Horizontal multinational firms, vertical multinational firms and domestic investment

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1 Hoizontal multinational fims, vetical multinational fims and domestic investment Julian Emami Namini and Enico Pennings still peliminay 1st August 2008 Abstact We constuct a dynamic geneal equilibium model with 2 counties, hoizontal and vetical multinational activity and endogenous domestic and foeign investment. It is found that hoizontal multinational activity always leads to a complementay elationship between domestic and foeign investment. Vetical multinational activity, in contast, leads to a substitutional o complementay elationship between domestic and foeign investment, depending on the values of model paametes. We test the theoetical implications with a panel of U.S. multinationals and find empiical suppot. JEL classification: E22, F21, F23 Keywods: Hoizontal multinational fims, vetical multinational fims, domestic investments, neoclassical gowth model Emami Namini: Depatment of Economics, Easmus Univesity Rottedam, PO Box 1738, 3000DR Rottedam, the Nethelands, emami@few.eu.nl; Pennings: Depatment of Applied Economics, Easmus Univesity Rottedam, PO Box 1738, 3000DR Rottedam, the Nethelands, pennings@few.eu.nl. 1

2 1 Intoduction Rising multinational activity has aised impotant questions about how foeign diect investment FDI affects domestic capital fomation. Recent empiical evidence fo the U.S. Desai et al., 2005a shows that the pessimists may be wong as thee seems to be a complementaity elationship between foeign and domestic capital expenditues, athe than a substitutional elationship. Intuitively, a distinction between the motives fo FDI is cucial fo undestanding the elation between domestic and foeign capital expenditues. While hoizontal multinationals invest aboad as to seve new makets, vetical multinationals invest in ode to educe the cost of poduction. Theefoe, the aggegate finding of foeign and domestic investments being complements may be athe distinct fo eithe of the two types of multinationals. Ou pape intends to contibute to the debate by building a geneal equilibium model, which extends Makusen s 2002 Knowledge Capital model of the multinational fim by endogenous domestic and foeign investment. Aftewads, we test the theoetical implications with U.S. data on the opeations of multinational fims. Ou theoetical and empiical implications show the impotance of the motive fo FDI in explaining the link between domestic and foeign capital expenditues. The empiical liteatue on the link between domestic and foeign investment has stated with Feldstein 1995 who found a negative coelation between FDI and domestic investment in a sample of OECD counties, suggesting that outwad FDI educes domestic investment. Moe ecently, Desai et al. 2005a edid his analysis on a subsample of domestic investment and FDI by examining domestic and foeign capital expenditues of U.S. multinationals. Instead of a negative elation between domestic and foeign capital expenditues, they find a positive and significant link between the two vaiables. One possible explanation they put fowad is that the USA may be diffeent fom othe OECD counties. By finding substitutability of domestic and foeign investment fo Geman data while confiming complementaity fo U.S. data, Heze and Schooten 2008 find some evidence fo this explanation. A second explanation they put fowad elates to the activities of multinational fims which ae diffeent fom the activities of the aveage fim. A thid explanation elates to the composition of FDI and domestic investment in both samples in the sense that aggegate FDI data contain financing flows wheeas the data fo multinationals ae esticted to capital expenditues. In a pooled panel of U.S. multinationals with moe than 2,000 obsevations and peiod fixed effects, Desai et al. 2005b find that a 10% incease in foeign investment inceases domestic investments by appoximately 2%, confiming the aggegate esults. We test the implications of ou theoetical model in an econometic analysis using a U.S. 1

3 panel of foeign and domestic investments at the secto level ove the peiod In ode to test the implications fom the theoetical model, we test whethe the link between domestic and foeign investment is diffeent fo hoizontal and vetical multinationals. The esults of ou panel with andom and fixed secto effects confim the findings by Desai et al. 2005b fo the sign of foeign investment. As to account fo pesistence in domestic investment we take lagged domestic investment as an explanatoy vaiable in a dynamic panel model. As to distinguish between hoizontal and vetical multinationals, we follow empiical evidence by Hanson et al and assume that fims in the manufactuing sectos ae mainly vetical multinationals while multinationals opeating in the othe sectos ae mainly hoizontal. We find that complementaity elation between domestic and foeign investment emains fo hoizontal multinationals, but find a substitution elation fo vetical multinationals. If we futhe efine the link between domestic and foeign investments, the econometic esults show that the substitution effect fo vetical MNE is modeated if the facto shaes of the intemediate goods ae moe equal and if the shaes of the intemediate goods in final goods poduction ae moe equal. This esult is also pedicted by the theoetical model. This pape is oganized as follows. Section 2 descibes the theoetical model. Section 3 pefoms a compaative steady state analysis of the theoetical model and deives empiically testable pedictions. Section 4 tests the pedictions of the theoetical model. Section 5 concludes. 2 Basic model This pape analyzes a geneal equilibium model, which is a dynamic extension of the Knowledge Capital model by Makusen The model consists of two counties, a home county H and a foeign county F. The epesentative household in each county consumes seveal vaieties of a diffeentiated good X and a homogeneous good Z. Good X is poduced by multinational fims. It is assumed that households aggegate the vaieties of good X accoding to a CES function like in Dixit and Stiglitz Futhemoe, it is assumed that the numbe of fims in secto X is sufficiently lage so that the maket fo good X is chaacteized by lage goup monopolistic competition e.g., Makusen and Venables, Secto Z fims behave pefectly competitively. The home county H and the foeign county F ae endowed with two factos of poduction, labo L and capital K. Both factos ae mobile between sectos but immobile between counties. 2

4 Both factos ae used fo the following poduction activities: fist, labo and capital ae used to poduce the homogeneous final good Z. Second, labo and capital ae used to poduce two intemediate goods v 1 and v 2 ; both intemediate goods ae assembled to give a unique vaiety of the diffeentiated final good X. Each county s labo endowment is constant ove time. Each county s capital endowment, in contast, is detemined endogenously via the Ramsey gowth model and theefoe flexible in the long un. Relative facto endowments ae theefoe flexible in the long un as well. Due to this dynamic extension of Makusen s 2002 Knowledge Capital model the fim egime has to be detemined exogenously. In the fist egime, only hoizontal multinational fims ae active. In the second egime, only vetical multinational fims ae active. The eason fo the exogenous detemination of the fim egime is the following: in the dynamic setup of this pape a unique causal elationship between the fim egime and the counties elative facto endowments is missing. On the one hand, the fim egime influences elative facto demands and, theefoe, elative facto pices in each county. Relative facto pices, in tun, influence the investment behavio of households, which finally detemines the counties elative facto endowments in the steady state. 1 On the othe hand, the counties elative facto endowments influence elative facto pices, which detemine the fim egime. 2 Two diffeent geneal steady state equilibia accodingly exist in this dynamic setup. Fist, a geneal equilibium with hoizontal multinational fims and the coesponding elative facto endowments in the steady state. Second, a geneal equilibium with vetical multinational fims and the coesponding elative facto endowments in the steady state. This pape accodingly detemines the fim egime exogenously. Aftewads, the counties coesponding elative facto endowments in the steady state ae deived. In the fist fim egime with only hoizontal multinational fims, each fim has two poduction plants, one in county H and one in county F. Both poduction plants poduce both intemediate goods v 1 and v 2. In the second fim egime with only vetical multinational fims, each fim has also two poduction plants, one in county H and one in county F. Howeve, each poduction plant poduces only one of the two intemediate goods v 1 and v The esult that a county s elative facto endowment in the steady state of a Ramsey gowth model depends on the fims technologies, the household s time discount ate and the capital depeciation ate is oiginally deived by Baxte The influence of the counties elative facto endowments on the fim egime is explained by the Knowledge Capital model by Makusen Note that the Knowledge Capital model is a static model, i.e. the elative facto endowments ae exogenously given and not influenced by the fim egime. 3 Note that the definition of hoizontal and vetical multinational fims in this pape diffes fom the definition in the Knowledge Capital model by Makusen No intemediate goods exist in the Knowledge Capital model. Hoizontal multinational fims in the Knowledge Capital model poduce the final good diectly with labo and capital in both counties; headquate sevices ae only poduced in one county, but ae used fo both poduction plants. Vetical multinational fims in the Knowledge Capital model poduce the final 3

5 Both hoizontal and vetical multinational fims poduce with economies of scale, which ae due to the existence of fixed poduction costs. Seveal assumptions ae necessay in ode to get staightfowad analytical esults. Fist, both counties ae completely identical with espect to technology paametes and pefeence paametes. The only exception is the income shae households spend on the vaieties of good X and on good Z, which is allowed to diffe between counties. Second, intenational tade of both intemediate goods, the vaieties of good X and good Z is assumed to be costless. Thid, this pape assumes that eithe only hoizontal multinational fims o only vetical multinational fims ae active. Fouth, this pape assumes a anking of the facto intensities of all 4 goods, which is in line with pevious empiical studies. Finally, the model only consides the counties steady states; theefoe, the time index is included only when necessay. In ode to analyze whethe domestic and foeign capital expenditues ae complements o substitutes, the steady state of the wold will be distubed by a vaiety of exogenous shocks. If the capital stocks of both counties move into the same diection due to the exogenous shock, domestic and foeign capital expenditues ae complements. If the capital stocks of both counties move into diffeent diections due to the exogenous shock, domestic and foeign capital expenditues ae substitutes. The following subsections sepaately descibe the ingedients into the dynamic geneal equilibium model. Subsection 2.1 descibes the poduction side of both counties, subsection 2.2 descibes the dynamic stuctue of the model, subsection 2.3 deives facto pice equalization between both counties in the steady state, subsection 2.4 defines hoizontal and vetical multinational fims and subsection 2.5 descibes the demand side of both counties. Subsections 2.6 and 2.7 descibe two additional conditions which have to hold in each peiod of the steady state: fist, the fee enty condition into the multinational fims secto and, second, the tade balance equation. 2.1 Poduction Both counties have the same poduction technologies fo poducing intemediate goods and final goods. The homogeneous good Z is poduced accoding to the following Cobb Douglas poducgood diectly with labo and capital in one county only; headquate sevices ae poduced in the othe county and ae expoted to the poduction plant. The additional sepaation of the poduction pocess into 2 intemediate goods like in this pape takes into account that vetical multinational fims in geneal neve sepaate the entie poduction pocess fom the headquate sevices, but only the most labo intensive pat of the poduction pocess e.g., UNCTAD,

6 tion function: Z L β K 1 β ; 1 β β 1 β 1 β since good Z epesents the aveage outside good, its facto shaes ae assumed to be aveage as well. Theefoe, β will be set equal to 0.5 duing the compaative steady state analysis in section 3. The pe unit cost function which is dual to the poduction function in equation 1 is given by: c Z w i, i w β i 1 β i. 2 Since secto Z fims behave pefectly competitively, they sell thei good at pice p Z c Z. Intemediate goods v 1 and v 2 ae poduced accoding to the following Cobb Douglas poduction functions: v 1 v 2 L φ1 K 1 φ 1 φ φ φ, 1 1 φ 1 with 0 φ 1 0.5, 3 L φ2 K 1 φ 2 φ φ φ, 2 1 φ 2 with φ 2 1 φ 1 ; 4 note that intemediate good v 1 is assumed to be moe capital intensive than the outside good Z, while intemediate good v 2 is assumed to be moe labo intensive than the outside good Z. These assumptions on φ 1 and φ 2 theefoe conside the empiical fact that multinational fims, if they ae vetical, elocate the most labo intensive poduction activities to the foeign county, while they keep the moe capital intensive poduction activities at home Blomstöm and Kokko, 1997; Hummels et al., The maginal cost functions which ae dual to the poduction functions in equations 3 and 4 ae given by: c v1 w i, i w φ 1 i 1 φ 1 i and c v2 w i, i w φ 2 i 1 φ 2 i, i H, F. 5 The vaiables w i and i stand fo the pice pe unit labo and the capital ental ate in county i. Intemediate goods v 1 and v 2 ae assembled to a unique vaiety of the diffeentiated final good X accoding to the following Cobb Douglas poduction function: X v 1 α v 2 1 α α α 1 α, with 0 α α The pe unit cost function which is dual to the poduction function in equation 6 is given by: 5 c X w i, w j, i, j c α v 1 c 1 α v 2 w φ 1 α i w φ 2 1 α j α 1 φ 1 i 1 φ 2 1 α j, i, j H, F. 4 The assumption that φ 2 exactly equals 1 φ 1 simplifies calculations, but is not cucial fo the final esults. 5 If the fim has a hoizontal oganization of its poduction, i.e. intemediate goods v 1 and v 2 ae poduced in the same county, the pe unit cost function simplifies to c X w i, i w φ 1 α+φ 2 1 α i α 1 φ 1+1 φ 2 1 α i. 5 7

7 2.2 Dynamic stuctue The model is extended to a Ramsey gowth setup. Including the time index t, utility in a single peiod t in county i, i H, F, is given by the following Cobb Douglas function: U i,t X γ i i,t Z1 γ i i,t, 0 < γ i < 1, 8 whee X i,t denotes a CES aggegate of all consumed vaieties of good X in peiod t in county i and Z i,t the consumption of good Z in peiod t in county i. County i s capital stock K i,t in peiod t is detemined endogenously via the investment decision by county i s epesentative household. It is assumed that only good Z is used fo investment. The household chooses the consumption and investment level in each peiod such that lifetime utility V is maximized. If ρ denotes the time discount ate, lifetime utility of the households is given by: 6 V i whee u epesents the household s instantaneous utility function. t ρ t u U i,t, 9 If δ stands fo the pe peiod depeciation ate fo capital, investment into the county s capital stock in peiod t of the steady state is given by: 7 I i,t K i,t+1 1 δ K i,t. 10 I i,t denotes the amount of good Z, which is invested in peiod t. Equation 10 implies that one unit of good Z, which is invested in peiod t, leads to one unit of capital in peiod t + 1. It is assumed that the county s household and secto Z fims behave pefectly competitively. The household owns the poduction factos and lends them out to fims fo poduction puposes. The steady state of the economy is then descibed by seveal necessay fist ode conditions. 8 Fou of these necessay fist ode conditions aleady detemine the county s facto pice atio in the steady state: i,t + 1 δ p Z,i,t p K,i,t 11 1 β β i,t p Z,i,t LZ,i,t 12 β K Z,i,t β 1 β w i,t p Z,i,t 1 β KZ,i,t 13 L Z,i,t p K,i,t+1 p Z,i,t, ρ 6 All paametes with a county index ae assumed to be identical acoss counties. 7 Note that the county s labo endowment is assumed to be constant ove time. Investment in the steady state theefoe only compensates fo depeciation. 8 Cf. Baxte 1992, p

8 whee p K,i,t denotes the pice pe unit capital in county i peiod t and L Z,i,t and K Z,i,t the labo and capital input in secto Z of county i in peiod t. Equation 11 is the abitage condition fo the household s capital lending behavio: households ae only willing to lend out capital to fims if the capital ental ate i,t plus the value of the emaining unit of capital in peiod t + 1, which is given by 1 δ p Z,i,t, equals the pice pe unit capital today. Equations 12 and 13 ae the usual conditions fo a pofit maximizing facto input choice by fims. Equation 14 denotes the Eule equation, which descibes the dynamically optimizing behavio of a household: the household chooses the investment level such that, in the steady state, the discounted value of a unit capital in t + 1 equals the value of a unit of good Z in t. The time index t is omitted fom now on since only the steady state is consideed in the following. Substituting equation 14 into equation 11 leads to i + 1 δ p Z,i 1 + ρ p Z,i, i which can be simplified to p Z,i ρ + δ. Substituting i p Z,i ρ + δ into equation 12 and solving fo K Z,i L Z,i 1 1/β. ρ+δ Substituting K Z,i L Z,i Dividing w i p Z,i by i p Z,i 1 β β gives: esults in K Z,i L Z,i 1 β β 1/β 1 ρ+δ into equation 13 esults in w i p Z,i ρ + δ β 1/β. w i i ρ + δ 1/β. 15 The futhe analysis simplifies consideably since, in this dynamic setup, the facto pice ation in the steady state is aleady detemined by the paametes ρ, δ and β. Theefoe, in this dynamic setup, it is not necessay to take the facto maket equilibium conditions to detemine the facto pice ation in the steady state. 9 Instead, the facto pice atio fom equation 15 can be substituted into the facto maket equilibium conditions. The facto maket equilibium conditions can then be used to solve fo the steady state capital stock, which is endogenous in this dynamic setup. Futhemoe, section 3 shows that the facto maket equilibium conditions can be used to solve fo the numbe of multinational fims in the steady state. Most impotantly, section 3 shows that the facto maket equilibium conditions ae linea in the steady state capital stock and the numbe of fims, i.e. the facto maket equilibium conditions can be solved analytically fo these two vaiables. 9 Note that the facto maket equilibium conditions ae non linea in facto pices if, e.g., Cobb Douglas poduction technologies ae used. Theefoe, in a static setup, in which the equilibium facto pice atio has to be detemined by the facto maket equilibium conditions, analytical solutions ae typically not available. 7

9 2.3 Facto pice equalization in the steady state The assumption of identical technologies and pefeences in both counties implies that the paametes ρ, δ and β ae identical in both counties, i.e. Futhemoe, costless tade of good Z between counties leads to: w H H w F F due to equation 15. p Z,H w β H 1 β H w β F 1 β F p Z,F 16 β β wh wf H F. 17 H Since w H H w F F in the steady state, equation 17 implies that H F in the steady state. If the capital ental ate is identical, the pice pe unit labo must be identical in both counties in the steady state as well. The facto pices ae theefoe witten without a county index in the following. The pe unit costs fo a vaiety of good X can accodingly be witten as: F c X w ξ 1 ξ, with ξ φ 1 α + φ 2 1 α Hoizontal vesus vetical multinational fims Hoizontal multinational fims A single hoizontal multinational fim with headquates in county i, i H, F, has two poduction plants, one in county H and one in county F. Each poduction plant poduces both intemediate goods v 1 and v 2 and assembles them to a unique vaiety of good X. Since each poduction plant poduces a unique vaiety of good X, the final output of each poduction plant is sold domestically and expoted to the othe county. Note that a single hoizontal multinational fim sells two unique vaieties of good X since it owns two poduction plants. Chat 1 of figue 1 illustates the allocation of poduction activities acoss counties fo hoizontal multinational fims. The aows fom headquate sevices HQS to both poduction plants PP indicate that headquate sevices ae poduced in one county, but supplied to the poduction plants in both counties Vetical multinational fims A single vetical multinational fim with headquates in county i, i H, F, has two poduction plants as well, one in county H and one in county F. Howeve, each poduction plant poduces only eithe intemediate good v 1 o intemediate good v 2. Since vetical multinational fims typically have an identical allocation of poduction activities acoss counties 8

10 e.g., Makusen, 2002, it is assumed that intemediate good v 1 is only poduced by poduction plants fom county H and intemediate good v 2 is only poduced by poduction plants fom county F. Theefoe, the poduction plants in county H impot intemediate good v 2 and the poduction plants in county F impot intemediate good v 1. Each poduction plant then assembles both intemediate goods to a unique vaiety of good X. Since each poduction plant poduces a unique vaiety of good X, each poduction plant sells its vaiety both domestically and to the othe county. Note again that a single vetical multinational fim sells two unique vaieties of good X since it owns two poduction plants. Chats 2 and 3 of figue 1 illustate the allocation of poduction activities acoss counties fo vetical multinational fims. 2.5 Demand The household s utility in county i in a single peiod of the steady state is given by: U i X γ i i Z 1 γ i i, 0 γ i 1, 19 with X i N H + N F X σ 1/σ ii + N H + N F X σ 1/σ σ/σ 1 ji, σ > 1 and Z i Z ii + Z ji. N H and N F stand fo the numbe of multinational fims with headquates in county H and F ; note that these fims ae eithe hoizontal o vetical multinational fims. X ii stands fo the supply of a poduction plant fom county i to county i. X ji stands fo the supply of a poduction plant fom county j to county i. Similaly, Z ii stands fo the supply of good Z fom county i to county i and Z ji stands fo the supply of good Z fom county j to county i. It is assumed that the sum N H + N F is sufficiently lage so that the maket fo good X is chaacteized by lage goup monopolistic competition. Pofit maximizing secto X fims then supply thei unique vaieties of good X at pice p X σ σ 1 c X. Since facto pices ae identical in both counties in the steady state, c X does not have a county index. The pice index which is dual to the CES aggegate X i is then given by: P N H + N F 1/1 σ σ σ 1 wξ 1 ξ 2 1/1 σ. 20 If M i L i w + K i 21 9

11 denotes aggegate facto income of county i, i H, F, the supply demand conditions esult as X ii p σ P σ 1 M i γ i and, similaly, γ i σ 1 σ X ij γ j σ 1 σ σ σ σ 1 wξ 1 ξ σ σ 1 wξ 1 ξ σ 1 2 N H + N F M i γ i 1 w ξ 1 ξ M i, i H, F, 22 2 N H + N F 1 w ξ 1 ξ M j, i, j H, F, i j N H + N F Note that the left hand sides of equations 22 and 23 denote the supply of a single poduction plant fom county i to county i o j. The ight hand sides of equations 22 and 23 accodingly denote the demand in county i o j fo a unique vaiety which is poduced by a poduction plant fom county i. The supply demand condition fo good Z and county i can be deived as: 2.6 Fee enty condition Z ii + Z ji M i p Z 1 γ i, i, j H, F, i j. 24 If enty into secto X is unesticted, the fee enty condition fo secto X has to hold in each peiod of the steady state. The fee enty condition equalizes total makup evenue of a single secto X fim with total fixed costs of this fim. The fee enty condition of a single multinational fim is given by: p X c X X HH + X HF + X F F + X F H F HQS+P P + F P P, 25 whee the left hand side of equation 25 denotes total makup evenue of a single multinational fim and the ight hand side of equation 25 denotes total fixed costs of this fim. p X c X stands fo the makup evenue pe unit of good X sales. The sum X HH + X HF denotes total sales of the fim s poduction plant in county H and the sum X F F + X F H denotes total sales of the fim s poduction plant in county F. F HQS+P P stands fo the fixed capital input in the county of the fim s headquates. F HQS+P P is used fo unning the entie fim, i.e. fo poducing headquate sevices HQS, and fo maintaining the poduction plant PP in the county of the fim s headquates. F P P stands fo the fixed capital input in the host county. F P P is used fo maintaining the poduction plant in the host county. The tem F HQS+P P + F P P accodingly denotes total fixed capital expenditues of a single fim. 10

12 Since F P P wheeas F HQS+P P only includes the fixed capital input fo maintaining a poduction plant, additionally includes the fixed capital input fo poducing headquate sevices, F HQS+P P > F P P is assumed fo the compaative steady state analysis in section 3. Substituting the expessions fo X HH, X HF, X F F and X F H cf. equations 22 and 23 into equation 25 and consideing that p X simplification of the fee enty condition: σ σ 1 c X σ σ 1 wξ 1 ξ leads to the following L H w H + K H H γ H + L F w F + K F F γ F σ N H + N F F HQS+P P + F P P Tade balance equation The tade patten between counties depends on whethe hoizontal o vetical multinational fims ae active. In the egime with hoizontal multinational fims, counties only tade the vaieties of the diffeentiated good X and good Z. 10 In the egime with vetical multinational fims, counties additionally tade intemediate goods v 1 and v The tade balance equation is theefoe deived sepaately fo eithe fim egime Tade balance equation with hoizontal multinational fims Tade between county H and county F is balanced if the value of expots equals the value of impots, i.e. if the following holds: Z HF p Z + N H + N F X HF p X Z F H p Z + N H + N F X F H p X. 27 The left hand side ight hand side of equation 27 denotes the value of county H s expots impots. Since X HF and X F H stand fo expots of a single poduction plant fom county H and F, the quantities X HF and X F H have to be multiplied by N H +N F. The sum N H +N F denotes the total numbe of fims, which own a poduction plant in both counties. Consideing that county H s impots of good Z ae county F s expots of good Z, Z F H can be set equal to zeo and Z HF is allowed to be negative. Substituting the expessions fo X HF p X and X F H cf. equation 23 into equation 27 and consideing p Z w β 1 β and σ σ 1 wξ 1 ξ leads to the following expessions fo the tade balance equation: Z HF L H w + K H γ H L F w + K F γ F 2 w β 1 β Note that the vaieties of good X ae taded even between completely identical counties due to the Dixit Stiglitz fomulation of the pefeences fo good X e.g., Makusen and Venables, Good Z is only taded if tade in the vaieties of good X is not balanced. 11 Stictly speaking, intemediate goods v 1 and v 2 ae taded within the fim. Howeve, poduction of intemediate goods leads to facto income, which leads to demand fo final goods in the county of poduction. Tade of intemediate goods theefoe has to be consideed as well in the tade balance equation. 11

13 2.7.2 Tade balance equation with vetical multinational fims Tade of intemediate goods between counties has to be consideed as well. c X c v2 County H s impots of intemediate good v 2 ae equal to: c X c v2 X HH + X HF N H + N F. 29 denotes the input of intemediate good v 2 pe unit of good X due to Shephad s Lemma. X HH + X HF N H + N F denotes total poduction of good X in county H. Consideing equations 5 and 7, c X c v2 c X c v2 1 α cv1 c v2 can be calculated as: α w φ 1 H 1 α α 1 φ 1 H w α φ1 φ 2 w φ 2 F 1 α 1 φ 2, 30 F whee the last equality uses the fact that facto pices ae identical in both counties in the steady state with fee tade. Similaly, county F s impots of intemediate good v 1 ae equal to: c X c v1 X F F + X F H N H + N F. 31 Again, c X c v1 denotes the input of intemediate good v 1 pe unit of good X due to Shephad s Lemma and X F F + X F H N H + N F denotes total poduction of good X in county F. Consideing equations 5 and 7, c X c v1 α cv2 c v1 c X c v1 esults as: 1 α w φ 2 F α 1 α 1 φ 2 F w 1 α φ2 φ 1 w φ 1 H α 1 φ 1, 32 H whee the last equality again uses the fact that facto pices ae identical in both counties in the steady state with fee tade. The tade balance equation in the egime with vetical multinational fims accodingly esults as follows: w 1 α φ2 φ 1 Z HF p Z + α XF F + X F H w φ1 1 φ 1 + X HF p X N H + N F w α φ1 φ 2 Z F H p Z + 1 α XHH + X HF w φ2 1 φ 2 + X F H p X N H + N F. Again, Z F H is set equal to zeo and Z HF is allowed to be negative since county H s impots of good Z ae equal to county F s expots of good Z. Substituting the expessions fo X HH, 33 12

14 X F F, X HF and X F H into equation 33 and consideing p Z w β 1 β and p X leads to the following expession fo the tade balance equation: Z HF σ 1 σ L H w + K H γ H + L F w + K F γ F 2 w β 1 β 1 2 α 3 Geneal steady state equilibium σ σ 1 wξ 1 ξ + L H w + K H γ H L F w + K F γ F 2 w β 1 β. 34 The geneal steady state equilibium fo this 2 county wold is chaacteized by: the condition w ρ + δ 1/β since counties ae in thei steady state the fee enty condition fo secto X the tade balance equation 2 facto maket equilibium conditions fo each county. The condition w ρ + δ 1/β, the fee enty condition fo secto X and the tade balance equation can be substituted into the 2 facto maket equilibium conditions fo each county. The geneal steady state equilibium fo this 2 county wold can then be epesented by a system of 4 equations, which ae linea in 4 vaiables. The 4 vaiables ae the numbes of multinational fims N H and N F and the counties capital endowments K H and K F in the steady state. If N H, N F, K H and K F ae known and if one poduction facto, e.g., labo in county H, is chosen as the numéaie good, all quantity vaiables and elative pices of the model can then be deived immediately: the elative pice of capital follows fom equation 15. The elative pices of intemediate goods v 1 and v 2 follow fom equation 5. The elative pices of the final goods Z and X follow fom equations 2 and 18. Aggegate facto income in both counties follows fom equation 21. Demand fo the vaieties of good X follows fom equations 22 and 23. Aggegate demand fo good Z follows fom equation 24. Tade in the vaieties of good X follows fom equation 23. Tade in good Z follows fom equations 28 and 34. Tade in intemediate goods v 1 and v 2 in the egime with vetical multinational activity follows fom equations 29 and 31. Finally, utility of eithe county follows fom substituting the consumed quantities into equation 19. Since hoizontal and vetical multinational fims have diffeent poduction pattens, the facto maket equilibium conditions diffe between both fim egimes. Theefoe, the geneal steady state equilibium is deived sepaately fo both fim egimes. 13

15 In ode to simplify the setup of the geneal steady state equilibium, the capital depeciation ate δ is nomalized to zeo. Since each county s labo endowment is assumed to be constant ove time, investment in the steady state is theefoe equal to zeo. If a pesistent exogenous shock in the compaative steady state analysis shifts the county to a new steady state with a lage smalle capital stock, investment is tempoaily positive negative. 3.1 Hoizontal multinational fims Hoizontal multinational fims poduce both intemediate goods v 1 and v 2 in each poduction plant. The pe unit costs of good X accodingly esult as: c X w i, i w φ 1 α i w φ 2 1 α i 1 φ 1 α i 1 φ 2 1 α i w ξ 1 ξ, 35 with ξ φ 1 α + φ 2 1 α. Applying Shephad s Lemma, the facto input coefficients fo labo and capital, a X L w, and a X K w,, ae given by: a X L w, c X w, w a X K w, c X w, 1 ξ ξ 36 w w ξ 1 ξ. 37 The coesponding facto input coefficients fo good Z ae given by: a Z L w, c Z w, w a Z K w, c Z w, 1 β β 38 w w β 1 β. 39 a X L w,, ax K w,, az L w, and az K w, ae used to deive the facto maket equilibium conditions fo eithe county. Note that N H and N F stand fo the mass of active hoizontal multinational fims and X HH, X HF, X F F single hoizontal multinational fim: equilibium on labo maket county H: and X F H stand fo the supply of a 1 ξ 1 β ξ XHH + X HF N H + N F + β ZHH + Z HF L H 40 w w equilibium on capital maket county H: w ξ 1 ξ NH + N F X HH + X HF w β +N H F HQS+P P + N F F P P + 1 β ZHH + Z HF K H 41 14

16 equilibium on labo maket county F: 1 ξ 1 β ξ XF F + X F H N H + N F + β ZF F L F 42 w w equilibium on capital maket county F: w ξ 1 ξ NH + N F X F F + X F H w β +N H F P P + N F F HQS+P P + 1 β ZF F K F. 43 Substituting the expessions fo X HH, X HF, X F F and X F H equations 22 and 23 into the facto maket equilibium conditions, consideing the fee enty condition equation 26 and the tade balance equation equation 28 leads to the following simplification of the facto maket equilibium conditions: ξ σ 1 2 w F HQS+P P + F P P N H + N F + L H + w K H β 1 γ H 2 + L F + w K F β γ F 2 L H 44 1 ξ σ 1 2 w F HQS+P P + F P P N H + N F + N H w F HQS+P P + N F w F P P + L H + w K H 1 β 1 γ H + L F + 2 w K F 1 β γ F 2 w K H 45 ξ σ 1 2 w F HQS+P P + F P P N H + N F + L H + w K H β γ H + 2 L F + w K F β 1 γ F 2 L F 46 1 ξ σ 1 2 w F HQS+P P + F P P N H + N F + N H w F P P + N F w F HQS+P P + L H + w K H 1 β γ H + L F + 2 w K F 1 β 1 γ F 2 w K F. 47 Note that the facto pice atio w is aleady fixed by the model paametes ρ, δ and β cf. equation 15, i.e. equations ae linea in the 4 vaiables N H, N F, K H and K F. The steady state of this 2 county wold, which is descibed by equations 44 47, is now distubed by 4 diffeent exogenous shocks. The fist shock is a symmetic demand shift in favo of good X in both counties, i.e. dγ H dγ F > 0. The second shock is a demand shift in favo of good X only in county H, i.e. dγ H > 0 and dγ F 0. The thid shock is a symmetic incease in population size in both counties, i.e. dl H dl F > 0. The fouth 15

17 shock is an incease in population size only in county H, i.e. dl H > 0 and dl F 0. Note that these 4 shocks ae the only elevant ones. 12 If the capital stocks of both counties, K H and K F, move into the same diection due to the exogenous shock, domestic and foeign investment ae complements. If the capital stocks K H and K F move into opposite diections due to the exogenous shock, domestic and foeign investment ae substitutes. Based on the compaative steady state analysis, which is elegated to appendix A, we can deive the following hypotheses on the elationship between K H and K F if multinational activity is hoizontal: H1: In the case of a symmetic demand shift dγ H dγ F > 0 an asymmetic demand shift dγ H > 0 and dγ F 0 a symmetic incease in population size dl H dl F > 0 domestic and foeign capital ae complements with dk H. H2: In the case of an asymmetic incease in population size dl H > 0 and dl F 0 domestic and foeign capital ae complements with dk H Φ and Φ > 0. Poof: See appendix A. 3.2 Vetical multinational fims Vetical multinational fims poduce intemediate good v 1 in thei poduction plant in county H and intemediate good v 2 in thei poduction plant in county F. The pe unit costs of good X accodingly esult as: c X w H, w F, H, F w φ 1 α H wφ 2 1 α F 1 φ 1 α H 1 φ 2 1 α F In the case of an asymmetic shock in the poduction technologies, counties completely specialize in the poduction of eithe good X o good Z cf. Baxte, Howeve, if thee is complete specialization in poduction, no hoizontal multinational fims, which poduce good X in both counties, do exist. In the case of an asymmetic shock in the elasticity of substitution σ, the model is not analytically solvable any moe. The eason is as follows: if σ diffes between counties, equation 26 becomes γ H M H/σ H + γ F M F /σ F N H +N F 1 F HQS+P P + F P P. Howeve, the sum Xii +X ij in the facto maket equilibium conditions equals σh 1 σ H γ H M H + σ F 1 σ F γ F M F N H + N F 1 if σ diffes between counties. Theefoe, X ii + X ij in the facto maket equilibium conditions cannot be substituted by F HQS+P P + F P P σ 1 fom equation 26 if σ diffes between counties. Howeve, this substitution is necessay to get the facto maket equilibium conditions linea in N H and N F like in equations

18 Applying Shephad s Lemma and consideing facto pice equalization in the steady state, the facto input coefficients fo labo and capital, a X L,i w H, w F, H, F and a X K,i w H, w F, H, F, i H, F, ae given by: a X LH w H, w F, H, F c X w H, w F, H, F w H φ 1 α w φ 1 α 1 H w φ 2 1 α F 1 φ 1 α H 1 φ 2 1 α F 1 ξ φ 1 α, with ξ φ1 α + φ 2 1 α 49 w a X KH w H, w F, H, F c X w H, w F, H, F H 1 φ 1 α w φ 1 α H wφ 2 1 α F 1 φ 1 α 1 H 1 φ 2 1 α F w ξ 1 φ 1 α 50 a X LF w H, w F, H, F c X w H, w F, H, F w F φ 2 1 α w φ 1 α H wφ 2 1 α 1 F 1 φ 1 α H 1 φ 2 1 α F 1 ξ φ 2 1 α 51 w a X KF w H, w F, H, F c X w H, w F, H, F F 1 φ 2 1 α w φ 1 α H wφ 2 1 α F 1 φ 1 α H 1 φ 2 1 α 1 F w ξ 1 φ 2 1 α. 52 Note that a X L,i w H, w F, H, F and a X K,i w H, w F, H, F stand fo the amount of labo and capital pe unit of good X. 13 The coesponding facto input coefficients fo good Z ae again given by: a Z L w, c Z w, w a Z K w, c Z w, 1 β β 53 w w β 1 β. 54 Equations ae used to deive the facto maket equilibium conditions fo eithe county. N H and N F stand fo the mass of active vetical multinational fims and X HH, X HF, X F F, X F H stand fo the supply of a single vetical multinational fim: equilibium on labo maket county H: 1 ξ 1 β φ 1 α XHH + X HF N H + N F + β ZHH + Z HF L H 55 w w 13 Altenatively, the labo and capital input pe unit of intemediate goods v 1 and v 2 could be deived. If these facto input coefficients ae multiplied by the input of v 1 and v 2 pe unit of good X, the esulting input of labo and capital pe unit of good X would be as deived by equations

19 equilibium on capital maket county H: w ξ 1 φ 1 α NH + N F X HH + X HF w β +N H F HQS+P P + N F F P P + 1 β ZHH + Z HF K H 56 equilibium on labo maket county F: 1 ξ 1 β φ 2 1 α XF F + X F H N H + N F + β ZF F L F 57 w w equilibium on capital maket county F: w ξ 1 φ 2 1 α NH + N F X F F + X F H w β +N H F P P + N F F HQS+P P + 1 β ZF F K F. 58 Substituting the expessions fo X HH, X HF, X F F and X F H equations 22 and 23 into the facto maket equilibium conditions, consideing the fee enty condition equation 26 and the tade balance equation equation 34 leads to the following simplification of the facto maket equilibium conditions: φ 1 α σ 1 2 w F HQS+P P + F P P N H + N F + L H + w K H β 1 γ H 2 + L F + w K F β γf 2 2 α σ σ 2 α 1 σ 1 σ L H 59 1 φ 1 α σ 1 2 w F HQS+P P + F P P N H + N F + N H w F HQS+P P + N F w F P P + L H + w K H 1 β 1 γ H 2 α σ σ + L F + w K F 1 β γf 2 α 1 σ 1 2 σ w K H 60 φ 2 1 α σ 1 2 w F HQS+P P + F P P N H + N F + L H + w K H β γh 1 2 α 2 σ 1 α 2 σ + L F + w K F β 1 γ F 2 α σ 1 α 2 σ L F 61 1 φ 2 1 α σ 1 2 w F HQS+P P + F P P N H + N F + N F w F HQS+P P + N H w F P P 18

20 + L H + w K H + L F + w K F 1 β γh 2 1 β 1 2 α 2 σ 1 α σ 1 γ F 2 α σ 1 α 2 σ w K F. 62 Again, since the facto pice atio w is fixed by the model paametes ρ, δ and β cf. equation 15, equations ae linea in the 4 vaiables N H, N F, K H and K F. The steady state in the 2 county wold with vetical multinational activity is descibed by equations In ode to analyze whethe vetical multinational activity leads to a diffeent elationship between the capital stocks K H and K F, the steady state with vetical multinational activity is distubed by the same 4 exogenous shocks as befoe. The compaative steady state analysis fo vetical multinational activity is elegated to appendix B. The elationship between the capital stocks K H and K F in the egime with vetical multinational activity is summaized by hypotheses H3 H5: H3: In the case of a symmetic demand shift dγ H dγ F > 0 ; an asymmetic demand shift dγ H > 0 and dγ F 0 domestic and foeign capital ae substitutes, i.e. dk H Ψ, with Ψ < 0, if: the labo shae of the intemediate good which is poduced in county H φ 1 is sufficiently small; the shae of intemediate good v 1 in final goods poduction lage. α is sufficiently If φ 1 is not sufficiently small and if α is not sufficiently lage, domestic and foeign capital ae complements, i.e. Ψ > 0. H4: In the case of an asymmetic incease in county size dl H > 0 and dl F 0 domestic and foeign capital ae substitutes, i.e. dk H Θ, with Θ < 0, if: the labo shae of the intemediate good which is poduced in county H φ 1 is sufficiently small; the shae of intemediate good v 1 in final goods poduction lage. α is sufficiently If φ 1 is not sufficiently small and if α is not sufficiently lage, domestic and foeign capital ae complements, i.e. Θ > 0. 19

21 H5: In the case of a symmetic incease in county size dl H dl F > 0 domestic and foeign capital ae complements, i.e. dk H, with > 0, fo all possible values of φ 1 and α. Poof: See appendix B. Figue 2 summaizes the esults of ou compaative steady state analysis fo both fim egimes. 4 Empiical model Data fo the empiical analysis ae taken fom the website of the Bueau of Economic Analysis BEA. We constucted a panel with 42 sectos see table A1 of the appendix, and 7 yeas The BEA data divides the opeations of multinational companies into the opeation of the Ameican paent company and its foeign affiliates. Fo the data of the foeign affiliates, the BEA allows to choose between data fo majoity owned foeign affiliates only o all foeign affiliates, whee the latte ae defined as outwad foeign diect investment with owneship o contol by the paent fim of at least 10%. 14 We have chosen to use the data fo all these foeign affiliates. As initial yea, 1999 is chosen as the BEA switched fom SIC to the NAICS classification in that yea. Fo the yea 2005, sales of the foeign affiliates in ou sample cove 90% of the total sales of all foeign affiliates. In ode to test the peviously deived hypotheses, we constuct fou vaiables at the secto level: i Domestic Investment, defined as domestic capital expenditues of U.S. paent companies as pat of total value added of U.S. paent companies; ii Foeign Investment, defined as foeign capital expenditues of U.S. paent companies as pat of total value added of U.S. paent companies; iii Labo Shae, defined as the compensation of U.S. paent companies as pat of total value added of U.S. paent companies; iv Shae Intemediate, defined as one minus the impots of goods shipped to U.S. paents fom foeign affiliates as pat of the value added of U.S. paent companies. The last two vaiables ae poxies fo α and φ 1, espectively, as defined peviously. As to test diffeences in the elationship between domestic and foeign investment between hoizontal and vetical MNEs, we make the assumption that MNEs in the manufactuing sectos ae mainly vetical, while MNEs in othe sectos ae mainly hoizontal. 15 The mean of Shae Intemediate, as shown in table A2 of the appendix, indicates that tade in intemediates is almost absent in the non manufactuing industies, while impots of intemediates fom affiliates constitutes aound 19% of the value 14 A moe complete desciption of the BEA data on the opeations of U.S. multinational companies can be found in Slaughte The manufactuing sectos have a NAICS code stating with 3 in table A1 of the appendix. 20

22 added of U.S. paent fims. Theefoe, the distinction between manufactuing and non manufactuing seems to captue the main diffeence between hoizontal and vetical MNEs emakably well. 4.1 Empiical esults We test the implications of the theoetical model in an econometic model using a U.S. panel of foeign and domestic investments at the secto level ove the peiod The esults of ou panel with andom and fixed secto effects confim the findings by Desai et al. 2005b fo the estimated sign of foeign investment. Table 1 columns 1 and 2 shows that the estimated coefficient is equal to 0.10 with andom and with fixed effects. Column 3 shows that accounting fo a common autoegessive tem in the distubances estimated at a value of 0.6 deceases the estimated coefficient in the andom effects model to As thee is stong autocoelation in the distubances, in column 4, we include lagged domestic capital expenditues in the panel and use the Aellano Bond GMM estimation of the paametes in the dynamic model. The estimate of fo the lagged coefficient of domestic investment and the estimate of fo domestic capital investments imply a esponse of 0.10 in the steady state 0.065/ The Aellano Bond test statistics fo autocoelation indicates that the dynamic model is well specified. The main novelty in the egessions is to allow fo secto specific estimates of the coefficient fo foeign investment. Table 2 splits the sample in manufactuing and non manufactuing sectos and shows the egession esults fo both categoies with andom effects acoss sectos and fixed time effects. The sign of the link between foeign investment and domestic investment is opposite fo the manufactuing and the non manufactuing sectos. Including lagged domestic investment as explanatoy vaiable widens the gap between the two estimates. While the sign is positive and significant fom zeo fo the non manufactuing sectos, the sign is negative fo the manufactuing sectos. Hence, unde the assumption that vetical MNEs ae pimaily active in manufactuing sectos and hoizontal MNEs ae pimaily active in non manufactuing sectos, we can confim ou fist hypothesis that thee is a positive elationship between domestic and foeign capital expenditues when MNEs ae hoizontal while thee is a possibility that foeign capital expenditues have a negative effect on domestic capital fomation when MNEs ae vetical. As a futhe test fo diffeences in the link between domestic and foeign investment, we include in table 3 inteaction tems between foeign investment and centalized labo shae in a secto and between investment and the shae of the intemediate good poduced by the U.S. paent. In line with the pedictions fom the theoetical model, the signs fo 21

23 the inteaction tems ae negative fo the manufactuing sectos. Howeve, only the esult fo the shae of intemediate goods is significant. The esult indicates that manufactuing sectos with a elatively high labo shae and a elatively high shae of the intemediate good ae chaacteized by a negative elationship between foeign and domestic investment. If the labo shae and the shae of the intemediate good ae elatively low, howeve, thee is a possibility that the sign fo foeign investment becomes positive. An example of such a secto is petoleum and coal poducts whee the aveage labo shae ove the sample peiod is 0.2 and the aveage shae of the intemediate goods equals about 0.1. Calculating the centalized labo shae and centalized shae of intemediate good gives a coefficient of about 0.1 fo foeign investment. As to check whethe simila esults can be obtained fo non manufactuing sectos, we include the same inteactions in the egessions fo the sample of non manufactuing sectos. We find no convincing evidence that the inteaction effects ae significant fo the non manufactuing sectos. Futhemoe, it appeas impossible to find a secto whee the sign fo the foeign investment vaiable tuns out to be negative. 5 Conclusions Ou pape has shown a clea distinction between hoizontal and vetical multinationals in explaining the link between domestic and foeign capital expenditues. In the analytical geneal equilibium model we deive a complementay elationship between domestic and foeign capital expenditues if multinational activity is hoizontal. Howeve, if multinational activity is vetical, the elationship between domestic and foeign capital expenditues is substitutional o complementay, depending on technology paametes. We test out theoetical implications with a panel of U.S. multinationals and find empiical suppot. Fist, we find that hoizontal multinational activity leads to a complementay elationship between domestic and foeign capital expenditues, iespective of the values fo elevant technology paametes. Second, we find a substitutional elationship between domestic and foeign capital expenditues if multinational activity is vetical. In ode to efine ou empiical esults, we show that the empiical influence of elevant technology paametes on this substitutional link is as pedicted by the theoetical model. 22

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