Journal of Economic Behavior & Organization

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1 Journal of Economc Behavor & Organzaton 94 (2013) Contents lsts avalable at ScenceDrect Journal of Economc Behavor & Organzaton j ourna l ho me pag e: Incomplete contracts and the boundares of the multnatonal frm Nathan Nunn a,, Danel Trefler b a Department of Economcs, Harvard Unversty, 1805 Cambrdge Street, Cambrdge, MA 02138, USA b Rotman School of Management and Department of Economcs, Unversty of Toronto, Toronto, Ontaro M5S 3E6, Canada a r t c l e n f o Artcle hstory: Receved 4 November 2011 Receved n revsed form 16 May 2012 Accepted 1 October 2012 Avalable onlne 13 October 2012 JEL classfcaton: F14 F23 L14 L33 Keywords: Intra-frm trade Incomplete contracts Vertcal ntegraton Outsourcng Fxed-costs a b s t r a c t Usng data on U.S. ntra-frm and arm s-length mports for 5705 products mported from 220 countres, we examne the determnants of the share of U.S. mports that are ntra-frm. We examne two predctons that arse from Antràs (2003), Antràs and Helpman (2008) and Antràs and Helpman (2004). Frst, we fnd that, consstent wth the mplct logc of Antràs (2003) and the explct predctons of Antràs and Helpman (2008), vertcal ntegraton s ncreasng n the mportance of non-contractble headquarter nputs relatve to non-contractble suppler nputs. In other words, we show that only non-contractble headquarter nputs affect the frm s make-or-buy decson. Second, we also provde emprcal support for the Antràs and Helpman (2004) predcton that ntra-frm trade s largest where non-contractble headquarter nputs are mportant and productvty s hgh Elsever B.V. All rghts reserved. 1. Introducton Recently, a rch research agenda examnng the determnants of ntra-frm trade has developed. The lterature has been able to develop deep nsghts nto the multnatonal frms decson regardng the elements of nternatonal trade that are done nternally to the frm and whch are done outsde the boundares of the frm. 1 In ths paper, we are nterested n a strand of the lterature that examnes the relatonshp between a multnatonal frm and ts suppler. Each contrbutes a customzed nput that s non-contractble. As a result, there s a classc hold-up problem and the multnatonal must decde whether to vertcally ntegrate ts suppler or outsource to ts suppler. One strand of the lterature treats the dfference between these two organzatonal forms as the dfference between the outsde optons of the multnatonal n the event that the hold-up problem cannot be resolved through barganng. Ths treatment of the dfference between vertcal ntegraton and outsourcng orgnates wth Antràs (2003) and appears agan n Antràs and Helpman (2004, 2008). The authors thank Pol Antràs, Jan De Leocker, Rob Feenstra, Elhanan Helpman, Gene Grossman, Wlhelm Kohler, Marc Meltz, Ralph Ossa, Stephen Yeaple and semnar partcpants at Texas A&M Unversty, a Prnceton IES Summer Workshop, and an NBER ITI Workng Group Meetng. We are especally grateful to Joel Blt for facltatng constructon of the data base. Correspondng author. E-mal addresses: nnunn@fas.harvard.edu (N. Nunn), dtrefler@rotman.utoronto.ca (D. Trefler). URLs: (N. Nunn), dtrefler (D. Trefler). 1 Semnal contrbutons nclude McLaren (2000), Antràs (2003, 2005), Grossman and Helpman (2002, 2003, 2004, 2005), and Antràs and Helpman (2004) /$ see front matter 2012 Elsever B.V. All rghts reserved.

2 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) These papers yeld two mportant nsghts about the determnants of the share of total U.S. mports that are mported by U.S. multnatonals from ther foregn afflates (.e., ntra-frm). Frst, Antràs (2003) argues that when the U.S. headquarters frm provdes the bulk of the non-contractble nputs, undernvestment n nputs s reduced by hghly ncentvzng the headquarter. Vertcal ntegraton provdes such ncentves because t allows the headquarter to control at least some of the suppler s nputs even f blateral barganng breaks down. In contrast, when the foregn suppler provdes the bulk of the non-contractble nputs, the foregn suppler must be hghly ncentvzed. Ths s done by outsourcng: outsourcng strps the headquarters frm of any control over the suppler s nputs and thus strengthens the blateral barganng poston of the suppler. In short, the share of U.S. mports that are ntra-frm s ncreasng n the share of (non-contractble) nputs provded by the U.S. headquarters frm. 2 Whle Antràs (2003) examnes the smplfed case where all nputs are non-contractble, Antràs and Helpman (2008) allow a porton of the nputs to be contractble. (An alternatve nterpretaton s that they allow all nputs to be partally contractble.) Because Antràs (2003) assumes all nputs were non-contractble, n hs model what matters s the relatve mportance of total headquarter-provded nputs relatve to suppler nputs. However, as Antràs and Helpman (2008) llustrate, when some nvestments are contractble t s now only necessary to ncentvze the non-contractble nvestments. Therefore, what matters s the mportance of non-contractble headquarter nvestments relatve to non-contractble suppler nvestments. The second predcton about the share of total U.S. mports that s ntra-frm s developed n Antràs and Helpman (2004). The authors start wth the well-known fact that frms dsplay heterogeneous productvtes. They then argue that the fxed costs of producng abroad are lower when outsourcng to a foregn suppler than when usng foregn drect nvestment (vertcal ntegraton). Snce only the most productve frms capture the market share needed to offset the hgh costs of vertcal ntegraton, not all frms dentfed by Antràs (2003) as canddates for vertcal ntegraton wll n fact ntegrate. Only the most productve wll. Thus, the share of U.S. mports that are ntra-frm wll be large when two condtons are smultaneously satsfed: () the share of nputs provded by the headquarters frm s large (as n Antràs, 2003) and () frm productvty s hgh. Usng data on U.S. ntra-frm and arm s-length mports for 5705 products mported from 220 countres, we examne these determnants of the share of U.S. mports that are ntra-frm. Our conclusons mrror the two predctons lsted above. () In terms of the Antràs (2003) and Antràs and Helpman (2008) mechansm, we fnd support for the role of the mportance of noncontractble headquarter nputs relatve to non-contractble suppler nputs. () We also fnd strong support for the Antràs and Helpman (2004) predcton that ntra-frm trade s largest where headquarter nputs are mportant and productvty s hgh. The paper s organzed as follows. Secton 2 examnes the predctons of Antràs (2003) and Antràs and Helpman (2008), and Secton 3 examnes the predctons from Antràs and Helpman (2004). Secton 4 concludes. 2. The boundary of the frm and the role of (Antràs, 2003; Antràs and Helpman, 2008) We begn by revewng the salent features of the Antràs (2003) and Antràs and Helpman (2004, 2008) models from the perspectve of the emprcal work to follow. Snce the models have been presented and summarzed elsewhere, we only revew ts most mportant features here. 3 A U.S. frm produces a brand of a dfferentated varety j of a product n ndustry. Demand s generated by CES preferences. To produce the good, the frm must use two nputs, those produced by the U.S. frm (h (j) for headquarters) and those produced by a foregn suppler (m (j) for ntermedates). Output of the fnal good s gven by a Cobb Douglas producton functon wth two key parameters: a Hcks-neutral productvty parameter (j) that s varety (.e., match) specfc and the cost share of the nput provded by the frm, whch s an ndustry-specfc parameter. Specfcally, producton s gven by: ( h ) (j) ( ) 1 m q (j) = (j) (j). (1) 1 In Antràs (2003) and Antràs and Helpman (2004) t s assumed that the two nputs are entrely customzed and not contractble. Ths assumpton s relaxed n Antràs and Helpman (2008). Customzaton rases qualty to a threshold whch allows the fnal good to be sold to consumers. Unfortunately, for the U.S. frm and ts foregn suppler, the nvestments n customzaton are non-contractble and they have no value outsde of the relatonshp. Thus, there s a standard hold-up problem. After the nvestments n customzaton have been made there s renegotaton over how the ex post quas-rents from the relatonshp wll be shared. The tmng of the game played by the U.S. frm and ts foregn suppler s as follows. After the two partes match, the U.S. frm chooses the organzatonal form. Then nvestments n customzed nputs are made. Fnally, the ntal contract s renegotated and, f there s agreement, the product s sold. Let ˇ be the generalzed Nash share of the ex post quas-rents from the relatonshp that go to the U.S. frm. The U.S. frm receves ths share plus ts outsde opton. The organzatonal form vertcal ntegraton versus outsourcng chosen by the 2 Ths logc s a specfc nstance of the larger property rghts approach to the frm e.g., Grossman and Hart (1986). 3 See Helpman (2006) and Nunn and Trefler (2008).

3 332 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) headquarter alters the outsde opton of the U.S. frm. Regardless of the organzatonal form, the suppler earns nothng and ts outsde opton s 0. Ths s also the case for the U.S. frm under outsourcng. However, for a headquarter that has vertcally ntegrated wth ts suppler, f barganng breaks down, then the headquarter can stll produce some output by forcng ts now-dsgruntled suppler to do at least some work. Vertcal ntegraton s therefore a way for the frm to mprove ts outsde opton. Ths dfference n the headquarter s outsde optons under the two organzatonal forms leads to a trade-off. Although vertcal ntegraton allows the frm to grab a larger share of the pe, t also potentally leads to a smaller pe because of ncreased undernvestment by the suppler. Ths s modeled mathematcally as follows. Let k = V, O subscrpts denote the organzatonal form wth V for vertcal ntegraton and O for outsourcng. Recall that ˇ s the share of the ex post quas-rents that goes to the frm. Let R k (j) be the revenue generated when there s an agreement. If there s no agreement the frm can only sell a porton ı of the fnal output. Wth CES preferences and constant markup 1/, ths generates a revenue of ı R V (j). Therefore, the frm receves ts outsde opton ı R V (j) plus a share ˇ of the quas-rents (R V (j) ı R V (j)). That s, the frm receves [ı + ˇ(1 ı )]R V (j). Let ˇV = ı + ˇ(1 ı ) be the frm s share of revenues under vertcal ntegraton. Under outsourcng, the outsde opton s 0 and the quas-rents are R O (j) so that the frm receves 0 + ˇ(R O (j) 0) = ˇR O (j). Let ˇO = ˇ be the frm s share of total revenues under outsourcng. The upshot of all ths s the central result that the organzatonal form alters the U.S. frm s share of revenue. In partcular, ˇV > ˇO. Both the U.S. frm and the foregn suppler nvest and hence each must worry about the other s undernvestment. Where s large, the surplus generated by the relatonshp s partcularly senstve to the amount of nvestment undertaken by the U.S. frm. To reduce the degree of undernvestment by the U.S. frm, the frm must be gven a large share of the revenue. Ths share s largest under vertcal ntegraton because ˇV > ˇO. Ths s a specfc nstance of the Grossman and Hart (1986) property-rghts theory of the frm where resdual control rghts are allocated to the U.S. frm. In contrast, when s small, the surplus generated by the relatonshp s partcularly senstve to the amount of nvestment undertaken by the suppler. To reduce suppler undernvestment, the suppler must be gven a large share of the revenue. Outsourcng accomplshes ths because 1 ˇO > 1 ˇV. In Antràs (2003) t s assumed that (j) = 1 for all headquarter-suppler pars. The results when ths assumpton s relaxed are analyzed n Antràs and Helpman (2004). We descrbe ths case n Secton 3. Wth the assumpton that (j) = 1, Antràs (2003) shows that there s a unque value of (call t c ) such that the U.S. frm prefers vertcal ntegraton for > c and prefers outsourcng otherwse. Hypothess 1. There exsts a unque cut-off c wth the followng property. If > c then the frm wll vertcally ntegrate wth the suppler. If < c then the frm wll outsource from the suppler. We begn by testng Hypothess 1. The followng secton descrbes the data used to test Hypothess 1 and subsequent hypotheses whch are derved from Antràs and Helpman (2004, 2008) Data sources To nvestgate Hypothess 1 we use data on ntra-frm and total trade from the U.S. Census Bureau. Importers brngng goods nto the Unted States are requred by law to report whether or not the transacton s wth a related party. Ths nformaton allows us to dentfy whether mports are ntra-frm (related party) or at arm s-length (non-related party). See Appendx A for detals. The trade data are at the 6-dgt Harmonzed System (HS6) level for the year Our key dependent varable s ntra-frm mports as a share of total U.S. mports. Let ndex ndustres and let M V be the value of ntra-frm U.S. mports n ndustry. The V superscrpt s for vertcal ntegraton. Let M O be the value of arm s-length U.S. mports n ndustry. The O subscrpt s for outsourcng. M V + M O s total U.S. mports and M V /(M V + M O ) s ntra-frm mports as a share of total U.S. mports n ndustry. Antràs (2003) takes a stand on how we measure the headquarter ntensty of an ndustry, argung that captal nvestments can be provded by the headquarter, but not labor nvestments. In subsequent papers, the headquarter ntensty has been nterpreted as ncludng nputs such as R&D, advertsng, and manageral skll (see Antràs and Helpman, 2004, 2008; Yeaple, 2006). At the outset, we do not take a stance on whch characterstcs best measure nputs provded by the headquarter. Instead, we construct measures of each type of nput and let the data speak, ndcatng whch measure produces results that are consstent wth the model. We construct three measures that potentally capture the headquarter ntensty of an ndustry. The frst s the orgnal measure proposed n Antràs (2003), captal ntensty. We also construct measures of skll-ntensty and R&D ntensty to capture manageral nputs and R&D nputs, both of whch are potentally nputs provded by the headquarter. As a test of the model we also construct a factor ntensty measure for whch t s lkely that the nput s not provded by the headquarter. The measure s materal ntensty. Captal, skll, and materal ntenstes are constructed usng data on the factor ntensty of producton n each ndustry, whch are from the U.S. Census Bureau s 2005 Annual Survey of Manufactures. We use U.S. factor ntenstes, assumng that they are correlated wth the factor ntensty of producton n other countres. For each 6-dgt NAICS ndustry we 4 We are grateful to Andy Bernard for drawng our attenton to these data. See Bernard et al. (2005) for an example of how the data have been used.

4 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) Table 1 Headquarter ntensty and ntra-frm trade: testng Antràs (2003), lookng across ndustres. Dependent varable: M V /(M V + M O ) (1) (2) (3) (4) (5) ln R and D/Sales 0.318*** 0.310*** 0.213*** 0.273*** 0.288*** (0.056) (0.055) (0.072) (0.072) (0.069) ln Sklled Labor/Worker 0.172*** 0.208*** 0.236*** 0.302*** 0.239*** (0.102) (0.057) (0.082) (0.081) (0.075) ln Materals/Worker ** 0.155** 0.147* (0.065) (0.065) (0.074) (0.076) (0.076) ln Captal/Worker 0.167*** (0.064) ln Buldngs/Worker (0.064) (0.071) (0.076) ln Machnery/Worker 0.269*** (0.072) ln Computers/Worker (0.078) ln Autos/Worker 0.245*** (0.069) ln Other Machnery/Worker 0.197** 0.207** 0.203** (0.089) (0.092) (0.086) ln Non-Specfc Machnery/Worker (0.074) ln Non-Specfc Captal/Worker (0.074) Number of observatons R-Squared Notes: The dependent varable M V /(M V + M O ) s U.S. ntra-frm mports as a share of total U.S. mports. An observaton s a 6-dgt NAICS ndustry. Standardzed beta coeffcents are reported wth ther standard errors n brackets. ***, ** and * ndcate sgnfcance at the 1, 5 and 10 percent levels, respectvely. Non-Specfc Machnery s Computers + Autos. Non-Specfc Captal s Buldngs + Computers + Autos. Other Machnery s (total) Captal mnus Buldngs, Computers, and Autos. collect nformaton on annual captal expendtures, wages of producton workers and non-producton workers, and total expendtures on materals. Usng ths nformaton we construct measures of captal ntensty denoted K /L, skll-ntensty S /L and materal ntensty N /L. Captal ntensty K /L s measured as the natural log of captal expendtures dvded by all worker wages. Smlarly, materal ntensty N /L s measured as log materal expendtures dvded by worker wages. Skll ntensty S /L s the log rato of non-producton worker wages to total worker wages. Because the Annual Survey of Manufactures does not nclude nformaton on R&D expendtures, the data used to construct R&D ntensty are taken from the Orbs database, whch has nformaton on over 30 mllon companes worldwde. The database, constructed by Bureau van Djk Electronc Publshng, s constructed usng nformaton from over 40 dfferent nformaton provders. Both prvate and publc companes are lsted n the database, wth over 99 percent of the companes beng prvate. We measure R&D ntensty, whch we denote RD /Q, by the natural log of global R&D expendtures dvded by frm sales n each ndustry Examnng hypothess 1 (Antràs, 2003) Antràs (2003) examned Hypothess 1 usng BEA data on ntra-frm U.S. mports as a share of total U.S. mports. As we noted above, he related ths share to captal ntensty, hs proxy for. We start by examnng hs relatonshp wth roughly 300 NAICS 6-dgt ndustres. In partcular, we consder the followng cross-ndustry regresson: M V M V + M O S = + RD S + N R + K N + K + ε L Q L L, (2) where M V /(M V + M O ) s the share of U.S. mports n ndustry that are ntra-frm; S /L s log of non-producton worker wages to total worker wages; RD /Q s the log of R&D expendtures dvded by sales; N /L s the log of expendtures on materals dvded by total worker wages; K /L s the log of captal expendtures dvded by total worker wages. Estmates of Eq. (2) appear n column 1 of Table 1. The coeffcent for captal ntensty s postve and statstcally sgnfcant, a result that confrms the prevous fndngs of Antràs (2003), Yeaple (2006), Bernard et al. (2008), and Nunn and Trefler (2008). The estmated coeffcents for skll-ntensty and R&D ntensty are also postve and statstcally sgnfcant. The postve 5 If we do not take the natural log of K /L, S /L, and RD /Q, these measures are left skewed. Takng the natural log results n dstrbutons that are more normally dstrbuted.

5 334 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) coeffcent for R&D ntensty confrms the fndng of Antràs (2003) and Yeaple (2006), whle the postve coeffcent for skllntensty dffers from Antràs (2003) and Yeaple (2006), who fnd no statstcally sgnfcant relatonshp, but s consstent wth the postve coeffcent for skll-ntensty found by Bernard et al. (2008). The dfference n the results may be that Antràs (2003) and Yeaple (2006) use data from a much smaller sample of countres and more aggregate ndustry data than ether us or Bernard et al. (2008). Because we report standardzed beta coeffcents, one can easly assess and compare the magntudes of the coeffcents for the captal, skll and R&D ntensty measures. Accordng to the estmates of column (1), a one standard devaton ncrease n captal results n a.167 standard devaton ncrease n the share of ntra-frm mports. Ths s an economcally large effect. The estmated coeffcents for skll and R&D ntensty, whch are even larger, are.172 and.318, respectvely. Recall that n Antràs (2003) the nput beng produced q (j) s a customzed varety j of a good n ndustry. Because the nput s specfc to the varety, and therefore to the headquarter-suppler match, t s assumed that nvestments n h and m are also relatonshp-specfc. That s, they have no value outsde of the match. Ths s an mportant aspect about the nvestments n the producton of the nput whch has been taken for granted n prevous emprcal work such as Yeaple (2006) and Nunn and Trefler (2008). Ths suggests that when examnng captal nvestments what s mportant are captal nvestments that are relatonshp-specfc and therefore have no value outsde of the match. We examne ths mplcaton of the model by examnng dfferent forms of captal, each wth dfferent resale values outsde of the relatonshp. To do ths we agan rely on data from the 2005 Annual Survey of Manufactures. The survey reports total captal dvded nto the followng categores: () buldngs, () computers, () automobles, and (v) other machnery. Among these, buldngs, computers, and automobles have a hgher outsde value than other forms of machnery. Buldngs can be resold and used n the producton of other goods. Ths s n contrast to specalzed machnery, whch has sgnfcantly less use outsde of ts ntended producton process. Smlarly, computers and automobles, can be resold and have a use outsde of the relatonshp. Computers nclude standard desktop computers. Automobles only nclude standard vehcles that are drven on roads and do not nclude specalzed vehcles. Both computers and automobles have much greater outsde uses relatve to machnery that can only be used drectly n the producton process. We construct multple measures of captal ntensty usng the captal expendture data from the 2005 Annual Survey of Manufactures and nclude these n Eq. (2). The results are reported n columns (2) (5) of Table 1. Each captal ntensty measure s constructed as the natural log of the relevant captal expendtures dvded by total worker wages. We begn by dvdng captal between buldngs and machnery (whch s total captal mnus buldngs). If captal s an nput provded by the headquarter as asserted by Antràs (2003), and f machnery s relatonshp-specfc, then a greater machnery ntensty ncreases the need to ncentvze the headquarter, and, therefore, there should be more vertcal ntegraton and a greater share of ntra-frm mports. As reported n column (2), ths s ndeed what we observe n the data. The coeffcent for machnery ntensty s postve and statstcally sgnfcant. Note however, that f buldngs are not relatonshp-specfc as we argue, then an ncrease n the buldng ntensty of an ndustry does not ncrease the need to ncentvze the headquarter and therefore t should not ncrease the share of U.S. mports that are ntra-frm. Ths s what we observe n the data. The coeffcent for buldng ntensty s not postve and sgnfcant lke machnery ntensty. Instead, t has a negatve and statstcally nsgnfcant effect on the share of mports that are ntra-frm. We examne ths result further n column (3), where we dsaggregate captal further, and separately nclude measures of the factor ntensty of buldngs, computers, automobles, and other machnery (total captal mnus buldngs, computers and autos). Because the value of buldngs, computers and automobles outsde of the relatonshp s lkely hgher than other forms of captal, we do not expect a postve relatonshp between these factor ntenstes and the share of trade that s ntra-frm. The estmaton results are consstent wth ths. Only the estmated coeffcent for other machnery ntensty s postve and statstcally sgnfcant. In columns (4) and (5) we report alternatve specfcatons. In column (4) we aggregate computers and automobles and nclude ths measure, whch we label non-specfc machnery, along wth buldngs and other machnery n the estmatng equaton. In column (5) we nclude an aggregated measure, called non-specfc captal (the sum of buldngs, computers and automobles), along wth other machnery n the estmatng equaton. In both specfcatons, the coeffcent for the resdual captal ntensty measure other machnery s the only coeffcent that s postve and statstcally sgnfcant. Overall, the results of columns (2) (5) of Table 1 show that only for the relatonshp-specfc captal ntensty measure do we fnd the predcted postve relatonshp wth the share of mports that are ntra-frm. The valdty of estmatng Eq. (2) rests on the assumpton that we can aggregate across exportng countres. Yet as Schott (2004) notes, ths may be msleadng because an HS6 good produced n a poor country may be very dfferent from an HS6 good produced n a rch country. To address ths, we follow Nunn and Trefler (2008) and estmate a regresson that examnes varaton across ndustres and countres: M V c S M V c + M O = c + RD S + N R + K N + K + ε L c Q L L c, (3) where now subscrpts HS6 products rather than 6-dgt NAICS ndustres, and c denotes countres. M V c /(MV c + M O c ) s the share of U.S. mports from country c n ndustry that are ntra-frm. As before S /L s the log of non-producton worker wages to total worker wages; RD /Q s the log of R&D expendtures dvded by sales; N /L s the log of expendtures on

6 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) Table 2 Headquarter ntensty and ntra-frm trade: testng Antràs (2003), lookng across ndustres and countres. Dependent varable: M V c /(MV c + M O c ) (1) (2) (3) (4) (5) Determnants of the share of U.S. mports that are ntra-frm ln R and D/Sales 0.074*** 0.062*** 0.051*** 0.064*** 0.065*** (0.014) (0.013) (0.014) (0.015) (0.015) ln Sklled Labor/Worker 0.070*** 0.090*** 0.121*** 0.130*** 0.122*** (0.024) (0.025) (0.028) (0.026) (0.024) ln Materals/Worker 0.029* (0.017) (0.016) (0.017) (0.017) (0.016) ln Captal/Worker 0.043** (0.017) ln Buldngs/Worker 0.046*** 0.034* 0.039* (0.010) (0.034) (0.020) ln Machnery/Worker 0.078*** (0.028) ln Computers/Worker (0.020) ln Autos/Worker 0.052*** (0.014) ln Other Machnery/Worker 0.095*** 0.087*** 0.082*** (0.019) (0.019) (0.019) ln Non-Specfc Machnery/Worker (0.021) ln Non-Specfc Captal/Worker 0.053** (0.018) Country fxed effects Yes Yes Yes Yes Yes Number of observatons 119, ,973 92,611 92,611 94,749 Number of clusters R-Squared Notes: The dependent varable M V c /(MV c + M O c ) s U.S. ntra-frm mports as a share of total U.S. mports. An observaton s a HS6-country par. All equatons nclude country fxed effects. Standardzed beta coeffcents are reported wth ther standard errors, clustered at the 6-dgt NAICS ndustry level, n brackets. ***, ** and * ndcate sgnfcance at the 1, 5 and 10 percent levels, respectvely. Non-Specfc Machnery s Computers + Autos. Non-Specfc Captal s Buldngs + Computers + Autos. Other Machnery s (total) Captal mnus Buldngs, Computers, and Autos. materals dvded by total worker wages; K /L s the log of captal expendtures dvded by total worker wages. We control for exporter heterogenety by allowng for country fxed effects c. Estmates appear n Table 2. Because our varables of nterest K /L, RD /Q and S /L only vary at the 6-dgt NAICS ndustry level, whle the unt of observaton s a country and HS6 good, we report standard errors clustered at the 6-dgt NAICS level. The estmates, consstent wth the cross-ndustry estmates of Table 1, show that the captal, R&D, and skll ntensty of an ndustry are postvely correlated wth the share of ntra-frm trade. The estmates n columns (2) (5) further show that ths postve relatonshp s drven solely by the part of captal whch s more relatonshp-specfc. Overall, these results combned wth the cross-ndustry results of Table 1 provde support for Hypothess Explctly allowng for partally contractble nvestments (Antràs and Helpman, 2008) In Antràs and Helpman (2008), the assumptons of complete relatonshp-specfcty and non-contractblty of nvestments are relaxed. Instead, t s assumed that a fracton h and m of the nputs provded by the headquarter and suppler are ether not relatonshp-specfc or are contractble. (Only one of these two condtons need to be met to allevate undernvestment.) In other words, for the fracton 1 h and 1 m of h and m nputs (respectvely), the nvestments are relatonshp-specfc and ex post enforceable contracts cannot be wrtten. In Eq. (10) of Antràs and Helpman (2004), the headquarter s proft-maxmzng barganng share as a functon of s gven. Slght manpulaton of ths expresson yelds: ˇ h = h(1 m ) h m (1 h )(1 m ) h m. (4) Ths can be compared to the optmal barganng share from Antràs and Helpman (2008), where nvestments are partally contractble. In Antràs and Helpman (2008), the optmal barganng share s gven by: ˇ h = ω h(1 ω m ) ω h ω m (1 ω h )(1 ω m ), (5) ω h ω m where ω h (1 h ) and ω m (1 m )(1 ).

7 336 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) Table 3 Partally contractble captal and ntra-frm trade: testng Antràs and Helpman (2008). Dep var: share of ntra-frm trade, M V /(M V + M O ) Industry-Country Regressons Industry Regressons (1) (2) (3) (4) ln Captal/Worker, K /L 0.032* 0.035** 0.188*** 0.170*** (0.018) (0.018) (0.065) (0.065) Buldngs/Total Captal, x 1 (Buldngs + Autos + Computers)/Total Captal, x *** (0.011) (0.056) 0.048*** 0.121** (0.012) (0.053) All Control Varables Yes Yes Yes Yes Number of observatons 119, , Country fxed effects Yes Yes n/a n/a Number of clusters n/a n/a R-Squared Notes: The dependent varable M V c /(MV c + M O c ) s U.S. ntra-frm mports as a share of total U.S. mports. An observaton s an HS6-country par. Standardzed beta coeffcents are reported wth ther standard errors n brackets. In columns 1 and 2, standard errors are clustered at the 6-dgt NAICS ndustry level. ***, ** and * ndcate sgnfcance at the 1, 5 and 10 percent levels, respectvely. The Industry-Country Regressons of columns 1 and 2 nclude country fxed effects. All Control Varables ncludes H /L, M /L, and RD /Q. Comparng Eqs. (4) and (5), t s clear that the expresson for the headquarter s optmal barganng share has the same functonal form n the two papers except that when the fracton h of headquarter nvestments are contractble then s replaced wth (1 h ). Smlarly, 1 s also replaced wth (1 m )(1 ). The ntuton for ths s straghtforward. In Antràs (2003), ncreases vertcal ntegraton because t ncreases the mportance of the headquarter s undernvestment and the need to ncentvze the headquarter. When part of the headquarter s nvestments are contractble, then no longer measures the undernvestment of the headquarter. Ths s gven by the fracton of nvestments that are non contractble (1 h ) multpled by. Assume for the moment that, as n Antràs (2003), the fxed costs of vertcal ntegraton and the fxed costs of outsourcng are equal. The only effect that the choce of organzatonal form has s on ˇ, the share of the ex post surplus that accrues to the headquarter. From Antràs and Helpman (2008) we then have the followng hypothess. Hypothess 2. There exsts a unque cut-off hc wth the followng property. If > hc then the frm wll vertcally ntegrate wth the suppler. If < hc then the frm wll outsource from the suppler. In addton, the cut-off hc s hgher the hgher s h and the lower s m. From Hypothess 2 t follows that as before the share of trade that s ntra-frm should be ncreasng n. As well, the share of ntra-frm trade should be decreasng n the share of headquarter-nvestments that are not contractble h. We test ths predcton of Antràs and Helpman (2008) by focusng on the contractblty of headquarter nvestments, h. Usng our dsaggregated captal expendture data from the 2005 ASM, we construct two ndustry-specfc measures of h. The frst measure of, whch we denote x 1, s the fracton of captal expendtures on buldngs: x 1 = Buldngs Total Captal. The second measure s the fracton of expendtures on buldngs, automobles, and computers: x 2 = Buldngs + Autos + Computers Total Captal. The measure of contractblty of captal nvestments s dfferent from other measures of contractblty that exst n the lterature. The measure of contractblty n Nunn (2007) s the share of ntermedate nputs used n producton that can be bought and sold n thck markets. Bernard et al. (2008) use the share of U.S. mports controlled by wholesale and retal frms, measured at the HS10 level. The measures constructed here are not measures that attempt to quantfy how contractble goods n an ndustry are. Therefore t s conceptually very dfferent from the measure from Bernard et al. (2008). Instead the measures here quantfy the share of captal nvestments typcally made n an ndustry that have value outsde of the relatonshp.e., that are not relatonshp-specfc. It s more smlar to the measure from Nunn (2007), whch quantfes the relatonshp-specfcty of the ntermedate nputs used n the producton process. Smlar to ths measure, x 1 and x 2 quantfy the relatonshp-specfcty of captal used n the producton process. Estmates of our baselne equatons (2) and (3), wth the x measures ncluded, are reported n Table 3. Columns (1) and (2) report estmates of the country-ndustry level regresson equaton (3) and columns (3) and (4) report the estmates of ndustry level equaton (2).

8 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) U.S. (Parent) Imports Foregn (Subsdary) Fg. 1. U.S. mports: The ownershp structure consstent wth Antràs (2003) and Antràs and Helpman (2004, 2008). U.S. (Subsdary) Imports Foregn (Parent) Fg. 2. U.S. mports: The ownershp structure not consstent wth Antràs (2003) and Antràs and Helpman (2004, 2008). Overall, the estmaton results are consstent wth the predctons of Antràs and Helpman (2008). In all specfcatons, the estmated coeffcents for captal ntensty are postve and hghly sgnfcant, whle the coeffcents for the x varables are negatve n all four specfcatons and sgnfcant n three of the four Robustness check: correctly dentfyng the parent and the subsdary The results of Antràs (2003) and Antràs and Helpman (2004, 2008) are based on a specfc envronment. A key assumpton s that the ntermedate nput s produced n the foregn subsdary s country and s then shpped to the headquarter country. We have been assumng that the U.S. s the headquarter and the foregn country s the subsdary, and that the observed ntra-frm mports are mports beng shpped from a foregn subsdary to a U.S. headquarter. In realty, these mports could be mports beng shpped from a foregn parent to a U.S. subsdary. If ths s the case, then ths envronment s very dfferent from that modeled n Antràs (2003) and Antràs and Helpman (2004, 2008). If, for example, the good s produced by a foregn headquarter and shpped to a U.S. subsdary, then the crucal assumpton that the headquarter can only provde headquarter nputs when producng the nput s no longer realstc. In Antràs (2003) t s assumed that the headquarter cannot provde labor nputs because t s not famlar wth foregn labor markets and because t s dffcult to have a manageral presence n the foregn country (Antràs, 2003, p. 1379). But f the nput s beng produced n the headquarter s country then these arguments no longer apply. There s no reason that the headquarter cannot provde all of the nputs requred to produce the ntermedate nput. It s also no longer clear that captal s the nput provded by the headquarter. Therefore, there s no longer a reason to expect captal ntensty to be correlated wth vertcal ntegraton. Fgs. 1 and 2 report the two possble scenaros, when examnng U.S. mports. Fg. 1 shows the case where goods are beng mported from a foregn subsdary to a U.S. headquarter. Ths s the envronment beng modeled n Antràs (2003) and Antràs and Helpman (2004, 2008). Fg. 2 shows the other case where a good s beng shpped from a foregn parent to a U.S. subsdary. Ths case, as we have argued, does not ft the models beng examned here. To dstngush emprcally between the two cases shown n Fgs. 1 and 2, we use data from Bureau van Djk s Orbs Database, whch provdes nformaton on the name and country of the headquarters and subsdares of global multnatonals, as well as the ndustry that the frms are classfed under. Usng ths nformaton we dentfy all subsdary headquarter pars n whch ether the subsdary or the headquarter are from the U.S. (pars n whch both the subsdary and the headquarter are from the U.S. are excluded). We then calculate for each foregn country () the number of pars for whch the headquarter s from the U.S., () the number of pars for whch the subsdary s from the U.S., and () the fracton of pars for whch the U.S. s the headquarter. Ths nformaton s reported n Table 4 for all countres for whch the share of pars for whch the U.S. s the parent below 75 percent. As shown, only 18 countres fall nto ths category. Ths ndcates that for the vast majorty of countres, the U.S. s generally the headquarter. The countres for whch ths s not the case tend to be developed countres, such as Italy, Sweden, Swtzerland and Japan. We use the nformaton from Table 4 to dentfy countres for whch ntra-frm mports are more lkely to be from a foregn subsdary to a U.S. parent (the case from Fg. 2) and construct a restrcted sample of countres for whch the share of U.S. headquarters s above 50 percent. Ths amounts to removng Iceland, Italy, Fnland, Lechtensten, and Swtzerland from the sample. Table 5 reproduces the estmates of Table 1 usng the more restrcted sample of countres. As shown, the results are qualtatvely dentcal. 6 An alternatve scenaro that fts the Antràs (2003) and Antràs and Helpman (2004, 2008) models cleanly s the case of exports from a U.S. subsdary to a foregn parent. Here the nterpretaton s that an ntermedate nput s produced by a U.S. subsdary and then t s exported to a foregn parent. Fg. 3 shows ths case. 6 An alternatve strategy s to calculate the fracton of partnershps for whch the U.S. s the headquarter for all country and ndustry pars. The ndustrycountry measures can then be used to omt observatons from the sample. Results are smlar f ths strategy s pursued.

9 338 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) Table 4 Average natonalty of the parent (foregn vs. U.S.) by country. Number of relatonshps wth: Share of relatonshps wth a U.S. parent Country A U.S. parent A foregn parent Iceland Italy Fnland Lechtensten Swtzerland Sweden Tawan Belgum Bermuda Norway Denmark Korea Japan Span Israel Austra France Germany Notes: The table reports the total number of parent subsdary pars dvded nto cases n whch the parent/headquarter s a U.S. frm and n whch the parent/headquarter s a foregn frm. The fnal column reports the fracton of relatonshps n whch the parent s a U.S. frm. These fgures are reported separately for each country. The table only reports the 18 countres wth the lowest average U.S. parent share. Data are from the Orbs Database. Table 5 Imports nto the U.S. among a restrcted sample of countres: testng Antràs (2003) and Antràs and Helpman (2008). Dep var: M V c /(MV c + M O c ) Restrcted sample: HQ US c > HQ F c (1) (2) (3) (4) (5) ln R and D/Sales 0.074*** 0.062*** 0.051*** 0.064*** 0.065*** (0.015) (0.013) (0.015) (0.016) (0.016) ln Sklled Labor/Worker 0.068*** 0.088*** 0.118*** 0.127*** 0.120*** (0.024) (0.025) (0.045) (0.026) (0.024) ln Materals/Worker 0.031* (0.017) (0.016) (0.017) (0.017) (0.017) ln Captal/Worker 0.041** (0.017) ln Buldngs/Worker 0.047*** 0.036* 0.040* (0.017) (0.020) (0.020) ln Machnery/Worker 0.077*** (0.016) ln Computers/Worker (0.025) ln Autos/Worker 0.052*** (0.014) ln Other Machnery/Worker 0.094*** 0.085*** 0.081*** (0.019) (0.019) ln Non-Specfc Machnery/Worker (0.021) ln Non-Specfc Captal/Worker 0.054*** (0.019) Country fxed effects Yes Yes Yes Yes Yes Number of observatons 111, ,065 86,622 86,622 88,579 Number of clusters R-Squared Notes: The dependent varable M V c /(MV c + M O c ) s U.S. ntra-frm mports as a share of total U.S. mports. An observaton s a HS6-country par. All equatons nclude country fxed effects. Standardzed beta coeffcents are reported, wth standard errors clustered at the 6-dgt NAICS ndustry level n brackets. ***, ** and * ndcate sgnfcance at the 1, 5 and 10 percent levels, respectvely. Non-Specfc Machnery s Computers + Autos. Non-Specfc Captal s Buldngs + Computers + Autos. Other Machnery s (total) Captal mnus Buldngs, Computers, and Autos. U.S. (Subsdary) Exports Foregn (Parent) Fg. 3. U.S. exports: The ownershp structure consstent wth Antràs (2003) and Antràs and Helpman (2004, 2008).

10 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) U.S. (Parent) Exports Foregn (Subsdary) Fg. 4. U.S. exports: The ownershp structure nconsstent wth Antràs (2003) and Antràs and Helpman (2004, 2008). Table 6 Exports nto the U.S. among a restrcted sample of countres: testng Antràs (2003) and Antràs and Helpman (2008). Dep var: X V c /(XV c + X O c ) Restrcted sample: HQ F c /(HQ F c + HQ US c ) >.65 (1) (2) (3) (4) (5) ln R and D/Sales 0.075*** 0.064*** 0.060*** 0.068*** 0.069*** (0.016) (0.016) (0.018) (0.018) (0.018) ln Sklled Labor/Worker 0.080** 0.100*** 0.149*** 0.154*** 0.144*** (0.036) (0.037) (0.034) (0.032) (0.029) ln Materals/Worker (0.021) (0.020) (0.024) (0.025) (0.022) ln Captal/Worker 0.074*** (0.022) ln Buldngs/Worker 0.043** (0.018) (0.023) (0.024) ln Machnery/Worker 0.109*** (0.019) ln Computers/Worker (0.025) ln Autos/Worker 0.041** (0.017) ln Other Machnery/Worker 0.118*** 0.113*** 0.109*** (0.023) (0.023) (0.022) ln Non-Specfc Machnery/Worker (0.008) ln Non-Specfc Captal/Worker 0.048** (0.020) Country fxed effects Yes Yes Yes Yes Yes Number of observatons 29,965 29,784 22,610 22,610 23,232 Number of clusters R-Squared Notes: The dependent varable X V c /(XV c + X O c ) s U.S. ntra-frm exports as a share of total exports from the U.S. An observaton s an HS6-country par. All equatons nclude country fxed effects. Standardzed beta coeffcents are reported, wth standard errors, clustered at the 6-dgt NAICS ndustry level, n brackets. ***, ** and * ndcate sgnfcance at the 1, 5 and 10 percent levels, respectvely. Non-Specfc Machnery s Computers + Autos. Non-Specfc Captal s Buldngs + Computers + Autos. Other Machnery s (total) Captal mnus Buldngs, Computers, and Autos. The last possble scenaro s where a U.S. headquarter produces the ntermedate nput and exports t to a foregn subsdary. Ths s shown n Fg. 4. The same argument and dscusson as for Fg. 2 also apples to Fg. 4. Therefore, there s no reason to expect the predctons of the Antràs (2003) and Antràs and Helpman (2004, 2008) models to be relevant for ths case. We try and dstngush emprcally the case shown n Fg. 3 from the case n Fg. 4 by examnng the determnants of ntra-frm exports from the U.S. to countres for whch the headquarter s typcally the foregn country and the U.S. s the subsdary. We dentfy these countres agan usng the Orbs data. We choose to nclude n the sample the 15 countres wth the lowest share of U.S. headquarters. Ths s equvalent to choosng a cut-off of 65 percent. 7 These results are reported n Table 6. Overall, the results are consstent wth the results obtaned when U.S. mports are examned (reported n Tables 2 and 5). The share of ntra-frm exports from the U.S. are hgher n headquarter-ntensve ndustres, as measured by captal ntensty. Ths s shown n column (1). Columns (2) (5) show that ths effect s drven by the relatonshp-specfc components of captal, and not by buldngs, computers or autos. 8 7 The coeffcent estmates are smlar, but wth larger standard errors, f one chooses a cut-off of 50 percent so that only 5 countres are ncluded n the sample. 8 Agan, one can pursue the alternatve strategy of constructng country-ndustry specfc measures of the share of relatonshps for whch the parent s the foregn country. Examnng exports and restrctng observatons usng ths measure also yelds results that support Hypothess 1.

11 340 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) π O (θ ) (θ ) π V π O (θ ) (θ ) π V θ α /( 1 α ) α /( 1 α ) -F O θ -F O -F V η < η c Incentvze Foregn Suppler All frms prefer Outsourcng to Vertcal Integraton -F V η > η c Incentvze U.S. Suppler Productve frms prefer Vertcal Integraton to Outsourcng Fg. 5. The outsourcng decson wth frm-specfc productvty dfferences. 3. Productvty heterogenety (Antràs and Helpman, 2004) Antràs and Helpman (2004) relax the assumpton of the same productvty across frms. That s, (j) n Eq. (1) s allowed to vary across frm-suppler relatonshps. Let k be varable profts for a frm wth = 1 that uses organzatonal form k = V, O. Then, as s well known, profts for a frm wth productvty that adopts organzatonal form k are lnear n /(1 ) : k () = /(1 ) k F k, (6) where F k s the fxed costs of offshorng usng organzatonal form k. Antràs (2003) assumes that all frms have the same productvty ( = 1) and the same fxed costs (F V = F O ). Under these assumptons the Antràs effect states that V > O f and only f > c.e., the U.S. frm prefers vertcal ntegraton to outsourcng when the frm s share of nputs s large. Heterogenety of productvty by tself does not alter ths concluson t smply magnfes the advantages (or dsadvantages) of vertcal ntegraton. 9 However, when the fxed costs of outsourcng vary across organzatonal forms then productvty heterogenety matters. How heterogenety matters depends on whether F V F O s postve or negatve. Antràs and Helpman assume that F V > F O. 10 Fg. 5 llustrates what happens when heterogenety s ntroduced. The fgure plots profts under outsourcng O () and vertcal ntegraton V (). From Antràs (2003, lemma 3), we know that V / O s ncreasng n and equals 1 for = c. Ths together wth Eq. (6) mples that V () s steeper than O () for > c and flatter for < c. From the left-hand panel of Fg. 5 where < c and F V > F O, t must be that outsourcng s always preferred to vertcal ntegraton. The Antràs effect and the lower fxed costs of outsourcng both work n favor of outsourcng. When > c, as n the rght-hand panel of Fg. 5, V () s steeper than O (). It follows that the two curves must cross. Frms wth productvty to the rght of the crossng pont wll vertcally ntegrate. Frms to the left wll outsource. The tenson here s that fxed costs push for outsourcng whle the Antràs effect pushes for vertcal ntegraton. Snce the Antràs effect s greatest for the most productve frms, the Antràs effect domnates for productve frms. All of ths leads to an nterestng emprcal predcton about the share of U.S. mports that are ntra-frm, M V c /(MV c + M O c ). The share should depend on an nteracton of wth (j). In ndustres for whch < c, we have that M V c = 0 so that an ncrease n the productvty of a match (j) has no effect on ts organzatonal form and M V c /(MV c + M O c ) = 0. In ndustres wth > c, an ncrease n (j) ncreases the lkelhood that vertcal ntegraton s chosen and therefore t wll ncrease M V c /(MV c + M O c ). If one assumes, as Antràs and Helpman (2004) do, that frm productvty follows a Pareto dstrbuton, then these predctons can be stated n terms of dfferences n the dsperson of frm productvty wthn ndustres, whch we denote by x. When > c, then n ndustres wth a greater dsperson of frm productvtes (.e., a hgher x ), we should see a larger share of frms that vertcally ntegrate,.e. a hgher M V c /(MV c + M O c ). On the other hand, when < c, an ncrease n x has no effect on M V c /(MV c + M O c ), snce ths s ndependent of productvty and equal to zero. Therefore, we have the followng hypothess from the Antràs-Helpman (2004) model. 9 That s, f F V = F O then V () > O () V > O and t remans true that the frm prefers vertcal ntegraton f and only f > c. 10 They argue that vertcal ntegraton creates a need to supervse the producton of ntermedate nputs, thus creatng manageral overload.

12 N. Nunn, D. Trefler / Journal of Economc Behavor & Organzaton 94 (2013) Hypothess 3. Assume F V > F O. Let x be the dsperson of across frms wthn ndustry. Then, (a) If < c then dsperson does not affect the ntra-frm share of mports: MV c /(MV c +MO c ) = 0. (b) If > c then dsperson ncreases the ntra-frm share of mports: MV c /(MV c +MO c ) > 0. x x 3.1. Examnng Hypothess 3 (Antràs and Helpman, 2004) Testng Hypothess 3 requres a measure of productvty dsperson x. The strategy we pursue here follows the basc logc of Helpman et al. (2004) and Yeaple (2006) who use the standard devaton of frm sales wthn an ndustry as a measure of dsperson. In the theory (j) s par specfc. Therefore, productvty vares across matches, wth part of the match beng a U.S. frm and part of the match beng a foregn frm. As well, (j) maps drectly onto frm sales Q f,,c. Although we observe sales at the frm level, we do not observe the trade data at the frm level. Ths s only observed at the ndustry-country level. Therefore, we need to thnk carefully about how we wll match our constructed measure of productvty to the trade data. In the trade data we can dentfy the locaton of the headquarter and suppler. We know the country the goods are beng shpped from and the country they are beng shpped to. We also have a sense of whch s most lkely the headquarter and whch s most lkely the subsdary. (Assume for the moment that we restrct our sample to cases where the headquarter s n the U.S.) Next, we need to thnk about whether we can dentfy the ndustry of the headquarter and the subsdary. If we can do ths, then we can map headquarter and/or subsdary productvtes to the trade data. The ndustry of the subsdary, who produces the nput, s easy to dentfy snce the ndustry of the nput, and therefore ts producer, s recorded n U.S. trade statstcs. However, the ndustry of the headquarter cannot be determned drectly from the data unless one assumes that the ndustry of the headquarter s the same as the ndustry of the suppler. Although prevous studes have made ths assumpton, t may be naccurate n many cases. 11 Take for example a Korean tre manufacturer that shps tres to a car manufacturer n the Unted States. The tres beng shpped (and the tre manufacturer) are classfed n the trade data under the NAICS 6-dgt category Tre manufacturng. For ths par, (j) can arse from ether () the productvty of the Korean tre manufacturer or () the productvty of the U.S. car manufacturer. The productvty dsperson measures that would be relevant would be ether () the productvty dsperson of Korean tre manufacturers or () the productvty dsperson of the U.S. car manufacturer. However, n ths case, usng the productvty dsperson of U.S. tre manufacturers would be ncorrect. 12 Note that between measures () and (), only () s easly dentfable. From the trade data we do not know the ndustry of the mportng headquarter, only the ndustry of the exportng subsdary. Therefore, for our analyss we use measure (), whch s the productvty dsperson n the ndustry and country of the exportng subsdary. Ths mplctly only consders the nfluence on (j) exerted by the suppler sde of the match. Ths s clearly ncomplete. However, t s drven solely by data lmtatons. 13 Our measure of dsperson s the standard devaton of the log of plant sales ln Q f,,c wthn an ndustry and a country c: x c V(ln Q f,,c ), (7) where V s the varance operator. 14 We use data on plant sales from the Orbs database, whch reports data on frm sales annually from 1998 to Our sample ncludes all 760,000 plants n the database wth sales n The average number of plants n a country-ndustry par s 90. To llustrate our measure, consder agan the example of Korea tre manufacturers. One observaton of x c wll be the log dsperson of frm sales across tre manufacturers n Korea. The model of Antràs and Helpman (2004) predcts that when dsperson (and average productvty) s hgh among tre manufacturers n Korea, then the productvty of the match (j) s more lkely to be hgh, and therefore we are more lkely to observe a vertcally ntegrated relatonshp (f tre manufacturng s a headquarter-ntensve (hgh ) ndustry). 11 See for example Yeaple (2006). In effect, the assumpton s that (j) s determned solely by the U.S. headquarter and that the headquarter s ndustry s the same as the subsdares (whch s reflected n the trade data). If these assumptons are satsfed, then an acceptable measure of productvty dsperson s the productvty dsperson of U.S. frms wthn an ndustry. 12 In Yeaple s (2006) emprcal analyss the dsperson measures are constructed for 51 ndustres. We have argued that an mportant assumpton of the measure s that the ndustry of the headquarter s the same as the ndustry of the subsdary. Lookng wthn more aggregated ndustres t s much more lkely that ths assumpton s satsfed. Therefore, when workng wth more aggregate data U.S. productvty dsperson may be a perfectly fne measure to use. However, when movng to the NAICS 6-dgt level, t becomes much less lkely that the ndustry of the suppler s the same as the ndustry of the headquarter. 13 In future work, t would be possble to use U.S. Input Output tables to estmate probablstcally the ndustry of the headquarter. 14 See Helpman et al. (2004, p. 307) for an explanaton of how the standard devaton of the log of frm sales recovers the Pareto dsperson parameter.