A Model of Endogenous Trading-Bloc Formation

Transcription

1 A Model of Endogenous Trading-Bloc Formation Lingling Zhang McGill University This version: January 2008 Abstract I study a dynamic process of trading-bloc formation in an n-country international trade model of imperfect competition. Countries differ in their industrialization levels and market sizes. In this model, both the formation of trading-blocs and countries external tariffs are endogenously determined. The impacts of free trade areas (FTAs) and customs unions (CUs) on trade liberalization are evaluated and compared. I demonstrate that global free trade is always achieved in equilibrium either sequentially or simultaneously when politically motivated protection (e.g., protection induced by lobbying) is absent. Moreover, I demonstrate in a three-country model that the equilibrium path towards global free trade depends on the type of regional trade agreements, the characteristic terms of each country, and the common discount factor, which is in contrast to Aghion et al. (2007) where equilibrium path is determined by the sign of externalities. Sufficient conditions under which a country prefers bilateralism or multilateralism are identified. In addition, when a country prefers bilateralism, it always tends to firstly approach either a less developed country or a country with a relatively small market size. This finding is consistent with Japan s recent FTA strategies and the United States strategies in the formation of NAFTA. I would like to thank Professor Licun Xue, Professor Ngo Van Long, and Professor William Watson for helpful discussions and suggestions and Social Science and Humanities Research Council of Canada (SSHRC) and Fonds québécois de la recherche sur la société et la culture (FQRSC) for financial support. Department of Economics, McGill University, 855 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2T7; lingling.zhang@mail.mcgill.ca 1

2 1 Introduction Regional trading blocs, small and large, are emerging all over the world. Preferential Trade Agreements (PTAs) permitted under the GATT/WTO have become increasingly salient to the Multilateral Trading System. Currently, all WTO Members except Mongolia are party to a PTA. Around 368 PTAs have been reported to the GATT/WTO and 215 PTAs are currently in force up to For instance, in Asia, frenetic trade negotiations between China, India, Japan and member countries in ASEAN 2 are in progress. While these countries seem to share a common goal of eliminating trade barriers among them, they are pursuing different strategies. Japan, for example, has started negotiating bilateral trade agreements with ASEAN member countries individually since China, in contrast, prefers an FTA with ASEAN collectively. The largest FTA ever negotiated, the China-ASEAN FTA, is under development 4. India is also in the process of negotiating an FTA with ASEAN and has started negotiating an FTA with Japan in This revival of regionalism not only shows in the increasing number of PTAs, but also in their growing influences on international trade (e.g., EU and NAFTA). On the other hand, the World Trade Organization negotiations have encountered difficulties in recent years. For instance, the Doha Development Round was suspended in 2006 after five years of troubled negotiations. Given the prevalence of reginal trade negotiations, a question calling for answers is whether the formation of PTAs undermines the realization of a global free trade. Furthermore, why and how do incentives and strategies of different countries (e.g., developed or less developed, large or small) vary toward different types of regional trade agreements? The question of regionalism vs multilateralism has attracted the attentions of both economists and policymakers for a long time. Studies on trading-bloc formation have mainly focused on analyzing two types of PTAs permitted under GATT Article XXIV, customs unions (CUs) and free-trade areas (FTAs) 5. Bhagwati (1993) 1 For more information, see e/region e/region e.htm 2 Association of Southeast Asian Nations is a political and economic organization of 10 countries, including Indonesia, Malaysia, the Philippines, Singapore and Thailand. 3 Japan has signed FTAs with Malaysia (in 2005), Philippines (in 2006), and Indonesia (in 2007). 4 The China-ASEAN FTA framework agreement has been announced in 2002, aiming to have an FTA in place by In a CU, the member countries set the internal tariffs to zero and they cooperatively choose a common external tariff level on imports from outside countries. In an FTA, the internal tariffs are 2

3 distinguishes two main approaches within this literature. The first approach, called static analysis, focuses on the immediate welfare analysis of exogenously determined PTAs to address the impact of regionalism on the multilateral trading regime. In Viner (1950) s words, the main issue to be addressed is whether PTAs lead to trade creation (i.e., trade is created by the formation of a trading bloc) or trade diversion (i.e., trade is diverted from a more efficient exporter towards a less efficient one by the formation of a trading bloc). However, one important question that can not be addressed within a static environment is the following. Even if the formation of a PTA is welfare-improving in one period, could it impede further liberalization? The other approach, as pointed out by Bhagwati (1993), focuses on the dynamic time-path of regional trading-bloc formation 6. This approach investigates whether PTAs create incentives towards establishing global free trade (i.e., PTAs are building blocs) or towards undermining global liberalization (i.e., PTAs are stumbling blocs). This so-called dynamic approach can be divided into the following two categories. dynamic analysis of exogenously determined PTAs; dynamic analysis of endogenously determined PTAs. Krugman (1993) has made a key contribution to the first dynamic approach. Neglecting how the trading blocs form, he studies welfare changes on given paths of PTA expansion and observes that small numbers of trading blocs tend to make cooperative solutions more likely. The second approach investigates the incentives of countries to form trading blocs. Krishna (1998) and Ornelas (2005), for example, assess the conditions under which a country is willing to join an FTA to answer the question whether trading blocs are stumbling blocs or building blocs. Non-cooperative games are also used to model the process of trading-bloc formation. These games specify the way countries eliminated as well, however, each member country sets its own external tariffs against nonmember countries. 6 Another strand of literature analyzes whether global free trade is a stable outcome. In Furusawa and Konishi (2002), the formation of bilateral trade agreements are studied in a symmetric n-country model without transfers using network theory (see, e.g., Jackson and Wolinsky (1996)). They show that the global free trade network is pairwise-stable(in a pairwise-stable free trade network, no country has an incentive to cut a link and no pair of unlinked countries have incentives to form a link). Later, Furusawa and Konishi (2005) investigate a similar free trade network model with asymmetric countries. Again, the global free trade network is pairwise-stable when transfers are allowed. 3

4 negotiate and explain how the PTAs form. Yi (1996) and Yi (2000), for instance, consider an open regionalism game in which each country announces an address simultaneously or sequentially and a trading bloc forms among countries with the same address. Thus, a country can freely join any PTA without consent of its member countries. Yi shows that the grand CU forms in both the simultaneous and sequential open regionalism game. Yi (1996) and Yi (2000) also apply results from a sequential coalition formation game developed by Bloch (1996), which does not allow compensational transfers or coalition expansions. Both CUs and FTAs are found to be stumbling blocs in this framework. Burbidge et al. (1997) consider a one-good model of capital tax competition with international trade of mobile capital for the consumption good. They analyze a oneshot noncooperative game of coalition formation in the first stage where countries simultaneously announce their partners for trading blocs. Their model allows for both transfers and externalities. They show that when there are more than two countries, global free trade may not be an equilibrium outcome. Following the same approach, Aghion et al. (2007) develop a dynamic bargaining model in which a leading country (the agenda setter) 7 chooses whether to negotiate regional trade agreements sequentially with subsets of countries or to undertake multilateral negotiations simultaneously with all other countries. They show that global free trade is an equilibrium outcome and the type of negotiation in equilibrium is determined by whether the formation of FTAs creates positive or negative externalities. In particular, the existence of negative externalities leads to sequential trade negotiation while positive externalities lead to multilateral negotiation. They use a competitive model of international trade without politically motivated protection 8 to illustrate the possibility of both types of equilibrium. In their trade model, an FTA is an agreement in which members remove the internal tariffs while maintaining their original external tariffs on outside countries. In other words, the external tariffs in their model are exogenously given. PTAs are binding to the extent that expansion of PTAs is permitted, while merger between PTAs and breaking-up of a PTA are forbidden. Following the same dynamic approach, Macho-Stadler and Xue (2007) study a 7 In their three-country dynamic negotiation game, the agenda-setter, who has the power to propose to countries to form a trading bloc, is exogenously given. The game ends when any country rejects the agenda-setter s proposal but they have discussed different rules of negotiation. 8 One example of politically motivated protections is a uniform tariff imposed by a central government as a means of raising revenue. Such protection could be induced by lobbying. 4

5 different dynamic trade negotiation game among three countries. They adopt an imperfect competition trade model to endogenously determine both internal tariffs and external tariffs of each customs union. In their model, existing trading blocs can not break-up but they can admit new members and merge with other blocs. Another feature is that the agenda-setting power shifts across countries. In addition, a rejection from a country will not end the game. Further more, countries cumulate payoffs as they negotiate. However, they impose an exogenously given sharing rule. Thus, instead of making transfers, countries have a predetermined agreement about the way they are going to share the aggregate welfare of a trading bloc if it forms. Macho-Stadler and Xue (2007) show that global free trade is always achieved in equilibrium without politically motivated protection. They observe that some country may be worse-off under global liberalization than in the initial state with no trading blocs if global free trade is reached gradually. In the present paper, I study endogenous trading-bloc formations as a dynamic coalition formation game in an n-country international trade model of imperfect competition. Countries differ in their industrialization levels and market sizes and are free to negotiate the formation of trading blocs (FTAs or CUs) either bilaterally or multilaterally. In this unified setting 9, both the formation of trading-blocs and countries external tariffs are endogenously determined. In Section 2, the infinitehorizon dynamic game is developed. Time is discrete. Each period of the game contains the following three stages: a negotiation stage where countries negotiate the formation of a trading bloc; a tariff-setting stage where the equilibrium external tariff of each country is determined; a production stage where firms compete in a Cournot fashion internationally. The negotiation stage builds on the recent literature on endogenous coalition formation in environments with externalities (see, e.g., Bloch (1996), Ray and Vohra (1999), Gomes (2005), and Hyndman and Ray (2007)). In this model, each country is ranked according to its bargaining power which is defined by the size of its population (or the size of its domestic market) and its industrialization level. Countries with higher bargaining power obtain the agenda-setting power earlier. In addition, instead of predetermining a country as the agenda-setter as specified in Aghion et al. (2007), I allow agenda-setting power to shift across countries. Moreover, trading blocs form in real time in that trade negotiations and productions happen 9 The trade negotiation, tariff setting, and production are all considered in one model. 5

6 in each period. Both compensational transfers and expansion of PTAs (by either admitting new members or merging with other coalitions) are allowed (as in, e.g., Gomes (2005)). Thus, in contrast to Macho-Stadler and Xue (2007) who impose a fixed sharing rule, the redistribution of gain from trade among countries in my model is endogenously determined. In the negotiation stage, countries interact in the following ways. At the beginning of each period, a country is chosen as the agenda-setter according to the ranking of bargaining powers. The agenda-setter invites a subset of countries to form a trading bloc with by proposing each of them transfers. Prospective members make their decisions to accept or reject this offer sequentially. If there is unanimous consent, the proposed trading bloc forms. If any country rejects the offer, the current round of negotiation ends. In both cases, the agenda-setting power shifts to another country according to the ranking of bargaining powers. Thus, trade negotiation in the game can potentially last for infinitely many periods. Following the literature, Markov perfect equilibrium (MPE) is adopted as the solution concept. In Section 3, the strategy profile and MPE of the endogenous trading-bloc formation game are formally defined. In addition, the existence of a pure-strategy MPE is discussed since in the game theory literature existence of MPE normally requires mixed strategies. In order to support the idea that neither FTAs nor CUs serve as stumbling blocs towards global liberalization, in Section 4, it is demonstrated that in every MPE of the n-country game, global liberalization can always be achieved either sequentially or simultaneously. In Section 5, the signs of externalities imposed by either FTAs or CUs in the n-country model are examined. It is observed that the formation of FTAs creates positive externalities while the formation of CUs creates negative externalities. This finding is consistent with empirical analysis of the effects of regionalism on external trade liberalization (see, e.g., Bohara et al. (2004) and Estevadeordal et al. (2006)). In a three-country model, two types of equilibrium are found: a multilateral equilibrium and a bilateral equilibrium. In contrast to Aghion et al.(2007), the sign of externalities cannot fully determine the equilibrium path. In particular, global free trade may be achieved sequentially or simultaneously when only positive externalities prevail and the attaintment of global liberalization may also be realized in one shot when there are negative externalities. It is demonstrated that the equilibrium path in the three-country game depends on the type of regional trading blocs, the characteristic terms of each country (which determine the magnitude of external- 6

7 ities), and the common discount factor. Since countries can differ in both their market sizes and industrialization levels, they are divided into four different types (e.g., developed large countries, less developed large countries, developed small countries, and less developed small countries). Thus, the strategic behaviors of different types of countries can be analyzed. For instance, this model can not only be applied to analyze global free trade, but also can be applied to study how and why countries in a region (e.g., North America or Asia) negotiate free trade among themselves. In addition, four examples are presented in Section 5 to provide simple illustrations of the propositions found in the three-country model. Section 6 summarizes the main results and discusses future extensions. 2 The model 2.1 Basic setup Consider a world divided into n( 3) countries. Countries are free to choose to form trading blocs either regionally or multilaterally. There are infinitely many periods. Time is discrete. All countries share a common discount factor. Trading blocs form sequentially (i.e., one bloc forms at each time). In each period, countries negotiate the formation of trading blocs; each country sets its external tariffs given the current coalition structure 10 and the trade agreement it has signed; firms produce. Formally, each period is divided into the following three stages. A negotiation stage, where countries negotiate the formation of a trading bloc using a two-stage mechanism 11. The compensational transfers and which bloc should form are determined in this stage. A tariff-setting stage, where each country s equilibrium external tariffs is determined by either solving a national welfare maximizing problem (in the case of FTA-formation) or a coalitional welfare maximizing problem (in the case of CU-formation). A production stage, where each firm competes in a Cournot fashion internationally. Each firm s equilibrium quantities of production are determined in 10 A coalition structure is a partition of n countries. For example, if there are three countries and two of them form a trading bloc, the coalition structure can be given by {{i, j}, {k}}. 11 It includes a proposing stage and a responding stage. 7

8 this stage. Note that each firm in this model produce in real time. In other words, negotiation and production both occur in each period. After a trading bloc forms, the tariff levels of each country will be reset according to the new trading-bloc structure and trade policies. Each country is assumed to impose tariffs on its imports, while it doesn t set any tax or subsidies on its exports. Also, each country is assumed to initially impose nondiscriminatory tariffs on all imports 12. In addition, after joining a PTA, each country should eliminate all internal tariffs 13. Following Brander and Krugman (1983) and Brander and Spencer (1984), I assume that market in each country is segmented. There is no transportation costs in delivering the goods abroad, and the competition of firms is the single cause of international trade 14. Each country has two sectors: the competitive sector I and the oligopolistic sector II. Sector I produces the numeraire good y. Its price is assumed to be one and it is freely traded 15. Sector II produces good x, which contains n i ( 1) oligopolistic firms in each country i 16. Thus, the total number of all oligopolistic firms in the world is given by N = i N n i, where N is the set of all countries. Both goods are assumed to be homogeneous and require only labor as input. Each unit of good y is assumed to be produced with one unit of labor. In any equilibrium, the wage rate should equal 1 as long as good y is produced. For good x, the fixed costs of production is zero and marginal costs of production are constant at c. 17 In addition, the labor supply in country i is assumed to be inelastic. The aggregate consumption of good x in country i s market is given by Q i = k N z N k q z (i), where N k is the set of all oligopolistic firms in country k and q z (i) denotes the number of good x that a firm z in country k produces for country i. Since all oligopolistic firms in each country are identical, it is reasonable to assume that firms 12 which is consistent with the most favored nation (MFN) clause of the GATT Articles of Agreement. 13 Internal tariffs refer to tariffs set by a member country to imported goods from another member country in the same PTA. 14 The background trade model studied in this paper is an extension of the Cournot duopoly model in Brander and Krugman(1983). This duopoly model has been extended by Krishna(1998) to a three-country model with asymmetric number of firms and then by Ornelas(2005) to an n- country model with symmetric number of firms. I examine the formation of FTAs in an n-country model with asymmetric number of firms. 15 Following Brander and Krugman (1983), good y is introduced in this model to settle the balance of trade. 16 I capture the asymmetric of each country s industrialization levels by allowing each country to have different number of firms 17 For example, the production of one unit of good x requires c units of labor. 8

9 in each country produces the same number of good x for each market in equilibrium. Thus, Q i = k N n k q k (i), where q k (i) is the quantity supplied by one of the firms of country k in country i s market. The utility function for the consumers in each country is assumed to be quasilinear. Thus the aggregate utility in country i is given by U i = y i + u i (Q i ), where u i (Q i ) = A i Q i Q 2 i /2. Hence, the demand function for the oligopolistic good is represented by P i (Q i ) = A i Q i. Note that the parameter A i can be regarded as the measurement of the population or the market size of country i. Countries in the model therefore can differ from one another in both the market size (A i ) and the level of industrialization (n i ). A i > c holds for each country i. Each country is assumed to initially impose nondiscriminatory tariffs on all imports. Also, after it joins an PTA, it sets uniform tariffs on imports from any nonmember country. Let t i (j) to represent the tariff rate set by country i on imports from country j, it is given by t i (> 0) if j and i are not members of the same PTA t i (j) = 0 if j and i are members of the same PTA. 2.2 The production stage Given that the market in each country is segmented and firms in Sector II compete in a Cournot fashion, an oligopolistic firm z s per-period profit maximization problem in country j s market is given by max π z (j) = q z (j)[a j Q j (c + t j (z))]. q z(j) Solving the above Cournot game by taking tariffs as given 18, I obtain the following. First, the equilibrium quantity of each firm in country i that is produced for the market in country j is identical and it is given by q i (j) = [(A j c)/(n + 1) + k N n k t j (k) t j (i)]. N + 1 Second, the equilibrium quantity is determined by the trading-bloc structure and the types of trading blocs. Moreover, the export profits of each country are exclusively 18 When I solve this problem, I assume that each firm takes other firms quantities as given including the domestic firms and foreign firms. 9

10 depend on the market size and tariff levels of other countries. In other words, export profits are independent of the domestic economic characteristics. 2.3 The tariff-setting stage In the tariff-setting stage, the equilibrium tariffs are determined according to the current trading-bloc structure and trade policies. Since Customs unions (CUs) and freetrade areas (FTAs) are two types of PTAs permitted under GATT Article XXIV, the equilibrium tariffs are analyzed in both cases FTAs and equilibrium tariffs When countries form FTAs, the equilibrium external tariff of country i is determined by maximizing its per-period national welfare taken the tariffs set by all other countries as given. The national welfare function for country i is the summation of the consumer surplus, the tariff revenue, and the aggregate profits in Sector II, which is given by W i = CS i + T R i + Π i 19. Let S i represent the FTA that country i belongs to. Let K i be the aggregate number of all oligopolistic firms in all the countries outside S i. We have K i = k N \S i n k. Since the export profits solely depend on foreign tariffs as we have shown, the first-order-condition for the national welfare optimization problem can be given by: F.O.C. dcs i dt i + dt R i dt i + dπd i dt i = 0. Plugging the profit-maximizing qualities into the F.O.C., the equilibrium external tariff for country i is obtained as below: t i = (2n i + 1)(A i c) 2(N + 1) 2 K i [2(N + 1) + 2n i + 1] Therefore, the equilibrium external tariff in one country is a function of the number of firms in its FTA, but not a function of foreign tariffs. In the initial state where each country is free of commitment, the initial optimal tariff for country i can be 19 where CS i = u i (Q i ) P i Q i = 1 2 Q2 i, T R i = j i n j q j (i) t i (j), and Π i = n i j N [q i(j)] 2. Note that the aggregate profits can also be written as the summation of export profits( Π EX i ) and domestic profits (Π D i ). 10

11 given by t 0 i = (2n i + 1)(A i c) 2(N + 1)(n i + 1) (N n i )(2n i + 1). It is easy to see that dt i dk i > 0. The implication is simple. When the free trade area including country i becomes larger, country i sets non-zero tariffs to less countries. At the same time, the equilibrium external tariff set by country i also falls CUs and equilibrium tariffs A customs union is a trade agreement not only to eliminate trade barriers amongst its members but also to share a common external tariff which maximizes the joint welfare of all member countries. In equilibrium, each custom union (S i ) chooses its uniform external tariff (t S i ) to maximize its joint welfare by taking the tariffs set by all others as given. The aggregate welfare can be given by W Si = i S i W i = i S i [CS i + T R i + Π i ]. The equilibrium uniform tariff of customs union S i is given by t S i = where K i = k N \S i n k and AC i = [1 + 2(N K i )]AC i [2(N + 1)(N K i + 1) K i (1 + 2N 2K i )]. i S (A i c) i S i = i S i (A i c) S i. The formation of custom union affects a member country i s external tariffs through AC i and K i. I verify the signs of the partial derivatives of the function of the equilibrium tariff with respect to AC i. t S i AC i = 1 + 2(N K i ) [2(N + 1)(N K i + 1) K i (1 + 2N 2K i )] > 0 Hence, if countries form a new CU, or an existing CU admits new members, or two existing CUs merge, if its average AC term rises, then the formation of such CU partially causes the optimal external tariff to rise. In sum, a country s external tariff rises when it forms a CU with countries with relatively higher population. On the other hand, its external tariff falls when it forms a CU with countries with relatively smaller population. 11

12 2.4 The negotiation stage In this model, countries are free to form trading blocs either bilaterally or multilaterally. In the game theory literature, coalition formation has been extensively studied in recent years. One of the main approaches of studying coalition formation is the so-called noncooperative approach. Such an approach, following Nash (1951), models coalition formation as a dynamic game which specifies explicitly how agents make proposals and counter-proposals in the process of forming a coalition. In particular, the formation of coalitions is often modeled as sequential processes in the spirit of Rubinstein (1982) s alternating offers bargaining game and its extensions to n players by Selten (1981) and Chatterjee et al. (1993). In view the fact that in many social and economic situations, there are widespread externalities, there has been growing interest in the study of coalition formation in environments with externalities. Among the recent contributions are Bloch (1996), Ray and Vohra (1999), Hyndman and Ray (2004), and Gomes (2005). For instance, in the sequential coalition formation games as described in Bloch (1996), agents make the decisions of forming coalitions first. It potentially can last for infinitely many periods if there is no agreement can be achieved. After all rounds of negotiation are completed, agents start taking other actions (e.g., producing, designing policies etc.). One of the other features of the model in Bloch (1996) is that all agreements are assumed to be non-renegotiable. In other words, a coalition is forbidden to expand, breakup, or merge with other coalitions. In addition, transfers are not allowed during the negotiation. However, the trading-bloc formation game in this paper is modeled differently. The negotiation mechanism constructed in this paper is a hybrid of those in Bloch (1996) and Gomes (2005). As in Bloch (1996), the order of moves by countries is exogenously given, that is, countries take actions sequentially following a given rule. Each country is ranked according to its market size and level of industrialization. There are two reasons to adopt this exogenous order. Firstly, in real life situations, countries with higher levels of industrialization and larger market sizes usually have more bargaining power. Thus, it is reasonable letting them have the right to move first. One main theme of the literature is that the combination of coalition formation and externalities often leads to inefficient outcomes. It is also the main reason that a randomization mechanism is used to replace the fixed rule of order (e.g., Gomes (2005)). While in this model, the exogenous order is not a source of inefficiency. 12

13 The given rule of order is defined as follows. As I have defined, n i is the number of oligopolistic firms in country i and A i is a measurement of country i s market size. Country i s bargaining power BP i is given by 20 BP i = n i + A i. Each country s bargaining power is assumed to be unique. As in Gomes (2005), transfers or side-payments are considered in my model as strategy variables. It is reasonable to assume transferable utility since the gains from trade liberalization can be redistributed by the exchange of yielding on non-traderelated issues. Following Gomes (2005), I assume trade agreements are binding in a sense that coalitions are allowed to admit new members and merge with other coalitions but is forbidden to break-up. Like Aghion et al. (2007), at the beginning of a round of negotiation, a country will be assigned with the agenda-setting power, that is, the power to choose a subset of countries and propose to form a trading bloc among them. In my mechanism, however, the agenda-setting power always shifts to another country when a new round of negotiation starts. For instance, in period t, all countries except the agendasetter in period t 1 are candidates to be chosen as a new agenda-setter. Free-sanding countries always have priorities over countries with commitments 21. In each period, the free-standing country with the highest bargaining power becomes a new agendasetter. If all candidates are currently belonging to coalitions, agenda-setting power then shifts to the country with the highest bargaining power. The two-stage negotiation mechanism is introduced as follows. The proposing stage In this stage, the agenda-setter invites one or several countries to participate the negotiation of forming a trading bloc and offers each participant a lump-sum transfer. Each transfer can be positive or negative. The agenda-setter is free to propose to form a new coalition or to merge coalitions into one. The responding stage In this stage, each invited country responds to the offer sequentially 22. If there is unanimous consent, the preferential trade agreement is signed by the agendasetter and invited countries. Proposed transfers are paid as a trading bloc forms. Therefore, this game does not require any commitment from the agenda setter about 20 It is always feasible to put different wights on these two facts. 21 A singleton coalition in my game is considered as a free-standing country. 22 Note that the order of responding is irrelevant. 13

14 transfers as discussed in Aghion et al. (2007), where the payment of transfers is made after coalitions form. If any of the responders rejects the proposal, the current round of negotiation ends. As a result, no trading bloc forms and no transfers are paid in the current period. 3 Strategies and equilibrium Following the literature, I adopt Markov perfect equilibrium (MPE) as the solution concept for my dynamic game. I begin with a definition of a state. Formally, a state a can be written as a = (π(a), w(a), L). π(a) is the current coalition structure. For example, if there are three countries: 1, 2 and 3. Currently, country 2 and country 3 belong to an FTA. The coalition structure can be given by π(a) = {{1}, {2, 3}}. The vector w(a) represents the per-period national welfare for each country, that is, w(a) = (W i (a)) i N. L is the agenda-setter. At state a, with a slight abuse of notations, a pure Markovian strategy profile σ i for the negotiation stage is formalized as below. In the proposing sub-stage, σ L (a) = Γ L (a) = [S L, (βi L ) i SL \{L}], where S L is the selected subset of countries including the agenda-setter, and βi L R represents the proposing transfers from country L to country i; in the responding sub-stage, σ i (a, Γ L ) = λ i, if Γ L (a), where λ i {Yes, No}. Note that actions that countries and firms take in the tariff-setting stage and the production stage affect the negotiation strategies via state a, since state a is determined by each country s national welfare. A strategy profile σ = (σ i ) n i=1 is a Markov Perfect Equilibrium (MPE) if for each player i, σ i is a Markovian strategy, and after every history of play, σ i is a bestresponse for player i when other players i play according to σ i. Note that in the game theory literature, demonstrating the existence of equilibrium is crutial. For instance, in Bloch (1996), the stationary subgame perfect equilibrium of the n-player sequential coalition formation game may fail to exist. The existence issue may not be critical or technically difficult for the three-country finite horizon game as in Aghion et al.(2007) where it has been omitted. However, for an n-country infinite horizon game with expansionary agreements and externalities, the existence of MPE, especially a pure strategy one seems to be important. Gomes (2005) has proved that 14

15 a similar stochastic coalition formation game admits an MPE by allowing mixed strategies. Their existence result, however, can not be applied to my game because of two reasons. First, while in their game the proposer is randomly chosen with equal probabilities, the proposer (i.e., the agenda-setter) in my game is chosen according to its bargaining power. Second, the coalition bargaining game in Gomes (2005) requires that all responders leave the game and the proposer take over the entire coalition after it forms, that is, each coalition is considered as a single entity; in my game, on the other hand, each member country only promises to cooperate on setting tariffs but still keeps its independence on other matters. Fortunately, the existence of a pure strategy MPE of my game can be demonstrated by construction Global free trade One of the main objectives of this paper is to show that neither the formation of FTAs or the formation of CUs undermines global liberalization in a model without political-economy motive protection (e.g., lobby),. In this section, I fulfill this goal in two steps. First, I show that Grand Coalition superadditivity holds in the model. Second, I demonstrate that the coalition formation game studied in this paper exhibits efficiency, that is, global free trade is always achieved in equilibrium. I begin with the definition of Grand Coalition superadditivity. Definition 4.1. Grand Coalition superadditivity requires the following. Under any coalition structure, the joint welfare of all n countries are always less than that under the grand coalition structure. U({1, 2,..., n}) U(π) for any partition π on n countries. Proposition 4.2. In our model, Grand Coalition superadditivity holds. In other words, global free trade is always Pareto efficient. Proof. This proposition can be demonstrated using Karush-Kuhn-Tucher theorem. The formal proof is provided in the appendix. Proposition 4.3. In every MPE of our trading-bloc formation game, global free trade is always achieved. 23 Because the length of this paper, the proof is not included here. 15

16 Proof. Suppose there exits an equilibrium σ where countries belong to different coalitions. For example, the equilibrium coalition structure is π = {S 1, S 2,... S m }. This implies that no country has incentive to change the current coalition structure. Suppose country α with the highest bargaining power proposes to form a grand coalition. Its proposal is written as Γ α ( N, (β α i ) i N \{α} ). In the equilibrium σ, each country i s present value is given by u i(π). If country i 1 δ accepts this offer, it obtains u i (G) 1 δ + βα i. Because the grand coalition superadditivity holds ( i N u i(g) > i N u i(π)), it is always feasible for country α to offer every other country some value no less than its equilibrium value and still make itself better-off. u i (G) 1 δ + βα i u i(π) 1 δ u α (G) 1 δ i N \{α} β α i i N \ {α}, > u α(π) 1 δ. Next, I show that there exists an offer Γ ( ) α N, (βi α ) i N \{α} that is profitable for country α and is also acceptable. In the negotiation mechanism, if country α s proposal is rejected, the agenda-setting power shifts to the country, say α, that has the second highest ranking. If the proposal of country α is rejected, the agendasetting power then shifts back to country α. Hence, other countries besides α and α can not obtain the agenda-setting power by rejecting proposals. To make them accept the proposal Γ α, country α simply need to give each of them its equilibrium value plus a very small amount ɛ(> 0). Country α will accept the proposal if it obtains 24 u α (π) 1 δ + δ[w G W π ]. 1 + δ Thus, the vector of transfers made by country α is given by β α i = u i(g) u i (π) 1 δ + ɛ i N \ {α}, 24 See the proof in Rubinstein s alternating bargaining game 16

17 Country α obtains β α α = u α (G) u α (π) 1 δ [ u α (π) 1 δ + WG W π 1 + δ + δ[w G W π ]. 1 + δ ] (n 2)ɛ. Since ɛ 0 and W G W π > 0, country α is strictly better-off. Thus, there exists a profitable deviation from equilibrium σ. Contradiction! From the analysis above, I have shown that G. C. superadditivity hold in our model and it is a sufficient condition to guarantee efficiency of the game, that is, global liberalization can always be achieved. Therefore, neither FTAs or CUs, are stumbling blocs in a world without political-economy motive protection. My results confirm that in Aghion et al. (2007) and Macho-Stadler and Xue (2007) in an n-country world (n 3) where free trade is negotiated using my mechanism. 5 The equilibrium path In this section, I study the equilibrium path leading to global free trade. As shown by Aghion et al. (2007), coalition externalities play an important role in determining the way through which global liberalization is achieved. I examine the sign of externalities associated with both FTAs and CUs in the n-country model. In addition, to compare and analyze the results with those in Aghion et al.(2007) (e.g., Free Trade Proposition), I study a three-country model and identify conditions under which global free trade is achieved either multilaterally or bilaterally. In contrast to Aghion et al.(2007), I show that the equilibrium path depends on not only the sign of externalities, but the magnitude of externalities and the discount factor as well. By dividing countries into four types, a developed large country, a less developed large country, a developed small country, and a less developed small country, I analyze the strategic behaviors of different types of countries (e.g., Japan, USA, China, etc.) in trade negotiation 25 and the way a reginal trading-bloc among these types of countries forms. 25 For example, aiming at forming a reginal trading bloc with several countries, a country may prefer approaching other countries bilaterally to multilaterally. Moreover, this country may choose to approach a particular type of countries first. 17

18 5.1 Externalities In this model, I consider PTAs imposing externalities only, which is also true in the background trade model. The analysis of the case without externalities is omitted for two reasons: In reality, externalities induced by trading-bloc formation are significant and common; Models free of externalities have been discussed extensively in literature. For instance, Aghion et al. (2007) has observed that the agenda-setter is indifferent between sequential and multilateral bargaining when externalities are not considered. The sign of the externalities prevailing in the model are summarized in the following two propositions. Proposition 5.1. In our model where countries are free to form free trade areas, an outside country always experiences positive externalities when a new FTA forms. Proof. See the proof in the appendix. Proposition 5.2. In our model where countries are free to form custom unions, after S forms, an outside country z must experience negative externalities, if the profit-maximizing quantity of each firm in z produced for each country in S is nonnegative (no corner solutions). Proof. The proof is relegated to the appendix. The economic intuitions of Proposition 5.1. and Proposition 5.2. are simple. In our model where countries form free trade areas, the formation of an FTA not only eliminates trade barriers among its member countries, but also lowers each member country s external tariffs on imports from outside countries so deep that non-member countries benefit from it. In contrast, in a world where countries form CUs, members share a common external tariff. It implies that a CU protects its members against the rest of the world in a firmer way than an FTA does. This common external tariff maximizes the aggregate welfare of a CU and it can be higher than the average of the external tariffs setting by member countries before such a CU forms. Hence, outside countries experiences negative externalities if they keep on producing for each member of the customs union. There are some empirical studies of the effects of regional trading blocs on external tariffs. Bohara et al. (2004), for instance, observe that members in Mercosur tend to lower their external tariffs after the integration. In order to fully capture the 18

19 relationship between the type of PTAs and the sign of externalities, Estevadeordal et al. (2006) analyze the effects of FTAs and CUs on external trade liberalization using data from Latin American countries. They find that the formation of FTAs promotes external tariffs reduction, while the formation of CUs does not have such effects, which are consistent with what the model predicts in this paper. 5.2 A three-country game In order to compare the results of bilateralism and multilateralism with those in Aghion et al. (2007), I illustrate the equilibrium path using a three-country model. Two types of equilibria are observed. A multilateral equilibrium is one in which the grand coalition is achieved simultaneously. In this type of equilibrium, the country with the highest bargaining power invites the other two countries to eliminate all trade barriers among them by offering them transfers 26. With no rejections from the other two countries, a three-country trading bloc forms as a result of the first round of negotiation. A bilateral equilibrium is one in which the grand coalition is achieved sequentially. In this type of equilibrium, countries prefer bilateralism to multilateralism. Moreover, countries prefer forming a trading bloc with countries with lower bargaining power first. Sufficient conditions that determine the equilibrium path are also identified. These results can be applied to two scenarios. Firstly, if the focus is on analyzing global liberalization, I demonstrate that global free trade can always be achieved in the model and the equilibrium path leading to trade liberalization is determined by the types of PTAs, the magnitude of externalities, and the common discount factor. Therefore, this paper supports the point of view that the revival of regionalism (i.e., the formation of both FTAs and CUs) paves the way to global liberalization. Secondly, by dividing countries into the four types, a developed large country (e.g., United States) 27, a less developed large country (e.g., China), a developed small country (e.g., Japan), and a less developed small country (e.g., Malaysia), I analyze the strategic behaviors of these types of countries in trade negotiations. For instance, Japan s recent FTA strategies can be well explained in this model. In the following analysis, without loss of generality, I assume that the ranking of 26 These transfers can be positive or negative. 27 A country with a relatively larger number of firms in Sector II are called developed country and vice versa. A country with a relatively larger market size is called a large country and vice versa. 19

20 bargaining power is τ = {1 > 2 > 3}. For simplicity, the combination (a i, L) denotes a state where grand coalition is not formed 28. The state where grand coalition forms is called state g 29. Since each country s per-period national welfare function is associated with the coalition structure, I use w i (a i ) to represent country i s perperiod national welfare function at a i. Sufficient conditions to guarantee a bilateral equilibrium and to induces a multilateral equilibrium in the three-country model are presented in the following propositions. Proposition 5.3. In a three-country trade model, if countries are free to form FTAs and the national welfare functions of three countries satisfy the following conditions: (1) w 2 (a 2 ) w 2 (a 0 ) > w 1 (a 2 ) w 1 (a 0 ) + w 3 (a 2 ) w 3 (a 0 ), (2) w 1 (a 3 ) w 1 (a 0 ) > w 2 (a 3 ) w 2 (a 0 ) + w 3 (a 3 ) w 3 (a 0 ), country 1 and country 2 both prefer multilateralism and global free trade is achieved simultaneously in equilibrium regardless of the common discount factor δ. Proof. I prove this proposition in three steps. Firstly, I construct a strategy profile for the three-country game; secondly, I prove that the constructed strategy profile is an MPE; in the last step, I show the uniqueness of MPE. More details are relegated to the appendix 30. Proposition 5.4. In a three-country model, if countries are free to form CUs and the national welfare functions of three countries satisfy the following conditions: (1) w 1 (a 3 ) w 1 (a 0 ) < i N[w i (g) w i (a 3 )], (2) w 2 (a 2 ) w 2 (a 0 ) < i N[w i (g) w i (a 2 )], (3) w 3 (a 1 ) w 3 (a 0 ) > δ2 δ δ [w i (g) w i (a 1 )], 28 The symbol, a i (i {0, 1, 2, 3}), represents a coalition structure and the corresponding national welfare functions of three countries and L (L {country 1, country 2, and country 3}) represents the current agenda-setter. The mapping from a symbol a l to a coalition structure is given by π(a 0 ) = {{1}, {2}, {3}}, π(a 1 ) = {{1, 2}, {3}}, π(a 2 ) = {{1, 3}, {2}}, π(a 3 ) = {{1}, {2, 3}}. 29 Since the game ends when the grand coalition forms, no agenda-setter is needed. 30 Because of the similarity and the limitation of the length of this paper, the proofs for Proposition 5.4 and 5.5 are omitted. 20 i N

21 country 1 and country 2 always prefer bilateralism. Moreover, they both prefer forming a reginal trading bloc with country 3 first and approach the other country later. Thus, global free trade is achieved sequentially in equilibrium regardless of the common discount factor δ. Proposition 5.5. In a three-country trade model, if countries are free to form FTAs and the national welfare functions of three countries satisfy the following conditions: 1. w 2 (a 2 ) w 2 (a 0 ) < w 1 (a 2 ) w 1 (a 0 ) + w 3 (a 2 ) w 3 (a 0 ), 2. w 1 (a 3 ) w 1 (a 0 ) < w 2 (a 3 ) w 2 (a 0 ) + w 3 (a 3 ) w 3 (a 0 ); or in a three-country trade model, if countries are free to form CUs and the national welfare functions of three countries satisfy the following conditions: 1. w 1 (a 3 ) w 1 (a 0 ) > i N [w i(g) w i (a 3 )], 2. w 2 (a 2 ) w 2 (a 0 ) > i N [w i(g) w i (a 2 )], 3. w 3 (a 1 ) w 3 (a 0 ) > δ2 δ 1 1+δ i N [w i(g) w i (a 1 )], then the strategic behaviors of country 1 and country 2 in trade negotiation and the way global free trade is achieved in equilibrium depends on the size of the common discount factor δ. When countries are patient enough (δ > δ), both country 1 and country 2 prefer bilateralism and global free trade is achieved sequentially in equilibrium; when countries are not patient enough (δ < δ), country 1 and country 2 prefer multilateralism and global free trade is achieved simultaneously in equilibrium, where δ = max [δ 1, δ 2], δ = min [δ 1, δ 2], δ 1 = δ 2 = b (a 2, g)[ (g, a 2 ) + 2 (a 2, a 0 )] b 1, 2 (a 2, g) b 1 = (a 0, a 2 ) + 2 (a 2, a 0 ), b (a 3, g)[ (g, a 3 ) + 1 (a 3, a 0 )] b 2, 2 (a 3, g) b 2 = (a 0, a 3 ) + 1 (a 3, a 0 ). 21

22 Corollary 5.6. When country 1 or country 2 favors bilateralism in the three-country game, in equilibrium, it always chooses to sign a bilateral trade agreement (an FTA or a CU) with country 3 first. Although the finding that global free trade can always be achieved in equilibrium is consistent with Free Trade Proposition in Aghion et al.(2007) (AP hereafter), the results in this section contradicts AP in the following respects. First of all, AP states that the leading country who has the absolute agenda-setting power strictly prefers sequential bargaining whenever there are negative externalities. On the contrary, as shown in Proposition 5.5., the agenda-setter (could be either country 1 or country 2) may favor multilateral bargaining with moderate negative externalities if countries are not patient enough and the agenda-setter may prefer sequential bargaining when moderate positive externalities prevails if countries are patient enough. Secondly, AP states that the leading country strictly prefers multilateral bargaining when positive externalities prevails. In contrast, Proposition 5.5. shows that the agendasetter may favor sequential bargaining even with positive externalities if countries are patient enough. To sum up, the above three propositions demonstrate that the equilibrium path depends on the type of trading blocs (which determines the sign of externalities), the magnitude of externalities, and the discount factor. These results may help to explain the revival of the formation of regional free trade areas, which has been shown by empirical observations creating positive externalities (see, e.g., Estevadeordal (2006)). The United States and NAFTA Since each country s bargaining power is related to its market size and number of firms, country 1 can interpreted as a developed country with large market size (e.g., the United states); country 2 can be interpreted as a less developed country with a large market size (e.g., Mexico); country 3 can be interpreted as a developed country with a small market size (e.g., Canada) 31. Thus, the formation of NAFTA (North American Free Trade Agreement) can be explained by Corollary Japan s FTA strategies In Asia, Japan can be considered as country 1 from its economic prospect. Recently, 31 At the first glance, it seems difficult to decide either Canada or Mexico should be treated as country 2. However, since Mexico s population size is three times larger than that of Canada, it is reasonable to consider Mexico as country Canada and the United States signed an FTA in In 1994, it was superseded by NAFTA. 22