South Preferential Trade Agreements Undermine the ...

Do South-South Preferential Trade Agreements Undermine the Prospects for Multilateral Free Trade?

Paul Missios and Halis Murat Yildizy

February 24, 2015

Abstract Due to trade diversion, there has been concerns expressed over the proliferation of preferential trade agreements (PTAs) between South countries. In this paper, we compare welfare across the various forms of bilateral free trade agreements (FTAs) and customs unions (CUs) and examine their implications for the stability of multilateral free trade. While North-North PTAs tend to yield higher welfare, we …nd certain cases where South-South agreements are more likely to lead to global free trade than North-North or North-South agreements, but other cases where multilateral cooperation over free trade is the least likely under South-South agreements. We also examine how the expansion of existing agreements, or the combination of separate agreements, a¤ects the potential for free trade. Keywords: trade agreements; free trade; development; tari¤s JEL Classi…cations: F12, F13, O19, O24

y

Ryerson University, 350 Victoria Street, Toronto, ON, Canada M5B 2K3. E-mail: [email protected]. Ryerson University, 350 Victoria Street, Toronto, ON, Canada M5B 2K3. E-mail: [email protected].

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1

Introduction

Over the last six decades, countries have pursued trade liberalization along several fronts: unilaterally, preferentially with a few partners, and multilaterally. While the heart of the WTO system is multilateral non-discrimination, article XXIV of the GATT instead permits WTO member countries to form preferential trade agreements (PTAs) such as free trade agreements (FTAs) and customs unions (CUs) under which members can grant tari¤ concessions to each other while not extending such concessions to other WTO members.1 Bhagwati (1991) has forcefully argued forcefully that PTAs are fundamentally incompatible with the WTO’s stated goal of multilateral trade liberalization and many researchers have questioned whether multilateral free trade is more likely to be achieved if no exceptions to non-discriminatory trade liberalization were permitted.2 As of Jan. 2015, the WTO’s website lists that it had received noti…cation of 604 such arrangements, with 398 agreements in force at that time, and most WTO members belong to multiple PTAs. While FTAs constitute an overwhelming majority of PTAs, the existing CUs involve some of the major economies of the world: for example, the Latin American CU MERCOSUR counts Argentina, Brazil, Paraguay, and Uruguay as its members while the EC (27) –a CU that extends across both goods and services –comprises most major European economies. While the formation of PTAs has accelerated signi…cantly, there has been little progress towards multilateral trade concessions in the last two decades. Further, many of the more recently signed agreements are between lower-income (South) partners, particularly among countries in Asia and Latin America. In addition to MERCOSUR, other major recent South-South PTAs include ASEAN (Association of Southeast Asian Nations FTA), CAFTA (Central America FTA), SAFTA (South Asia FTA) and the EAC (East African Community). This proliferation of South-South PTAs has posed an important concern to many in light of the trade diversion that is expected to occur under these agreements.3 The main questions we address in this paper concern the role of various PTAs for the multilateral negotiations over free trade. First, in a variation of the oligopoly trade model of Brander and Krugman (1983), we brie‡y examine how di¤erent compositions of PTAs (North-North, SouthSouth and North-South) a¤ect the welfare of member and non-member countries and the world as a whole, among countries of di¤erent production e¢ ciency. Similar to Das and Ghosh (2006), we employ an asymmetric four country model in order to accommodate the division of world economy into more than one trade block at a time. Then, using in…nitely repeated interaction, we examine whether these arrangements make multilateral free trade more or less likely to be sustainable, where cooperation is required to be self-enforcing as in Riezman (1991), Bagwell and Staiger (1997a, 1

Another important exception to non-discrimination is the Enabling Clause that allows developed members to give di¤erential and more favorable treatment to developing countries. 2 See Das and Ghosh (2006), Goyal and Joshi (2006), Furusawa and Konishi (2007), Saggi and Yildiz (2010, 2011 and 2013) for a detailed discussion. 3 As noted in Demir and Dahi (2011), South-South trade has become a substantial force in world trade. Between 1978 and 2005 the share of the South in world manufactures exports increased from 5% to 32%. The annual growth rate of real South-South manufactures exports has also been signi…cantly higher than the world average reaching 14% as opposed to 6% for the latter. Krishna and Mitra (2008) also points out that by the late 1980s there was a “rush to free trade” among countries in the developing world (see Rodrik, 1994, Bhagwati and Panagariya, 1996, Ray, 1998, and Das and Ghosh, 2006).

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1997b, 1998, 1999), Bond et al. (2001), and Saggi (2006, 2009). We also show that the results in the oligopoly setup are broadly consistent with those of a perfectly competitive, endowment framework. We begin with the role of single bilateral PTAs of di¤erent types and di¤erent compositions, but also consider the implications of both multiple bilateral agreements and larger coalitions for the likelihood of sustainability of multilateral free trade. As we show, there are signi…cant di¤erences in these implications depending on whether the PTA is a free trade agreement (FTA) or a customs union (CU), and how the agreement expands or is combined with other agreements. We show that a North-North PTA leads to a larger reduction in the external tari¤s of member countries on non-member countries (greater tari¤ complementarity e¤ect), while a South-South PTA results in the smallest reduction. Comparing agreement types, FTAs result in larger external tari¤ reductions than CUs, which leads to non-member countries being better o¤ under FTAs but worse o¤ under CUs. While world welfare is always higher with a PTA than without, North-North PTAs yield the highest world welfare while South-South PTAs yield the lowest among agreements (due to substantial trade diversion). The implications of PTAs on the sustainability of free trade lead to signi…cantly di¤erent results than the one-period welfare comparisons. Underlying these di¤erences are two channels that we identify to help understand the intuition of the paper: the membership e¤ ect and the asymmetry e¤ ect. While these concepts will be described in more detail later, we can think of the membership e¤ ect as related to the impact of defecting from free trade from being a member of a pre-existing PTA relative to being a non-member, holding the costs of all countries the same, and the asymmetry e¤ ect as the impact from cost (or endowment) di¤erences among countries, holding membership constant. As the impact on outside (non-member) countries radically di¤ers between FTAs and CUs, the membership e¤ect works in opposite directions across the agreement types. On the other hand, the asymmetry e¤ect works in the same direction regardless of the agreement: high cost countries are less willing to cooperate over multilateral free trade. These two e¤ects combine to result in a sustainability ranking of FTAs that is sometimes the opposite of the welfare ranking (for example, when the production e¢ ciency is moderately asymmetric, multilateral free trade is more likely to be sustainable under a South-South FTA relative to all other bilateral agreements). Since the membership e¤ect works di¤erently for CUs, this reversal does not occur, and we show that countries are most willing to cooperate over free trade under a North-North CU and least willing under a South-South CU. In addition to bilateral agreements, we extend our analysis to include the expansion of existing PTAs and the formation of additional PTAs and their implications for the sustainability of free trade. To date, this has not received much attention in the literature and cannot be examined in most papers. In this, we show that expanding North-North agreements to include South members or additional South-South agreements generally makes free trade harder or impossible to sustain, unless the countries are very symmetric (that is, the South is not substantially di¤erent from the North). As the majority of the initial agreements of the world have tended to be NorthNorth in nature, this has important implications for current multilateral negotiations. The failures at multilateral negotiation rounds in Cancun and Doha have led to an increase in South-South

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agreements, as the South has seen more scope for trade among each other in the absence of the deal they want with countries of the North. In our model, we show this implies that achieving free trade will be more di¢ cult, as the expansion of North-North agreements (FTA or CU) with an additional South member or the addition of a South-South FTA or CU act as stumbling blocks to multilateral negotiations. There are important exceptions in terms of incentives to move to free trade when the initial agreement is North-South or South-South. For example, when there is an existing (polarized) inter-regional PTA, an additional inter-regional PTA of the same type as the status-quo agreement always facilitates multilateral cooperation over free trade. This suggests that global free trade is more likely when agreements are mixed (North-South) rather than polarized (North-North and South-South). Finally, the impact of initial South-South agreements can lead to improved prospects for free trade, but this depends crucially on the extent of the asymmetry between the North and South and the type of agreement. Our line of research extends the literature in important ways. In a similar model, Das and Ghosh (2006) provides an endogenous FTA formation model that generates FTAs among similar countries. Whereas Das and Ghosh (2006) di¤erentiates countries by market size, we employ di¤erences in production cost to separate the North countries from the South countries. Unlike Das and Ghosh (2006), we examine both FTAs and CUs and focus on the role of the formation of PTAs for the sustainability of the multilateral cooperation over free trade. The baseline model is very similar to Saggi (2006) that develops a (mostly symmetric) three country model to examine similar sustainability questions. However, there are several results in the present paper that complement Saggi (2006) and extend the discussion to a much richer set-up. First, Saggi (2006) provides only a numerical analysis under asymmetry in a three country set-up and the focus is on the North-North PTA only. We extend the single bilateral PTA analysis to all possible types of agreements: NorthNorth, South-South or North-South bilateral agreements and provide analytical results. Second and more importantly, while the implications of the expansion of a PTA and the formation of additional PTAs is at the core of the present paper, these analyses are impossible in a highly restrictive three country framework used in most of the literature, including Saggi (2006). The remainder of the paper is organized as follows. Section 2 presents the framework of analysis with two sets of asymmetric countries, two lower cost ‘North’ countries and two higher cost ‘South’countries, followed in section 3 by the one period tari¤ game outcomes of the cases of no agreement, a bilateral FTA and a bilateral CU. The next section introduces the dynamic game, an in…nite repetition of the one-period game and evaluates the incentives for countries to deviate from multilateral free trade under di¤erent PTAs relative to no agreement. In Section 5, we extend the model to incorporate multiple bilateral agreements and the expansion of existing bilateral agreements to plurilateral agreements and again investigate the incentives to deviate from global free trade. In section 6, we brie‡y show that the results of our model are broadly consistent with a model with a quite di¤erent market structure: a perfectly competitive, endowment model where countries di¤er by endowment (North have high endowment, South have low endowment) and countries are competing exporters. We o¤er our conclusions in Section 7.

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2

The model

We develop a simple oligopoly model of trade between two regions: North and South. There are four countries: n, n0 , s and s0 ; where countries n and n0 are symmetric North countries while countries s and s0 are symmetric South countries.4 The regions are distinguished by asymmetry in production costs: cs > cn where cs (cn ) denotes the marginal cost of production of South (North) …rms.5 Two goods are produced in each country: x and y. Good x is produced by a single pro…t-maximizing …rm in each country at a constant marginal cost in terms of the numeraire good y that is produced under perfect competition with constant returns to scale.6 For simplicity, we use the same notation for …rms as that of their corresponding countries. Preferences over the two goods are assumed to be quasi-linear: Ui (xi ; yi ) = u(xi ) + yi P

where xi is the total output sold in country i: xi

(1)

xji and xji denotes the output sold by

j

country j’s …rm in country i. Furthermore, u(xi ) is assumed to be quadratic so that the demand curve for good x is linear in each country: pi (xi ) =

xi

(2)

In the absence of any PTAs, …rm j faces a speci…c tari¤ tij when exporting to country i. Since Article I of the GATT forbids tari¤ discrimination, we restrict attention to the case where tij = ti for all i and j.7 Firm i’s e¤ective marginal cost of exporting to country z, denoted by ciz , is ciz = ci + tz where z 6= i. Firm j’s pro…ts from exporting xji to country i, denoted by ji , can be written as: cji xji (3) ji = pi (xi )xji First order conditions (FOCs) for pro…t maximization for exporters are pi + p0i xji = cji

(4)

Utilizing the demand function in (2) and the above FOCs can be solved for equilibrium outputs and pro…ts of all …rms: 4ci + xii =

P

z6=i

5

4ck +

cz + 3ti

P

cz

z6=k

; xki =

and xi =

5 ii

= x2ii and

2ti

P z

ji

= x2ji

4 xzi =

P

cz

3ti

z

5 (5)

4 From hereon, for notational simplicity, n denotes the representative north …rm and country while s denotes the representative south …rm and country. 5 For simplicity, …xed costs and transportation costs are assumed to be zero. 6 The gains from trade stem from reduced market power in the domestic industry. To this end, the monopoly assumption is not crucial but is the simplest way to represent market power. 7 It is obvious that tii = 0 for all i since countries do not impose taxes on their local …rms and there are no tari¤s on the numeraire good (that may be traded internationally in order to balance trade).

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The following comparative statics are standard: @xii dxi @xzi cn = 0. The following optimal tari¤s obtain under no agreement h i: tn =

9

2c 33

> ts =

6

9

7c 33

(10)

3.2

Bilateral preferential trade agreements

Given that our objective is to examine the static and dynamic implications of di¤erent forms of PTAs, we initially allow single bilateral PTAs only.8 Therefore, beside f g, the following trade policy regimes can arise: (i) North-North PTA fnn0 g; (ii) South-South PTA fss0 g; (iii) North-South PTA fnsg. In order to di¤erentiate CUs from FTAs, we use a superscript u for CU, i.e. while fnn0u g denotes North-North CU, fnn0 g denotes North-North FTA. 3.2.1

Free trade agreements

Suppose countries i and j enter into an FTA fijg under which they impose zero tari¤s on each other: tij = tji = 0. Under fijg, member country i solves max Wi (ti ; tz ); where z 6= i; j ti

(11)

where tz is a vector of tari¤s member countries’…rms face in non-member countries’markets while ti denotes the external tari¤ country i imposes on the imports from non-member countries. The following optimal tari¤s obtain: tnn n = 3.2.2

3c 8

; tss s =

+ 2c ns 6 + 7c 6 13c ; tn = and tns s = 8 48 48

(12)

Customs unions

As per Article XXIV of the GATT, when countries form a CU (say fij u g), we assume that they eliminate the internal tari¤s on each other (tij = tji = 0) and impose common external tari¤ u (ti (ij u ) = tj (ij u ) = tij ) on the non-member countries. As a result, due to the market segmentation, member countries (i and j) solve the following problem: u

u

max wi (tij ; tz ) + wj (tij ; tz ); where z 6= i; j u tij

(13)

where tz is a vector of tari¤s member countries’…rms face in non-member countries’markets while u tij denotes the common external tari¤ member countries impose on the imports from non-member countries. The following optimal tari¤s obtain under CUs: c

0u

tnn =

4

0u

; tss =

u

4

and tns =

2

c 8

where z = n; s

(14)

where z = s, n. We proved in the appendix that export of South …rms under all PTAs is non-negative i¤ c c = 11 holds. From hereon, we assume that c < c holds.9 8

Later on, we will examine the implications of having additional bilateral PTAs and the expansion of PTAs to more than two members. 9 The complete derivation and formulae we do not report in the text can be found in the appendix.

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3.2.3

Tari¤ comparisons

In order to minimize the potential harmful e¤ects of PTAs, Article XXIV of the GATT requires that member countries not raise tari¤s (or any other trade restrictions) on non-members. In our model, as in Bagwell and Staiger (1997a, 1999), we …nd that this requirement is not binding since the formation of a bilateral PTA induces each member to lower its tari¤ on the non-member country relative to the status quo (i.e. the model exhibits tari¤ complementarity).10 The intuition can be explained as follows: when PTA members reduce their tari¤ on each other to zero, exports of the non-member countries decrease and thus they become a less important rent-extracting source. We denote the tari¤ complementarity e¤ ect realized under an FTA fijg and under a CU fij u g u u in a member country i by i (ij) = ti tij tij > 0, respectively. It is i > 0 and i (ij ) = ti straightforward to show that the tari¤ complementarity e¤ect is larger under an FTA relative to a CU of the same composition: i (ij) > i (ij u ) and the formation of a N orth N orth (South South) PTA leads to the largest (smallest) external tari¤ reduction relative to no agreement. For the former, unlike an FTA, a CU takes into account the export pro…ts that members derive from each other’s markets and thus members impose higher external tari¤s on non-members under a CU relative to an FTA of the same composition. The latter argues that the tari¤ complementarity e¤ ect decreases (increases) in the average cost of the member (non-member) countries. When the member countries of a PTA are more e¢ cient than the non-member countries, the non-members’ exports to member countries fall relatively more, further reducing the protection incentives of the member countries. Consequently, since the average cost of the member countries is the lowest, a North-North PTA yields the largest tari¤ complementarity e¤ect while the opposite is true for a South-South PTA. This tari¤ complementarity is consistent with that previously found in both theoretical and empirical literature.11 Using a general equilibrium analysis with Cobb-Douglas preferences, Bond et al. (2004) shows that, in response to internal trade liberalization, FTA members have an incentive to reduce their external tari¤s by an amount that exceeds the Kemp–Wan tari¤ reduction, a stronger result than the tari¤ complementarity e¤ect named by Bagwell and Staiger (1997a). As in Syropoulos (1999), depending on comparative advantage, Bond et al. (2004) shows that tari¤ complementarity is di¤erent under a CU than an FTA, and CU members may actually increase external tari¤s. A similar CU result may arise under a multi-country oligopoly model with dif10

The proof can be found in the appendix.

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World Bank (2005) argues that no clear evidence shows that the formation of a PTA leads member countries to become more protectionist towards non-member countries. Tari¤ complementarity has been found empirically in several studies. Foroutan (1998) examines how countries forming regional trade agreements adjust their external tari¤s and …nds that both integrating and non-integrating countries reduced their tari¤s. Magee and Lee (2001) shows that the formation of European Economic Community (EEC) induced members to reduce their external tari¤s. Baldwin and Seghezza (2010) study the relationship between preferential and MFN tari¤s in 23 developed and developing countries and …nd that tari¤ complementarity holds. Using a detailed cross industry data set on Argentina, Bohara et. al (2004) examine the in‡uence of imports from Brazil on Argentina’s external tari¤s and …nd that increased preferential imports in an industry reduced the external tari¤s of Argentina, especially in industries that experienced trade diversion. Estevadeordal et. al (2008) evaluate empirically the e¤ect of preferential tari¤s on external trade liberalization in a large group of developing countries. Their results indicate that tari¤ complementarity e¤ect exists. The e¤ect is stronger in industries where agreement partners are more important suppliers.

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ferentiated products and linear demand as in Mrazova et al. (2013). However, once we exclude prohibitive costs and guarantee non-negative exports of South …rms in our model, we prove in the appendix that tari¤ complementarity e¤ect always holds under both FTA and CU. 3.2.4

Welfare comparisons

In terms of welfare, while member countries are better o¤ under any PTA relative to no agreement, non-member countries are better o¤ under FTAs and worse o¤ under CUs relative to no agreement. Accordingly, aggregate world welfare under a PTA is always larger relative to that under no agreement while North-North PTA (South-South PTA) yields the highest (lowest) world welfare. From each country’s perspective, a PTA embodies the following trade-o¤. On the one hand, forming a PTA lowers a member country’s domestic surplus relative to the case where it can use its optimally chosen tari¤(s). On the other hand, being part of a PTA increases export pro…ts in other member’s market. We …nd that, when c c holds, the latter e¤ect dominates the former so that countries always have an incentive to form a PTA.12 Furthermore, we can make two immediate points for non-member countries: (i) due to market segmentation, a PTA does not alter the domestic surplus of a non-member country and (ii) quantity competition in the product market implies that equilibrium export pro…ts are directly related with the total exports. Since the non-member countries’exports increase when the other countries form an FTA, their welfare levels increase relative to the no agreement. On the other hand, non-member countries’ exports decrease when the other countries form a CU as the tari¤ complementarity is not large enough to o¤set the discrimination they face relative to member countries and their welfare decreases relative to no agreement.13 This result implies that the PTAs can have harmful e¤ects on the non-member countries unless they are accompanied by su¢ cient external tari¤ reductions. Since North-North PTA leads to larger trade creation and smaller trade diversion relative to a South-South PTA (and North-South PTA), world welfare follows the same ranking as that of the tari¤ complementarity e¤ects (i.e. higher complementarity is associated with higher welfare). The discussion so far does not speak about the welfare of member countries under FTAs relative to CUs of the same composition. When a PTA involves symmetric countries, member countries are better o¤ under a CU relative to an FTA of the same composition. This stems from the fact that, unlike an FTA, a CU takes into account the export pro…ts that members derive from each others’ markets in the joint welfare maximization. Thus, we obtain wn (nn0u ) > wn (nn0 ) and ws (ss0u ) > ws (ss0 ) for all c

(15)

However, when a PTA involves asymmetric members (such as North-South PTA), while common external tari¤ setting always bene…ts the North member, it harms the South member country if it 12 Using welfare levels reported in the appendix, it is straightforward to prove all the results based on welfare comparisons. 13 Winters (1997) and Chang and Winters (2002) argue that welfare of non-member countries need not be perfectly correlated with their exports. Our results mainly rely on the assumptions of market segmentation and Cournot competition.

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is su¢ ciently high cost: wn (nsu ) > wn (ns) for all c while ws (nsu ) > ws (ns) i¤ c < cns s

(16)

where cns s < c holds. To this point, since we have not allowed for multilateral tari¤ reductions, the only way to achieve tari¤ levels lower than the one under the no agreement is via bilateral PTAs. Next we examine the following question: how does bilateral trade liberalization (via an FTA or a CU) a¤ect incentives for multilateral tari¤ cooperation over free trade?

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Multilateral cooperation over free trade

Similar to the existing literature, multilateral tari¤ cooperation over free trade is modeled as a stationary repeated game where cooperation can be sustained only if it is incentive compatible for all countries.14 In previous models, cooperation is self-enforcing in the sense that each country balances the current bene…t of deviating from free trade against the future losses caused by the breakdown of multilateral cooperation that results from its defection. We assume that countries sustain cooperation via trigger strategies and defection by any country results in a multilateral trade war. It is useful to note an important di¤erence between no agreement and PTAs. By assumption, PTAs are permanent in nature so that member countries of a PTA retain zero tari¤s on each other even if cooperation with non-member countries breaks down. On the other hand, countries revert to optimally chosen individual MFN tari¤s in the absence of PTAs.

4.1

Cooperation under no agreement

Suppose that each country employs zero tari¤ until any one of them defects. Once defection happens, countries switch back to their optimally chosen individual MFN tari¤s. Let Wi (t = 0) denote the per period welfare of country i under cooperation: Wi (t = 0) = Si (ti = 0) +

X

iz (tz

= 0)

(17)

z6=i

where Si (ti = 0) is the domestic surplus and

P

iz (tz

= 0) equals the total exporting pro…t of

z6=i

country i under free trade. Next, we de…ne the welfare of country i that defects from zero tari¤ to its optimal MFN tari¤ under no agreement (ti ) while other countries cooperate: Wi (ti ) = Si (ti ) +

X

iz (tz

= 0)

(18)

z6=i

Note that since markets are strategically separated from each other, defection from free trade to ti does not a¤ect the total export pro…ts of country i whereas it increases its domestic surplus from Si (ti = 0) to Si (ti ). Since defection by any country leads to a permanent multilateral trade 14

See Riezman (1991), Bagwell and Staiger (1997a, 1997b, 1998, 1999), Bond et al. (2001), and Saggi (2006, 2009).

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war where all countries impose their optimally chosen individual MFN tari¤s, welfare levels under trade war (No agreement) are as follows: Wi (t ) = Si (ti ) +

X

iz (tz

)

(19)

z6=i

where t denotes the vector of optimally chosen tari¤s by all countries while tz excludes ti from t . Using the expressions in (17), (18) and (19), we are able to de…ne one period bene…t and cost of defection for countries. First, we de…ne the bene…t from the defection: Bi (ti ) = Wi (ti )

Wi (t = 0)

(20)

= Si (ti ) Si (ti = 0) {z } | >0

Similarly, per period cost of defection to a country is given by15 Ci (t ) = Wi (t = 0)

Wi (t )

2 X = Si (ti = 0) Si (ti ) + 4 | {z } z6=i Bi (ti ;t)0

3

(21)

iz (t~i )5

}

In order for tari¤ cooperation to be self-enforcing, the one period bene…t from defection must be less than the discounted lifetime cost of defection since defection leads to permanent multilateral trade war. In other words, the incentive compatibility (IC) constraint must hold for each country as follows: Bi (ti ) Ci (t ) 1 where denotes the discount factor and 1 Ci (t ) measures the trade war’s life-time cost of defection to each country under f g. For each country, the critical discount factor i above which cooperation over free trade is self-enforcing obtains when Bi (ti ) = 1 Ci (t ) holds. Next, we examine the nature of per period bene…t and cost of defection from the perspective of South and North countries. Before proceeding, it is important to note that countries’incentives for cooperation di¤er across the regions because of the underlying di¤erences in production costs. In this case, the bene…t of defection to a country can be shown to be decreasing both in that country’s cost of production and in the other countries’costs, while the cost of defection is decreasing in its own cost and increasing in the other countries’costs.16 Regarding the bene…ts, the intuition has to do with the fact that tari¤s are used to extract rents in the model: since demand is symmetric across countries, any given reduction in imports decreases consumer welfare in a roughly equal way in all countries whereas it results in a greater increase in domestic …rm’s local pro…ts in lower cost 15

Note that under complete symmetry (cs = 0), following Brander and Krugman (1983), it is straightforward to argue that the second term in (21) is greater than the absolute value of the …rst term so that Ci (t ; t) is always positive. This implies that under symmetry, if countries were to completely discount the future payo¤s, multilateral tari¤ cooperation would not be feasible. 16

Formally, for z 6= i;

@Bi (ti ) @ci

< 0 and

@Bi (ti ) @cz

< 0;

@Ci (t ) @ci

11

< 0 and

@Ci (t ) @cz

> 0.

countries due to higher mark-ups. Thus, the bene…t from defection rises as a country becomes more e¢ cient. Similarly, when the rival countries become more e¢ cient, the incentive to extract rent increases and thus the bene…t from defection rises. The e¤ects with respect to cost of defection can be explained as follows. Due to the smaller volume of exports, countries with higher costs of production bene…t less from tari¤ reductions granted by others. Similarly, such countries have relatively more to lose from eliminating their own optimal tari¤s since they apply to relatively larger import volumes. Thus, the cost of defection from tari¤ cooperation of a country depends negatively on its own cost. Finally, the higher the cost of the other countries, the larger the increase in export pro…ts due to the tari¤ cooperation over free trade, and the smaller the loss due to its own trade liberalization since tari¤ reduction applies to smaller volume of imports (due to higher cost of the other countries). Therefore, the cost of defection falls when other countries become more e¢ cient. Since the bene…t from defection rises while the cost of defection falls when the other countries become more e¢ cient, we know that, under f g, the range of discount factors above which North country is willing to cooperate over free trade is always larger than that above which South countries are willing to cooperate: s n . Thus, multilateral cooperation over free trade is sustainable if and only if s. This informs us that, under no agreement, the critical discount factor above which South countries are willing to cooperate over free trade binds for the sustainability of multilateral cooperation over free trade. Next, we consider how the formation of PTAs of di¤erent compositions changes the incentives for multilateral cooperation over tari¤s.

4.2

Cooperation under PTAs

Suppose two countries sign a binding PTA and eliminate tari¤s on each other. As mentioned above, we assume that countries are bound to their original PTAs, implying that member countries retain zero tari¤s on each other even when the multilateral cooperation breaks down. How does the formation of a PTA (fijg if it is an FTA or fijgu if it is a CU) alter the costs and bene…ts of multilateral tari¤ cooperation for member and nonmember countries? To address this question, …rst consider the perspective of the non-member countries. 4.2.1

Cooperation incentives of non-members under PTAs

It is straightforward to argue that when countries cooperate over free trade, the per period welfare of a non-member country under free trade and in the defection period (thus the bene…t of defection from cooperation for the non-member country) stays the same under a PTA as under f g. After the breakdown of cooperation, a non-member country (say country k) responds via raising its tari¤ from zero to tk as under f g from next period on, but faces tz in the other non-member country z while u ij ij u facing tij and tij under a CU). Since the i and tj in member countries’markets under an FTA (ti j bene…t from the defection of a non-member country under a PTA is the same as the one under no @Bkr (tk ) @Bkr (tk ) < 0 and < 0, where z 6= k agreement, it behaves the same way as outlined earlier: @c @cz k u and r = fijg; fijg . However, for a non-member country, the formation of a PTA yields a reinforcing e¤ect on the cost of defection. The lower the cost of the member countries, the larger the tari¤ 12

complementarity e¤ect under a PTA the non-member country enjoys. Thus, the cost of defection @C r (tr ;tr ;t )

@C (t )

k i j k k from cooperation falls as member countries become more e¢ cient: > @c > 0, where @ci i u r = fijg; fij g. The following ranking is immediate from non-member countries’perspective:

nn0 s nn0u s

ns s0 nsu s0

ns ss0 n0 > n nsu ss0u n0 > n

(22)

The above ranking provides support for the idea that the lower the cost of member countries of a PTA, the less willing the non-member countries to cooperate over free trade. Similarly, when nonmember countries are asymmetric (as under a North-South PTA), the South non-member country’s incentive to cooperate is lower than that of the North non-member country. Note that the critical discount factors for the non-member countries follow the same ranking of the tari¤ complementarity e¤ects of PTAs described earlier. Next, we compare the incentives of non-member countries under a PTA relative to no agreement. The earlier welfare comparisons show that a non-member country is better (worse) o¤ under an FTA (a CU) relative to no agreement. The per period cost to a non-member country of the breakdown of cooperation is then smaller (greater) under an FTA (a CU) relative to that under f g while the bene…t of defection stays the same. Therefore, an FTA (a CU) makes non-member 0 0u countries less (more) willing to cooperate multilaterally over free trade: (i) nn > s > nn ; (ii) s s ns nsu ns nsu ss0 ss0u s0 > s > s0 ; (iii) n0 > n > n0 and (iv) n > n > n . Combining this with the ranking in (22), we can summarize the ranking structure of critical 0 ns nn0u nsu discount factors: nn s s and s > s s0 s0 . The results so far speak out for the sustainability of multilateral cooperation over free trade only from non-member countries’perspectives. Since the incentive constraint of the least willing participant determines the sustainability of multilateral free trade, we can argue by focusing on non-member countries that if multilateral free trade cannot be supported under no agreement ( < s ), it can never be sustained under the North-North FTA and North-South FTA as well (the formation of these agreements hinders multilateral tari¤ cooperation). Unlike bilateral FTAs, non-member countries under CUs of the same composition have stronger incentives to cooperate relative to no agreement. In order to see the full picture, we have to consider the incentives of member countries for multilateral tari¤ cooperation under PTAs. To this end, we examine bilateral FTAs and CUs in isolation. 4.2.2

Cooperation incentives of FTA members

With a pre-existing FTA, the FTA member i defects from free trade and raises its tari¤ (from zero to tij i ) only on non-member countries. In subsequent periods, there is a trade war in which countries apply their optimal tari¤s under the initial FTA.17 The FTA member’s bene…t from defection equals the increase in domestic surplus due to the ability to raise its tari¤ from zero to tij i : ij ij Biij (tij S ij (ti = 0) i ) = Si (ti ) {z i } |

(23)

>0

17

A more detailed analysis of the welfare levels and bene…t and cost of defection is provided in the appendix.

13

and thereafter faces tz in non-members’markets while the other FTA member j raises its tari¤ on non-members from zero to tij j , so that the per period cost of defection equals X X ij ij ij (24) Ciij (tij Siij (tij iz (tz = 0) ij (tj ) iz (tz ) i ; tj ; tz ) = Si (ti = 0) i )+ | {z } z6=i

Biij (tij i )0

< 0 hold, if member countries are asymmetric, the one with a higher cost is less

willing to cooperate relative to its FTA partner (with a lower cost) and (ii) since ij @Ciij (tij i ;tj ;tz ) @cz

@Biij (tij i ) @cz

< 0

> 0 hold, member countries are more willing to cooperate as the non-member and countries become less e¢ cient. Therefore, we obtain the following ranking: ss0 s

4.2.3

ns s

nn0 n

ns n

(25)

Sustainability of multilateral free trade under FTAs

Sustainability hinges on the discount factor of the country that is least willing remain in the agreement. To this end, we identify two distinct e¤ects that arise upon the formation of an FTA: the membership e¤ ect and the asymmetry e¤ ect. First, we isolate the former e¤ect by assuming that all countries are symmetric with respect to cost of production (c = 0). Under such a case, while both the bene…t and cost of defection for members are lower (countries i and j) relative to that of non-members, the di¤erence in the cost of defection is relatively smaller: Biij (tij i ) ij Ciij (tij i ; tj ; tz ) 18

Bzij (tz ) =

3 2 < 0, where z 6= i; j 88

(26)

21 2 < 0, where z 6= i; j 3872

ij Czij (tij i ; tj ; tz ) =

(27) ij

Formally, where z 6= i; j denotes the non-member country under an FTA hfijgi. Then: (i)

ij ij @Bi (ti ) @cj

> 0 and

ij ij @Bi (ti ) @cz

ij

< 0 and (ii)

ij

ij

@Ci (ti ;tj ;tz ) @ci

ij

< 0,

14

ij

ij

@Ci (ti ;tj ;tz ) @cj

ij

< 0 and

ij

ij

@Ci (ti ;tj ;tz ) @cz

> 0.

ij

@Bi (ti ) @ci

< 0,

and Bzij (tz )

ij ij ij Biij (tij i ) > Cz (ti ; tj ; tz )

ij Ciij (tij i ; tj ; tz ), where z 6= i; j

(28)

Thus, when countries are symmetric, non-member countries are less willing to cooperate relative ij ij to member countries: ij z > i = j , where z 6= i; j and we call this the membership e¤ ect. We also know from the bene…t and cost of defection discussions above that the higher the cost of a country, the less willing it is to multilaterally cooperate over free trade and we refer to this as the asymmetry e¤ ect, which becomes stronger as the cost asymmetry gets larger.19 As represented in Figure 1, since these two e¤ects reinforce each other under fnn0 g, the South non-member countries’ incentive is binding for the sustainability of multilateral cooperation, or multilateral cooperation nn0 over free trade is sustainable if and only if s . [Insert Figure 1] Similarly, under North-South agreement fnsg, both the membership e¤ ect and the asymmetry e¤ ect work in the same direction for the South non-member country which, as the least willing country, determines the critical discount factor. Here it is worth mentioning that asymmetry e¤ ect dominates the membership e¤ ect for the South member country relative to the North non-member country and thus we obtain (see Figure 1): ns s0

>

ns s

>

ns n0

>

ns n

(29)

ns so that, under fnsg, multilateral cooperation over free trade is sustainable if and only if s0 . 0 Finally, consider the South-South agreement fss g. We …nd that asymmetry e¤ect dominates 0 ss0 the membership e¤ect if and only if South countries are su¢ ciently high cost: ss s n if and only 0 ss if c c (see Figure 1). In other words, when countries are relatively symmetric, the North nonmember country’s incentive is pivotal for multilateral cooperation but the South member countries’ incentives determine the critical discount factor when they are su¢ ciently high cost. Accordingly, 0 ss0 under fss0 g, multilateral cooperation over free trade is sustainable if and only if > max( ss s ; n ) 0 0 ss0 where ss css . In essence, in the critical discount factor Figures, we are most s n i¤ c interested in the country with the highest critical curve at each cost level. Next, we compare the range of discount factors above which multilateral cooperation over free trade is sustainable under di¤erent compositions of FTAs. Before proceeding, let cr v denote the cost threshold at which the critical discount factors under FTAs r and v are equal. Combining these results with (22), we can state our main result in the FTA context (see Figure 5): Proposition 1 While the range of discount factors above which multilateral cooperation over 0 ns free trade is sustainable is larger under fnsg relative to fnn0 g for all c: nn s s0 , we obtain 0 0 0 0 0 0 0 0 0 ss ss ns ss ss nn ns ss nn ss max( s ; n ) c and max( s ; n ) i¤ c c , where cns ss < s s0 i¤ c 0 0 cnn ss . While multilateral cooperation over free trade is easier to sustain under f g relative to

fnsg and fnn0 g for all cost levels, it is harder to sustain under f g relative to fss0 g when c 0 c c ss holds. 19

ss0

This e¤ect works in the same manner for the competitive endowment model of Section 6 where the asymmetry is in terms of the endowment (North has high endowment, South is low endowment).

15

The …rst part of the above proposition is immediate from (22) and it argues in favor of the idea that while aggregate world welfare is higher under fnn0 g relative to fnsg, multilateral free trade is easier to sustain under fnsg relative to fnn0 g. The primary reason for this result is that the non-member South country is less willing to cooperate as average e¢ ciency of FTA members rises since the tari¤ complementarity e¤ect (thus the free rider e¤ect) is larger under fnn0 g relative to fnsg. Thus, the external trade liberalization of FTA members itself reduces the incentives of non-members for multilateral trade liberalization making multilateral cooperation less likely to be sustainable. The second part of the above proposition informs us that when South countries are su¢ ciently 0 low cost (c < cns ss ), multilateral free trade is easier to sustain under fss0 g relative to other 0 0 compositions of FTAs. To understand the intuition, note that since css < cns ss holds we have to 0 ss0 ss0 and (ii) ss0 > ss0 when cns ss0 > c > css0 . consider two cost ranges: (i) ss s < n when c < c s n 0 ss0 ss Suppose …rst that c < c holds and accordingly n is the critical discount factor under fss0 g. 0 nn0 ns ss0 It is immediate from (22) that ss n < s0 (thus n < s ) holds since (i) country n is more e¢ cient relative to country s0 and (ii) average cost of members is lower under fss0 g relative to 0 0 0 0 fnsg. Consider now that cns ss > c > css holds and ss s is the critical discount factor under fss g. Over this range, both the bene…t and cost of defection of country s under fss0 g is lower than the ones of country s0 under fnsg and the di¤erence in costs is smaller relative to the di¤erence in bene…ts. Thus, cooperation is easier to sustain under fss0 g relative to fnsg and (thus relative to fnn0 g). On the other hand, as c rises, the South member countries’cost of defection under fss0 g falls more rapidly relative to the South non-member country under fnsg and fnn0 g and thus we obtain that the critical discount factor under fss0 g exceeds the one under fnsg when c is su¢ ciently 0 0 nn0 high: c cns ss . A similar argument applies for the comparison of ss s and s . As a result, when countries are relatively symmetric, multilateral cooperation over free trade is easier to sustain under fss0 g relative to other compositions of FTAs. Under such a case, it is important to note that the critical discount factors under di¤erent FTAs follow the same ranking as of the aggregate world welfare (that is, the highest welfare outcome is associated with the lowest sustainability of free trade). In other words, positive sustainability implications comes at the expense of a welfare loss. However, when South countries are su¢ ciently high cost, the opposite result obtains and the welfare and sustainability implications become aligned. Relative to no agreement, we know from above that fnsg and fnn0 g raise the critical discount factor above which multilateral cooperation over free trade is sustainable relative to no agreement: nn0 ns ss0 ss0 s s0 > s . What remains is the comparison of s and max( s ; n ). As discussed above, 0 0 when countries are relatively symmetric, ss n binds under fss g due to signi…cant tari¤ complementarity the North countries enjoy as non-members, implying that the membership e¤ect dominates 0 the asymmetry e¤ect that arises for the South country under no agreement: ss n > s . As the 0 cost asymmetry rises, the membership e¤ect weakens (lowering ss n ) while the asymmetry e¤ect 0 0 strengthens (raising s ). When the cost asymmetry is su¢ ciently large, ss s binds under fss g. The cost and bene…t of defection of a South country are lower under fss0 g relative to f g and 0 the reduction in the former dominates the reduction in the latter so that ss s > s obtains. At

16

0

0

0

ss intermediate cost asymmetry (between c ss0 and c ss in Figure 1), s > max( ss s ; n ) obtains, making multilateral cooperation easier to sustain under fss0 g relative to f g. There has been widespread concern regarding that the formation of South-South trade agreements undermines multilateral trade liberalization e¤orts. In this, we have shown that a SouthSouth FTA is the only bilateral FTA that can facilitate multilateral cooperation when the degree of cost asymmetry across countries is at a moderate level. However, we have to be cautious since multilateral free trade is less likely to be sustainable under South-South FTA relative to all other possible trade regimes when South countries are su¢ ciently high cost. We next consider the incentives of CU members for multilateral cooperation.

4.2.4

Cooperation incentives of CU members

Again, with a pre-existing CU, defection from free trade involves both countries (this is required to revert to the original CU), so that both CU members defect from free trade and raise their tari¤s u (from zero to tij ) on non-member countries. In essence, a member country cannot revert to its CU position without the support of its original CU partner (due to the common external tari¤ of a CU). In this case, the CU member’s bene…t from defection equals the increase in (i) domestic U surplus due to the ability to raise its tari¤ from zero to tij i and (ii) export pro…ts in CU partner’s u market since tij applies to non-member countries only: u

u

u

u

u

u

Biij (tij ) = Siij (tij ) Siij (ti = 0) + ij (tj = tij ) {z {z } | |

ij (tj

>0

>0

= 0) }

(30)

Note that the second e¤ect does not arise under an FTA since only one country deviates in that case. Thus, a member’s bene…t from defection under a CU is always larger relative to that under an FTA of the same composition: u

u

Biij (tij ) > Biij (tij i ) for all c When a member i defects from cooperation, from next period on, it faces tz in non-members’ u markets while the CU’s tari¤ on non-members stays the same as tij , so that a CU member’s per period cost of defection equals u

u

Ciij (tij ; tz ) =

u

u

Biij (tij i )+

X

iz (tz

= 0)

iz (tz

)

(31)

z6=i;j

It is immediate from (15) that cost of defection of member countries under fnn0u g and fss0u g is smaller relative to the one under fnn0 g and fss0 g. Moreover, we know from (16) that while the North member’s cost of defection under fnsu g is always lower relative to fnsg, the opposite obtains for the South member only when it is su¢ ciently high cost. Overall, for that range, the e¤ect on the bene…t dominates the e¤ect on the cost for the South member country under fnsu g relative to fnsg, so that member countries have weaker incentive to cooperate multilaterally over free trade 0u 0 0 ss0u under a CU relative to an FTA of the same composition: (i) nnn > nn > ss s ; (iii) n ; (ii) s 17

nsu n

u

ns > ns > ns s . This implies, when combined with the FTA analysis above, that n and (iv) s the range of discount factors for which a member (non-member) country is willing to cooperate over multilateral free trade is smaller (larger) under a CU than that under an FTA of the same composition. Next, we examine the critical discount factors under di¤erent compositions of CUs.

4.2.5

Sustainability of multilateral free trade under CUs

As under FTAs, we focus on the least willing country’s incentive that determines the critical discount factor over which multilateral tari¤ cooperation is sustainable under a CU. Thus, we combine the incentives of non-member countries and member countries. Before proceeding, note that while the membership e¤ ect and the asymmetry e¤ ect arise under the formation of both FTAs and CUs, the nature of these e¤ects is quite di¤erent. On one hand, the two factors together imply that the direction of the membership e¤ect under a CU is the opposite to that under an FTA: (i) the common external tari¤ under a CU is higher than the individual external tari¤ under an FTA and (ii) unlike an FTA, the defection of CUs from multilateral cooperation involves both members. As before, in order to isolate the membership e¤ect, we assume that asymmetry e¤ect does not exists (c = 0). We show that, when countries are completely symmetric, the bene…t from defection for members (countries i and j) is higher while their cost of defection is lower relative to non-members: u 1 u u Biij (tij ) Bzij (tz ) = ( )2 > 0 11 10 and u 1069 u u u ( )2 < 0 Ciij (tij ; tz ) Czij (tij ; tz ) = 2 110 Thus, opposite to FTAs, member countries are less willing to cooperate relative to non-member ij ij countries under complete symmetry: ij z < i = j , where z 6= i; j and c = 0. In other words, the membership e¤ect acts in the reverse direction under the formation of a CU relative to an FTA. On the other hand, the joint determination of external tari¤s has an important implication on the asymmetry e¤ ect for asymmetric member countries (such as fnsu g): while the bene…t and cost of the North member country is larger relative to that of the South member country under fnsu g as under fnsg, the di¤erence in costs of defection dominates the di¤erence in bene…ts from defection under fnsu g unlike fnsg. Thus, the North member country is less willing to cooperate relative u u to the South member country under fnsu g: ns > ns n s . The nature of the asymmetry e¤ ect for non-member countries under a bilateral CU remains the same as that under bilateral FTAs. In the light of the above discussion it is immediate that the membership e¤ect and the asymmetry e¤ect reinforce each other under hfss0u gi and thus the South member countries’incentive is 0u 0u binding for the sustainability of multilateral cooperation under fss0u g: ss > ss (represented in s n 0u Figure 2), so that multilateral cooperation over free trade is sustainable if and only if > ss s . [Insert Figure 2] Similarly, we show that the North member country’s incentive determines the critical discount factor under fnsu g (see Figure 2), and multilateral cooperation over free trade is sustainable if and nsu only if n . 18

Consider now fnn0u g where the membership e¤ect and the asymmetry e¤ect work in opposite directions. We show that, when the South non-member countries are su¢ ciently high cost, the latter e¤ect dominates the former and thus the South non-member countries’ incentive binds for 0u 0u nn0u the multilateral cooperation over free trade: snn i¤ c cnn . Therefore, multilateral n 0u 0u 0u nn0u cooperation over free trade is sustainable if and only if max( nn ; nn ) where nn s n s n 0u nn i¤ c c . Next, using these three results, we obtain one of our main results that compares the critical discount factors under di¤erent compositions of CUs. Proposition 2 The range of discount factors above which multilateral cooperation over free 0u nsu trade is sustainable is the largest under fnn0u g and the smallest under fss0u g: ss s n 0u 0u ), where equality obtains only when c = 0. While multilateral cooperation over free ; nn max( nn n s trade is always easier to sustain under f g relative to fnsu g and fss0u g, it is harder to sustain 0u under f g relative to fnn0u g when c cnn holds. The above proposition argues that the critical discount factors under di¤erent CUs follow a reverse ranking to that of aggregate world welfare. Speci…cally, fnn0u g not only yields the highest aggregate world welfare but also multilateral cooperation over free trade is more likely to be sustainable under fnn0u g relative to other CUs. Note that, when the degree of cost asymmetry across countries is not very large, this result provides a sharp contrast to Proposition 1. Under such a case, in terms of sustaining cooperation, while hfnn0u gi serves as the best agreement among bilateral CUs, fnn0 g is the worst agreement among bilateral FTAs. With respect to no agreement, we note that the membership e¤ ect and the asymmetry e¤ ect reinforce each other under hfss0u gi so that multilateral cooperation is harder to sustain under fss0u g 0u relative to f g: ss > s for all c. While the membership e¤ect and asymmetry e¤ect work in s opposite directions under fnsu g, the former e¤ect dominates the latter and the following obtains: nsu > s for all c. Finally, consider fnn0u g which is the best possible CU in sustaining multilateral n cooperation. We …nd that, when South countries are su¢ ciently high cost, the formation of fnn0u g 0u 0u facilitates multilateral cooperation relative to no agreement f g: s max( nn ; nnn ) i¤ c s 0u 0u 0u cnn holds. To understand this result, …rst note that cnn < cnn holds. Therefore, we have 0u 0u 0u 0u to consider three distinct cost ranges: (i) when c < cnn holds, max( nn ; nnn ) = nn and s n 0u 0u nn0u nn0u nn0u nn0u nn0u nn nn > s obtain; (ii) when c >c>c holds, max( s ; n ) = n and n < s n 0u nn0u nn0u nn0u nn0u nn obtain, and (iii) when c > c holds, max( s ; n ) = s and s < s obtain. The intuition behind part (i) and part (ii) is as follows. When the degree of cost asymmetry is su¢ ciently 0u small (c < cnn ), the asymmetry e¤ ect for South countries under f g is small and dominated by the membership e¤ ect for the North member under fnn0u g. The opposite obtains when c exceeds 0u the critical threshold, i.e. when c > cnn holds. Together with results of FTAs, we can see how the formation of PTAs a¤ects multilateral cooperation over free trade depends on (i) whether a bilateral PTA is in the form of an FTA or a CU; (ii) the country composition of an FTA and a CU and (iii) the degree of cost asymmetry between the North and South. Speci…cally, while a North-South PTA (FTA or CU) unambiguously hampers the obtainment of multilateral free trade, whether the formation of North-North and

19

South-South PTAs facilitates the obtainment of free trade depends on the form of a PTA and the degree of cost asymmetry across regions. Next, we consider a scenario in which we allow two bilateral PTAs and expansions to more than two members.

5

Cooperation under multiple bilateral PTAs, mixed PTAs and PTA expansion

Allowing for the formation of multiple bilateral PTAs yields two distinct trade agreement networks: (i) an inter-regional PTA network: two North-South PTAs (denoted by fns; n0 s0 g if agreements are in the form of FTAs, fnsu ; n0 s0u g if they are CUs, and fns; n0 s0u g and fnsu ; n0 s0 g if they are mixed agreements), and (ii) an intra-regional PTA network: North-North and South-South PTAs (denoted by fnn0 ; ss0 g if agreements are in the form of FTAs, fnn0u ; ss0u g if they are CUs, and by fnn0 ; ss0u g and fnn0u ; ss0 g if they are mixed agreements). Expansions of existing agreements form another possibility, where a non-member country joins to the existing FTAs or CUs (3 country agreements, all of which in this context are inter-regional). Here, we will consider how each of these agreements impacts the sustainability of free trade. In terms of mixed agreements, we can also examine the order of agreements: does it matter that an FTA was formed and then a CU added, or vice versa? For each of these questions, we will begin with one of the six possible initial bilateral agreements: fnn0 g; fnn0u g; fns0 g; fns0u g; fss0 g or fss0u g; and determine how an additional member or additional agreement impacts critical discount factors and therefore the potential for free trade. Due to market segmentation, the same tari¤ rates apply under a bilateral PTA when an additional PTA forms. However, as a bilateral FTA or CU expands to include new members, the external tari¤ of member countries change. In these cases, the optimum tari¤s are as follows: 0

s tnn = n

0

tnss = n

3

9c 37

0

s ; tnn = s

3

19c 37

3 + 16c nss0 3 + 6c ; ts = 37 37

0 u

0 u

s tnnn s = tnn = s

7

11c 33

and 7 + 4c 33 The previous discussion of the membership e¤ect and the asymmetry e¤ect under bilateral PTAs continue to apply when PTAs have three members. When a South country is a non-member under an FTA of three countries (i.e. fnn0 sg), its incentive binds for the sustainability of free 0 s0 trade and thus the critical discount factor under fnn0 sg is nn . When a North country is a s0 0 non-member under an FTA of three countries (i.e. fnss g), both North non-member and South 0u

0u

tnnss = tnss = s

20

member countries’incentives bind for the sustainability of free trade and thus the critical discount 0 nss0 factor under fnss0 g is max( nss ). Similarly, under CUs with three members, North member n0 ; s 0 su country’s incentive is pivotal for the sustainability of free trade and thus nn is the critical n nss0u 0 u 0u discount factor under fnn s g and n is the critical discount factor under fnss g. Now consider the trading regimes where there are two independent PTAs. Using the membership and asymmetry e¤ect, we can easily show that the South member country’s incentive binds for the 0 ;ss0 sustainability of free trade when we have (i) two intra-regional FTAs: nn is the critical discount s ns;n0 s0 0 0 factor under fnn ; ss g; (ii) two inter-regional FTAs: s is the critical discount factor under nn0u ;ss0u 0 0 fns; n s g; (iii) two intra-regional CUs: s is the critical discount factor under fnn0u ; ss0u g 0 ;ss0u is the critical and (iv) intra-regional North-North FTA and intra-regional South-South CU: nn s 0 0u discount factor under fnn ; ss g. Similarly, the North member country’s incentive binds for the u 0 0u sustainability of free trade when we have (i) two inter-regional CUs: nns ;n s is the critical discount u ;n0 s0 factor under fnsu ; n0 s0u g; (ii) one inter-regional FTA and one inter-regional CU: ns is the n critical discount factor under fnsu ; n0 s0 g; (iii) intra-regional North-North CU and intra-regional 0u ;ss0 0u ;ss0 South-South FTA: max( nn ; nn ) is the critical discount factor under fnn0u ; ss0 g. n s Proposition 3: Suppose that the status quo agreement is fnn0 g. Then, the following obtains: (i) an additional FTA fss0 g (leading to fnn0 ; ss0 g) reduces the range over which free trade is sus0 ;ss0 0 0 0 0 tainable unless countries are su¢ ciently symmetric: nn > nn when c > cnn ss nn ; (ii) free s s 0 ;ss0u trade is never sustainable with an additional CU fss0u g (leading to fnn0 ; ss0u g): nn > 1 for s 0 all c and (iii) an additional South FTA member (leading to fnn sg) always reduces the range over 0s 0 which free trade is sustainable: nn > nn for all c. s s0 When an additional FTA is added to fnn0 g; leading to fnn0 ; ss0 g, note that while the South non-member country’s incentive is binding for the sustainability of free trade under fnn0 g, it is the South member country’s incentive that determines the sustainability of free trade under fnn0 ; ss0 g . From the South country’s perspective, both the one period bene…t from defection and lifetime cost of defection under fnn0 ; ss0 g are lower relative to fnn0 g. When countries are completely symmetric, the reduction in one period bene…t from defection dominates the reduction in the lifetime cost of defection and thus additional fss0 g expands the range over which free trade is sustainable. However, once we have a very small degree of asymmetry (when we have a true South country: 0 0 0 c > cnn ss nn ), the result gets reversed: the reduction in one period bene…t from defection is dominated by the fall in the lifetime cost of defection and thus the additional fss0 g agreement decreases the likelihood free trade to be sustainable. For an additional CU fss0u g; again it is the case that the South’s incentive is binding as a nonmember under fnn0 g but as a member under fnn0 ; ss0u g (see Figure 3 for critical discount factors). The South member countries not only bene…t from coordination of their external tari¤s under the customs union but also enjoy large tari¤ complementarity under the FTA between the North countries. As a result, the South countries’welfare levels under fnn0 ; ss0u g exceed those under free trade and the cost of defection is negative while the bene…t of defection is positive. Multilateral cooperation over free trade is then impossible to sustain, as the South countries strictly prefer fnn0 ; ss0u g to free trade. 21

An expansion of fnn0 g always takes the same form to fnn0 sg: In both the initial and expended agreements, the South non-member country’s incentive is binding for the sustainability of free trade. While the one period bene…t from defection stays the same under both trade regimes, the lifetime cost of defection is smaller under fnn0 sg relative to fnn0 g due to higher tari¤ complementarity under the former agreement. Therefore, when the status-quo agreement is fnn0 g, due to the free riding incentives stemming from the tari¤ complementarity, an additional South FTA member always makes the multilateral cooperation over free trade less likely to be sustainable. [Insert Figure 3] Proposition 4: Suppose that the status quo agreement is fnn0u g. Then, the following obtains: (i) an additional FTA fss0 g (leading to fnn0u ; ss0 g) always reduces the range over which 0u ;ss0 0u ;ss0 0u 0u free trade is sustainable: max( nn ; nn ) > max( nn ; nn ) for all c; (ii) an additional n s n s CU fss0u g (leading to fnn0u ; ss0u g) reduces (increases) the range over which free trade is sustain0u ;ss0u 0u 0u able when countries are su¢ ciently asymmetric (symmetric): nn > max( nn ; snn ) when s n 0u 0u 0u c > cnn ;ss nn ; (iii) an additional South CU member (leading to fnn0 su g) always reduces the 0 su 0u 0u range over which free trade is sustainable: nn > max( nnn ; nn ) for all c. n s If we instead start with the status-quo of a North-North CU fnn0u g; the addition of a SouthSouth FTA makes free trade harder to sustain (see Figure 4 for critical discount factors). While the one period bene…t defection of the North countries under fnn0u ; ss0 g and fnn0u g is the same, the lifetime cost of defection is lower under fnn0u ; ss0 g relative to fnn0u g due to the tari¤ com0u ;ss0 0u plementarity e¤ect and thus nn > nn . From South countries perspectives, over the range n n where their incentives bind, both the one period bene…t from defection and the lifetime cost of defection under fnn0u ; ss0 g are lower relative to fnn0u g but the reduction in one period bene…t from defection is dominated by the reduction in the lifetime cost of defection and thus the additional 0u 0 0u fss0 g agreement reduces the range over which free trade is sustainable ( snn ;ss > nn ). s 0u Adding a second CU to the initial fnn g has similar e¤ects if the North and South are quite di¤erent in their costs but can improve sustainability if the costs are not too asymmetric. If the countries were symmetric, the North member country’s incentive would be binding for the sustainability of free trade under fnn0u g while it would be the South country’s incentive that binds 0u ;ss0 0u under fnn0u ; ss0u g and nn < nn holds so that free trade becomes easier to sustain. As the s n 0u nn0u ;ss0 cost asymmetry rises, s rises while nnn falls so that when South countries are su¢ ciently 0u 0 0u 0u 0u 0u high cost (c > cnn ;ss nn ) we have snn ;ss > nn . That is, when the countries are su¢ ciently n asymmetric, the South non-member country’s incentive is binding for the sustainability of free trade under fnn0u g and the bene…t-cost ratio of defection rises as the South countries form a CU and multilateral cooperation over free trade becomes harder to sustain. The expansion of fnn0u g to fnn0 su g always make free trade less sustainable. Unless the South countries are su¢ ciently high cost, the North member countries’ incentives are binding for the sustainability of free trade under both fnn0 su g and fnn0u g. From the North countries’perspective, when a South country (an attractive partner) joins to North-North CU, the cost of defection falls but the bene…t of defection falls by a smaller amount, making the multilateral cooperation over free 22

0 u

0u

s . When South countries are su¢ ciently high cost, it is the > nn trade harder to sustain: nn n n South countries’incentives that bind for the sustainability of free trade under fnn0u g. Under such a case, the expansion of a North-North CU with an additional South country raises the membership e¤ect large enough for North member under fnn0 su g to dominate the asymmetry e¤ect for South 0 su 0u non-member country under fnn0u g and thus we obtain: nn > nn . n s The above two propositions provide important insights for the evolution of today’s trade. Given that the world’s initial preferential trade agreements took place mostly between developed countries, policy makers and researchers have been concerned with the implications of preferential trade agreements with less developed countries (the polarization of the world trade). The response of the South countries to failure at multilateral negotiation rounds in Cancun and Doha has been to look for an alternative in South-South trade agreements, believing that there is more scope for trade among each other if they cannot get the deal they want with the North. When we have true South-North distinction in terms of cost asymmetry, the above two propositions deliver negative news for the sustainability of the multilateral cooperation over free trade: when a North-North FTA or CU are in place, the expansion of the FTA/CU with an additional South member and the creation of an additional South-South FTA or CU act as stumbling blocks, making multilateral cooperation over free trade less likely to be sustainable.

[Insert Figure 4] Proposition 5: Suppose that the status quo agreement is fnsg. Then, the following obtains: (i) an additional FTA fn0 s0 g (leading to fns; n0 s0 g) always expands the range over which free trade 0 s0 < ns is sustainable: sns;n 0 s0 for all c; (ii) free trade is never sustainable with an additional CU 0 s0u 0 0u 0 fn s g (leading to fns; n s0u g): ns;n > 1 for all c; (iii) an additional North FTA member n 0 (leading to fnn sg) always reduces the range over which free trade is sustainable: nn0s > ns s0 s0 for all c and (iv) when the degree of cost asymmetry is moderate, an additional South FTA member 0 nss0 (leading to fnss0 g) expands the range over which free trade is sustainable: max( nss ) < ns n0 ; s s0 0 ns 0 nss holds, and decreases the range otherwise. when cnss ns > c > c Now, let us turn to the case where the status quo is an inter-regional FTA fnsg: The South nonmember country’s incentive is binding for the sustainability of free trade under fnsg: If the countries outside that agreement create their own FTA fn0 s0 g, it is then a South member country’s incentive that determines the sustainability of free trade under fns; n0 s0 g (see Figure 5). From that South country’s perspective, both the one period bene…t from defection and the lifetime cost of defection under fns; n0 s0 g are lower relative to fnsg. We …nd that the reduction in one period bene…t from defection dominates the reduction in the lifetime cost of defection and thus an additional FTA fn0 s0 g (leading to fns; n0 s0 g) always expands the range over which free trade is sustainable. If the outside countries instead form a CU fn0 s0u g; the North CU member country n0 under fns; n0 s0u g not only bene…ts from coordination with its most preferable CU partner (a high-cost country) but also enjoys large tari¤ complementarity under fnsg. These two e¤ects yields that the welfare of country n0 under fns; n0 s0u g exceeds that under free trade and thus the cost of defection is negative while the bene…t of defection is positive. As a result, the North CU members will always 23

defect from free trade to improve its welfare, and the additional CU fn0 s0u g makes the multilateral cooperation impossible. The expansion of fnsg can take two forms: adding the North country n0 or adding the South country s0 . For the former, under both fnsg and fnn0 sg, the South non-member country’s incentive is binding. While the one period bene…t from defection stays the same under both trade regimes, the lifetime cost of defection is smaller under fnn0 sg relative to fnsg due to higher tari¤ complementarity under the former trade agreement. Therefore, when the status-quo agreement is fnsg, an additional North member always makes the multilateral cooperation over free trade less likely to be sustainable. For the latter, …rst note that, when the degree of cost asymmetry is relatively small, the South member countries’incentives are binding under fnss0 g while the North 0 0 nss0 if and only if c < cnss . We …nd that non-member country’s incentive binds otherwise: nss n0 < s 0 nss0 ns and (ii) nss0 > ns i¤ c > cnss0 ns . Therefore, for an additional South (i) nss > ns s n0 s0 s0 i¤ c < c FTA member to make the multilateral cooperation over free trade to be sustainable, the degree of cost asymmetry must be moderate. Here, we should note that among all the three country PTAs relative to no agreement, fnss0 g is the only one that can facilitate multilateral cooperation over free trade relative to no agreement (when the degree of cost asymmetry across countries is at an intermediate range). [Insert Figure 5] Proposition 6: Suppose that the status quo agreement is fnsu g. Then, the following obtains: u ;n0 s0 (i) free trade is never sustainable with an additional FTA fn0 s0 g (leading to fnsu ; n0 s0 g): ns > n 0 0u u 0 0u 1 for all c; (ii) an additional CU fn s g (leading to fns ; n s g) always expands the range over u ;n0 s0u u which free trade is sustainable: ns < ns for all c; (iii) an additional South CU member n n 0u u 0u (leading to fnss g) always reduces the range over which free trade is sustainable: nss > ns n n for all c and free trade becomes unsustainable when countries are su¢ ciently asymmetric and (iv) when the degree of cost asymmetry is su¢ ciently large, an additional North CU member (leading to 0 su u 0 u u fnns0u g) expands the range over which free trade is sustainable: nn < ns when c > cnn s ns n n holds, and reduces the range otherwise. Beginning with fnsu g; an additional FTA between non-members mimics the second part of the proposition 5 and thus the same intuition applies: the North CU member always prefers its CU position to free trade, and therefore free trade is impossible to sustain. The addition of a second CU is quite di¤erent, however. In this case, it is the North member country’s incentive is binding for the sustainability of free trade under both fnsu g and fnsu ; n0 s0u g (see Figure 6). While the one period bene…t from defection stays the same, the cost of defection rises with the formation of fn0 s0u g since country n faces higher tari¤s in the export markets outside the CU under fnsu ; n0 s0u g relative to fnsu g and thus when an inter-regional CU is in place, an additional inter-regional CU always facilitates multilateral cooperation over free trade. As the inter-regional FTA above, expansion can take two forms, with potentially di¤erent e¤ects on the sustainability of free trade. Consider …rst the expansion with a South country to fnss0u g. If the countries are relatively symmetric, both the one period bene…t from defection and the lifetime cost of defection 24

of the North CU member country under fnss0u g is lower relative to fnsu g but the reduction in one period bene…t from defection is dominated by the reduction in the lifetime cost of defection, and 0u u the additional South member reduces the range over which free trade is sustainable: nss > ns n n . When there is su¢ ciently high cost asymmetry, the bene…ts from another South country joining to the CU is so large that the welfare of country n under fnss0u g exceeds the one under free trade and thus the cost of defection is negative. Under such a case, an additional South CU member makes the North member always prefer to deviate from free trade and multilateral cooperation becomes impossible. The expansion of the inter-regional CU with a North country to fnns0u g instead makes free trade easier to sustain if the North and South di¤er signi…cantly in cost. To see this, note that both the one period bene…t from defection and the lifetime cost of defection of the North CU member country under fnn0 su g is lower relative to fnsu g but the reduction in one period bene…t 0 u u from defection is dominated by the reduction in the lifetime cost of defection when c < cnn s ns and thus an additional North member reduces the range over which free trade is sustainable. The 0 u u opposite obtains when the non-member country is su¢ ciently high cost (c > cnn s ns ) since the bene…t of defection falls and cost of defection rises considerably and thus the additional North CU member makes the multilateral cooperation over free trade easier to sustain. One common point deserves attention from Proposition 5 and Proposition 6: when there is an inter-regional PTA, an additional inter-regional PTA of the same type as the status-quo agreement 0 s0 u nsu ;n0 s0u < ns < ns always facilitates multilateral cooperation over free trade: ns;n n . s0 and n s0 Further, expansion of inter-regional PTAs can also pave the way to free trade: an inter-regional FTA must add a South country when the cost asymmetry is moderate, and an inter-regional CU must add a North country when the cost asymmetry is su¢ ciently high. [Insert Figure 6] Proposition 7: Suppose that the status quo agreement is fss0 g. Then, the following obtains: (i) an additional FTA fnn0 g (leading to fnn0 ; ss0 g) reduces the range over which free trade is sustainable 0 ;ss0 0 ss0 nn0 ;ss0 ss0 ; (ii) an unless countries are almost symmetric: nn > max( ss s s ; n ) when c > c additional CU fnn0u g (leading to fnn0u ; ss0 g) expands the range over which free trade is sustainable 0u ;ss0 0u 0 ss0 when South countries are su¢ ciently high cost: max( nn ; nnn ;ss ) < max( ss0 s s ; n ) when c > 0u 0 0 cnn ;ss ss and (iii) an additional North FTA member (leading to fnss0 g) expands the range over 0 nss0 which free trade is sustainable when South countries are su¢ ciently high cost: max( nss )< n0 ; s 0 ss0 ss0 ss0 nss max( s ; n ) when c > c . From our analysis of bilateral FTAs, a South-South FTA fss0 g was the only PTA that makes multilateral cooperation easier to sustain relative to no agreement. Next, we consider fss0 g as the status-quo and examine the implications of the expansion of the FTA and the formation of additional PTAs. As in the opposite ordering above, an additional FTA fnn0 g generally makes free trade harder to sustain. When countries are completely symmetric, the North non-member country under fss0 g enjoys large tari¤ complementarity and once it defects from free trade it is not restricted in imposing its tari¤s. These two e¤ects tilt the bene…t-cost of defection ratio in favor of North non-member country under fss0 g relative to the South member country under fnn0 ; ss0 g 25

and free trade would be easier to sustain. However, as South countries become slightly higher cost 0 0 0 (that is, when we have a true distinction between South and North: c > cnn ;ss ss ), the South’s 0 ;ss0 0 ss0 incentive becomes binding and the result gets reversed as nn > max( ss s s ; n ) obtains for all c; and an additional FTA fnn0 g makes multilateral cooperation harder to sustain. Adding a CU to fss0 g makes free trade easier to sustain with large cost di¤erences between the North and South, and harder to sustain at low cost di¤erences. From Figure 7, it is clear 0u ;ss0 0 nn0u ;ss0 that nn > ss0 < ss n n and s s for all c. Therefore, the implications of an additional CU 0u ;ss0 fnn0u g can be captured via the comparison of nn and ss0 n s . When countries are relatively symmetric, the external tari¤ coordination under a CU and higher tari¤ complementarity in the 0u 0 0 nn0u ;ss0 ss0 . However, export markets under an FTA together imply that nnn ;ss > ss s when c < c note that both of these e¤ects get weaker as the South country becomes su¢ ciently high cost and 0u 0 asymmetry e¤ect starts dominating and thus nnn ;ss falls with c while ss0 s rises. Under such a 0u ;ss0 ss0 nn 0u case (when c > c ), the formation of fnn g facilitates multilateral cooperation over free trade. Expansion of fss0 g always adds a North country, and has a similar impact as adding a CU. 0 0 0 nss0 Again, from Figure 7, it is clear that ss and nss > ss s > n0 s n for all c and thus the implications 0 0 of an additional North FTA member can be captured via the comparison of nss and ss s s . When 0 0 countries are relatively symmetric (c < cnss ss ), both the one period bene…t from defection and the lifetime cost of defection of the South countries under fnss0 g are lower relative to fss0 g but the reduction in one period bene…t from defection is dominated by the reduction in the lifetime cost of defection and thus an additional North member reduces the range over which free trade is 0 0 nss0 ss0 . As the South countries become su¢ ciently high cost, sustainable: nss > ss s s when c < c being an FTA partner with a North country is less attractive relative to having free access to all markets and thus the reduction in one period bene…t from defection dominates the reduction in the lifetime cost of defection and thus an additional North member expands the range over which free 0 0 nss0 ss0 . trade is sustainable: nss < ss s s when c > c [Insert Figure 7] Proposition 8: Suppose that the status quo agreement is fss0u g. Then, the following obtains: 0u nn0 (i) free trade is never sustainable with an additional FTA fnn0 g (leading to fnn0 ; ss0u g): ss >1 s 0u 0u 0u for all c; (ii) an additional CU fnn g (leading to fnn ; ss g) always expands the range over which 0u 0u ;ss0u free trade is sustainable: ss > nn for all c and (iii) an additional North member (leading s s 0u 0u 0u to fnss g) always reduces the range over which free trade is sustainable: nss > ss for all n s 0u 0u nss0u nss nss c 1 when c > c . Finally, we consider an initial South-South CU fss0u g. As above, combining this with a NorthNorth FTA means that a South country under fnn0 ; ss0u g not only bene…ts from the external tari¤ coordination with the best possible partner, but also it enjoys tari¤ complementarity under fnn0 g. These two factors lead to the fact that South country’s welfare under fnn0 ; ss0u g is higher than that under free trade and thus the cost of defection is negative while the bene…t from defection is positive. As a result, multilateral cooperation becomes impossible (see Figure 8). This is quite 26

di¤erent than the addition of another CU, where free trade is easier to sustain. Here, we …rst note the one period bene…t from defection remains the same for the South country under fss0u g and fnn0u ; ss0u g while the cost of defection is larger under the latter. As a result when fss0u g is the status-quo regime, an additional CU fnn0u g always facilitates multilateral cooperation. Expansion of the South-South CU to include a North member makes free trade impossible to sustain. While the South countries’ incentives bind under fss0u g it is that of the North member country under fnss0u g. The North member country has a CU with both of its most attractive trade partners fnss0u g and as the inter-regional cost di¤erence rises, the North member country’s welfare under fnss0u g exceeds that of free trade. [Insert Figure 8] In summary, expansion of existing bilateral PTAs to 3 countries is never unambiguously a building block to free trade. There are situations, however, where expansion improves the prospects for free trade. Mixed agreements (a CU combined with an FTA) generally make free trade harder or impossible to sustain, with the exception of adding a North-North CU to a pre-existing South-South FTA when the South is su¢ ciently high cost. Table 1 summarizes the cases in which expansion or additional agreements make free trade more likely to be sustainable (building block), as well as the cases where free trade becomes impossible. All other cases are stumbling blocks to free trade. As a con…rmation of our results, we brie‡y show that the qualitative results of our model are consistent with a di¤erent model speci…cation, namely perfect competition with competing exporters.

6

Robustness: Perfect competition, endowments and competing exporters

Next, to see that the results of our model are not speci…c to the oligopoly framework detailed above, we utilize a model of trade agreements based on an adapted version of the competing exporters model of Bagwell and Staiger (1999). In a perfectly competitive world, again there are two regions (North and South) each of which has two countries i = s; s0 ; n; n0 . There are four (non-numeraire) goods: g = N , N 0 , S and S 0 and a numeraire good v0 . Each country’s market is served by three competing exporters and I denotes the good that corresponds to the upper case value of i. For example, if i = n then I = N . Country i is endowed with zero units of good I and ei units of the other three goods where North countries have larger endowments than the South countries: en = en0 and 1.20 On the demand side, the representative citizen’s utility es = es0 = e function is linear in the numeraire good and additively separable in the three non-numeraire goods: U (v; v0 ) = u(v) + v0 ;

(32)

where v = [vN ; vN 0 ; vS ; vS 0 ] is the consumption vector for the four non-numeraire goods, and v0 denotes the consumption of the numeraire good. We assume that the sub-utility function u(v) is 20

In addition, all countries have large enough endowments of the numeraire good v0 to ensure trade balance.

27

quadratic, so that the demand for good g in country i is given by dgi (pgi ) =

pgi :

(33)

where pgi denotes the consumer price of good g in country i. Since each country possesses only three goods while it demands all four, country i must import good I in order to consume it and it can import it from either trading partner. For example, country n imports good N from countries n0 , s and s0 while it exports good N 0 to country n, good S to country s and good S 0 to country s0 . Let tij be the tari¤ imposed by country i on its imports of good I from country j. Ruling out prohibitive tari¤s yields the following no-arbitrage conditions for good I: pIi = pIj + tij ; j 6= i

(34)

where i; j = s; s0 ; n; n0 . Let mIi be country i’s imports of good I. Since country i has no endowment of good I, we have mIi = d(pIi ) = pIi (35) Each country’s exports of a good must equal its endowment of that good minus its local consumption: xIj = ej [ pIj ] (36) Market clearing for good I requires that country i’s imports equal the total exports of the other two countries: X mIi = xIj (37) j6=i

Using equations (34) through (37), we can easily obtain the equilibrium prices and volume of trade. From a welfare perspective, given the partial equilibrium nature of the model, it su¢ ces to consider only protected goods. A country’s welfare is de…ned as the sum of consumer surplus, producer surplus, and tari¤ revenue over all such goods: X X wi = CSiz + P Siz + T Ri (38) z

z

The following optimal tari¤s obtain under di¤erent agreements:

0

e( 2 + 1) ; 30 e(2 + 1 ) 0u nsu = tnn ; = t = 0 s s 30 e(3 2 ) ss0 e(6 5 ) ns e( 3 2) tns = ; t = ; ts = ; n s 28 28 28 e(2 1 ) e(1 + 1 ) 0u nsu nsu tss = and t = t = s n s 12 24 0u

u

tn

ns ss = tss = tns n = tn0 = tn n0 =

ts

= tnn = tns s s0

0

tnn n

0u

tnn n

0

= =

e( 6 5) ; 28 e( 2 1) ; 12

From hereon, in order to guarantee positive export and tari¤ levels under all possible PTAs, we 6 0 0 assume that 1 [5; 6] 5 holds and for simplicity assume that en = en = 6 and es = es 28

It is critical to note that as in the oligopoly model, South countries are large importers and small exporters while the North countries are the large exporters and small importers. To save space, we move immediately to the dynamic implications of bilateral PTAs for the sustainability of multilateral cooperation over free trade. As we see below in detail, our main results under oligopoly model remains unchanged qualitatively.

6.1

Bilateral PTAs

Similar to the discussion under oligopoly, when we examine bilateral FTAs and countries are symmetric, non-member countries are less willing to cooperate relative to member countries and as before we call this e¤ect the membership e¤ ect. The smaller the endowment of a country the less willing it is to multilaterally cooperate over free trade and we refer to this as the asymmetry e¤ ect. We …rst …nd that, since South countries import more and export less relative to North countries and thus their incentives are binding for the sustainability of free trade under no agreement f g: s > 0 n (see Figure 9) Similarly, since South countries are non-member under fnn g and have smaller endowments, both e¤ects reinforce each other and thus South countries are less willing to cooperate 0 0 over free trade: nn > nn s n . Now consider an inter-regional FTA fnsg under which the South nonmember country’s incentive binds for the sustainability of free trade and ns s0 is the critical discount 0 factor. Finally, the two e¤ects counteract each other under fss g and South member countries and North non-member countries’ incentives together determine the critical discount factor and thus 0 ss0 multilateral cooperation over free trade is sustainable when > max( ss s ; n ). Figure 9 and the following proposition summarize our …ndings under no agreement and bilateral FTAs: Proposition 1a: Suppose the status-quo agreement is f g. Then, the following obtains: (i) unless the degree of asymmetry is at a medium range, the formation of a bilateral FTAs of any type reduces the range of discount factors over which multilateral cooperation over free trade is sustainable: 0 0 ss0 ss0 ns nn0 or ess ns < es < ess holds and obtains when es > ess0 s < max( s ; n ) < s0 < s 0 ns ns ss0 ss0 nn0 ss 0 obtains when es < e holds and (ii) fss g is the only type s < s0 < max( s ; n ) < s of FTA that makes multilateral cooperation over free trade easier to sustain relative to f g and it 0 ss0 ns nn0 happens when the degree of asymmetry is at a medium range: max( ss s ; n ) < s < s0 < s 0 obtains when ess0 > es > ess holds. [Insert Figure 9] Next, Figure 10 and the following proposition show that our bilateral CU results under the oligopoly model remain unchanged under the competing exporters model (see Figure 10): Proposition 2a: Among bilateral customs unions, the range of discount factors above which multilateral cooperation over free trade is sustainable is the largest under fnn0u g and the smallest 0u 0u 0u nsu under fss0u g: ss max( nn ; nn ). While multilateral cooperation over free trade is s n s n always easier to sustain under f g relative to fnsu g and fss0u g, it is harder to sustain under f g 0u relative to fnn0u g when e < enn holds. [Insert Figure 10] 29

It is important to note that the above competing exporters model leads to the same set of results as the one under oligopoly model. While fss0 g is the only type of FTAs that makes multilateral cooperation over free trade easier to sustain relative to f g, fnn0u g is the only type of CU that facilitates multilateral cooperation over free trade. This suggests that the incentives structure for multilateral cooperation remains unchanged regardless of the type of the model as long as we interpret the asymmetry across countries in terms of large-small importing-exporting countries.

7

Conclusion

In this paper, we have considered how the formation of PTAs among cost-asymmetric North and South countries impacts non-member countries, world welfare and the sustainability of multilateral of free trade. By utilizing a four-country setup with multiple high cost and low cost countries, we were able to di¤erentiate the roles of both cost (high versus low) and membership status (member versus non-member) in bilateral FTAs and CUs, and for the prospects of global free trade. In our framework, the asymmetry e¤ ect serves to make high cost countries less willing to participate in multilateral free trade, independently of whether they were initially part of an FTA or a CU or a non-member. The feasibility of free trade then hinged upon the membership e¤ ect that works in the same direction as the asymmetry e¤ect under CUs while working in the opposite direction under FTAs. Our model exhibits some commonly voiced concerns regarding South-South agreements, particularly that these arrangements lead to higher levels of protection and lower welfare than North-North and North-South agreements. This result is more prominent when the initial PTA is a customs union than when it is a FTA. However, in terms of sustainability, we …nd certain cases where SouthSouth agreements are more likely to lead to global free trade than North-North or North-South agreements, but other cases where multilateral cooperation over free trade is the least likely under South-South agreements. In this way, we have shown that both the composition of agreement (CU versus FTA) and the extent of cost variation between the North and South are critical in the evaluation of whether South-South trade agreements are bene…cial or harmful for the prospects of global free trade. Our other key …ndings relate to the expansion of bilateral PTAs or the additions of other PTAs to existing PTAs. Expansions of North-South FTAs with South countries, North-South CUs with North countries, and South-South FTAs with North countries, can lead to improved prospects for free trade (under particular cost conditions). Mixing agreement types, such as adding a CU to an existing FTA, generally makes free trade less likely, including making the potential move to free trade impossible in some cases (from a North-North FTA, a North-South FTA, a NorthSouth CU, and a South-South CU). One important exception is adding a North-North CU to an existing South-South FTA, which can improve the prospects for free trade. We have also shown that combining agreements of the same type, especially inter-regional agreements, tends to improve the sustainability of free trade in many cases.

30

8

Appendix

In this Appendix we provide the necessary supporting calculations and proofs.

8.1

Tari¤ and welfare levels

We begin by reporting welfare levels under di¤erent policy regimes as a function of tari¤s and then derive optimum tari¤s. Using the welfare and tari¤ levels reported below, we can easily obtain the formulae for optimum welfare levels under all possible regimes. No agreement f g

wn ( ) =

(4

2c 3tn 2 ) 5

+( } |

2 {z

|

CSn ( )

and ws ( ) =

(4

+ 2c + 2c + 3tn 2 P ( ) + 5{z 5 } |z6=n {z P nn ( )

nz (

3c + 3ts 2 P 3c ) + ( 5{z 5 } z6|=s {z P ss ( )

+( } |

2 {z

CSs ( )

)2 + tn ( } |

)

z6=n

2c 3ts 2 ) 5

|

2tz

sz (

2tz

)

z6=s

where tn = tn0 =

9

2c 33

and ts = ts0 =

9

3

)2 + ts ( } |

4c {z5

6tn

T Rn ( )

3 +c {z5

6ts

T Rs ( )

) }

) }

7c 33

Preferential Trade Agreements North-North PTA - Suppose trade regime r represents a North-North FTA or CU: r = fnn0 g if it is an FTA and fnn0u g if it is a CU. Then, we have wn (r) =2( | (4

ws (r) = |

2

c 5 {z

CSn (r)

2cs 3trs 2 ) 5

2 {z

CSs (r)

trn

P + 2c + 2trz 2 P + 2c )2 + ( ) + ( 5 5 0 z=s;s0 } z=n;n | {z } | {z P P nz (r)

nz (r)

z=n;n0

z=s;s0

3cs 2trs0 2 P ) + ( 5{z } |z=n;n0

3cs + 3trs 2 ) +( 5{z } |

+( } |

ss (r)

ss0 (r)

0

0u

tnn n

3c

0

= tnn n0 =

8 c

0u

= tnn = n0

)2 +2trn ( } |

3cs 5 P {z

sz (r)

z=n;n0

where r = fnn0 g, fnn0u g and tnn n

2trz

4

0

0

; tnn = tnn s s0 = 0u

0u

; tnn = tnn = s s0

31

9

7c 33

9

;

7c 33

3trz

3c {z5

T Rn (r)

)2 +trs ( } |

3trn

) }

3 + cs {z5

T Rs (r)

6trs

) }

South-South PTA - Suppose trade regime r represents a South-South FTA or CU: r = hfss0 gi if it is an FTA and hfss0u gi if it is a CU. Then, we have wn (r) =

(

4

2c 3trn 2 ) 5

2 {z

|

}

CSn (r)

ws (r) = 2(

2

nn (r)

trs

c 5 {z

|

+ 2c 2trn0 2 P + 2c ( ) + 5{z 5 0 } z=s;s {z | P nn0 (r)

+ 2c + 3trn 2 ) +( 5{z | } |

+(

CSs (r)

where r = fss0 g, fss0u g and

|

tss s tss s

0

0u

nz (r)

z=s;s0

P 3c + 2trz 2 3c ) + ( 5 5 z=n;n0 {z } | {z P P

P

( )2 + } z=s;s0

sz (r)

2trz

sz (r)

z=s;s0

0

3trz

z=n;n0

)2 +trn ( } |

)2 +2trs ( } |

3

6trn

4c {z5

T Rn (r)

3trs

+ 2c {z5

T Rs (r)

) }

) }

+ 2c ss0 9 2c 0 ; tn = tss n0 = 8 33 9 2c ss0u ss0u = ; tn = tn0 = 4 33

= tss s0 = = tsss0

0u

North-South PTA - Suppose trade regime r represents a North-South FTA or CU: r = fnsg if it is an FTA and fnsu g if it is a CU. Then, we have wn (r) = 2(

2

|

ws (r) = 2(

wn0 (r) =

w (r) = s0

4

2

( |

trs

2c 5

)2

2 {z

CSs0 (r)

where r = fnsg,

+( } |

fnsu g

P

)2 + ( } z=n;s

+( } |

3trs0

+ 2c 5 P {z

z=n;s

2c 3trn0 2 ) 5 CSn0 (r)

4

c 5 {z

P P + 2c + 2trz 2 )2 + ( ) + ( 5 z=n0 ;s0 } |z=n;s {z } | P nz (r)

CSs (r)

2 {z

|

trn

CSn (r)

|

(

c 5 {z

and

|

u

nz (r)

z=n0 ;s0

P 3c + 2trz 2 ) + ( 5 z=n0 ;s0 } | P {z sz (r)

z=n;s

3c 5 P {z

)2 + trn ( } |

2trz

sz (r)

z=n0 ;s0

)2 +trs ( } |

+ 2c + 3trn0 2 + 2c 2trs0 2 P + 2c ( ) +( ) + 5{z 5 5 } | {z } z=n;s | {z P n0 n0 (r) n0 s0 (r) z=n;s

3c + 3trs0 2 ) +( 5{z } | s0 s0 (r)

3c 2trs0 2 P ) + ( 5{z } z=n;s | s0 n0 (r)

3trz

n0 z (r)

3c 5 {z P

z=n;s

3trz

s0 z (r)

2

32

c {z5

6trn

c {z5

6trs

T Rn (r)

2

T Rs (r)

)2 +trn0 ( } |

)2 +trs0 ( } |

13c ns 9 6 + 7c ns 6 2c ns 9 7c ; ts = ; tn0 = ; ts 0 = 48 48 33 33 2 c nsu 9 2c nsu 9 7c nsu = ts = ; tn0 = ; ts 0 = 8 33 33

tns = n tns n

2trz

3

) }

) }

4c {z5

6trn0

T Rn0 (r)

3 +c {z5

T Rs0 (r)

6trs0

) }

) }

Inter-regional PTA network : r = fns; n0 s0 g, fnsu ; n0 s0 g, fnsu ; n0 s0u g. Then, we have wn (r) = 2(

2

|

c 5 {z

trn

c 5 {z

trs

P P + 2c + 2trz 2 ( ( )2 + ) + 5 z=n0 ;s0 } |z=n;s } | P {z

CSn (r)

ws (r) = 2(

2

|

nz (r)

z=n;s

|

CSs (r)

and 0 0

tnns;n s

0 0

tns n

z=n;s

u ;n0 s0u

= tns n

u ;n0 s0

u ;n0 s0

Intra-regional PTA network : r = wn (r) = 2(

2

|

c 5 {z

trn 2

c 5 {z

trs

CSn (r)

ws (r) = 2(

2

|

u ;n0 s0

0 0

s = tsns;n 0

= tnns0

= tsns

2trz 2

) + } |

z=n;n0

|

and 0

0

tnnn ;ss

u ;n0 s0u

P

(

= tsns0

u ;n0 s0u

+ 2c 5 {z P

nz (r)

sz (r)

sz (r)

z=n;n0

0

0

0

0u

0u

=

c {z5

6trs

T Rs (r)

2

) }

) }

c 8

3trz 2

P 3c 3c + 2trz 2 ) + ( 5 5 0 z=n;n {z } | {z P P 0

6trn

T Rn (r)

fnn0u ; ss0u g.

z=s;s0

z=s;s0

=

2

sz (r)

fnn0 ; ss0u g,

z=s;s0

nz (r)

CSs (r)

)2 +trs ( } |

3trz

3c 5 {z P

c {z5

6 + 7c 48 6 13c = 48

fnn0u ; ss0 g,

P + 2c + ( ) + 5 } |z=n;n0 P {z

P

2

=

u ;n0 s0u

fnn0 ; ss0 g,

)2 + ( } z=s;s0

)2 + trn ( } |

z=n0 ;s0

0 0

= tsns 0

tsns;n s

sz (r)

s tns;n = tns n0 n0

=

nz (r)

z=n0 ;s0

P 3c + 2trz 2 ( ) + 5 z=n0 ;s0 } | P {z

P

)2 + ( } z=n;s

3trz

+ 2c 5 {z P

;ss ;ss ;ss = = tnn = tnn tnn n n0 n0

) + 2trn ( } |

3trz

)2 +2trs ( } |

Then, we have 3c {z5

3trn

+ 2c {z5

3trs

T Rn (r)

T Rs (r)

3c

8 + 2c = = = = 8 0u ;ss0 0u ;ss0u c 0u 0u 0u 0 nn nn ;ss ;ss tnn = tnn = tn0 = tn0 = n n 4 nn0u ;ss0u nn0 ;ss0u nn0u ;ss0u nn0 ;ss0u ts = ts 0 = ts = ts 0 = 4 Three country PTA network with two North countries: r = fnn0 sg, fnn0 su g. Then, we have 0 ;ss0 tsnn 0

0 0 tsnn ;ss

1 4 |2

wn (r) = (

1 4 2 |

ws (r) = (

2c 5 {z

trn

CSn (r)

2c 5 {z

CSs (r)

0u 0 tsnn ;ss

0u ;ss0 tsnn 0

P + 2c + trz 2 )2 + ( ) +( } |z=n;n0 ;s {z 5 } | P nz (r)

z=n;n0 ;s

trs

P

3c + trz 2 ) +( 5 } | P {z

)2 + ( } z=n;n0 ;s

|

sz (r)

z=n;n0 ;s

33

+ 2c 2trz 2 ) + trn ( 5{z } | ns0 (r)

3c 2trz 2 1 r ) + ts ( 5{z } |5 ss0 (r)

3c {z5

4trn

3c {z 5

4trs

T Rn (r)

T Rs (r)

) } ) }

) }

) }

1 4 |2

3trs0

2c 5 {z

ws0 (r) = (

P

( )2 + } z=n;n0 ;s |

CSs0 (r)

P {z

z=n;n0 ;s

and 0

0 su tnn n

3

0

tnnn s =

s tnn = n 0 su tnn n

=

9c 37

=

0 su tnn s

4trz

3c 5 s0 z (r)

)2 + ( } |

3c + 2trs0 2 1 r 3 + c ) + ts 0 ( 5{z } |5 {z 5

6trs0

T Rs0 (r)

s0 s0 (r)

) }

19c nn0 s 9 7c ; ts 0 = 37 33 9 7c 7 11c nn0 su ; ts 0 = = 33 33 0

s ; tnn = s

3

Three country PTA network with two South countries: r = fnss0 g, fnss0u g. Then, we have 1 4 |2

1 4 2 |

CSn (r)

2c 5 {z

ws (r) = (

1 4 2 |

wn0 (r) = (

trn

2c 5 {z

wn (r) = (

nz (r)

z=n;s;s0

trs

CSs (r)

3trn0

2c 5 {z

and

tnss n

0

0u

= =

P

3c + trz 2 ) +( 5 } | P {z

)2 + ( } z=n;n0 ;s

|

sz (r)

z=n;s;s0

P

+ 2c 5 {z P

( )2 + } z=n;n0 ;s |

CSn0 (r)

tnss n

P + 2c + trz 2 )2 + ) +( ( 5 0 ;s } z=n;n | } | P {z

z=n;s;s0

4trz

n0 z (r)

)2 + ( } |

+ 2c 2trn0 2 + 2c ) + trn ( 5{z } | {z5

4trn

3c 2trn0 2 1 r + 2c ) + ts ( 5{z } |5 {z 5

4trs

nn0 (r)

sn0 (r)

T Rn (r)

T Rs (r)

+ 2c + 3trn0 2 1 r 3 ) + tn0 ( 5{z } |5 n0 n0 (r)

4c {z 5

T Rn0 (r)

) } ) }

6trn0

) }

3 + 6c nss0 9 2c 3 + 16c nss0 0 ; ts = tnss = ; tn0 = s0 37 37 33 7 + 4c nss0u 9 2c nss0u nss0u ts = ts 0 = ; tn0 = 33 33

Proofs of the propositions, critical cost thresholds, inequalities and …gures provided in the text are based on the above welfare levels and tari¤ expressions. Critical Cost Thresholds We next examine the export of South …rms under di¤erent trade agreements. Then, we restrict the cost range so that the export of Southern …rms is guaranteed to be non-negative under all possible trade regimes. To this end, our focus is on the export of South …rms in the export markets of countries which are not partner. xsn ( ) = xsn (ss0 ) = xsn (n0 s0 ) = xsn (ss0u ) = xsn (n0 s0u ) = 3 3319c 0 i¤ c 319 xsn (nn0 ) = xsn (nn0 ; ss0 ) = xsn (nn0 ; ss0u ) = 83c 0 i¤ c 3 xs0 n (ns) = xs0 n (ns; n0 s0 ) = xs0 n (ns; n0 s0u ) = 2 1611c 0 i¤ c 211 xss0 (n0 s0 ) = xss0 (ns; n0 s0 ) = xss0 (nsu ; n0 s0 ) = 2 167c 0 i¤ c 27 xsn (nn0u ) = xsn (nn0u ; ss0u ) = xsn (nn0u ; ss0 ) = 209c 0 i¤ c 9 34

xs0 n (nsu ) = xs0 s (nsu ) = xs0 n (nsu ; n0 s0u ) = xs0 s (nsu ; n0 s0u ) = xs0 n (nsu ; n0 s0 ) = xs0 s (nsu ; n0 s0 ) = 2 21c 0 i¤ c 221 40 xs0 n (nn0 s) = 3 > 0 for all c and xs0 n (nn0 su ) = 3311c 0 i¤ c 11 Based on these threshold cost levels, the market access of South …rms under any trade regime is guaranteed if c c = 11 holds. Tari¤ Complementarity Given that c c = 11 holds, we next show that the formation of a PTA induces countries to lower their pre-PTA optimum tari¤s and thus tari¤ complementarity e¤ect always obtains: 0

tnn n tss s

0

0

0u

0u

tns n

u

0

0u ;ss0

0u

0u ;ss0

tnn = s

0

0u ;ss0u

0u ;ss0u

tn = tns n

0 0

s tns s = tns;n s

u ;n0 s0

0 0u

0 0u

0 0

tnn s = tnns

0 0

tns s = tsns

s tn = tnn n

0

s ts = tnn s

s tnn s

0

0

tnn = s

0

0 u

s ts = tnn s

s tnn s

c

78 + 31c