Contractual Frictions and Global Sourcing

Transcription

1 Contractual Frictions and Global ourcing Pol Antràs and Elhanan Helpan Departent of Econoics, Harvard University May 6, 27 Abstract We generalize the Antràs and Helpan (24) odel of the international organization of production in order to accoodate varying degrees of contractual frictions. In particular, we allow the degree of contractibility to vary across inputs and countries. A continuu of rs with heterogeneous productivities decide whether to integrate or outsource the production of interediate inputs, and fro which country to source the. Final-good producers and their suppliers ake relationship-speci c investents which are only partially contractible, both in an integrated r and in an ar s-length relationship. We describe equilibria in which rs with di erent productivity levels choose di erent ownership structures and supplier locations, and then study the e ects of changes in the quality of contractual institutions on the relative prevalence of these organizational fors. Better contracting institutions in the outh raise the prevalence of o shoring, but ay reduce the relative prevalence of FDI or foreign outsourcing. The ipact on the coposition of o shoring depends on whether the institutional iproveent a ects disproportionately the contractibility of a particular input. A key essage of the paper is that iproveents in the contractibility of inputs controlled by nal-good producers have di erent e ects than iproveents in the contractibility of inputs controlled by suppliers. Keywords: contractual frictions, trade, FDI, sourcing. JEL Classi cation: D23, F, L23. This paper was prepared for the CEPR Globalization and the Organization of Firs conference in Munich, February 27. We thank Morten Olsen for excellent research assistance and Gianarco Ottaviano for helpful coents. Helpan thanks the ational cience Foundation for nancial support.

2 Introduction Insights fro neoclassical trade theory and new trade theory have iproved our understanding of the structure of foreign trade and investent. Recent developents in the world econoy have sparked, however, an increased interest in new theoretical approaches designed to better understand the evidence about rs that organize production on a global scale. These developents include the growing role of ultinational corporations in the global econoy, their engageent in ore coplex integration strategies, 2 and the growing share of interediate inputs in trade ows. 3 Although traditional theories allow for trade in interediate inputs and for the eergence of international production networks, 4 they cannot explain soe newly observed phenoena. 5 First, while the traditional approaches assue that rs are (for the ost part) syetrically structured within industries, the data exhibit substantial within-industry heterogeneity, both in the size distribution of rs and in their participation in foreign trade. 6 econd, in developing global sourcing strategies rs decide on where to locate the production of di erent parts of their value chains and also on the extent of their control over these activities. Which activities should they locate in the hoe country and which should they o shore? If they choose to o shore, should they engage in foreign direct investent (FDI) and iport interediate inputs within their boundaries or should they outsource the production of interediates to independent foreign suppliers? is well known fro the work of Coase (937), Williason (975, 985), and Grossan and Hart (986), these questions cannot be answered in a coplete-contracting fraework of the type used in traditional theories of international trade. In Antràs and Helpan (24) we developed a siple two-country Ricardian odel of international trade in order to address soe of these issues. In our odel, rs in the orth develop di erentiated products. Then they decide whether to integrate the production of interediates or outsource the. In either case rs have to decide in which country to source these inputs, in the high-cost orth or the low-cost outh. Production entails relationship-speci c investents by both the nal-good producers (or product developers) and their suppliers, and we assued that the nature of these investents does not enable the parties to specify the in an enforceable contract. As in the work of Grossan and Hart (986), we envisioned a world in which incoplete contracting creates ine ciencies even when the production of interediate inputs is carried out by integrated suppliers. The key di erence between integration and outsourcing is that only the forer gives the nal-good producer property rights over the fruits of the relationship-speci c investents. The gross product (value-added) of ultinational rs is roughly 25 percent of world GDP (UCTAD, 2). Leaving out the value-added generated by parent rs, about percent of world GDP is accounted for by foreign a liates, and this ratio has been increasing over tie. 2 ee UCTAD (998) and Feinberg and Keane (23). 3 ee for instance Huels, Ishii and Yi (2) and Yeats (2). Feenstra and Hanson (996) estiate that the share of iported interediates increased fro 5.3% of total U.. interediate purchases in 972 to.6% in 99. Capa and Goldberg (997) nd siilar evidence for Canada and the U.K., but not for Japan. 4 ee Helpan and Krugan (985, Chapters -3) and Jones (2). 5 ee Helpan (26) for a review of the newly observed phenoena and theoretical attepts to explain the. 6 ee Bernard and Jensen (999) or Bernard et al. (23) for evidence on heterogeneity in the exporting decision, and Bernard, Redding and chott (25) for evidence on heterogeneity in the iporting decision. As

3 Our odel focused on the choices between integration and outsourcing and between doestic sourcing and foreign sourcing. In particular, we described an equilibriu in which rs with di erent productivity levels choose aong the four feasible organizational odes: doestic outsourcing, doestic integration, foreign outsourcing (and thus iports of interediate inputs at ar s length), and foreign integration (and thus FDI and intra r iports of inputs). We then studied the e ects of variations in country and industry characteristics on the relative prevalence of these organizational fors. In this paper we generalize the Antràs and Helpan (24) odel to accoodate varying degrees of contractual frictions. 7 In particular, we adopt the forulation of partial contracting fro Aceoglu, Antràs and Helpan (26). Final-good producers and their suppliers undertake a continuu of relationship-speci c activities aied at producing an interediate input used in the production of the nal good. A fraction of these activities is ex-ante contractible while the rest cannot be veri ed by a court of law and therefore are noncontractible. Both parties are bound to perfor their duties in the contractible activities, but they are free to choose how uch they invest in the noncontractible activities. Moreover, a party can withhold its noncontractible services at the bargaining stage over the division of surplus if it is not satis ed with the outcoe. Every party s expected payo in the bargaining gae deterines its willingness to invest in the noncontractible activities. uppliers of interediate inputs do not expect to receive the full arginal return fro their investent in noncontractible activities, and therefore tend to underinvest in these activities relative to a coplete-contracting benchark. The larger the fraction of noncontractible activities is, the larger the distortions in production are. We allow the degree of contractibility to vary across inputs and countries. 8 As in Antràs and Helpan (24), we describe equilibria in which rs with di erent productivity levels choose di erent ownership structures and supplier locations. We then study the e ects of changes in the quality of contracting institutions on the relative prevalence of these organizational fors. We begin the analysis with a closed econoy in which an organizational choice boils down to outsourcing versus integration. We show that, as in our previous work, the relative iportance of the inputs provided by di erent parties is a crucial deterinant of the ake-or-buy decision. 9 In particular, regardless of the degree of contractibility of the inputs, integration is pro t-axiizing if and only if the production process is su ciently intensive in the input provided by the nal-good producer. The new interesting result is that the degree of contractibility of di erent inputs plays a central role in the integration decision. Iproveents in the contractibility of an input provided by the nal-good producer encourage outsourcing while iproveents in the contractibility of 7 Using data on the activities of U.. ultinational rs, Yeaple (26) presents evidence supporting soe salient cross-industry iplications of our odel. In particular, he nds that the share of intra r iports in total U.. iports (a easure of the relative prevalence of FDI over foreign outsourcing) is higher in industries with high R&D intensity and high productivity dispersion. Although the generalized odel developed in this paper also iplies a positive correlation between the share of intra r trade and productivity dispersion, it iplies a ore nuanced correlation with R&D intensity. 8 But we aintain the standard assuption that the set of available contracts does not vary with r boundaries. 9 ee also Grossan and Hart (986) and Antràs (23, 25). 2

4 an input provided by a supplier encourage integration. This contrasts with the transaction-costs literature (e.g., Williason, 975, 985), where any type of contractual iproveent tends to favor outsourcing. We next extend the analysis to a two-country world in which nal-good producers can contract with suppliers in their hoe country, orth, or a foreign country, outh. Wages are higher in orth, but orth has better contracting institutions in the sense that larger fractions of activities are contractible in orth. Although nal-good producers always locate in orth and ake their investents there, we allow the contractibility of these investents to be a function of the location of suppliers. This re ects the notion that certain clauses of a contract ay be harder to enforce when the contract governs an international transaction or when one of the parties resides in a country with weaker contracting institutions. Having constructed equilibria in which rs with di erent productivity levels sort into di erent organizational fors, we proceed to study the e ects of iproveents in contractibility on the relative prevalence of these organizational fors. We rst derive the result that iproveents in contractibility in outh raise the share of orthern rs that o shore the production of interediate inputs. In contrast, iproveents in contractibility in orth reduce the share of o shoring rs. These results are in line with recent arguents that the quality of contracting institutions ipacts coparative advantage (see Helpan (26) for a suary); the work of unn (26) provides epirical support. We also show, however, that the e ect that changes in contractibility have on the relative prevalence of particular organizational fors depends iportantly on the nature of the contractual iproveents. In particular, better contracting in outh, which raises o shoring, ay reduce the relative prevalence of FDI if the institutional iproveent a ects disproportionately the contractibility of inputs provided by the nal-good producer. And better contractibility in outh ay reduce the share of rs engaged in o shore outsourcing when the contractual iproveents are biased toward inputs provided by suppliers rather than the nal-good producer. One has to be indful of the ipact that iproveents in legal systes have on the contractibility of speci c inputs when predicting the prevalence of particular organizational fors. The rest of the paper is organized as follows. ection 2 develops our odel of the r in the presence of partial contracting. ection 3 studies the ake-or-buy decision in a closed econoy. ection 4 extends the analysis to a two-country world. ection 5 concludes. 2 Technology and Investent In this section we generalize the odel of the r that we developed in Antràs and Helpan (24) in order to accoodate varying degrees of contractual frictions. For this purpose we rst focus on a single r that produces a brand of a di erentiated product, for which it faces a deand unn s (26) estiates suggest that the ipact of cross-country variation in contracting institutions on trade ows is of the sae order of agnitude as the ipact of cross-country variation in huan capital. 3

5 function q = Ap =( ) ; < <, where q is quantity, p is price, A easures the deand level, and is a paraeter that controls the deand elasticity; the larger is the larger the elasticity of deand = ( ) is. As is well known, this for of deand results fro constant elasticity-of-substitution preferences for brands of a di erentiated product. This deand function yields revenue R = A q : () Output q is produced with two inputs, headquarter services X h and an interediate input X, using a Cobb-Douglas production function q = Xh h h X ; < h < ; = h ; where represents productivity, which ay vary across rs, and h is a paraeter that easures the technology s headquarter intensity. As in Antràs and Helpan (24), both inputs are brandspeci c. That is, X h and X have to be designed to precisely t the needs of this brand; otherwise the services derived fro the inputs equal zero. Moreover, an input designed to t this brand cannot be usefully eployed in the production of other brands of the product. We follow Aceoglu, Antràs and Helpan (26) in assuing that each one of the specialized inputs is produced with a set of activities indexed by points on the interval [; ], according to the Cobb-Douglas production function Z X j = exp log x j (i) di ; j = h; ; where x j (i) is the investent in activity i for input j. Investent in activities is input-speci c: they can be used only to produce the input for which they were designed. We assue that activities connected with input j in the range ; j, j, j = h;, are contractible, in the sense that the characteristics of these activities can be fully speci ed in advance in an enforceable ex-ante contract. The reaining activities ( j ; ] are not contractible. The nal-good producer has to supply headquarter services and she has to hire a supplier for the interediate input. The supplier of X can be the r s eployee or an outside agent. At this point we put aside the question of whether the r integrates the production of the interediate input or outsources it; we will deal with this question later. For now note that in either case there is an agency proble, because by assuption the r needs a supplier. The organizational for deterines (i) xed costs, to be speci ed later; (ii) variable costs of investent c j per unit x j (i) for j = h; and i 2 [; ], where c h is borne by the nal-good producer while c is borne by the supplier; (iii) the fractions of contractible activities j, j = h; ; and (iv) the fraction h 2 (; ) of the revenue that the nal-good producer obtains at the bargaining stage, and the 4

6 fraction = h of the revenue that the supplier of X obtains. We will discuss the details of alternative organizational fors in due course. The tiing of events is as follows:. The nal-good producer enters the industry and nds out her productivity level. 2. The nal-good producer chooses to leave the industry or stay and produce. 3. If she chooses to stay, the nal-good producer chooses an organizational for. 4. The nal-good producer coits to invest fx hc (i)g h i= in the contractible activities of headquarter services and she o ers potential suppliers a contract, which stipulates the supplier s required investent in the contractible activities of the interediate input fx c (i)g i= and an upfront payent of to the supplier, which can be positive or negative. 5. A large pool of potential suppliers can earn incoe w ; and they are willing to accept the r s contract if the payo fro supplying X is at least as large as w. This payo consists of the upfront payent plus the fraction of the revenue that they expect to receive at the bargaining stage, inus the cost of the inputs fx (i)g i=. Potential suppliers apply for the r s contract and the r chooses one supplier. 6. The supplier and the nal-good producer siultaneously choose their investent levels x j (i) = x jc (i) in the contractible activities i 2 ; j, j = h;, as speci ed in the contract, and both sides choose independently their reaining investent levels x j (i), i 2 ( ; ], j = h; ; in the noncontractible activities. 7. Output h R i q exp log x h (i) di A h h R exp log x (i) di h A (2) is sold and the resulting revenue is distributed between the nal-good producer and the supplier in proportions h and, respectively. (We will discuss the details of the bargaining later on.) We seek to characterize a syetric subgae perfect equilibriu (PE) of this 7-stage gae. To characterize an PE of this gae rst consider stage 6, in which the nal-good producer and the supplier each choose their investent levels in the noncontractible activities. Using the revenue function (), the nal-good producer s proble is Z ax h A fx h (i)g i= h q c h x h (i) di; h 5

7 subject to equation (2), x j (i) = x jc (i) for the contractible activities, and given investent levels x (i) in the supplier s noncontractible activities. iilarly, the supplier s proble is Z ax A fx (i)g i= q c x (i) di; subject to equation (2), x j (i) = x jc (i) for the contractible activities, and given investent levels x h (i) in the r s noncontractible activities. The ash equilibriu of this noncooperative gae yields j j x j (i) = x jn c j R; for i 2 ( j ; ]; j = h; ; (3) for the noncontractible activities. It follows that the investent in noncontractible activities is 2 3 x j (i)! = A h h 4exp X Z ` ` log x` (i) di5 (4) where!` = ` ( j j c j `=h;!k k!k k ; for i 2 ( c j ; ]; j; k = h; ; k 6= j; k `) for ` = h; ; and! = P`=h;!`. ote that! h easures the iportance of the noncontractible activities of headquarter services in the production of the nal good; it represents the elasticity of output with respect to x hn. iilarly,! easures the iportance of the noncontractible activities of the interediate input in the production of the nal good; it represents the elasticity of output with respect to x n. These easures of the ipact of the noncontractible activities on the production of the nal good play an iportant role in our applications of the odel. Fro the de nition of!`; noncontractible activities of input ` are ore iportant the larger the weight ` of input ` is in the production function and the saller the fraction of contractible activities ` is. That is,!` results fro an interaction of technological features with contracting frictions. For stage 5 of the gae to generate a non-epty set of applicants for the supply of X the nal-good producer needs to o er a contract that satis es the suppliers participation constraint, which is Z R c x (i) di + w ; (5) where the left-hand side represents a supplier s payo fro foring a relationship with the nalgood producer and the right-hand side represents his outside option before he fors this relationship. In this participation constraint the investent levels in the noncontractible activities satisfy equation (4); the investent levels in the contractible activities are x jc (i) for i 2 ; j, j = h;, as speci ed in the contract; and revenue R and output q are given by () and (2), respectively. In stage 3 the nal-good producer chooses the contract to axiize her payo Z h R c h x h (i) di ; 6

8 subject to (), (2), the participation constraint (5), and the incentive copatibility constraints (4). As long as there are no constraints on the upfront payent, the participation constraint is satis ed with equality at the solution to this proble. Therefore we can solve the upfront payent fro the participation constraint treated as an equality and substitute the result into the nalgood producer s objective function. Under these circustances the nal-good producer s choice of contractible investents is the solution to ax fx h (i)g i= ;fx(i)g i= Z Z R c h x h (i) di c x (i) di w ; subject to the incentive copatibility constraints (4) and the revenue and output equations () and (2). The solutions of x j (i) for i 2 ; j, j = h;, yield the contractible investent levels xjc (i) for i 2 ; j, j = h;. Using the rst-order conditions of the axiization proble together with (3) they can be expressed as x j (i) = x jc P`=h; `!`! Coparing this equation with (3) we obtain: j c j R; for i 2 ; j ; j = h; : (6) Lea For every input j = h; ; investent in contractible activities is larger than investent in noncontractible activities, i.e., x jc > x jn ; for j = h;. Evidently, when investent in contractible activities exceeds investent in noncontractible activities the investent levels do not axiize overall pro ts, because the two types of investent are equally costly. Moreover, the relative investent levels in the contractible activities, x hc =x c = ( h =c h ) = ( =c ), are pro t axiizing, while the relative investent levels in the noncontractible activities, x hn =x n = ( h = ) ( h =c h ) = ( =c ), are not. The latter results fro the fact that each party s return on its investent in noncontractible activities depends on its bargaining share j, and these shares are not necessarily equal. If they are equal, there is no distortion in the relative investent in noncontractible activities. Finally, note that the optial investent levels for a pro t-axiizing r are x j (i) = j =c j R for j = h;. Therefore in the equilibriu the noncontractible activities are underinvested and the contractible activities are overinvested relative to the revenue level R. This characterization of the contractible investent levels yields + j j j x jc = K c c j k c k k k ; for j; k = h; and k 6= j; (7) where K c = P `=h; `!`!! A h h! h h c c h!h : For a derivation of the pro t function and proof of Lea, see the Appendix. 7

9 This iplies that the nal-good producer s pro ts are = Z w ; (8) where = =( ) is an alternative easure of productivity, and Z = ( 2 6 ) A 4 c h h c!! h h P`=h; `!` (!)!! (9) is a derived paraeter which is proportional to the deand level; it depends on the costs of inputs, on the bargaining shares, and on the iportance of contractual frictions for headquarter services and interediate inputs. As expected, the pro ts of the nal-good producer are higher the higher the deand level A is, the lower the costs of inputs c h and c are, and the less attractive the suppliers outside option w is. In addition, her pro ts are lower the larger! h or! is, which iplies that her pro ts are higher the larger the fraction of contractible activities in headquarter services and/or in interediate inputs is. These results are suarized in 2 Proposition The pro ts of the nal-good producer are decreasing in input costs c j, j = h;, declining in the outside option of suppliers, w, and increasing in the shares of contractible activities j, j = h;. Bearing in ind that = h, note that pro ts are not onotonic in h, rather they are sallest when the revenue share of the nal-good producer equals zero or one, and pro ts are higher for interediate values. o consider the shares h and that axiize pro ts. To nd the, we axiize!! h X `=h; `!` A! ; subject to the constraint h = is given by j =! j (! k ), and h 2 (; ). The solution to this proble is unique; it p!h! (! h ) (! )! j! k for j; k = h; ; k 6= j; () and it iplies that ( h ) (! h! ), with strict inequality holding when! h 6=!. That is, the nal-good producer wants to give the supplier less than half the revenue if and only if the noncontractible activities in are less iportant than the noncontractible activities in h. Moreover, j is increasing in! j and declining in! k, k 6= j, and h = = =2 for! h =!. In other words, the nal-good producer wants to give the supplier lower shares of the revenue the less iportant noncontractible activities in are and the ore iportant noncontractible activities in 2 For proofs of Propositions, 2, and 3, see the Appendix. 8

10 * β h β hv β ho η hl η hc η hh η h Figure : Bargaining shares and headquarter intensity h are. ince! j = j j, it also iplies that the nal-good producer s optial h is increasing in h, declining in h ; and increasing in. Finally, pro ts are rising with j for < j < j and declining with j for j < j <. These results are suarized in Proposition 2 The optial shares h and have the following properties: (i) ( h ) (! h! ), with strict inequality for! h 6=!, and h = = =2 for! h =!. (ii) h is increasing in h, declining in h ; and increasing in. (iii) Pro ts are rising with j for < j < j and declining with j for j < j <, j = h;. We will use these results in the following analysis. 3 The Make-or-Buy Decision We now consider the tradeo between integration and outsourcing; that is, whether to ake the interediate input in-house or outsource it to an outside supplier. In this section we focus on the case in which both choices are ade in the sae country, say the hoe country of the nal-good producer. In this event input costs do not depend on the organizational for, nor do the degrees of contractual friction. 3 Moreover, the outside option of suppliers, w, does not depend on the ake-or-buy decision. Under the circustances we can focus on di erences in the revenue shares j. In view of part (iii) of Proposition 2 the nal-good producer prefers organizational fors with h closer to h. 3 One could, of course, allow to vary with the internalization decision, but we prefer to avoid this coplication. 9

11 Figure depicts h as a function of h. In view of part (ii) of Proposition 2 this is an increasing function, and it is easy to verify that h approaches when h! and h approaches when h!, as shown in the gure. ow consider what deterines the share h under outsourcing and integration. In stage 7 of the gae the investent levels x h (i) and x (i) are predeterined and therefore so are the input levels X h and X of headquarter services and coponents. At this stage the supplier and the nal-good producer bargain over the distribution of revenue R that they will receive when the nal goods are sold in the arket. Under outsourcing, X belongs to the supplier, while X h belongs to the nal-good producer. If the bargaining fails, output q equals zero and so does revenue. Moreover, given the high speci city of these inputs, which have no value outside the relationship, the outside option of every player equals zero. We assue that the parties engage in generalized ash bargaining with a bargaining weight 2 (; ) for the nal-good producer and 2 (; ) for the supplier. Therefore the solution to the bargaining gae, which gives every player his/her outside option plus the bargaining weight ties the ex-post gains fro the relationship, delivers the nal-good producer the payo + (R ) = R. aely, it gives her the fraction of the revenue. By siilar reasoning the supplier gets ( ) R. It follows fro this analysis that under outsourcing the nal-good producer gets the fraction ho = of the revenue, while the supplier gets the fraction O =. ext consider integration. Under this arrangeent the supplier is the nal-good producer s eployee and therefore the supplier does not own the interediate input. As a result the outside option of the supplier equals zero. Following Grossan and Hart (986), we assue that in the absence of the supplier s cooperation the nal-good producer, who owns both X h and X, cannot produce as e ciently with these inputs on her own as she can with the cooperation of the supplier. In particular, we assue that the nal-good producer can produce on her own only a fraction 2 (; ) of the output that she can produce with the cooperation of the supplier, i.e., q instead of q, where q is given in (2). In these circustances the revenue is R instead of R, where R = A q is the revenue generated by q (see ()). It follows that now the outside option of the nal-good producer is not zero but R, and this outside option is saller the larger is the e ciency loss fro the departure of the supplier. As a result, the nal-good producer s payo fro bargaining is R + (R R ) = hv R, where hv = + ( ) is the share of the revenue accruing to the nal-good producer. The supplier obtains the revenue share V = hv. Evidently, hv > = ho, which eans that the nal-good producer gets a larger share of the revenue under integration than under outsourcing. In what follows, our analysis proceeds under the assuption that hv > ho.

12 Figure depicts the revenue shares ho and hv and the headquarter intensities hl and hh for which each one of these shares axiizes pro ts. Part (iii) of Proposition 2 iplies that all rs with intensity below hl prefer to outsource and all rs with intensity above hh prefer to integrate. By continuity, rs with intensity slightly above hl also prefer to outsource and rs with intensity slightly below hh also prefer to integrate. And we show in the Appendix that a unique critical intensity level exists between hl and hh, denoted in the gure by hc, at which a r is just indi erent between outsourcing and integration. Firs with headquarter intensity below hc outsource and those with intensity above hc integrate. 4 result in Antràs and Helpan (24). This result is siilar to our In order to study the ipact of the quality of legal systes on industrial structure we need to understand how contractual frictions a ect the ake-or-buy decision. To this end rst consider an iproveent in contracting for interediate inputs, re ected in an increase in, the fraction of contractible activities in the anufacturing of coponents. Part (ii) of Proposition 2 iplies that this raises the optial revenue share h. In Figure this translates into an upward shift of the h curve. As a result, the critical intensity levels hl and hh decline. We show in the Appendix that the critical intensity level hc also declines. 5 The iplication is that in response to iproveents in contracting possibilities for coponents, ore rs, i.e., rs with a larger range of headquarter intensities, choose to integrate. The reason is that with better contracting in interediate inputs, nal-good producers are less dependent on the power of the incentives they can o er suppliers, and for this reason outsourcing which gives the suppliers stronger incentives than integration becoes less attractive. Iportantly, the opposite happens when contracting iproves in headquarter services. In this case part (ii) of Proposition 2 iplies that the optial revenue share h declines for every r and the cuto hc rises. 6 As a result rs with a larger range of headquarter intensities choose outsourcing over integration. The reason is that with better contracting in headquarter services it becoes ore iportant to give suppliers better incentives, because contractual frictions now play a relatively ore iportant role in coponents. In response ore rs choose outsourcing, which gives the suppliers ore powerful incentives. These results are suarized in the following: Proposition 3 Let xed and variable costs be the sae under integration and outsourcing. Then: (i) There exists a unique headquarter-intensity cuto hc 2 (; ) such that pro ts are higher under 4 The last stateent follows fro the fact that the critical value hc is unique, as we show in the Appendix. ote that at this critical value pro ts (8) are the sae when the r outsources or integrates, which eans that the value of Z is the sae under both organizational fors. Let Z ( h ; h ) be the value of Z when the nal good producer receives a fraction h of the revenue and headquarter intensity is h. Then the de nition of h iplies that Z ( ho ; hl ) > Z ( hv ; hl ) and Z ( ho ; hh ) < Z ( hv ; hh ). For this reason the continuity of the function Z () iplies that there exists a critical value hc 2 ( hl ; hh ) such that Z ( ho ; hc ) = Z ( hv ; hc ). The uniqueness of hc results fro the fact that the ratio Z ( ho ; h ) =Z ( hv ; h ) is declining in h. 5 This stes fro the fact that the ratio Z ( ho ; h ) =Z ( hv ; h ) (de ned in the previous footnote), which is declining in h at h = hc, also is declining in at h = hc. 6 The last result stes fro the fact that the ratio Z ( ho ; h ) =Z ( hv ; h ), which is declining in h at h = hc, is increasing in h at h = hc.

13 outsourcing for h < hc and higher under integration for h > hc. (ii) The cuto hc is higher the larger h is and the saller is. This proposition iplies that whenever sectors di er by headquarter intensity and organizational choices do not a ect xed and variable costs, the ake-or-buy decision does not depend on a r s productivity, only on its sectoral a liation. All rs in low headquarter intensity sectors choose outsourcing and all rs in high headquarter intensity sectors choose integration. Moreover, the fraction of sectors that choose integration is larger the larger is the fraction of contractible activities in coponents and the saller is the fraction of contractible activities in headquarter services. We next exaine the ipact of xed costs on the ake-or-buy decision of rs with di erent productivity levels. To this end suppose that there are di erent xed costs of running an integrated or an outsourcing enterprise, which we denote by F V circustances we can replace the pro t function (8) with and F O, respectively. Under these i = Z i w F i ; for i = O; V; () where i represents the organizational for, and Z i is the derived paraeter Z when evaluated at h = hi and the industry s h. At this point we take variable costs c h and c to be the sae for both organizational fors, and therefore for a given industry, Z i varies only with hi. Proposition 3 iplies that Z O > Z V for h < hc and Z O < Z V for h > hc. Following Antràs and Helpan (24), we now assue that integration involves higher xed costs than outsourcing. Two opposing forces deterine these costs. On the one hand anagerial overload is larger in an integrated enterprise, because anageent has to pay attention to any ore tasks. On the other hand there are econoies of scope in anageent. If the anagerial overload iposes larger costs than the costs saved due to econoies of scope then F V > F O. In the opposite case F V < F O. For concreteness we assue F V > F O. Under the circustances pro ts fro outsourcing are higher than pro ts fro integration in all sectors with h < hc, independently of a r s productivity level. The pro t function O is depicted in Figure 2; it has an intercept at inus w + F O and a constant slope Z O. The resulting pro ts are negative for <. For this reason only rs with higher productivity anufacture in this industry. We also depict in this gure the pro t function fro integration, V ; it has a lower intercept because F V > F O and a lower slope because Z V < Z O. This shows that in industries with low headquarter intensity all pro table rs outsource. Figure 3 depicts the two pro t functions O and V in a sector with high headquarter intensity. ow the xed costs still give outsourcing an advantage, as they did in the low headquarter intensity sector. But this is partly o set by lower-power incentives to the supplier, which helps the nal-good producer (i.e., Z V > Z O ). As a result, outsourcing doinates integration only for low-productivity rs, those with < O. 7 It follows that rs with productivity below do not produce, those 7 ote that in sectors with h close to hc the cuto O is strictly above, but in sectors with h close to it 2

14 π i π O π V w F O w F V Θ Θ Figure 2: Pro t function in a sector with h < hc π i π V π O w F O Θ Θ O Θ w F V Figure 3: Pro t function in a sector with h > hc 3

15 with productivity between and O outsource, and rs with productivity above O integrate. Our results on the choice of organizational fors by rs with di erent productivity levels are suarized in Proposition 4 Let variable costs be the sae under integration and outsourcing and let xed costs be higher under integration. Then: (i) In every sector there exists a cuto such that rs with productivity below do not produce. (ii) In a sector with h < hc ; all rs with productivity above outsource. (iii) In a sector with h > hc ; there exists a cuto O such that all rs with productivity above this cuto integrate. If this cuto is above, then all rs in the productivity range (; O ) outsource. This proposition shows how xed-cost di erences between organizational fors interact with productivity di erences across rs in shaping sectoral ake-or-buy decisions. In econoies with higher xed costs of integration, high-productivity rs integrate and low-productivity rs outsource in sectors with high headquarter intensity. rs outsource. In sectors with low headquarter intensity all ow consider the ipact of contractual frictions on the relative prevalence of integration and outsourcing. Evidently, this analysis applies only to sectors with h > hc, in which the two organizational fors coexist. As in Antràs and Helpan (24), we easure the prevalence of an organizational for by the fraction of rs that adopt it. For this purpose let the cuulative distribution function of productivity be G (). Then in sectors with O > the fraction of rs that integrate is V = G ( O) G () : ext suppose that is distributed Pareto with shape paraeter, so that 8 G () = in for in > and > 2. (2) Then V = : It follows that the share of integrating rs is larger the larger the ratio = O is. de nition of these cuto s we nd that O Fro the = w + F O Z O ; can be below. In the latter case all pro table rs in the industry integrate. 8 There is a productivity distribution of, say G (), and this distribution induces a distribution of = =( ), G (). When is distributed Pareto with the shape paraeter k then is also distributed Pareto with the shape paraeter = k= ( ) : 4

16 F O O = F V : Z V Z O Therefore V is larger the larger the ratio Z V =Z O is. We show in the Appendix that this ratio is decreasing in h and increasing in. As a result, the share of outsourcing rs, which equals V, is increasing in h and declining in. We therefore have Proposition 5 Let variable costs be the sae under integration and outsourcing and let xed costs be higher under integration. Then in sectors with h > hc in which O > the share of outsourcing rs is increasing in h and declining in. It follows fro this proposition that larger contractual frictions in headquarter services encourage integration and larger contractual frictions in coponents encourage outsourcing. For this reason overall iproveents in the quality of the legal syste, which raise the fraction of contractible activities in both headquarter services and coponents, ay raise the relative prevalence of integration or outsourcing. 9 A key insight fro this proposition is that contractual iproveents per se do not bias the industrial structure toward outsourcing, because the di erential ipact of the iproveent on contractual frictions in the two inputs plays an iportant role. ote that Proposition 5 describes the ipact of variations in contractual frictions on the prevalence of outsourcing even when there are general equilibriu e ects, as long as the general equilibriu feedbacks do no ipact the relative cost ratio (w + F O ) = (F V F O ), because the unit costs c h and c do not a ect the Z V =Z O ratio, nor does the deand level A. It is therefore evident that this proposition holds in the general equilibriu of a one-factor econoy, in which the xed costs F i, i = O; V, and w are proportional to the price of the factor. In fact, in this case we can think of w as the factor price. 2 4 Foreign ourcing ext consider foreign sourcing. We assue that the nal-good producer is located in orth, which is a high-cost country. But orth has good contracting institutions so the fraction of activities that are contractible is larger in orth. ow a r is not required to source the interediate 9 To clarify this point, let be an index of the quality of a country s legal syste and let i (), i = O; V, be increasing functions of this index. Then the arginal e ects i (), i.e., the slopes of these functions, can di er substantially. We have no theory to tell how they di er, and it is clear fro our analysis that there are di erences that lead to a rise in the prevalence of outsourcing and other di erences that lead to a rise in the prevalence of integration. Moreover, the shift in industrial structure ay depend on sectoral characteristics, such as headquarter intensity. We show in the Appendix an exaple with i () = for i = O; V, in which the ratio Z V =Z O is rising in for h = :4 and declining in for h = :5, where both these h s are above hc. 2 In our analysis we have assued that F V > F O. uppose instead that the xed costs of outsourcing are higher than the xed costs of integration. In this case we obtain the following results. First, in every sector there exists a cuto such that rs with productivity below do not produce. econd, in a sector with h > hc ; all rs with productivity above integrate. Third, in a sector with h < hc there exists a cuto V such that all rs with productivity above this cuto outsource, and if V >, then all rs in the productivity range (; V ) integrate. Finally, in an industry in which soe rs integrate and soe rs outsource, we nd that the share of outsourcing rs is increasing in h and declining in, just as in Proposition 5. Hence, the e ect of contractual frictions on the relative prevalence of integration or outsourcing is independent of the ranking of xed costs. 5

17 input in its hoe country; it has a choice to source it in orth or outh. Unlike orth, outh is a low-cost country, but its contracting institutions are weaker and therefore saller fractions of activities are contractible there. In what follows we denote with the superscript variables that are a liated with orth and superscript variables that are a liated with outh. Our assuption can therefore be represented by j > j for j = h;. In addition we assue that the nal-good producer has to produce headquarter services in orth, but she can produce interediate inputs in orth or outh, with c < c. In either case, i.e., independently of whether she produces coponents in orth or outh, she has the option to do so in-house or to outsource. When she chooses integration in outh she engages in foreign direct investent (FDI). When she chooses outsourcing in outh she engages in an ar s-length transaction. In the forer case there is intra r iports of coponents; in the latter case there is ar s-length iports of coponents. To siplify the analysis we assue that the revenue shares hi, i = O; V, are the sae in orth and outh. As a result we can characterize the relative size of the cuto hc, which now depends on whether coponents are produced in orth or outh. The cuto hc is de ned in the sae way as before; it represents the headquarter intensity at which the nal-good producer is indi erent between outsourcing and integration when the variable costs and xed costs are the sae in both cases, and the contractual frictions j, j = h;, are those prevailing in orth. In other words, hc solves ZO = Z V, where in coputing these Zs we use equation (9) evaluated at orthern variable costs. We have shown in the appendix that the ratio ZO =Z V does not depend on the variable costs and that it declines in h. As a result the solution to hc is unique. We now de ne analogously hc as the headquarter intensity easure at which Z O = Z V, where Z i represents the derived paraeter Z in equation (9) evaluated at the unit cost of headquarter services in orth, c h, the unit cost of coponents in outh, c, the outhern easure of contractual friction for headquarter services, h, and the outhern easure of contractual frictions for coponents,. ow too the cuto hc does not depend on unit costs and the ratio Z O =Z V is declining in h. As a result, the cuto hc is unique. The iplication is that in industries with h < hc we have Z O > Z V ; and in industries with h > hc we have Z O < Z V. It then follows that aong the rs who choose to o shore the production of interediate inputs, those with h < hc prefer to outsource, and those with h > hc prefer to integrate, unless the xed costs of integration and outsourcing are not the sae. j ote that the ratio ZO =Z V di ers fro Z O =Z V only as a result of the di erence between j and for j = h;. In the previous section (see Appendix for a foral proof), we have established that Z O =Z V is decreasing in and increasing in h. As a result, the lower contractibility of coponents in outh, <, tends to ake the ratio Z O =Z V higher than the ratio Z O =Z V. On the other hand, our forulation iplies that foreign sourcing also reduces the contractibility of headquarter services even though these are produced in orth, h < h. The idea is that, as in Antràs (25), all parts of a contract governing an international transaction are relatively harder to enforce. The lower contractibility of headquarter services associated with o shoring tends to ake 6

18 the ratio ZO =Z V lower than the ratio Z O =Z V. Overall, whether Z O =Z V is higher or lower than ZO =Z V depends on the relative agnitude of h h and. Because it sees natural that the contractibility of an interediate input is disproportionately a ected by the contracting institutions of the country in which this input is produced, in the reainder of the paper we focus on situations in which the di erence h h is low relative to the di erence. This allows us to establish the following result: Proposition 6 When h h is su ciently saller than, the cuto hc is higher when coponents are produced in outh than when they are produced in orth; that is, hc > hc. This proposition iplies that when weak institutions in outh have a stronger e ect on the contractibility of coponents than headquarter services, then ore sectors nd outsourcing advantageous when they o shore than when they do not. 2 A direct corollary of this proposition is Corollary When h h is su ciently saller than, the slopes of the pro t functions satisfy: (i) Z O > Z V and Z O > Z V for h < hc : (ii) Z O > Z V and Z O < Z V for hc < h < hc : (iii) Z O < Z V and Z O < Z V for h > hc : We are now ready to characterize the joint o shoring and ake-or-buy decisions. For this purpose we assue, as we did in the previous section, that the xed costs of integration are higher than the xed costs of outsourcing. Moreover, we assue that the xed costs of o shoring are higher than the xed costs of producing at hoe. In addition, we ake the soewhat stronger assuption F V + w > F O + w > F V + w > F O + w : In this ordering the xed costs of doing business in outh are substantially higher than the xed costs of doing business in orth, and this di erence overwhels the outh s cost advantage in w. The resulting pro t functions are ì = Zì w` F ` i, i = O; V; and ` = ; : (3) As in Antràs and Helpan (24) it is now useful to study the equilibriu in sectors that di er by headquarter intensity, h. 4. Low Headquarter Intensity ector First consider an industry with headquarter intensity h saller than hc. Fro Corollary this iplies ZÒ > Z`V for ` = ;. Given that the overall xed costs of integration w` + F `V are 2 Forally, the result follows fro the fact that ZÒ=Z`V is declining in h and ` Hence, by the iplicit function theore, ` hc than, we thus have that hc < hc. and increasing in ` h is increasing in ` h and decreasing in `. For h h for ` = ;. su ciently saller 7

19 j π i π O π O w F O Θ Θ O Θ w F O Figure 4: Pro ts fro outsourcing when h < hc and Z O > Z O higher than the overall xed costs of outsourcing w` + FÒ, it follows that in an industry with this headquarter intensity outsourcing doinates integration in orth as well as in outh, independently of a r s productivity level, i.e., Ò > `V for ` = ; and all. Under the circustances the e ective choice is between outsourcing at hoe and outsourcing in outh. ince the xed costs of outsourcing in outh are higher than the xed costs of outsourcing in orth, there is a tradeo between these two organizational fors only if ZO > Z O ; otherwise outsourcing in outh doinates outsourcing in orth. But the slope di erential between the two pro t functions fro outsourcing is driven by two considerations. On the one hand the variable unit costs of producing coponents are lower in outh, i.e., c > c, which raises ZO relative to Z O. On the other hand contractual frictions are higher in outh, i.e., j > j for j = h;, which reduces ZO relative to Z O. In other words, the arginal pro tability fro higher productivity can be higher or lower in outh depending on di erences in unit costs and in contractual frictions. 22 In industries with Z O < Z O ; all rs outsource in orth. In industries with ZO > Z O ; high-productivity rs outsource in outh. Figure 4 depicts the tradeo for ZO > Z O. Firs with productivity below lose oney either way, and they do not produce. Firs with productivity between and O outsource in orth, and those with productivity above O outsource in outh. This sorting pattern is siilar to Antràs and Helpan (24), except that now the case ZO < Z O can also arise, in which all rs outsource in orth. ote also that in the case depicted in the gure it is possible that all rs will outsource in outh if > O ; otherwise the two organizational fors coexist in the industry. We now calculate the fraction of rs that outsource in outh that is, the fraction of rs 22 In Antràs and Helpan (24) we had no di erences in contractual frictions, as a result of which we had ZO > ZO. There the assuption was ` j = for j = h;, and ` = ;. 8

20 that o shore assuing the Pareto distribution of productivity (2). This fraction is given by O = ; O where and O = = w + F O Z O F O + w Z O ; (4) FO + w : (5) Z O It follows fro these equations that O is larger the larger the ratio Z O =Z O is. aturally, this ratio is larger the larger the unit cost advantage of the outh c =c is. Moreover, fro Proposition, the ratio Z O =Z O is larger the larger is the fraction of contractible activities in outh, either or h, and the saller is the fraction of contractible activities in orth, either or h. In suary, we have Proposition 7 Consider an industry with h < hc. Then no r integrates and there exists a cuto given by (4) such that rs with productivity < do not produce. In addition: (i) If ZO < Z O then all rs with > outsource in orth. (ii) If ZO > Z O then there exists a cuto O given by (5) such that all rs with > O outsource in outh, and if O > then all rs with 2 ; O outsource in orth. (iii) If O > then the fraction of o shoring rs is larger the larger are the fractions of contractible activities in outh and the saller are the fractions of contractible activities in orth. A key iplication of this proposition is that lower contractual frictions in outh encourage o shoring, while lower contractual frictions in orth discourage o shoring. Although our ephasis in this paper is on the roles played by contractual frictions, it is useful to note that two additional sectoral characteristics also a ect the extent of foreign sourcing: productivity dispersion and headquarter intensity. As to productivity dispersion, Helpan, Melitz and Yeaple (24) show that it varies substantially across sectors. We have a natural easure of dispersion, ebodied in the shape paraeter of the Pareto distribution; productivity dispersion is larger the saller this paraeter is. It is evident fro the forula for the share of o shoring rs, O = = O, that this share is declining in. Therefore, o shoring is ore prevalent in sectors with ore productivity dispersion. ext consider the ipact of h on the extent of foreign sourcing. In Antràs and Helpan (24) we found that o shoring is less prevalent in sectors with higher headquarter intensity. This is easily generalized in the current odel, in which contractual frictions vary across inputs and countries. uppose that contractual frictions vary across inputs but not across countries, i.e., = = 9