Offshoring and Skill-upgrading in French Manufacturing: A Heckscher-Ohlin-Melitz View

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1 Offshoring and Ski-upgrading in French Manufacturing: A Heckscher-Ohin-Meitz View Juan Caruccio Aejandro Cuñat Harad Fadinger Christian Fons-Rosen March 015 Abstract We present a factor proportion trade mode in which heterogeneous firms can offshore intermediate inputs subject to fixed offshoring costs. In the ski-abundant country, highproductivity firms offshore a arger range of abor-intensive inputs to the abor-abundant country than ow-productivity firms. Differenty from the traditiona versions of factor proportions trade theory, Heckscher-Ohin forces operate at the within-industry eve, eading to an endogenous within-industry variation in ski intensity that is positivey correated with firm productivity. Using French firm-eve data for the years 1996 to 007, we provide empirica support for the factor proportions channe through which offshoring to abor-abundant countries affects the firm-eve ski intensities of French manufacturers. KEY WORDS: offshoring, heterogeneous firms, firm-eve factor intensities, Heckscher- Ohin. JEL CLASSIFICATION: F11, F1, F14 We are gratefu to Andrew Bernard, Hoger Breinich, Paoa Conconi, Donad Davis, Hartmut Egger, Carsten Ecke, Manue Garcia Santana, Marc Meitz, John Morrow, Voker Nocke, Ferdinand Rauch, Eric Verhoogen, Jaume Ventura and seminar participants at Banque de France, Bayreuth, Bergen, Copenhagen Business Schoo, Centra European University, CREI, ECARES, Essex, IIES, Humbodt, Innsbruck, Mannheim, Passau, Southampton, Surrey, Vienna, the CES-ifo Dephi Conference and the Barceona GSE Summer Institute for hepfu comments. Cuñat gratefuy acknowedges financia support by the Austrian Science Fund (FWF #AP344-G11). Banque de France and University of Surrey. Emai: juan.caruccio@gmai.com. University of Vienna. Emai: aejandro.cunat@univie.ac.at. University of Mannheim. Corresponding author. Adress: Department of Economics, University of Mannheim, L7 3-5, D Mannheim, Germany. Emai: harad.fadinger@uni-mannheim.de. Universitat Pompeu Fabra. Emai: christian.fons-rosen@upf.edu. 1

2 1 Introduction The heterogeneous-firm iterature of the ast 15 years has not ony uncovered important withinindustry differences in productivity and export performance, but more recenty aso a substantia within-industry variation of ski intensities between firms, with ski intensities correating positivey with productivity. Athough this within-sector variation is arger than differences in ski intensities between narrowy defined industries (e.g., Corcos et a., 013), most of trade theory ignores it (e.g., the Heckscher-Ohin mode). The few studies that aow for within-sector heterogeneity in factor intensities simpy take it as given (e.g., Crozet and Trionfetti, 013). Simiary, some recent contributions just posit a positive correation between productivity and factor intensities (e.g., Harrigan and Reshef, forthcoming). In this paper, we present a factor proportions mode with heterogeneous firms and costy offshoring that endogenousy generates within-industry dispersion in ski intensities that is positivey correated with firm productivity. Our study sheds ight on the specific microeconomic channes that ead firms to sef-seect into offshoring; determine the type of goods they offshore as we as the country characteristics of their offshoring destinations. We aso show how changes in offshoring costs affect the reative demand for skis at the firm and the industry eve. We provide empirica evidence for the factor proportions mechanism of offshoring using a quasi-exhaustive pane dataset of French manufacturing firms for the period In the mode, intermediate inputs differ in their reative factor intensity and countries have different reative factor endowments, as in the traditiona Heckscher-Ohin theory. Firms are heterogeneous in terms of productivity and offshoring of intermediates requires the payment of per-input fixed offshoring costs. Firms must therefore weigh the ower margina cost resuting from offshoring say a abor-intensive input to a abor-abundant country against the fixed costs impied by such a decision. From the perspective of a ski-abundant country, in equiibrium, the ow-productivity firms produce a inputs domesticay. Sufficienty productive firms offshore the most abor-intensive inputs to very abor-abundant countries. Firms with even higher productivity eves find it profitabe to aso import reativey more ski-intensive inputs from not-so-abor-abundant countries. Such imports substitute for domestic unskied empoyment, making domestic production more ski intensive. Thus, at the firm eve, productivity and ski intensity of domestic production are positivey correated, generating endogenous within-industry variation in ski intensities. Reductions in offshoring costs ead to an increase in imports from abor-abundant countries and to an increase in the ski bias of domestic production. Our mode is abe to expain a set of styized facts for the manufacturing industry in France (a ski-abundant country) inking firm productivity, import behavior, and the ski intensity of domestic empoyment, that we present in the empirica part of the paper. A first ook at the data shows that the strong within-industry dispersion in ski intensities is much arger for importers from abor-abundant countries than for non-importers. Moreover, importers from abor-abundant countries are more ski intensive than non-importers, and the increasing trend in offshoring to

3 these countries since the mid-nineties runs parae to the increase in the ski intensities of those importers. Our econometric anaysis reveas an additiona set of facts that square with our mode s predictions: (i) the firm-eve ski content of imports from abor-abundant countries is positivey correated with firm productivity; (ii) for a given abor-abundant country of origin, more productive firms import more ski-intensive products on average; (iii) out of the set of abor-abundant countries, ony the more productive firms import from the reativey more skiabundant ones; (iv) firms that increase imports form abor-abundant countries experience a substantia increase in their domestic ski intensities; (v) firms that raise the ski-intensity of imports from abor-abundant countries increase the ski intensity of their domestic empoyment; (vi) our instrumenta-variabes estimates, which expoit reductions in EU externa tariffs, provide causa evidence that the increase in the ski intensity of imports from abor-abundant countries (induced by tariff reductions) has ead to an increase in the French manufacturing industry s ski intensity over the sampe period. The insights of our work compement our understanding of a number of issues that have received much attention in the internationa trade iterature. In particuar, we highight that an important channe of factor proportions trade operates within industries and even within firms rather than between industries, which has been the focus of traditiona Heckscher-Ohin theory. This is important in order to understand the impact of internationa trade on factor prices and the factor content of trade. Whereas the between-industry variation in factor intensities is a necessary assumption in the standard Heckscher-Ohin mode, the within-industry variation arising here is a subte manifestation of Heckscher-Ohin forces at work in combination with firm-heterogeneity in size or productivity. Second, we provide microeconometric evidence on the reationship between offshoring and firm-eve ski intensity that operates via the factor proportions channe. We contribute to different strands of the iterature. Our modeing approach is inspired by Hepman (1984), who provides a Heckscher-Ohin mode of mutinationas in which production is verticay disintegrated according to comparative advantage. Aso cosey reated is Feenstra and Hanson (1997), where firms offshore some of their abor-intensive activities in response to iberaization of capita markets, thereby reducing the demand for skied abor in the U.S. We extend their work by introducing firm heterogeneity into the theoretica framework, and by deriving and testing impications at the firm eve. A quite different view of the effect of offshoring on factor demand and wages has been put forward by Grossman and Rossi-Hansberg (008). In their mode there exist compementarities between domesticay performed and offshored tasks. As a consequence, offshoring of unskied tasks may benefit both unskied and skied workers. In contrast, in our mode offshoring and domestic production are perfect substitutes, thus offshoring reduces demand for the offshored factor and its price. Our theoretica mode fits in the iterature of Heckscher-Ohin trade with heterogeneous firms. Bernard, Redding and Schott (007) (henceforth BRS) buid a two-country, two-sector, two-factor Meitz (003) mode, where sectors differ in their factor intensities, firms are homogeneous in terms of factor intensities within a given sector and a factor-proportions trade is in fina goods between sectors. Recenty, Crozet and Trionfetti (013) have extended their mode to aow for 3

4 exogenous within-industry differences in factor intensities. In contrast, our mode endogenousy generates differences in factor intensities within sectors due to factor proportions trade in inputs. Ma et a. (014) deveop a muti-product version of BRS and show that Chinese firms that start exporting focus on their core competencies and expand the production of reativey abor-intensive products. In a mode with heterogeneous firms but with no factor proportions trade, Antràs et a. (014) characterize offshoring patterns for U.S. firms and estimate them structuray using a quantitative muti-country, many-good mode à a Eaton and Kortum (00) that features compementarities between sourcing ocations. Simiary to their mode, aso in ours are compementarities in import choices present. Importing from one country reduces firms unit costs and increases saes, thereby making importing from other destinations profitabe. Moreover, our mode deivers a natura pecking order of offshoring destinations driven by the forces of comparative advantage due to the factor proportions. In particuar, firms from the ski-abundant country woud first import the most abor-intensive inputs from the most abor-abundant countries. Finay, we aso contribute to the empirica iterature on offshoring and domestic ski demand using firm-eve data. Kramarz and Biscourp (007) study the effect of imports on empoyment growth and ski upgrading for a sampe of French firms during They find that imports of finished goods from ow-wage countries are associated with ower empoyment growth, with the effects present ony in the case of arge firms. Mion and Zhu (013), using data on Begium firms, find that import competition from China induces ski upgrading of the domestic workforce. Hummes et a. (014) use data on Danish importers to provide evidence that the empoyment and wages of high-skied workers are positivey affected by offshoring. 1 Differenty from these papers, which are purey empirica, we investigate the specific theoretica mechanisms through which ski demand at the firm eve is affected by offshoring to abor-abundant countries. In particuar, we carefuy measure the ski content of imported goods and show that it matters for the determining the ski intensity of domestic production. The rest of the paper is structured as foows. Section presents styized facts of the French manufacturing industry that provide the motivation for our modeing approach. Section 3 deveops our theoretica mode and derives the empirica predictions. Section 4 discusses the French firm-eve data, whie Section 5 reports our empirica strategy as we as the corresponding resuts. Section 6 concudes. A Preiminary Look at the Data In this section we describe some of the saient features of the French manufacturing empoyment and import data, which provide the motivation for our theoretica mode. We use the detaied administrative firm-eve data that we describe in Section 4. We begin by anayzing the extent of intra-industry heterogeneity in firm-eve ski intensities 1 Using French data, Caruccio et a. (015) find that offshoring of finished goods increases the wages of managers but has no effect on the wages of bue-coars. 4

5 in French manufacturing. Figure 1 iustrates the amount of intra-industry heterogeneity in firmeve ski intensities in French manufacturing by potting the kerne density of the firm-eve (og) ski ratio, defined as the proportion of non-bue-coar empoyment reative to bue-coar empoyment. Here, (og) ski ratios have been demeaned at the 4-digit sector eve, so that the density can be interpreted as pure within-industry heterogeneity in firm-eve (og) ski ratios. The distribution of (og) ski ratios is approximatey norma, with a standard deviation of Thus, there is evidence for pervasive intra-industry heterogeneity in ski ratios. Tabe 1 presents compementary evidence: for each year from 1996 to 007 we report the mean, the standard deviation and the coefficient of variation (standard deviation/abs(mean)) of (og) ski ratios, as we as a within/between sector variance decomposition. The disaggregation of the manufacturing industries is again at the 4-digit eve. The coefficient of variation is arge (around.1) and 80 percent of the variance of ski intensity is expained by within-sector variation between firms, whie ony 0 percent of the variation is between sectors. These patterns are remarkaby stabe over time. During the same sampe period, offshoring to abor-abundant countries has gained much reevance in French manufacturing. Here, we define abor-abundant countries aternativey as those with ess than 80 or ess than 95 percent of the French eve of secondary schooing in the popuation. Figure presents the aggregate trend in offshoring to abor-abundant countries measured as the fraction of French manufacturing imports originating in abor-abundant countries: from 1996 to 007 there has been a arge increase in imports from these countries, from ess than 1 to more than 18 percent of tota French manufacturing imports (considering the 80 percent cutoff). Figure 3 provides some preiminary evidence that the trends in ski intensities and offshoring patterns might be reated. It shows that, at the same time, firms offshoring to abor-abundant countries have become substantiay more ski-intensive (as far as their French abor force is concerned). It pots the mean (og) ski-ratio of French manufacturing firms, separatey for a firms, importers from abor-abundant countries, and non-importers. Here importers are defined as firms that import in the current period from abor-abundant countries, whie non-importers are firms that never import during the sampe period. It is apparent that on average French manufacturing firms have become more ski-intensive during the sampe period. However, whie the ski-ratio of non-importers has hardy changed, importers from abor-abundant countries have experienced a arge increase in their ski ratios. Tabe provides simiar evidence. It shows the average ski intensity by year separatey for non-importers and importers from abor-abundant countries. First, note that importers from abor-abundant countries are more ski-intensive than non-importers: the og ski ratio is for importers from abor-abundant countries (again considering the 80 percent schooing cutoff) reative to for non-importers. Moreover, the increase in ski intensity was aso much arger for importers from abor-abundant countries (from to -0.5) than for non-importers, for which it actuay decreased during the sampe period (from to ). Finay, Tabe shows that importers from abor-abundant countries have much more dispersion in ski intensities We discuss our data sources and construction of variabes in detai in section 4. 5

6 than non-importers: the coefficient of variation is for importers compared to.07 for nonimporters. Moreover, such dispersion has increased reativey more for the group of importers than for the group of non-importers. Last, but not east, note that the firm-eve (og) ski ratio is highy correated with og (TFP): a simpe regression reveas a highy significant sope coefficient of around 0.4 and this reationship is robust to incuding sector and year fixed effects (regressions not reported). 3 The Mode This section presents a styized mode of offshoring with heterogeneous firms in a Heckscher-Ohin environment. For tractabiity purposes, we make a number of simpifying assumptions here, some of which we reax in the next section. There are two countries, Home and Foreign (denoted by a star), endowed with different amounts of skied abor ( skis ) H, and unskied abor ( abor ) L. We assume that Home is ski abundant, H/L > H /L. For simpicity, we assume a very symmetric scenario, whereby H = L > L = H. Other than this, the two countries are identica in their preferences, technoogies, and parameter vaues. There is one fina-good industry, that we mode roughy aong the ines of Meitz (003). Consumers derive utiity from a Dixit-Stigitz aggregate of fina-good varieties: [ Q = ω Ω ] σ q(ω) σ 1 σ 1 σ dω, (1) where σ > 1. Ω denotes the set of avaiabe varieties of the fina good. Each firm produces a different variety of the fina good, over which it has monopoy power. Varieties are produced with two intermediate inputs, y 1 and y. We assume the foowing production and associated margina-cost function for fina goods: ( ) 1/ ( ) 1/ y1 y q(γ) = γ, () 1/ 1/ MC (γ) = γ 1 p 1/ 1 p 1/. (3) There is firm heterogeneity in the productivity γ with which the two intermediates are transformed into output. We assume γ is distributed Pareto with ocation parameter k = 1 (γ 1) and shape parameter a > σ 1, thus eading to the density g (γ) = aγ (a+1). Intermediate inputs are produced with the extreme factor intensities specified in the foowing production functions: 3 y 1 = h/τ j, (4) y = /τ j, (5) 3 This assumption is harmess in terms of the intuitions discussed beow, and simpifies the agebra notaby. 6

7 where h is the skis input and is the abor input and j = o, n denotes the decision of the firm whether to outsource (o) or not (n) the production of intermediate inputs. If the intermediate inputs are produced in-house by the fina-good producers, then τ n = 1. If produced out of the firm, then τ o (1, H/L). 4 Besides this variabe cost, a fixed cost f o in terms of good Q must be paid per type of intermediate input not produced in-house. Internationa trade of both intermediate inputs and fina goods is subject to no variabe transportation costs. Skis and abor are internationay immobie. Factor and intermediate-input markets are perfecty competitive. Before entry, fina-good producers must pay a fixed cost f e in terms of good Q in order to pick a draw of γ from its distribution. For simpicity, we assume no fixed cost must be paid in order to suppy positive amounts of a variety to a particuar market. Hence, a firms that incur the fixed cost f e operate in both the domestic and foreign markets regardess of their reaization of γ. We take the domestic return of skis as the numéraire: w h = 1 and denote the domestic unskied abor wage rate with w. Given the mode s symmetry, in equiibrium M = M, E = E, P = P, w = wh, w h = w, γ o = γo, where M is the mass of firms that incur fixed cost f e, P is the aggregate price index and E w h H + w L denotes expenditure. γ o is expained beow Offshoring Decision Notice that no firm finds it worth to outsource in the own country because of the outsourcing costs f o, τ o and the ack of any cost advantage. Assuming w = w h > w h = w = 1 (this wi be proven beow), it is not worth offshoring abroad the intermediate input intensive in the own country s abundant factor. 6 Hence, the offshoring decision is reduced to a decision about whether or not to offshore abroad the intermediate input intensive in the own country s scarce factor. Since, in this respect, fina-good producers wi simpy weigh the gain from a ower margina cost against a fixed cost, we can mode the offshoring decision as a threshod γ o : for γ γ o, the firm offshores the entire production of the intermediate input (intensive in the own country s scarce factor); for γ < γ o, the firm produces the two intermediate inputs in-house. This argument can be better understood by examining the profit function of Home s finagood producers. They charge a markup σ/ (σ 1) over their margina cost, and make profits (abstracting from the sunk cost P f e ) Π j (γ) = ( ) σ 1 σ E [ MC j σ 1 σp 1 σ (γ) ] 1 σ I (γ) P f o, (6) 4 We avoid modeing any type of hod-up probem. See Antràs (003) and Antràs and Hepman (004). 5 As we discussed, the mode s symmetry impies that the abor-abundant country is a mirror image of the ski-abundant one. This woud not be the case if, for exampe, the abor-abundant country had a comparative disadvantage in assembing the fina goods. In this case, trade patterns woud consist primariy of fina goods being exported by the ski-abundant country in exchange for the abor-intensive intermediates. 6 The assumption that w h < w is admittedy rather unreaistic. This is an artifact of symmetry. The key resuts of the mode woud not change if we aowed for productivy shifts for skied workers. A that matters for our resuts is that the ski premium in the ski-abundant country is ower than in the abor-abundant country. 7

8 where j = o and I (γ) = 1 for γ γ o and j = n and I (γ) = 0 for γ < γ o, MC o (γ) = γ 1 (τ o ) 1/, (7) MC n (γ) = γ 1 w 1/. (8) Figure 1 pots the profit function of equation (6) for j = o, n against γ σ 1. The function Π o ( γ σ 1) is steeper than Π n ( γ σ 1) because MC o (γ) < MC n (γ) Equiibrium The mode s equiibrium conditions can be expressed as foows: 8 1. The fina-good firm s indifference between offshoring or not (Π o (γ o ) = Π n (γ o )) pins down the threshod productivity eve γ o : ( ) σ 1 σ E [ σ 1 σp 1 σ MC o (γ o ) 1 σ MC n (γ o ) 1 σ] P f o = 0. (9). The price eve P is simpy the CES idea price index. Given the symmetry assumptions we impose, it simpifies to ( ) σ 1 σ [ γo ( ) P 1 σ = M γ 1 w 1/ 1 σ σ 1 dg (γ) + (τ o ) 1 σ 1 γ o ] γ σ 1 dg (γ). (10) 3. Free entry eads to expected zero profits for the producers of fina-good varieties. Notice that, in comparison with Meitz (003), a firms paying fixed cost f e wi produce positive amounts, as we assume away the presence of fixed associated to suppying individua markets. 9 1 [ ( ) σ 1 σ E [ MC j σ 1 σp 1 σ (γ) ] ] 1 σ P I j (γ) f o dg (γ) = P f e. (11) 4. Putting together the market cearing conditions for skis and abor, ( 1 γo 1 γ 1 w 1/ 1 w 1 ) 1 σ dg (γ) + (τ o ) 1 σ γ o γ σ 1 dg (γ) ( ) γ 1 w 1/ 1 σ = H L. (1) dg (γ) γo 1 The first term in the numerator is associated to the demand for Home s skis by the Home firms that do not offshore. The second term in the numerator is associated to the demand for 7 Beow we prove that w > τ o in equiibrium. 8 Given the mode s symmetry, we need ony need to consider the equiibrium conditions reated to Home. 9 The assumption that fixed costs are in terms of good Q eads to a tricky issue. For σ = the price eve P cances out from the free-entry condition: when P changes, revenues and fixed costs move in ockstep, thus eaving profits unaffected. This eads to the indeterminacy of M. To avoid this probem, we impose the constraint σ >. In this case, revenues rise faster than fixed costs with an increase in P. 8

9 Home s skis by offshoring Home and Foreign firms. Finay, the term in the denominator is associated to the demand for Home s abor by the Home firms that do not offshore. Home s (and Foreign s) offshoring firms do not demand any Home abor. Condition 4 can be rewritten as Φ F MC (γ o, w, H/L, τ o ) = γ a σ+1 o 1 w 1 σ 1 w 1 σ ( w 1 H/L 1 ) ( w 1 H/L 1 ) + (τ o ) 1 σ = 1, (13) whereas conditions 1-3 yied Φ OF E (γ o, w, H/L, τ o, f e /f o ) = [ a σ+1 a γo σ 1 (τ o ) 1 σ w 1 σ w 1 σ ] (γ a o + f e /f o ) ( ) 1 γ σ a 1 o + γ σ a 1 o = 1. (14) Equations (13) and (14) constitute a system of two non-inear equations in w and γ o. Once we sove this system, we can find positive soutions for M and P from conditions and 3 (see the Appendix). We now characterize the schedues γ o (w ) that resut from equations (13) and (14), and discuss some comparative statics exercises. (See Figure for a graphica representation and the Appendix for detais). Our arguments are based on the guess that the soution must entai τ o < w < H/L, which wi be verified. This guess is obviousy not random. First, it is easy to see that prohibitive costs of offshoring (e.g. f o =, τ o = ) ead to an equiibrium in which w = H/L. Since offshoring reduces the reative demand for each country s scarce factor, we shoud expect a ower w when offshoring costs are not prohibitive. Second, notice from our discussion above on the offshoring decision that τ o > w woud impy no offshoring, ruing out the reaization of gains from trade in the mode. The factor-market cearing condition (13) yieds a positive reationship between γ o and w : the fewer firms offshore, the stronger the reative demand for abor at home, and therefore the higher the reative factor price w. For w = 1, γ o > Since γo F MC (w ) is continuous and positivey soped, for w = τ o > 1, γ o > 1, too. Finay, γ o is associated with w H/L: if no firm offshores, then the reative wage matches its counterpart for the case with prohibitive offshoring costs. 10 γ o = 1 woud vioate abor-market equiibrium, as non woud empoy unskied workers. 9

10 Notice that equation (14) can ony hod for w > τ o. Under the (sufficient) condition 11 a σ + 1 σ 1 f o < 1, (15) f e equation (14) yieds a negative reationship between γ o and w : the higher the reative factor price w, the more home firms find it optima to offshore. w τ o is associated with γ o : for a reative wage w = τ o, no firm finds it optima to offshore for a positive f o. The characteristics of these two schedues guarantee the existence of a unique intersection in the sub-space [w γ o w (τ o, H/L), γ o (1, )]. In spite of the mode s Heckscher-Ohin favor, the equiibrium does not yied factor price equaization because of the offshoring frictions. 1 We now derive a number of comparative-statics resuts. 3.3 Comparative Statics 1. An increase in f o shifts the OFE-schedue upwards, thus eading to a higher γ o and a higher w. A higher f o makes offshoring non profitabe for some firms; this raises the reative demand for abor, thus raising its reative price w.. An increase in τ o shifts the OFE-schedue upwards (a higher τ o reverses the profitabiity of offshoring for some firms) and the FMC-schedue downwards (for a given γ o = γ o, the reative demand for the abundant factor by the rest of the word decreases, as offshoring is now subject to a higher variabe cost). Thus, an increase in τ o raises w. The Appendix shows that the effect on γ o is aso unambiguousy positive, that is, the vertica upward shift of the OFE-schedue dominates the shift of the FMC-schedue in the opposite direction. 3. An increase in f e shifts the OFE-schedue downwards, thus eading to a ower γ o and a ower w. The higher f e, the ess firms in the market; this raises the price eve P, and makes firms arger (in terms of saes); therefore it pays off for more firms to offshore, thus eading to downward pressure on the reative factor price w. 4. An increase in H/L shifts the FMC-schedue to the right, thus eading to a ower γ o and a higher w. A higher H/L makes abor reativey more scarce; this raises the reative price of abor, and makes offshoring profitabe for firms with ower productivity eves. The two-sector mode captures most of the styized facts, which we have described in section : it generates within-sector heterogeneity in ski intensity; moreover, ski intensity correates 11 Reca that equation (14) is the resut of combining equiibrium conditions 1-3. When differentiating (14) with respect to γ o, we come across effects that operate in different directions in the numerator of equation (14): (i) The difference in variabe profits under offshoring and non-offshoring of condition 1 depends positivey on γ o, since more productive firms experience a arger increase in profits from offshoring given their arger saes. (ii) The fixed costs that enter the free-entry condition 3 depend negativey on γ o as the probabiity of paying the fixed cost to offshore decreases with a higher offshoring threshod productivity eve. Sufficient equation (15) assumes that the former effect is stronger than the atter. This enabes us to sign the derivative of (14) with respect to γ o as positive, and subsequenty the impicit derivative of γ o with respect to w as negative. Notice that the sufficient condition hods for an f o sufficienty sma reative to f e. 1 It is easy to show that as ong as f o > 0 factor price equaization is not possibe (even if τ o = 1). 10

11 positivey with productivity; finay, firms that offshore to abor-abundant countries are more ski-intensive in their domestic production than non-offshorers. 3.4 A Many-country Mode with a Continuum of Intermediate Inputs In this section we extend our framework in order to derive a number of additiona empirica impications of our theory. We consider a word composed of three countries that differ in their reative factor prices, and assume that fina-good firms in a countries produce their fina varieties with a continuum of intermediate inputs, each produced with a different ski intensity. In this extended setup, the offshoring decision facing firms incudes (i) whether to offshore or not, (ii) which range of inputs to offshore, and (iii) from which country of origin. Here are the changes in assumptions we make: 1. There are three countries indexed with j = 1,, 3.. Firms make fina goods by assembing a continuum of intermediate inputs where γ is firm-specific. production of the fina-good variety. [ 1 ] q (γ) = γ exp n x (z) dz, (16) 0 x (z) denotes the quantity of intermediate input z used in the 3. Intermediate inputs are produced with the foowing Cobb-Dougas technoogies: y (z) = Z (z) h (z) z (z) 1 z, (17) where y (z) denotes the quantity produced of intermediate input z; Z (z) = z z (1 z) z 1 ; and h (z) and (z) denote, respectivey, the skis and abor aocated to the production of intermediate input z. Notice that ski intensities are increasing in z. 4. Firms are now aowed to choose different ranges of offshored intermediates. They have to incur a fixed cost f o (in terms of the fina good Q) per input offshored. For simpicity we abstract from the variabe offshoring cost τ o here. 13 We choose the wage of unskied workers in country as the numéraire: w = 1. The compexity of the extended mode prevents us from soving for the genera equiibrium anayticay. We assume w h1 = w 3 > w = w h = 1 > w 1 = w h3. 14 Figure 7 pots the ogarithm of the unit cost function of input z if produced in country j as a function of the index of ski intensity z. In abor-abundant country 1 unit costs of inputs rise with ski intensity, whereas in the skiabundant country 3 unit costs of inputs decrease with ski intensity. The ine is horizonta in the 13 We wi introduce them in the next draft of this paper. 14 This wi be the case if we assume a symmetric word as far as factor endowments are concerned: H 1 = L 3 < H = L < H 3 = L 1. 11

12 case of the intermediate country. 15 Foowing standard Heckscher-Ohin intuition, countries comparative advantages depend on their reative endowments: abor-abundant country 1 has a comparative advantage in ow-z goods, ski-abundant country 3 has a comparative advantage in high-z goods, and country has a comparative advantage in the production of goods that are neither too abor bundant nor too ski abundant. By continuity, it is possibe to derive cutoff points defining the range of inputs for which each country has the owest (variabe) production costs: [0, z 1 ] for country 1, z 1 < 1/; (z 1, z 3 ) for country, z 3 > 1/; and [z 3, 1] for country Foowing the intuition of the two-input mode, offshoring decisions wi vary by firm within each country. We focus on firms ocated in ski-abundant country 3. (In our empirica section, we wi think of France as country 3.) Given the structure of costs iustrated in Figure 7, firms in country 3 wi ony find it profitabe to offshore inputs that are on average more abor-intensive than those produced in-house. These inputs wi be offshored to the more abor-abundant countries 1 and. The profit function of a country-3 firm can be expressed as Π [γ, z o 3 (γ)] = π [γ, z o 3 (γ)] z o 3 (γ) P f o P f e, (18) with π [γ, z3 o (γ)] = p [γ, zo 3 (γ)] q [γ, zo 3 (γ)] MC [γ, zo 3 (γ)] q [γ, zo 3 (γ)] denoting variabe profits. The offshoring decision of an individua producer in country 3 can be represented by a cutoff input z o 3 (γ) z 3 that denotes the most abor-intensive input produced in-house. The firm-eve offshoring patterns that can be derived from the maximization of profit function (18) constitute the main firm-eve predictions of our theory, and share many of the intuitions we derived in the two-input mode: country-3 firms wi simpy weigh the margina increase in variabe profits from offshoring a arger range of abor-intensive inputs to more abor-abundant countries against the margina cost of doing so. The margina increase in variabe profits from offshoring decreases with the ski intensity of offshored inputs: the higher the ski intensity, the ower the difference in unit costs between country 1 and country 3, or between country and country 3. The margina cost of offshoring P f o is invariant to ski intensity. Thus, country-3 firms wi aways start by offshoring the most abor-intensive inputs to country 1, and suffcienty productive firms might aso source from country. Figure 8 pots the margina increase in variabe profits from offshoring additiona inputs and the margina cost of offshoring against z. The intersection of the two curves pins down the optima cutoff z3 o (γ) that defines the range of offshored inputs. In the Appendix we show π (γ, z3 o) / zo 3 > 0 and π (γ, z3 o) / zo 3 γ > 0. Variabe profits π (γ, zo 3 ) increase with zo 3 because a arger z3 o impies ower margina costs. A higher productivity γ enhances this effect, as more productive firms have higher variabe profits other things equa. Thus, more productive (arger) 15 These stark resuts are driven by the mode s symmetry assumption. In a more genera mode, we woud at east have the same type of argument in reative terms. 16 For exampe, input z 1 is equay expensive to produce in countres 1 and, whereas inputs z < z 1 are produced more cheapy in more abor-abundant country 1. Inputs z (z 1, z 3) are produced more cheapy in not-so-abor-abundant country. 1

13 firms wi find it optima to outsource a arger range of intermediate inputs (that is, they have a arger z3 o ), thereby keeping in-house production of the very ski-intensive inputs ony. Notice the resuting positive correation between the ski intensity of offshored inputs and the ski intensity used in-house by the firm. Figure 9 iustrates these patterns: a country-3 firm with a high productivity γ offshores a wider range [0, z3 o (γ)] of intermediate inputs than a firm with ower productivity γ < γ: z3 o (γ ) < z3 o (γ). This makes the average ski intensity of the range increase in comparison with a ow-productivity firm. At the same time, this impies that the firm produces a more ski-intensive input mix in-house (z o 3, 1]. Moreover, note that more productive firms in country 3 wi offshore a more ski-intensive mix of inputs by country. Besides, for a given source country, this input mix wi aso be more heterogeneous in terms of ski intensities for more productive firms, as their imports span a wider range of inputs. Finay, notice according to the mode the ski-abundant country s more productive firms offshore to a set of countries that is more heterogeneous in terms of ski abundance: highy productive country-3 firms wi find it profitabe to offshore not ony to country 1, but aso to country, whereas ow-productivity firms may choose not to offshore at a, or offshore to abor-abundant country 1 ony. 3.5 Summary of Empirica Predictions A number of testabe predictions arise from our theory, which we summarize beow. From the perspective of France, which is a ski-abundant country: 1. There is significant variation in the ski intensity of production across French firms within a given sector; there is more variation in ski intensity across firms that import from aborabundant countries than across non-importing firms.. For French firms importing from abor-abundant countries, the ski intensity of imports is increasing in firm-eve productivity. 3. Hoding constant a given abor-abundant source country, more productive firms import more ski-intensive goods from that country compared to ess productive ones; in addition, more productive firms have more variation in the ski intensity of their imports from a given abor-abundant country compared to ess productive ones. 4. For French firms importing from the set of abor-abundant countries, ess productive ones import ony from the most abor-abundant countries, whie more productive firms import aso from reativey more ski-abundant countries; moreover, more productive firms have more variation in the ski abundance of countries from which they import compared to ess productive ones. 5. French firms that import from the set of abor-abundant countries are more ski-intensive in their production in France than French non-importers and French firms that import from other countries. 13

14 6. For French firms importing from the set of abor-abundant countries, the ski intensity of their production in France is increasing in the ski intensity of their imports from those countries. 4 Data The empirica anaysis is based on French firm-eve data. We obtain our sampe by merging severa datasets: 1. The BRN dataset provides us with firm-eve baance sheet information on vaue added, saes, empoyment, materia usage, capita and main sector of activity at the 4-digit NAF Rev eve 17 (pus other variabes). The data is provided by INSEE and constructed from tax records which are mandatory for firms with turnover higher than 730k euro/year, and optiona for firms beow this threshod. The origina fie has information on around firms/year beonging to a sectors of the economy. We restrict the sampe to firms in manufacturing, but eave out those in the -digit NAF 19 sector ( Coke and Raffinage ). We appy some additiona data ceaning (eiminate observations without firm identifiers, inconsistent baance sheets, deeting outiers). We use BRN to construct measures of tota factor productivity (TFP) as the residua of a Cobb-Dougas production function. TFP is estimated separatey for each -digit industry. Our preferred measure uses the Levinsohn- Petrin method.. The French Customs data provides us with information on import and export fows, broken down at the firm-product-country eve. Products are cassified at the CN 8-digit eve (EU - Combined Nomencature), but we aggregate them at the HS6 eve. We use the data for The data is virtuay exhaustive. Fows with non-eu countries whose vaue is beow 1,000 are not in the dataset. In the case of EU countries, the threshod is arger, varying from 40,000 to 150,000 depending on the year. These threshods eave out a very sma proportion of French trade fows. The BRN dataset eaves out sma firms, but accounts for over 90% of the vaue of trade fows in the Customs dataset. We use the Customs data to construct trade variabes at the firm/year eve: the vaue of imports originating from abor-abundant countries (see beow) and a firm-year indicator variabe for importing from these countries. Most importanty, we construct measures of the ski intensity of firms imports, which are centra to our anaysis. We proceed as foows. Denoting product-eve ski intensity with skiint p and the share of imports of product p by firm f in tota imports from abor abundant countries as w f,p,t, we define the factor intensity of imports as s f,t = p I f,t skiint p w f,p,t, which is a firm-eve import-share weighted average of factor intensities, where I f,t is the set of products which firm f imports 17 Cose to the 4-digit NACE Rev Cassification (athough sighty more disaggregated), which in turn is cose to the 4-digit ISIC Rev3 Cassification. 14

15 from the set of abor-abundant countries in that period. measures of factor intensities beow. We describe our product-eve 3. The DADS (Décaration Annuee de Données Sociaes) dataset affords us information on the occupationa structure at the pant eve. It is constructed from mandatory empoyer reports of their workers characteristics. The data is coected at the worker eve, but the version we have access to is aggregated at the pant eve ( DADS étabissement ). For every pant in France with at east one empoyee we have information on the number of jobs ( postes ) in each of five categories: = Firms owners receiving a wage; 3=Administrative and commercia managers (incudes engineers); 4=Technicians and supervisors; 5=White Coar empoyees; 6= Production workers (Bue Coar). 18 These are based on the French Nomencature des professions et catégories socioprofessionnees, PCS. 19 We first aggregate the data by summing across pants beonging to the same firm. We then construct our main measure of ski intensity at the firm eve as the fraction of non-production workers in tota empoyment, i.e., ski ratio (+3+4+5)/(6). 0 It measures the reative empoyment of non-production workers at the firm eve and corresponds quite cosey to the product-eve measure of ski intensity (see next paragraph). 4. We use the NBER manufacturing database (Bartesman and Gray, 1996) to construct measures of ski intensity at the product eve. The advantage of using U.S. industry data is that it is exogenous to events in France. The data are avaiabe up to 005. We define ski intensity as the ratio of non-production to production workers. Both measures are avaiabe at the NAICS97 6-digit eve. We map them into HS6 codes using the concordance tabe provided by Pierce and Schott (009). When more than one NAICS97 code maps into a singe HS6 code, we take a simpe average. To further avoid endogeneity issues, we use factor intensity in the pre-sampe year Moreover, we use information on country-eve ski abundance from Barro and Lee (013). We empoy this information to construct the set of countries, which are ess ski abundant than France. As our main measure of ski abundance we use years of secondary schooing in the popuation over 15. This information is avaiabe ony for the years 000 and 005. We consider the set of countries that have ess than 80 and ess than 95 percent of the French eve of secondary education. 6. Finay, to construct exogenous variation in imports, we empoy information on EU externa tariffs at the importer-product eve. We extract information on appied tariffs (simpe 18 Each job corresponds to an individua working in a pant. Given that the data is yeary, it might happen that a worker moved between two pants of the same firm. However, for over 98% of observations the number of jobs is equa to the number of empoyees. 19 The nomencature underwent a change in 003. This change ony affected the 3-digit disaggregation, whie the 1-digit cassification we are using remained unchanged. 0 Eaton et a. (01) use the same nomencature to ook at how trade affects wages according to the worker s skis. Caiendo et a. (01) shows that average wages are inversey inked to the position in the PCS. 15

16 averages) at the 6-digit HS eve from the Wordbank s WITS database for our sampe period. The estimating sampe is an unbaanced pane covering 1996 to 007 with 646,90 firm/year observations for 104,036 manufacturing firms. Of these 11,763 (1,714) import at east once from the set of countries with ess than 80 (95) percent of the French eve of secondary schooing in the popuation. 5 Empirica Resuts In this section we present evidence for the empirica predictions derived from our mode. Given that our theoretica mode focuses on trade between ski-abundant and ski-scarce countries, we ony consider imports of French firms from countries which are ess ski-abundant than France (the domestic economy). We consider French manufacturing firms that import either from the set of countries with ess or equa than 80 percent of the French eve of secondary schooing, or, aternativey, firms importing from the set of countries with ess or equa than 95 percent of the French eve of secondary schooing. We do this in order to show that our resuts are not sensitive to the specific choice of the schooing cutoff. 1. Tabe A1 ists the set of abor-abundant countries for both cutoff eves of secondary education. We have aready provided empirica evidence for Prediction 1 which states that there is significant within-sector variation in firm-eve ski ratios in the section on descriptive statistics. We therefore start with testing Prediction. Prediction states that for firms importing from abor-abundant countries, the ski content of imports is increasing in firm-eve productivity. To test this prediction, we regress the ski content of imports from countries beow a given threshod of secondary schooing reative to France on firm-eve productivity (measured as the one period ag of (og) TFP to mitigate endogeneity of TFP to importing). The regression specification is as foows: s f,t = β 0 + β 1 og(t F P ) f,t 1 + β X f,t + ɛ f,t (19) Here s f,t is the ski content of imports from the set of abor-abundant countries, og(t F P ) f,t 1 is the one-period ag of firm-eve og(tfp) and X f,t is a vector of contro variabes, which depending on the specification incudes either 4-digit sector fixed effects and year fixed effects or firm fixed effects and year fixed effects. In addition, to contro for other factors that might be correated both with the ski content of imports and productivity, we incude the number of empoyees, the capita/abor ratio, the vaue of exports and the vaue of imports (a in ogs) in some specifications. 1 We excude from the set of these countries any od-eu-member countries that fa beow these cutoffs. We do this for two reasons: first, because we do not consider these countries as truey abor-abundant, since they are a margina cases; second, in the IV exercise we use EU externa tariffs to construct our instrument, so we cannot incude these countries. However, most of the empirica resuts are robust to incuding them in the set of abor-abundant countries. Those countries are: Begium, Denmark, Finand, Greece, Ireand, Itay, Luxemburg, Portuga, Spain and the UK. 16

17 The resuts for these regressions are reported in Tabe 3. In coumns (1)-(4) we consider countries with ess than 80 percent of the French eve of secondary schooing, whie in coumns (5)-(8), we consider countries with ess than 95 percent of this vaue. In coumns (1),(),(5) and (6) we report resuts incuding period and 4-digit sector fixed effects, which expoit the cross-section variation of the data. In contrast, in coumns (3),(4),(7) and (8), we focus on the within-firm variation by adding firm and year fixed effects. We aways custer standard errors at the firm eve. In a these regressions, the coefficient of og(tfp) is positive and highy statisticay significant, confirming our theoretica prediction. This resut is robust to incuding further contros. Thus, the prediction that more productive firms import a more ski-intensive mix of products from abor-abundant countries is confirmed by the data. We now investigate the precise channes through which the positive correation between firmeve productivity and the ski content of firms imports from abor-abundant countries comes about. In particuar, our mode predicts that when considering importers from a specific aborabundant country, one woud expect that more productive firms import a more ski-intensive mix of products from that country compared to ess productive ones (Prediction 3, Part 1). To test this prediction, we run the foowing gravity regression: og(imports) f,p,c,t = β 0 + β 1 og(t F P ) f,t + β skiint p + (0) + β 3 og(t F P ) f,t skiint p + β 4 X f,c,t + ɛ f,p,c,t. Here og(imports) f,p,c,t is the (og) import vaue of product p by firm f from country c in year t, og(t F P ) f,t is og TFP, skiint p is the ski intensity of product p and the vector X f,c,t aways incudes country and year fixed effects. Depending on the specification, it aso incudes empoyment, the capita-abor ratio and the vaue of exports (a in ogs). Observe that incuding country and year fixed effects impies that our regression expoits the within-country cross-section variation across firms and products. According to our theory, we expect the coefficient on ski intensity to be negative, since the comparative advantage of abor-abundant countries is in abor-intensive sectors. More importanty, we expect, β 3, the interaction term between product-eve ski intensity and firm-eve TFP to be positive. We report the resuts for these regressions in the first four coumns of Tabe 4. In coumns (1) and () we consider the 80% schooing threshod and in coumns (3) and (4) the 95% threshod. Again we custer standard errors at the firm eve. As expected, in a specifications, the interaction term between product-eve ski intensity and og TFP is positive and statisticay highy significant. This confirms that more productive firms import more ski-intensive products from a given abor-abundant country. In addition to the resut that ony sufficienty productive firms shoud import reativey skiintensive products from abor-abundant countries, our theory aso predicts that a importers from those countries shoud import the reativey abor-intensive products. We thus expect that more productive importers shoud have a arger variation in the ski intensity of those products which they import from a given country (Prediction 3, part ). In order to test this prediction, 17

18 we compute for each firm the dispersion of the ski-intensity of its imports from any given aborabundant country. As our measure of ski dispersion, we consider the ratio of the 75th to the 5th percentie of ski intensity of products imported by a given firm from a given country (using other measures of dispersion, such as the standard deviation or the ratio of the 90th to the 10th percentie gives very simiar resuts). We then regress this measure of ski dispersion on firm-eve productivity (averaged over a years the firm is in the sampe). The regression specification is: dispersion f,c = β 0 + β 1 og(t F P ) f + β X f,c + ɛ f,c. (1) Here, the vector of contros incudes the number of empoyees, the capita-abor ratio, the vaue of exports and the number of products a given firm imports from a given country (a in ogs). We incude the ast variabe in order to avoid any confusion with the mechanica resut that firms which sampe more products randomy from a given country wi have a arger dispersion in the ski intensity of their samped products. Resuts are reported in Tabe 5 for the 80 percent threshod (coumns (1) and ()) and the 95 percent threshod (coumns (3) and (4) of secondary schooing. In a specifications, the coefficient of og(tfp) enters positivey and is strongy statisticay significant, which is consistent with our hypothesis. We now turn on to the next theoretica prediction. Prediction 4 states that out of the set of abor-abundant countries, ony sufficienty productive firms wi find it profitabe to import some products not ony from the very abor-abundant countries but aso from the reativey more ski-abundant ones. To test this prediction, we change the specification of our gravity regression as foows: og(imports) f,p,c,t = β 0 + β 1 og(t F P ) f,t + β sec.schooing c + () + β 3 og(t F P ) f,t sec.schooing c + β 4 X f,c,t + ɛ f,p,c,t, where sec.schooing c is the ski abundance (measured in terms of years of secondary schooing) of country c reative to France and where the vector X f,c,t aways incudes year fixed effects. Depending on the specification, it aso incudes firm-specific contros (empoyment, the capitaabor ratio, the vaue of exports (a in ogs)) and a set of country-specific gravity contros (distance from France, GDP, GDP per capita, area (a in ogs), dummies for common anguage, common border, coony). We expect sec.schooing c to enter negativey (because cost advantages of importing from reativey more ski-abundant countries are smaer) and the interaction term between sec.schooing c and og(t F P ) f,t to have a positive coefficient (since ony sufficienty productive firms wi import from more ski-abundant countries). Resuts for this specification are reported in coumns (5)-(8) of Tabe 4. Again, coumns (5) and (6) consider the 80 percent schooing threshod, whie coumns (7) and (8) present resuts for the 95 percent threshod. In a specifications, sec.schooing c enters negativey and is statisticay strongy significant. More importanty, the interaction term between 18