Endogenous Flows of Foreign Direct Investment and International Real Business Cycles

Transcription

1 Endogenous Flows of Foreign Direc Invesmen and Inernaional Real Business Cycles Nicolas Perosky-Nadeau Carnegie Mellon Universiy January 2011 Absrac This paper models flows of foreign direc invesmen (FDI) in awocounry,wo secor DSGE framework. The allocaion of capial o producion capaciy abroad is subjec o a search-and-maching fricion wih endogenous capial reallocaion. The model is calibraed on observed inflows and ouflows of FDI and leads o dynamics of foreign direc invesmen consisen wih he empirical evidence documened in his paper: relaive o domesic invesmen, FDI is more volaile, and inward and ouward flows of FDI are posiively correlaed. This conrass wih a sandard Inernaional Real Business Cycle model which predics a negaive correlaion and low volailiy. Moreover, he model generaes cross-counry aggregae invesmen correlaions consisen wih he daa. JEL classificaion: F41 E32 E22 Keywords: Inernaional business cycles; foreign direc invesmen; co-movemens. This paper has benefied from conversaions wih Seve Ambler, Alain Delacroix, Nicolas Marceau, Michel Normandin and Éienne Wasmer and commens from anonymous referees. Andres Bellofao provided excellen research assisance. Financial suppor from FQRSC is graefully acknowledged. Conac address: Nicolas Perosky-Nadeau, Tepper School of Business, Carnegie Mellon Universiy, 5000 Forbes avenue, Pisburgh, PA, npn@cmu.edu 1

2 1 Inroducion Generally foreign invesmen is welcomed for bringing new capial o an economy and increasing produciviy hrough he arrival of new echnologies. This has also been he main focus of he heoreical and empirical lieraures concerned wih foreigndirecinvesmen. Lile aenion has been paid, however, o he shor and medium run behavior of foreignconrolled firms and, in general, o heir imporance in undersanding he business cycle of open economies. This seems somewha surprising, as a commonly used measure of he rae a which foreigners gain conrol over a domesic economy, flows of foreign direc invesmen (FDI), are large and very volaile. In Canada, for example, foreign-owned firms generae up o one hird of employmen and conrol over a fifh of allasses,ashareha has been sable over he las four decades. 1 The bulk of FDI, among developed counries, involves he replicaion of producion capaciy abroad, or wha is known as horizonal FDI, and in paricular for he purpose of serving he hos marke (Brainard 1993, 1997). Wha is less wellknown,andisdocumened in deail for he case of Canada and oher major developed economies in Secion 2, is ha boh ne inflows ino, and ouflows from, a hos economy of FDI by foreigners increase during an upurn. Moreover, business cycle flucuaions in ne FDI in Canada and ne Canadian invesmen abroad are posiively correlaed.thus periods of increased ne inflows ino an expanding economy are also periods of increased invesmen abroad by ha same economy. The classic inernaional real business cycle model,however,generaesa negaive correlaion beween hese flows. The approach aken by his paper, in Secion 3, is o model flows ofhorizonalforeign direc invesmen in a wo-counry, wo-secor model, in which he allocaion of capial o producion abroad is subjec o a fricion of he search and machingype:bringingo fruiion a new invesmen projec abroad is cosly and ime consuming and, once in place, faces an endogenous erminaion probabiliy. The model herefore provides a heoreical framework wih endogenous gross inflows and ouflows of foreign direc invesmen in 1 These figures are for he manufacuring secor, see Baldwin and Dhaliwal (2001) and Baldwin and Gellaly (2005). The imporance of FDI does no limi iself o he case ofcanada. Forexample,heraioofFDIo domesic invesmen in he US has risen from 6% in he 1970s o 15% in he 2000s. Lipsey (2000) repors raios above 10% for many indusrialized counry over he period 1970 o

3 which congesioneffecs on foreign invesmen markes impac he response of invesmen paerns o changes in produciviy. Several consideraions moivae he modeling sraegy adoped here. Firs, as argued by Gordon and Bovenberg (1996), due o a lack of knowledge of he domesic economy foreign firms are a a disadvanage in seing up and running a firm. While hese auhors capure his idea by assuming ha oupu a foreign firms is reduced by some fixed proporion, in he presence of search and maching fricions he cosofinvesmenwillbe afuncionofcongesiononforeigninvesmenmarkes. Theprobabilisic naure of he maching process capures he fac ha foreigners incur he cosofmoreimeinseingup anewproducionfaciliyoracquiringinformaionabouarisky invesmen projec, as in Gopinah (2004), and congesion effecs are a novel allocaive signal. Quaniaively, he model generaes he high cyclical volailiy of ne FDI flows,and he posiive correlaion of ne foreign direc invesmen inflows and ouflows observed in he daa. By conras, a sandard IRBC model wih invesmen adjusmen coss predics a negaive correlaion, and lower volailiies of FDI flows. As Secion 4 elaboraes in assessing he quaniaive implicaions of he model, he allocaion fricion is cenral o explaining his posiive correlaion of ne inflows and ne ouflows of FDI. Following a posiive echnology shock in he hos economy, wheher in a sandard IRBC model wih invesmen adjusmen coss or a search in FDI model, flows of ne inward FDI increase on impac. In he sandard IRBC model, by simple arbirage, gross flows of FDI from he hos economy abroad decrease on impac, generaing a counerfacual negaive correlaion. However, in he proposed model his same drop in he pool of capial goods available for allocaion abroad increases he allocaion probabiliy for he capialownerinheshorrun,husmiigaing he drop in new allocaions abroad and producing he posiive correlaion beween inward and ouward flows observed in he daa. This is because,inhisconex,newallocaions are a funcion of boh he pool of capial available and he allocaion probabiliy, or congesion on he foreign capial marke. The model is exended in a variey of dimension in order he verify he robusness of he main resuls. For insance, he he inroducion of mach specific produciviy shocks allows for a noion of endogenous capial reallocaion. Endogenous gross repariaion of capial abroad will move inversely wih he originaing counry s business cycle. As a 3

4 resul, he decline in ne FDI during an expansion is furher limied by a drop in he gross flow of capial repariaed and improves he model s fi wih hedaa. This paper is relaed o he growing lieraure on inernaional real business cycles, daing back o he seminal conribuion of Backus, Kehoe and Kydland (1992), and o he ransmission channels of inernaional business cycles. This paper considers horizonal FDI, reaed in he rade heory lieraure by papers such as Markusen (1984), Markusen and Venables (2000), and Helpman, Meliz and Yeaple (2004). TheseProximiy-concenraion models of FDI, generally assume a fixed cos o seing up operaions abroad, above he he cos of enering he domesic marke. As will be discussed below, foreign affiliaes pay acosperinvesmenprojeciniiaion. Alhoughallocaion of capial o domesic firms will be fricionless, his is only a special case of he searchenvironmenwhenheiniiaion cos is nil. This seup was explored exensively in a closed economy seing for he allocaion of physical capial by Kurmann and Perosky-Nadeau (2009). Gopinah (2004) models he difficuly in acquiring he informaion on invesmen projecs in emerging projecs as aimeconsumingsearchprocess. One measure of he inernaional ransmission of business cycles, he cross counrycorrelaion of aggregae variables, poses a problem for sandard IRBC models known of he quaniy problem. Tha is, he ordering of oupu and consumpion cross correlaions in he model is opposie o ha in he daa, (see Backus, Kehoe and Kydland, 1995 or Crucini, 2008). While many papers have made conribuions in reducing orsolvinghisproblem, few address anoher quaniy problem involving aggregae hours and invesmen. A resul of focusing on ne flows of FDI is ha he model solves he invesmen quaniy puzzle. Tha is, conrary o oher inernaional real business cycle model,hepresenceofcongesion on foreign invesmen markes generaes a posiive cross-counry correlaion of aggregae invesmen coheren wih he daa. To undersand his resul, consider ha aggregae invesmen has domesic and foreign componens. During an expansion in one counry, boh he domesic and he foreign componens increase as invesors are drawn o he higher reurns. In a sandard IRBC seing, boh he domesic and foreign componens invesmen in he oher counry decrease in he meanime such haaggregaeinvesmen in he wo counries are negaively correlaed. However, by geing he correc posiive correlaion beween ne flows of FDI in he search based model, heforeigncomponenof 4

5 invesmen increases in boh counries, raising in he cross-counrycorrelaion ofaggregae invesmen. 2 Flows offdi and Canada- U.S. business cycles This secion reviews evidence on he cyclical characerisics of FDI flows oulined in he inroducion. While he Canadian economy is of paricular ineres for his sudy because of he large and hisorically sable share of economic aciviy originaing in he foreign secor, i is increasingly significan for oher indusrialized economies as hey furher inegrae. The secion also documens similar observaions on flows for FDI for oher major developed counries. Flows of foreign direc invesmen ino Canada, and flows of Canadian direc invesmen abroad, concerning overwhelmingly he Unied Saes, he focus is placed on he similariies and inerdependence of boh counries. 2.1 Canadian and U.S. business cycles Despie a large difference in absolue size, in per capia erms he Canadian and U.S. economies are remarkably similar. The evoluion of hours worked (indexed), real oupu, invesmen and consumpion per capia in boh counries, over he period , have bu for a few episodes followed each oher closely. 2 One example is he oupu per capia gap beween he U.S. and Canada appearing during he 1990s, which also shows up as a gap in average hours worked. While aggregae rends have been similar, Table 1 examines differences in cyclical flucuaions of prominen macroeconomic variables, measured as 2ndmomensforHodrick- Presco filered quarerly daa over 1976:1-2005:4. The Canadian and U.S. economies display approximaely he same business cycle characerisics of hese variables, alhough here is evidence of less aggregae consumpion smoohing in Canada,seenashelarger relaive volailiy of consumpion, observaions also made inbaxerandcrucini(1995), Ambler, Cardia and Zimmermann (2004). One indicaor of business cycle synchronizaion, he cross-counry conemporaneous 2 Adaaandechnicalappendixisavailableuponreques.Theime series for he menioned variables are ploed in Figure 1 of said appendix. 5

6 Table 1: Business cycle momens for Canada and he U.S. 1976:1-2005:4 Canadian daa U.S. daa Cross-counry variable: a b a b correlaions Consumpion Hours Invesmen Oupu :sandarddeviaion;a:sandarddeviaionrelaiveooupu; b: conemporaneous correlaion wih oupu. All momens are Hodrick-Presco filered. correlaion of prominen macroeconomic variables, is repored in he las column of Table 1. In heir exensive sudy of inernaional business cycles, Ambler, Cardia and Zimmermann (2004) find much lower, alhough posiive, cross counry correlaions han hose for he Canada - U.S. pair, suggesing a higher han average degree of inegraion of boh economies. While boh heoreical and empirical work have ofen followed rade as a vecor of synchronizaion, he increasingly imporan channel of flows of foreign direc invesmen is explored in he nex subsecion Flows of FDI and foreign conrolled firms in Canada There are essenially wo ways in which foreigners can access adomesiceconomy:(i)by esablishing a branch or new business; (ii) hrough mergers and acquisiions of domesic firms. A commonly used measure of he rae a which foreigners access a domesic economy, flows of foreign direc invesmen, can furher be caegorized as eiher "horizonal" or "verical". As described by Markusen (2002), horizonal FDI refers o he replicaion of ca- 3 Sales by mulinaional firms have oupaced he expansion of rade in manufacures over he las decades. See Markusen (2004). Kose and Yi (2001) explore and discuss he limiaions of he rade approach o solving he quaniy puzzles. Ambler, Cardia and Zimmermann (2002) explore he poenial of a wo counry muli-secor model wih rade in inermediae goods in addressing he same issue. Oher avenues have been explored, such as variable capial uilizaion in Baxer and Farr(2005),orradeincapialgoodsinBoileau (1999). Iacoviello and Minei (2006) explore he implicaions of imperfec cross-border credi relaions for oupu cross-correlaions. See also Schmi-Grohé (1998) for an evaluaion of various mechanisms. 6

7 paciy abroad, and verical FDI o he division of he producion process globally in order o exploi he benefis offered by differen markes. As Brainard (1997) documens and argues,he majoriy of FDI beweendevelopedcounries is horizonal. In addiion, he large majoriy of foreign affiliae sales are desined o he hos marke. Brainard (1993) esimaes ha approximaely 92% of foreign affiliae producion in he Unied Saes is desined for he hosmarke. There remains, however, a debae overhe principle mode of accessing an economy, alhough Helpman, Meliz and Yeaple (2004) argue ha i occurs mainly hrough "greenfield" invesmen. 4 In order o assess he exen and effec of foreign conrol over he naional economy, in 1962 he Canadian governmen passed he Corporaions Reurns Ac (CRA), requiring firms doing business in Canada o repor financial and ownership daa. Of he reporing firms in 2004, foreign conrolled corporaions accouned for 30.7% of oal operaing revenues and 28.5% of all asses held in Canada, 5 shares ha have hisorically remained sable. The Unied Saes play a cenral role in he foreign conrol of he Canadian economy, generaing 62.6% of he operaing revenues of foreign conrolled corporaions. The closes behind are he Unied Kingdom and Germany wih, respecively, 7% and 6.5% of operaing revenues. As seen by indusrial secor, foreign conrol is mos imporan in oil and gas, manufacuring and mining, and significan in wholesale rade, uiliies, and ransporaion and warehousing. 6 Manufacuring sands ou as a secor wih a large share of employmen and high degree of foreign conrol, involving nearly one fifh of employmen and where jus over half of he revenues and asses are under foreign conrol. In fac, Baldwin and 4 By "greenfield" invesmen, one refers o he esablishmen of a branch or new business. The posiion aken by Helpman e al. (2004) differs from ha of Graham and Krugman (1995) according o whom he evidence is less clear and leans raher owards a larger role for mergers and acquisiions. While his paper will follow Helpman e al. (2004), i worh noing a recen conribuion by Nocke and Yeaple (2007). These auhors invesigae he heoreical deerminans of FDI by M&A or greenfield invesmen. 5 "The noion of conrol encompasses boh direc and effeciveconrol.direcconrolisdefinedasaperson, group or corporaion holding, direcly or indirecly, more han 50% of he voing equiy. Effecive conrol implies conrol hrough mehods oher han ownership of he majoriy voing equiy, such as when more han 50% of he direcors of a corporaion are also direcors of anoher corporaion." For addiional informaion, see "Corporaions Reurns Ac, 2004," caalogue no SaisicsCanada,volXIE,p.3. 6 See Baldwin and Gellaly(2005). 7

8 log(real FDI per capia) Paymens Receips Year Figure 1: Flows of foreign direc invesmen, Canadian Balance of Paymens Gellaly (2005) esimae he share of manufacuring employmen originaing in he foreign secor o be 30% of oal secoral employmen. Togeher, secors wih more han 20% foreign conrol, in erms of asses, involve 55% of employmen. These measures give a sense of he imporance of foreign conrolled firms for aggregae oucomes Flows of foreign direc invesmen Flows of foreign direc invesmen in Canada and flow of Canadian direc invesmen abroad from he Canadian Balance of Paymens are large, hisorically around 20% of aggregae Canadian invesmen. 7 The source and desinaion of hese flows is overwhelmingly he U.S., he source of 44% of inflows and desinaion for 58%ofouflows. Excep for a brief period in he early 1990s, paymens have always exceeded receips, leading o a persisen defici offse only by Canada s hisorically posiive rade balance (see Figure 1). The business cycle componen of ne flows of FDI ino Canada and flowsofcanadian direc invesmens abroad, along wih heir cross-correlaion are presened in Table 2. Boh flows are highly volaile, wih H.-P. filered sandard deviaions relaive o oupu of and 8.8, respecively. By comparison, he relaive volailiy of aggregae invesmen is of he order of Boh ne inflows and ne ouflows, ha is ne FDI in Canada and ne Canadian Direc Invesmen Abroad move srongly wih hecanadianbusiness cycle, wih respecive conemporaneous correlaions wih Canadian GDP of 0.36 and Moreover, Table 2 also reveals ha ne inward and ne ouward flows are posiively corre- 7 I is imporan o sress ha flows of porfolio invesmen are excluded, keeping only flows of direc invesmen. 8

9 Table 2: The business cycle of foreign direc invesmen in Canada 1976:1-2005:4 Ne inflow Ne ouflow Sd. dev. rel. o oupu Conemp.corr. wih oupu Volailiy of ouflow o inflow 0.62 Conemporaneous correlaion, inflow-ouflow nd momens compued for Hodrick-Presco filered daa. Source: Saisics Canada laed. Tha is, periods of increased ne inflows of FDI ino Canada are also accompanied by increased ne Canadian direc invesmens abroad. This fac has no received much aenion, equilibrium models ending o predic ha capial wouldsimulaneouslyflowo high produciviy and ou of low produciviy counries. 2.3 Evidence for oher indusrialized naions This paern in conemporaneous inflows and ouflows of foreign direc invesmen for a hos economy is no unique o he Canada-U.S. pair, as repored in Table 3 using annual daa colleced by he OECD over he period 1985 o The conemporaneous correlaion beween flows of FDI from France o he Unied Kingdom and in he opposie direcion is 0.42, while wih he core 15 members of he European Union his correlaionis0.44. Table 3: The business cycle of foreign direc invesmen - oher counries UK Germany EU15 Japan France 1985:2007 Volailiy of ouflow o inflow Conemp. correlaion, inflow-ouflow nd momens compued for Hodrick-Presco filered daa. Source: OECD 9

10 3 IRBCwihsearchin FDI The model develops a framework wih ne inflows and ne ouflows of foreign direc invesmen in a wo counry, wo secor DSGE model, where gross invesmen flows in boh direcions evolve endogenously wih he business cycle. Each counry is populaed by domesic and foreign firms and a represenaive household. For simpliciyhemodelab- sracs from rade in consumpion goods. Households decide on opimal consumpion, an aggregae of goods produced by boh ypes of firms, and allocaion of invesmen goods o firms locaed a home or abroad. In order o iniiae a new invesmen projec abroad, foreign affiliaes mus disburse a flow cos κ. Thiscosispaidunilheprojecisbrough o fruiion, a ime consuming ask absraced as a search and maching process wih invesmen goods available for allocaion abroad. No such fricion applies o changing producion capaciy a domesic plans locaed in he home economy. 8 Thus domesic firms ren capial on spo markes while foreign affiliaes choose he amoun of new projecs o iniiae. Firms, domesic and foreign, hire labor on compeiive domesic markes. As a maer of noaion, he firs counry is referred o as he "Home" counry and he second as he "Foreign" counry. Throughou, variables relaing o he Foreign economy will be disinguished by an aserisk. For example, k fdi denoes he sock of capial held by foreigners in he "Home" economy while k fdi denoes he sock of capial held by foreigners in he "Foreign" counry, i.e. held by residens of he Home counry. We begin by describing he fricion o allocaing physical capial abroad, domesic and foreign firms, and hen examine he problem faced by he represenaive household in he Home economy, he problem in he Foreign economy being symmerical. 3.1 Underaking a foreign direc invesmen In order o form a uni of capial abroad, a new projec, v,musbeiniiaedaacosofκ by a foreign affiliae. This cos is reminiscen of Gordon and Bovenberg (1996) who assume ha foreign invesors, due o a lack of knowledge of he domesic economy, are a a disad- 8 In fac, he fricionless capial marke is a special case of he search environmen wih κ = 0. This exreme assumpion of no fricion o allocaing invesmen goods o domesic firms a home is made for simpliciy. As long as allocaing invesmen goods abroad is relaively more cosly han he allocaion a home, he resuls go hrough. 10

11 vanage in seing up and running a firm. They capure his idea by assuming ha oupu by foreign firms is reduced by some fixed proporion. Gopinah (2004) assumes ha invesors in emerging markes mus disburse a cos o acquire informaion on invesmen projecs while he lengh of he acquisiion period is subjec o search fricions. Meanwhile, a pool of liquid capial, l, musbemadeavailableobeallocaedabroadoncehe righ locaion has been found. This process of maching new projecs and liquid capial is absraced by a consan reurns o scale maching echnology m(v, l). Denoingθ = l v as a relaive measure of ighness on inernaional capial markes, he probabiliy for a given projec iniiaion of becoming a producive uni of capial in he curren period is given by m(v,l) v = m(1, θ) = P(θ), wih P(θ)/ θ > 0. The equivalen probabiliy for liquid capial is jus m(v,l) l = m(1/θ,1)=q(θ), Q(θ)/ θ < 0. Once in place, a paricular uni of foreign capial faces an probabiliy s of being erminaed. When his occurs he uni of capial reurns o he pool of liquid capial, ne of depreciaion, for reallocaion. As a resul, he oal amoun of liquid capial available for allocaion abroad in he curren period is defined as l = i fdi +(1 δ)sk + u, (1) where u =(1 Q(θ 1 ))l 1 is unmached liquid capial from he previous period carried forward wih no ne reurn, and i fdi capial. are new invesmen goods added o he pool of liquid These assumpions resul in he following law of moion for he sock of foreign capial in he Home economy k fdi fdi +1 =(1 δ)(1 s)k + m(v, l ). (2) For easeof comparison wih he Balance of Paymens, i is useful o rewrie he law of moion as k fdi fdi +1 =(1 δ)k + m(v, l ) (1 δ)sk fdi.theexpressionm(v, l ) corresponds o gross inflows of foreign direc invesmen while (1 δ)sk fdi corresponds o gross ouflows of foreign direc invesmen, he difference being ne flows of inward FDI. The Home economy s direc invesmen abroad is likewise decomposed ino gross ouflows m(v, l ) and gross inflows (1 δ)s k fdi (i.e., reurning from he Foreign counry). 11

12 3.2 Domesic and foreign producers Domesic and foreign firms produce inermediae goods aggregaed ino a final homogeneous consumpion good by an Armingon (1969) aggregaor y = G y d, y fdi ( ) [ ] = φ(y d )ν +(1 φ)(y fdi 1 ) ν ν,wihelasiciyofsubsiuionψ = 1/(1 ν) and relaive shares deerminedby he parameer φ. The relaive price of he foreign firm s good is hen ( ) ( ) simply p fdi = G 2 y d, y fdi and ha of he domesic firm s good p d = G 1 y d, y fdi. Domesic firms produce wih echnology y d = A (n d )1 α (k d )α,where0< α < 1and A denoe oal facor produciviy in he Home counry, hiring bohfacorsofproducion from households on compeiive markes. Opimizaion yields he following wo firs order condiions for he demand of domesic labor and capial (n d ) : w d =(1 α) pd yd n d (k d ) : r d = α pd yd k d ; (3) ; (4) where w d and rd are, respecively, he remuneraions of labor and capial a domesic firms. Foreign firms in he Home economy hire domesic labor, n fdi,andmakecapialadjusmen decisions by choosing he number of new projecs o iniiae, v, wih he producion echnology y fdi = A (n fdi ) 1 α (k fdi ) α.givenallocaionprocessforfdioulineabove,foreign firms face he following dynamic program: [ ) = max J(k fdi n fdi,v p fdi y fdi w fdi n fdi r fdi k fdi κv + βe λ +1 subjec o k fdi fdi +1 =(1 δ)(1 s)k + P(θ )v, λ J(k fdi +1 ) ] where J(k fdi ) is he value of he foreign firm given is curren capial sock, andw fdi r fdi are, respecively, he remuneraions of labor and capial a foreign firms. The foreign λ affiliae uses he sochasic discoun rae is βe +1 λ as all profis are ransferred o he foreign household. Opimizaion yields he following wo firs order condiions: (n fdi ) : w fdi (v ) : =(1 α) p fdi κ P(θ ) = βe n fdi y fdi λ +1 λ J k fdi(k fdi +1 ); and ; (5) 12

13 where J k fdi(k fdi +1 ) is he marginal value of an addiional uni of capial o he firm. While he firs condiion deermining he demand for labor is quie sandard, some inerpreaion of he opimaliy condiion for projec iniiaions is in order. This saes ha, a he margin, he discouned expeced reurn o an addiional uni of capial mus be equal o he average cos of seing i up, κ P(θ ),asheaverageduraionolocaeasupplyofcapial is approximaely he inverse of he probabiliy P(θ). Assuch,hismaybeinerpreedasa projec creaion condiion akin o he job creaion condiion in labor search and maching models. Differeniaing he firm s value funcion, he marginal value of and addiional uni of capial is J k fdi(k fdi +1 fdi p y fdi )=α k fdi r fdi +(1 δ)(1 s)βe λ +1 λ J k fdi(k fdi ). In combinaion wih he firs order condiion for projec iniiaions, his yields he forward looking condiion κ P(θ ) = βe λ +1 λ 3.3 Domesic households {α p fdi y fdi } +1 k fdi r fdi +1 +(1 δ)(1 s) κ P(θ +1 ) +1 Households choose a level of aggregae consumpion of he final homogeneous good, hours o supply o boh domesic and foreign employers, n d and n fdi (6) respecively, and have wo capial invesmen opions: invesing in firms a home, i d,orinvesingincapaciy abroad, i fdi.inaddiion,hereareconvexcosoproducingnewinvesmens goods, domesic and foreign, respecively q d fdi and q. 9 The resuling dynamic program for he represenaive household is hus V(k d, k fdi, u )= max subjec o and c,n d,n fdi,i d,i fdi w d nd + w fdi n fdi [ u(c,1 n )+βe V(k d +1, k fdi +1, u +1 ) ] + r d kd + r fdi k fdi k fdi +1 =(1 δ)(1 s )k fdi + Q(θ )l + Π = c + q d id + q fdi i fdi 9 I is well known (see Backus, Kehoe and Kydland (1992), Baxer andcrucini(1995))hawihouan adjusmen cos o he producion of new capial goods he volailiy of new invesmen would be much oo large in his seing. 13

14 where n = n d + n fdi, Π = p fdi operaing abroad, and i d direc invesmen are defined as i fdi y fdi w fdi n fdi r fdi k fdi κv are profis for firms = k d +1 (1 δ)kd.newinvesmengoodsdesinedforforeign = l (1 δ)s k fdi u,where(1 δ)s k fdi is capial recuperaed from erminaed operaions abroad ne of depreciaion, and u are unis of invesmen goods no ye allocaed. Again, l is herefore he oal amoun of invesmen goodsavailable for allocaion o producion abroad. Finally, under he assumpion ha he cos of adjusing physical capial is governed by he funcion Φ( ij ), asinhayashi(1982), k j 1 his price of capial goods is given by q j [Φ = ( ij )],forj = d, fdi,wihφ ( ) > 0and k j Φ ( ) < 0, and such ha in he seady sae q = 1. Denoing he muliplier on he budge consrain λ,heopimaliycondiionsare (c ) : u c (c,1 n )=λ (7) (n d ) : u n d(c,1 n )=λ w d (8) (n fdi ) : u n fdi(c,1 n )=λ w fdi (9) [ ] (i+1 d ) : λ q d = βe λ +1 r+1 d + qd +1 (1 δ) (10) [ ] (i fdi ) : λ q fdi = βe Q(θ )V k fdi (k d +1, k fdi +1, u +1 )+(1 Q(θ ))V u (k d +1, k fdi +1, u +1 (11) ) The Euler equaion for allocaion of invesmen goods o domesic firms, equaion (10), has he usual inerpreaion of equaing he opporuniy cos of he invesmen, in erms of curren period forgone consumpion, o he expeced reurn ne of depreciaion. The Euler equaion governing foreign invesmen decisions, equaion (11), has a similar inerpreaion. The expeced reurn, however, is an average of he marginalvaluesofmached (V k fdi (k d +1, k fdi +1, u +1 ))andunmached(v u (kd +1, k fdi +1, u +1 ))capial,weighedbyhemaching probabiliy Q(θ ). The marginal values of allocaed and non-allocaed invesmen goods are given by V u (k d, k fdi, u ) = λ q fdi ; [ V k fdi (k d, k fdi, u ) = λ r fdi + q fdi (1 δ)s ] +(1 δ)(1 s )βe V k fdi (k d +1, k fdi +1, u +1). Since unmached liquid capial yields no ne reurn, is marginal value is simply he opporuniy cos of funds. The marginal value of mached capial consiss of he earnings on he uni, r fdi,andhevalueofcapialseparaedforreallocaionneofdepreciaion. The las erm capures he coninuaion value if reallocaion does no occur. 14

15 3.4 Repaymen on foreign capial Each uni of capial allocaed abroad generaes a surplus for he foreign affiliae and he capial lender. The repaymen on capial allocaed abroad is deermined by Nash bargaining over he oal surplus generaed by he relaionship, defined as S V k fdi(k d,k fdi,u ) V u (k d λ,k fdi,u ) r fdi. Thisresulsin hefollowing repaymenrule: 10 = J(k fdi )+ = ηα p fdi y fdi k fdi +(1 η)q fdi δ + η(1 δ)(1 s) κ (12) θ By he firs erm, he repaymen is increasing in he marginal produc of capial. secondermcapures he loss of value due ophysical depreciaion, measured by he price of invesmen goods, he cos of which is spli according o he lender s bargaining weigh η. The long-erm naure of he relaionship is capured by he final erm. I represens he iniiaion coss saved by he firm in he coninued operaion of he uni of capial. By changing he relaive hrea poin of he firm in negoiaions, a rise in κ pus upward pressure on he repaymen. The compeiive equilibrium is a soluion for he quaniies {y, c, n d, n fdi λ, Π, l, u, v, θ },prices{p d, p fdi, w d, w fdi, r d, r fdi, k d, k fdi The, i d, i fdi,, q d, q fdi } and meeing raes {Q(θ ), P(θ )} in he Home and he Foreign counries ha saisfy household, domesic and foreign firm opimizaion, he renal rae is he soluion o he Nash bargaining game, he labor markes clear and he aggregae resource consrain is saisfied. 4 Quaniaiveresuls The model is solved for he raional expecaions equilibrium of he log-linear sysem of equaions wih he algorihm developed by King and Wason (1998). The quaniaive implicaions are evaluaed hrough impulse responses and uncondiional second momens. The resuls for flows of FDI are discussed firs, before looking a aggregae variables and cross-counry correlaions. In all insances he resuls are conrased wih hose for a sandard IRBC wih invesmen adjusmen coss. 11 The robusness of he resuls is examined 10 The appendix provides deails on he derivaion of his repaymen rule. 11 The deails hese models are presened in he appendix. I is imporan o noe ha he firs corresponds o he search model wihou allocaion fricions, i.e. a model wih κ = 0. 15

16 in an exension in which he rae of separaion of capial from i suseabroadisendogenized. 4.1 Shocks and calibraion Exracion of a Solow Residual. The underlying exogenous processes for echnology, as in Backus, Kehoe and Kydland (1992), is assumed saionary and o follow a VAR(1) process wih possible cross-counry spill-overs. Parameer esimaes are obained by exracing Solow residuals for he Canadian and U.S. economies and hen esimaing he following bivariae VAR(1): Acan A us = ρ c ρ c,us ρ us,c ρ us Acan 1 A us 1 + ecan e us The resuls of he esimaion are presened below for he period 1976:1-2005:4. As is usual in his sor of esimaion, he persisence parameer is very high. Also, as can be gleaned from he covariance marix, Canadian and U.S. innovaions o he exogenous process for echnology are posiively correlaed. In a subsecion below, he sensiiviy of he quaniaive resuls o he specificaion of he exogenous process for echnology will be examined. ρ c ρ c,us = Residuals Covariance marix : ρ us,c ρ us Paramerizaion and calibraion Time periods are considered o be quarers, and he discoun facor is se o β = 0.99, corresponding o an average annual real yield on a risk-less bond of 4.1%. Preferences are separable in consumpion and leisure, and ake he form u(c,1 n )=log(c )+ ϖ(1 n ) 1 ξ 1 ξ. The parameer ϖ is fixed such ha he average fracion of oal hours worked equals n = 0.2. Togeher wih ξ = 4hisresulsinaFrischelasiciyoflaborsupplyof1.Furhermore, he share domesic goods in he producion of he final good, φ, is se such as o equalize he wage across secors in he seady sae. The share of capial in he producion funcion is se o α = 1/3, and he rae of depreciaion of capial o δ = 0.025, which corresponds o an annual decline of he producive use of capial of 10%. The elasiciy of he invesmen 16

17 adjusmen cos is 0.025, wihin a range of values used in differen sudies (e.g., Baxer and Crucini, 1995, Ambler, Cardia and Zimmermann, 2002, and Baxer and Farr, 2005). Finally, he parameer ν in he Armingon aggregaor is chosen such ha ha he seady sae equilibrium hours worked in he foreign secor are 1/4 of oal hours, which is in he range of employmen shares repored earlier, and implies anelasiciyofsubsiuion beween he foreign and domesic firms goods of approximaely1.5. To calibrae parameers relaive o foreign direc invesmen, i is useful o le he heory shed some ligh on he daa. Recall he foreign capial accumulaion equaion k fdi fdi +1 =(1 δ)k + inflow ouflow. As he Balance of Paymens provides informaion on foreign direc invesmen gross inflows and ouflows, given a rae of capial depreciaion one can compue he implied foreign capial sock in he hos economy, using he seady saeproperyk fdi = [inflow ouflow] /δ o iniiae he capial sock. I is hen possible, using he ime series on ouflows, o obain aimeseriesforhereallocaionraeas s = ouflow (1 δ)k fdi, resuling in a mean rae of s = , which we use o se he value of he exogenous separaion rae, and an H.-P. filered sandard deviaion relaive o oupu of 1.45 and conemporaneous correlaion wih oupu of The laer informaion will be used for he calibraion o endogenous capial reallocaion. Nex i is assumed ha i akes on average a lile more han a quarer before liquid capial is allocaed and becomes producive, i.e. Q(θ) =0.75 in seady sae, and we se he household s bargaining weigh o η = 0.5, in he mid-range of possible values. 12 The final parameer lef o calibrae is he elasiciy of he maching funcion, which is of he form m(v, l )=χ(v ) ɛ (l ) 1 ɛ.thisparameeronlyinfluenceshedynamicsofhemodel bu does no affec he seady sae as he value of he level parameer χ is chosen o mach he arge meeing rae Q(θ). The baseline simulaion ses ɛ = 0.8, he reason for which 12 As i is well know ha he resuls of he search and maching model of equilibrium unemploymen are sensiive o he value of his parameer (see Hagedorn and Manovskii, 2008), a series of sensiiviy es will be performed below. 17

18 Panel A % deviaion from seady sae Ne flows of FDI search in FDI Ne inward flows Ne ouward flows Periods % deviaion from seady sae Panel B Ne flows of FDI IRBC Periods Figure 2: IRFs o a posiive "Home" sourced echnology shock will be apparen in he exensiono endogenouscapial reallocaion. A sensiiviy analysis of resuls o variaions in hese parameers is performed below. Wih hese calibraions here is sufficien informaion o endogenously deermine he remaining seady sae variable and parameers (i.e. θ, κ, σ) suchhahesysemofseady sae equaions is saisfied. The resuling long-run raios of ineresarehefollowing: he consumpion-oupu raio equals 76.52% in line wih King and Rebelo (1999); he labor share of income amouns o 0.67, which lies in he range repored by Gollin (2002); Furhermore, his calibraion implies ha he seady sae raio of nefdioaggregaeinvesmen is 23%, ha he average iniiaion cos relaive o oupu equals vκ/y fdi = 1%. 4.2 Flows of foreign direc invesmen Figure 2 plos he impulse responses o a posiive echnologyshockinhehomeeconomy of ne inward and ouward foreign direc invesmen for ha expanding economy. The significan difference beween he responses of he proposed model (Panel A) and an IRBC model (Panel B), beyond heir magniude, is he behavior of ne ouward flows (see circled line of panels A and B). In he search model, ouward flows drop progressively, whereas in he sandard model he drop occurs on impac, generaing he posiive cyclical correlaion of inward and ouward flows ha is a characerisic of he daa. To deail he response of ne ouward direc invesmen flows,iisusefulorecallis definiion as he difference beween gross ouflows and gross inflows from he Home o 18

19 he Foreign economy: Ne ouward : l Q(θ ) (1 δ)s k fdi The iniial response of ne ouward FDI is deermined by ha of he gross ouflow, l Q(θ ), as k fdi is predeermined. As he opporuniy cos of capial abroad increases, households diminish heir pool of liquid capial l, shifing resources o domesic firms, which leads o a decline in he Home counry s pool of capial available for invesmen abroad, l.this is he only source of change in ne ouflows in he model wihou allocaion fricions,and herefore he drop in ouward FDI is immediae. When allocaion fricions are presen, however, he decline in he pool of liquid capial is larger han he iniial decline in projec iniiaions a foreign affiliaes for wo periods afer he shock, leading o a shor lived increase in he capial allocaion probabiliy Q(θ ).13 This reducion in marke congesion couners he drop in l upon impac, and is seen in he mued iniial decline in new allocaions abroad. As he easing of congesion in allocaion Q(θ ) dissipaes hereafer, new allocaions of FDI decline, reaching heir lowes 3 quarersfollowingheshock. Table 4 presens uncondiional second momens for flows of foreign direc invesmen in he daa and generaed by he compeing models. The sandard IRBC model, for he reasons jus oulined, generaes a srong negaive conemporaneous correlaion beween ne inflows and ouflows of FDI of The proposed model is a subsanial improvemen, almos perfecly maching he daa wih a conemporaneous correlaion of 0.25 compared o 0.27 in he daa. Thus he model is able o replicae he fachaperiodsofincreasedne invesmen abroad are also characerized by increased ne inflow of foreign invesmen. Inhe daa, he relaive volailiy of nefdi ouflowsand inflows is approximaely wo hirds, and ne ouflows are as procyclical as ne inflows. The sandard IRBC model fails on boh hese couns. The raio of H.-P. filered sandard deviaions is only 0.37, and he correlaion of ne ouflows wih he source counry s business cycle is srongly negaive a -0.55, while he correlaion of ne inflows is oo high a On he oher hand, he proposed model of search in FDI performs well wih respec o he relaive volailiy of ne inflows and ouflows, he raio being 0.67 compared o 0.62 in he daa. However, while 13 Kurmann and Perosky-Nadeau (2008) show ha under relaively weak condiions, if preferences are addiive and concave in consumpion for example, ha congesionon he invesmen markewill be increasing in he expeced growh rae of he marginal uiliy of consumpion. 19

20 Table 4: 2nd momens for flows of foreign direc invesmen 1976:1-2005:4 Canadian daa Search in FDI IRBC wih FDI a b a b a b Ne inflow of FDI Ne ouflow FDI c d c d c d Ne ouward / Ne inward FDI a: Sandard deviaion relaive o oupu; b: Conemporaneous correlaion wih oupu; c: Raio of ouward o inward FDI flow sandard deviaions; d: conemporaneous corr., inward-ouward ne flows. All momens are Hodrick-Presco filered. he model raises he correlaion of ne ouflows wih he domesic business cycle, under he presen calibraion i is insufficien o be consisen wih he daa. 4.3 Robusness of resuls Firs, given he lack of direc evidence on he mean allocaion rae Q(θ), heeffecsofis variaion on he main resuls, along wih he consequence of varying he mean reallocaion rae s, arepresenedintable5. Inaddiion,heresulsareexamined wih respec o he bargaining weigh η, as he work of Hagedorn and Manovskii (2008) has shown ha he dynamics of search unemploymen models are sensiive o his parameer. Second,we explore he imporance of he specificaion of he exogenous echnological process, and hird of endogenizing he reallocaion probabiliy s Sensiiviy o search parameers Beginning wih he mean allocaion rae, is principle effec is o change he relaive sandard deviaion of ne foreign direc invesmen flows. The change o he correlaion beween ne inward and ouward flows of FDI when decreasing he degree of congesion in he allocaion of capial abroad (i.e., increasing he mean Q(θ)) beweenapproximaelya year and a half and jus over a quarer is virually no noiceable. 20

21 Table 5: Sensiiviy o search parameers and calibraion Baseline s = 0.04 s = 0.08 Q(θ) =0.65 Q(θ) =0.85 η = 0.1 σ(ne in f low)/σ(y) corr(inflow, Y) σ(ne ou f low)/σ(y) corr(ouf low,y) σ(ne ou f low)/σ(ne in f low) corr(inflow, ouf low) All momens are Hodrick-Presco filered. As he mean rae s may be affeced by he iniial foreign capial sock used in is impuaion, i is reassuring ha he resuls are very robus o changes in is average value. The volailiy of ne inward FDI and he relaive volailiy of ne inward and ouward flows change lile. The main effec is o increase he correlaion beweeninwardandouward flow, from 0.15, when s = 0.04, o 0.31, when s = Reducing he lender s bargaining weigh from 0.5 o 0.1 reduces he relaive volailiy of ne inward foreign invesmen from o This occurs because, for lower values of he bargaining weigh, he expeced benefi of a new uni of capial allocaed abroad is less elasic o changes in produciviy. I also has he effec of reducing boh he relaive volailiy of ne inward o ouward invesmen and he correlaion beween boh flows, suggesing ha he model is a beer fi of he daa wih a higher bargainingweigh,wih he excepion of he relaive volailiy of ne inward invesmen Sensiiviy o he specificaion of he echnological process An alernaive specificaion of he exogenous process for echnology cus off cross-counry spill-overs while fixing idenical persisence parameers: ρ c ρ c,us ρ us,c ρ us = Covariance marix :

22 Table 6: Sensiiviy o he specificaion of exogenous processandendogenousseparaion Search in FDI IRBC wih FDI Search in FDI baseline no spillovers no spillovers End. Sep. a b a b a b a b Ne inflows of FDI Ne ouflows of FDI Ne ouflows / c d c d c d c d Ne inflows FDI a: Sandard deviaion relaive o oupu; b: Conemporaneous correlaion wih oupu; c: Raio of ouward o inward FDI flow sandard deviaions; d: conemporaneous corr., inward-ouward ne flows. All momens are Hodrick-Presco filered. The resuls for such a specificaion are presened in Table 6. Changing he specificaion of he exogenous process has lile effec on he relaive volailiies of ne inward and ouward flows of FDI, bu increases he conemporaneous correlaion of ne invesmen abroad wih he domesic business cycle in all models. In paricular, hecorrelaionofneouflowswih he domesic business cycle increases o 0.24, compared o 0.4 in he daa. The raio of volailiies of inward and ouward flows hardly changes excep in he IRBC model, for which he raio becomes close o he daa. However, heconemporaneous correlaion of ne inward of ouward flows remains srongly negaive, a -0.31, while for he proposed model i remains close o he daa Exension o endogenous capial reallocaion I has so far been assumed ha capial allocaed o foreign producion is reallocaed every period a a consan rae s which is independen of economic condiions. I is likely ha he opporuniy cos of mainaining hose unis in place dependsonhereurnsfromalernaive opporuniies ha evolve over he business cycle. We exam he implicaions of his for he main resuls by endogenizing he separaion, or reallocaion, rae s. As in Morensen and Pissarides (1994) for he labor marke, we assume he exisence of mach specific ran- 22

23 dom idiosyncraic produciviy shocks. Denoe mach produciviy as a > 0, where a is independenly disribued over ime wih probabiliy densiy h(a), cumulaivedensiyh(a) and mean E(a) =1, and follows a log normal disribuion log(a) N( σ2 log(a) 2, σ 2 log(a) ).The surplus generaed by he relaionship beween a foreign affiliae and he capial lender (i.e. he household) is an increasing funcion of his shock, S(a ).Thushereisareservaion sraegy for boh paries who, once he shock is observed, disconinue he mach for realizaions of a < a,wherea is defined as S(a )=0andheseparaionraeiss = H(a ). Using a resul of Nash bargaining, he separaion hreshold is defined by 14 r fdi a α p fdi y fdi k fdi κ (1 δ)(1 s ) P(θ ) = 0 (13) In effec, he mach is disconinued if he realized marginal producofcapiala α p fdi y fdi k fdi plus he search cos saved by mainaining he curren uni of capial is inferior o he negoiaed repaymen. An increase in he average search cos κ P(θ ),forexample,byincreasing he opporuniy cos of exiing he mach, lowers he separaion probabiliy. In order o close his exended model, an insurance mechanism funded ou of profis from coninuing relaionships is assumed o insure ha, ex-pos, he household receives he full ex-ane reurn o foreign capial, and ha he full wage bill and coss of projec iniiaions are covered. 15 Thus aggregae profis reurned o he household are Π = a [ + a 0 ap fdi [ Π = p fdi y fdi y fdi ap fdi y fdi w fdi n fdi w fdi n fdi w fdi n fdi ] r fdi k fdi κv dh(a) ] r fdi k fdi κv dh(a) r fdi k fdi κv (14) The calibraion involves choosing he elasiciy of he maching funcion, ɛ. This parameer is seleced such ha he relaive volailiy of he reallocaion rae s is close o he daa, which is achieved for ɛ = 0.8. The sandard deviaion of he idiosyncraic produciviy shock is equal o σ a = 0.27 such ha he seady sae separaion rae equals See appendix for deails. 15 Gordon and Bovenberg (1996) use a similar assumpion abou he realizaion of an idiosyncraic produciviy shock, and use he law of large numbers o argue ha hereisnoaggregaeuncerainy. Here,an insurance funded ou of aggregae profis is used o address he issue. 23

24 % Deviaion from seady sae Foreign counry separaion rae Periods Figure 3: IRF of he separaion rae s o a Home counry posiive echnology shock. As repored in Table 6, endogenous reallocaion of capial already abroad increases he correlaion beween inflows and ouflows even furher. Figure 3 shows ha a posiive innovaion in he Home counry causes he reallocaion rae in he foreign counry o drop, reducing he gross flow (1 δ)s k fdi on impac. This drop pulls ne ouward flows from he Home o he Foreign counry upward such ha, on impac, ne ouward flows change very lile. Thus he key o undersanding he response of ne foreign direc invesmen flows are he ime-varying congesion, and o a lesser exen reallocaion raes, effecs ha are absen in he sandard model of inernaional business cycles. 4.4 Aggregae variables Figure 4 plos he impulse responses of oupu, hours and capial, a domesic firms, foreign firms and in he aggregae, o a Home sourced posiive echnology shock. Panel A presens resuls for he proposed search model wih endogenous reallocaion, while Panel BreporsresulsforheIRBCmodel. The firs observaion is ha he responses of aggregae variables are quie similar for boh models. The differences arise in he response of foreign firms when invesing in capaciy abroad is subjec o a ime consuming search process. On impac, hours a foreign firms rise more han a domesic firms in boh models. However, he ensuingaddiional increase in hours a foreign firms is more pronounced in he proposed model, and sems from he differen capial sock dynamics: he sock of foreign capial rises more quickly hen in he sandard case, pushing he labor demand of foreignesablishmensupfurher. In boh models, hours a foreign firms are more volaile han a domesic firms over he business cycle, which is suppored by recen empirical evidence from Europe. Checchi e 24

25 Panel A 2 Deviaion from seady sae Oupu Periods Panel B 1.5 Deviaion from seady sae Oupu Periods Deviaion from seady sae Deviaion from seady sae Hours Periods Hours Periods Deviaion from seady sae Deviaion from seady sae Capial Domesic variables 0 Foreign variables Aggregae Periods Capial Domesic variables 0 Foreign variables Aggregae Periods Figure 4: IRFs o a posiive "Home" counry echnology shock al. (2003) find ha foreign conrolled firms end o make larger and more frequen employmen adjusmens. However, here is no direc evidence of sysemaic differences in he response of hours o he business cycle. Table 7 presens he 2nd momens of prominen macroeconomic variables for he hree models and he daa. Boh in erms of sandard deviaions and correlaions wih oupu, all hree models are similar in being close o he daa, wih he well known excepion of he volailiy of hours. Thus, he abiliy of he model o generae high volailiy in flows of FDI does no come a he expense of creaing oo much volailiy in aggregae invesmen. A well know deficiency of sandard IRBC models, he quaniy problem, concerns he ordering of cross counry correlaions of consumpion, oupu, invesmen and hours. The problem of he ordering of consumpion and oupu cross correlaions is he mos known of he quaniy problems, as raised in he work of Backus, Kehoe and Kydland (1995), while he shorcomings relaed o he cross correlaion of hours and invesmen have been raised in papers such as Ambler, Cardia and Zimmermann (2004). Table 7showsheperformance of he search in FDI model wih his respec. All models ge he orderingofhigheroupu han consumpion cross-correlaions righ, alhough he cross-correlaion of consumpion is lower han in he daa, and he hree models perform quie well wih respec o he labor marke. This is due, essenially, o he correlaion srucure o innovaions and he presence of invesmen adjusmen coss. This was firs poined ou by Backus, Kehoe and Kydland 25

26 Table 7: 2nd momens for prominen macro variables 1976:1-2005:4 Canadian daa Search in FDI model IRBC wih FDI Endogenous reall. Exogenous reall. a b c a b c a b c a b c Consumpion Hours Invesmen Oupu :sandarddeviaions;a:sandarddeviaionrelaiveooupu; b: Conemporaneous correlaion wih oupu c: cross counry conemporaneous correlaions. All momens arehodrick-prescofilered (1992), bu made more explici in Baxer and Crucini (1995). However, where aggregae invesmen is concerned, he cross-correlaion is posiive inhemodelswihsearchfric- ions in foreign direc invesmen, while an IRBC model wih invesmen adjusmen coss generaes a negaive correlaion. The role of foreign direc invesmenincorrecinghis correlaion is clear when he aggregae invesmen is seen as hesumofinvesmenindomesic and foreign firms. Driving he poin furher, raising he size of he foreign secor (as a fracion of oal hours) from one quarer o one half, raises he cross-counry correlaion of aggregae invesmen from 0.13 o 0.20 in he model wih search in FDI, while he correlaion is reduced from o in he sandard IRBC model. 5 Conclusion Acommonlyusedmeasureofheraeawhichforeignersgainconrol over a domesic economy, flows of foreign direc invesmen (FDI), represenincreasinglyimporanshare of aggregae invesmen in indusrialized economies as hey furherinegrae. Givenhe imporance of he foreign secor for aggregae oucomes and he relaively high volailiy of direc invesmen flows, quaniaive models of open economies need o be consisen wih heir dynamics. As his paper has shown, a combinaion of fricions in he allocaion of physical capi- 26