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## R&D in the Network of International Trade: Multilateral Versus Regional Trade Agreements

Working paper by Teteryatnikova, Mariya / European University Institute, 2008

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Staff Working Paper ERSD-2009-03 November 2008

World Trade Organization

Economic Research and Statistics Division

R&D in the Network of International Trade:

Multilateral versus Regional Trade Agreements

Mariya Teteryatnikova

European University Institute

Manuscript date: November 10, 2008

Disclaimer: This is a working paper, and hence it represents research in progress. This

paper represents the opinions of the author, and is the product of professional research. It is

not meant to represent the position or opinions of the WTO or its Members, nor the official

position of any staff members. Any errors are the fault of the author. Copies of working

papers can be requested from the divisional secretariat by writing to: Economic Research and

Statistics Division, World Trade Organization, Rue de Lausanne 154, CH 1211 Geneva 21,

Switzerland. Please request papers by number and title.

R&D in the Network of International Trade: Multilateral versus

Regional Trade Agreements ∗

Mariya Teteryatnikova†

European University Institute

November 10, 2008

Abstract

Recent empirical evidence has shown that trade liberalization promotes innovation and pro-

ductivity growth in individual firms. This paper argues that different types of trade liberalization

– multilateral versus regional – may lead to different R&D and productivity levels of firms. Trade

agreements between countries are modelled with a network: nodes represent countries and a link

between the nodes indicates the existence of a trade agreement. In this framework, the mul-

tilateral trade agreement is represented by the complete network while the overlap of regional

trade agreements is represented by the hub-and-spoke trade system. Trade liberalization, which

increases the network of trade agreements, reinforces the incentives for firms to invest in R&D

through the creation of new markets (scale effect) but it may also dampen these incentives through

the emergence of new competitors (competition effect). The joint action of these two effects within

the multilateral and the regional trade systems gives rise to the result that, for the same number

of direct trade partners, the R&D effort of a country in the multilateral agreement is lower than

the R&D effort of a hub but higher than the R&D effort of a spoke. This suggests that a ”core”

country within the regional trade system has higher R&D and productivity level than a country

with the same number of trade agreements within the multilateral system whereas the opposite is

true for a ”periphery” country. Additionally, the paper finds that while multilateral trade liberal-

ization boosts productivity of all countries, regional trade liberalization increases productivity of

core economies but may decrease productivity of periphery economies if the level of competition

in the new trade partner countries of the periphery economy is ”too high”. Furthermore, the

aggregate level of R&D activities within the multilateral trade agreement exceeds that in the star

– the simplest representative of the hub-and-spoke trade system.

JEL Classification: O31, D85, D43, F13

Keywords: Trade, multilateralism, regionalism, R&D, network, oligopolistic competition

∗I would like to thank my advisors Morten Ravn and Fernando Vega-Redondo for guidance, helpful comments and support.

I also thank the research staff of the WTO, especially Michele Ruta, Patrick Low and Roberta Piermartini, the participants of

the 6th ELSNIT conference in Florence on October 24-25, and Francis Bloch for useful suggestions and positive feedback.

†European University Institute, Department of Economics, Via della Piazzuola 43, 50133 Firenze, Italy e-mail:

mariya.teteryatnikova@eui.eu

1 Introduction

In the era of unprecedented proliferation of regional trade agreements and simultaneous developments

in the WTO, assessments of relative economic benefits of multilateralism versus regionalism takes on

special significance. Numerous studies investigate the difference in welfare benefits, trade volumes,

GDP levels and GDP growth rates across multilateral and regional trade arrangements.1 However,

the existing literature has not examined the issue of possible variations in the impact of different

types of trade liberalization on countries’ productivity.

The latter is surprising at least for two reasons. First, productivity is a key determinant of

aggregate output, which is found to vary across different types of trade arrangements. Secondly,

recent empirical evidence has shown that in general trade liberalization has a significant effect on the

productivity level of the country. Bustos (2007) finds that during the period of trade liberalization

between Argentina and Brazil, companies in sectors benefiting from a comparatively higher reduction

in Brazil’s tariffs increased their spending on purchases of technology goods. Likewise, Trefler (2004)

observes that the U. S. tariff concessions caused a boost in labor productivity of the Canadian firms

in the most impacted, export-oriented group of industries. Similar patterns are shown by Bernard

et al. (2006) for the U. S., by Topolova (2004) for India, by Aw et al. (2000) for Korea and

Taiwan, by Alvarez and Lopez (2005) for Chile, and by Van Biesebroeck (2005) for sub-Saharan

Africa.2 Additionally, the positive effect of trade liberalization on productivity is substantiated by

the extensive theoretical work.3

The aim of this paper is to contribute to the literature on the impact of trade liberalization on

firms’ productivity by studying how this impact varies across two types of trade liberalization –

multilateral versus regional. I consider a model in which firms can improve their productivity by

investing in costly R&D. Here R&D is viewed broadly as any activity aimed at reducing the marginal

cost of production.4

I study the mechanisms through which trade can affect the return to innovation within different

1For an extensive research of theoretical models on this subject see Panagariya (2000). The empirical works are

summarized in De la Torre and Kelly (1982), Srinivasan et al. (1993), and Frankel (1997). Other theoretical and

empirical works include Krueger (1999), Bhagwati (1993), Kowalczyk and Wonnacott (1992), Deltas et al. (2005),

Goyal and Joshi (2006), Diao et al. (2003).

2The evidence on industry-level productivity improvements is presented in Baggs et al. (2002) for Canada, in

Pavcnik (2002) for Chile, in Muendler (2004) for Brazil, in Bernard et al. (2006) for the U. S., and in Del Gatto et al.

(2006) for Europe.

3The theoretical models identify several channels through which international trade affects productivity at the in-

dustry and/or at the firm level: the improved allocation of resources through specialization (Grossman and Helpman

(1991)), the knowledge spillovers effect (Rivera-Batiz and Romer (1991), Devereux and Lapham (1994)), the realloca-

tion of economic activities from less to more productive firms (Melitz (2003), Bernard et al. (2007), Yeaple (2005)),

the exploitation of economies of scale (Krugman (1980)), the pro-competitive effect of trade openness (Aghion et al.

(2005), Peretto (2003), Licandro and Navas-Ruiz (2007)), and others. See World Trade Report 2008 for the survey.

4Examples include developing new production technology, training of employees, internal re-organization of re-

sources and factors of production.

1

types of trade systems. The two major mechanisms are the scale effect due to the increased size of

the market and the competition effect due to the increased number of competitors in the markets.

The focus of this paper is on the interaction of the two effects within multilateral and regional types

of trade agreements.

I model trade agreements between countries with a network. Nodes represent countries and a

link between the nodes indicates the existence of a trade agreement. In every country, there is a

single firm producing one good. The good is sold domestically and in markets of the trade partner

countries subject to oligopolistic competition. There is, therefore, an intra-industry trade between

countries which are directly linked in the network.

The advantage of modelling trade agreements with a network is that it enables distinction between

various types of trade systems. In particular, it allows me to focus on such differences between trade

systems as the degree of countries’ trade involvement (the number of trade agreements signed)

and the nature of market interaction between countries (who trades and competes with whom, on

which markets, how many traders are present in each market, etc). Given the focus of the paper

on interaction between the scale and the competition effects of trade liberalization within different

types of trade systems, capturing exactly these differences is key.

I constrain the analysis to two specific classes of network structures associated with the multi-

lateral and the regional scenarios of trade liberalization. The first class of networks is symmetric, or

regular, networks. It incorporates the case of a complete network structure – a network where any

one country is directly linked to every other country. The complete network in this model represents

the multilateral trade agreement. The second class of networks is asymmetric networks with two

types of nodes: high and low degree nodes. This class of networks captures the basic characteris-

tics of the so-called hub-and-spoke trade system, where some countries (hubs) have relatively large

number of direct trade partners as compared to other countries (spokes), which are mainly involved

in trade agreements with hubs. According to a number of contributions on regional trade agree-

ments, the hub-and-spoke trade arrangement has become a typical outcome of the regional trade

liberalization.5

The modelling approach in this paper is closely related to the common approach in the strand

of literature on R&D co-operation between firms in oligopoly. This strand of literature is well

represented by the seminal papers D’Aspremont and Jacquemin (1988) and Goyal and Moraga

(2002). They consider a framework of Cournot competition, where at a pre-competitive stage firms

5To my knowledge, the concept of hub-and-spoke trade arrangement was first introduced in Lipsey (1990) and

Wonnacott (1990). It was further developed in Lipsey (1991), Wonnacott (1991, 1996), Kowalczyk and Wonnacott

(1991, 1992), Baldwin (2003, 2005), De Benedictis et al. (2005), and others.

2

can exert a cost-reducing effort. The typical element of this approach is that the rationale of

co-operation between firms is the existence of R&D spillovers, which creates an externality. Co-

operation is intended to internalize such an externality.

Similarly to models with R&D co-operation, in this model, firms compete in a Cournot fashion

choosing individual R&D efforts and production levels in a two-stage non-cooperative game. How-

ever, in contrast to D’Aspremont and Jacquemin (1988), Goyal and Moraga (2002) and the related

literature, I abstract from R&D collaboration and spillovers. Instead, I concentrate purely on the

effects of market access and competition faced by firms within various types of trade agreements on

innovation intensity of the firms. Furthermore, unlike the assumption of standard oligopolistic com-

petition between firms in one common market imposed in D’Aspremont and Jacquemin (1988) and

Goyal and Moraga (2002), the central assumption in the present framework is that firms compete

not only in one, but in several separate markets and every market is accessible only to those firms

which have a trade agreement with that market. Clearly, this assumption results in heterogeneity

between firms in terms of their market size, a feature which is absent from the previous models.

The primary result of the paper is that the impact of trade liberalization on firms’ R&D efforts

depends crucially on the features of the trade agreements. Basically, the sizes of the scale effect and

the competition effect, due to a new trade partner, vary across the multilateral and the regional trade

systems since both effects are predetermined by the structure of the trade system. For example, with

regard to the scale effect, gaining access to a new market in either a multilateral or bilateral context

enhances incentives for firms to innovate. Yet, the ”net worth”, or the effective size, of the new

market depends on the number of other firms present in the market and on the competitive power of

these firms – their R&D and production levels. Those are both determined by the structure of the

trade system. Similarly, with respect to the competition effect, a new trade partner of a firm both in

the multilateral and in the regional agreement becomes an additional rival of the firm in its domestic

market. However, depending on the structure of the trade system, it may also become a rival in

some, all or none of the firm’s foreign markets. In addition, the size of the market share obtained by

the new rival in firm’s domestic and foreign markets depends on the number and on the competitive

strength of other firms present in these markets, as well as on the competitive strength of the rival

himself. Those are defined by the structure of the trade system and by the market interactions of

the firms with their own trade partners.

The difference in the scale and in the competition effects of trade liberalization and the resulting

difference in the effective sizes of markets across the multilateral and the regional trade systems leads

to the variation in levels of R&D efforts across systems. I show that for the same number of direct

3

trade partners, the R&D effort of a hub in the regional trade system is higher than that of a country

in the multilateral agreement. On the other hand, the R&D effort of a spoke is lower than that of a

hub and lower than the R&D effort of a country in the multilateral agreement, even if a country in

the multilateral agreement has the same number of direct trade partners as a spoke.6 Additionally,

for the aggregate levels of R&D activities I find that the aggregate R&D effort within the multilateral

trade agreement exceeds that in the star – the simplest representative of the hub-and-spoke trade

system.7

Some other findings of the paper concern the change in R&D investments by firms as the network

of trade agreements expands. First, consistently with the empirical evidence discussed at the outset,

I find that both, in the multilateral and in the regional trade systems, an increase in the number of

direct trade partners enhances innovation of a firm, at least as soon as the number of other firms

present in the new trade partner countries is not ”too large”. Secondly, in the multilateral trade

agreement, the rate of an increase in firm’s R&D effort is declining in the size of the agreement.8

I show that this result is implied by the decreasing market-enhancement effect of the new trade

partners. In addition, for any equal number of direct trade partners of a country in the multilateral

trade agreement and of a hub (spoke) in the regional trade system, an increase in the R&D effort

caused by a new direct trade partner proves to be smaller for a firm in the multilateral trade system

than for a firm in a hub (spoke).

The paper is organized as follows. Section 2 presents the model and describes the two-stage

game between firms. Sections 3 and 4 describe the solution of the second and of the first stage of the

game, respectively. Section 5 discusses the scale and the competition effects of trade liberalization

on firms’ innovation decisions. The joint action of these two effects within the multilateral and the

hub-and-spoke trade systems is studied in Scenario 1 and in Scenario 2 of trade liberalization. The

scenarios are compared in Section 6 and their policy implications are discussed in Section 7. Finally,

Section 8 concludes.

2 The model

Network of regional trade agreements

Consider a setting with N countries where some countries are participants of one or more trade

6The same relative effects are found for the welfare and the real income values of countries in the stylized 3-country

model by Deltas et al. (2005) and by Kowalczyk and Wonnacott (1992).

7Formally, the star network is a network in which there is a central country (hub) which is directly linked to every

other country (spoke), while none of the other countries have a direct link with each other. The star in the present

model is essentially a set of bilaterals of a hub with spokes, where each spoke has a trade agreement only with the hub.

8This finding is consistent with the hump-shaped relationship between competition and innovation derived by

Aghion et al. (2005).

4

agreements (TAs) within a certain industry. I model trade agreements between countries with a

network: countries are the nodes of the network and each link indicates the existence of a trade

agreement between the two linked countries. If two countries have negotiated a TA, then each offers

the other a privileged access to its domestic market: the tariffs and restrictions on trade are reduced.

Otherwise, for simplicity I assume that tariffs and restrictions on trade between countries which did

not sign a TA are trade-prohibitive. So in fact, trade may only exist between countries which have

negotiated a TA, that is, only between countries which are directly linked in the network. For any

i ∈ 1 : N , I will denote by Ni the set of countries with which country i has a trade link in the

network of TAs. These are direct trade partners of i. Let |Ni| be the cardinality of set Ni.9 Also, let

N2i be the set of direct trade partners of direct trade partners of i, different from i. In other words,

N2i is the set of two-links-away trade partners of i in the network of TAs. Notice that some countries

may simultaneously be direct and two-links-away trade partners of i. Let |N2i | be the cardinality of

set N2i

This model takes the network of trade agreements as exogenously given. Besides, since the trade

agreement between any two countries are reciprocal, all links in the network are undirected and no

multiple links exist.

Demand and cost structure

In every country, there is a single firm producing one good. The firm in country i can sell its good

in the domestic market and in the markets of those countries with which i has a trade agreement.

Let the output of firm i (from country i) produced for consumption in country j be denoted by yij .

The total output of firm i is given by yi =

∑

j∈Ni∪{i} yij . Each firm i exporting its good to country

j ∈ Ni ∪ {i} faces an inverse linear demand in country j given by

pj = a− b

yij + ∑

k∈Nj∪{j},k 6=i

ykj

, (2.1)

where a, b > 0 and

∑

k∈Nj∪{j} ykj ≤ a/b.

Let τ denote the trade costs faced by every firm per unit of exports to any of its direct trade

partners. These costs include tariffs on unit of export, transportation costs, etc.10 The total trade

costs faced by firm i are equal to

ti({yij}j∈Ni) = τ

∑

j∈Ni

yij . (2.2)

9This is the degree of i in the network.

10The analysis carries over in a setting where τ = 0. The assumption of zero trade costs is standard in the literature

on the formation of the network of TAs. See, for example, Furusawa and Konishi (2007), Goyal and Joshi (2006), and

Mauleon et al. (2006).

5

In addition, each firm can invest in R&D. The R&D effort of the firm helps lower its marginal

cost of production. The cost of production of firm i is therefore a function of its production, yi, and

the amount of research xi that it undertakes. I assume that the cost function of each firm is linear

and is given by

ci(yi, xi) = (α− xi)yi, (2.3)

where 0 ≤ xi ≤ α ∀i ∈ 1 : N . In the following, I will also assume that a is sufficiently large as

compared to α and the costs of trade between countries. Namely, let

Assumption 1 a > α (1 + maxi∈1:N |Ni|) + 2τ .

This assumption ensures that the demand for a good is high in all markets, so that in equilibrium,

all firms produce strictly positive amounts of both the physical and the technological good. The

R&D effort is costly: given the level xi ∈ [0, α] of effort, the cost of effort of firm i is

zi(xi) = δx2i , δ > 0. (2.4)

Under this specification, the cost of the R&D effort is an increasing function and reflects the existence

of diminishing returns to R&D expenditures.11 The parameter δ measures the curvature of this

function. In the following, it is assumed that δ is sufficiently large so that the second order conditions

hold and equilibria can be characterized in terms of the first-order conditions and are interior.12

Two-stage game

Firms’ strategies consist of the level of R&D activities and a subsequent production strategy based

on their R&D choice. Both strategies are chosen via interaction in a two-stage non-cooperative game.

In the first stage, each firm chooses a level of its R&D effort. The R&D effort of a firm determines

its marginal cost of production. In the second stage, given these costs of production, firms operate in

their domestic market and in the markets of their trade partners by choosing production quantities

{yij}i∈1:N,j∈Ni∪{i} for every market. Each firm chooses the profit-maximizing quantity for each

market separately, using the Cournot assumption that the other firms’ outputs are given.

Notice the specific nature of interaction between firms in this game. First, firms compete with

each other not in one but in several separate markets. Secondly, since countries trade only with those

countries with which they have a trade agreement (a direct link in the network), a firm competes

11An important justification of this assumption is that ”the technological possibilities linking R&D inputs and inno-

vative outputs do not display any economies of scale with respect to the size of the firm in which R&D is undertaken”

(Dasgupta (1986), p. 523).

12The assumptions imposed on the parameters of the demand and cost functions are standard in the models with

linear-quadratic specification of the objective function (the firm’s profit function in this case). This is admittedly a

special setting. Yet, even in this simple case, the analysis of the interaction between markets and R&D efforts of firms

in the network is quite complicated.

6

only with its direct and two-links-away trade partners. Furthermore, any direct trade partner of

firm i competes with i in its own market and in the market of firm i, while any two-links-away trade

partner of i, who is not simultaneously its direct trade partner, competes with i only in the market(s)

of their common direct trade partner(s). This two-links-away radius of interaction between firms

does not mean however that R&D and production choices of firms are not affected by other firms.

As soon as the network of TAs is connected,13 firms that are further than two links away from i

affect R&D and production strategies of i indirectly, through the impact which they have on R&D

and production choices of their own trade partners and trade partners of their partners, etc.

The game is solved using backward induction. Each stage is considered in turn.

3 Solving the second stage

In the second stage, each firm i ∈ 1 : N chooses a vector of its production plans {yij}j∈Ni∪{i} so as

to maximize its profit, conditional on R&D efforts {xi}i∈1:N . The profit of firm i is

pii =

∑

j∈Ni∪{i}

a− byij − b ∑

k∈Nj∪{j},k 6=i

ykj

yij − (α− xi)yi − δx2i − τ ∑

j∈Ni

yij =

=

∑

j∈Ni∪{i}

−by2ij − b ∑

k∈Nj∪{j},k 6=i

ykjyij

+ (a− α+ xi)yi − δx2i − τ ∑

j∈Ni

yij . (3.1)

Notice that function pii is additively separable and quadratic in the output levels {yij}j∈Ni∪{i}

of firm i. This leads to linear first-order conditions and guarantees the existence and uniqueness

of the solution of each firm’s maximization problem.14 Simple algebra results in the Nash-Cournot

equilibrium production levels {yij}i∈N,j∈Ni∪{i} of every firm i for consumption in country j:15

yii =

1

b(|Ni|+ 2)

a− α+ (|Ni|+ 1)xi −∑

j∈Ni

xj + |Ni|τ

, (3.2)

yij =

1

b(|Nj |+ 2)

a− α+ (|Nj |+ 1)xi − ∑

k∈Nj∪{j},k 6=i

xk − 2τ

, i ∈ 1 : N, j ∈ Ni. (3.3)

So, the equilibrium output of firm i in country j ∈ Ni ∪ {i} is increasing in firm’s own R&D

13The network is connected if there exists a path between any pair of nodes.

14Since b > 0, the second order conditions hold.

15Notice that since xk ≤ α,∑

k∈Nj∪{j}

ykj =

|Nj |+ 1

b(|Nj |+ 2)(a− α) +

1

b(|Nj |+ 2)

∑

k∈Nj∪{j}

xk − |Nj |

b(|Nj |+ 2)τ ≤

|Nj |+ 1

b(|Nj |+ 2)a−

|Nj |

b(|Nj |+ 2)τ <

a

b

.

In addition, since 0 ≤ xk ≤ α and Assumption 1 holds,

ykj ≥ 1

b(|Nj |+ 2)(a− α− |Nj |α− 2τ) =

1

b(|Nj |+ 2)(a− (α+ α|Nj |+ 2τ)) > 0 ∀k ∈ 1 : N ∀j ∈ Nk ∪ {k}.

7

effort and it is decreasing in R&D efforts of i’s rivals in market j. That is, the higher the equilibrium

R&D effort of i and the lower the equilibrium effort of every k ∈ Nj ∪ {j}, k 6= i, the higher the

share of market j gained by i.

Additionally, notice that the presence of non-negative trade costs τ gives any firm i the competi-

tive advantage over its rivals on the domestic market and implies at least as high production of i for

the domestic market as for the markets of its direct trade partners. Indeed, as soon as xi = xj for

some j ∈ Ni, the equilibrium level of production for market i of firm i is at least as high as that of

firm j. Similarly, if for some j ∈ Ni |Ni| = |Nj | and

∑

k∈Ni,k 6=j xk =

∑

k′∈Nj ,k′ 6=i xk′ , the equilibrium

level of production of firm i for the domestic market is at least as high as its production for market

j.

4 Solving the first stage

At the first stage, firms choose R&D efforts. Plugging expressions (3.2)– (3.3) for the output levels

{ykj}k∈Nj∪{j} of Cournot competitors in country j into the profit function (3.1) of firm i, we obtain

the function of the R&D effort levels {xk}k∈Nj∪{j}. After some calculations, the profit of firm i can

be written as

pii =

[

1

b

∑

j∈Ni∪{i}

(|Nj |+ 1)2

(|Nj |+ 2)2 − δ

]

x2i +

2

b

[

(a− α− 2τ)

∑

j∈Ni

|Nj |+ 1

(|Nj |+ 2)2 + (a− α+ |Ni|τ)

|Ni|+ 1

(|Ni|+ 2)2

]

xi

− 2

b

∑

j∈Ni

[ |Ni|+ 1

(|Ni|+ 2)2 +

|Nj |+ 1

(|Nj |+ 2)2

]

xixj − 2

b

∑

j∈Ni

∑

k∈Nj ,k 6=i

|Nj |+ 1

(|Nj |+ 2)2xixk + f({xk}k∈Ni∪N2i ), (4.1)

where f({xk}k∈Ni∪N2i ) is a function of R&D efforts of i’s competitors in different markets which does

not distort i’s equilibrium effort:

f({xk}k∈Ni∪N2i ) =

1

b

∑

j∈Ni

1

(|Nj |+ 2)2

(

a−α−2τ−

∑

k∈Nj∪{j},k 6=i

xk

)2

+

1

b

1

(|Ni|+ 2)2

(

a−α+|Ni|τ−

∑

j∈Ni

xj

)2

.

The profit function (4.1) of firm i is quadratic in i’s own R&D effort xi. Besides, if δ is sufficiently

high, so that the R&D cost function zi is sufficiently steep, the profit function of i is concave in xi.

To be more precise, for a given network of trade agreements, as soon as

δ >

1

b

max

i∈N

∑

j∈Ni∪{i}

(|Nj |+ 1)2

(|Nj |+ 2)2 , (4.2)

the second order conditions hold and the profit maximizing R&D efforts of all firms can be found as

a solution to the system of linear first-order conditions:

8

[

− 1

b

∑

j∈Ni∪{i}

(|Nj |+ 1)2

(|Nj |+ 2)2 + δ

]

xi +

1

b

∑

j∈Ni

[ |Ni|+ 1

(|Ni|+ 2)2 +

|Nj |+ 1

(|Nj |+ 2)2

]

xj + (4.3)

+

1

b

∑

j∈Ni

∑

k∈Nj ,k 6=i

|Nj |+ 1

(|Nj |+ 2)2xk =

1

b

(a− α− 2τ)

∑

j∈Ni

|Nj |+ 1

(|Nj |+ 2)2 +

1

b

(a− α+ |Ni|τ) |Ni|+ 1(|Ni|+ 2)2

for all i ∈ 1 : N . In the matrix form, this system can be written as

Σ · x = u, (4.4)

where x∈ RN is a vector of unknowns, u∈ RN , and Σ is (N × N) square matrix. As soon as the

network of trade agreements is connected, the matrix Σ is generically nonsingular and the right-hand

side vector u is non-zero. Then (4.4) has a unique generic solution in RN , denoted by x∗. Below

it is shown that if δ satisfies an additional restriction, stronger than condition (4.2), this solution is

ensured to be such that for all i ∈ 1 : N , 0 < x∗i ≤ α.

First, note that in the ith first-order condition in (4.3), the value of the expression on the right-

hand side and the coefficients multiplying all xk, k ∈ Ni∪N2i ∪{i}, are positive. Therefore, the value

of xi is larger the smaller the values of xj and xk for all j ∈ Ni and k ∈ N2i . Hence, the condition

sufficient for x∗i > 0 is that (4.3) evaluated at xj = xk = α ∀j ∈ Ni, k ∈ N2i defines the value of

xi, which is greater than zero. This condition is provided by Assumption 1. Similarly, the sufficient

condition for x∗i ≤ α is that (4.3) evaluated at xj = xk = 0 ∀j ∈ Ni, k ∈ N2i defines xi, which is

smaller than or equal to α. This condition is equivalent to

Assumption 2 δ ≥ 1αbmaxi∈N

[ ∑

j∈Ni

|Nj |+1

(|Nj |+2)2

(

α|Nj |+ a− 2τ

)

+ |Ni|+1

(|Ni|+2)2 (α|Ni|+ a+ |Ni|τ)

]

.

Under Assumption 1, the right-hand side of inequality in Assumption 2 is strictly larger than

1

b maxi∈N

∑

j∈Ni∪{i}

(|Nj |+1)2

(|Nj |+2)2 from the earlier restriction on δ in (4.2). Therefore, Assumption 2

is stronger. Together, Assumptions 1 and 2 guarantee that solution x∗ of a system of the first-order

conditions (4.3)(or (4.4)) is such that 0 < x∗i ≤ α for all i ∈ 1 : N , and the second order conditions

hold. Moreover, if the inequality in Assumption 2 is strict, solution x∗ is interior.16

The specification of the first-order conditions (4.3) suggests that an increase in R&D efforts of

i’s direct and/or two-links-away trade partners trigger a downward shift in i’s response. Intuitively,

by exerting higher R&D efforts, i’s rivals capture larger shares of the markets and dampen the

incentive of i to invest in R&D. We say that the efforts of firm i and its direct and two-links-away

trade partners are strategic substitutes from i’s perspective.

16Intuitively, when Assumption 1 holds, the demand for a good in each market is large, which stimulates R&D

investment (x∗i > 0). On the other hand, by Assumption 2, the cost of R&D is high, which confines the amount of

R&D expenditures (x∗i ≤ α).

9

The first-order conditions (4.3) imply that in equilibrium the profit function of firm i is given by

pii =

[

− 1

b

∑

j∈Ni∪{i}

(|Nj |+ 1)2

(|Nj |+ 2)2 + δ

]

x∗2i + (4.5)

+

1

b

∑

j∈Ni

1

(|Nj |+ 2)2

a− α− 2τ − ∑

k∈Nj∪{j},k 6=i

x∗k

2 + 1

b

1

(|Ni|+ 2)2

a− α+ |Ni|τ −∑

j∈Ni

x∗j

2 .

The short proof of this statement is provided in Appendix A.

5 The impact of trade liberalization on equilibrium R&D efforts

In the framework of the present model, trade liberalization can be defined as an expansion of the

network of trade agreements through an increase in the number of concluded trade agreements (links

or links and nodes).

First, consider an impact of trade liberalization on equilibrium R&D efforts of firms in two

countries which negotiate a trade agreement with each other. There are two major mechanisms at

work. On the one hand, a new trade agreement creates an additional market for each firm (scale

effect). This amplifies the return to productivity-enhancing investment, increasing the equilibrium

R&D effort of each firm. On the other hand, the new agreement opens the markets of both countries

to a new competitor (competition effect). This has two opposite effects on R&D. The enhanced

competition dampens the return to R&D through a reduction in the domestic market share of

each firm (market share effect of competition); yet, it also increases the return to R&D through

a depreciation of markups, which expands the domestic market (markups effect of competition).

Thus, overall trade opening between two countries has an ambiguous effect on their equilibrium

R&D efforts.

In addition, trade liberalization between any two countries affects R&D decisions of firms in other

countries, too. For example, when i and j negotiate a trade agreement, R&D efforts of other direct

trade partners of i and j are affected because firms in these countries face higher competition in i

and j. Then the impact on R&D efforts of the direct trade partners of i and j ”spreads” to a larger

network: direct trade partners of the direct trade partners of i and j face different R&D efforts and

hence, competitive power of their trade partners, which has an impact on their own optimal R&D,

etc.

Thus, scale and competition effects of trade liberalization (in any part of the network) can

reinforce or dampen the incentive for firms to invest in R&D, the sign and strength of the impact

being determined by the precise network structure. In the following section, this issue is addressed in

case of multilateral and regional trade liberalization, where each type of liberalization is represented

10

by the specific type of network.

6 Two scenarios of trade liberalization: Multilateralism versus re-

gionalism

Scenario 1: Symmetric network of trade agreements. Multilateral trade system

Consider a class of symmetric networks of degree n ≥ 1. A symmetric, or regular, network of degree

n is a network where every node has the same number n of direct contacts. Given the aim of the

paper, we are mainly interested in one representative of this class – a complete network. A complete

network of degree greater than one represents a multilateral trade system, where all participant

countries have a trade agreement with each other and neither country has a trade agreement with a

third party. In this framework, an expansion of the multilateral trade system represents a scenario of

multilateral trade liberalization. When multilateral trade liberalization involves all world economies,

the resulting trade system is a ”global free trade”.

In addition, the class of symmetric networks comprises a case of one or several simple bilaterals,

where every country signs a trade agreement with one and only one other country.17 This case

corresponds to the symmetric network of degree one.

Figure 1: Complete network of degree 7 – multilateral trade agreement between 8 countries

In the symmetric network, all countries/firms are identical and hence, exert identical R&D efforts.

Denote the level of this effort by x. Then the (single) first-order condition (4.3) can be written as

follows:[

−(n+ 1)

3

(n+ 2)2

+ δb

]

x+ 2n

n+ 1

(n+ 2)2

x+ n

(n+ 1)(n− 1)

(n+ 2)2

x =

(n+ 1)2

(n+ 2)2

(a− α) + n+ 1

(n+ 2)2

(−2τn+ τn).

From this equation, the equilibrium effort x∗ can be computed to be

x∗ =

a− α− nn+1τ

−1 + δb(1 + 1n+1)2 . (6.1)

17Up to the early 1990s, trade agreements were, with only a few exceptions, a set of non-intersecting bilateral or

”small” multilateral trade agreements (the latter are also called plurilateral RTAs). The source of this evidence is for

example, Lloyd and Maclaren (2004).

11

Now, using this expression for x∗ and formula (4.5) for the equilibrium profit function, we derive

the profit of any firm in the symmetric network:

pi =

(

−1

b

(n+ 1)3

(n+ 2)2

+ δ

)(

a− α− nn+1τ

−1 + δb(1 + 1n+1)2

)2

+

n

b(n+ 2)2

(

a− α− 2τ − n a− α−

n

n+1τ

−1 + δb(1 + 1n+1)2

)2

+

1

b(n+ 2)2

(

a− α− n

(

a− α− nn+1τ

−1 + δb(1 + 1n+1)2 − τ

))2

. (6.2)

The usual comparative statics analysis leads to the following result:

Proposition 1 Suppose that Assumptions 1 and 2 hold for all n < n̄, where n̄ ≥ 1. Then for any

n < n̄, firm’s equilibrium R&D effort x∗ is monotonically increasing in n, while firm’s profit pi is

monotonically decreasing in n.

Proposition 1 is illustrated with Figure 2, where the equilibrium R&D effort and the profit of a

firm in the symmetric network are drawn against the network degree n.18

Figure 2: Equilibrium R&D effort and profit of a country in a symmetric network of degree n

Proposition 1 suggests that multilateral trade liberalization depreciates firms’ profits. However,

the incentive for firms to invest in R&D increase. The intuition for this result is easy to grasp.

As a new country enters the multilateral trade agreement (or any other agreement which can be

represented by the symmetric network), the reduction in the domestic and foreign market shares

suffered by each firm is exactly compensated by the participation in the entrant’s market. That is,

18The simulation is done for the specific parameter values: α = 7, b = 1, n̄ = 10, and τ = 2; a and δ fulfill

Assumptions 1 and 2.

12

the negative market share effect of the increased competition is exactly compensated by the positive

scale effect associated with access to a new market. As a result, trade liberalization affects R&D

only through the reduction in markups – the remaining component of the competition effect. Since

the reduction in markups increases the aggregate market size of a firm, the optimal R&D of each

firm in the multilateral agreement is increasing in the size of the agreement.

On the other hand, Figure 2 shows that the rates of increase in R&D and decrease in profits

are both declining as the number of participant countries (size of the agreement) grows. This

observation is implied by the fact that the markups-reducing effect of trade liberalization in the

multilateral agreement is declining in the size of the agreement. Basically, using the definition of the

demand function in (2.1), I find that the price of the good in each market is given by the decreasing

and convex function of n:

p =

δb(n+ 2)(a+ α(n+ 1) + τn)− a(n+ 1)2

−(n+ 1)2 + δb(n+ 2)2 . (6.3)

Figure 3: Price on the market of a country in a symmetric network of degree n

Furthermore, notice that Proposition 1 allows for the comparison of the equilibrium R&D effort

and an individual firm’s profit in the multilateral agreement with those in the bilateral agreement

and in autarky. Denote by x∗a and pia the equilibrium R&D effort and the profit of a firm in autarky,

by x∗b and pib, the R&D effort and the profit of a firm in the bilateral agreement, and by x

∗(n) and

pi(n), the R&D effort and the profit of a firm in the multilateral agreement of degree n (of size n+1).

Then we obtain

Corollary 1 For any 2 ≤ n < n̄, x∗a < x∗b < x∗(n) and pia > pib > pi(n).

The individual R&D investment of a firm is higher in the multilateral agreement than in the bilateral

13

agreement and in autarky, while the profit of a firm in multilateral agreement is the lowest.

Finally, for aggregate levels of R&D, Proposition 1 and Corollary 1 imply that the aggregate

level of R&D activities within the multilateral trade system is increasing in the size of the system

and exceeds the aggregate R&D effort of the same number of countries where each country has

negotiated one bilateral trade agreement.

Scenario 2: Asymmetric network of trade agreements. Hub-and-spoke trade system

I now examine the case of regional trade liberalization. In the process of regional trade liberaliza-

tion, some countries (or groups of countries) negotiate one or several bilateral and/or plurilateral

agreements with each other. Thus, in contrast to the multilateral type of liberalization considered in

Scenario 1, each country may actually be a party to several different trade agreements where other

countries do not necessarily have an agreement with each other. As a result, a complex trade system

emerges where various regional (preferential) agreements overlap. In the literature, this system is

often described as a hub-and-spoke trade system, where some countries (hubs) have a relatively large

number of direct trade partners as compared to other countries (spokes), which are mainly involved

in trade agreements with hubs.

In this model, I approximate the hub-and-spoke structure by the asymmetric network with two

types of nodes – nodes of high degree n (hubs) and of low degree m (spokes), 1 ≤ m < n. I assume

that a fixed positive share of direct trade partners of hubs and spokes is represented by countries of

the opposite type. For any hub, other hubs form a share 0 ≤ ψ < 1 of its direct trade partners while

a share 0 < 1− ψ ≤ 1 is represented by spokes. Similarly, for any spoke, other spokes form a share

0 ≤ ϕ < 1 of its direct trade partners and the remaining positive share 0 < 1−ϕ ≤ 1 is represented

by hubs.19 The assumption of fixed (and identical across countries of the same type) shares ψ and

ϕ significantly simplifies calculations and enriches the comparative statics analysis. For example, it

facilitates the study of the effects of variation in the proportion of hubs to spokes among countries’

direct trade partners while the number of these direct trade partners remains unchanged.20

Some examples of the hub-and-spoke trade system are demonstrated in Table 1.

In any given hub-and-spoke trade system, all hubs exert identical R&D effort (xh) and likewise,

all spokes exert identical R&D effort (xs). Then the system (4.3) of the first-order conditions reduces

19Notice that in case when ψ = 1 (ϕ = 1), we obtain the complete network of degree n (m).

20See Proposition 2.

14

Table 1: Examples of hub-and-spoke trade system

Network characteristics Network

Type 1: Single star (n bilaterals of a hub with spokes)

n > 1, m = 1, ψ = 0, ϕ = 0

Type 2: Stars with linked hubs

n > 1, m = 1, ψ > 0, ϕ = 0

Type 3: Stars sharing spokes

n > 1, m > 1, ψ = 0, ϕ = 0

Type 4: Stars with linked hubs, sharing spokes

n > 1, m > 1, ψ > 0, ϕ = 0

Type 5: Stars where some spokes are linked with ech other

n > 1, m > 1, ψ = 0, ϕ > 0

Remark: Red nodes stand for hubs, green nodes stand for spokes.

to two equations:(

− (1− ψ)n(m+ 1)

2

(m+ 2)2

− (nψ + 1)(n+ 1)

2

(n+ 2)2

+ δb+ ψn

2(n+ 1)

(n+ 2)2

+ (1− ψ)n m+ 1

(m+ 2)2

((1− ϕ)m− 1)

+ ψn

n+ 1

(n+ 2)2

(ψn− 1)

)

· xh + (1− ψ)n

(

n+ 1

(n+ 2)2

+

m+ 1

(m+ 2)2

+

n+ 1

(n+ 2)2

nψ +

m+ 1

(m+ 2)2

ϕm

)

· xs

= (a− α− 2τ)

(

(1− ψ)n m+ 1

(m+ 2)2

+ ψn

n+ 1

(n+ 2)2

)

+

n+ 1

(n+ 2)2

(a− α+ nτ) (6.4)

(

− (1− ϕ)m(n+ 1)

2

(n+ 2)2

− (ϕm+ 1)(m+ 1)

2

(m+ 2)2

+ δb+ ϕm

2(m+ 1)

(m+ 2)2

+ (1− ϕ)m n+ 1

(n+ 2)2

((1− ψ)n− 1)

+ ϕm

m+ 1

(m+ 2)2

(ϕm− 1)

)

· xs + (1− ϕ)m

(

n+ 1

(n+ 2)2

+

m+ 1

(m+ 2)2

+

n+ 1

(n+ 2)2

nψ +

m+ 1

(m+ 2)2

ϕm

)

· xh

= (a− α− 2τ)

(

(1− ϕ)m n+ 1

(n+ 2)2

+ ϕm

m+ 1

(m+ 2)2

)

+

m+ 1

(m+ 2)2

(a− α+mτ) (6.5)

These equations uniquely identify equilibrium R&D efforts of a hub and a spoke. Extensive

calculations lead to the closed-form solution (x∗h, x

∗

s), which has a cumbersome representation and

therefore, is left for the Appendix.21

21See the proof of Proposition 2 in Appendix A.

15

Consider the impact of trade liberalization in the hub-and-spoke trade system on equilibrium

R&D efforts x∗h, x

∗

s. In contrast to the case with the multilateral trade system, in the asymmetric hub-

and-spoke structure, the negative component of the competition effect of trade liberalization (market

share effect of competition) is generally not compensated by the positive scale effect. Therefore, a

priori the impact of trade liberalization on R&D in the hub-and-spoke system is ambiguous. However,

the comparative statics of x∗h and x

∗

s reveal some insights about the effects of an expansion/variation

of the hub-and-spoke trade structure on the R&D effort of a firm.

Proposition 2 Suppose that Assumptions 1 and 2 hold for all m < n ≤ n̄, where n̄ > 1. Then

there exists ∆ > 0 such that for any δ ≥ ∆ and for any m < n < n̄, the following statements are

fulfilled:

1. the equilibrium R&D effort x∗h of a hub is monotonically increasing in n and monotonically

decreasing in m and in ψ;

2. the equilibrium R&D effort x∗s of a spoke is monotonically decreasing in n and monotonically

increasing in ϕ. Furthermore, x∗s is monotonically increasing in m if at least one of the

conditions holds:

(a) the trade costs are sufficiently high: τ ≥ 1−ϕ3−2ϕ(a− α);

(b) the share of other spokes among direct trade partners is at least 1/3: ϕ ≥ 13 ;

(c) the gap between n and m is relatively small: n ≤ m2 , that is, 1 < nm ≤ m.

Proposition 2 states that as soon as the specified parameter restrictions hold (including conditions

(a) – (c)), the equilibrium R&D effort of a hub (spoke) is increasing in the number of its direct trade

partners but is decreasing in the number of direct trade partners of spokes (hubs). In addition,

for both a hub and a spoke, the higher the share of hubs among their direct trade partners, the

lower the optimal R&D effort. Thus, the larger the number of directly accessible markets and the

lower the number of competitors in these markets, the higher the incentive for firms to innovate.

This observation suggests that, in the hub-and-spoke trade system, the competition effect of trade

liberalization on firm’s R&D is negative but the positive scale effect of any direct trade partner

dominates its negative competition effect.

The negative impact of competition on equilibrium R&D decisions of spokes sheds light on

conditions (a) – (c), which guarantee that an increase in m enhances spokes’ R&D investments.

Recall that the specification of a hub-and-spoke trade system in this model is such that an increase

in the number of a spoke’s direct trade partners m is associated with an increase in the number of

16

both types of partners – hubs and spokes.22 Since the market of a hub is ”small” – smaller than the

market of a spoke, an increase in the spoke’s foreign market share may actually be smaller than a

decrease in the share of the domestic market. As a result, the positive scale effect of an increase in

m on R&D investment of a spoke may be dominated by the negative competition effect. Conditions

(a) – (c) ensure that this would not be the case if: (a) the trade costs of firms are sufficiently high

to restrict the amount of exports from new trade partners, (b) hubs represent only a minor share

of direct trade partners of a spoke, or alternatively, (c) the number m of competitors in the spoke’s

market is comparable to n, so that the loss in the domestic market share of the spoke is not larger

than the gain in the market of a new hub market.

The results of Proposition 2 are illustrated with Figures 5 and 6 in Appendix B.23

Comparison of multilateral and regional trade systems

In this section I examine how the impacts of different types of trade liberalization compare in terms

of R&D investments of firms. The comparison is made in two steps. First, I investigate the basic

relationship between the R&D level of a firm in the multilateral trade agreement and a firm in

the regional, hub-and-spoke trade system. After that I distinguish between different types of the

hub-and-spoke system and study the ranking of R&D efforts of firms across various types of the

hub-and-spoke system and the multilateral system. Consider each step in turn.

Step 1 To gain some insights about the sources of variation in R&D efforts of a firm across the

multilateral and the regional, hub-and-spoke trade systems, let us first assume that the demand/price

for the good is the same across markets, and that all firms operating in the market of a country

obtain the same share of the market. Then, given the fixed number of direct trade partners, it is

purely the number of other firms/competitors present in each trade partner country that determines

the aggregate market size of a firm. The fewer competitors, the larger the aggregate market size of

a firm and the higher the return to R&D investment.

In this simplified framework, for any number n of direct trade partners, the aggregate market

size of a hub in any hub-and-spoke trade system is larger than that of a firm in the multilateral

agreement. The opposite is true for spokes. For any number m of direct trade partners, the total

market size of a spoke is smaller than that of a country in the multilateral agreement. To clarify

the first statement, observe that while in the multilateral agreement (of degree n), the number of

competitors of a firm is n in each of its n foreign markets, in the hub-and-spoke trade system, the

number of competitors of a hub is n only in ψ · n of its foreign markets and it is less than n in the

22The proportion of spokes to hubs among the new trade partners is determined by ϕ: the lower ϕ, the higher the

relative number of hubs.

23Both figures are produced using the same parameter values as for Figure 2 in Scenario 1. In addition, for Figure

5, I set ψ = ϕ = 0 and for Figure 6, n = 6, m = 2.

17

remaining markets. A similar argument is applicable for spokes.

Recall that these conclusions are derived under the assumption of equal demand and equal market

shares of firms in every market. But in fact, they hold without this assumption. Formally, the result

is an immediate implication of Proposition 2 and the short proof is provided in Appendix A:

Proposition 3 For any 0 ≤ ψ,ϕ < 1 and for any n,m > 1 such that n > m,

x∗h > x

∗(n) > x∗(m) > x∗s.

Moreover, the same inequalities hold when a hub and a spoke belong not just to one, but to any

different types of the hub-and-spoke structure.24

Step 2 Now, I compare equilibrium R&D efforts of firms across various types of the hub-and-

spoke trade structure. To that end, I restrict attention to the specific types of the hub-and-spoke

structure presented in Table 1. Notice that by Proposition 3, it only remains to compare separately

R&D efforts of hubs and R&D efforts of spokes, since R&D of a hub is always higher than R&D of

a spoke both in one and in different types of the hub-and-spoke structure.

As before, assume that the demand for the good is the same in all markets and that all firms

(hubs and spokes) share each market equally. Consider the differences in market sizes of hubs and

spokes across various hub-and-spoke structures. With regard to hubs, observe that for any number,

n, of a hub’s direct trade partners, a hub in the star (Type 1 system) enjoys the lowest competition

in any of its foreign markets as compared to hubs in the other systems. Therefore, a hub in the

star has the largest total market size. As a number of firms (competitors) in markets of a hub’s

direct trade partners grows, the aggregate market size of the hub decreases. This is the case when

either the number of a spoke’s direct trade partners, m, grows (Type 3 system), the share of hubs

among direct trade partners, ψ, increases (Type 2 system) or when both changes in m and ψ happen

simultaneously (Type 4 system). Furthermore, the larger the increase in m and/or ψ, the smaller

the size of a hub’s aggregate market.

For spokes the situation is symmetric. Given any number, n, of a hub’s direct trade partners, a

spoke in the star (Type 1 system) has access to a single foreign market (m = 1). Therefore, a spoke’s

market in the star is smaller than a spoke’s market in any other hub-and-spoke trade system.25 As

the number of direct trade partners of a spoke, m, increases (Type 3 system), the market of a spoke

expands. It expands even further if the share of spokes among direct trade partners, ϕ , grows (Type

24Recall from Scenario 1 that x∗(n) denotes the equilibrium R&D effort of a firm in the multilateral agreement of

degree n.

25In fact, on the assumption of equal demand and equal market shares of firms in every market, the market size of

a spoke in Type 2 system is the same as in the star.

18

5 system). Moreover, the larger the increase in m and/or ϕ, the larger the aggregate market size of

a spoke.

As in Step 1, the insights gained on the assumption of equal demand and equal market shares of

firms in every market prove to be valid when the assumption is relaxed. This leads to Proposition 4,

which is formally derived in Appendix A. To state the proposition, I denote by x∗hi the equilibrium

R&D effort of a hub and by x∗si, the equilibrium R&D effort of a spoke in the hub-and-spoke trade

system of Type i, i ∈ 1 : 5.

Proposition 4 Consider Types 1–5 of the hub-and-spoke trade structure. Suppose that (i) n is the

same across all types, (ii) m is the same across all types where m > 1 (Types 3, 4 and 5), and (iii)

ψ is the same across all types where ψ > 0 (Types 2 and 4). Let x∗(n) and x∗(m) be defined for n

and m > 1, identical to those in Types 1 – 5 of the hub-and-spoke structure. Then firms’ equilibrium

R&D efforts in Types 1–5 of the hub-and-spoke structure and in the multilateral agreement rank as

follows:

x∗h1 > x

∗

h3 > x

∗

h4 > x

∗(n) > x∗(m) > x∗s5 > x

∗

s3 > x

∗

s1.

With respect to the equilibrium R&D effort x∗h2 of a hub and x

∗

s2 of a spoke in Type 2 system, the

following inequalities hold:

x∗h1 > x

∗

h2 > x

∗

h4 and x

∗

s4 > x

∗

s2.

Proposition 4 is illustrated with Figure 4 and Figure 7.

Thus, the R&D efforts of firms in the multilateral system and in various types of the hub-and-

spoke trade systems vary substantially. The highest R&D incentives exist for a hub, especially for

a hub in the star (Type 1 system), whereas for a spoke in the star the incentives are the lowest. As

the number of direct trade partners of a spoke and/or the share of spokes (hubs) among direct trade

partners of each spoke (hub) increase, the levels of R&D investment of hubs and spokes converge.

They coincide at the level of R&D investment of a firm in the multilateral agreement, which therefore,

takes an average position: it is lower than R&D of a hub but higher than R&D of a spoke.

Further to comparing individual R&D investments by firms, I compare the aggregate levels of

R&D activities of the same total number of countries in the multilateral trade agreement and in the

star – bilateral agreements of one country (a hub) with the others (spokes). I find that although the

individual R&D effort of a hub in the star is much higher than the R&D effort of a single country

in the multilateral agreement, the aggregate R&D in the star is lower than in the multilateral

agreement. This observation is demonstrated by Figure 8 in Appendix B.

Finally, Figures 4 and 7 provide some insights concerning the rates of an increase in firms’

19

Figure 4: Equilibrium R&D efforts in the multilateral and in the hub-and-spoke trade system as a

function of n (the upper sub-figure) and as a function of m (the lower sub-figure).

20

individual R&D efforts as the network of trade agreements expands. They show that under the

conditions of Proposition 2 (parameter restrictions (9.3)–(6.8) and conditions (a)–(c)), for any equal

number of direct trade partners of a country in the multilateral trade agreement and of a hub

(spoke) in the hub-and-spoke trade system, an increase in the R&D effort caused by a new direct

trade partner is smaller for a firm in the multilateral trade system than for a hub (spoke).

7 Policy implications

The previous analysis suggests that the structure of the network of trade agreements and the position

of a country in this network are key for understanding the differences in R&D and productivity levels

of firms across the multilateral and the regional types of trade systems. This feeds into the ongoing

debate on gains and losses of multilateralism versus regionalism, especially with respect to the

intensive proliferation of regional trade agreements among the WTO member countries. The paper

suggests that productivity gains of regionalism versus those of multilateralism depend heavily on

the relative number of regional trade agreements signed by countries. If a country signs relatively

large number of trade agreements within the regional system (core country), then its R&D and

productivity are higher than R&D and productivity of a country in the multilateral system. At the

same time, a country that signs relatively small number of trade agreements within the regional

system (periphery country) has lower productivity gains than a country in the multilateral system.

This observation suggests that from a perspective of a small economy, which normally becomes a

spoke/periphery in the regional trade system, the prospects for productivity improvements within

the multilateral trade system are generally better than within the regional system.26

In addition, the finding of the unambiguously positive impact on R&D of the multilteral trade

liberalization indicates that the expansion of the WTO as well as the consolidation of several pluri-

lateral blocks or their accession to the WTO enhance R&D in every country.27

8 Conclusion

This paper develops a model of international trade with firm-level productivity improvements via

R&D. Firms in different countries sell their product and compete in a Cournot fashion with other

26The finding of a substantially lower R&D and productivity levels in a spoke economy as compared to those in a hub

and in a country within the multilateral system, supports the argument of earlier studies about the disadvantageous

position of spokes. For instance, Baldwin (2003), Kowalczyk and Wonnacott (1992), Deltas et al. (2005), Lloyd and

Maclaren (2004), and De Benedictis et al. (2005) find that welfare and income levels are lower for spokes than for hubs

and than for countries in the complete network.

27According to Fiorentino et al. (2007), the number of merging regional trade agreements is currently increasing.

Examples include EC-GCC, SACU-MERCOSUR, among others.

21

firms in the domestic market and in the markets of their trade partners. The trade partners of

any country/firm are defined by the network of trade agreements: countries which are linked in the

network are (direct) trade partners of each other.

I focus on two specific types of networks: the complete and the hub-and-spoke network. In

the model, these networks represent trade arrangements which arise as a result of multilateral or

regional trade liberalization, respectively. I study how the structure of the trade arrangement and

the position of a country in this structure affect R&D investments by firms. In this manner I address

the issue of the difference in the impact of multilateral and regional types of trade liberalization on

firms’ R&D and productivity.

I show that the R&D response of firms to trade liberalization is the net outcome of two different

effects: one, stimulating R&D through the creation of new markets (scale effect), and the other,

deterring or improving R&D through the emergence of new competitors (competition effect). I

find that the sizes of both effects vary across the multilateral and the regional/hub-and-spoke trade

systems. Basically, a new country entering the multilateral or the hub-and-spoke trade system

represents different ”value added” for firms in every system since the effective size of the new market

and the competitive impact of the new firm depend on the structure of the trade system.

The variations in the scale effect and the competition effect of trade across structures leads to

variations in firms’ aggregate market sizes. In turn, the difference in firms’ market sizes explains the

difference in levels of firms’ R&D investments. For the same number of direct trade partners, the

R&D effort of a hub in the hub-and-spoke trade system is higher than the R&D effort of a country

in the multilateral agreement. On the other hand, R&D of a spoke is lower than R&D of a hub and

lower than R&D of a country in the multilateral agreement, even if a country in the multilateral

agreement has the same number of direct trade partners as a spoke.

In addition, consistently with the empirical evidence, I find that a new market opening increases

R&D of a firm in the multilateral system and R&D of a hub in the regional system. It also increases

R&D of a spoke, at least as soon as the level of competition in the new spoke’s trade partner is not

too high.28 However, the size of an increase in R&D varies across different types of trade systems.

I show that for any equal number of direct trade partners of a country in the multilateral trade

agreement and of a hub (spoke) in the hub-and-spoke trade system, the growth of the R&D effort

caused by a new direct trade partner is lower for a firm in the multilateral trade system than for a

28Recall that in the regional hub-and-spoke trade system, R&D of a spoke declines in response to a new market

opening if the negative competition effect on R&D of the spoke’s new trade partners outweighs the positive scale effect.

However, by simulating the model for the star network under various parameter assumptions, I find that opening trade

with the hub decreases R&D of a spoke when the number of competitors in the hub’s market is ”unrealistically high”

(more than 100).

22

hub (spoke) in the regional system. Furthermore, for the aggregate levels of R&D activities, I find

that the aggregate R&D effort within the multilateral trade agreement exceeds that in the star –

the simplest representative of the hub-and-spoke trade system.

The paper suggests some policy implications. For example, with regard to benefits and losses of

regionalism versus multilateralism, the paper indicates that the regional trade liberalization is likely

to be more beneficial than the multilateral trade liberalization for R&D and productivity level of

”strong negotiators” (hubs) – countries which sign sufficiently many regional trade agreements. At

the same time, R&D and productivity level of weaker negotiators are higher if the countries choose

the multilateralist alternative.

Lastly, it is important to emphasize that the results of this paper are driven purely by the

scale effect and the competition effect of trade liberalization, which are in turn determined by the

structural characteristics of trade agreements. In order to precisely isolate the impact of the structure

of trade agreements, the model abstracts from other channels through which trade liberalization may

affect R&D. For example, the excluded channels are the R&D spillover effect and the firms selection

effect of trade.29 Additionally, for the sake of simplicity, the model disregards important inequalities

in terms of geographical size and initial income/resources across countries. These limitations of the

paper suggest directions for further research. In particular, the empirical test of the model could

provide more insights.

29As suggested by Melitz (2003), the firms selection effect results from the initial difference in productivity of multiple

domestic firms in each country and from the existence of the fixed costs of production and exporting.

23

9 Appendix

Appendix A: Proofs

Derivation of the profit function in (4.5)

The profit function in (4.1) can be written as

pii = 2x∗i

[

1

b

(a− α− 2τ)

∑

j∈Ni

|Nj |+ 1

(|Nj |+ 2)2 +

1

b

(a− α+ |Ni|τ) |Ni|+ 1(|Ni|+ 2)2 −

− 1

b

∑

j∈Ni

[ |Ni|+ 1

(|Ni|+ 2)2 +

|Nj |+ 1

(|Nj |+ 2)2

]

x∗j −

1

b

∑

j∈Ni

∑

k∈Nj ,k 6=i

|Nj |+ 1

(|Nj |+ 2)2x

∗

k

]

−

−

[

− 1

b

∑

j∈Ni∪{i}

(|Nj |+ 1)2

(|Nj |+ 2)2 + δ

]

x∗2i + f({xk}k∈Ni∪N2i ).

By the first-order conditions (4.3), this reduces to

pii = 2

[

− 1

b

∑

j∈Ni∪{i}

(|Nj |+ 1)2

(|Nj |+ 2)2 + δ

]

x∗2i −

[

− 1

b

∑

j∈Ni∪{i}

(|Nj |+ 1)2

(|Nj |+ 2)2 + δ

]

x∗2i +

+ f({xk}k∈Ni∪N2i ) =

[

− 1

b

∑

j∈Ni∪{i}

(|Nj |+ 1)2

(|Nj |+ 2)2 + δ

]

x∗2i +

+

1

b

∑

j∈Ni

1

(|Nj |+ 2)2

a− α− 2τ − ∑

k∈Nj∪{j},k 6=i

x∗k

2 + 1

b

1

(|Ni|+ 2)2

a− α+ |Ni|τ −∑

j∈Ni

x∗j

2 .

Proof of Proposition 1

First, notice that in case of a symmetric network of degree n, the right-hand side of inequality in

Assumption 1 is an increasing function of n and also the right-hand side of inequality in Assumption

2 is an increasing function of n, provided that Assumption 1 holds. Therefore, for Assumptions 1

and 2 to be fulfilled for all n < n̄, it is enough to ensure that these assumptions hold for n = n̄. The

resulting restrictions are

a > α(1 + n̄) + 2τ, and (9.1)

δ ≥ 1

αb

(n̄+ 1)

(n̄+ 2)2

((αn̄+ a)(n̄+ 1)− τ n̄). (9.2)

The proof of Proposition 1 is established in two steps.

1. R&D effort x∗ is monotonically increasing in n

24

Taking a derivative of x∗ in (6.1) with respect to n, we obtain:

∂x∗

∂n

=

− τ

(n+1)2

(− 1 + δb(1 + 1n+1)2)+ 2δb(1 + 1n+1) 1(n+1)2 (a− α− nn+1τ)(− 1 + δb(1 + 1n+1)2)2 =

=

1

(n+1)2

(

τ + δb

(

1 + 1n+1

)(− τ(1 + 1n+1)+ 2(a− α− nn+1τ)))(− 1 + δb(1 + 1n+1)2)2 .

The sign of this derivative is positive as soon as

2

(

a− α− n

n+ 1

τ

)

> τ

(

1 +

1

n+ 1

)

.

One can readily see that this inequality holds due to the restriction on a in (9.1).

2. profit pi is monotonically decreasing in n

Due to the computational complexity, I present only a schematic proof of this statement.

Taking the derivative of pi in (6.2) with respect to n, we obtain the expression represented by

the product of the ratio 1

b(2n−4bδ+n2−4bnδ−bn2δ+1)3 and the quadratic polynomial of τ . The ratio

is negative for any n ≥ 1 due to the restriction on δ in (9.2). On the other hand, the value

of the polynomial is positive for any n ≥ 1 as soon as parameters satisfy the restrictions (9.1)

and (9.2). The latter is established via two steps.

• First, I find that due to the restriction (9.2) the coefficient of the polynomial at the

quadratic term τ2 is negative for any given n ≥ 1. Besides, the constant term is positive.

Hence, the graph of the quadratic function is a parabola with downward-directed branches

and two real roots – one positive and one negative.

• Since the unit trade cost τ is positive and by the restriction (9.1), it does not exceed

1

2(a−α), to establish that the value of the polynomial is positive for all τ ∈ (0, 12(a−α)),

it suffices to show that the value of the polynomial is positive at τ := 12(a− α). One can

find that this is indeed the case, provided that (9.1) and (9.2) hold.

Thus, for all n ≥ 1 and any parameter values satisfying the conditions (9.1) and (9.2), the

derivative of pi with respect to n is negative, so that the profit function is decreasing in n.

Sketch of the proof of Proposition 2

Notice that to ensure that Assumptions 1 and 2 hold for all m < n ≤ n̄, it is enough to impose

25

the restrictions

a > α(1 + n̄) + 2τ, and (9.3)

δ ≥ 1

αb

[

n̄+ 1

(n̄+ 2)2

n̄(αn̄+ a− 2τ) + 2

9

((αn̄+ a)(n̄+ 1)− τ n̄)

]

. (9.4)

The equilibrium R&D effort of a hub and a spoke are given by the solution to the system of

equations (6.4) – (6.5):

x∗s =

(

(a− α− 2τ)(1− ϕ)m(n+ 1)(m+ 2)2 + (m+ 1)(n+ 2)2[(a− α− 2τ)ϕm+ a− α+mτ])·

·

(

(n+ 2)2

[

bδ(m+ 2)2 − n(1− ψ)(m+ 1)(2 + ϕm)]− (nψ + 1)(n+ 1)(n(1− ψ) + 1)(m+ 2)2)−

−(1− ϕ)m

(

(nψ + 1)(n+ 1)(m+ 2)2 + (ϕm+ 1)(m+ 1)(n+ 2)2

)

·

·

(

(a− α− 2τ)[nψ(n+ 1) (m+ 2)2 + (n− nψ)(m+ 1) (n+ 2)2 ]+ (n+ 1) (m+ 2)2 (a− α+ nτ))(

(n+ 2)2

[

bδ(m+ 2)2 − n(1− ψ)(m+ 1)(2 + ϕm)]− (nψ + 1)(n+ 1)(n(1− ψ) + 1)(m+ 2)2)·

·

(

− (1− ϕ)m(m+ 2)2(nψ + 2)(n+ 1) + (n+ 2)2δb(m+ 2)2−

−(n+ 2)2[(ϕm+ 1)(m+ 1)2 −mϕ(m+ 1)(1 + ϕm)])−

−(1− ϕ)(1− ψ)mn

(

(n+ 1)(m+ 2)2(1 + nψ) + (m+ 1)(n+ 2)2(1 + ϕm)

)2

x∗h =

(a− α− 2τ)(nψ(n+ 1)(m+ 2)2 + (n− nψ)(m+ 1)(n+ 2)2)+ (n+ 1)(m+ 2)2(a− α+ nτ)−

−x∗s(n− nψ)

(

(m+ 1)(n+ 2)2 + (n+ 1)(m+ 2)2 + ϕm(m+ 1)(n+ 2)2 + nψ(n+ 1)(m+ 2)2

)

bδ(n+ 2)2(m+ 2)2 − (nψ + 1)(n+ 1)2(m+ 2)2 − (n− nψ)(m+ 1)2(n+ 2)2+

+nψ(2n+ 2)(m+ 2)2 + ((1− ϕ)m− 1)(n− nψ)(m+ 1)(n+ 2)2 + nψ(nψ − 1)(n+ 1)(m+ 2)2

Taking a derivative of x∗h and x

∗

s with respect to each of the parameters m, n, ϕ and ψ, we obtain a

ratio, where the denominator is unambiguously positive while the sign of the numerator is determined

by the sign of a cubic polynomial in δ. As soon as δ is sufficiently large – greater than the largest

real root of the polynomial, the sign of the polynomial is defined by the sign of the coefficient at the

highest degree.

Thus, to simplify calculations, I assume that δ is large enough (δ > ∆) and focus on the sign of the

polynomial’s coefficient at δ3. I obtain that under the parameter restriction (9.3), partial derivatives

∂x∗s

∂n ,

∂x∗h

∂m , and

∂x∗h

∂ψ are negative and the derivatives

∂x∗h

∂n and

∂x∗s

∂ϕ are positive. As regarding the

derivative ∂x

∗

s

∂m , this derivative is positive if and only if the following inequality holds:

(a−α−2τ)(1−ϕ) ·A+ (a−α−2τ) ·B+ τ ·C > (a−α−2τ)(1−ϕ) ·D− (a−α−2τ)ϕ ·E, (9.5)

26

where

A = m6n4 + 7m6n3 + 18m6n2 + 20m6n+ 8m6 + 12m5n4 + 84m5n3 + 216m5n2 + 240m5n+ 96m5,

B = −30m4n4ϕ+ 50m4n4 − 300m4n3ϕ+ 380m4n3 − 840m4n2ϕ+ 1000m4n2 − 960m4nϕ

+1120m4n− 384m4ϕ+ 448m4 + 40m3n4ϕ+ 100m3n4 − 320m3n3ϕ+ 880m3n3

−1280m3n2ϕ+ 2400m3n2 − 1600m3nϕ+ 2720m3n− 640m3ϕ+ 1088m3 + 240m2n4ϕ

+120m2n4 + 240m2n3ϕ+ 1200m2n3 − 480m2n2ϕ+ 3360m2n2 − 960m2nϕ+ 3840m2n

−384m2ϕ+ 1536m2 + 288mn4ϕ+ 112mn4 + 576mn3ϕ+ 1024mn3 + 384mn2ϕ+ 2816mn2

+3200mn+ 1280m+ 16n5ϕ+ 96n4ϕ+ 64n4 + 192n3ϕ+ 448n3 + 128n2ϕ+ 1152n2 + 1280n+ 512,

C = 160n4 + 1024m+ 1280n+ 768m2 + 256m3 + 32m4 + 1280n2 + 640n3 + 512 + 16n5

+1929m2n2 + 960m2n3 + 640m3n2 + 320m3n3 + 80m4n2 + 24m2n5 + 80m3n4 + 40m4n3

+1286mn3 + 8m3n5 + 10m4n4 +m4n5 + 2560mn+ 2560mn2 + 1920m2n+ 640m3n

+80m4n+ 32mn5 + 320mn4 + 240m2n4,

D = m4n5 + 6m3n5 + 12m2n5 + 8mn5,

E = 2m4n5 + 14m3n5 + 36m2n5 + 40mn5.

Notice that A, B, C, D, and E are all positive, so that the left-hand side of (9.5) is positive, while

the sign of the right-hand side is determined by relative values of (1 − ϕ) ·D and ϕ · E. It is easy

to see that 2D < E. Hence, for ϕ ≥ 1/3, (1 − ϕ) · D < ϕ · E and the right-hand side of (9.5) is

negative. This establishes condition (b) of the proposition.

Observe also that C > D. Then as soon as τ ≥ (a− α− 2τ)(1−ϕ), inequality (9.5) holds. This

justifies condition (a).

Finally, condition (c) follows from the series of inequalities. First, when n ≤ m2,

A > m4n5 + 12m3n5 + 7m2n5 + 84mn5. (9.6)

Secondly, since m > n,

m4n5 + 12m3n5 + 7m2n5 + 84mn5 > m4n5 + 6m3n5 + 13m2n5 + 84mn5 > D. (9.7)

Combining (9.6) and (9.7), we obtain that A > D, so that inequality (9.5) is satisfied.

Proof of Proposition 3

First, notice that a complete network of degree n (m) can be regarded as a hub-and-spoke

27

network ”composed only of hubs”, that is, where ψ = 1 (composed only of spokes where ϕ = 1).

Then inequality x∗h > x

∗(n) follows from part 1 of Proposition 2, stating that x∗h is decreasing in

ψ. Similarly, x∗(m) > x∗s is implied by the result that x∗s is increasing in ϕ. Lastly, inequality

x∗(n) > x∗(m) follows from Proposition 1.

Proof of Proposition 4

Consider the first series of inequalities in Proposition 4:

x∗h1 > x

∗

h3 > x

∗

h4 > x

∗(n) > x∗(m) > x∗s5 > x

∗

s3 > x

∗

s1.

There, the first three inequalities follow from part 1 of Proposition 2: x∗h1 > x

∗

h3 since x

∗

h is

decreasing in m, while x∗h3 > x

∗

h4 > x

∗(n) since x∗h is decreasing in ψ. Similarly, the last three

inequalities are implied by part 2 of Proposition 2: x∗(m) > x∗s5 > x∗s3 since x∗s is increasing in ϕ,

while x∗s3 > x∗s1 since x∗s is increasing in m. The intermediate inequality x∗(n) > x∗(m) is a result

of Proposition 1.

Likewise, with regard to the equilibrium R&D efforts x∗h2 and x

∗

s2 in Type 2 system, the inequality

x∗h1 > x

∗

h2 follows from the fact that x

∗

h is decreasing in ψ, while x

∗

h2 > x

∗

h4 and x

∗

s4 > x

∗

s2 are the

result of x∗h and x

∗

s being decreasing and increasing in m, respectively.

Appendix B: Figures

28

Figure 5: Equilibrium R&D efforts in the hub-and-spoke trade system as a function of n (the upper

sub-figure) and as a function of m (the lower sub-figure).

Figure 6: Equilibrium R&D efforts in the hub-and-spoke trade system as a function of ψ (the upper

sub-figure) and as a function of ϕ (the lower sub-figure).

29

Figure 7: Equilibrium R&D efforts in Type 2 system as compared to R&D efforts in other hub-and-

spoke systems and to R&D of a country in the multilateral agreement.

Figure 8: Aggregate equilibrium R&D efforts of n countries in the star and in the multilateral

agreement.

30

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