessτ constraint = W 1 1 u F L * F L _2 and = deliver the efficient trade volume, so that = Λ + ( − α) [ ( ( )) − (τ + τ) ( )] “shallow” negotiations designed in this way are 1 2 F L , indeed sufficient to place countries on the effi- + ( / ) τ ( ) ciency frontier. where we suppress the dependence of L on s* and * for ease of notation. Foreign III. Matching welfare (τ is +composed τ) of the bargaining surplus from the 1 2 Foreign local matches minus the We now depart from a price mechanism associated /labor subsidy, the Foreign share of fully disciplined by aggregate market clear- bargaining surplus from the 1 2 international ing, and suppose instead that the price at which / goods are exchanged between buyers and sell- 2 In Antràs and Staiger 2012 , we establish the robust- ers is determined through bilateral bargaining. ( ) Specifically, we assume that the measure 1 of ness of our results to less extreme matching models where: i if negotiations break down, agents can resort to a second- consumers is each randomly matched with the ary( ) market; ii producers can choose in which market to measure 1 of producers and there is no possi- search for matches;( ) and iii production decisions are made bility of rematching, so that the outside option before matching occurs. ( ) VOL. 102 NO. 3 Trade Agreements and Price Determination 475 matches minus the associated labor subsidy, To show this more formally, we return again plus tariff revenue associated with international to our thought experiment in which we set matches: 0 and in effect allow Foreign to optimize overτ = the mix of * and s* as long as equilibrium trade volumesτ correspond to those of W * 1 u F L * 1 L  * 1 *F L = Λ + _2 ( ( )) − _2 + _2 τ ( ) the efficient policies. Recall that trade volumes are given by F L s*, * and hence Ls* ( (* τ + τ)) 1 u F L * F L 1 L  , determined by , as defined by 1 , + _2 α[ ( ( )) − (τ + τ) ( )] − _2 which implies that( trade τ + τvolumes) are constant( ) as long as changes in * and s* satisfy d * ds* where again we suppress the dependence d L ds* dL  d *τ. Facing this marketτ/ of L * on s * and of L  on s * and * for ease access= − ( constraint,/ )/( the/ τ Foreign) choices of * and of notation. (τ + τ) s* will then satisfy the following first-orderτ con- Efficient policies maximize world wel- dition with W * evaluated at 0 : fare W W W W *, which does not depend ( τ = ) directly on = policies + because their direct effect in dW * W * W * dL  ds* this environment is simply to shift surplus across ∂ ∂ / 0, _ds* = _s* − _* _d L d * = agents and such surplus-shifting itself has no ∂ ∂τ / τ bearing on world welfare. As a result, the impact of policies on world welfare travels entirely which can be simplified to yield through their impact on the labor decisions L and L *, and recall also that labor decisions * F L only depend on s * and in the case of L  the sum 1 * * d L 1 ( ) _ u F L F L 1 _* _− α _ . of tariffs T *. ( ) 2 [ ′( ( )) ′( ) − ] ds = − α F L ′( ) The efficient = τ + tariffs τ T and labor subsidy s* must satisfy the first-order conditions W W T Because dL  * ds* 0, this condition implies that 0 and W W s* 0, which using 1∂ and / ∂2 s*R must ensure/ that > u F L * F L * 1, which can= be manipulated∂ /∂ = to yield ( ) ( ) in turn from 2 implies′( ( )s)*R′( s) *e< 1 . Thus, despite the( ) presence of a> market = access − α preservation constraint, “shallow” negotia- T e 0, s*e 1 . = = − α tions designed in this way will not achieve the efficiency frontier in the current environment, Efficient intervention requires a Foreign labor because such negotiations cannot fully eliminate subsidy to resolve the underinvestment in L, but terms-of-trade manipulation. there is no role for tariffs. This result can be further understood by The noncooperative Nash policies are deter- defining the “world” exporter per-unit price mined by the three first-order conditions at which the goods are/ exchanged in the bilat- W * * 0, W * s* 0, and W 0. eral bargain. In this environment, the world Using∂ /∂ τ1 =and ∂2 , /these∂ =first-order ∂ /conditions∂ τ = price is given by p w u F L F L can be (manipulated) ( ) to show that 1 * , but it is = then α ( clear( )) /that( )the + (increases − α) τ in − s ατ* and * that hold L  and hence s*N 1 , N *N 0. trade volume fixedτ will nevertheless( raise p w > − α τ + τ > and hence confer) the benefit of a terms-of-trade Hence, as in both the competitive and the improvement on Foreign. monopoly models considered above, Nash In sum, and in contrast to the two models tariffs are inefficiently high T N T e . And analyzed above where international prices are like the monopoly model, the (level > of the ) Nash fully disciplined by aggregate market-clear- Foreign subsidy differs from the efficient level. ing conditions, when international prices are But unlike in the monopoly model and as we instead determined by bargaining, “deep” inte- next confirm, the Nash or best-response gration—under which both trade and domestic Foreign subsidy is not set efficiently( even con)- policies are the direct focus of negotiations— ditional on the Nash or best-response trade may be required to achieve the efficiency volume. ( ) frontier. 476 AEA PAPERS AND PROCEEDINGS MAY 2012

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