The Margins of Global Sourcing: Theory and Evidence from U.S. Firms by Pol Antràs, Teresa C. Fort and Felix Tintelnot

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1 The Margns of Global Sourcng: Theory and Evdence from U.S. Frms by Pol Antràs, Teresa C. Fort and Felx Tntelnot B Onlne Theory Appendx Not for Publcaton) B.1 Proofs of Man Propostons Proof of Proposton 1 Proof of part a): Consder two frms wth productvtes ϕ H and ϕ L, wth ϕ H > ϕ L. Denote by J ϕ H ) = {j : I j ϕ H ) = 1} and J ϕ L ) = {j : I j ϕ L ) = 1} the optmal sourcng strateges of these frms, and suppose that J ϕ H ) J ϕ L ) when J ϕ H ) = J ϕ L ) the result n the Proposton holds trvally). For frm ϕ H to prefer J ϕ H ) over J ϕ L ), we need ϕ σ 1 H γθ J ϕ H ))) σ 1)/θ B j J ϕ H ) whle ϕ L preferrng J ϕ L ) over J ϕ H ) requres ϕ σ 1 L γθ J ϕ H ))) σ 1)/θ B Combnng these two condtons, we fnd [ ϕ σ 1 H j J ϕ H ) f j > ϕ σ 1 H γθ J ϕ L ))) σ 1)/θ B j J ϕ L ) f j < ϕ σ 1 L γθ J ϕ L ))) σ 1)/θ B ] [ ϕσ 1 L Θ J ϕ H )) σ 1)/θ Θ J ϕ L )) σ 1)/θ] γ σ 1)/θ B > 0. Gven ϕ H > ϕ L, ths necessarly mples Θ ϕ H ) > Θ ϕ L ). Proof of part b): j J ϕ L ) As noted n the man text, when σ 1) /θ > 1, the proft functon n 11) features ncreasng dfferences n I j, I k ) for j, k {1,..., J} wth j k. Furthermore, t also features ncreasng dfferences n I j, ϕ) for any j J. Invokng Topks s monotoncty theorem, we can then conclude that for ϕ H ϕ L, we must have I 1 ϕ H ), I 2 ϕ H ),..., I J ϕ H )) I 1 ϕ L ), I 2 ϕ L ),..., I J ϕ L )). Naturally, ths rules out a stuaton n whch I j ϕ H ) = 0 but I j ϕ L ) = 1, and thus we can conclude that J ϕ L ) J ϕ H ) for ϕ H ϕ L. Proof of Proposton 2 Consder frst the case, j / J. The mappng V j ϕ, J) defned n the Proposton, s such that V j ϕ, J) = 1 f ϕ σ 1 γ σ 1)/θ B Θ J j) σ 1)/θ Θ J ) σ 1)/θ) > f j and V j ϕ, J) = 0, otherwse. Because of ncreasng dfferences see the proof of Proposton 1), the term Θ J j) σ 1)/θ Θ J ) σ 1)/θ s ncreased by the addton of elements to the set J. As a result, for J J, we cannot possbly have V j ϕ, J ) = 1 and V j ϕ, J ) = 0. Instead, we must have ether V j ϕ, J ) = V j ϕ, J ) = 0, V j ϕ, J ) = V j ϕ, J ) = 1, or V j ϕ, J ) = 0 and V j ϕ, J ) = 1. f j, f j. 1

2 Second, consder the case j J. The mappng V j ϕ, J) defned n the Proposton, s such that V j ϕ, J) = 1 f ϕ σ 1 γ σ 1)/θ B Θ J ) σ 1)/θ Θ J \ j) σ 1)/θ) > f j and V j ϕ, J) = 0, otherwse. Smlarly to above, the term Θ J ) σ 1)/θ Θ J \ j) σ 1)/θ s ncreased by the addton of elements to the set J. As a result, for J J, we cannot possbly have V j ϕ, J ) = 1 and V j ϕ, J ) = 0. Instead, we must have ether V j ϕ, J ) = V j ϕ, J ) = 0, V j ϕ, J ) = V j ϕ, J ) = 1, or V j ϕ, J ) = 0 and V j ϕ, J ) = 1. Thus, we can conclude that V j ϕ, J ) V j ϕ, J) for J J, as stated n the Proposton. Proof of Proposton 3 Remember from equaton 8) that Θ ϕ) k J ϕ) T k τ k w k ) θ and thus Θ ϕ) corresponds to the sum of sourcng potentals of the countres belongng to the set J ϕ). The weakly) postve effect, holdng B constant, of any sourcng potental T k τ k w k ) θ on nput flows when σ 1) /θ 1 s then obvous from nspecton of equaton 12). The postve effect of a reducton of any fxed cost f k on frm-level nput flows follows from the fact that, holdng constant B and when σ 1 θ, a reducton n a fxed cost f k cannot possbly reduce the proftablty of any frm selectng nto mportng from any country j, but t may well ncrease t drectly f k = j or ndrectly f selectng nto k enhances the proftablty of mportng from j remember that the proft functon features ncreasng dfferences whenever σ 1 > θ). Proof of Proposton 4 Gven a vector of wages, equatons 13) and 14) determne the equlbrum values of B and N. Notce that the frm-level global sourcng problem depends only on B, w and exogenous parameters, and not drectly on N. As a result, f a unque soluton for B exsts, all thresholds ϕ j for any par of countres, j) wll be pnned down unquely, gven wages. Hence, f a unque soluton for B n equaton 13) exsts, we can ensure that there wll be a unque value of N solvng 14). Let us then focus on studyng whether 13) ndeed delvers a unque soluton for B. For gven wages, the equlbrum condton 13) can be rearranged as follows w f e = B ϕ ϑ) γθ ϕ)) σ 1)/θ ϕ σ 1 dg ϕ) w ϕ ϑ) j J ϕ) f j dg ϕ), B.1) where ϑ ) denotes the locaton from whch the least productve actve frm n country sources ts nputs, or formally, ϑ ) = {j J : ϕ j ϕ k for all k J}. Note that ϑ ) satsfes ϕϑ) ) σ 1 B γt ϑ) τϑ) w ϑ) ) θ ) σ 1)/θ = w f ϑ). B.2) Remember also that Θ ϕ) k J ϕ) T k τ k w k ) θ, and J ϕ) J s the set of countres for whch a frm based n wth productvty ϕ has pad the assocated fxed cost of offshorng w f j. 1 Computng the dervatve of the rght-hand-sde of B.1) wth respect to B, and usng B.2) to 1 To be precse, t could be the case that the least productve actve frm n country mght source nputs from more than one locaton. In such a case, the left-hand-sde of equaton B.2) would ncorporate the other locaton s sourcng potental, but equaton B.3) below would reman unaltered. 2

3 elmnate the effects workng through changes n ϕ ϑ), we can wrte ths dervatve as smply ϕ ϑ) ϕ σ 1 γθ ϕ)) σ 1)/θ B w j J ϕ) f j ) B dg ϕ) > 0. B.3) The fact that ths dervatve s postve follows drectly from the frm s global sourcng problem n 11). In partcular, holdng constant the frm s sourcng strategy J ϕ) and thus Θ ϕ), t s clear that an ncrease n B wll ncrease frm-level profts ϕ σ 1 γθ ϕ)) σ 1)/θ B w j J ϕ) f j. Now such an ncrease n B mght well affect the proft-maxmzng choce of J ϕ) and thus Θ ϕ), but frm profts could not possbly be reduced by those changes, snce the frm can always decde not to change the global sourcng strategy n lght of the hgher B and stll obtan hgher profts. 2 We can thus conclude that the rght-hand-sde of B.1) s monotoncally ncreasng n B. It s also clear that when B, all frms wll fnd t optmal to source everywhere and the rght-hand-sde of B.1) becomes B γ T k τ k w k ) θ) σ 1)/θ ϕ σ 1 dg ϕ) w k J and thus goes to. Conversely, when B 0, no frm can proftably source to any locaton, gven the postve fxed costs of sourcng, and thus the rght-hand-sde of B.1) goes to 0. It thus only remans to show that the rght-hand-sde of B.1) s a contnuously non-decreasng functon of B. Ths may not seem mmedate because frm-level profts jump dscontnuously wth B whenever such changes n B lead to changes n the global sourcng strategy of frms. It can be shown, however, that ) Θ ϕ)) σ 1)/θ B ϕ σ 1 dg ϕ) ϕ ϑ) B s contnuously dfferentable n B. To see ths, one can frst follow the same steps as n the proof of Proposton 1 to show that Θ ϕ; B ) must be non-decreasng not only n ϕ, but also n B and B ϕ σ 1. We can then represent Θ ϕ)) σ 1)/θ B ϕ σ 1 as a non-decreasng step functon n ϕ, n whch the jumps occur at dfferent levels of B ϕ σ 1. Ths s analogous to wrtng θ 1 B ϕ σ 1 f ϕ < b 1 /B 1/σ 1) Θ ϕ)) σ 1)/θ B ϕ σ 1 θ 2 B ϕ σ 1 f b 1 /B 1/σ 1) ϕ < b 2 /B 1/σ 1) =.. θ J B ϕ σ 1 f b J 1 /B 1/σ 1) ϕ. B.4) Hence, we have ϕ j J f j ϕ ϑ) Θ ϕ)) σ 1)/θ B ϕ σ 1 dg ϕ) = b1 /B 1/σ 1) ϕ ϑ) θ 1 B ϕ σ 1 dg ϕ) + b2 /B 1/σ 1) b 1 /B 1/σ 1) θ 2 B ϕ σ 1 dg ϕ) θ J B ϕ σ 1 dg ϕ). b J 1 /B 1/σ 1) 2 Followng the same steps as n the proof of Proposton 1 we can show that both Θ ϕ) and j J ϕ) f j are actually non-decreasng n B. Ths result s mmateral for the proof of exstence and unqueness n the case of free entry, but can be used to prove the same result for the case of an exogenous number of frms N. 3

4 It s then clear that the dervatve of ths expresson wth respect to B s a sum of contnuous functons of B, and thus s contnuous n B tself. 3 Usng smlar arguments we can next show that ) f j ϕ ϑ) w j J ϕ) B dg ϕ) B.5) s also contnuously dfferentable n B. Frst, a smple proof by contradcton can be used to show that j J ϕ) f j s non-decreasng n B ϕ σ 1. More specfcally, suppose that for B ϕ σ 1) H > B ϕ σ 1) L we also had j J H f j < j J L f j. Gven the non-decreasng dependence of Θ ϕ) on B ϕ σ 1, we would then have γθ H ϕ)) σ 1)/θ B ϕ σ 1) L j J H f j > γθ L ϕ)) σ 1)/θ B ϕ σ 1) L j J L ϕ) f j, whch clearly contradcts J L beng optmal gven B ϕ σ 1 = B ϕ σ 1). Wth ths result, L f j j J ϕ) can then be expressed as a step functon analogous to that n B.4), n whch the poston of the steps s contnuously dfferentable n B. Ths n turn ensures that B.1) s contnuous n B and concludes the proof that there exsts a unque B that solves equaton 13). B.2 Equlbrum n the Complements-Pareto Case In Proposton 1, we have establshed that whenever σ 1 > θ, the model delvers a peckng order n the extensve margn of offshorng. For each country, we can then rank foregn countres n terms of some ndex of sourcng appeal. We shall assume, for the tme beng, that ths rankng s strct n the sense that the set of frms sourcng from any two dstnct countres j and k do not concde; more specfcally, the measure of frms sourcng from the strctly more attractve country s necessarly larger. Ths assumpton s farly mmateral, as we shall show below. Suppose also for smplcty that ϕ = ϕ, so that all frms that source a postve amount.e., all frms that are actve) do so, at least n part, from Home. Denote by r the r-th least appealng country from whch frms from source from, so Home s r = 1. Defne also Θ r = r T j τ j w j ) θ. j=1 Note that Proposton 1 mples that the set of productvty thresholds ϕ r defned n the man text wll be such that any frm wth productvty above that threshold ϕ r necessarly sources from country r, or n terms of the notaton n equaton 17), I r ϕ) = 1 for all ϕ > ϕ r. 3 The two last expressons assume that there are J 1 jumps, mplctly assumng that at each jump, only one country s added to the sourcng strategy. Gven the complementartes n our model, and as ponted out n footnote 1, an ncrease n B mght well lead to the smultaneous ncluson of two or more locatons. In such a case, there would be less than J 1 jumps, but the contnuous dfferentablty of B.4) would clearly be preserved. 4

5 In lght of the proft functon n 10, these thresholds are gven by ϕ σ 1 1 = ϕ σ 1 r = w f 1 γ σ 1)/θ B T w ) θ) σ 1)/θ ; w f r ) for r > 1. B.6) γ σ 1)/θ B Θ σ 1)/θ r Θ σ 1)/θ r 1 Consder now the ndustry equlbrum. Usng the above notaton, we can wrte the free entry condton 13) as J 1 γ σ 1)/θ B r=1 Θ σ 1)/θ r ϕr+1 ϕ r ϕ σ 1 dg ϕ) w J f r r=1 ϕ r dg ϕ) = w f e. Next, nvokng the Pareto dstrbuton, G ϕ) = 1 ϕ /ϕ) κ, and solvng for the ntegrals, we obtan: J 1 ) γ σ 1)/θ B Θ σ 1)/θ κ ϕr ) r κ ϕ σ κ 1 ϕ r+1 ) σ κ 1 w κ σ + 1 r=1 Pluggng the thresholds n B.6) delvers ) κ ϕ κ w f 1 κ σ + 1 ϕ 1 ) J 1 κ + κ ϕ r=2 κ ϕ κ σ + 1 ϕ 2 Θ σ 1)/θ r ϕ r ) κ w f r ) κ Θ σ 1)/θ 1 Θ σ 1)/θ r Θ σ 1)/θ 2 Θ σ 1)/θ r 1 Θ σ 1)/θ 1 J r=1 )w f 2 ) ϕ κ f r = w f e. ϕ r Θ σ 1)/θ r+1 ) ϕ r+1 ) κ w f r+1 κ σ + 1 w J r=1 Θ σ 1)/θ r ) ) ϕ κ f r = w f e. ϕ r Expandng the summaton nvolvng the terms Θ r, cancelng the terms n Θ σ 1)/θ r Θ σ 1)/θ r 1, and smplfyng, we fnally obtan σ 1 J ) ϕ κ f r = f e. B.7) κ σ + 1 r=1 It s worth emphaszng that ths equaton holds regardless of the relatve values of σ 1 and θ as long as these parameters and the degree of heterogenety n fxed costs are such that a herarchy n sourcng decsons exsts. The key nsght of Proposton 1 s that σ 1 > θ s a suffcent condton for ths herarchcal structure to emerge regardless of the values of the fxed costs of offshorng f j. In dervng equaton B.7), we have assumed that, from the pont of vew of frms n country, the rankng of the appeal of the varous source countres was strct. Whenever σ 1 > θ, the complementary n the sourcng decsons of frms mples, however, that the set of frms sourcng from two dstnct countres j and k can n prncple concde. Intutvely, t could be the case that sourcng from country j can only be proftable when a frm n also sources from country k, and vce versa. Fortunately, the above analyss can be readly adapted to deal wth ths sort of stuatons. More specfcally, t suffces to defne a merged country j k wth a sourcng potental equal to the sum of j s and k s sourcng potental and wth a sourcng fxed cost also equal to the sum of j s and k s sourcng fxed costs. Ths merged country can then be assgned a poston r n the rankng of 5 ϕ r

6 sourcng appeal across countres, and then t only suffces to be careful to run the summatons n the expressons above replacng J wth J M where M s the number of countres that have been dropped by beng merged wth other countres. It s then straghtforward to see that one can agan fnd ts way to equaton B.7). Note that equaton B.7) n turn mples that ) σ 1 f j dg ϕ) + f e = κ σ f e, ϕ j J ϕ) and thus pluggng ths expresson n 14), we can conclude that N = σ 1) ηl σκf e, B.8) as clamed n footnote 12. Some of the above expressons are useful n dervng the gravty equaton n 18) characterzng blateral manufacturng trade flows n the case of ndependent entry decsons.e., σ 1 = θ). To see ths, begn wth equaton 15) and plug the formula for the Pareto dstrbuton n 16) to obtan M j = σ 1) N B γt j τ j w j ) θ κϕ κ ϕ j ) σ 1 κ κ σ + 1. Wth ndependent entry decsons, the threshold n B.6) smplfes to ϕ σ 1 j = w f j γb T j τ j w j ) θ. Pluggng ths expresson for ϕ σ 1 j nto the prevous one for M j, mposng θ = σ 1, and manpulatng the resultng expresson n a manner analogous to the dervaton of the general gravty equaton n 17), we obtan M j = N B ) κ σ 1 τj ) κ ϕ κ w f j ) 1 κ σ 1 Q j k N k B k ) κ σ 1 τkj ) κ ϕ k ) κ w k f kj ) 1 κ σ 1. Usng 3) and B.8) and defnng we thus obtan equaton 18) n the man text. Ψ = f e ϕ κ P L κ w κ/σ 1) 1, B.3 Detals on Some Extensons of the Model Towards the end of secton 1, we brefly mentoned three extensons of our theoretcal model. In ths secton of the Onlne Appendx we provde more detals on these extensons. Because we do not ncorporate these features nto the structural estmaton and quanttatve analyss, we wll lmt ourselves to dscussng the effects of these extensons on frm behavor, and not on the aggregate mplcatons of the model. 6

7 A. Tradable Fnal Goods: Exportng and Importng In the benchmark model n the man text, we have assumed that fnal-good varetes are prohbtvely costly to trade across borders. We have done so to focus our analyss on the determnants and mplcatons of selecton nto global sourcng. In ths secton, we brefly relax ths assumpton and demonstrate the exstence of ntutve complementartes between the extensve margn of exportng and that of mportng at the frm level. Suppose then that trade n fnal-varetes s only partally costly and nvolves both ceberg trade costs τj X as well as fxed costs fj X of exportng. Frm behavor condtonal on a sourcng strategy s largely analogous to that n secton 2.1. In partcular, after observng the realzaton of ts suppler-specfc productvty shocks, each fnal-good producer wll contnue to choose the locaton of producton for each nput to mnmze costs, whch wll lead to the same margnal cost functon c ϕ) obtaned above n equaton 9). The man novelty s that the frm wll now produce output not only for the domestc market but also for a set of endogenously chosen foregn markets, whch consttute the frm s exportng strategy. We can then express the problem of determnng the optmal exportng and sourcng strateges of a frm from country wth core productvty ϕ as: max I M j {0,1}J j=1 I X k {0,1}J k=1 π ϕ, I M, I X) = ϕ σ 1) γ w J Ij M T j τ j w j ) θ j=1 J Ij M f j w j=1 J Ik X f j X, k=1 σ 1)/θ J k=1 I X k τ X k ) 1 σ Bk Note that I M and I X denote the vector of extensve margn mport and export decsons, respectvely. It s straghtforward to see that, whenever σ ) 1) /θ > 1, ths more general proft functon contnues to feature ncreasng dfferences n Ij M, Ik M for j, k {1,..., J} wth j k, and also features ) ncreasng dfferences n Ij M, ϕ for any j {1,..., J}. As a result, Proposton 1 contnues to apply here and we obtan a peckng order n the extensve margn of offshorng n the complements case. The key new feature of ) the above proft functon π ϕ, I M, I X) s that t also exhbts ) ncreasng dfferences n Ij M, Ij X for any j, k {1,..., J} and ncreasng dfferences n I j X, ϕ for any j {1,..., J}. Ths has at least two mplcatons. Frst, regardless of whether σ 1 > θ or σ 1 < θ, any change n parameters that ncreases the sourcng capablty Θ ϕ) of the frm such as reducton n any τ j or an ncrease n any T j wll necessarly lead to a weak) ncrease n the vector I X, and thus weakly) ncrease the export margn of exportng. Second, restrctng attenton to the complements case σ 1) /θ > 1, the model delvers a complementarty between the exportng and mportng margns of frms. For nstance, holdng constant the vector of resdual demand parameters B, reductons n the costs of tradng fnal goods across countres wll not only ncrease the partcpaton of frms n export markets, but wll also ncrease the extensve margn of sourcng, n the sense that vector I M s non-ncreasng n τk X. Furthermore, as frm productvty ncreases, the partcpaton of frms n both export and mport markets ncreases, and at a faster rate than when one of these margns s shut down. B. Introducng Value Added n Assembly In our benchmark model, we assume that the margnal cost of fnal-good producers conssts of the cost of procurng a measure one of ntermedate nputs. Here we consder the case n whch fnal-good 7

8 producers also hre local labor to assemble the bundle of nputs. In partcular, let the margnal cost for frm ϕ based n country of producng a unt of a fnal-good varety now be c ϕ) = 1 1 1/1 ρ) w ) µ z v, ϕ; J ϕ))) dv) 1 µ)1 ρ), B.9) ϕ 0 whch s analogous to equaton 5) except for value-added labor payments) accountng for a share µ 0, 1) of the costs of assembly. It should be clear that the use of labor n fnal-good producton does not affect the locaton from whch nputs are sourced condtonal on a sourcng strategy. Followng the same steps as n the benchmark model, we fnd the same ntermedate nput mport shares as n equaton 7), the same sourcng potental as n 8), and a resultng proft functon condtonal on a sourcng strategy J ϕ) equal to π ϕ) = ϕ σ 1 w ) µσ 1) γθ ϕ)) 1 µ)σ 1)/θ B w f j, B.10) j J ϕ) whch s analogous to equaton 10) n the man text. The two man dfferences are that country s wage rate now drectly affects operatng profts, and that the elastcty of frm profts to the frm s sourcng capablty s equal to 1 µ) σ 1) /θ rather than σ 1) /θ, as n our benchmark model. The proft functon π contnues to be supermodular n ϕ and Θ ϕ), but now features ncreasng dfferences n I j, I k ) for j, k {1,..., J} and j k, whenever 1 µ) σ 1) /θ > 1. As a result, the man Propostons 1-3 characterzng the optmal sourcng strategy and frm-level comparatve statcs contnue to hold n ths extenson, except that the regon of the parameter space n whch mport entry decsons are complementary s gven by 1 µ) σ 1) /θ > 1 nstead of σ 1) /θ > 1. Clearly, for large values of µ t s possble that σ 1) /θ > 1 but 1 µ) σ 1) /θ < 1. One mght then be concerned that, because n our estmaton we back out σ from markup data and θ from the effect of cost-shfters on the mport shares n 9), we mght nfer that the complements case best descrbes the data when n fact 1 µ) σ 1) /θ < 1, and thus mport entry decson are substtutes. Nevertheless, as we descrbe n Appendx A.1, when constructng our measure of domestc ntermedate nput purchases, we add a frm s total producton-worker wage bll n manufacturng to ts total expendtures on materal nputs. We nclude producton worker wages n a frm s nput costs because our complete-contractng model does not determne whether ntermedate nputs are sourced from external supplers or are provded wthn frm boundares, thus consttutng value added whch maps to the share µ n ths extenson). In sum, our constructon of domestc nput shares s such that our model nterprets some of the domestc ntermedate nputs sourced by the frm as beng provded wthn the frm by producton workers. Of course, these producton worker servces do not consttute the entre amount of domestc labor servces used by the frm. Yet, ths s unlkely to overturn our key condton σ 1) /θ > 1 for two reasons. Frst, the majorty of non-producton worker labor n our framework s more lkely to consttute a fxed rather than a margnal cost, and wll therefore not affect µ. Second, even f some non-producton worker labor relates to margnal costs, these are lkely a small fracton, and our benchmark estmates of σ = 3.85 and θ = mply that small changes n µ wll not affect our concluson. C. Endogenous Input Varety Our benchmark model assumes that all fnal good producers use a measure one of nputs. We next brefly outlne how our results extend and generalze to the case n whch the fnal-good producer s allowed to choose the complexty of producton, as captured by the measure of nputs used n producton see Acemoglu et al., 2007). As we shall see, ths ends up producng an equlbrum 8

9 essentally dentcal to the one we have descrbed above, but wth addtonal mplcatons for how the measure of nputs purchased by frms changes wth frm productvty. The formal detals of ths extenson are as follows. Fnal-good producton contnues to combne nputs accordng to a CES technology, but we now let the measure of nputs be frm-specfc and gven by n ϕ). More specfcally, we generalze the margnal cost functon n 5) as follows: c {j v)} 1 v=0, ϕ ) ) 1/1 ρ) = 1 n ϕ n ϕ) 1/ρ 1) λ ϕ) ) 1 ρ τjv) a jv) v, ϕ) w jv) dv. 0 A hgher value of n ϕ) enhances productvty va an nput varety effect. As n Acemoglu et al. 2007), we ntroduce the term n ϕ) 1/ρ 1) λ n front of the ntegral n order to control the mportance of varety effects for productvty va a parameter λ dsentangled from the elastcty substtuton between nputs ρ. In order to create a check on the optmal degree of complexty, we assume that frms face a fxed cost equal to w n ϕ) f n when combnng n ϕ) nputs n producton. As n our benchmark model, n each of the countres n whch the fnal-good producer ncurred the fxed cost of sourcng, there s a compettve frnge of potental supplers that can provde dfferentated nputs to the frm wth a frm-specfc ntermedate nput effcences drawn from a Fréchet dstrbuton. Wth a contnuum of nputs, the equlbrum measure of nputs used n producton by a fnal-good producer has no mplcatons for the dstrbuton of nput prces faced by that producer. Explotng ths feature, we can use dervatons analogous to those n the benchmark model and n Eaton and Kortum 2002), to wrte the margnal cost of producton as c ϕ) = 1 ϕ n ϕ)) λ γθ ϕ)) 1/θ, B.11) and the frm s profts condtonal on a sourcng strategy J ϕ) as π ϕ) = ϕ σ 1 n ϕ)) σ 1)λ γθ ϕ)) σ 1)/θ B w j J ϕ) f j w n ϕ) f n, where B s agan gven n 3). It s clear that condtonal on a sourcng strategy J ϕ) and thus a value of Θ ϕ) ths proft functon s supermodular n productvty and the measure of nputs n ϕ). 4 Hence, a novel predcton from ths extenson s that more productve frms wll tend to source more nputs from all sources combned domestc and foregn) than less productve frms, even when these frms share a common sourcng strategy. 5 In the complements case wth σ 1 > θ, ths varant of the model also predcts that more productve frms wll tend to buy weakly) more nputs from any source than less productve frms. As ponted out n the man text, t s mportant to emphasze that nput-specfc fxed costs do not serve as a substtute for country-specfc fxed costs of sourcng. By ths we mean that, n the absence of the latter type of fxed costs, our framework would not be able to account for the key facts motvatng our benchmark model, snce n such a case, all frms would source nputs from all countres, thus volatng the patterns n Fgure 1 and Table 1 n the Introducton. 4 For the choce of n ϕ) to satsfy the second-order condtons for a maxmum, we need to mpose that the effcency gans from nput varety are small enough to guarantee that σ 1) λ < 1 holds. 5 Although our benchmark model s also consstent wth more productve frms mportng more nputs than less productve frms, wth a common measure of nputs, ths could only be ratonalzed by havng more productve frms sourcng less nputs domestcally than less productve frms. 9

10 C Onlne Data Appendx Not for Publcaton) C.1 Sample Table C.1 provdes detals of all frms n the Economc Censuses wth postve sales and employment. The frst row corresponds to frms that consst only of manufacturng establshments M frms). The second row presents nformaton for all frms wth one or more manufacturng establshments and at least one establshment outsde of manufacturng M+ frms). Together, these two types of frms comprse our sample. Table C.1: Sample of frms Imports Empl Sales Fracton Frms Frm Type $mllons 000s $bllons Importers Manufacturng Only M) 238,800 76,020 5,869 1, Manufacturng Plus M+) 11, ,592 20,581 9, Other O) 4,006, ,169 77,400 12, Wholesale Only W) 300, ,077 3,489 2, Wholesale and Other WO) 7, ,753 6,365 2, Total 4,564,600 1,388, ,704 27, Notes: Table provdes nformaton on frms n the Economc Census wth postve sales and employment. Analyss n paper based on all M and M+ frms. Numbers rounded for dsclosure avodance. Imports exclude products classfed under mnng. C.2 Prema and Decomposton Followng Bernard et al. 2007), we report employment, sales, and productvty prema for frms that mport n To do so, we regress the log each of these varables on an mporter dummy and ndustry controls. Table C.2 reports the results. The top panel presents results usng 2007 values of frm sze and productvty and the bottom panel uses 2002 values. The frst column of the table shows that frms mportng n 2007 are larger and more productve than non-mporters. In addton, these prema for 2007 mport status were present n The magntude of these mport prema s smlar to those typcally found for exporters, wth mporters beng on average about three tmes larger and about eght percent more productve than non-mporters. We confrm the mportance of the extensve margns of trade, both n terms of the number of mported products and the number of mportng frms, frst documented by Bernard et al. 2009). Followng those authors, we decompose total U.S. mports M US,j from country j accordng to lnm US,j ) = lnn frms US,j ) + lnn prods US,j ) + ln N frms US,j O US,j N prods US,j ) + ln MUS,j O US,j where O US,j s the number of frm-product combnatons wth postve mports from j. The frst two terms represent the unque numbers of frms N frms US,j ) mportng and products N prods US,j ) mported ), 10

11 Table C.2: Prema for 2007 mporters All Frms Non-2002 Importers 2007 Log employment Log sales Log value-added per worker Log employment Log sales Log value-added per worker Notes: All results are from OLS regressons of the varable lsted on the left on an ndcator equal to one f the frm mported n The frst column ncludes all frms 250,300 n top panel and 181,500 n bottom). The second column s based on the subset of frms that dd not mport n ,800 frms). Results wth 2002 varables are based only on the subset of frms that exsted n All regressons nclude four dgt ndustry controls. All coeffcents are statstcally sgnfcant at the one percent level. from country j. The thrd term, referred to as the densty, captures the fracton of frm-producton combnatons wth postve mport values. The fnal term captures the ntensve margn. It measures the average mport value per frm-product observaton, for all combnatons wth postve mports. Table C.3 presents coeffcents from OLS regressons of the logarthm of each margn on the logarthm of total trade. As s well known, these OLS coeffcents sum to one, wth each coeffcent representng the share of overall varaton explaned by each margn. As n prevous work, we fnd that varaton n the extensve margns account for the majorty of the varaton n aggregate mport volume across countres. The extensve margns account for a total of 65 percent, whle the ntensve margn explans just 35 percent of the total varaton. Table C.3: Extensve and ntensve margn decomposton Log of number Log of number of Log of Log of average of mportng mported products Densty mport value per frms product per frm ) 0.015) 0.014) 0.018) Adj. R Observatons Notes: Each column corresponds to results from regressng the log of each margn on the log of total mport values. The coeffcents are a measure of the fracton of varaton n aggregate mport volumes across countres explaned by that margn. Densty represents the fracton of all possble frm-product combnatons wth postve mport values. The estmated coeffcents sum to one. 11

12 C.3 Prema Fgures In the Introducton, we plot the relatonshp between the log of frm sales and the mnmum number of countres from whch a frm sources. To construct the fgure, we regress the log of frm sales on cumulatve dummes for the number of countres from whch a frm sources and ndustry controls. The omtted category s non-mporters, so the prema are nterpreted as the dfference n sze between non-mporters and frms that mport from at least one country, at least two countres, etc. The horzontal axs denotes the number of countres from whch a frm sources, wth 1 correspondng to frms that use only domestc nputs. The ntroducton fgure controls for frm ndustry wth varables that measure the share of a frm s employment n four-dgt NAICS ndustres. These are smply ndustry fxed effects for all frms that span only one ndustry.) Here we show that the patterns depcted n the ntroducton are robust when consderng a frm s sze pror to mportng and when controllng for the products that a frm mports or exports. Fgure C.1 plots the relatonshp between a frm s log sales n 2002 and the number of countres from whch t sources n 2007, for frms that dd not mport n Fgure C.2 depcts the relatonshp when controllng for the number of products a frm mports left panel) and the number of products the frm exports rght panel). In addtonal undsclosed results, avalable upon request, we show smlar patterns when usng frm employment and the log of value-added labor productvty. Fgure C.1: Importer prema for frm s 2002 sales, lmted to frms that do not mport n 2002, 2002 Premum Mnmum number of countres from whch frm sources Premum 95% CI C.4 Measurng Total and Domestc Input Use We construct a measure of a frm s total ntermedate nput purchases usng materal nput purchases from the Censuses of Manufactures, Constructon, and Mnng and merchandse purchases from the Census of Wholesale. Ths approach ensures a more complete metrc of a frm s nputs than tradtonal measures based purely on manufacturers use of materals because t takes nto account the nput usage of both the manufacturng as well as the wholesale establshments of U.S. frms. 6 6 The wholesale sector ncludes a sgnfcant number of plants that desgn goods and coordnate producton, often by offshorng, but do not perform physcal transformaton actvtes see Bernard and Fort, 2015, for 12

13 Fgure C.2: Importer prema wth product controls a) Controllng for number of products mported by the frm b) Controllng for number of products exported by the frm The model does not take a stance on whether ntermedate nputs are sourced wthn or across frm boundares. For the purposes of ths paper, ths s of lttle relevance for nternatonal transactons, but t mght lead to mportant bases n our measure of overall nput use f a sgnfcant share of domestc nputs s produced wthn the frm and s recorded as value added. For ths reason, we add a frm s total producton-worker wage bll to the frm s total nput purchases. In terms of our model, ths corresponds to assumng that the fnal-good producer employs producton workers to manufacture nternally any nputs produced by the frm, whle t uses the other factors of producton nonproducton workers, physcal captal, and land) to combne ntermedate nputs and cover all fxed costs. Ths approach s also motvated by the noton that the servces typcally provded by producton workers are partcularly offshorable. Table C.4 presents summary statstcs on foregn nput shares. The mean share of mported nputs s 0.14, wth a standard devaton of Table C.4: Summary statstcs on frms share of foregn nput sourcng mean std. dev. medan 75 pctle 90 pctle Notes: Ths table reports statstcs on the share of mported nputs for the subset of offshorng frms. a descrpton). Ignorng these plants nputs could severely understate mult-sector frms total nputs. For example, Feenstra and Jensen 2012) fnd that a sgnfcant fracton of some manufacturng frms mports are not reported as nput purchases. We address ths ssue by ncludng a frm s wholesale plants nputs. Although there s no way to measure nputs for establshments outsde the manufacturng and wholesale sectors, those plants are much less lkely to be nvolved n producton or mportng. An alternatve approach would be to use an estmate of the demand elastcty σ and explot the CES structure of our model to back out nput usage from sales data. 13

14 Ths new measure of total ntermedate nput purchases s hghly correlated wth tradtonal nput measures for manufacturng frms based on reported nputs of materals and parts from only the Census of Manufactures. A frm s share of nputs from country j, χ j, s computed as mports from j dvded by total nput purchases. A frm s share of domestc nputs, χ, s smply the dfference between ts total nput purchases and mports, dvded by total nput purchases. A very small fracton of frms has negatve values for ther mpled domestc nput purchases usng ths approach. Ths occurs when a frm s total nput purchases are less than ts mports. Lkely explanatons for ths are measurement error and mports of captal equpment. To address any potental bas from droppng these frms, we therefore use the maxmum of a frm s mpled domestc nput use and ts producton worker wages as ts domestc nput usage and adjust total nput usage accordngly. 7 C.5 Robustness of Country Sourcng Potentals In ths secton we further elaborate on our approach to estmatng and nterpretng country sourcng potentals. To assess the robustness of our estmates, we re-estmate sourcng potentals usng frms that mport from one country, 2 countres, 3 countres, 4-9 countres, countres, and 20+ countres. The correlaton coeffcents between our baselne estmates and those usng the samples of frms that source from just one country, and those sourcng from just 2 countres are qute low. Ths seems to be drven by strange selecton crtera, snce a frm sourcng only from a non-top country e.g., El Salvador) s qute dfferent from the average frm, and not representatve of the aggregate patterns our theory seeks to explan. When we lmt the set of countres to the top 10 countres based on number of frms as lsted n Table 1), we fnd a correlaton coeffcent of for frms sourcng from just one country. The correlaton coeffcent between our baselne estmates and the other samples s hgher for all other samples we have not dsclosed each correlaton due to dsclosure concerns). The correlaton coeffcent between our baselne estmates and the sample of frms sourcng from three countres s across all countres, and becomes substantally hgher as the sourcng set grows. As an alternatve check, we also examned the trade-weghted correlaton coeffcents between our baselne estmates and those based on each of the samples descrbed above. The trade-weghted correlaton coeffcents for all subsamples are n the same range, or substantally hgher, as the coeffcent for frms sourcng from at least three countres. When estmatng sourcng potentals, we have also notced that the estmates are somewhat senstve to controllng for frm sze. Large frms tend to have larger domestc shares, a feature at odds wth our theory. On the other hand, there are certan countres from whch some extremely large frms mport dsproportonately large shares of nputs e.g., Mexco). Ths heterogenety s beyond the scope of ths paper, but suggests there s substantal scope for explorng ths varaton n future work. C.6 Estmaton of the Trade Elastcty We dentfy the frm-level trade elastcty, θ, usng varaton n country wages. The wage data are from the Internatonal Labor Organzaton reported average nomnal monthly wages n local currences for These wages were converted to USD usng exchange rates from the World Bank. When data for 2007 were mssng, we used data for the next closest year wthn a two-year range. To address the fact that skll levels dffer across countres, we follow Eaton and Kortum 2002) and use human 7 Ths approach leads to a tny number of frms wth zero mpled domestc sourcng. In an alternatve approach, we have lmted the sample of frms n the structural analyss to frms wth at least ffty percent of ther sales n manufacturng. We do not report the numbers from ths analyss here to mnmze dsclosure ssues, but note that the numercal results are very smlar and the qualtatve nterpretatons reman unchanged. 14

15 captal adjusted wages, w HCadj = w )e 0.06H, where H s the years of schoolng from Barro and Lee 2010) and 0.06 represents the return to educaton estmated n Bls and Klenow 2000). Table C.5 presents several robustness tests for estmaton of the frm-level trade elastcty. We use data on country GDP from the World Bank Development Indcators WDI) and country tarffs are the smple average of country tarffs from the World Bank WITS database. Column 1 shows that our estmate of θ s somewhat smaller, suggestng greater complementarty, when controllng for GDP. Column 2 shows that t s vrtually unchanged when controllng for tarffs. In column 3 we report the results of constranng the coeffcent on tarffs and wages to be the same. Fnally, column 4 shows results when we do not control for the number of frms n an country. Table C.5: Robustness estmates for the frm-level trade elastcty Dependent varable s log ξ IV R1 IV R2 IV R3 IV R4 HC adjusted wage ) 0.71) 0.75) log1+tarff)+ log wage ) log dstance ) 0.35) 0.26) 0.36) Common language ) 0.32) 0.26) 0.32) log R&D ) 0.13) 0.11) 0.09) log KL ) 0.40) 0.33) 0.45) Control of corrupton ) 0.31) 0.27) 0.36) log GDP ) log 1+tarff) ) log no. of frms ) 0.13) 0.12) Constant ) 2.36) 1.96) 2.73) Observatons F-Stat Notes: Standard errors n parentheses. The human captal-adjusted wage s nstrumented by populaton. In IV R3, the coeffcent on wages and tarffs s constraned to be dentcal. For ths specfcaton, both populaton and tarffs are the nstruments. F-Stat s the Cragg-Donald F-statstc for the excluded nstruments). In secton 4.2 of the man text, we clam that the orthogonalty condton that ensures that our frm-level estmates of θ are consstent, does not guarantee that the estmate n column 5 s consstent as well. We now substantate ths clam. Remember from equaton 19) that χ n j χ n = T j τ j w j ) θ ɛ n j, C.1) 15

16 where ɛ n j represents measurement error, or a shock that s only observed by frms after ther sourcng strategy s selected. Under these condtons, we have E log ɛ n j log T j τ j w j ) θ)) = 0. In the man text, we leveraged ths orthogonalty condton to obtan a consstent estmate of log ξ j = log T j τ j w j ) θ) usng frm-level data and then projected ths estmate on human-captal-adjusted wages to obtan an estmate of θ n a smple cross-country regresson. As ponted out n sectons 2.4 and 4.2, as a potental alternatve way to back out θ, we could have smply aggregated the mport data at the country-level and estmated θ explotng the relatonshp: χ n j = T j τ j w j ) θ χ n ɛ n j. C.2) {n:j J n } {n:j J n } In the man text, we note that f ɛ n j = 1, ths mples that a gravty equaton that controls for the domestc nput purchases of frms that source from j should delver a trade elastcty equal to θ. In the presence of measurement error,.e., ɛ n j 1, t s not clear however that such a regresson would provde a consstent estmate of θ. To see ths, note that we can wrte equaton C.2) as log χ n j log ) χ n = log T j τj θ θ log w j + u j, where {n:j J n } u j = log {n:j J n } χ n ɛ n {n:j J n } {n:j J n } χn j It s then clear that even f log T j τ j w j ) θ) and ɛ n j are uncorrelated, log T j τ j w j ) θ) and u j may well be correlated because the sourcng potental of a country drectly mpacts the set of frms sourcng from j.e., n such that j J n ), as well as the share of ther spendng on domestc nputs.e., χ n ). For these reasons, we treat the estmate of θ n column 5 of Table 4 wth cauton and consder nstead the one n column 2, based on frm-level data, as our benchmark one. C.7 Moments and Model Ft - Varous Models In Tables C.6 and C.7 we present the value of the moments used n the estmaton for varous models at the estmated parameters. C.8 Lower Chnese Fxed Costs Counterfactual As an alternatve to an ncrease n Chnese sourcng potental from 1997 to 2007, we explore the effects of a change n fxed costs of sourcng from Chna that s calbrated to explan the growth n the share of aggregate mports from Chna from 1997 to 2007 same target as n the man secton of the paper). We fnd that under constant sourcng potentals, n 1997 fxed costs of sourcng from Chna would have needed to be 8.85 tmes larger than ther sze n Table C.8 s analogous to Table 7 n the man text and llustrates the thrd country effects of ths shock to the fxed costs of sourcng from Chna. It s vsble that the thrd market effects are qualtatvely smlar to those n obtaned for an ncrease n the Chnese sourcng potental, but compared to the data, ths alternatve counterfactual underpredcts the fracton of frms that would have mported from Chna n Wth respect to the prce ndex, the effects are smlar to the Chnese sourcng potental ncrease dscussed n the man text, also mplyng about a 0.19 percent fall n the prce ndex. Fnally, ths counterfactual fals to. 16

17 Table C.6: Moments and other statstcs at estmated parameters Varous Models Baselne Independent Unversal Common Data model entry decsons mportng fxed costs model model across countres θ = 2.85) model Targeted moments: ˆm 1 ˆδ) frst element) ˆm 1 ˆδ) second element) ˆm 2 ˆδ): corrmodel,data) ˆm 3 ˆδ) Share of frms sourcng from Chna Untargeted moments: Share of mports n total sourcng Imports by ctr: corrmodel,data) Share of Chna n aggregate mports Total followng peckng order Notes: The moments are descrbed n the text above equaton 21). The detaled lst of ˆm 2 ˆδ) for the varous models s presented n Table C.7 below. One may be surprsed to see that the Total followng peckng order statstc s not equal to zero for the Common fxed costs across countres and Unversal mportng models. We note that for those models, the share of frms followng the peckng order s equal to zero up to row 9 n Table 6. generate an expanson n the U.S. and thrd-market sourcng of contnuers. C.9 Reduced-Form Evdence on Interdependences Constructng Chna Shock Measures We construct the Chna shocks usng blateral trade data from the UN Comtrade database, whch we map from sx-dgt HS codes to sx-dgt NAICS ndustres usng the concordance from Perce and Schott 2012). Ths concordance does not always map to a sx-dgt NAICS. In those cases where the concordance maps to a fve-dgt NAICS, we aggregate the analyss accordngly. In addton, the concordance mples zero trade for a number of sx-dgt NAICS ndustres. We use the 2007 Census of Manufacturers data to assess the credblty of zero trade flows. Snce plants classfed n these ndustres often have sgnfcant exports, we conclude that the mpled zero trade flows are a data measurement ssue. We therefore aggregate the trade data as needed to ensure that every ndustry has postve mports, though we mantan the dsaggregated nformaton whenever t s avalable. For example, consder a four-dgt NAICS that s an aggregaton of four sx-dgt NAICS codes. If we have detaled mport shares at the NAICS6 level for two of the detaled NAICS6 ndustres, we use the sx-dgt shares for those ndustres. For the remanng two NAICS6 codes wth mpled zero shares, we aggregate to the lowest level of aggregaton necessary to ensure non-zero flows for all codes and assgn the aggregate share to the remanng NAICS6 codes that would otherwse have had zero mpled shares. Ths frm-level shock s gven by shock nput n = h n s nh Chna nput h2007 s nh Chna nput h1997, h n C.3) 17

18 where s nh s ndustry h s share of frm n s manufacturng sales n The mportance of Chnese mports as nputs n a partcular ndustry s Chna nput ht = m h s mh EU15mports Chna mt EU15mports W orld/us mt where s mh s the expendture share of nputs from ndustry m n ndustry h and, EU15mportsChna mt EU15mports W orld/us mt s Chna s share of EU15 country mports n ndustry m and year t, excludng mports from the US, as well as trade among the EU15 countres. We measure the expendture shares of nputs usng the 1997 BEA nput-output tables. We measure Chnese market shares usng UN Comtrade data. We follow the general approach n Autor et al. 2013) and use Chnese exports to the followng orgnal European Unon countres: Austra, Belgum, Denmark, Fnland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Span, Sweden, and the U.K. 8 The underlyng shock measure s thus a weghted average of changes n Chnese market share n these countres for a frm s nputs, makng t unlkely that demand or supply shocks for U.S. frms drve the varaton. Deflatng Inputs and Imports We deflate all nomnal values to 1997 values usng ndustry deflators from the NBER-CES productvty database for sx-dgt NAICS 1997 codes. We use the Fort-Klmek NAICS 2002 codes to classfy establshments n both 1997 and 2007 on a consstent ndustry bass. 9 There s a one-to-one mappng from NAICS 1997 codes to NAICS 2002 codes for manufacturng ndustres. For plants outsde of manufacturng, and for frm mports outsde manufacturng, we deflate plant-level varables usng the Bureau of Labor Statstcs Consumer Prce Index for urban consumers, all tems, taken from FRED. Ths deflator value s between 2007 and We use the deflator seres pmat to deflate plant-level non-mported nput expendtures, by ndustry. Snce the model mplctly treats producton workers as substtutable wth purchased materal nputs, we deflate ther wages usng the pmat deflator for the plant s ndustry. Wholesale plant nput purchases are deflated usng the CPI. After deflatng, we compute real total nputs as Inputs n = MatP urch n + Merch whole n + P rodw orkerw ages manuf n. We use the deflator seres pshp to deflate plant sales. We also deflate frm mports by ndustry usng the pshp deflators. Frm mports are reported at the level of HS10, 2007 vntage. We frst apply the Perce-Schott HS10 to NAICS concordance to convert mport values to NAICS We then concord the NAICS 2007 codes to NAICS 2002 codes usng sales shares we construct from the 2007 CM data. 10 We then deflate frm mports by the ndustry of the mports themselves, usng the pshp ndustry deflators. Fnally, we compute real domestc nputs as deflated total nputs - deflated total mports. We drop a very small number of frms for whch mpled deflated domestc nput purchases are zero or negatve. 8 We use EU15 countres snce we do not face the same data constrants as ADH who need trade data back to All our results are robust to usng the ADH countres, but our frst stage statstcs are somewhat weaker, especally for the results n Onlne Appendx Table C.11, where we nstrument for both frm-level Chnese mports and Chnese mport penetraton n a frm s ndustry. 9 See Fort and Klmek 2016) for detals on these ndustry codes. 10 The 2007 CM collects establshment-level data on a NAICS 2002 and NAICS 2007 bass, whch allows us to construct an aggregate sales-weghted concordance. 18

19 Robustness Tests for the Evdence on Interdependences Here we present summary statstcs for manufacturng frms n 1997 by ther Chna mport status see table C.9). We also show that the evdence presented n secton 5.4 s robust to controllng for mport penetraton n a frm s ndustry and to nstrumentng for mport penetraton n a frm s ndustry see Tables C.10 and C.11, respectvely). We measure Chnese mport penetraton as total Chnese mports n an ndustry dvded by total US absorpton n the ndustry. We measure absorpton usng shpments and exports from the CM, and mports from Comtrade data. We aggregate ndustres as necessary to ensure a postve measure of mports for all ndustres. In undsclosed results avalable nternally to researchers wth access to the data) we also ensure that the results are robust to excludng Canada and to lmtng the treatment group to new Chna mporters. The former s mportant snce the match rates from the EC data to the mport data are sgnfcantly lower for Canada pror to Frst Stage Statstcs Table C.12 presents frst-stage estmates for all the specfcatons. C.10 Countres per Product Counts In secton 3.2, we show that most frms source most products from a sngle locaton. Table C.14 reproduces these results rght panel), and also shows that n contrast, frms tend to mport multple products from a partcular country. Table C.15 shows that the pattern of sourcng most nputs from one locaton perssts for frms that source from at least three foregn countres. We also compare these frm-level statstcs to the same numbers for exportng. To make a vald comparson, we must frst aggregate to the HS6 level. Ths ensures the same number of product categores for mports and exports. Table C.16 shows that, even at the HS6 level, most frms source most products from one locaton. Ths s n contrast to frms exportng decsons, where we see that the medan frm sells at least one product to three destnatons and the 95th percentle sells to 21 countres. We conclude by reportng some fgures that llustrate the superor performance of mporters n our sample. Even though U.S. mporters consttute only 25.8 % of U.S. frms that perform some manufacturng, the sales of these mporters consttute 95.6% of the sales of all frms performng some manufacturng, and ther manufacturng sales account for 92.1% of U.S. manufacturng sales. More broadly, when lookng at frms n all sectors of the U.S. economy, the sales of mporters are 70.2% of the total sales of all U.S. frms. These fgures are comparable on the exportng sde. The sales of manufacturng exporters consttute 93.7% of the sales of all manufacturng frms, wth ther manufacturng sales accountng for 90.1% of U.S. manufacturng sales. Furthermore, the sales of exporters n all sectors account for 61.8% of the total sales of U.S. frms. 19