International Trade and Finance Association. FDI and International Trade Relations: A Theoretical Approach

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1 International Trade and Finance Association International Trade and Finance Association Working Papers 2008 Year 2008 Paper 31 FDI and International Trade Relations: A Theoretical Approach Grigoris Zarotiadis Departent of Econoics, University of Ioannina, Greece This working paper site is hosted by The Berkeley Electronic Press (bepress) and ay not be coercially reproduced without the publisher s perission. Copyright c 2008 by the author.

2 FDI and International Trade Relations: A Theoretical Approach Abstract The ainstay theory provides arguents for both copleentary and substitute links between FDI and international trade. In accordance to that, a nuber of epirical investigations indicate a replaceent of trade flows by FDI, while other studies reveal a copleentary effect between the two. The present study odels autarky and trade between two countries in a anner that resebles the real world trade patterns. The objective is to provide the theoretical basis upon which one ay introduce bilateral FDI flows. The odel follows Fujita s et al. (1999) logic which is based on a spatial transforation of the Dixit-Stiglitz approach with onopolistic copetition, increasing returns to scale and iceberg-type transport costs. We introduce capital as an additional production factor and assign arginally different capital intensity to each different industry. Letting capital (and/or labor) be obile provides a fraework that incorporates different relations between FDI and trade, at each level of aggregation, offering interesting theoretical conclusions. In the following, we discuss the features and the dynaics of a siplified version of the odel, with no trade-costs and with a specific value for consuers preferences for variety (?=5). It allows for different effects at the level of each fir, of each industry (in ters of the notation used in previous pages, branch i) and of the whole anufacturing sector (econoy-wide). Therefore, although siplified, the odels provides us with a picture where, as capital (and/or labor) flows fro one country to the other, it generates well-defined, but at the sae tie partly nononotone and contradictory, effects on trade flows. This paper was presented May 23, 2008, at the 18th International Conference of the International Trade and Finance Association, eeting at Universidade Nova de Lisboa, Lisbon, Portugal.

3 1. Introduction Epirical studies on FDI-Trade interaction provide opposing evidence as to whether FDI copleents or substitutes trade. Country-specific characteristics as well as special features of the studied period, together with differences in the applied epirical ethodology give reasons for any of the observed contradictions. For instance, Helpan et al (2003) point out that the substitutability reported by Graha (1999) for the USA and by Ma et al (2000) or Bayoui and Lipworth (1997) for Japan ay depend upon freight and tariff costs effects. 1 On the other hand, Pfafferayer (1996) follows an atypical ethodology, estiating a siultaneous equation syste using tie series and cross-sectional industry-level data fro Austrian anufacturing. He finds a significant copleentary relationship between FDI and exports in the 1980 s and early 1990 s. Liu et al (2001) apply a panel data approach using data fro China and conclude on a cyclical copleentary relationship between trade flows (iports and exports) and FDI, which fits well to the experiences over the last two decades of the 20 th century in the specific country. Swenson (2004) and Mylonidis and Zarotiadis (2008) decopose the effect at the different levels of aggregation (econoy-, anufacturing- and industry-wide). They find substantial evidence for the presence of both substitute and copleentary relationships, at the different levels of aggregation, which iplies various theoretical conclusions. In fact, we should not be surprised by the inconclusiveness of the existing epirical literature, as it siply addresses the coplex reality. A long series of theoretical considerations enlightened different aspects regarding ultinationals, trade and FDI, which are often inadequately explained by standard trade theory. Batra and Raachandran (1980) integrated ultinationals into a Heckscher-Ohlin fraework, but as Markusen (1984) pointed out, foral trade theory has largely failed to provide a rationale as to why these corporations exist at all. His odel allowed, under certain conditions, the eergence of a ulti-plant equilibriu with horizontal FDI, while Helpan (1984) developed a general equilibriu odel of international trade that justified the existence of vertical FDI otivated by differences in factor prices. Brainard (1993) developed the proxiity-versus-scale approach, arguing for the relevance of two factors, naely trade costs and econoies of scale. Markusen and Venables (1998, 2000) who allow ultinationals to arise endogenously using a Cournot oligopoly odel with hoogeneous goods and positive trade costs, as well as Baldwin and Ottaviano (2001), who posit a odel where ultiproduct firs siultaneously engage in intraindustry FDI and intraindustry trade, provide a theoretical justification for the siilarity in trade and FDI patterns. The following table provides an overview of the aforeentioned theoretical discussion regarding the effects of FDI flows on bilateral trade. It presents three fundaental justifications (cases) that explain the choice of the location and the resulting FDI flows, cobined with arguents fro the tradition of ultinationals literature. First, based on the standard trade theory, FDI flows fro country o (origin country) to country h (host country) are due to less relative abundance of capital in h. Econoy-wide effects on trade are clearly negative: both iports fro and exports to o (and to the rest of the world) are eroded (partially or fully) as the coparative advantage that stiulates this trade is suppressed. Second, FDI eerge fro the existence of coparative advantages, other than capital s scarcity, in country h (e.g., weather or culture, political situation etc). Capital is 1 This is probably why, Brainard (1997) and Clausing (2000) for the U.S.A. and Co (1997) for Japan, who use data fro slightly different periods, find evidence of FDI-trade copleentarity. 1 Hosted by The Berkeley Electronic Press

4 FDI flow fro country o to country h needed to flow in country h in order to activate the specific underused coparative advantages. In this case of supply-driven FDI, exports fro country h to the rest of the world (including country o) are increased 2. Notice that the first two cases provide the basis for vertical FDI flows between dissiilar regions (Markusen and Maskus, 2002). Third, we have the case of a sufficient and secure deand surplus in country h. Foreign firs choose either to export (low constant / high arginal cost) or to relocate their production facilities in h (high constant / low arginal cost). The size of h and the existence of trade barriers and transportation costs are decisive for the final choice. 3 Deand-driven FDI substitutes country h s iports, thus creating horizontally structured MNEs. Table 1: Overview of the theoretically docuented FDI-trade relations 4 Case Effect on iports (M) of country h fro country o Effects on exports (X) fro country h to country o Standard Trade Theory Country o has a relative abundance of capital and h accordingly of labour. Supply-driven FDI Spatial Arguents Country h has a coparative advantage in specific productions, which is not related to the use of capital. Supply-driven FDI Standard MNE Theory Country h has a sufficient and (relative) secure deand surplus. Deand-driven FDI Basically M decreases because country o s coparative advantage is eroded (partially or fully) Econoy-wide effect there is no obvious overall effect M decreases because initial iports are substituted by the sales of the affiliate in h (proxiity arguent) Industry-wide effect but if there are affiliates M increases, as interediate goods are iported fro o for the needs of the affiliate Manufacturingand industry-wide effect M increase, as interediate goods are iported fro o for the needs of the affiliate Manufacturingand industry-wide effect M increase, as interediate goods are iported fro o for the needs of the affiliate Manufacturingand industry-wide effect or if tastes adjust M increases, as consuer tastes in country h ove towards other o- originated products Manufacturing-wide effect M increase, as consuer tastes in country h ove towards other o- originated products Manufacturing-wide effect M increase, as consuer tastes in country h ove towards other o- originated products Manufacturing-wide effect Basically X decreases because country h s coparative advantage is eroded (partially or fully) Econoy-wide effect there is no obvious overall effect there is no obvious overall effect but if there are affiliates X increases, as affiliates cheaper production is partly sold back in country o (reverse iporting) Industry-wide effect X increases, as affiliates cheaper production is partly sold back in country o (reverse iporting) Industry-wide effect - or in case of returns to scale X increases as the invested capital benefits fro increasing returns to scale of the industry as a whole. Industry-wide effect X increases as the invested capital benefits fro increasing returns to scale of the industry as a whole. Industry-wide effect X increases as the invested capital benefits fro increasing returns to scale, at industry- or at fir-level (reverse iporting). Industry-wide effect 2 See Greaney (2003) for an alternative justification of reverse iporting, based on network effects. 3 Vernon s (1966) product cycle hypothesis discusses also this trade-off between FDI and iports relating it to different phases of the developent of the targeted arket. 4 A first version of a table giving the overview of FDI-Trade relations has been presented in the Mylonidis and Zarotiadis FDI and Trade in the UK: Substitutes or Copleents?, presented in the European Trade Study Group of 2005 in Dublin. Note that beside to the effects on the bilateral trade relations, FDI flow in country h ight affect its trading activity in the rest of the world. 2

5 The picture copletes with three additional arguents fro ultinationals literature that we cobine with the above discussed cases. i. Increasing returns to scale (at the industry- of at the fir-level), which cause a copleentary relationship between FDI and exports fro the country h. ii. Consuers tastes in country h ay change, as people becoe ore failiar with country o s products due to the presence of ultinationals (Swenson 2004). iii. Finally, interediate goods needed for the production of the affiliates located in h are preferably obtained fro country o, either through the arket (fro other firs sited in o), or through internalized exchanges with the parentcopany (intra-fir trade, see Tang and Madan 2003). 5 Beside to the co-existence of several, opposing effects, the above presentation provides an additional interesting reark: FDI and trade relations arise at different levels of aggregations. This is consistent to the epirical decoposition applied by Mylonidis and Zarotiadis (2008) and Swenson (2004). The approach we present in the following sets off the possibility of having different effects at the different aggregation levels. Inspired by the diversity and the ultidiensionality of the underlying relations, we proceed with a odel based on a spatial transforation of the Dixit-Stiglitz fraework for onopolistic copetition, increasing returns to scale and iceberg-type transport costs. We introduce capital as an additional production factor and assign arginally different capital intensity to each of the different industries. The reainder of this paper is organized as follows. Section 2 outlines the odel and solves for the autarky equilibriu. Next, we proceed by odeling the case of bilateral trade and we let capital and/or labor oving fro the one country to the other. Section 4 discusses the ain conclusions, derived out of the different siulations we use, and presents the possibilities for considering different theoretical scenarios on the basis of the developed fraework. 2. Autarky equilibriu in a country Think of a closed econoy with infinitely differentiate goods of any different branches. Following the Dixit-Stiglitz approach, deand can described as follow. First we have to define the consuer s Utility function: U= Π(M i ) µ Α 1-µ (1) i=1 M i represents a coposite of the consuption of differentiated goods fro each anufacturing branch i (i=1,2,,) and A the consuption of the hoogenous agricultural (non-traded) good. To be ore precise M i is a sub-utility function representing the cobined satisfaction that we get by consuing the differentiated goods fro branch i: M i =[ x ijρ dj] 1/ρ (2) where x ij is the consuption of variety j fro anufacturing branch i and represents the integral over the whole range of varieties in that branch [0,n i ]. Further, 0<ρ<1 5 Blonigen (2001), Zeile (1998), Bergsten and Noland (1993) and Swenson (1997) argue that firs exhibit a hoe-bias in their input purchasing patterns. Yet, Swenson (2004) suggests that this bias declines as foreign investent activity increases in the country h, hence providing an additional reason for substituting iports fro country o. 3 Hosted by The Berkeley Electronic Press

6 represents the intensity of the preference for variety in anufactured goods and σ 1/(1- ρ) is the elasticity of substitution between any two varieties. 6 Consuer s decision can be deterined in two steps 7 : First, they iniize costs ( p ij x ij dj) for attaining a given M i (subject to the above expression of M i ), where p ij is the price of variety j in anufacturing branch i. Fro this iniization proble we get the copensated deand function: x ij =(p ij /G i ) 1/ρ-1 Μ i (3) where G i is an expression for a price index of all the varieties in branch i, G i =[ p ij ρ/ρ-1 dj] ρ-1/ρ (4) Second, they axiize utility (U) subject to the overall incoe constrain of the whole econoy, Σ G i M i + p A A=Y (5) i=1 Thereby, we get the uncopensated aggregate deand functions: A=(1-µ)Y/p A (6) and M i =µy/g i, or equally, given the iniu costs expression, x ij =µυg i (σ-1) p ij -σ (7) Moving on to the behavior of the firs, we assue that the hoogenous agricultural good is produced using a constant returns to scale technology under conditions of perfect copetition. Manufacturing, however, involves econoies of scale at the level of each variety, because of the fix (capital) costs: C ij =rk i + wγ i q ij (8) where q ij is the produced quantity of variety j in branch i. As it is coon in the siplified version of the Dixit-Stiglitz fraework, all varieties of each branch i are produced using the sae technology. Yet, there are two innovative characteristics in the above defined cost function: First, we introduce capital (k i ) as an additional (pseudo-) production factor. Second, as we let the existence of ore than one anufacturing branches in the econoy, we assue that technology differs aong the branches: arginal labor requisites, γ i, and fix capital costs, k i, are branch specific. We could iagine an order of the different anufacturing branches: dk i /di>0 and dγ i /di<0. 8 Next, we can define the profit function for each variety: π ij =p ij q ij - rk i - wγ i q ij (9) Recall that the sold quantity q ij is given by the deand function: q ij =x ij =µυg i (σ-1) p ij -σ 6 We assue for the oent that ρ is the sae for all anufacturing branches. 7 A two stage budgeting procedure is applicable because preferences are separable between agriculture and each branch of anufactures, M i, the sub-utility function for anufacturers, is hoothetic in the quantities ij. (Deaton A. and J. Muellbauer, 1980). For a ore detailed presentation of the derivation that we use here see in Fujita, Krugan & Venables, For instance, the siplest way of doing that is by setting: k i=φi and γ i=φ/i, where φ>0. 4

7 If we assue that each fir takes the branch specific price index G i as given, we can derive that perceived elasticity of deand is σ. 9 Based on that, one can easily show that arginal revenues are p ij [1-(1/σ)], or equally p ij ρ. Profit axiization iplies that each producer has to produce till the point where arginal revenues are equal to arginal costs. Therefore, we derive the equilibriu (π-axiizing) prices: p ij *=p i *=wγ i /ρ (10) The last expression gives the price at which each producer can sell the profit axiizing output. Note that the price for selling the profit axiizing output is the sae for all varieties of a branch. Given equation (10), the axiized profit for each anufacturing fir in branch i is: π ij = wγ i q ij /(σ-1) rk i (11) Next, we assue free entry or exit. Therefore, as soon as any fir producing a variety j in branch i akes positive profit, new firs producing a differentiated variety of branch i enter. As n i increases, the branch specific price index decreases (dg i /dn i <0) and, hence the deand curve for each one variety in branch i shifts downwards. 10 This continues till the axiu profit that can be achieved by each fir in branch i equals zero. Zero profit condition iplies that the equilibriu output of any active fir in branch i is: q ij *= q i *= r(wγ i ) -1 ρ(1-ρ) -1 k i (12) Siilarly, we can also calculate equilibriu labor input of any active fir in that branch: l ij *= l i *=γ i q i *= r(w) -1 ρ(1-ρ) -1 k i (13) Figure 1: Branch specific equilibriu output C i, p i q i q i q i q i q 1 * q 2 * q 3 * q i 9 We siply need to calculated the expression p ij x ij/x ij p ij and consider thereby G i as an exogenous paraeter (will be shown in the appendix). 10 Recall again that q ij=x ij=µυg i (σ-1) p ij -σ! 5 Hosted by The Berkeley Electronic Press

8 Note that if dk i /di>0 and dγ i /di<0, branch specific equilibriu output (and eployent) for each fir is higher in branches with higher required fixed capital investent and labour productivity (1/γ). This can be graphically depicted as in the figure. The bold straight lines represent the cost functions for each branch, and the concave lines show the total revenue curves for each branch. While no fir akes positive profit, firs belonging in capital intensive branches eploy ore labour and produce ore (q 1 *<q 2 *<q 3 *). 11 Finally, before we proceed with solving the equilibriu for this single econoy (autarky equilibriu), we need to define the country s factor endowents. There is a constant endowent of capital and labor, K and L, respectively. Capital is needed as a constant fixed initial investent in order to facilitate production. 12 Hence, the aount of invested capital is siply the integral of capital requireents over the whole range of the anufactured varieties (n i ) in all anufacturing branches: Σ k i dj = Σ n i k i (14) i=1 i=1 In order to derive the inputs of anufacturing labor (eployees), we need to consider the extent of production in each variety: Σ l i * dj = Σ γ i q i * dj = Σ n i k i r(w) -1 ρ(1-ρ) -1 (15) i=1 i=1 i=1 Given the above definitions, we can easily derive the two full-eployent conditions (K and L shows the country s capital and labor endowents respectively): Σ n i k i =K (16a) i=1 Σ n i k i r(w) -1 ρ(1-ρ) -1 =L i=1 (16b) Solving now for the autarky equilibriu, not only factor-, but also productarkets have to be cleared, which iplies q i *=x ij. If we substitute equation (7) and (12), this clearing condition can be written as follow: r(wγ i ) -1 ρ(1-ρ) -1 k i = µυg i (σ-1) p ij -σ G i =p i *n i 1/(1-σ) Since all varieties in branch i set the sae price p i *: Using (18) and substituting prices fro equation (10) yields the following siplified version of the product arket clearing condition: r(1-ρ) -1 k i = µυ(n i ) -1 (19) Next, we can solve equation (19) for k i and put it in the full eployent conditions for capital and labour (equations 16a,b). We will get: (17) (18) 11 Note that output here is expressed in a coon easure (for instance, easured in units of utility or units of produced value-added ). If branch 1 produces clothes and branch 3 produces cars, it is not iplied that a shirt is ore expensive than a car. It eans, however, that the value of a unit of utility (or of value-added) produced in the clothing industry is higher than the value of a unit of utility (or of valueadded) produced in the autoobile industry. 12 When we presented the cost function we ephasize the introduction of capital as a pseudo-production factor: as it is obvious fro equation (8), the quantity of produced output is fully deterined by labor input, given that the necessary aount of capital has been invested in order to set up the production site. 6

9 r* = (1-ρ)µY K -1 (20a) w*= ρµy L -1 (20b) Econoy s incoe (Y) can be deterined as the su of the produced value: Σ p i *q i * dj + p A A=Y i=1 or equally: Σ(n i p i *q i *) + p A A=Y (21) i=1 Now, substitute prices, fro equation (10), and write output in ters of labour inputs (q i *= l i */γ) and we will get: (w/ρ) Σ(n i l i *) + p A A=Y i=1 or equally: (w/ρ) L + p A A=Y (21 ) Finally, we can substitute Y in the above-derived equations for the factors rewards (20a,b) and rearrange in order to get: r* = µ (1-ρ) p A A [1+µ(1-µ) -1 ] K -1 (20 a) w*= µ ρ p A A (1-µ) -1 L -1 (20 b) The solution for an autarkic econoy has already been copleted. Moving on, we can derive soe expressions that give us a better picture of the odel s behavior. First, we can substitute w* and r* in the derived expression for the equilibriu output of all firs in each branch i, q i * (equation 12). After rearranging the following expression is derived: 13 q i *= (L/K) (k i /γ i ) (22) Next, we substitute (21 ) in (19) and replace w and r fro (20 a) and (20 b). After rearranging we obtain: n i = Κ (k i ) -1-1 (23) Finally, we can derive an expression for the total output of branch i, based on equations (22) and (23): n i q i * = Κ (k i ) -1-1 (L/K) (k i /γ i ) = L (γ i ) -1-1 (24) We can also derive an expression for the value of total output of branch i: p i *n i q i * = (wγ i /ρ) L (γ i ) -1-1 = (w/ρ) L -1 (25) Based on the above derivations, we can discuss the coparative static in autarky. Naely, as we ove to branches of higher capital intensity (higher i) we observe: less firs and therefore, less differentiated products, but, higher labor input in each different fir, eaning the branch consists of bigger firs, 13 If we set k i=φi and γ i=φ/i, where φ should be greater than zero, the expression becoes: q i*= (L/K) i 2 7 Hosted by The Berkeley Electronic Press

10 lower prices, total output increases, but the value of branch s total output is the sae; it does not depend on branch s order (i). 14 Last, but not least, we should also find an expression for real factors incoe in autarky eqilibriu: We can derive the equilibriu real wage (ω*) and equilibriu real interest (ε*), by dividing w* and r* by the cost of living index (CLI). This can be defined as follow: CLI=Π(G i ) µ p Α 1-µ =Π(p i *n i 1/(1-σ) ) µ i=1 i=1 p Α 1-µ If we substitute price fro (10) and n i fro (23) and if we set γ i =φ/i and k i =φi, we get: CLI = (w/ρ) µ (Κ/) µ/(1-σ) φ µσ/(σ-1) p Α 1-µ Π(i µ(σ-2)/(1-σ) ) (26 ) Using this expression enables us to deterine ω* and ε* as follow: 15 ε* =(L µ /Κ (σ-1-µ)/(σ-1) ) µ/(1-σ) Α (1-µ) φ µσ(1-σ) Π(i µ(σ-2)/(σ-1) )(1-ρ)(1-µ) µ µ 1-µ [1+ξ] -1 (27a) ω* =(Κ µ/(σ-1) /L 1-µ ) µ/(1-σ) Α (1-µ) φ µσ(1-σ) Π(i µ(σ-2)/(σ-1) ) ρξ 1-µ (27b) Based on the last two equations we can derive the following conclusions for the case of autarky: An increase of L, other things equal, boosts real interest but reduces real wages. An increase of K leads always to higher real wages. If 1<σ<1+µ, it will boost real interest too! Otherwise, if σ>1+µ, an increase of K will reduce real interest. 16 Introduction of new branches of higher order (increase of ) has also an abiguous consequence: the greater is K and L, copared to A, the ore likely it is that the effect on ω and ε will be a positive one. (Yet, keep in ind that any increase of ight be accopanied with a decrease of µ, as µ<1.) The following three diagras siulate the arguents of the first two points, naely the effects to ω and ε, caused by variations in factors supply. (26) 14 It would be different only if we let µ i being different fro branch to branch. 15 ξ stands for the expression µ/(1-µ). 16 Note that if ρ 0,5, it eans that σ 2. In that case, σ will be for sure greater than 1+µ, because µ<1 by definition. 8

11 Figure 2: The effects of a changing L other things equal Real Factor Returns by L 1,20 1,00 0,80 0,60 ω ε 0,40 0,20 0,00 Labor Supply Figure 3: The effects of a changing K for σ>1+µ other things equal Real Factor Returns by K (σ>1+µ) 1,20 1,00 0,80 0,60 ω ε 0,40 0,20 0,00 Capital Supply Figure 4: The effects of a changing K for σ<1+µ other things equal Real Factor Returns by K (σ<1+µ) 50,00 45,00 40,00 35,00 30,00 25,00 20,00 ω ε 15,00 10,00 5,00 0,00 Capital Supply 9 Hosted by The Berkeley Electronic Press

12 3. The case of bilateral trade and obile factors The next step is to introduce bilateral trade relations, assuing the existence of two countries. Recall that the ain purpose of the present paper is to reveal the ain characteristics of the developed theoretical fraework. Therefore, for the oent, we will focus on a very siplified version of the odel: both countries have the sae technology (identical k i and γ i ), produce in all different branches (nuber of branches,, is the sae in both countries) and have also identical consuers preferences (µ and ρ are the sae). Following the logic of Fujita, Krugan and Venables (1999), we assue that each variety is produced in only one country. In other words, a good produced in a different region iplies that consuers recognize it as a different variety. Further, assue, for the oent, that consuers are indifferent regarding the origin of goods. Finally, we introduce trade barriers in the for of iceberg-type transport costs. Specifically, if a unit of a variety is shipped fro one country to the other, only a fraction, 1/τ, of the original unit actually arrives. Constant τ represents the aount of good dispatched per unit received. Note that for goods produced and sold in the sae country, τ=1. This type of transport costs iplies that if f.o.b. price (price in the region of production) is p, c.i.f. price (price in the region of consuption) is: p = p τ. Let us now redefine the deand side of each econoy. Starting fro the utility function, it reains the sae as in the autarky case. Consuers cover their needs by consuing the hoogenous agricultural (non-traded) good and the different varieties of goods fro each anufacturing branch i (M i ). Also sub-utility function reains basically the sae. Note, however, that in the expression M i =[ x ijρ dj] 1/ρ, represents now the integral over the su of the range of varieties produced in that branch in both countries [0, n ih +n if ]. 17 Regarding now the behavior of consuers, uncopensated aggregate deand functions reain as in the autarky case. However, we need to redefine p and G, because any of the consued goods are iported. The price index for varieties in branch i is defined as G i =[ p ij ρ/ρ-1 dj] ρ-1/ρ. Yet, as soe of the i-varieties coe fro the other country, their c.i.f. price is: p ij =p ij τ. Recall now that all varieties of branch i produced in a country have the sae technology and face the sae factor costs, therefore they have the sae price. Consequently, G i for each country can be written as follow 18 : G ih =[n ih p ih 1-σ +n if (p if τ) 1-σ ] 1/(1-σ) G if =[n if (p if τ) 1-σ +n if p if 1-σ ] 1/(1-σ) (28a) (28b) Based on the uncopensated deands for each country, odified according to the above redefinition of price indices and prices, we can deterine world deand (deand in both countries) for any variety of each branch. 19 x ih =p ih -σ µ(υ h G ih (σ-1) +Y f G if (σ-1) τ -σ ) x if =p if -σ µ(υ h G ih (σ-1) τ -σ +Υ f G if (σ-1) ) (29a) (29b) 17 Where n ih, n if represents the range of produced varieties in branch i of hoe and of foreign country respectively. 18 Notice that τ represents the transport costs for both directions, i.e., fro country 1 to 2 and vice versa. 19 Derivation of 28a,b and 29a,b will be shown in details in the appendix. 10

13 Next, we have to discuss the behavior of producers. Cost functions reain the sae as in equation (8). We siply have to rewrite the for each country by considering that we have country specific factor rewards (costs): C ijh =r h k i +w h γ i q ijh C ijf =r f k i +w f γ i q ijf (8 a) (8 b) Each fir belonging in a specific branch and being situated in a specific country, is facing the above defined branch/country-specific world deand 20. As in the autarky, each fir is supposed to take the branch/country-specific price index G i1 and G i2 as given. Consequently, profit axiization (and 0-profit condition) leads again to the well known expression for the price, at which each producer can sell the profit axiizing output 21 : p ih *=w h γ i /ρ p if *=w f γ i /ρ (10 a) (10 b) Subsequently, profit axiizing (0-profit) output and the respective labor input can be written as follow: q ih *=r h (w h γ i ) -1 ρ(1-ρ) -1 k i q if *=r f (w f γ i ) -1 ρ(1-ρ) -1 k i l ih *=γ i q ih *= r h (w h ) -1 ρ(1-ρ) -1 k i l if *=γ i q if *= r f (w f ) -1 ρ(1-ρ) -1 k i (12 a) (12 b) (13 a) (13 b) Following the sae path as in autarky, in order to solve for bilateral-tradeequilibriu, we start fro the product arket clearing condition. If we set equal (12 a) with (29a) and (12 b) with (29b) and substitute G ih and G if fro (28a) and (28b) respectively, we will get: r h k i (1-ρ) -1 =µ{y h [n ih +n if (τp if /p ih ) 1-σ ] -1 + Y f τ 1-σ [n ih τ 1-σ +n if (p if /p ih ) 1-σ ] -1 } r f k i (1-ρ) -1 =µ{y f [n if +n ih (τp ih /p if ) 1-σ ] -1 + Y h τ 1-σ [n if τ 1-σ +n ih (p ih /p if ) 1-σ ] -1 } (30a) (30b) Consider now the full eployent conditions we deterined by solving for autarky (equations 16a,b), specified for each country separately. 22 Substituting k i fro (30a) and (30b) respectively in full eployent conditions and putting in place of n if /n ih the equivalent K f /K h, 23 in order to get rid of the su, yields the following expressions: r h =(1-ρ)µ(K h ) -1 {Y h [1+τ 1-σ (K f /K h )(w f /w h ) 1-σ ] -1 + Y f [1+τ σ-1 (K f /K h )(w f /w h ) 1-σ ] -1 } r f =(1-ρ)µ(K f ) -1 {Y f [1+τ 1-σ (K h /K f )(w h /w f ) 1-σ ] -1 + Y h [1+τ σ-1 (K h /K f )(w h /w f ) 1-σ ] -1 } (31a) (31b) 20 Notice that, because of our iceberg costs assuption, in order to cover the world deand, it is not enough for each fir to produce x i1 (or x i2). To supply the part of this consuption that responds to foreign deand (the deand of the other country) it has to ship τ ties this part. Therefore, it has to produce ore than x i1 (or x i2): its production has to coe up to q i1 = p i1 -σ µ (Υ 1G i1 (σ-1) +Y 2G i2 (σ-1) τ 1-σ ) and respectively up to q i2 = p i2 -σ µ (Υ 1G i1 (σ-1) τ 1-σ +Υ 2G i2 (σ-1) ). 21 Notice that the price for selling the profit axiizing output is not, at least directly, affected by the fact that the fir has to copete with foreign copetitors when it distributes its output in both countries. Global conditions ight affect prices set by doestic producers only indirectly, as far as they will affect doestic wages. 22 In full eployent equations, the country specific variables are n i, r, w, K and L. 23 When we discussed autarky, we saw that an unconditional result of equilibriu is that the range of varieties in each branch is analogue to country s capital endowents: recall equation (23), where n i = Κ (k i) Hosted by The Berkeley Electronic Press

14 and for wages: w h =ρµ(l h ) -1 {Y h [1+τ 1-σ (K f /K h )(w f /w h ) 1-σ ] -1 + Y f [1+τ σ-1 (K f /K h )(w f /w h ) 1-σ ] -1 } w f =ρµ(l f ) -1 {Y f [1+τ 1-σ (K h /K f )(w h /w f ) 1-σ ] -1 + Y h [1+τ σ-1 (K h /K f )(w h /w f ) 1-σ ] -1 } (32a) (32b) In the following, we should focus on a siplified version of the above generalized equilibriu expressions in order to reveal easily the ain characteristics of the presented fraework. 24 Naely, let us assue that ρ=0,5 (which eans that σ=2) and also the absence of trade costs (τ=1). The above equations will be siplified as follow: r h =[(1-ρ)µ/K h ][(Y h +Y f )/(1+K f w h /K h w f )] r f =[(1-ρ)µ/K f ][(Y h +Y f )/(1+K h w f /K f w h )] r h =(ρµ/k h )[(Y h +Y f )/(1+K f w h /K h w f )] r f =(ρµ/k f )[(Y h +Y f )/(1+K h w f /K f w h )] (31 a) (31 b) (32 a) (32 b) The above expressions provide us with exact solutions for the noinal and real capital- and labor-returns in both countries. 25 Before discussing the analytical conclusions, we can have a quite convincing picture of the odel s features by looking at the following siulations. Our interests lie on the effects of a oveent of production factors (especially capital) fro one country to the other. The following two diagras depictures the developent of noinal and real factor returns, in both countries, associated with an increasing ratio K h /K f. 26 Figure 5: Noinal Factor Returns in Open Econoies by relative Capital Abbundance 6,0 5,0 4,0 3,0 w-hoe w-foreign r-hoe r-foreign 2,0 1,0 0,0 K-hoe / K-foreign The picture of noinal factor-returns is a standard one. Both, w and r, in hoe and foreign country develop in a usual way. Regarding the effect on capital s real returns, as it was the case in autarky, it depends on consuers preference for vartiety (ρ) and the preference for anufactured products in general (µ). Yet, in our siplified case with 24 Notice that, even for this non-siplified version of the fraework, relative expressions of factors rewards is not coplex at all: (r/w) h,f =(K/L) h,f (1-ρ)/ρ and (w h r f )/(w f r h )=(K h L f )/(K f L h ). 25 A detailed solution will be presented in the appendix, after we substitute Y h and Y f fro equation (21 ) and using the definition of CLI according to (26). 26 This stands for a gradual oveent of capital fro foreign to hoe country. Note that in this way we siulate the effects of FDI that arise due to (relative) capital scarcity, or in other words the 1 st case in Table

15 ρ=0,5 the effects of capital transfer on ε h and ε f can only be negative (recall the 16 th note in page 9 of the present paper). 27 Figure 6: Real Factor Returns in Open Econoies by relative Capital Abbundance 8,0 7,0 6,0 5,0 4,0 3,0 ω-hoe ω-foreign ε-hoe ε-foreign 2,0 1,0 0,0 K-hoe / K-foreign Things becae ore interesting if we look at the siulated effects on volue and value of each country s exports. Before we proceed discussing the derived pictures, we need to ention the following, straightforward definitions: Export volue (in ters of production) by fir in branch i: ξ ih =µy f (n ih p ih ) -1 (1+K f w h /K h w f ) -1 ξ if =µy h (n if p if ) -1 (1+K h w f /K f w h ) -1 (33a) (33b) Export value by fir in branch i: p ih ξ ih =µy f (n ih ) -1 (1+K f w h /K h w f ) -1 p if ξ if =µy h (n if ) -1 (1+K h w f /K f w h ) -1 (34a) (34b) Export volue (in ters of production) by branch i: n ih ξ ih =µy f (n ih p ih ) -1 (1+K f w h /K h w f ) -1 n if ξ if =µy h (p if ) -1 (1+K h w f /K f w h ) -1 (35a) (35b) Export value by branch i: p ih n ih ξ ih =µy f (1+K f w h /K h w f ) -1 p if n if ξ if =µy h (1+K h w f /K f w h ) -1 (36a) (36b) The following diagras depicture the siulated developent of the above defined easures (for the case of three different anufacturing branches). Thereby, we will conclude on the specific effects on trade activity, captured by this (siplified) version of the odel. Before we proceed, note that firs in higher ranked branches are always ore export intensive, at least in absolute ters. Moving on, the fir-level effect of an inflow 27 In case of igration fro foreign to hoe country (increasing L h/l f), noinal and real factors returns, in both countries, will also follow a usual path, siilarly to autarky. 13 Hosted by The Berkeley Electronic Press

16 of capital sees to be clearly negative, both in ters of export-volues and in ters of export-values too (see figure 7 and 8). Figure 7: Figure 8: Volue of exports by fir of sector i in h-country with rising relative capital abundance Value of exports by fir of sector i in h-country with rising relative capital abundance ξ1-hoe ξ2-hoe ξ3-hoe p1 ξ1-hoe p2 ξ2-hoe p3 ξ3-hoe K-hoe / K-foreign K-hoe / K-foreign Figure 9: Figure 10: Volue of exports by sector i in h-country with rising relative capital abundance Value of exports by sector i in h-country and total exports for the whole country, with rising relative capital abundance n1 ξ1-hoe n2 ξ2-hoe n3 ξ3-hoe ξi-hoe Ξ-hoe K-hoe / K-foreign K-hoe / K-foreign Branch effect, in ters of export-volues, is also negative (figure 9). But, in ters of values, branch-wide exports follow a non-onotone path, being positively affected at the beginning and negatively, after a critical value of K h /K f. The sae holds also for the value of exports, econoy wide (Ξ in figure 10). Although it is not referring to the ain questions we set at the beginning of this paper, it is worthy to take a closer look on the analogue export-effects derived out of igration fro foreign into hoe country (increasing L h /L f ). Here the effects follow the siilar non-onotone path (first positively and then negatively affected) at all level of aggregations. Figure 11: Figure 12: Volue of exports by fir of sector i in h-country with rising relative labour abundance Value of exports by fir of sector i in h-country with rising relative labour abundance ξ1-hoe ξ2-hoe ξ3-hoe p1 ξ1-hoe p2 ξ2-hoe p3 ξ3-hoe L-hoe / L-foreign L-hoe / L-foreign 14

17 Figure 13: Figure 14: Volue of exports by sector i in h-country with rising relative labour abundance Value of exports by sector i in h-country and total exports for the whole country, with rising relative capital abundance n1 ξ1-hoe n2 ξ2-hoe n3 ξ3-hoe ξi-hoe Ξ-hoe L-hoe / L-foreign L-hoe / L-foreign 4. Concluding rearks and future steps Our ain task was to develop a theoretical fraework that can siulate the coplex, ultidiensional relations between trade and flows of production factors. Reviewing the relevant literature that concentrates on the links aong FDI and trade provided us with the ain arguents. The fraework we developed follows Fujita s et al. (1999) logic which is based on a spatial transforation of the Dixit-Stiglitz approach with onopolistic copetition, increasing returns to scale and iceberg-type transport costs. We take into account the existence of any differentiated anufacturing branches, we introduce capital as an additional production factor and assign arginally different capital intensity to each branch. In the present issue of the paper, we discussed the features and the dynaics of a siplified version, with no trade-costs and with a specific value for consuers preferences for variety (ρ=5). The odel is structured deliberately in a way that allows for different effects at the level of each fir, of each industry (in ters of the notation used in previous pages, branch i) and of the whole anufacturing sector (econoywide). Therefore, although siplified, it provided us with a picture where, as capital (and/or labor) flows fro one country to the other, it generates well-defined, but at the sae tie partly non-onotone and contradictory, effects on trade flows. The usefulness of this result is quite iportant: recent epirical investigations have pointed out that there are different effects fro FDI on trade, at different levels of aggregations (fir- and/or industry-, sector- and econoy-wide). The authors claied that we should not be surprised by the inconclusiveness of the existing epirical literature regarding the sign of FDI-trade linkages, as it siply addresses the ultidiensional, non-onotone character of this relation. The presented theoretical fraework offers a theoretical basis for analyzing the odifications that ay result out of changes in the underlying paraeters. There are several further steps that can be taken in order to coplete the analysis of the odel. As the present version of the paper is not necessarily the final one, discussing briefly those steps will be beneficial: Present in the appendix the analytical solution of the siplified version of the odel (ρ=0,5 and τ=1). Solve the general version for bilateral trade (τ>1 and 0<ρ<1). Introduce the condition for capital (and/or labor) bilateral stability, in other words when there will be no reason to ove fro one country to the other. 15 Hosted by The Berkeley Electronic Press

18 (Note that this condition ight be helpful to solve the general version for bilateral trade, because it will set equal r h with r f and/or w h with w f..) Introduce the effects of exogenous changes that ight alter, exogenously, the country s incoe (Y h or Y f ). This would be a discussion of the effects fro FDI due to the third case/scenario of table 1. The odel already considers IRS and also product differentiation. Think of odifications that could relate the consuers preferences to the intensity of igration and FDI, or introduce affiliate relations aong the firs. 16

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20 Mylonidis N. and Zarotiadis G., 2008, The Ipact of Inward FDI Flows on Trade Patterns: The Case of the UK, The Epirical Econoics Letters, 7(3), pp Pfafferayer M., 1996, Foreign Outward Direct Investent and Exports in Austrian Manufacturing: Substitutes or Copleents?, Weltwirtschaftliches Archiv, vol. 132, no. 3, pp Swenson D.L., 2004, Foreign Investent and the Mediation of Trade Flows, Review of International Econoics, vol.12, no.4, pp Swenson D.L., 1997, Explaining Doestic Content: Evidence fro Japanese and US Autoobile Production in the United States, in Feenstra R.C. (ed), Effects of US Trade Protection and Prootion Policies, Chicago: University of Chicago Press, pp Tang L. and Madan V., 2003, The Relative Efficiency of Ownership Structures and Intra-Fir Trade, The International Trade Journal, vol. 17, no. 2, pp Vernon R., 1966, International Investent and International Trade in the Product Cycle, Quarterly Journal of Econoics, vol. 80, pp Zeile W., 1998, The Doestic Orientation of Production and Sales by US Manufacturing Affiliates and Foreign Copanies, Survey of Current Business, April, pp

21 APPENDIX 19 Hosted by The Berkeley Electronic Press