A Solution to Two Paradoxes of International Capital Flows

Transcription

1 7TH JACQUES POLAK ANNUAL RESEARCH CONFERENCE NOVEMBER 9-10, 2006 A Soluton to Two Paradoxes of Internatonal Captal Flows Jandong Ju Unversty of Oklahoma Shang-Jn We Internatonal Monetary Fund Paper presented at the 7th Jacques Polak Annual Research Conference Hosted by the Internatonal Monetary Fund Washngton, DC November 9-10, 2006 The vews expressed n ths paper are those of the author(s) only, and the presence of them, or of lnks to them, on the IMF webste does not mply that the IMF, ts Executve Board, or ts management endorses or shares the vews expressed n the paper.

2 A Soluton to Two Paradoxes of Internatonal Captal Flows Jandong Ju and Shang-Jn We August, 2006 Abstract Internatonal captal ows from rch to poor countres can be regarded as ether too small (the Lucas paradox n a one-sector model) or too large (when compared wth the logc of factor prce equalzaton n a two-sector model). To resolve the paradoxes, we ntroduce a non-neo-classcal model whch features nancal contracts and rm heterogenety. In our model, free trade n goods does not mply equal returns to captal across countres. In addton, rch patterns of gross captal ows emerge as a functon of nancal and property rghts nsttutons. A poor country wth an ne cent nancal system may smultaneously experence an out ow of nancal captal but an n ow of FDI, resultng n a small net ow. In comparson, a country wth a low captal-to-labor rato but a hgh rsk of expropraton may experence out ow of nancal captal wthout compensatng n ow of FDI. Keywords: Captal Bypass Crculaton, Expropraton Rsk, Gross Captal Flow, Heterogeneous Entrepreneurs, Fnancal Development JEL Class caton Numbers: F11, F21, and F33 Unversty of Oklahoma, E-mal: jdju@ou.edu; **Internatonal Monetary Fund and NBER, E-mal: swe@mf.org, Web page: We are grateful to Chrstan Broda, Jngqng Cha, Fabo Ghron, Pere-Olver Gournchas, Kevn Grer, Kala Krshna, Maurce Obstfeld, Arvnd Panagarya, Roman Rancer, Kenneth Rogo and semnar/conference partcpants at the NBER Summer Insttute, the Econometrc Socety Far Eastern Meetng, IMF, Graduate Insttute of Internatonal Studes (Geneva), and Unversty of Maryland for helpful dscussons. All remanng errors are our own. 0

3 1 Introducton The paper has two objectves. Frst, t proposes a model wth an am to resolve two opposng paradoxes regardng nternatonal captal ows. Second, t provdes a framework to study the role of nancal and property rghts nsttutons n determnng patterns of captal ows. In partcular, t suggests a novel explanaton for two-way captal ows (smultaneous out ows and n ows of captal) one observes for some countres: to bypass the ne cent nancal systems n these countres that otherwse have low captal-to-labor ratos. Whle cross-border captal ows worldwde have rsen substantally, reachng nearly $6 trllon n 2004, less than 10 percent of them go to developng countres. Lucas (1990) famously ponted out that, relatve to the mpled d erence n the margnal returns to captal between rch and poor countres n a one-sector model, t s a paradox that not more captal goes from rch to poor countres (the paradox of too small ows). The Lucas paradox could be turned on ts head n a two-sector, two-factor, neoclasscal trade model. A well-known result n such a model s factor prce equalzaton (FPE): wth free trade n goods, returns to factors are equalzed between countres even wthout factor moblty. In other words, a small frcton to captal moblty can completely stop cross border captal ows. Gven ths, any amount of observed captal ows s excessve (the paradox of too large captal ows). A number of solutons to the Lucas paradox have been proposed n the lterature. We wll argue that most such explanatons cannot escape from the tyranny of the FPE when generalzed to a two-sector, two-factor model. Smlarly, whle a number of reasons have been proposed to explan why FPE does not hold, we wll argue that most do not smultaneously resolve the Lucas paradox. We argue that t s useful to thnk outsde the neoclasscal box and propose a new mcro-founded theory to understand goods trade and factor moblty. We ntroduce a nancal contract model followng Holmstrom and Trole (1998) and 1

4 heterogeneous rms nto the Heckscher-Ohln-Samuelson framework. A key feature of the new theory s that the return to nancal nvestment s generally not the same as the return to physcal nvestment. Fnancal nvestors (or savers) obtan only a slce of the return to physcal captal, as they have to share the return to captal wth entrepreneurs. The more developed a nancal system s, the greater the slce that goes to the nvestors. As an mplcaton, a poor country wth an ne cent nancal sector may experence a large out ow of nancal captal, but together wth nward foregn drect nvestment (FDI), resultng n a small net n ow. Besdes nancal development, our model also ncorporates property rghts protecton as another nsttuton. Countres wth poor property rghts protecton (hgh expropraton rsk) may very well experence an out ow of nancal captal wthout a compensatng n ow of FDI. To break FPE, one needs to show that factor prces are determned by varables n addton to product prces. One way to do t s to assume that the producton functon s decreasng return to scale (DRS) (e.g., Kraay and others, 2005; and Wynne, 2005). Whle ths assumpton may be approprate n the short run, t s hard to explan why rms cannot adjust ther factor usage n the long run. In our model, we retan constant returns to scale at the rm level but endogenously generate decreasng returns to scale at a sector level. Spec cally, entrepreneurs are assumed to be heterogeneous n ther ablty to manage captal. As a sector expands, more entrepreneurs enter and the ablty of the margnal entrepreneur declnes and so does the return to nvestment at the sector level. Although free trade n goods equalzes product prces, factor returns reman d erent across countres. Other thngs equal, the nterest rate s lower and the wage rate s hgher n the captal-abundant country. In other words, our two-sector model restores these results from a typcal one-sector model (but stll predcts a small net captal ow between rch and poor countres). Whle many papers n the lterature have emphaszed rsk sharng as a motve for nternatonal captal ow, our model delberately avods ths by assumng that 2

5 all entrepreneurs and nancal nvestors are rsk-neutral. Addng rsk-sharng would enrch patterns of captal ow but would not lkely undo the basc mechansms n ths model. Even wthout a rsk sharng motve, our model can generate two-way gross captal ows. For example, consderng the case n whch the expropraton rsk s dentcal across countres, entrepreneurs are perfectly moble, but nancal sector e cency s uneven across countres, the paper shows that the unque equlbrum n the world captal market s one n whch the less developed nancal system s completely bypassed by nancal nvestors and entrepreneurs. The country wth the less developed nancal system may experence a complete exodus of ts savngs n the form of nancal captal out ow to the country wth a better nancal system, but see n ow of FDI from the other country. Whle the lterature sometmes lumps together varous types of nsttutons, nancal and property rghts nsttutons play very d erent roles n ths model. Whereas an ne cent nancal system can be bypassed, hgh expropraton rsk cannot be. Indeed, f rsk of expropraton d ers across countres, there may not be a complete bypass of the ne cent nancal system ether. Fnancal captal stll leaves the country wth an ne cent nancal system, but FDI may be deterred by a hgh expropraton rsk n spte of a low labor cost n the country. In equlbrum, we show that the wage rate s always hgher n the country wth better nancal or property rghts nsttutons, rrespectve of the country s ntal endowment. Ths paper s related to the theoretcal lterature that nvestgates the e ects on captal ows of nancal market mperfecton. Gertler and Rogo (1990) show that a moral hazard problem between foregn nvestors and domestc entrepreneurs may cause captal ow from poor to rch countres. Gordon and Bovenberg (1996) develop a model wth asymmetrc nformaton between countres that explans possble d erences n the real nterest rates. Shlefer and Wolfenzon (2002) show that a country wth better nvestor protecton has a hgher nterest rate. Matsuyama (2004, 2005) and Aok, Bengno, and Kyotak (2006) study the e ect of credt market 3

6 constrant on captal ows. Stulz (2005) develops a model of agency problems of government and entrepreneurs that lmt nancal globalzaton. Caballero, Farh, and Gournchas (2005) show that lower capacty to generate nancal assets reduces the nterest rate. Our theory d ers from these papers n three ways. Frst, all of the above papers use a one-sector model, whose predcton on captal ows does not generally survve an extenson to a two-sector, two-factor model. Second, our model endogenously generates two-way gross captal ows wth a small net ow. 1 Thrd, our model s the rst n the lterature that studes possble contrastng e ects of nancal development and expropraton rsk on captal ow. Obstfeld and Rogo (1997, p 438) and Ventura (1997) have already ponted out that the senstvty of the nterest rate to the captal-labor rato s a specal feature of the one-sector model. They do not, however, develop a new two-sector model that breaks the factor prce equalzaton, and therefore, do not explan why some captal would ow nternatonally n a mult-sector model. Our model features heterogeneous entrepreneurs, whch s somewhat related to the models of heterogeneous rms n the nternatonal trade lterature. Meltz (2003) develops a monopolstc competton model wth heterogeneous rms. Bernard, Reddng, and Schott (2005) ncorporate rm heterogenety and product varety nto an HO framework and mantan the factor prce equalzaton. Ghron and Meltz (2005) study trade and macroeconomc dynamcs wth heterogeneous rms. To the best of our knowledge, our model s the rst that studes the e ect of rm (entrepreneur) heterogenety on nternatonal captal ows n a two-sector, two-factor framework. 2 The rest of paper s organzed as follows. Secton 2 examnes the two paradoxes 1 Caballero, Farh, and Gournchas (2005) have as an extenson of the model that ncludes multple sectors. Ther purpose s to study the e ect of exchange rate adjustment. Factor allocaton across sectors and therefore possble factor prce equalzaton across countres are not studed n ther paper. Whle they also allow for two-way gross ows, ts mcro-foundaton, however, s not developed. 2 Frms entry and ext are studed n Ghron and Meltz (2005). Interpretng a new rm as one unt of captal, Ghron and Meltz (2005) model can be extended to nternatonal captal ows. 4

7 of captal ows wthn the con ne of a neoclasscal framework, though a detaled dscusson of the lterature s relegated to Appendx A. Secton 3 sets up our model. Sectons 4 and 5 study the aggregaton and equlbrum condtons, and some key comparatve statcs, respectvely. Secton 6 analyzes d erent forms of nternatonal captal ow under free trade n goods. Secton 7 concludes. Appendx B provdes the formal proofs for the propostons n the text and a table of the notatons, and a set of gures. 2 Paradoxes of Internatonal Captal Flows In ths secton we examne return to captal n standard neoclasscal models. The producton functons generate constant returns to scale, and rms are perfectly compettve. We begn wth a one-sector model before movng to a two-sector model. 2.1 The Lucas Paradox of Too Small Captal Flows Usng a one-sector model, Lucas (1990) suggested that t was a paradox that more captal does not ow from rch to poor countres. Hs reasonng goes as follows. Let y = f(l; K) be the producton functon where y s the output produced usng labor L and captal K: Let p be the prce of goods, and w and r be returns to labor and captal, respectvely. Frm s pro t maxmzaton problem gves r = p@f(l; K)=@K = p@f(1; K=L)=@K (1) Wth free trade, the prce of goods s equalzed across countres. The Law of Dmnshng Margnal Product mples that r s hgher n the country wth lower per capta captal. As an llustraton, Lucas calculated that the return to captal n Inda should be 58 tmes as hgh as that n the Unted States. Facng a return d erental of ths magntude, Lucas argued, we should observe massve captal ows from rch to poor countres. That t does not happen has come to be known as the 5

8 Lucas paradox. 2.2 The Opposte Paradox of Too Large Captal Flows The logc of the Lucas paradox can be turned on ts head n a mult-sector model. Spec cally, n a standard Heckscher-Ohln-Samuelson two goods, two factors, and two countres model, rms earn zero pro t. So we must have: p 1 = c 1 (w; r) and p 2 = c 2 (w; r) (2) where c(:) s the unt cost functon and subscrpts represent sectors. Comparng to the one-sector model, now r = (1; K =L )=@K = (1; a K =a L )=@K; for = 1; 2 (3) where a K =a L (w;r)=@w s captal-labor rato per unt of producton. For gven product prces, the wage rate w and the nterest rate r; and therefore a K =a L ; are determned and ndependent from factor endowments L and K the well-known factor prce nsenstvty (Leamer, 1995). Increases n K change the composton of outputs: more captal-ntensve goods and less labor-ntensve goods, wll be produced, but the margnal return to physcal captal n each sector stays unchanged. Free trade equalzes product prces, and therefore equalzes the return to factors across countres, even n the absence of nternatonal factor movements. Ths result was rst proved by Samuelson (1948, 1949) and has come to be known as the Factor Prce Equalzaton Theorem (FPE). Countres ndrectly export ther abundant factors through trade n goods. The captal ow s completely substtuted by goods trade. There s no ncentve for any amount of captal to ow between countres once there s free trade n goods. One mght thnk that the assumptons needed for FPE are surely too restrctve to be realstc and are not lkely to hold once one goes beyond the

9 model. Deardo (1994) derves a necessary condton of the FPE, known as the lens condton n a n goods, m factors, and H countres model. The condton has also been proved to be su cent n a model of n goods, 2 factors, and H countres by Xang (2001). 3 In Appendx A, we o er an ntutve verson of su cent condton of FPE, labelled as chan rule of FPE. As we wll see, such a condton s relatvely weak. A number of solutons to the Lucas paradox have been proposed n the lterature: () thnkng of a worker n a rch country as e ectvely equvalent to multple workers n a poor country, () addng human captal as a new factor of producton, and () allowng for soveregn rsk. We wll argue n Appendx A that none of these explanatons can escape from the tyranny of the FPE. On the other hand, whle the FPE can be relaxed n a number of ways, we argue n Appendx A that very few of them mply a pattern of captal ows that resolves the Lucas paradox. Both the Lucas paradox and FPE rely on the assumpton that margnal product of physcal captal determnes captal ow. 4 In general, however, the return to nancal nvestment and the return to physcal captal do not have to be the same. By ntroducng a nancal contract between entrepreneurs and nvestors, together wth heterogeneous rms nto the HOS framework, our model predcts that the nterest rate s determned by both factor endowments and nsttutons, whle the wage rate s hgher n the country wth a more e cent nancal system or better property rghts protecton. 3 The Model The model embeds two non-neo-classcal twsts n an otherwse standard neo-classcal two-sector, two-factor, and two-country setup. The two twsts are nancal contracts 3 For a recent dscusson on the lens condton and addtonal lterature revew, readers are guded to Bernard, Robertson and Schott (2004). 4 Ths vew s common n the lterature. In models wthout rsk, Ventura (2003, p. 488) states that the rule s: nvest your wealth n domestc captal untl ts margnal product equals the world nterest rate. 7

10 between nvestors and entrepreneurs a la Holmstrom and Trole (1998), and entrepreneurs heterogenety. 3.1 Basc Setup We start from a sngle country economy. To capture the dea that rms generally need outsde nancng, we assume that each entrepreneur s endowed wth one unt of captal but has to rase the rest of the funds from other nvestors. The nal output depends n part on the entrepreneur s level of e ort, whch s not observable by the nvestors. Due to ths moral hazard problem, a porton of the revenue per unt of nvestment must be pad to the entrepreneur to nduce her e ort. The producton process s assumed to take two perods. After an ntal nvestment, a stochastc lqudty shock hts n the form of an addtonal amount of resource requred for the rm to contnue to operate. In an optmal nancal contract, the entrepreneur maxmzes the net return to her captal endowment by choosng an amount of ntal nvestment, a project contnuaton rule for every realzaton of the lqudty shock, and a compensaton to the entrepreneur that would nduce her to exert a hgh level of e ort. Let each rm have a stochastc technology. The rst perod producton functon of ndustry s y 1 = G (L 1 ; K1 ) ( = 1; 2), where the superscrpt 1 denotes date 1. The labor-captal rato, L 1 =K1 ; s assumed to be xed and denoted by a : The wage rate and the nterest rate are denoted by w and r, respectvely. The tmng of events s descrbed n Fgure 1. There are K amount of captalsts n the economy. Each captalst s assumed to be born wth 1 unt of captal and an ndex n, whch determnes her cost of e ort and s observable. She can choose to become ether an entrepreneur or a nancal nvestor at the the begnnng of date 1: If she chooses to be an entrepreneur, she would manage one project, nvestng her 1 unt of captal (labeled as nternal captal) and rasng K X1 n amount of external captal from nancal nvestors. The total ntal nvestment n the rm s the sum 8

11 of nternal and external captal, or Kn 1 = 1 + KX1 n, whch s njected to the rm at date 1. Correspondngly, a K 1 n amount of labor s hred. At the begnnng of date 2; a lqudty shock occurs. An addtonal and uncertan amount K 1 n > 0 of nancng s needed to cover operatng expendtures and other needs. The lqudty shock per unt of captal,, s dstrbuted accordng to a cumulatve dstrbuton functon F () wth a densty functon f (): The rm (entrepreneur) then makes a decson on whether to contnue or abandon the project. If K 1 n s pad, the project contnues and output G (a ; 1)Kn 1 wll be produced at the end of date 2. In the process, a Kn 1 amount of addtonal labor s hred, whch s pad as a part of the addtonal nancng. 5 If K 1 n s not pad, however, the project s termnated and yelds no output. The faled projects are then lqudated and factors are reallocated. Investment n the rm s subject to a moral hazard problem. The utlty for entrepreneur n 1 of managng one unt of captal n sector s de ned as V n (e) = (e)r E n c n (e) (4) where e denotes the level of e ort whch takes a bnary value of ether hgh, e H (work), or low, e L (shrk). R E n s what the entrepreneur gets from managng one unt of captal f the project succeeds. If the entrepreneur works, the probablty of success s (e H ); f she shrks, the probablty of success s (e L ). For smplcty, the probablty of success s assumed to be dentcal across all entrepreneurs. However, the cost of work, c n (e H ), s heterogeneous across entrepreneurs. We normalze the cost of shrk to zero. Furthermore, n subsequent dscusson, we assume 1 (e H ) = 2 (e H ) = and normalze (e L ) = 0: The rm s run by the entrepreneur who owns a part of the rm. In the absence of proper ncentves, the entrepreneur may delberately reduce the e ort level n order to reduce the e ort cost. The entrepreneur makes a decson on the e ort 5 conssts of addtonal captal and labor expendture per unt of ntal nvestment. The captal unt s chosen so that a w < 1:The assumpton s made to smplfy the subsequent algebra. 9

12 level after the contnuaton decson s made at date 2. The labor s pad at w n the second perod f the project succeeds and zero f t fals. Consumpton takes place at the end of the second perod. The total return to one unt of ntal captal f the project succeeds, R ; s determned by rm s zero pro t condton p y 1 wl 1 = [p G (a ; 1) wa ] K 1 = R K 1 (5) On date 2; the rst perod nvestment K 1 s sunk. The net present value of the nvestment s maxmzed by contnung the project whenever the expected return from contnuaton, R ; exceeds the cost ; that s, R 0: Let 1 = R (6) be the rst-best cuto value of. As n Holmstrom and Trole (1998), we assume that the project s net present value s postve f the entrepreneur works; but negatve f she shrks. Therefore, we only need to consder those contracts that mplement a hgh level of e ort. One nsttutonal feature emphaszed n ths model s property rghts protecton, or control of the rsk of expropraton. An emergng lterature has suggested that cross-country d erences n property rghts protecton are a major determnant of cross-country d erences n long-run economc growth and patterns of nternatonal captal ow (see, for example, Acemoglu, Johnson, and Robnson, 2001; and Alfaro, Kaleml-Ozcan, and Volosovych, 2005). One could convenently thnk of a hgher value of n our model as representng better property rghts protecton (or lower expropraton rsk). Equvalently, a hgher value of also represents a lower tax rate on captal return. 10

13 3.2 Fnancal Contracts The entrepreneur n and nancal nvestors sgn a contract at the begnnng of date 1; whch spec es the total amount of nvestment, her plan on whether to contnue or termnate the project for every realzaton of the lqudty shock, and how the nal project return s gong to be dvded between the nancal nvestors and herself. More precsely, let C n = fkn 1 ; n( ); Rn E ( )g be the nancal contract, where n ( ) s a state-contngent polcy on project contnuaton (1 = contnue; 0 = stop), and Rn E ( ) s the entrepreneur s porton of the revenue per unt of nvestment. For every dollar of nvestment, nvestors are left wth R R E n ( ). If the project s termnated, both sdes are assumed to receve zero. An optmal contract can be found by choosng fk 1 n ; n( ); R E n ( )g to solve the followng entrepreneur s optmzaton problem. max U n = Z 1 Kn r R E n( ) n ( )f ( )d 1 (7) subject to Z 1 Kn r f[r R E n( )] g n ( )f ( )d K X1 n (8) and R E n( ) c n (e H ) 0 (9) Expresson (7) s the present value of the rm s net return to nternal captal. (8) s the partcpaton constrant for outsde nvestors, whle (9) s the entrepreneur s ncentve compatblty constrant. Solvng the above problem, the optmal contnuaton polcy n (b n ) takes the form of a cuto rule so that the project contnues, or n ( ) = 1 f b n, and termnates, or n ( ) = 0 f > b n : As s shown n Holmstrom and Trole (1998), 11

14 the ncentve compatblty constrant (9) must be bndng, whch gves R E n = c n(e H ) (10) The partcpaton constrant (8) s also bndng, whch mples that the rm s ntal nvestment s K 1 n(:) = (1 + r) 1 + r R bn (11) 0 0 n f ( )d where 0 n = [R R E n( )] = R c n (e H ) (12) Substtutng bndng constrants (8) nto (7), the rm s net return to nternal captal becomes where U n (b n ) = R h(b n ) h(b n ) 0 n h (b n ) = (1 + r) + R b n 0 f ( )d F (b n ) (13) (14) h (b n ); n the termnology of Holmstrom and Trole (1998), s expected unt cost of total nvestment, whch s the opportunty cost of ntal nvestment at date 1; (1 + r) ; plus the expected nancng for the lqudty shock at date 2, R b n 0 f ( )d ; under the condton that the project contnues. Maxmzng U n (b n ) s equvalent to mnmzng h(b n ): The rst order condton then gves Z opt n 0 F ( )d = 1 + r (15) opt n shocks. gves the second-best soluton to the project cuto pont n response to lqudty Note that equaton (15) mples that opt n entrepreneurs n sector have the same optmal cuto, opt n shows opt s ndependent of n: Thus all = opt : Equaton (15) ncreases as r ncreases. Intutvely, as the nterest rate ncreases, the 12

15 opportunty cost of the nvestment becomes hgher. To attract nvestors to the project, the rm needs to promse a hgher probablty that the project wll contnue n the face of a lqudty shock, whch mples hgher optmal cuto pont opt : We wll assume that f 1 ( 1 ) = f 2 ( 2 ) = f() has a unform dstrbuton n [0; ] thereafter. Then equaton (15) gves the soluton of opt = opt as opt = [2 (1 + r) ] 1 2 (16) We now ntroduce nancal development nto our model. We use to represent the level of nancal development of a country. More precsely, we assume only lqudty shocks b n opt can be met by the nancal system where 0 1. Hgher represents a more developed nancal system. 6 Two nterpretatons are possble: ether each rm s nanced up to the lqudty shock b n = opt ; or porton of rms are nanced up to opt and 1 porton of rms are not nanced for any shock. Let b n = opt : Expresson (14) now becomes h (b n ) = h(r; ) = p 2 [(1 + r) ] 1 2 (17) It s easy to see > 0 < 0: Let there be a contnuum of entrepreneurs ( rms) n type n wth a unt mass. F ( ) denotes both the ex ante probablty of a rm facng a lqudty shock below ; and a realzed fracton of rms wth lqudty shock below n sector : The total captal usage by type n entrepreneur s the sum of ntal nvestment K 1 n (:) 6 may also represent the level of credt constrant, whch has been used to represent the level of nancal development by Matsuyama (2004, 2005) and Aok, Bengno, and Kyotak (2006). Other theoretcal ndces of nancal development nclude the level of nvestor protecton by Shlefer and Wolfenzon (2002) and the country s capacty of external captal by Ju and We (2005). 13

16 and expected lqudty shocks. Denotng the total captal usage by K n ; K n (:) = = " 1 + Z # 1 opt 1 + r f ( )d Kn(:) 1 0 (1 + r) + R opt 0 f ( )d R opt (18) (1 + r) 0 0 n f ( )d The labor-captal rato for rm n n the entre producton process s a n = L n K n = a (19) whch s dentcal for all entrepreneurs n sector : 3.3 Allocaton of Captal and Market for Entrepreneurs There are two sectors n the economy. Sector 1 s assumed to be one n whch entrepreneurs cost of work d ers. We rank entrepreneurs by ther costs of work from low to hgh, and ndex them by n drectly. Entrepreneur n has lower cost of work than that of the entrepreneur n 0 f n < n 0 : In other words, the cost of work by entrepreneur n n sector 1, c n1 = c n1 (e H ), s an ncreasng functon n n. We wll assume c n1 = c 1 n for smplcty. Expresson (12) gves 0 n1 = R 1 c 1 n; whch s decreasng n n: Expresson (13) then mples that the rm s net return to nternal captal n sector 1; U n1 (:) s decreasng n n: In Sector 2, all entrepreneurs are assumed to have the same cost of work. That s, c n2 (e H ) = c 2. Expresson (12) ndcates that 0 n2 = R 2 c 2 ; whch s dentcal for all entrepreneurs. Thus, all entrepreneurs have the same pro t, U 2 (:); n sector 2. Let N 1 be the number of rms n Sector 1. N 1 solves for U N1 1 = R 1 h(r; ) h(r; ) [R 1 c 1 N 1 ] = U 2 (20) As Fgure 2 llustrates, entrepreneurs n the nterval of [1; N 1 ] enter Sector 1 and 14

17 earn the net return to nternal captal U n1 U 2 : Entrepreneurs of n > N 1 enter Sector 2 and earn the net return to nternal captal U 2 : We assume that a captalst (a potental entrepreneur) needs to pay a xed entry cost of f unts of the numerare good at the begnnng of the rst perod to become an entrepreneur. The net return to nternal captal n Sector 2; U 2 ; should be equal to f. On the other hand, the margnal entrepreneur n Sector 1, N 1 ; should have the same net return to nternal captal as f; whle all other entrepreneurs n Sector 1 earn hgher net returns. Usng equaton (20), the condtons can be stated as U N1 1 = U 2 = R 1 h(r; ) h(r; ) [R 1 c 1 N 1 ] = f R 2 h(r; ) h(r; ) [R 2 c 2 ] = f (21) The career choce of a captalst (between beng an entrepreneur and a nancal nvestor) s determned by the nterest rate r. If the return to nvestment r ncreases, the net return to nternal captal n sector 2; U 2 ; declnes. Thus, some entrepreneurs n Sector 2 would ext and become nancal nvestors. It s clear from (8) that nvestors expected revenue from the project s larger as entrepreneur s pay to work, Rn E, becomes smaller. For a gven nterest rate r; that means date 1 nvestment K 1 n s larger. Expresson (18) then mples that total captal managed by the entrepreneur n Sector 1 s larger for more productve managers (smaller n). We summarze our results by the followng lemma. Lemma 1 As the nterest rate ncreases, fewer captalsts choose to become entrepreneurs at the begnnng of date 1: Among the entrepreneurs, the more productve ones enter the heterogeneous sector, whle the less productve ones enter the homogeneous sector. In the heterogeneous sector, the more productve entrepreneurs manage more captal. 15

18 Note that part of the lemma resembles the results n Shlefer and Wolfenzon s (2002) one-factor model. In partcular, n ther model, t s also the case that fewer captalsts become entrepreneurs when the nterest rate ncreases, and more productve entrepreneurs manage more captal. 4 Aggregaton and Equlbrum Condtons The rst set of equlbrum condtons are free entry condtons whch are summarzed by equatons (21). Rewrte them as R 1 = h(r; ) + fc 1N f R 2 = h(r; ) + fc f (22) whch we label as captal revenue-sharng condtons. The left hand sdes of equatons (22) are expected margnal products of physcal captal n two sectors, respectvely. Each s a sum of an expected unt cost of total nvestment, h(r; ), and a payment to the entrepreneurs e orts. The second set of equlbrum condtons comprses full employment condtons. Each entrepreneur n Sector 2 manages K 2 (:) amount of captal. Entrepreneur n n Sector 1 manages K n1 (:) amount of captal. (19) mples that the labor-captal rato s dentcal for all entrepreneurs wthn a sector. Let the number of entrepreneurs n Sector 2 be N 2 : Let L and K be the country s labor and captal endowments, respectvely. The full employment condtons are Z N1 a 1 K n1 (:)dn + a 2 K 2 (:)N 2 = L (23) 1 Z N1 1 K n1 (:)dn + K 2 (:)N 2 = K (24) Substtutng (10), (14), and (22) nto (18), we obtan 16

19 K n1 (:) = h(r; ) c 1 [n (fn 1 ) = (1 + f)] and K h(r; ) (1 + f) 2(:) = (25) c 2 Applyng expressons (25) to (23) and (24), we can rewrte the full employment condtons as follows: N 1 a 1L ln + a 2L N 2 = L (26) 1 + f fn 1 N 1 a 1K ln + a 2K N 2 = K (27) 1 + f fn 1 where a 1L = a 1h(r; ) h(r; ) ; a 1K = c 1 c 1 a 2L = a 2 (1 + f) h(r; ) (1 + f) h(r; ) ; and a 2K = (28) c 2 c 2 We close ths secton wth the market-clearng condtons n product markets. The rms expected output (or the realzed ndustry output) n Sector 1 s Z N1 y 1 = F 1 ( opt )G 1 (a 1 ; 1) Kn1(:)dn 1 0 = G 1(a 1 ; 1) (1 + r) N 1 ln c f fn 1 (29) where we have used (11), (14) and (22) to derve the second equalty. The expected output n Sector 2 s y 2 = F 2 ( opt )G 2 (a 2 ; 1)K 1 2(:)N 2 = G 2(a 2 ; 1) (1 + r) (1 + f) N 2 c 2 (30) We assume that the representatve consumer s preference s homothetc. Thus, the rato of the quanttes consumed n the country depends only upon the relatve 17

20 goods prce rato and can be represented by D( p 1 p 2 ): In equlbrum, the relatve supply equals the relatve demand. The condton s stated as h y 1 G 1 (a 1 ; 1)c ln 2 = y 2 G 2 (a 2 ; 1) (1 + f) c 1 N 1 1+f fn 1 N 2 = D (p) (31) where p = p 1 =p 2 : Let good 2 be the numerare good whose prce s normalzed to 1 n subsequent sectons. 5 Comparatve Statcs Substtutng (6), (10), and (17) nto (22), the free entry condtons can be wrtten as a 1 w a 2 w [2 (1 + r) ] 1 2 = pg 1 (a 1 ; 1) [2 (1 + r) ] 1 2 = G 2 (a 2 ; 1) fc 1 N f fc f (32) (33) The endogenous varables, w; r; p; N 1 and N 2 are determned by equatons (26), (27), (31), (32), and (33). The outputs y 1 and y 2 are then derved from expressons (29) and (30). We wll study the e ects of changes n endowments, the level of nancal development, and expropraton rsk on equlbrum prces and quanttes. 5.1 Determnaton of Factor Prces The free entry condtons (32) and (33) are represented by curves z z ( = 1; 2) n Fgure 3. They are convex toward orgn and downward slopng n (w; r) space. The slopes of the curves for gven p, N 1 and are dr dw = " # (1 + r) a for = 1; 2 (34) 18

21 Assume that a 1 < a 2 ; and so Sector 2 s more labor ntensve than Sector 1. As ndcated n Fgure 3, z 2 z 2 ; s steeper than z 1 z 1 : Let the ntal factor prce equlbrum be gven by pont M: A decrease n the relatve prce of good 1, or an ncrease n N 1 ; wll shft z 1 z 1 nward to z1 kzk 1, and move the equlbrum to pont A: It s clear that the wage goes up and the nterest rate declnes. When s ncreased, both z1 kzk 1 and z 2z 2 shft out to z1 z 1 and z 2 z 2. The equlbrum moves from pont A to pont B whch s vertcally above A: The wage rate stays at exactly the same level, whle the nterest rate ncreases. A better nancal system reduces the expected unt cost of total nvestment, h(r; ); and therefore ncreases the return to nvestment. The return to labor, however, s una ected by the nancal development due to the Leontf technology assumed n our model. As we formally prove n the Appendx B, under the condton that the hghest cost of entrepreneurs e ort n the heterogeneous sector s more than that n the homogeneous sector, the nterest rate ncreases but the wage rate declnes as ncreases. Our analyss s smlar to classcal Stolper-Samuelson (1941) theorem, augmented by e ects of entrepreneurs heterogenety, nancal development and expropraton rsk on factor prces. We summarze the above results by a Stolper-Samuelson plus theorem and relegate the formal proof to Appendx B. Proposton 1 (Stolper-Samuelson plus) Ceters parbus, a decrease n the prce of a good decreases the return to the factor used ntensvely n that good, and ncreases the return to the other factor. Furthermore, an ncrease n the number of entrepreneurs n the heterogeneous sector decreases the return to the factor used ntensvely n that sector and ncreases the return to the other factor. An mprovement n the level of nancal development ncreases the nterest rate but has no e ect on the wage rate. If the hghest cost of entrepreneurs e ort n the heterogeneous sector s more than that n the homogeneous sector, a lower expropraton rsk ncreases the nterest rate but reduces the wage rate. 19

22 Note that factor prce equalzaton does not hold n our model, makng t d erent from the textbook verson of the Heckscher-Ohln model. D erences n and make factor prces d er. Even f and are the same across countres, as we show next, more entrepreneurs enter the heterogeneous sector n the captal-abundant country. Then the proposton above ndcates that a larger N 1 results n a lower nterest rate r and a hgher wage rate w at the captal-abundant country. 5.2 Changes n Endowment and Insttutons We turn now to the response of outputs (represented by N 1 and N 2 ) to changes n exogenous varables: the Rybczynsk (1955) e ect of endowment, augmented by e ects of nancal development and expropraton rsk. Let equatons (26) and (27) be denoted as LL curve and KK curve, respectvely. The numbers of entrepreneurs (or amounts of nternal captal) n equlbrum, E = (N 1 ; N 2 ) are determned by the ntersecton of the LL and the KK curves, as ndcated n Fgure 4. KK curve s steeper than LL curve because Sector 1 s captal-ntensve. Totally d erentatng equatons (26) and (27) and usng Jones algebra (Jones, 1965), we obtan 1L b N1 + 2L b N2 = b L [ 1L ba 1L + 2L ba 2L ] 1K b N1 + 2K b N2 = b K [ 1K ba 1K + 2K ba 2K ] (35) We de ne dn 1 =N 1 = b N 1 ; and lkewse for all other varables. In addton, we de ne the fracton of labor used n ndustry by, 1L = a 1L ln [N 1 = (1 + f fn 1 )] ; L 2L = a 2LN 2 L a 1L (1 + f) and 1L = L (1 + f fn 1 ) (36) where 1L + 2L = 1: We de ne K and 1K n an analogous manner. Let the ntal equlbrum output be at pont E: The e ect of a change n 20

23 endowment s smlar to the standard HOS model. b L and b K represent the drect e ect of a change n endowment at gven product prces, whle the second terms on the rght hand sde of equatons (35) represent the feedback e ect of nduced factor prce changes on the factor usage per unt of producton. For gven factor prces, as depcted n Fgure 4, the drect e ect of an ncrease n the captal endowment shfts KK out to K 0 K 0 and moves the equlbrum to pont E 0. It s clear that N 1 goes up, whereas N 2 declnes. The ncrease n N 1 rases y 1, whle the decrease n N 2 reduces y 2. Thus, the relatve prce of good 1, p, decreases. By Proposton 1, both the decrease n p and the ncrease n N 1 reduces r whle ncreasng w. Usng (28), we know that both labor and captal usages per unt of producton decrease. Thus, the feedback e ect shfts the K 0 K 0 curve out further to K 00 K 00 and shfts the LL curve out to L 00 L 00, whch moves the equlbrum from E 0 to E 00. The shftng out of KK curve further ncreases N 1 and reduces N 2, whle the shftng out of LL curve reduces N 1 and ncreases N 2. As we formally prove n the Appendx B, f a mod ed condton for nonreversal of factor ntensty s sats ed, the overall e ect of an ncrease n K=L s to ncrease N 1 ; whle the overall e ect on N 2 s ambguous. However, the relatve prce p declnes, and as a result, the relatve output y 1 to y 2 ncreases. We now dscuss the e ect of a change n : As Proposton 1 shows, the ncrease n rases the nterest rate r but has no e ect on the wage w. That s, the mpact of changng n s completely absorbed by the ncrease of r, whle leavng w una ected. Expresson (5) and (22) then ndcate that the change n must be o set by the change n r so that h(r; ) stays constant. Usng (28), we know that a j must reman constant as changes. As a result, N 1 ; N 2 ; and p are not a ected by the ncrease n : Note that although the ncrease n does not a ect the number of entrepreneurs, t rases y 1 and y 2 by the same proporton as ndcated by expressons (29) and (30). The ncrease n rases the nterest rate so that h(r; ) s hgher. Expresson (28) ndcates that factor usages per unt of producton ncreases. Thus both, LL 21

24 and KK shft back, and equlbrum moves from E to E 000 n Fgure 4. N 1 and N 2 both declne. As we formally prove n the Appendx B, under the condton that the hghest cost of entrepreneur s e ort n the heterogeneous sector s more than that n the homogeneous sector, N 1 and N 2 decrease proportonally n the way that relatve prce p does not change. Lower expropraton rsk reduces the number of rms. Each rm, however, becomes larger and produces more. As we show n the Appendx B, the postve e ect of on nterest rate r domnates the negatve e ect on N ; Usng (29) and (30), ndustry outputs y 1 and y 2 are larger as ncreases. We summarze the above results by a Rybczynsk plus theorem. Proposton 2 (Rybczynsk plus) Suppose a mod ed condton for nonreversal of factor ntensty s sats ed, so that sector 1 s always captal-ntensve. An ncrease n captal endowment wll ncrease the number of entrepreneurs n sector 1, and decrease the relatve prce of good 1: Furthermore, an mprovement n the level of nancal development wll rase the output n both sectors proportonally, leavng the number of entrepreneurs and the relatve product prce unchanged. If the hghest cost of entrepreneurs e ort n the heterogeneous sector s more than that n the homogeneous sector, a lower expropraton rsk wll rase the output but reduce the number of entrepreneurs n both sectors proportonally and have no e ect on the relatve product prce. Propostons 1 and 2 together gve rse to predctons on how a change n endowment (or nancal and property rghts nsttuton) on factor prces. In partcular, an ncrease n captal endowment ncreases N 1 and reduces p by Proposton 2. Both e ects reduce r but ncrease w by Proposton 1. We can work out n a smlar way the e ects of an ncrease n or. For convenence, these results can be summarzed by the followng corollary. Corollary 1 In equlbrum, an ncrease n the captal-labor rato reduces the nterest rate but rases the wage rate. An mprovement n the nancal system rases the 22

25 nterest rate but leaves the wage rate unchanged. A reducton n the expropraton rsk rases the nterest rate but reduces the wage rate. 6 Free Trade and Captal Flows Usng the comparatve statcs results derved above, we are now ready to descrbe patterns of goods trade and captal ows. Consder two countres wth dentcal and homothetc tastes, dentcal technologes, dentcal lqudty shocks and managers behavor, but d erent factor endowments, levels of nancal development, and expropraton rsks. Labor s mmoble across countres. After studyng free trade n goods wthout nternatonal captal ow, we move sequentally by allowng only nancal captal ow at rst, only foregn drect nvestment (FDI) next, and both types of captal ows smultaneously n the end. 6.1 Free Trade n Goods Let varables n the foregn country be denoted by a superscrpt. The equlbrum autarky prces at home and abroad are represented by p and p ; respectvely. p may d er from p f L ; K, and are d erent from correspondng domestc varables. Comparng p wth p s equvalent to the exercse of comparatve statcs n the last secton that changes K=L, ; and to K =L, and ; respectvely. Let bp = (p p) =p be the percentage d erence n the autarky prces. Ignorng a second order e ect and usng equaton (66) n the Appendx, we have A p bp = b L b K (37) where A p = jj D = N > 0. L; b K; b b and b are now percentage d erences n the labor and captal endowments, nancal development, and rsk expropraton between two countres. Notng that b and b have no e ect on relatve product prces, our analyss of goods trade s essentally a generalzed Heckscher-Ohln model n an 23

26 envronment of mperfect captal market and heterogeneous entrepreneurs. Proposton 3 Suppose captal ow s prohbted. In ths model wth nancal market mperfecton and heterogeneous entrepreneurs, the Heckscher-Ohln result on trade patterns stll holds: each country produces and exports the good that uses ts relatvely abundant factor ntensvely. 6.2 Fnancal Captal Flows We now turn to captal ows under the equlbrum of free trade n goods. There are two types of nternatonal captal ows: nancal captal ows decded by nancal nvestors and FDI decded by entrepreneurs. Internatonal nancal ows occur when the nvestor nvests her endowment n a foregn nancal market (or drectly n a foregn entrepreneur s project). On the other hand, FDI occurs when the entrepreneur takes her project to the foregn country and produces there. Investors wll nvest n the country wth a hgher nterest rate (return to nancal nvestment), whle entrepreneurs wll locate ther projects n the country wth a lower producton cost. In the rest of ths subsecton, we dscuss the specal case n whch only nancal captal ow s permtted, but no FDI. The drecton of nancal ows s determned by br = (r r) =r: If br > 0; nancal captal wll ow from home to the foregn country. Otherwse, t wll ow n the reverse drecton. As we have shown n Corollary 1, f the country s ether relatvely abundant n labor, more nancally developed, or has less rsk of expropraton, ts nterest rate n the absence of nternatonal captal ow s hgher. In the equlbrum wth free trade n goods, the endogenous varables n each country are determned by equatons (26), (27), (32), and (33), and ther foregn-country counterparts. The product market clearng condton now becomes (y 1 + y1 ) = (y 2 + y2 ) = D(p): The equaton (60) n the Appendx no longer holds but s not needed snce bp = 0 n the free trade equlbrum. All other proofs n the Appendx go through. We agan gnore the second order e ect. Slghtly abusng notatons and substtutng 24

27 (65) nto (56), we obtan br = A L b L AK b K + A b + A b (38) where A L, A K ; A ; A are all postve. 7 We can summarze three polar cases wth the followng proposton. Proposton 4 Let there be free trade n goods, no barrer to nternatonal nancal captal ows, but no FDI s permtted. If two countres are the same n terms of nancal development and expropraton rsk but d erent n endowment, then nancal captal wll ow from captal-abundant country nto labor-abundant country. If the two countres have the same captal-labor rato and dentcal expropraton rsk but d erent levels of nancal development, nancal captal wll ow from the country wth a less developed nancal system nto the other one. If the two countres have the same captal-labor rato and levels of nancal development, nancal captal wll ow from the country wth a hgher expropraton rsk nto the one wth lower expropraton rsk. 6.3 Foregn Drect Investment We now allow projects and entrepreneurs to move freely across countres. Rewrte expresson (13) of entrepreneur s net return to nternal captal as U n (w; r; ; ) = p T G (a ; 1) wa 1+ 2 p 2 [(1 + r) ] p 2 [(1 + r) ] 1 2 p T G (39) (a ; 1) wa + cn where p T represents the product prce n free trade. It s easy to n =@w < n =@r < n =@ > 0; n =@ > 0: We assume that entrepreneurs collect the captal at home and utlze ther home nancal system even f they produce abroad. We rst consder the case of b = ( ) = = 0. In ths case domestc 7 A detaled proof of equatons (38) and (40) s avalable from authors upon request. 25

28 entrepreneurs wll have an outbound FDI f and only f w > w : Substtutng (65) nto (55), we obtan bw = B L b L + BK b K B b (40) where B L ; B K ; and B are all postve. Thus w > w f and only f the home country s captal-abundant. That s, entrepreneurs from a captal-abundant country wll engage n outbound FDI to take the advantage of lower labor cost abroad. Proposton 5 Wth free trade n goods, dentcal expropraton rsk but prohbton of nternatonal nancal captal ow, FDI wll go from the captal-abundant country to the labor-abundant one. 6.4 Complete Bypass of the Ine cent Fnancal System We now allow for both types of captal ows. Let both countres be dvers ed. We start wth the smplest case n whch expropraton rsk s dentcal across countres and entrepreneurs are perfectly moble. The unque equlbrum n ths case s a complete captal bypass crculaton n whch all captal owned by nancal nvestors (households) n the country wth a less developed nancal system leaves the country n the form of nancal captal out ow, but physcal captal (and projects) reenters the country n the form of FDI. The less developed nancal system serves no captal at all n the equlbrum. The proof s straghtforward: In the equlbrum, the nterest rates and wage rates must be equalzed across two countres. Snce entrepreneurs are perfectly moble, f entrepreneur n n a low country could be hred to manage a factory (project) n a hgh country, she would lke to move to the hgh country n =@ > 0. If some managers had used the nancal system of low country n the equlbrum, the most e cent manager among them would lke to brng the captal she collected and move to hgh country. That would reduce the wage rate n the low country (hence makng the low country more attractve to FDI from the hgh country), 26

29 and crowd out the less e cent managers n the hgh country whom would brng her project to low country (hence rasng the nterest rate n the hgh country n the process and makng t more attractve to nancal captal from the low country). Another wave of captal bypass crculaton would occur untl all nancal captal leaves the low country and enough FDI comes nto the low country so that factor prces are equalzed between two countres n the equlbrum. A mod ed graphcal representaton of an ntegrated world economy (Dxt and Norman, 1980; Helpman and Krugman, 1985) can help to llustrate the equlbrum. In Fgure 5, O and O represent the orgns for home and foregn countres, respectvely. Vectors OY 1 and OY 2 represent the world employment of captal and labor n Sectors 1 and 2 n the equlbrum of the ntegrated world economy, respectvely. Let L = L for smplcty. Suppose > : Pont H de nes the dstrbuton of factor endowments. Let home be captal-abundant so H s above the dagonal lne of the parallelogram OY 2 O Y 1 : Internatonal nancal captal ow equalzes the nterest rates, whle FDI equalzes the wage rates across two countres. For (w; r) to be equal n the two countres, from equatons (32) and (33), N 1 and N 1 must be the same snce nvestors n both countres use the same nancal system. Thus the factor usages of producton n the equlbrum must be n the mddle lne of the parallelogram, AA : That s, factor usages n Sector 1 represented by lengths of OA and O A must be the same for the two countres. Each country uses ts own labor endowment. Therefore, the ntersecton between AA and LF; represented by pont E; ndcates factor usages of producton n the equlbrum. E happens to be n the mddle of the parallelogram snce we assume L = L : OB and O B represent the factor usages n sector 2: All foregn captal ows nto the home country n the form of nancal captal ow snce > ; whch s represented by F H: FDI, however, ows to the foregn country and s represented by EF: The crcle F HEF represents the captal bypass crculaton. HE ndcates the net captal out ow of the home country. The home country experences a current account surplus as the captal 27

30 account s negatve. 8 To summarze, we have: Proposton 6 Let the expropraton rsk be dentcal and entrepreneurs be perfectly moble across two countres wth dentcal populatons. In the unque equlbrum, the less developed nancal system s completely bypassed. All captal owned by the country wth the less developed nancal system wll leave the country n the form of nancal captal ow. However, the country also experences captal n ow n the form of FDI. In equlbrum, the captal-abundant country ncurs a net captal out ow (and a trade surplus). The complete captal bypass crculaton equlbrum predcts the same drecton of net captal ow as a typcal neoclasscal one-sector model. The magntude of the nterest rate d erental (return to nancal nvestment), however, s d erent between ths model and a typcal one-sector model. To see ths, let b L = 0 for smplcty. Substtutng (65) nto (56), we obtan: 2w ( br = 2L + 2 ) 1N bk jj jj where 1N = fc 1 N 1 = (1 + f) : b K s no longer the only factor that determnes nterest rate d erental as n the Lucas paradox. The captal market mperfecton whch s measured by the cost of e ort n moral hazard problem c 1 ; the entry cost of entrepreneurs f, as well as the level of entrepreneurs heterogenety represented by the functon form of c n1 (:) all a ect br. In other words, even f the captal-labor rato s very d erent between two countres, as long as f or c 1 are su cently small, the d erence n the returns to nancal nvestment between the two countres can be small. 9 8 When entrepreneurs are not perfectly moble and expropraton rsk s not dentcal, a captal abundant country wth a developed nancal system and low expropraton rsk may experence a net captal n ow and therefore a current account de ct. 9 Casell and Freyrer (2005) computed that the rates of return to captal are very smlar across 53 developng and rch countres for whch they have the relevant data. 28