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1 Goba ourcing The Harvard community has made this artice openy avaiabe. Pease share how this access benefits you. Your story matters. Citation Pubished Version Accessed Citabe Link Terms of Use Antras, Po, and Ehanan Hepman Goba sourcing. Journa of Poitica Economy 112(3): doi: / December 29, :05:39 PM ET This artice was downoaded from Harvard University's DAH repository, and is made avaiabe under the terms and conditions appicabe to Other Posted Materia, as set forth at (Artice begins on next page)

2 Goba ourcing Po Antràs Harvard University and ationa Bureau of Economic Research Ehanan Hepman Harvard University, Te Aviv University, and Canadian Institute for Advanced Research We present a orth-outh mode of internationa trade in which differentiated products are deveoped in the orth. ectors are popuated by fina-good producers who differ in productivity eves. On the basis of productivity and sectora characteristics, firms decide whether to integrate into the production of intermediate inputs or outsource them. In either case they have to decide from which country to source the inputs. Fina-good producers and their suppiers must make reationship-specific investments, both in an integrated firm and in an arm s-ength reationship. We describe an equiibrium in which firms with different productivity eves choose different ownership structures and suppier ocations. We then study the effects of withinsectora heterogeneity and variations in industry characteristics on the reative prevaence of these organizationa forms. I. Introduction A firm that chooses to keep the production of an intermediate input within its boundaries can produce it at home or in a foreign country. When it keeps it at home, it engages in standard vertica integration. And when it makes it abroad, it engages in foreign direct investment (FDI) and intrafirm trade. Aternativey, a firm may choose to outsource an input in the home country or in a foreign country. When it buys the Antràs thanks the Bank of pain and Hepman thanks the ationa cience Foundation for financia support. We have received very hepfu comments from Gene Grossman, ancy tokey, two anonymous referees, and seminar participants at various institutions. [Journa of Poitica Economy, 2004, vo. 112, no. 3] 2004 by The University of Chicago. A rights reserved /2004/ $

3 goba sourcing 553 input at home, it engages in domestic outsourcing. And when it buys it abroad, it engages in foreign outsourcing, or arm s-ength trade. Inte Corporation provides an exampe of the FDI strategy: it assembes most of its microchips in whoy owned subsidiaries in China, Costa Rica, Maaysia, and the Phiippines. On the other hand, ike provides an exampe of the arm s-ength import strategy: it subcontracts most of its manufacturing to independent producers in Thaiand, Indonesia, Cambodia, and Vietnam. Growth of internationa speciaization has been a dominant feature of the internationa economy. Among the many exampes that iustrate this trend, two are particuary teing. Citing Tempest (1996), Feenstra (1998) iustrates Matte s goba sourcing strategy in the production of its star product, the Barbie do. Of the $2 export vaue for the dos when they eave Hong Kong for the United tates, he writes, about 35 cents covers Chinese abor, 65 cents covers the cost of materias [which are imported from Taiwan, Japan, and the United tates], and the remainder covers transportation and overhead, incuding profits earned in Hong Kong (p. 36). The Word Trade Organization provides another exampe in its 1998 annua report. In the production of an American car, 30 percent of the car s vaue originates in Korea, 17.5 percent in Japan, 7.5 percent in Germany, 4 percent in Taiwan and ingapore, 2.5 percent in the United Kingdom, and 1.5 percent in Ireand and Barbados. That is, ony 37 percent of the production vaue is generated in the United tates (p. 36). The increasing internationa disintegration of production is arge enough to be noticed in aggregate statistics. Feenstra and Hanson (1996) use U.. input-output tabes to infer U.. imports of intermediate inputs. They find that the share of imported intermediates increased from 5.3 percent of tota U.. intermediate purchases in 1972 to 11.6 percent in Campa and Godberg (1997) find simiar evidence for Canada and the United Kingdom (but not for Japan). And Hummes, Ishii, and Yi (2001) and Yeats (2001) show that internationa trade has grown faster in components than in fina goods. But how important is intrafirm reative to arm s-ength trade in intermediate inputs? A firm-eve data anaysis is needed to answer this question, and no such anaysis is avaiabe at this point in time. And despite the fact that the business press has stressed the spectacuar growth of foreign outsourcing, Hanson, Mataoni, and aughter (2003) document an equay impressive growth of trade within mutinationa firms. evertheess, the fact that, according to data from the Bureau of Economic Anaysis, imports from foreign affiiates of United tates based firms had faen from 23.9 percent of tota U.. imports in 1977 to 16.1 percent in 1982, and remained roughy at this eve unti 1999,

4 554 journa of poitica economy suggests that the growth of foreign outsourcing by U.. firms might have outpaced the growth of their foreign intrafirm sourcing. Other studies have documented a rise in the prevaence of domestic outsourcing by U.. firms. The Economist (1991), Bamford (1994), and Abraham and Tayor (1996) a report rising subcontracting in particuar industries or activities. A systematic anaysis of this trend is not avaiabe. evertheess, Fan and Lang (2000) provide indirect evidence of a decine in vertica integration. According to their data, the average number of four-digit standard industria cassification segments in which a U.. pubicy traded manufacturing company operates decined steadiy from 2.72 in 1979 to 1.81 in This suggests that U.. manufacturing firms have become more speciaized over time. To address issues that arise from the choice of outsourcing versus integration and home versus foreign production, we need a theoretica framework in which companies make endogenous organizationa choices. We propose such a framework in this paper by integrating two recent strands of the iterature. Meitz (2003) and Hepman, Meitz, and Yeape (2004) have studied the effects of within-sectora heterogeneity on the decisions of firms to serve foreign markets. By aowing productivity to differ across firms, they show that ow-productivity firms serve ony the domestic market, whereas high-productivity firms aso serve foreign markets. Aowing for horizonta foreign direct investment, Hepman et a. aso show that, among the firms that serve foreign markets, the more productive ones engage in foreign direct investment whereas the ess productive firms export, and affiiate saes reative to exports are arger in sectors with more productivity dispersion. Their approach emphasizes variations across firms within industries, without addressing the organizationa choices of firms that need to acquire intermediate inputs. Grossman and Hepman (2002) address the choice between outsourcing and integration in a one-input genera equiibrium framework, assuming that a firms of a given type are equay productive. Their firms face the friction of incompete contracts in arm s-ength reationships, which they weigh against the ess efficient production of inputs in integrated companies. As a resut, some sectors have ony verticay integrated firms whereas others have ony disintegrated firms. Grossman and Hepman identify sectora characteristics that ead to one or the other equiibrium structure. This approach has been extended by Antràs (2003a) to a trading environment, by introducing two new features. First, the friction of incompete contracts aso exists within integrated firms, and as in Grossman and Hart (1986) integration provides wedefined property rights. However, these property rights may or may not give integration an advantage over outsourcing. econd, there are two inputs, one controed by the fina-good producer and the other by

5 goba sourcing 555 another suppier, inside or outside the firm. The reative intensity of these inputs turns out to be an important determinant of the choice between integration and outsourcing. By embodying this structure in a Hepman and Krugman (1985) stye two-sector genera equiibrium mode of trading countries, Antràs shows that the sector that is reativey intensive in the input controed by the fina-good producer integrates, whereas the sector that is reativey intensive in the other input outsources. As a resut, in the former sector there is intrafirm trade in inputs, and in the atter sector there is arm sength trade. Buiding on this iterature, we deveop a theoretica mode that combines the within-sectora heterogeneity of Meitz (2003) with the structure of firms in Antràs (2003a). The fina-good producer contros the suppy of headquarter services, whereas a suppier of intermediate goods contros the quaity and quantity of the intermediates. This aows us to study the impact of variations in productivity within sectors and of differences in technoogica and organizationa characteristics across sectors on internationa trade, foreign direct investment, and the organizationa choices of firms. In this framework, trade, investment, and organization are interdependent. The incentives created by different organizations, differences in their fixed costs, and wage differentias across countries shape the equiibrium organizationa structure. We show that in a word of two countries, orth and outh, in which fina-good producers are based in the orth, fina-good producers that operate in the same sector but differ by productivity sort into integrated companies that produce inputs in the orth (do not engage in foreign trade in inputs), integrated companies that produce inputs in the outh (engage in FDI and intrafirm trade), disintegrated companies that outsource in the orth (do not engage in foreign trade in inputs), and disintegrated companies that outsource in the outh (import inputs at arm s ength). Moreover, we show that in sectors with ow headquarter intensity, firms do not integrate; ow-productivity firms outsource in the orth whereas high-productivity firms outsource in the outh. In sectors with high headquarter intensity, a four organizationa forms may exist in equiibrium, and, as in sectors with ow headquarter intensity, highproductivity firms import inputs whereas ow-productivity firms acquire them in the orth. However, among the firms that acquire inputs in the same country, the ow-productivity firms outsource whereas the highproductivity firms insource. This impies that the east productive firms outsource in the orth whereas the most productive firms insource in the outh via foreign direct investment. We use the mode to study the reative prevaence of different organizationa forms. We show how prevaence depends on the wage gap between the orth and the outh, the trading costs of intermediate

6 556 journa of poitica economy inputs, the degree of productivity dispersion within a sector, the distribution of bargaining power, the size of the ownership advantage (which may be different in the two countries), and the intensity of headquarter services. Our mode predicts that reativey more fina-good producers rey on imported intermediates in sectors with higher productivity dispersion or ower headquarter intensity. And in sectors with integration and outsourcing, which are the sectors with high headquarter intensity, industries with higher productivity dispersion have reativey more finagood producers that integrate. This is true for a comparison of integration versus outsourcing in each of the countries. As a resut, such sectors have more intrafirm trade reative to arm s-ength trade. These resuts iustrate the types of issues that can be addressed with our mode. Our mode is deveoped in ection II. In ection III, we characterize an industry s equiibrium. Then, in ection IV, we describe the equiibrium sorting of firms into different organizationa forms, and we study in ection V the prevaence of each mode of organization. This is aso the section that examines the effects of variations within and across sectors on the reative prevaence of organizationa forms. ection VI offers a short summary with concuding comments. II. The Mode Consider a word with two countries, the orth and the outh, and a unique factor of production, abor. The word is popuated by a unit measure of consumers with identica preferences represented by J 1 m 0 j m jp1 U p x X, 0! m! 1, where x0 is consumption of a homogeneous good, Xj is an index of aggregate consumption in sector j, and m is a parameter. Aggregate consumption in sector j is a constant easticity of substitution function 1/a a X j p x j(i) di, 0! a! 1, [ ] of the consumption of different varieties x j(i), where the range of i wi be endogenousy determined. The easticity of substitution between any two varieties in a given sector is 1/(1 a). We assume that a 1 m, so that varieties within a sector are more substitutabe for each other than they are for x 0 or for varieties from a different sector. This eads to the inverse demand function for each variety i in sector j: m a a 1 p j(i) p Xj x(i) j. (1) Producers of differentiated products face a perfecty eastic suppy of

7 goba sourcing 557 abor in each one of the countries. We denote by w the wage rate in the orth and by w the wage rate in the outh. These wage rates are fixed, and w 1 w. The assumption of fixed wage rates and a higher wage rate in the orth can be justified in genera equiibrium by assuming that w is the productivity of abor in producing x 0 in country, p,, and that abor suppy is arge enough in every country so that both countries produce x 0. The demand parameters m and a are the same in every industry, which heps to focus attention on cross-sectora differences in technoogy and organizationa costs. Our aim is to expore how differences in technoogy interact with organizationa choices in shaping industria structure, trade fows, and FDI. Ony the orth knows how to produce fina-good varieties. To start producing a variety in sector j, a firm needs to bear a fixed cost of entry consisting of f E units of northern abor. Upon paying this fixed cost, the unique producer of variety i in sector j draws a productivity eve v from a known distribution G(v). 1 After observing this productivity eve, the fina-good producer decides whether to exit the market or start producing; in the atter case, an additiona fixed cost of organizing production needs to be incurred. As discussed beow, this additiona fixed cost is a function of the structure of ownership and the ocation of production. Production of any fina-good variety requires a combination of two variety-specific inputs, h j(i) and m j(i), which we associate with head- quarter services and manufactured components, respectivey. Output of every variety is a sector-specific Cobb-Dougas function of the inputs, hj 1 hj h j(i) m j(i) [ h ] [ 1 h ] j j x (i) p v, 0! h! 1, (2) j where the productivity parameter v is firm-specific whereas the parameter hjis sector-specific. The arger hjis, the more intensive the sector in headquarter services. Headquarter services h j(i) can be produced ony in the orth, with one unit of abor per unit of output, whereas intermediate inputs m j(i) can be produced in the orth and in the outh, with one unit of abor per unit of output in each one of the countries. There are two types of agents engaged in production: fina-good producers, who suppy headquarter services, and operators of manufacturing pants, who suppy intermediate inputs. We use H to denote a finagood producer and M to denote a suppier of intermediate inputs. Every 1 To be more precise, the unique producer of variety i draws a particuar reaization v(i) from the distribution G(v). However, we drop the variety index i from v(i) in order to simpify the notation. For the same reason, we drop the sectora index j from the fixedcost variabe f and the distribution function G(7). E j

8 558 journa of poitica economy fina-good producer H needs to contract with a manufacturing pant operator M for the provision of components. We aow internationa fragmentation of the production process, so that H can choose to transact with a manufacturing pant operator M in the orth or in the outh. It foows from our assumptions that a fina-good producers ocate in the orth. Upon paying the fixed cost of entry, wf E, and observing the productivity eve v, the unique fina-good producer H of variety i in sector j seeks out a suppier of components M in the orth or in the outh. imutaneousy, H chooses whether to insource or outsource intermediate inputs. The joint management costs of fina and intermediate goods production, such as supervision, quaity contro, accounting, and marketing, depend on the organizationa form and the ocation of M. A these costs, the sum of which we term fixed organizationa costs, are denominated in terms of northern abor. We denote them by wf k, where k is an index of the ownership structure and is an index of the country in which M is ocated and the manufacturing of components takes pace. The ownership structure takes one of two forms: vertica integration V or outsourcing O. The suppier M is ocated in one of two sites: in the orth or in the outh. Therefore, k {V, O} and {, }. An organizationa form consists of an ownership structure and a ocation of M. We assume that the fixed organizationa costs are higher when M is ocated in the outh regardess of ownership structure, because the fixed costs of search, monitoring, and communication are significanty higher in the foreign country. amey, fk 1 fv and fk 1 fo for k p V, O. We aso assume that, given the ocation of M, the fixed organizationa costs of a V firm are higher than the fixed organizationa costs of an O firm, namey, fv 1 fofor p,. As a resut of these assumptions, the fixed organizationa costs are ranked as foows: fv 1 fo 1 fv 1 f O. (3) We adopt this ordering in order to avoid a taxonomy of cases. There exists a tension between two considerations that affect the ranking of fv and fo. On the one hand, the need to supervise the production of intermediate inputs in addition to other manageria tasks raises manageria overoad and the fixed organizationa costs of a V firm reative to an O firm. On the other hand, economies of scope in the management of diverse activities reduce the fixed organizationa costs of a V firm reative to an O firm. Our ordering amounts to assuming that manageria overoad is more important than manageria economies of scope. Athough we beieve this assumption to be appropriate in many instances, and we therefore maintain it in the main anaysis, we sha point out how some of the resuts change when f! f. V O

9 goba sourcing 559 The setting is one of incompete contracts. Fina-good producers and manufacturing pant operators cannot sign ex ante enforceabe contracts specifying the purchase of speciaized intermediate inputs for a certain price. In addition, the parties cannot write enforceabe contracts contingent on the amount of abor hired or on the voume of saes revenues obtained when the fina good is sod. One can use arguments of the type deveoped by Hart and Moore (1999) and ega (1999) to justify this specification, namey, that the parties cannot commit not to renegotiate an initia contract and that the precise nature of the required input is reveaed ony ex post and is not verifiabe by a third party. To simpify the anaysis, we just impose these constraints on the contracting environment. Because no enforceabe contract can be signed ex ante, fina-good producers and manufacturing pant operators bargain over the surpus from the reationship after the inputs have been produced. We mode this ex post bargaining as a generaized ash bargaining game in which the fina-good producer obtains a fraction b (0, 1) of the ex post gains from the reationship. 2 Foowing the property rights approach to the theory of the firm, we assume that ex post bargaining takes pace both under outsourcing and under integration. The distribution of surpus is sensitive, however, to the mode of organization. More specificay, the outside option of H is assumed to be different when it owns the manufacturing pant than when it does not. In the atter case, a faiure to reach an agreement on the distribution of the surpus eaves both parties with no income, because the inputs are taiored specificay to the other party in the transaction. However, by verticay integrating the production of components, H is effectivey buying the right to fire M and seize the inputs m j(i). If there were no costs associated with firing the operator of the manufacturing pant, the fina-good producer woud aways have an incentive to seize the inputs m j(i) ex post, and M woud have an incentive to choose m j(i) p 0 ex ante (which of course woud impy x j(i) p 0). In this case, integration woud never be chosen. We therefore assume that firing M resuts in a oss of a fraction 1 d of fina-good production, because H cannot use the intermediate inputs without M as effectivey as it can with the cooperation of M. 3 We aso assume that d d. This captures the notion that a contractua breach is ikey to be more costy to H when M is in the outh. More figurativey, we think of this assumption as refecting ess corruption and better ega protection in the orth. 2 This specification is simiar to the one in Grossman and Hepman (2002) and Antràs (2003a, 2003b). 3 The fact that the fraction of fina-good production ost is independent of h j greaty simpifies the anaysis, but it is not necessary for the quaitative resuts discussed beow.

10 560 journa of poitica economy As is cear from the weak inequaity, however, our resuts sti hod when d p d. 4 The ocation of M and the mode of ownership are chosen ex ante by H to maximize its profits. There is an infinitey eastic suppy of M agents in each one of the countries. Each fina-good producer H offers a contract that seeks to attract a pant operator M. The contract incudes an up-front fee for participation in the reationship that has to be paid by M. This fee can be positive or negative; that is, the operator can make a payment to the fina-good producer or vice versa. The purpose of the fee is to secure the participation of M in the reationship at minimum cost to H. When the suppy of M is infinitey eastic, M s profits from the reationship net of the participation fee are equa in equiibrium to its ex ante outside option. For simpicity, we set M s exante outside option equa to zero in both countries. It is, however, easy to extend the anaysis to cases in which these outside options are positive and different in the orth and in the outh. III. Equiibrium Consider the payoffs in the bargaining game for a pair of agents H and M in sector j. ince from now on we discuss a particuar sector, for simpicity we drop the index j from a the variabes. If the parties agree in the bargaining, the potentia revenue from the sae of the fina goods is R(i) p p(i)x(i), which, using (1) and (2), we can write as ah a(1 h) h(i) m(i) m a a[ h ] [ 1 h] R(i) p X v. (4) If they fai to agree, however, the outside option of M is aways zero, whereas that of H varies with the ownership structure and the ocation of components manufacturing. When H outsources components, its outside option is aso zero, regardess of the ocation of the manufacturing pant. In this event, H gets br(i) and M gets (1 b)r(i). As in Grossman and Hart (1986), our assumptions impy that the fina-good producer has more everage under vertica integration. When the parties fai to reach an agreement, H can se an amount dx(i) of output when its manufacturing pant is in country, which yieds the a revenue (d ) R(i). The ex post gains from trade in this case are [1 a (d )]R(i). In the bargaining, H receives its outside option pus a fraction 4 We maintain a distinction between d and d in order to show in ec. V that these two parameters affect the reative prevaence of different organizationa forms in distinct ways.

11 goba sourcing 561 a a b of the quasi rents, that is, (d ) R(i) b[1 (d )]R(i), and M obtains a (1 b)[1 (d )]R(i). otice that the payoffs in the bargaining game are proportiona to the revenue. With bkr(i) denoting the payoff of H under ownership structure k and the ocation of M in country, the assumption d d impies that b p (d ) b[1 (d )] b a a V V a a p (d ) b[1 (d )]1bO p bo p b. (5) That is, fina-good producers are abe to appropriate higher fractions of revenue under integration than under outsourcing, with this fraction being higher when integration takes pace in the orth. As in Grossman and Hart (1986), integration gives H residua rights of contro that aow it ex post to use the inputs produced by M, which in turn enhances H s bargaining position. As a resut, H gets a higher fraction of the revenue under integration. ince the deivery of the inputs h(i) and m(i) is not contractibe ex ante, the parties choose their quantities noncooperativey; every suppier maximizes its own payoff. In particuar, H provides an amount of headquarter services that maximizes bkr(i) wh(i), whereas M provides an amount of components that maximizes (1 b k)r(i) wm(i). Combin- ing the first-order conditions of these two programs, using (4), we can express the tota vaue of the reationship, as measured by tota operating profits, as where (m a)/(1 a) a/(1 a) p k(v, X, h) p X v w(h) k wf, k (6) 1 a[bh k (1 b k)(1 h)] k h 1 h a/(1 a) {(1/a)(w /b k)[w/(1 b k)] } w (h) p. (7) ote that among the arguments of the profit function p k(v, X, h), the first one is firm-specific whereas the others are industry-specific. Moreover, whie h is a parameter measuring the intensity of headquarter services, the consumption index X is endogenous to the industry but exogenous to the producer of a specific variety of the fina good. Our assumptions impy that the fina-good producer chooses the organizationa form that maximizes p k(v, X, h). To see why, reca that ex ante, before a reationship between H and M has been formed, H offers a contract designed to attract an M agent whose ex ante outside option is zero, and the contract incudes a participation fee, say t 0, that has to be paid by M. Under these circumstances the fina-good producer of brand i expects to earn operating profits phk p bkr(i) t wh(i) wf, where f represents the component of the fixed costs Hk Hk

12 562 journa of poitica economy that H has to bear when M is ocated in and the ownership structure is k. On the other hand, M expects to earn operating profits pmk p (1 b k)r(i) t wm(i) wfmkfrom the reationship with H, where f Mk represents the component of the fixed costs that M has to bear. By definition, fhk fmk p fk. ext, note that H has an incentive to raise t as much as possibe, as ong as the participation constraint pmk 0 is satisfied, because once a reationship between H and M is formed, the participation fee has no further effects on the outcomes. As a resut, the equiibrium vaue of t satisfies pmk p 0, which impies that phk p R(i) wh(i) wm(i) wf k. It foows that in a subgame-perfect equiibrium, phk p p k(v, X, h). Upon observing its productivity eve v, a fina-good producer H chooses the ownership structure and the ocation of manufacturing that maximizes (6), or exits the industry and forfeits the fixed cost of entry wf E. It is cear from (6) that the atter outcome occurs whenever v is beow a threshod v, denoted by v (0, ), at which the operating profits p(v, X, h) p max p k(v, X, h) (8) k {V,O}, {,} equa zero. amey, v is impicity defined by p(v, X, h) p 0. (9) This threshod productivity eve depends on the sector s aggregate consumption index X, that is, v(x ). In soving the probem on the right-hand side of (8), a fina-good producer effectivey chooses the tripet (b k, w, f k) that maximizes (6). It is straightforward to see that p k(v, X, h) is decreasing in both w and f k. For this reason, fina-good producers prefer to organize production so as to minimize both variabe and fixed costs. On account of variabe costs, southern manufacturing is preferred to northern manufacturing regardess of the ownership structure (because w 1 w ). On account of fixed costs, however, the ranking of profit eves is the reverse of the ranking of fixed-cost eves in (3). ext, note that if the fina-good producer coud freey choose its fraction of revenue bk, it woud choose b [0, 1] that maximizes w (h). This fraction is k h(ah 1 a) h(1 h)(1 ah)(ah 1 a) b (h) p 2h 1. (10) Athough a higher b k gives H a arger fraction of the revenue, it aso induces M to produce fewer components. As a resut, the fina-good producer trades the choice of a arger fraction of the revenue for a smaer revenue eve.

13 goba sourcing 563 Fig. 1. Distribution of revenue that maximizes joint profits The function b (h) is depicted by the soid curve in figure 1. It rises in h; b (0) p 0 and b (1) p 1. 5 To understand these properties, notice that in the ex post bargaining, neither H nor M appropriates the fu margina return to its investments in the suppy of headquarter services and components, respectivey. This eads them to underinvest in the provision of these inputs. Each party s severity of underinvestment is inversey reated to the fraction of the surpus that it appropriates. Ex ante efficiency then requires giving a arger share of the revenue to the party undertaking the reativey more important investment. As a resut, the higher the intensity of headquarter services (the arger h is), the higher the profit-maximizing fraction of the surpus accruing to the fina-good producer (the higher b is). Foowing Grossman and Hart (1986), we do not aow a free ex ante choice of the division rue of the surpus. The choice of ownership structure and the ocation of the manufacturing of components are the ony instruments for affecting the division rue, in the sense that the fina-good producer is constrained to choose a b k in the set {b V, b O, b, b }. When h is cose to one, higher vaues of b yied higher profits. V O k 5 otice aso that it does not depend on factor prices and that it is ess noninear the higher a is.

14 564 journa of poitica economy Given the ordering in (5), this impies that H woud have chosen domestic integration if there were no other differences in the costs and benefits of the competing organizationa forms. Conversey, when h is cose to zero, ower vaues of b k yied higher profits, and H woud have chosen outsourcing in the absence of other differences in the costs and benefits of the organizationa forms. aturay, there are other differences in the costs and benefits of various organizationa forms. As a resut, the profit-maximizing choice of an ownership structure and the ocation of the manufacturing of components depends on a firm s productivity eve. Free entry ensures that, in equiibrium, the expected operating profits of a potentia entrant equa the fixed cost of entry. From the discussion above, a firm that draws a productivity eve beow v(x ) chooses to exit because its operating profits are negative. On the other hand, firms with v v(x ) stay in the industry, and they choose organizationa forms that maximize their profits. Under the circumstances, the free-entry condition can be expressed as p(v, X, h)dg(v) p wf. E (11) v(x ) This condition provides an impicit soution to the sector s rea consumption index X. Using the sector s consumption index, we then can cacuate a other variabes of interest, such as the threshod productivity eve of surviving entrants, the organizationa forms of fina-good producers with different productivity eves, and the number of entrants. IV. Organizationa Forms The choice of an organizationa form faces two types of tensions. In terms of the ocation decision, variabe costs are ower in the outh, but fixed costs are higher there. In terms of the integration decision, insourcing entais higher fixed costs and gives H a arger fraction of the revenue. This does not necessariy benefit H; athough it raises H s incentive to suppy headquarter services, it reduces M s incentive to suppy components. If the effect on M s incentives is strong enough, H s profits may be ower under integration. These trade-offs are the centra considerations in the choice of an organizationa form. To simpify the discussion, we examine in this section organizationa forms in ony two types of sectors: those with reativey high headquarter intensity and those with reativey ow headquarter intensity. Intermediate cases can be simiary anayzed. We show beow that firms sort into organizationa forms according to the patterns depicted in figure 2. First, in component-intensive sectors (i.e., ow h), firms do not integrate;

15 goba sourcing 565 Fig. 2. Organizationa forms high-productivity firms outsource components in the outh, ow-productivity firms outsource them in the orth, and the east productive firms exit. On the other hand, integration takes pace in headquarterintensive sectors (i.e., high h). The most productive firms integrate in the outh and somewhat ess productive firms outsource in the outh. Firms with even ower productivity acquire components in the orth, and among them the more productive integrate and the ess productive outsource. The east productive firms exit. ote that surviving firms with the owest productivity outsource in the orth in a sectors. And more generay, ess productive firms acquire components in the orth whereas more productive firms acquire them in the outh. We now derive these resuts. First consider a sector with ow headquarter intensity h, such that b (h)! bo p bo p b; we refer to it as a component-intensive sector. This case is depicted in figure 1 by h p h M, where the arrows indicate the direction in which profits rise with changes in bk; that is, the profit function p(7) k is decreasing in bk. In this type of sector, H prefers outsourcing to insourcing in every country, because outsourcing has ower fixed costs and it gives H a ower fraction of the revenue. Under these circumstances, integration is not an optima strategy. In choosing between domestic and foreign outsourcing, however, H trades off the ower variabe costs of southern manufacturing against the ower fixed organizationa costs in the orth. Depending on whether the cross-country difference in the wage rate is sma or arge reative to the cross-country difference in the fixed organizationa costs, the resuting equiibrium can have outsourcing in both countries or outsourcing in the outh ony. Figure 3 depicts the first case, in which the wage differentia is sma (1 a)/a(1 h) reative to the fixed-cost differentia, that is, w /w! (f O /f O). a/(1 a) The variabe v is measured aong the horizonta axis and operating profits are measured aong the vertica axis. It is evident from (6) that a/(1 a) the operating profit function p k(7) is inear in v, and it has the intercept w fk. The sope of this function is proportiona to w k(h). It foows that the profit ine p O in figure 3 is steeper than the profit ine p OFirms, because wages are ower in the outh. with productivity beow vm expect negative profits under a organizationa forms. Therefore, they exit the industry. Firms with pro-

16 566 journa of poitica economy Fig. 3. Equiibrium in the component-intensive sector ductivity between vmand vmoattain the highest profits by outsourcing in the orth, whereas firms with productivity above v MO attain the highest profits by outsourcing in the outh. The cutoffs v and v M MOare given by (1 a)/a [ ] O w (fo f O) [ w (h) w (h) ] wf v p X (a m)/a O M, w (h) (1 a)/a (a m)/a vmo p X. (12) O O It aso is cear from figure 3 that the intersection point of the two profit ines takes pace at a negative profit eve when the fixed organizationa costs of outsourcing in the outh are cose to the fixed organizationa costs of outsourcing in the orth, that is, when w /w 1 (1 a)/a(1 h) (f /f ). In this case the threshod productivity eve v is de- O O M p O fined by the point of intersection of the profit ine with the horizonta axis. As a resut, a firms with productivity beow this threshod exit and a firms with higher productivity eves outsource in the outh. This describes the second type of equiibrium, in which no firm outsources in the orth. We sha treat the equiibrium with outsourcing in both countries

17 goba sourcing 567 Fig. 4. Equiibrium in the headquarter-intensive sector depicted in figure 3 as the benchmark case. In this event the freeentry condition (11), together with (6) and (8), impy w O(h)[V(v MO) V(v M)] w O(h)[V( ) V(v MO)] (a m)/(1 a) wx p, (13) fe f O [G(v MO) G(v M)] f O[1 G(v MO)] where v a/(1 a) V(v) p y dg(y). 0 Equations (12) and (13) provide impicit soutions for the cutoffs v M and v MO and for the aggregate consumption index X. We next consider a sector with high headquarter intensity h, such that b (h) 1 b V. We refer to it as a headquarter-intensive sector. A sector of this type is represented by h p h H in figure 1. In this sector, profits are increasing in b k, as shown by the arrows in the figure. In a head- quarter-intensive sector, the margina product of headquarter services is high, making underinvestment in h especiay costy and integration especiay attractive. This is refected in the sopes of the profit ines in figure 4; pvis steeper than pofor p,, because w V(h) 1 w O(h). ext compare the sopes of pv and po. On the one hand, integration gives the fina-good producer a arger fraction of the revenue, making

18 568 journa of poitica economy p V steeper. On the other hand, variabe production costs are ower in the outh, making p O steeper. For these reasons the profit ine of outsourcing in the outh can be steeper or fatter than the profit ine of integration in the orth. That is, w O(h) can be arger or smaer than 1 h w V(h). In particuar, w O(h) 1 w V(h) if and ony if (w /w ) 1 f(b V, h)/f(b, h), where 6 (1 a)/a h 1 h f(z, h) { {1 a[zh (1 z)(1 h)]} z (1 z). First consider the case in which the wage differentia is arge reative to the difference between bv and b, so that w O(h) 1 w V(h). Under these circumstances, w V(h) 1 w O(h) 1 w V(h) 1 w O(h). (14) Given the orderings in (3) and (14), the orders of the intercepts and the sopes of the profit functions are as depicted in figure 4. Moreover, the figure depicts our benchmark case for headquarter-intensive sectors, in which a four organizationa forms exist in equiibrium, with outsourcing and insourcing taking pace in both countries. Firms with productivity beow v exit the industry, those with productivity between v and v H H HO outsource in the orth, those with productivity between vho and vhv in- tegrate in the orth, those with productivity between v and v out- HV v HO source in the outh, and those with productivity above integrate in the outh (engage in vertica FDI). It is easy to see that either one of the first three organizationa forms may not exist in equiibrium but that the ast one aways exists in the absence of an upper bound on the support of G(v). That is, there aways exist high-productivity fina-good producers that choose to insource components in the outh. And more generay, the organizationa forms that survive in equiibrium attract firms according to the sorting pattern described in figure 4. If, for exampe, integration in the orth and outsourcing in the outh are viabe, firms that outsource in the outh have higher productivity than firms that insource in the orth. But insourcing in the orth woud not be viabe if its fixed organizationa costs were too high. In the next section, where we study variations in the reative preva- 6 1 h In component-intensive sectors, the inequaity (w /w ) 1 f(b V, h)/f(b, h) aways hods, because in these sectors f(z, h) is decining in z, and therefore the right-hand side is smaer than one (reca that bv 1 b). On the other hand, in headquarter-intensive sectors, the right-hand side is arger than one, because in such sectors f(z, h) is increasing in z. Therefore, the inequaity hods ony if the wage rate is sufficienty higher in the orth. HO

19 goba sourcing 569 ence of different organizationa forms, we focus on the benchmark case depicted in figure 4, for which the cutoffs are given by (1 a)/a [ ] O w (fv f O) [ w (h) w (h) ] V O w (fo f V ) [ w (h) w (h) ] O V w (fv f O) [ w (h) w (h) ] wf v p X (a m)/a O H, w (h) (1 a)/a (a m)/a vho p X, (1 a)/a (a m)/a vhv p X, (1 a)/a (a m)/a vho p X. (15) V O We can aso use the free-entry condition (11) to derive an equation that is anaogous to (13). This equation together with (15) can then be used to sove for the cutoffs and the consumption index X. ext consider the case in which the wage differentia is sma, so that 1 h (w /w )! f(b V, h)/f(b, h) in the headquarter-intensive sector. In this event, pv is steeper than po and the ordering in (14) is not preserved. In this case there are two possibiities ony: either w V(h) 1 w V(h) 1 w O(h) 1 w O(h) or w V(h) 1 w V(h) 1 w O(h) 1 w O(h) (because w O(h) 1 w O(h) ). When w V(h) 1 w V(h) 1 w O(h) 1 w O(h), integration in the orth domi- nates outsourcing in the outh, because the profit ine p V in figure 4 has a higher intercept and a arger sope than p O. As a resut, at most three organizationa forms exist in equiibrium: outsourcing in the orth, chosen by ow-productivity firms; insourcing in the orth, chosen by intermediate-productivity firms; and insourcing in the outh, chosen by high-productivity firms. On the other hand, when w (h) 1 w V V(h) 1 w O(h) 1 w O(h), integration in the orth dominates outsourcing and insourcing in the outh, in which case there is no internationa trade in intermediate inputs. As a resut, at most two organizationa forms can exist in equiibrium: outsourcing in the orth, chosen by ow-productivity firms, and insourcing in the orth, chosen by high-productivity firms. 7 7 Our anaysis has so far assumed that the ordering of the fixed costs (3) is satisfied. ow suppose instead that the fixed costs of outsourcing are higher than the fixed costs of integration in each one of the countries, but that the fixed costs of integration in the outh are higher than the fixed costs of outsourcing in the orth, i.e., fo 1 fv 1 fo 1 fv. In addition, suppose that the ranking of the sopes of the profit functions (14) hods. Then, in a headquarter-intensive sector, integration dominates outsourcing in both countries, because the fixed costs of integration are ower than the fixed costs of outsourcing and the profit ine of an integrated firm is steeper than the profit ine of an outsourcing

20 570 journa of poitica economy We have shown that in our benchmark cases the equiibrium organizationa forms foow the patterns depicted in figure 2. This sorting pattern differs from the sorting pattern derived by Grossman and Hepman (in press) for organizationa structures that use manageria incentives à a Homstrom and Migrom (1994). 8 Contrary to our resuts, in their mode, surviving ow-productivity firms acquire components in the outh. Within this group, ess productive firms outsource whereas more productive firms insource. Whie no one outsources inputs in the orth, there exist firms with modesty high productivity that integrate in the orth. However, the most productive firms, ike the east productive firms, outsource in the outh. Evidenty, these aternative theories of the firm predict different sorting patterns. Empirica evidence is needed to discriminate between them, but no such evidence is avaiabe for the time being. 9 V. Prevaence of Organizationa Forms Our mode predicts variations in organizationa forms across firms and industries. In the previous section we examined variations across firms. ow we ask, How does the prevaence of organizationa forms vary across industries? To answer this question, we use the fraction of firms that choose a particuar organizationa form as the measure of prevaence. We show in the Appendix, however, that using instead the market share of these firms as a measure of prevaence yieds simiar resuts. Foowing Hepman et a. (2004), we choose G(v) to be a Pareto distribution with shape z, that is, () z b G(v) p 1 for v b 1 0, (16) v firm. As a resut, no firm outsources and at most two organizationa forms exist in equiibrium: ow-productivity firms insource in the orth whereas high-productivity firms insource in the outh. On the other hand, in a component-intensive sector, a four organizationa forms can exist in equiibrium. In such an equiibrium the east productive firms insource in the orth, some more productive firms outsource in the orth, sti higherproductivity firms insource in the outh, and the most productive firms outsource in the outh. These resuts iustrate the infuence of fixed costs on the sorting patterns. ote, however, that independenty of whether the fixed organizationa costs of insourcing are higher than the fixed organizationa costs of outsourcing, integration is more prevaent in headquarter-intensive sectors. 8 They did not distinguish between component- and headquarter-intensive sectors, however, athough one can interpret their production technoogy as having h p 0, i.e., a zero output easticity with respect to headquarter services. For this reason a comparison of the cross-section variation of organizationa forms that is based on the component-intensive and headquarter-intensive distinction cannot be made with their work. 9 The empowerment of workers may aso be an important determinant of the structure of firms. Puga and Trefer (2002) and Marin and Verdier (2003) have deveoped genera equiibrium frameworks in which every firm chooses endogenousy the structure of authority within the organization.

21 goba sourcing 571 where z is arge enough to ensure a finite variance of the size distribution of firms. In this event the distribution of saes is aso Pareto, which is consistent with the evidence (see Axte 2001; Hepman et a. 2004). For concreteness we discuss ony the benchmark cases of componentand headquarter-intensive sectors as defined in ection IV. A. Component-Intensive ector Reca that in a component-intensive sector no firm integrates. In the benchmark case depicted in figure 3, firms with productivity beow v M exit the industry, those with productivity between vm and vmooutsource in the orth, and higher-productivity firms outsource in the outh. Denote by j MO the fraction of active firms that outsource in country. Then jmo p [1 G(v MO)]/[1 G(v M)] and jmo p 1 jmo. The Pareto z distribution (16) then impies that jmo p (v M/v MO). ubstituting (12) into this expression yieds [ ] z(1 a)/a w O(h) w O(h) f O MO w O(h) fo fo j p. (17) As is cear from equation (17), j MO is a function ony of the ratio of sopes w O(h)/w O(h) and the ratio of fixed costs f O /f O. In order to study how the different parameters of the mode affect the reative prevaence of foreign outsourcing, it is therefore sufficient to anayze their effect on these ratios. First consider the southern wage rate. A ower wage in the outh raises the profitabiity of outsourcing in the outh, that is, raises w O(h)/w O(h). As a resut, outsourcing in the outh becomes more prev- aent; that is, jmo increases. In addition, it can be shown that vm rises in the industry equiibrium, eading to exit of a arger fraction of firms. The mode can easiy be extended to incorporate transport costs for intermediate inputs. If the shipment of components is subjected to meting iceberg type transport costs, then a fa in transport costs is very simiar to a decine in the southern wage rate. It foows that, as in Meitz (2003), ower transport costs ead to more exit of ow-productivity firms and to more prevaence of foreign outsourcing. econd, consider an increase in the dispersion of productivity, which is represented by a decine of z. ince the expression in the brackets on the right-hand side of (17) represents the ratio of the cutoffs v M/vMO and this ratio is smaer than one, a rise in dispersion raises the fraction of firms that outsource in the outh This is simiar, in terms of the mechanism at work, to the finding in Meitz (2003) that more dispersion raises the share of exporting firms in domestic output and the finding in Hepman et a. (2004) that more dispersion raises horizonta FDI reative to exports.

22 572 journa of poitica economy Third, note that the headquarter intensity aso affects the prevaence of outsourcing in the two countries. ince w O(h)/w O(h) p (1 h)a/(1 a) (w /w ), it foows that foreign outsourcing is ess prevaent in sectors with higher headquarter intensity, because the ess important components in production are, the ess important the cost savings from outsourcing in the outh compared to the higher fixed organizationa costs of foreign outsourcing. Finay, we have assumed for simpicity that an outsourcing fina-good producer H appropriates a fraction b of the surpus from its reationship with an input suppier M, irrespective of whether M is in the orth or in the outh. Imagine, however, a situation in which this fraction can differ across countries, and H now gets a smaer fraction of the surpus from outsourcing in the outh, but sti higher than b (h), so that the sector remains component-intensive. This decine in H s bargaining power raises the profitabiity of outsourcing in the outh, making foreign outsourcing more prevaent. B. Headquarter-Intensive ector Four organizationa forms exist in the benchmark case of a headquarterintensive sector. Ordered from ow to high productivity, they are outsourcing in the orth, insourcing in the orth, outsourcing in the outh, and insourcing in the outh (see figs. 2 and 4). We denote by j Hk the fraction of firms that choose the organizationa form (k, ), where k is the ownership structure and is the ocation of M. Using the Pareto distribution (16) and the cutoffs (15), we can express these fractions as [ ] z(1 a)/a w V(h) w O(h) fo w O(h) w V(h) fo [ w (h) f f ] [ w (h) f f ] O V O O O V z(1 a)/a w O(h) w V(h) fo w V(h) w O(h) fo [ w (h) f f ] [ w (h) f f ] O O V O V O z(1 a)/a w V(h) w O(h) fo [ w (h) f f ] z(1 a)/a w V(h) w O(h) f O HO w O(h) fv fo j p 1, z(1 a)/a jhv p, z(1 a)/a jho p, jhv p. (18) O V O We again first consider a owering of the wage rate in the outh. Lower wages in the outh raise the profitabiity of foreign sourcing. In