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 September 015 Barceona GSE Working Paper Series Working Paper nº 845

2 Offshoring and Ski-upgrading in French Manufacturing: A Heckscher-Ohin-Meitz View Juan Caruccio Aejandro Cuñat Harad Fadinger Christian Fons-Rosen September 015 Abstract We present a factor-proportions 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 countries than ow-productivity firms. Differenty from the traditiona versions of factorproportions trade theory, Heckscher-Ohin forces operate at the within-industry eve, eading to endogenous variation in ski intensity across firms 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 numerous seminar participants at Banque de France, Bayreuth, Bergen, Copenhagen Business Schoo, Centra European University, CREI, ECARES, Essex, LSE, IIES, Humbodt, Innsbruck, Mannheim, Passau, Southampton, Surrey, Vienna, the CES-ifo Dephi Conference, the Barceona GSE Summer Institute, the IVIE Workshop on Trade and Growth and the CES-ifo Venice Summer Institute for hepfu comments. Cuñat gratefuy acknowedges financia support by the Austrian Science Fund (FWF #AP344-G11) and the hospitaity of CREI whie revising this paper. Fons-Rosen gratefuy acknowedges financia support by the Spanish Ministry of Economy and Competitiveness (ECO P). Banque de France and University of Surrey. Emai: University of Vienna and CES-ifo. Emai: University of Mannheim. Corresponding author. Adress: Department of Economics, University of Mannheim, L7 3-5, D Mannheim, Germany. Emai: Universitat Pompeu Fabra, Barceona GSE, and CEPR. Emai: 1

3 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 intensity, which correates positivey with firm productivity. Our study sheds ight on the specific microeconomic channes that ead firms to sef-seect into offshoring and 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. Moreover, 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 intensities 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 a boost in imports from abor-abundant countries and,

4 simutaneousy, 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 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 in their domestic production than non-importers, and the positive trend in offshoring to these countries since the mid-nineties runs parae to the surge 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 average ski intensity 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, ess productive firms import ony from the most abor-abundant countries, whie more productive firms import aso from the reativey more ski-abundant ones; (iv) firms that increase imports from 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 suppy shocks in France s trading partners and reductions in EU externa tariffs, provide causa evidence that the increase in imports from abor-abundant countries (induced by foreign suppy shocks and tariff reductions) has ed to a substantia increase in the French manufacturing industry s ski intensity over the sampe period. We find that a of the observed within-firm changes in ski intensity can be expained by increased offshoring to abor-abundant countries. 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 essentia 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. 3

5 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) 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 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 Bernard et a. (007) 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 Antràs et a. (014), our mode deivers a natura pecking order of offshoring destinations, which, however, is determined by the forces of factorproportions-driven comparative advantage. In particuar, firms from a ski-abundant country woud first import the most abor-intensive inputs from the most abor-abundant countries, as these provide the argest cost reductions. Our theory aso deivers compementarities across offshoring destinations, though generated by a different mechanism than in Antràs et a. (014). In particuar, our mode predicts that the impact of importing an additiona country-product combination on a firm s goba offshoring 4

6 strategy depends on the country s factor abundance and the input s factor intensity: in the case of a firm ocated in a ski-abundant country, having ower offshoring costs to other countries or for other inputs eads firms to import more from a given ocation. In addition, this effect is stronger if the other sourcing countries are more abor abundant or when the other imported inputs are more abor intensive. We show that this prediction is borne by the data: for French firms importing from the set of abor-abundant countries, hoding constant firm-eve productivity, firms importing more abor-intensive products from other origin countries import a arger vaue from a given ocation; moreover, firms sourcing from reativey more abor-abundant countries import a arger vaue from any given country. 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 Begian firms, find that import competition from China induces ski upgrading of the domestic workforce. Hummes et a. (014) empoy data on Danish importers to provide evidence that empoyment and wages of high-skied workers are positivey affected by offshoring. 1 In contrast to 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 factor-proportions channe of importing and show that it matters for determining the ski intensity of domestic production. 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 administrative firm-eve data that we describe in detai in Section 4. We begin by anayzing the extent of intra-industry heterogeneity in firm-eve ski intensities in French manufacturing. Figure iustrates the amount of intra-industry heterogeneity in firm-eve ski intensities 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, the 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-coar workers. 5

7 variabe of interest has 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 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. kerne density og ski ratio Figure 1: Distribution of og ski ratio. The figure pots the distribution of the firm-eve og ski ratio, defined as the ratio of empoyment of non-bue coar workers to bue-coar production workers per firm. Observations are deviations from the industry means. Thus, the distribution shows the within-sector dispersion in firm-eve og ski ratios. During the same sampe period, offshoring to abor-abundant countries has gained much reevance in French manufacturing. Here, we define abor-abundant countries as those with ess than 95 percent of the French eve of secondary schooing in the popuation. The eft pane of Figure presents the aggregate trend in offshoring to abor-abundant countries measured as the fraction of imports of French manufacturing firms originating in abor-abundant countries: from 1996 to 007 there has been a arge increase in imports from these countries, from ess than 16 to more than 0 percent of tota French manufacturing imports. The right pane of Figure 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 In the robustness checks in the Onine Appendix, we consider an 80-percent threshod and show that our resuts are not sensitive to the choice of the threshod. 6

8 Year Obs. Mean Std. Dev. Coeff. Frac. Variance Frac. Variance Variation between sectors within sectors , , , , , , , , , , , , A 646, Tabe 1: Firm-eve ski ratio: dispersion and variance decomposition The tabe shows means, standard deviations, and coefficients of variation (std./abs(mean)) of og firm-eve ski intensity (defined as non-bue-coar empoyment/ empoyment of bue-coar production workers) for the sampe of French manufacturing firms by year. It aso presents the fraction of the tota industry variance in ski intensity that is attributed to between-industry and within-industry variance. Figure : Trend in imports from abor-abundant countries and trends in og ski ratios. The eft pane pots the share of imports originating in abor-abundant countries (countries with ess than 95 percent of the French eve of secondary schooing) in tota French manufacturing imports. The right pane pots the average firm-eve og ski ratio, defined as the ratio of non-bue coar to bue-coar empoyment, separatey for three categories of firms: importers from countries with ess than 95 percent of the French eve of secondary schooing; firms that never import; a manufacturing firms. 7

9 abor-abundant countries have become substantiay more ski-intensive (as far as their domestic 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 nonimporters 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. Importanty, this increase is driven by importers from abor-abundant countries. By contrast, the ski-ratio of non-importers has hardy changed over the sampe period. 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 reative to for non-importers. Moreover, the increase in ski intensity was aso much arger for importers from abor-abundant countries (from to -0.19) than for non-importers, for which it actuay decreased during the sampe period (from to ). Finay, Tabe shows that importers from abor-abundant countries dispay a much arger dispersion in ski intensities than non-importers: the coefficient of variation is for importers compared to.07 for non-importers. Moreover, such dispersion has increased reativey more for the group of importers than for the group of non-importers. Finay, 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. This reationship is robust to incuding sector- and year-fixed effects (regressions not reported). 8

10 Non-Importers Importers (countries 95% French sec. schoo.) Year Obs. Mean Std. Dev. Coeff. Obs. Mean Std. Dev. Coeff. Variation Variation , , , , , , , , , , , , , , , , , , , , , , , , A 338, , Tabe : Firm-eve ski ratio: importers from abor-abundant countries versus non-importers The tabe shows means, standard deviations, and coefficients of variation (std./abs(mean)) of og firm-eve ski intensity (defined as non-bue-coar empoyment/ empoyment of bue-coar production workers) for the sampe of French firms by year. It aso presents the fraction of the tota industry variance in og ski intensity that is attributed to between-industry and within-industry variance. Non-importers incudes firms that never import during the sampe period. Importers (countries 95% French sec. schoo.) incudes firms that import from countries with years of secondary schooing in the popuation ower than 95% of that of France. 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 are reaxed in the next section. There are two countries, Home and Foreign (denoted by *), 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 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 9

11 two intermediate inputs, y 1 and y. We assume the foowing production function for fina goods: ( ) 1/ ( ) 1/ y1 y q(γ) = γ. () 1/ 1/ 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, (3) y = /τ j, (4) 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 firms need to pay a variabe iceberg outsourcing cost τ o (1, H/L). 4 This variabe offshoring cost can be interpreted as a friction (e.g., a trade barrier) and as a cost or productivity disadvantage due to distance. Besides this variabe iceberg 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 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. 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 = w h, w h = w, γ o = γ o, 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 the threshod 3 This assumption is harmess in terms of the intuitions discussed beow, and simpifies the agebra notaby. 4 We avoid modeing any type of hod-up probem. See Antràs (003) and Antràs and Hepman (004). For 10

12 productivity eve for offshoring, as 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, (5) 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/, (6) MC n (γ) = γ 1 w 1/. (7) The eft pane of Figure 3 pots the profit function of equation (5) 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 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 productivity 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 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. 11

13 Offshoring decision Equiibrium π(γ) π o (γ σ-1 ) γ o OFE FMC π n (γ σ-1 ) (γ o ) σ-1 γ σ-1 -Pf o 1 τ o K/L w Figure 3: Offshoring decision (eft pane), genera equiibrium (right pane). 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. (8). The price eve P is simpy the CES idea price index. Given the symmetry assumptions we impose, it simpifies to P 1 σ = M ( σ ) 1 σ [ γo ( σ 1 1 γ 1 w 1/ ) 1 σ dg (γ) + (τ o ) 1 σ γ o ] γ σ 1 dg (γ). (9) 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. (10) 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 γo 1 ( γ 1 w 1/ γ o γ σ 1 dg (γ) ) 1 σ = H L. (11) dg (γ) 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. 1

14 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 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, (1) 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. (13) Equations (1) and (13) 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 (1) and (13), and discuss some comparative statics exercises. (See the right pane of Figure 3 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 (1) 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 γ F MC o (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 no firm woud empoy unskied workers. 13

15 Notice that equation (13) can ony hod for w > τ o. Under the (sufficient) condition 11 a σ + 1 σ 1 f o < 1, (14) f e equation (13) 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 The tractabiity of the mode enabes us to carry out a number of comparative statics exercises: 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. In the empirica section beow we wi interpret changes in τ o as variation in import tariffs or, aternativey, as foreign export suppy shocks. Observe that a reduction in τ o can aso be interpreted as a positive aggregate productivity shock. 3. An increase in f e shifts the OFE-schedue downwards, thus eading to a ower γ o and a 11 Reca that equation (13) is the resut of combining equiibrium conditions 1-3. When differentiating (13) 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 (14) assumes that the former effect is stronger than the atter. This enabes us to sign the derivative of (13) 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). 14

16 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 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, firms face an offshoring decision which 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 the assumptions that we make: 1. There are three countries indexed with j = 1,, 3.. Firms make fina goods by assembing a continuum of intermediate inputs [ 1 ] q (γ) = γ exp n x (z) dz, (15) 0 where γ is firm-specific. x (z) denotes the quantity of intermediate input z used in the production of the fina-good variety. 3. Intermediate inputs are produced with the foowing Cobb-Dougas technoogies: y (z) = Z (z) τ j h (z) z (z) 1 z, (16) 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. 15

17 Figure 4: Cost function (eft pane), offshoring decision (right pane) 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. Intermediate inputs are aso subject to the variabe offshoring cost τ o > 1. For simpicity, we assume for the moment that τ o is equa across a country pairs. 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. 13 We focus on the offshoring decision of firms ocated in ski-abundant country 3 in our empirica section, we wi think of France as country 3. The eft pane of Figure 4 pots the ogarithm of the unit cost function of input z if offshored to countries 1 or (incusive of the variabe offshoring cost τ o ) and if produced in-house in country 3. In abor-abundant country 1 unit costs of inputs rise with ski intensity, whereas in the ski-abundant country 3 unit costs of inputs decrease with ski intensity. The ine is horizonta in the case of the intermediate country. 14 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-intensive nor too ski-intensive. By continuity, it is possibe to derive cutoff points defining the range of inputs for 13 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. Internationa differences in reative factor endowments must aso be arge enough in order for transport costs not to make trade in inputs prohibitive. In unreported numerica simuations we confirm this resut in genera equiibrium. 14 These stark resuts are driven by the mode s symmetry assumption. In a more genera mode, we woud at east have the same patterns in reative terms. 16

18 which each country has the owest production costs (incusive of the variabe offshoring cost τ o from country 3): [0, z 1 ] for country 1, (z 1, z 3 ) for country, and [z 3, 1] for country Foowing the intuition of the two-input mode, offshoring decisions wi vary by firm within each country. Given the structure of costs iustrated in the eft pane of Figure 4, firms in country 3 wi ony find it profitabe to offshore inputs that are on average more abor-intensive than those produced in-house, since offshoring inputs in the range [0, z 3 ) reduces the margina cost of country-3 producers of fina-good varieties. 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, (17) 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 (17) 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 sufficienty productive firms might aso source from country. The right pane of Figure 4 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 the cutoff z3 o because a arger zo 3 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) firms wi find it optima to offshore a arger range of intermediate inputs 15 For exampe, input z 1 is equay expensive to offshore to countries 1 and, whereas inputs z < z 1 are cheaper to offshore to more abor-abundant country 1. Inputs z (z 1, z 3) are cheaper to offshore to not-so-abor-abundant country than to offshore to country 1 or to produce in-house in country 3. 17

19 Figure 5: Offshoring range (eft pane), change in offshoring cost (right pane) (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. The eft pane of Figure 5 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 (z3 o (γ), 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. Notice aso that 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. Regarding changes in offshoring costs, the Appendix shows that π (γ, z o 3 ) / zo 3 τ o < 0: as iustrated in the right pane of Figure 5, a decrease in the variabe offshoring cost τ o makes it more profitabe to offshore inputs, thus increasing the optima range of offshored goods for country-3 firms. In addition, a decrease in τ o wi raise the share of imports in tota saes as imported inputs substitute away in-house produced tasks both through the intensive margin (an 18

20 increase in the voume imported of offshored inputs) and the extensive margin (an increase in the number of offshored inputs). As mentioned in the introduction, our theory aso has impications about compementarities across sourcing ocations. The two exampes that foow iustrate the kinds of arguments one can buid upon our mode in this respect. Consider two firms from country 3 with the same productivity γ. Assume that they face different variabe offshoring costs, high or ow, for different ranges of inputs: in particuar, et us assume firm 1 has ow offshoring costs for the most aborintensive decie of inputs whereas firm has ow offshoring costs for the second most aborintensive decie. Consider a situation in which γ is arge enough and both firms offshore these two ranges of inputs. The resuting decrease in margina costs is arger for firm 1 than for firm. Firm 1 s revenues wi be higher, thus making it more ikey that it offshores a arger voume of inputs and to more countries than firm, even if offshoring costs for these other countries or inputs are the same across the two firms. Consider now a many-(> 3) country word in which the fixed offshoring costs firms face, high or ow, vary by country. Let us assume firm 1 has ow fixed offshoring costs vis-à-vis the most abor-abundant country. Firm, with identica productivity eve, has a ow fixed offshoring cost vis-à-vis some other country. Having a ow offshoring cost vis-à-vis the most abor-abundant country wi give firm 1 a arger cost reduction, thus enabing it to gain size in comparison with firm : firm 1 is therefore more ikey to offshore a arger voume of inputs to any given country, even if offshoring costs for these other countries and inputs are the same across the two firms. 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- 19

21 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. For French firms importing from the set of abor-abundant countries, hoding constant firmeve productivity, firms importing more abor-intensive products from other import destinations import a arger voume from a given country of origin; moreover, firms sourcing from more aborabundant countries import a arger voume from any given country of origin. 6. 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. 7. 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 Firm-eve Data Our empirica anaysis is based on a detaied French firm-eve dataset that we obtain by merging severa administrative data sources using a common firm identifier. Trade data: Firm-eve trade data come from an exhaustive administrative fie coected by the French Customs Office. The yeary vaue of imports (by country of origin and product) and exports (by country of destination and product) are reported for a firms over the period Baance sheet data: The administrative BRN dataset ( Bénéfices Rées Normaux ) is constructed from tax records and provides baance-sheet information by year. We use data on saes, empoyment, materia usage, capita stock and main sector of activity at the 5-digit NAF Rev eve. 17 The dataset incudes over 60% of French firms. We use the BRN data to estimate 16 The data is virtuay exhaustive. Fows with non-eu countries whose vaue is beow 1,000 Euros are not in the dataset. In the case of EU countries, the threshod is arger, varying from 40,000 to 150,000 Euros depending on the year. These threshods eave out a very sma proportion of French trade fows. 17 NAF = French cassification of economic activities, the first four digits of which are identica to the NACE Rev cassification 0

22 firm-eve tota factor productivity (TFP) as the residua of a Cobb-Dougas production function, separatey for each -digit industry using data on 1,06,147 observations over the period Our preferred measure uses the Levinsohn and Petrin (003) method. Empoyment by ski data: We obtain information on the occupationa structure at the firm eve using the DADS dataset ( Décaration Annuee de Données Sociaes ). It is constructed from mandatory empoyer reports of their workers characteristics. For every firm in France with at east one empoyee, we have information on the number of workers by year in each of five categories: = Firm owners receiving a wage; 3=Administrative and commercia managers (incudes engineers); 4=Technicians and supervisors; 5=White Coar empoyees; 6= Production workers (Bue Coar). Categories are based on the French Nomencature des professions et catégories socioprofessionnees, PCS. 18 We construct our main measure of ski intensity at the firm eve as the fraction of non-production workers in tota empoyment. The ski ratio of firm f in year t is ski ratio ft ( )/(6). Country- and Product-eve Data We compement our firm-eve dataset with the foowing information: Country-eve human-capita data: We use information on country-eve ski abundance from Barro and Lee (013) to construct the set of countries which are ess ski abundant than France. Our measure of ski abundance is the number of years of secondary schooing in the popuation oder than 15. We consider the set of countries that have ess than 95 percent of the French eve of secondary education (in the robustness checks in the Onine Appendix we consider an 80-percent threshod). This information is avaiabe for the years 000 and 005; we use an average of the two data points. Tabe A- presents the set of countries. 19 Product-eve ski-intensity data: We use the NBER manufacturing database (Bartesman and Gray, 1996; avaiabe at to construct measures of ski intensity 18 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. Athough this variabe refers to occupations, it has often been used to proxy for the workers ski eve (e.g., Cahuc et a., 006). Caiendo et a., forthcoming show that average wages are inversey inked to the position in the PCS. 19 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. 1

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