Does Exporting Improve Matching? Evidence from French Employer-Employee Data

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Does Exporting Improve Matching? Evidence from French Employer-Employee Data Matilde Bombardini, Gianluca Orefice, and Maria D. Tito 2015-113 Please cite this paper as: Bombardini, Matilde, Gianluca Orefice, and Maria D. Tito (2015). “Does Exporting ImproveMatching? EvidencefromFrenchEmployer-EmployeeData,”FinanceandEconomics DiscussionSeries2015-113. Washington: BoardofGovernorsoftheFederalReserveSystem, http://dx.doi.org/10.17016/FEDS.2015.113. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Does Exporting Improve Matching? Evidence from French Employer-Employee Data Matilde Bombardini (University of British Columbia, CIFAR and NBER), Gianluca Orefice (CEPII), and Maria D. Tito (Federal Reserve Board) December 17, 2015 Abstract Does opening a market to international trade affect the pattern of matching between firms andworkers? Thispaperanswersthisquestionboththeoreticallyandempiricallyinthreeparts. We set up a model of matching between heterogeneous workers and firms in which variation in theworkertypeatthefirmlevelexistsinequilibriumonlybecauseofthepresenceofsearchcosts. When firms gain access to the foreign market, their revenue potential increases. When stakes are high, matching with the right worker becomes particularly important because deviations from the ideal match quickly reduce the value of the relationship. Hence, exporting firms select sets of workers that are less dispersed relative to the average. We then document a novel fact about the hiring decisions of exporting firms versus non-exporting firms in a French matched employer-employee dataset. We construct the type of each worker using both a traditional wage regression and a model-based approach and construct measures of the average worker type and worker type dispersion at the firm level. We find that exporting firms feature a lower type dispersion in the pool of workers they hire. This effect is comparable and larger than the commonfindingintheliteraturethatexporterspayhigherwagesbecause,amongotherfactors, they employ better workers. The matching between exporting firms and workers is even tighter in sectors characterized by better exporting opportunities as measured by foreign demand or tariff shocks. Finally, we show that revenue loss is lower relative to the optimum allocation for exporting and more productive firms. This analysis is suggestive of the potential presence of additional gains from trade due to improved sorting. This work benefited from a State aid managed by the National Agency for Research, through the program “Investissementsdevenir”withthefollowingreference: ANR-10-EQPX-17(RemoteAccesstodataCASD).Bombardini thanksSSHRCandCIFARforfinancialsupport. WewouldliketothankKristianBehrens,MikaelCarlsson,Andrew Chang, Leland Crane, Nils Gottfries, Keith Head, Hiroyuki Kasahara, Christopher Kurz, Julien Martin, Teodora Milicevic, Justin Pierce, John Romalis, Gisela Rua, Oskar Nordstrom Skans, Tomasz Swiecki, Francesco Trebbi, Farid Toubal, and seminar participants at the University of British Columbia, Universita` Bocconi, IES Summer Trade Workshop at Princeton University, EIIT at the University of Oregon, Peter B. Gustavson School of Business, UQAM, HEC Montreal, Uppsala University, Federal Reserve Board, University of Sydney, the West Coast Trade Workshop at Stanford University, Universit´e d’Orl´eans, and Rice University. The views expressed in the paper are those of the authors and do not necessarily reflect those of the Board of Governors or the Federal Reserve System. 1

1 Introduction The pattern of sorting of workers across firms has fundamental implications for the efficiency of the economy as well as for the inequality of wages in the labor force. The first implication has been a concern of the literature on assignment starting from Shapley & Shubik (1971) and Becker (1973). From those contributions we know that when firms and workers are complementary in production, then the allocation of the right worker to the right job maximizes output. The second implication has received attention more recently for example by Card et al. (2013), who show that sorting of good workers to good firms can explain as much as 35% of the recent increase in wage inequality in West Germany. The logic by which highly skilled workers are paid more not only because of their innatehigherproductivity,butalsobecausetheyworkwithhighlyproductivefirmsandco-workers, is common to the contribution by Kremer & Maskin (1996) as well. Inthispaper,westartfromthepremisethattheoptimalallocationofworkerscannotbereached because of the presence of search costs, and therefore firms accept some degree of mismatch in equilibrium because the cost of search exceeds the benefit from a more suited partner. We then explore whether the matching of firms and workers is affected by access of the former to the export market. But how can market integration affect how firms and workers are matched? When firms gain access to the foreign market, their revenue potential increases. When stakes are high, matching with the right worker becomes particularly important because deviations from the ideal match quickly reduce the value of the relationship. Using matched employer-employee data from France, we show that exporters select pools of workers characterized by a higher average type and, more importantly, a lower type dispersion than non-exporting firms. While the first effect is predicted by other models (Helpman et al., 2010 and Sampson, 2014), we believe we offer a novel way of testing this prediction, which disentangles pure exporter wage premia (deriving from profit-sharing with workers as in Amiti & Cameron, 2

2012) from the selection of better workers by exporting firms. The second effect – i.e. the influence of exporting on worker type dispersion – is unexplored in the literature and is, according to our results, quantitatively as strong as the effect of exporting on worker average type. We explore further the effect of exporting by building measures of the exporting opportunities in different sectors using tariffs and aggregate imports from the rest of the world of the various countries to which France exports. Whether we build these measures at the firm or sector level (using previous period export shares), we find that when exporters face lower tariffs or larger demand for imports in a foreign market, the dispersion of types in their pool of workers declines further. We believe this result is harder to reconcile with a view that the exporting and tightening of the matching are both driven by a common excluded factor. To study the impact of exporting on matching, we employ the model proposed by Eeckhout & Kircher (2011), in which exporting is identical to an increase in the firm’s type. Heterogeneous workers and firms face a dynamic problem. In the first period they meet at random and decide whether to accept the match. If they do not accept the match, they pay a search cost and proceed to the second period, in which perfect assortative matching prevails. The second period, rather than an infinite horizon, approximates the long-run outside option for both worker and firm. The presence of search costs creates an acceptance set, rather than a unique assignment outcome that prevails in the frictionless model. As shown by Eeckhout & Kircher (2011), the boundaries of such acceptancesetareincreasinginfirmtype,confirmingthepatternofpositiveassortativematchingin a model with frictions. We focus on a different dimension and we take the width of the acceptance set as a measure of the variability in worker type tolerated by the firm. On the one hand, because of complementarity, a worker with ability below the firm’s ideal creates a reduction in output that is larger when the firm is very productive. On the other hand, a worker type that is above the average type requires an increasing compensation due to her outside 3

option. Suchcompensationrisesmuchfasteratfirmsthataremoreproductivebecausetheyemploy, on average, more productive types. The result is that firms that are more productive, or that have access to the export market, tolerate less relative dispersion from their ideal worker type. In order to give a preliminary assessment of the welfare implications of this novel empirical finding, we derive a measure of the average revenue deviation for each firm type relative to the optimal assignment. We show that, according to this measure, a more productive firm (or an exporting firm) features a lower deviation from the optimal level of revenues created under perfect assortative matching. This is only a partial equilibrium result and cannot inform us as to whether there are overall gains from trade opening related to this matching channel. In particular, there are two counteracting forces when an economy opens to trade. On the one hand, import-competing firms receive a negative shock to their revenues and therefore their matching range tends to widen. On the other hand, exporting firms receive a positive shock and choose smaller deviations from the optimum. The overall welfare result depends on which effect prevails. Tito (2015) simulates an infinite horizon version of the model with two symmetric countries and calibrates it to French moments of the data in order to recover the parameters for search costs, transport costs and the elasticity of demand. She numerically shows that the gains from trade are larger as we increase the cost of search. This result seems to provide support to the idea that when an economy is characterized by high frictions, trade opening can be more beneficial than when the economy is essentially very close to the optimal worker-to-firm allocation. 1.1 Literature Review This paper contributes to the growing literature on international trade with heterogeneous workers and firms, which is surveyed in a recent chapter by Davidson & Sly (2012). More specifically, it belongs to a strand of research that investigates the effect of openness on the process of matching 4

betweenfirmsandworkers, whichisatthecoreofthecontributionbySampson(2014), whostudies its consequences for wage inequality.1 The most closely related work is a recent paper by Davidson et al. (2014), which shows, using Swedish data, that export-oriented sectors display a higher correlation between firm and worker types, estimated as firms’ and workers’ fixed effects in a wage regression as in Abowd et al. (1999)(henceforth AKM). Our approach shifts the focus on the firm-level decision rather than looking at the aggregate strengthofmatchingandthereforereliesonadifferenttypeofvariationtodetectdifferentmatching behavior by firms that are differentially exposed to international trade. In particular, it exploits within-sector variation between exporting and non-exporting firms, therefore isolating and controlling for other sector-level characteristics of the labor market that may affect the sorting of workers across firms. Moreover, because Eeckhout & Kircher (2011) prove that firms’ fixed effect deriving from a wage regression `a la AKM might be negatively or not correlated with the true firm type, we are careful to avoid using those fixed effects as proxies for the firm type. We use instead variables constructed from firm-level data, such as sales, value added, and total employment. From a theoretical standpoint, our approach differs from Davidson et al. (2008) in that we have a different focus. We are interested in deriving predictions at the firm level rather than at the aggregate level, and therefore we allow for a rich heterogeneity on both the worker and the firm side. Davidson et al. (2008) simplify those dimensions in order to obtain clean aggregate results. In particular, they have high and low types of workers and high and low technologies that are endogenously chosen by ex-ante homogeneous firms. Globalization can take the economy from an equilibrium in which high-tech firms employ high-type workers and low-tech firms employ both 1Ourpaperisalsorelatedtothelargeliteratureontheimpactoftradeoninequality,whichincludes,amongmany others, Feenstra & Hanson (1999), Costinot & Vogel (2010), Bustos (2012), Amiti & Cameron (2012), Verhoogen (2008), Krishna et al. (2014), and Fr´ıas et al. (2012). 5

high- and low-type workers to an equilibrium in which there is perfect assortative matching. The firm-level predictions in their setup between exporters and non-exporters are stylized in that there is no predicted variation in the type of workers hired by different types of firms under trade. The relationship of this paper to the theoretical framework in Helpman et al. (2010) and Helpman et al. (2015) deserves a more detailed analysis, since both models describe the matching of heterogeneous firms to heterogeneous workers in the presence of search frictions. The main conceptual difference between the two theoretical approaches is the nature of workers’ heterogeneity. In Helpman et al. (2010), workers are not ex-ante different, but they have a productivity draw that is firm specific. Therefore, there is no sense in which an ex-ante high-type worker is more likely to match with a high-type firm, since a firm simply selects the workers that have better productivity draws relative to that firm only. In general, our estimation procedure, which presumes the existence of a fixed worker type, is incompatible with their view of ex-ante identical workers. Let us for a moment set aside this difference and investigate the predictions of their model in terms of the dispersion of worker types within firms. Under the assumption of a Pareto distribution, exporters (and more productive firms in general) choose ahigher ability cutoff for theworkers theyhire. This choice results in a within-firm distribution of workers that has higher standard deviation, higher mean, and a constant coefficient of variation (the ratio of standard deviation to mean). Therefore, we need an alternative theoretical framework to investigate the impact of exporting on matching of permanently heterogeneous workers and firms that also face the possibility of exporting. The remainder of the paper is divided into four sections. Section 2 introduces the theoretical framework and derives the main result on the dispersion of worker types at the firm level. Section 3 presents the estimation of worker types and the empirical results linking export status and dispersion of worker type in the firm. Section 4 describes a partial equilibrium welfare result. Section 5 concludes. 6

2 Theoretical Framework The role of the theoretical framework is to understand why exporting firms may match with a different pool of workers from non-exporters. In particular, we are interested in two characteristics of the pool of workers hired by exporters: the average worker type and, most importantly, the variation in worker type at the firm level. The setup is borrowed from Eeckhout & Kircher (2011), a dynamic model in which heterogeneous firms and heterogeneous workers match in the presence of search frictions. There is a unit mass of workers and a unit mass of firms. A worker’s type θ is distributed according to a smooth density g(θ) on the interval [0,1], while a firm’s type ψ is distributed according to smooth density h(cid:48)(ψ) on the interval [0,1]. Output is produced by a firm that employs one worker, according to the production function f(θ,ψ) = (θψ)σ where σ > 0. 2 We embed the matching problem in a monopolistic competition model a` la Krugman (1979). Each firm produces a differentiated variety of a product. Demand for an individual variety is isoelastic with elasticity η > 1. Therefore, firms selling their output in the domestic market obtain total revenues σ(η−1) 1 R d (θ,ψ) = (θψ) η E d η where E represents domestic total real expenditure. Firm revenues are increasing in the firm d and worker type and feature complementarity between the two types, f > 0. Complementarity θψ is key for whether there is positive assortative matching in equilibrium between firms and workers. In the absence of frictions, we would observe perfect positive assortative matching and every 2Intheabsenceoffirm-levelresourceconstraints,anextensiontoafirmwithnworkersistrivialiftherearenocomplementaritiesamongworkers. Inthiscase,thefirmsolvesthesameproblemntimes. Ifweallowcomplementarities between workers, we can show that our basic result is confirmed. See section 2.1.4. 7

type of firm would be matched with a unique type of worker. In particular, a more productive firm would be matched with a more productive worker, but there would be no variation within the set of workers matched with firms of a given type ψ, as in Sampson (2014). We are interested in analyzing the variation between workers employed by the same type of firm. We therefore introduce frictions in the spirit of Atakan (2006), although we follow the timing simplification proposed by Eeckhout & Kircher (2011).3 There are two periods. In the first period, workers and firms meet at random, perfectly observe one another’s type and decide whether to produce. If they do not produce, they pay a cost c to search again in the second period. In the second period,4 matching happens in a frictionless and competitive setting; therefore, perfect assortative matching is the equilibrium outcome as in Becker (1973). Before describing how the equilibrium matching is determined, we describe how we interpret the exporting decision in this simple setup. We introduce exporting in the simplest possible way, yet one that has similar features to the rest of the literature. There are different options when introducing a firm-level exporting decision. The original contribution by Melitz (2003) simply introduces a fixed cost of exporting common to all firms. This modelling choice implies that we should never observe two firms of the same productivity, but different export status. The stark prediction that all exporters should be more productive than non-exporters is clearly not supported by the data, as argued, for example, by Bernard et al. (2003) and Helpman et al. (2015). In both U.S. and Brazilian data the distribution of productivity of exporters has a higher mean, but also displays a substantial overlap with the productivity distribution of non-exporters, a feature that is clearly shared by our French sample, as shown in Figure A4. 3Extendingthemodeltoaninfinitehorizonframeworkdoesnotalterthequalitativepredictionsoftheequilibrium. Theanalyticalcharacterization,however,requiresthatworkersandfirmshavethesamedistribution. Intheappendix, we also include a numerical simulation without assuming equal distributions of worker and firm types. 4We interpret the second period as the future in an infinite horizon framework. In fact, the frictionless payoffs share qualitative properties with the continuation values derived in an infinite horizon model. 8

Similarly to Helpman et al. (2015), in our exercise we focus on the effect of exporting separately fromthatoffirmproductivity;therefore,weallowdifferentfirmstohavedifferentcostsofexporting. This may reflect various idiosyncratic factors such as better knowledge of the export market that makes setting up an export operation less costly. Because our interest in this paper is exclusively in comparing exporters and non-exporters and not in the endogenous sorting into exporting or the estimation of the fixed cost of exporting, we make one further simplifying assumption. We assume that some firms draw a prohibitively high fixed cost of exporting, while the rest of the firms draw a negligible fixed cost. All firms that export face an iceberg transport cost τ > 1. This is the simplest way of introducing heterogeneous exporting behavior among firms of identical type.5 Whenafirmexports, itsrevenuesincreaseevenifthefirmisnotallowedtoadjustitsworkforce. The firm sells its output in a market where the first unit sold of its differentiated variety is valued muchmorebyforeignconsumersthanthelastunitsoldinthehomemarketwasvaluedbydomestic consumers. Thefirmallocatesoutputproducedbetweenthetwomarketssothatmarginalrevenues are equalized in the two markets. This implies that, similarly to Helpman et al. (2010), total revenues of a firm ψ that exports can be written as follows: R x (θ,ψ) = (θψ) σ(η η −1) (cid:0) E d +E x τ1−η(cid:1) η 1 , where E is foreign real expenditure. x It is straightforward to verify that, for given θ and ψ, revenues of an exporting firm are larger than those of a non-exporting firm. It is useful to rewrite revenues of an exporting firm and a 5Perhapsmoreimportantly,wedonotwanttointroducefurthercomplicationwhenthedatapointsagainstit. In our data set, the entry and exit margin in the export market seems to be quite inactive. When firms are present in the sample, they either export or they do not. 9

non-exporting firm with given productivity ψ as follows: σ(η−1) R d (θ,ψ) = (A d θψ) η , (1) σ(η−1) R x (θ,ψ) = (A x θψ) η (2) where A = Eσ(η 1 −1), A = (cid:0) E +E τ1−η(cid:1) σ(η 1 −1), and A > A . We therefore establish the d d x d x x d following property. Remark 1 Exporting is isomorphic to an increase in productivity for a firm of initial productivity ψ. Based on Remark 1, we are going to analyze the effect on matching of export status by characterizing the matching behavior of more productive versus less productive firms. Untilnow, wehavenotdiscussedthedistributionofworkertypesand, moreimportantly, offirm types. In principle, we could start with a specific distribution of firm types h(cid:48)(ψ), introduce export opportunities,andderiveadistributionoftypesbasedontheadjusted firmtypeA ψ wherei = d,x. i For the sake of tractability, we instead make an assumption directly regarding the distribution of adjusted firm types, ϕ = A ψ, and assume that such distribution h(ϕ) is uniform. We assume that i the distribution of worker types g(θ) is also uniform, as in Eeckhout & Kircher (2011). 6 2.1 Matching Problem We now solve the matching problem and derive predictions regarding the matching behavior of exporters versus non-exporting firms. We start by characterizing second period wages, profits, and assignment; then, we analyze first period firms’ and workers’ decisions. Once again, the problem is analyzed in terms of the adjusted firm type ϕ and of the worker type θ. We rewrite the revenue 6InsectionA.4,weusetheempiricaltypedistributionstocharacterizethepropertiesoftheequilibriummatching sets, key objects to our analysis. 10

function as R(θ,ϕ) = (θϕ)α where α = σ(η−1) . η 2.1.1 Second Period: Frictionless Market In the second period, assignment is positive assortative. The matching function, µ(θ) = ϕ, which assigns firm ϕ to worker θ, is therefore µ(θ) = θ. In a competitive equilibrium the wage function w(θ) must be such that the marginal revenues for a firm from hiring a better worker is equal to the marginal increase in the wage paid. The equilibrium wage is therefore given by θ (cid:90) dR(t,µ(t)) 1 w∗(θ) = dt = θ2α (3) dt 2 0 By symmetry, equilibrium profits in the second period take the same form: 1 π∗(ϕ) = ϕ2α (4) 2 2.1.2 Acceptance Sets We now determine the matching behavior of firms and workers in the first period. When a worker θ and a firm ϕ meet, they produce R(θ,ϕ). The outside option for the worker is w∗(θ)−c, while the outside option for the firm is π∗(ϕ)−c. Regardless of how surplus is split, the worker and the firm will accept to match if the surplus from the relationship is positive, i.e. if the following surplus condition holds: 1 1 (θϕ)α− ϕ2α− θ2α+2c ≥ 0 (5) 2 2 The surplus condition (5) defines the acceptance set, i.e. the set of pairs (θ,ϕ) sharing a mutually acceptablematch. ThesetofworkersthatmatchwithfirmϕaredenotedbyA(ϕ). Theboundaries ofthesetA(ϕ)areshownbyEeckhout&Kircher(2011)tobemonotonicallyincreasinginϕ, which 11

Θ 1.0 0.8 0.6 0.4 u(cid:72)(cid:106)(cid:76) 0.2 l(cid:72)(cid:106)(cid:76) (cid:106) 0.0 0.2 0.4 0.6 0.8 1.0 Figure 1: Acceptance Set with α = 1, c = 0.01 proves that positive assortative matching holds in the presence of constant search costs.7 Let us define u(ϕ) and l(ϕ), respectively, the highest and the lowest worker types that match with firm type ϕ. Figure 1 illustrates the acceptance set for α = 1 and c = 0.01, but in general u(ϕ) and l(ϕ) are not parallel. 2.1.3 Exporting and the Width of the Acceptance Set We now investigate whether exporting (or more productive) firms tolerate higher or lower variation in the set of workers with which they match. We adopt the matching range of firm type ϕ, d(ϕ), as a measure of the dispersion of worker types tolerated by the firm. The matching range d(ϕ) is defined as the difference between u(ϕ) and l(ϕ) and may be an increasing or decreasing function of ϕ. At this point it is important to discuss whether the absolute measure d(ϕ) is appropriate for the sake of comparing to comparing the dispersion of worker types within firms that exhibit differences also in the average type of worker hired. Let us take, for example, the parametrization in Figure 1 and consider two firms. Firm ϕ hires, on average, very high worker types and firm ϕ H L 7Positive assortative matching requires stronger restrictions on the production function if search costs are due to output loss as in Shimer & Smith (2000). 12

hires, on average, very low worker types. Figure 1 implies that we should observe the same d(ϕ) for both firms, but we would probably not conclude that the two firms tolerate the same degree of worker variation. This is because, in relative terms, firm ϕ tolerates less variation relative to the H average worker hired than firm ϕ . Hence, we argue that the correct way to analyze the matching L range is to adopt scale-free dispersion measures, and we propose two alternatives: (i) a normalized matching range d (ϕ) where we divide the matching range by the average 1 u(ϕ) worker type hired by firm ϕ, a(ϕ). Define d (ϕ) = u (ϕ)−l (ϕ) where u (ϕ) = and 1 1 1 1 a(ϕ) l(ϕ) l (ϕ) = 1 a(ϕ) (ii) a logarithmic matching range d (ϕ), a measure defined on a logarithmic scale so that dis- 2 persion is defined in relative revenue deviations. Define d (ϕ) = u (ϕ) − l (ϕ) where 2 2 2 u (ϕ) = lnu(ϕ) and l (ϕ) = lnl(ϕ). 2 2 The following proposition establishes the main result regarding variability of worker types at more productive firms and exporters. Proposition 1 Dispersion of worker types working at firm ϕ, as measured by (i) the normalized matching range d (ϕ) and 1 (ii) the logarithmic matching range d (ϕ) 2 is decreasing in firm type (and is therefore lower for exporting firms relative to non-exporting firms of identical initial productivity). Proof. (i) Itisimmediatetoshowthatu (ϕ) = (ϕα+2 √ c)α 1 = (cid:16) 1+ 2 √ c (cid:17) α 1 isadecreasingfunction 1 ϕ ϕα of ϕ. Similarly, one can show that l (ϕ) is an increasing function of ϕ. Therefore, the difference 1 between u (ϕ) and l (ϕ) is decreasing. 1 1 (ii) In order to prove that d (ϕ) is decreasing, we are going to show that du2(ϕ) < 1 and 2 dlnϕ that d d l l 2 n (ϕ ϕ ) > 1. Starting from u(ϕ) = (ϕα+2 √ c)α 1 , it is immediate to show that u 2 (ϕ) = 13

√ 1 ln (cid:0) eαlnϕ+2 c (cid:1) and that du2(ϕ) = eαlnϕ √ , which is always smaller than one. Similar steps α dlnϕ eαlnϕ+2 c imply that dl2(ϕ) > 1. dlnϕ In Appendix section A.1.1, we show that this proposition holds more in general as long as the production function is increasing, symmetric, homogeneous, and supermodular. Figure 2 presents the two normalized measures with the same parametrization as in Figure 1. Θ lnΘ a(cid:72)(cid:106)(cid:76) 1.0 4 0.8 2 0.6 (cid:106) 0.4 0.2 0.4 0.6 0.8 1.0 u (cid:72)(cid:106)(cid:76) 2 0.2 (cid:45)2 u 1 (cid:72)(cid:106)(cid:76) l 2 (cid:72)(cid:106)(cid:76) ln(cid:106) (cid:45)4 l 1 (cid:72)(cid:106)(cid:76) 0.0 0.2 0.4 0.6 0.8 1.0 Figure 2: Normalized Matching Range with α = 1, c = 0.01 The result in proposition 1 is easy to explain once we express the surplus condition (5) in terms of normalized worker types. Let us define θ(cid:98) = θ = θ, the type of a worker, relative to the a(ϕ) ϕ average type employed by a firm ϕ. Condition (5) can be rewritten as a function of θ(cid:98)as follows: (cid:20) (cid:21) 1 1 θ(cid:98) α− θ(cid:98) 2α− ϕ2α+2c ≥ 0 (6) 2 2 (cid:124) (cid:123)(cid:122) (cid:125) S(θ(cid:98),ϕ) (cid:16) (cid:17) We analyze the behavior of the function S θ(cid:98),ϕ and the search costs in Figure 3. The function (cid:16) (cid:17) S θ(cid:98),ϕ ismaximizedatθ(cid:98)= 1anddropsasonemovesawayfromthisperfectPAMallocation. The (cid:16) (cid:17) important feature for our purpose is that S θ(cid:98),ϕ drops more steeply on either side of θ(cid:98)= 1 when ϕ is higher. This means that the same proportional deviation from the optimal worker produces a larger loss in surplus at larger firms. Higher-type firms therefore have a narrower range over which 14

(cid:16) (cid:17) S θ(cid:98),ϕ > −2c as Figure 3 clearly shows. 0.01 0.00 1.0 (cid:45)0.01 (cid:45)0.02 (cid:45)0.03 0.0 0.5 (cid:106) (cid:96) 0.5 S(cid:72)Θ,(cid:106)(cid:76) (cid:45)2c (cid:96) 1.0 Θ 1.5 0.0 2.0 Figure 3: Surplus Condition as a Function of Normalized Worker Types for α = 1, c = 0.01 2.1.4 One Firm with Multiple Workers The model we have analyzed so far entails only one worker. In that context, we have said that we can interpret a firm as a collection of hiring decisions that are independent from one another. Onemaywonderwhetheraddingmoreworkerstotheproblemmodifiestheresults. Inprinciple, there is a somewhat distinct reason why firms may not want to hire very heterogeneous sets of workers and that is because worker types are complementary to one another, and not just to the firm. Nevertheless, because of complementarity with the firm type, this effect is stronger for more productivefirms. Asaresult,thiseffectwillstrengthenthelogicthatwehaveillustratedintheoneworker setup. Consider, for example, the case of two workers (each drawn from a distinct uniform productivity distribution): θ and θ where the production function is R(ϕ,θ ,θ ) = (ϕθ θ )α. 1 2 1 2 1 2 Assuming, as in this production function, that in case of disagreement the firm cannot produce with only one worker, the surplus condition is very similar to (6) and we can write it in normalized 15

terms analogously to (6): (cid:20) (cid:21) (cid:16) (cid:17)α 1 1 1 θ(cid:98)1 θ(cid:98)2 − 3 θ(cid:98) 1 3α− 3 θ(cid:98) 2 3α− 3 ϕ3α+3c ≥ 0, (7) whereθ(cid:98)i = θ ϕ i. Itisimmediatetoverifythatthesamelogicappliesinthiscase. Surplusdeclines faster for more productive firms as they consider worker types that are further away from their ideal. Hence, a higher ϕ firm will accept a narrower set of workers than a lower ϕ firm. Inthenextsection,weintroducedataandmethodologyaimedatverifyingtheempiricalcontent of the results in proposition 1. 3 Empirical Analysis Our empirical analysis proceeds in two steps. First, following the theory, we construct worker types using the average wage of the worker over her job spells. As a robustness check, we also estimate the worker types employing a methodology pioneered by Abowd et al. (1999) (AKM) and recently enriched by Card et al. (2013). We are careful to separately construct measures of the firm type that are not derived as firm fixed effects, due to considerations on the AKM methodology by EK. In a second step, we propose various measures that approximate the matching range of individual firms and show that those measures are systematically different between exporters and non-exporters, both in the cross section and when export markets are subject to shocks that affect the profitability of exporting. Before describing our empirical strategy in detail, we offer a brief overview of the features of the wage-setting institutions in France and of the data employed in this paper. 16

3.1 Data The data for our project come from three main sources: the D´eclaration Annuelle des Donn´ees Sociales (DADS), the Enquˆete Annuelle d’Entreprises (EAE), and the French Customs Data.8 DADS is an administrative database of matched employer-employee information collected by the INSEE (Institut Nationale de la Statistique et des Etudes Economique). The data are based on the mandatory reports, filed by employers, of the gross earnings of each employee in compliance with French payroll taxes. All wage-paying individuals and legal entities established in France are required to file payroll declarations; only individuals employing civil servants are excluded from filing such declarations. The INSEE prepares extracts of the original database for research purposes. We rely on the panel version of DADS, which covers all individuals employed in French enterprises born in the month of October of even-numbered years until 2001 and every year after that.9 This choice is motivated by the need to follow workers across years and job positions in order to recover their type (see subsection 3.3). Our extract stretches from 1995 to 2007. The initial data set contains around 24 million observations (corresponding to the triplet worker-firm-year) that are identified by worker and firm ID (respectively, nninouv and siren). For each observation, we have information on the individual’s gender, year and place of birth, occupation (both 2-digit CS and 4-digit PCS-ESE classification), job spell,10 full-time/part-time status, annualized real earnings, total number of hours worked, as well as the industry of the employing firm (NAF700, 4-digit industry classification). We restrict our sample to full-time employees in manufacturing (NAF 10-33), reducing the total number of observations to 2,662,411. 8These data are subject to statistical secrecy and have been accessed at CEPII. 9In 2002, the sampling methodology has been extended to include all individuals born in the month of October of every year. Currently, the DADS panel represents 1/12th of the total French workforce. 10DADS records both the job start date and the number of days the individual worked in a given firm during the calendar year. 17

Most full-time workers are employed at a single firm during the year. Only 6% have more than one employer in a given year; for those, we selected the enterprise at which the individual worked the greatest number of days during the year. Finally, to control for possible outliers, we remove those observations whose log annualized real earnings are more than 5 standard deviation away from a predicted wage, based on a linear model including gender, an ile-de-France dummy, and in-firm experience. We obtain a final sample of 2,579,414. FollowingEK,wehavetofindanalternativeproxyforthetypeoffirmtothestandardestimated firmfixedeffects. Soweenrichtheavailablesetoffirm-levelvariablesbymergingDADSwithEAE, a survey-based dataset containing balance-sheet information on French firms in manufacturing over theperiod1995-2007. TheunitofobservationinEAEisafirm-yearcombination; thefirmidentifier is the same as the firm ID in DADS (siren). EAE samples only medium-large enterprises with at least 20 employees. From EAE, we collect information on sales (domestic and exports), total employment, value added, and the main sector of the firm (NAF700 4-digit classification).11 The merge with EAE further reduces the sample availability. We restrict our sample to individuals working for firms whose characteristics are available from EAE. Furthermore, we remove those firms whose number of sampled employees from DADS is larger than the effective employment reported in EAE. This provides us a final sample of 1,673,992 observations on which we implement our empirical strategy. Export-related information on French firms comes from the French Customs. The customs data include export records at the firm-product-destination level for the universe of exporters located in France. Finally,aggregatedtradeflowsandappliedtarifflevelscomefromstandardsources,respectively COMTRADE and WITS. Aggregated trade flows are used to compute aggregated market shocks 11We compare the firm’s industry classification between EAE and DADS and keep only those observations whose industry information coincides between the two sources. 18

as (weighted) import demand by all potential French trade partners, while applied tariff levels are used as a second proxy for foreign market openness - average tariff reduction (across all French trade partners) representing a measure of higher market access for French firms. 3.2 Institutional Background It is important to discuss whether the features of the French institutional setting are a reasonable counterpart to the assumptions made in the theoretical framework. Our model assumes that wages are the outcome of a bargaining game between firms and workers. This condition is key to the empirical analysis in order for wage outcomes to reflect workers’ and firms’ characteristics. The question is whether the institutional restrictions leave enough room for wages to vary within firm and potentially within occupation. Since 1950, wage-setting institutions in France are organized according to a hierarchical principle. Wages are bargained at three different levels: (i) at the national level, a binding minimum wage (called Salaire Minimum Interprofessionnel de Croissance, SMIC) is set by the government;12 (ii) at the industry level, employers’ organizations and unions negotiate pay scales; wages are, then, negotiated occupation by occupation; and (iii) at the firm level, employers and unions usually negotiate wage increases. Typically, in the 1970s and 1980s collective agreements were negotiated within different sectors between unions and employer associations, then extended by the Ministry of Labor to the entire industry, becoming binding also for workers and firms not part of the original negotiation. At the end of the 1980s, more than 95% of the workforce was covered by those collective agreements. However, different laws have strengthened the decentralization of the wage bargaining process in France over the last 30 years. Three channels have been used to promote firm-level agreements: 12Until 2010, the SMIC was raised each year in July according to a legal formula based on partial indexation to past inflation and to past wage growth. 19

(i) the obligation for firms to negotiate wages each year, (ii) more possibilities offered to firms to deviate from industry-level agreements (escape clauses), and (iii) fiscal incentives.13 In 1982, the Auroux Law introduced the duty for firms with at least 50 employees and an elected union representative to negotiate wages with unions every year, although not the obligation to reach an agreement. Subsequent legislations concerning the working time reduction (Robien’s laws in 1996, the first Aubry’s law in 1998, the second Aubry’s law in 2000) allowed the application of escape clauses to working hours’ arrangements, reinforcing the trend toward decentralization. Escape clauses on pay were introduced in 2004; their use, however, has remained rather limited.14 Sincethe1980s,firm-levelnegotiationsacquiredprogressivelymoreimportance. TheICTWSS survey for France reports that bargaining predominantly15 alternates between sector and firm level since 1981. By 2005, 41% of the workers employed in private firms with more than 10 employees were covered by a wage agreement signed that very same year (Naboulet & Carlier, 2007).16 Firm-levelbargaining,however,doesnotguaranteethatworkersemployedatagivenfirmwithin the same occupation earn different wages. To provide evidence on worker-firm bargaining, we analyze the variability of wages across workers within firm-occupation cells in Figure A7. Figure A7 compares the overall (demeaned) wage distribution to the occupation-firm demeaned wage distribution. Although firm and occupation characteristics account for a large part of the overall wage variation, substantial variability in wages can stillbe observed across workers employed in the same occupation at the same firm. Table A4 precisely quantifies the importance of firm characteristics and worker observables in a wage variance decomposition. We start with a Mincerian specification of log wages on occupation dummies, gender, in-firm tenure, and a time-varying firm component; 13In2008,areductionofsocialsecuritycontributionspaidbyemployersbecameconditionaluponwagenegotiations occurring within the firm. 14Source: Institutional Characteristics of Trade Unions, Wage Setting, State Intervention and Social Pacts, 1960- 2011, (ICTWSS). 15A level is characterized as predominant if it accounts for at least 2/3 of the total bargaining coverage rate. 16In 1992, 40% of the workforce was covered by some firm-level agreement. Source: Abowd et al. (2012); authors’ calculation based on data from wage structure survey in 1992. 20

we use the Mincerian estimates to decompose the total wage variance into the contribution of worker observables, a between-firm component, the covariance between worker observables and the firm effect, and a within-firm component. The within-firm component accounts for a larger share of wage variation than what is jointly explained by firm and worker characteristics. In fact, the within-firm component explains 52% of the overall wage inequality in 1995; the percentage rises to 57.7% in 2007. This evidence corroborates the idea that the outcome of firm-level bargaining is not a common wage for all workers employed at a given firm within the same occupation, but rather than there is large scope for individual worker variation. 3.3 Constructing Worker Types We propose two strategies to construct worker type θ. The first strategy employs the average wage of the worker over the years in which she is present in our dataset. The second strategy adopts the methodology proposed by AKM of extracting the individual worker component from a wage regression. Worker Type Proxy: Average Lifetime Wage - θLW Our preferred methodology follows the model and uses the average wage of the worker over all her job spells - hereafter, average lifetime wage- to proxy for the worker type. In fact, according to the model, the average lifetime wage is monotonically related to the worker type θ: a more productive worker makes larger contributions to revenues and expects to match with a better firm in the frictionless equilibrium, obtaining, on average, a higher wage. From the model, the average lifetime wage of a worker of type θ, which we denote by θLW, takes the following expression: (cid:82)(θα+2 √ c)1/α(cid:104) θ2α + θαyα − y2α (cid:105) dy (θα−2 √ c)1/α 4 2 4 θLW = √ √ (8) (θα+2 c) 1/α −(θα−2 c) 1/α 21

InappendixsectionA.2, weformallyshowthattheaveragelifetimewageisincreasingintheworker type θ. However, for comparability with the earlier literature, we construct worker types employing a second strategy, the AKM methodology. Worker Type Proxy: Worker Fixed Effects - θAKM The AKM methodology aims at decomposing individual workers’ wages into a firm component and a worker component.17 The basic specification relates a measure of log compensation for worker i employed in firm j at time t to worker and firm effects: lnw = x(cid:48) β+θAKM +ψ +ε (9) it it i J(i,t) it where θAKM is worker i’s component and ψ is the firm component. The function J(i,t) = j i J(i,t) identifies the firm employing worker i at time t. The vector x includes time-varying worker it characteristics; therefore, the component θAKM captures persistent differences in compensation i explainedbyabilityandothertime-invariantworkercharacteristics. Weassumethattheerrorterm ε is i.i.d. across time and workers with mean zero. This assumption requires that employment it mobility is exogenous, depending only on observable characteristics, person, and firm effects. More precisely, the fixed effects estimator conditions on the whole sequence of establishments at which each worker is observed; this implies that the exogenous mobility assumption is not violated in the presence of systematic mobility patterns driven by the person effect θAKM and/or the sequence of i (cid:0) (cid:1) firm effects ψ ,ψ ,...,ψ . The assumption is, instead, violated if mobility depends, J(i,t) J(i,t+1) J(i,T) for example, on match-specific components of wages.18 Following Card et al. (2013), we perform a 17The AKM methodology has seen a very large number of applications, for example, Abowd et al. (2003), Abowd et al. (2005), Abowd et al. (2006), Abowd et al. (2007), Abowd et al. (2008), Abowd et al. (2009), Abowd et al. (2009), Carneiro et al. (2012), and Torres et al. (2013). 18The results estimated under the assumption that the error term ε includes a match effect η and an it iJ(i,t) idiosyncratictermasinCardetal.(2013)andWoodcock(2008)arequalitativelysimilartothoseinTables3and4. 22

diagnostic test on the interaction between wage changes and mobility patterns. Figure A8 reports wage changes associated with job transitions classified based on the quartile of the firm type proxied by the domestic market share - for the origin and destination workplace. We should expect littleornovariationinwagebeforethejobchangeifselectionortransitorywagecomponentsdonot affect mobility patterns. Workers moving from the fourth quartile do not experience a reduction in wages prior to their transition, while workers leaving firms in the lowest quartile of the firm productivity distribution seem to be influenced in their decision by transitory wage components. We believe that for those workers, selection might not exercise a strong influence as their wages after the transition appear to be of a similar level as before. As an additional indication against systematic mobility patterns, Table A6 documents the sign of wage changes for workers moving across jobs. In the presence of systematic mobility patterns, we should expect all wage changes to be positive; in our data, only half of the movers (around 52%) experience an increase in wages. WefollowAKMfortheexplicitspecificationof(9). Ourdependentvariableisthelogofannualized real wages.19 We include as time-varying controls a quartic in employer-specific experience,20 time-dummies, a dummy for workers residing in Ile-de-France, and time-varying gender effects (exactly, the interactions of sex with all the other variables). The panel version of DADS does not contain information on education. AKM obtain information on the highest degree attained from the permanent demographic sample (Echantillon D´emographique Permanent, EDP). However, this information would be available, in our case, only for about 20% of the workers in our sample. Thus, we decided not to include a control for schooling in our decomposition.21 19Working hours are often not reported. The restriction to full-time workers absorbs possible differences in hours worked across individuals. 20DADS contains information on the job starting date at a certain firm - we compute the employer-specific experience as a difference between the current year and the first year of employment at the firm. 21Inaddition,mostoftheeffectofschoolingwouldbeabsorbedbythepersoneffect. AKMmentionthatschooling does not time-vary over their sample. 23

As described in Abowd et al. (2002), fixed effects for workers and firms can be separately identified only for sets of firms and workers that are connected by moving workers. In fact, the person effect is common to all of the individual’s job spells; its identification requires observing the individual at different employers. Similarly, a firm effect is common to all employees of the firm; identifying the firm effect requires observations on multiple employees of the firm. Identifying both effects requires mobility of workers across firms.22 The movement of workers between firms characterizes a connected group. A connected group is defined by all workers who ever worked for any firm in the group and all firms whose workforce is included in the group. A second group is unconnected to the first if no firm in the first group has ever employed any worker from the second group and no firm in the second has ever employed workers from the first. Within each group, we normalize the mean of the fixed effects to zero; therefore, it is possible to identify all but one individual and one firm effects per group. Due to the normalization, comparing fixed effects between groups has no real meaning. Therefore, when comparing workers and firms, we only employ estimated fixed effects from the largest connected group, which represents 88% of the workers in our final sample. The estimation of the fixed effects is performed using the Gauss-Seidel algorithm, proposed by Guimaraes & Portugal (2010). This algorithm consists of solving the partitioned set of normal equations, associated to (9), starting with an initial guess on the coefficients. Workers’ and firms’ fixedeffectsarerecoveredascoefficientsonthedummyvariablesidentifyingtheworkerandthefirm at which the worker is employed. According to Smyth (1996), the Gauss-Seidel algorithm achieves a stable, but slow convergence, depending on the correlation between the parameter estimators. This implementation has the advantage of not requiring an explicit calculation of inverse matrices 22LetusconsiderasimpleexampleofhowtoimplementtheAKMmethodology. Consideraconnectedgroupwith 2firmsand Nworkersandsuppose thatatleastoneworker, individual1, isemployedinbothfirmsoverthesample period. The observed wage differential for individual 1 is entirely attributed to the difference between firms fixed effects. Normalizingthemeanfirmeffecttozero,itispossibletoidentifyoneofthefixedeffects. Asimilarargument applies to the identification of the person effect. 24

to determine the vector of coefficients; moreover, it does not force us to drop small firms due to the large number of firm effects to estimate.23 We recover estimates for the fixed effects for 406,404 individuals and 31,649 firms. In the appendix, we include the distribution of the worker fixed effects (Figure A5) and firm fixed effects (Figure A6) for the largest connected group. Average Worker Type and Variation of Worker Type at the Firm-Level With estimates of worker types at hand, we now proceed to construct measures of the average worker type and dispersion of worker type at firm j. Specifically, we construct the variables Av- WorkerType , SdWorkerType , and IQRWorkerType as jt jt jt 1 (cid:88) AvWorkerType = θˆ jt n i jt i∈Ijt (cid:118) 1 (cid:117)(cid:88) (cid:16) (cid:17)2 SdWorkerType = (cid:117) θˆ −AvWorkerType jt n (cid:116) i jt jt i∈Ijt IQRWorkerType = θˆj,75th−θˆj,25th jt where θˆdenotes our proxy for worker type, which is either θLW or θAKM, I is the set of workers jt employedbyfirmj attimet,w¯j,75th andw¯j,25th aretheworkertypesatthe75thand25thpercentile of firm j’s employee type distribution. We build these measures only for firms with more than 5 sampled workers. The choice of the threshold is a compromise between retaining a sample of satisfactory size and constructing sample measures that approximate the true underlying measures. On the one hand, a larger threshold forces us to cut a larger percentage of the sample. On the other hand, a larger number of sampled 23The number of firms’ fixed effect is too large for, e.g., the felsdv estimator. In such case, Andrews et al. (2006) suggest pooling small plants into a single superplant. However, we prefer not to implement a similar strategy, as, in our case, firms - not plants - are the units of observation. 25

workers reduces the noise in the estimation of a firm’s matching set. We consider each employment relation to be a realization of a match along the set of acceptable matches within a firm’s matching set. In the limit, increasing the number of match realizations, the constructed statistics of worker type converges to the true measure. Choosing a higher threshold does not affect the results. If including firms with fewer than 5 sampled workers, instead, the coefficients on our variables of interest are of the correct sign but in some specifications are not significant. In the appendix, we report the results from GLS regressions including all firms and weighting each observation by the number of workers; the GLS results are in line with those on the restricted sample of firms with more than 5 workers.24 3.4 Firm Types For the purpose of comparing matching choices of exporting and non-exporting firms, we need to control for the type of the firm. EK show that the relationship between true firm type and firm fixed effect estimated from a AKM-style wage regression is theoretically ambiguous – i.e., it can be positive, negative, or zero.25 EK also argue that the ideal firm component is a measure of firm type that is specific to every job within the firm, but measurable variables such as output and profits are obviously only observed at the aggregate firm level, not for each relationship within the firm. We thereforeadoptthreeproxiesforfirmtype: valueaddedperworkeroffirmj, VApw , thelogarithm j oftotalemploymentinfirmj, logEmp , andshareinthedomesticmarket, DomShare , definedas j j the ratio of firm j’s domestic sales to total domestic sales in the firm’s sector (each firm is classified as belonging to only one sector in each year).26 While the first two proxies are standard measures of the productivity or demand intensity for a firm product, the third is motivated by Eaton et al. 24See Tables A9-A12. 25Inarecentcontribution,Hagedornetal.(2014)showhowtocomplementwagedatawithlabormarkettransitions to identify the pattern of sorting. 26We consider sectors at the 4-digit level for the construction of market shares. 26

(2011). In particular, while the first two proxies contain a measure of success over all markets, including the foreign ones, the third variable better captures the success of the firm with respect to the domestic market before the choice of exporting. We average each proxy over the years the firm appears in the sample to smooth out the effect of changes in the workforce.27 We first confirm the hypothesis put forward by EK regarding the ability of the AKM firm fixed effects to capture the firm type. Table 1 shows the pairwise correlation between the AKM firm fixed effect, the three proxies for firm type, and the average worker type at firm j as measured by the average lifetime wage, Avg θLW, or by the average AKM worker fixed effect, Avg θAKM, over j j the sample period at firm j. The first striking fact is the negative and large correlation (−0.80) between average worker type and the AKM firm fixed effects ψ, confirming previous findings by Abowd et al. (2004). If instead we employ the three proxies for firm type, we observe for each of them a positive and significant correlation with either measure for the average worker type at the firm level. The three proxies for firm type are in turn all positively correlated with one another, but display small and sometimes opposite correlations with the AKM fixed effect ψ. In particular DomShare and VApw have a positive correlation of 0.01 and of 0.001 with ψ, respectively, while j j and logEmp displays a negative correlation of −0.01. j Table 2 shows that this correlation pattern is not unique to a few sectors. In column 4, we report the correlation between Avg θAKM and ψ by two-digit sector, while column 6 displays the j j analogous correlation between DomShare and Avg θLW. While the first set of correlations is j j always negative and significant, the second set of correlations is positive and significant, except in one case where the correlation is positive, but not significant. The evidence presented in Tables 1 27Ourmodelconfirmsthepositivecorrelationbetweenproductivity,valueaddedperworker,anddomesticmarket share. According to our theory, more productive firms tend to match with better workers, realizing, on average, larger revenues. Therefore, firms of higher productivity should display larger value added per worker and a larger share in the domestic market. The model is silent about employment differences due to variations in productivity, since we focus on one firm-one worker matching. If we introduce homogeneous labor in the production function, the model will also address the implication that more productive firms hire a larger workforce. 27

and 2 is consistent with the hypothesis put forward by EK that the AKM firm fixed effect may not be correlated with the true firm type, although it is still possible that, as in Abowd et al. (2004), there is truly negative assortative matching between workers and firms or that the negative result is purely due to the statistical bias arising from the short nature of the panel. 3.5 Empirical Specification 1: Export Status and Acceptance Set Wenowproceedtoillustratethespecificationsemployedtodescribethedifferentmatchingbehavior ofexportingandnon-exportingfirms. Thefirstimplicationofourmodelisthatexportingfirmshire workers of higher average type. This is a similar prediction to the models of Sampson (2014) and, under the interpretation of permanent worker heterogeneity, Helpman et al. (2010). We believe this is a novel method of corroborating such a prediction since it shows directly that an exporter pays higher wages because it employs better workers, not because it shares higher revenues with the same type of workers. The former is the mechanism involved in explaining the exporter wage premium in Helpman et al. (2010), but we believe it has not been tested before. In a pooled cross-section of firms over the sample period, the basic specification we employ is the following: AvWorkerType = β +β Export +β Firm Type +D +u (10) jt 0 1 jt 2 jt st jt where Export = 1 if firm j exports at time t and Firm Type is one or all of the three proxies for jt jt firm productivity, VApw , logEmp , and DomShare . j j j Differences in average worker type between exporters and non-exporters also reflect differences in the occupational structure. If, for example, exporters employ workers in occupations with higher average wage, they might also have higher average type, since the person effect contains all time- 28

invariant characteristics, like occupation, that rarely change over time for a given worker.28 We add the number of occupations, N.occ , and the share of white collar workers,29 whiteshare, to jt specification (10). Similarly, the number of exported products, log Products, which we include in the specification with all controls, is intended to capture structural differences in occupational complexity that might cause a spurious correlation of the exporting status with the average worker type. In addition, all specifications except the first include a quadratic in the number of sampled workers to control for the precision of our left-hand side estimates.30 Finally, all specifications include sector-year dummies, D . st The novel contribution of this paper is the prediction that exporters match with workers that are characterized by lower relative dispersion of ability. The specification that we employ is the following: SdWorkerType = β(cid:48) +β(cid:48)Export +β(cid:48)Firm Type +D +u(cid:48) . (11) jt 0 1 jt 2 jt st jt The theoretical section shows that the only robust prediction regarding the link between worker type dispersion and export status (and productivity) requires expressing such dispersion either in percentage terms or relative to the average worker type. In this regard, it is essential to remember thatthefixedeffectsareestimatedfromalog-linearizedequation, wheretypesarethereforealready expressed in percentage differences from one another. Nevertheless, we will add the average worker type in the specification with all controls.31 Similarlytospecification(10),weincludethenumberofoccupations,N.occ ,theshareofwhite jt 28Around 80% of the workers in the sample do not switch occupation during the time period analyzed. 29The blue vs white collar classification is based on occupational codes. We report the classification we adopt in Table A1. 30Inunreportedresults,wesimulatedthemodelandverifiedthatdifferencesinthenumberofobservationsavailable forexportersandnon-exportersdonotproducedifferentialbiasesthatcanjustifythequantitativeestimatesweobtain. Inotherwords,exportingfirmsdonothavealargeenoughnumberofobservationstomechanicallyinducedifferences in average worker type and standard deviation by the amount we observe. 31All results are very similar if we adopt the coefficient of variation of worker type as our dependent variable. 29

collar workers, white share, and the number of exported products, log Products, to control for differences in the occupational structure across firms with different export status. All specifications include sector-year dummies, D . st Ourspecificationsexploitthevariationwithinsectorsandacrossfirmswithdifferentexportstatus,conditionalonthefirmtypeandotherobservablecharacteristics. Althoughthetheorysuggests that the firms becoming exporters should also tend to select workers with lower ability dispersion, there is not enough variability in our sample to exclusively exploit this source of variation. Figure A9 shows the unconditional distribution of firms by number of years they operate in foreign markets. Around 13% of the total number of firms are exporting only one year; the percentage tends to decline if considering firms active abroad for a longer time span.32 Table A5 looks further into the variability of export status by number of years of activity abroad. The second column of Table A5 reports the average length of the non-exporting spells by category, while the last column shows the number of years a firm appears in the data. A firm that exports for 3 years, for example, tends to have a non-exporting spell of 1.4 years; however, those firms are present in the sample only for 4.89 years. Such a pattern, which is observed across all other categories, suggests that firms tend to switch their export status, on average, no more than once over the years they are in the sample. This is why we exploit the within-sector variability across exporting and non-exporting firms in our estimation. Both specifications (10) and (11) are estimated by OLS and standard errors are clustered at the level of the firm. We develop an alternative strategy to test the prediction that exporters select a set of workers characterized by a lower dispersion. We compare the rank correlation between the average worker type by firm and the firm type among exporters to the rank correlation between the average worker 32Theshareoffirmsraisesat13yearsduetothetruncationofourdata,asthecategoryoffirmsactivefor13years on the export market also includes firms that are active for a longer time period. 30

type and the firm types among non-exporters. In fact, the rank correlation captures the strength of sorting patterns. A lower dispersion among exporters implies better sorting and should be associated with a larger correlation. We construct the rank correlation separately for exporters and for non-exporters for each sector-year and we test the existence of systematic differences in the correlation by export status employing the following specification: Corr (cid:0) AvWorkerType ,DomShare (cid:1) = β(cid:48)(cid:48)+β(cid:48)(cid:48)Export +D +D +u(cid:48)(cid:48) (12) jt jt st 0 1 st s t st where Export = 1 if the correlation is constructed for the set of exporting firms in sector s st at time t. In addition to sector and time dummies, we also include the average (log) employment and the average domestic market share of firms in the same sector-year-export status cell because thosecharacteristicsmightdifferentiallyaffectthematchingpatternsandbecorrelatedwithexport status. Results The estimation results relative to specifications (10) and (11) are presented in Tables 3 and 4. Column 1 of Table 3 reports a positive and statistically significant relationship between export status and the average type of the worker employed by the firm (θLW). The positive relationship is of similar strength when we introduce, in turn, the three controls for firm type (domestic share, value added per worker, and employment). As predicted by the theory, the coefficient on all three proxies for firm type is positive and significant, like the one on export status. In the specification reported in column 4, we include the three controls for firm type in the same regression, and the coefficient on export (the one of our interest) remains positive and significant, like the ones on value added per worker and employment. Table 4 reports the results of the estimation of specification (11) and has a similar structure to 31

Table 3. Starting from column 1, where no controls are added, we document the expected negative andsignificantrelationshipbetweenexportstatusandvariabilityofworkertype. Theeffectpersists with a similar magnitude when we control for the above mentioned firm type controls (domestic share,employment,andvalueaddedperworker). Theinclusionofallthecontrolvariablesincolumn (6) does not alter the negative and significant coefficient on the export dummy. As predicted by the theory, the coefficient on two proxies for firm type is negative (columns 2 and 3); the table, however, also documents a positive and significant correlation between value added per worker and the dispersion of worker type (column 4 - 6), a pattern that is not in line with the predictions of the model. It is important to quantify the effect at the core of this paper. Based on our preferred specification in Table 4, column 6 where we include all controls, the expected difference on the dispersion of worker type between exporter and non-exporter firms is about 0.020 points (holding the other variables constant). Considering that the dependent variable has a standard deviation of 0.41, an exporter features worker variability that is lower by 4.9% standard deviations. The effect on the mean worker type can be calculated using the results from Table 3 and is of the same order of magnitude, but a little smaller: an exporting firm displays an average worker type that is 3% standard deviations higher.33 InTablesA7andA8, wereporttheresultsseparatelyforthesampleofnewlyhiredworkersand forthe stayers. Intuitively, theexportdummyisnegativeandsignificant onlywhenweconsiderthe newly hired sample, as documented in Table A7. This is a reasonable result given that firing costs and other labor market protection measures plausibly make the firing margin less flexible than the hiring one. Tables 5 and 6 report estimates for the same specifications as in Tables 3 and 4, but employ a 33ThismagnitudehasbeencomputedusingexportcoefficientofTable3,column6. Thestandarddeviationofthe average worker type is 0.81. 32

different proxy for the worker type, worker fixed effect from the AKM regression (θAKM). Table 5 reports again a positive relationship between export status and average worker type; the coefficient on export status remains positive but loses its significance when adding controls for firm type and theoccupationstructure. Table6confirmsanegativerelationshipbetweenthedispersionofworker type and export status. Controlling for the type of firm (by using employment, domestic market share, and value added per worker), the coefficient on export is negative and, once again, we find that firms with higher employment and higher domestic share have tighter worker type dispersion - coherently with the model. But, again, firms with high value added per worker have a wider variation. Endogeneity of Export Status We have not discussed so far the potential endogeneity of export status and the bias resulting from unobserved firm characteristics that may affect the export status and the standard deviation of worker types simultaneously. To address this concern, we develop an instrumental variable strategy. We instrument export status using a firm-level measure of tariff:   1 Firm Tariff jt = ln1+ (cid:80) Exports  (13) τ jr,t−1 sr srt Exports j,t−1 where τ is the tariff faced by firms in sector s exporting to country r at time t; we aggregate srt across countries using as weights the share of exports to country r of firm j over the total exports Exports of firm j at time t−1, jr,t−1. Then we take the inverse of the weighted average tariff faced Exports j,t−1 by firm j in order to have the instrumental variable positively correlated with the export status. In Table A15, we show the first stage regression results. The coefficient on the instrumental variable is positive and strongly significant in all specifications. The power of the instrument, expressed by the F-statistics of the first stage, is also shown in Table A15. Our F statistics are quite high, 33

well above 10, a value below which weak instrument concerns arise. The validity of our instrument relies on the orthogonality between the standard deviation of worker types (i.e., lifetime wages and AKM decomposition fixed effects) and the interaction between country-sector specific tariffs (τ ) srt Exports and the share of the firm’s exports to country r at time t−1, jr,t−1. Tariffs faced in export Exports j,t−1 markets are arguably orthogonal to firm specific composition of worker types. The firm’s export shares are also likely to be orthogonal to the worker composition of the firm since included at t−1. However, to strengthen the validity of our instrument, in equation (13) we use firm’s export share Exports also at t−3, jr,t−3 (see columns 4-6 in Tables 7 and 8). Exports j,t−3 Tables7and8reportthesecondstageresults. Thecoefficientonexportstatusremainspositive in Table 7, negative and significant in all specifications of Table 8 - independently of the number of (year) lags we use in building the instrument. In particular, the OLS regression estimates of β 1 seem to be biased towards zero; this is consistent with the idea that more productive firms possess a better technology to search for their workers. Commenting on the magnitudes, exporting firms tend to select a workforce that is 38.5% of a standard deviation (sd) less dispersed and has higher ability by 28.3% of a sd compared to a non-exporting firm Additional Robustness Table 9 presents the results for specification (11) with an alternative measure of dispersion, a weighted average of the standard deviation of ability among different groups of workers. In particular,wedivideoccupationsintomanagers,executives (whitecollaroccupations),andblue collar (as reported in Table A1) and we construct average employment shares for those occupational groups within the firm over time. We then weigh the standard deviation of lifetime wages for each group by its average employment share to construct our new dependent variable. The coefficient on the export dummy remains negative and significant in all specifications; in most columns, the magni- 34

tude of the coefficient is not significantly different from what is reported in Table 4. This suggests that our result is not due to compositional differences between exporters and non-exporters. Looking at the coefficients on firm-type controls (columns 2, 3, and 4 in Table 9) we discover thatemploymentanddomesticmarketsharehavetheexpectedsign, i.e. theyarenegativelyrelated with the standard deviation of worker types. The coefficient on value added per worker is positive and significant only in column 6, suggesting that the “puzzling” effect discussed above for Tables 4 and 6 might be related to changes in employment composition over time. Table 10 presents a further robustness of the result to the definition of worker type employed as dependent variable. In particular, we employ the interquartile range of worker type at firm j, as described earlier. It is easy to verify that all previously described patterns appear again in this table. Exporting firms choose a narrower range of worker types. Finally, Tables A13 and A14 confirm that differences in dispersions translate into higher rank correlation between average worker types and firm types for exporters compared to non-exporters, controlling for average size differences. Firm and worker types are more tightly correlated among exporters than non-exporters. 3.6 Empirical Specification 2: Market Access and Tariff Shocks Our first empirical strategy has relied on cross-sectional differences between exporting and nonexporting firms. Plausibly, the export dummy may be capturing the effect of other firms characteristics that are not included in our firm type proxies and that affect the matching behavior of firms. Our second strategy to detect the impact of exporting on matching between firms and workers aims at addressing this concern. We exploit differences in the opportunities offered by foreign markets, approximated by demand shocks and tariffs across sectors and countries over time. These 35

different shocks, which we indicate as market access, should affect exporting firms differentially from non-exporting firms. A positive demand shock in a foreign market or a lower tariff faced by French exporters should induce the exporting firm to select an even less dispersed labor force. The specification that we estimate is the following: AvWorkerType = γ +γ Mkt Access ×Export +γ Mkt Access jt 0 1 st jt 2 st +γ Export +D +v , (14) 3 jt st jt SdWorkerType = γ(cid:48) +γ(cid:48)Mkt Access ×Export +γ(cid:48)Mkt Access jt 0 1 st jt 2 st +γ(cid:48)Export +D +v(cid:48) (15) 3 jt st jt where (cid:88) French exports sr,t−1 MktAccess = MktAccess × , (16) st srt French exports s,t−1 r    Tariffs or   srt    MktAccess srt = Imports or , srt        Imports srt Tariffs srt Imports is the total value of imports by country r from the rest of the world,34Tariffs is the srt srt tariff faced by a French firm exporting to country r in sector s at time t, and French exports sr,t−1 is the value of exports from France to country r in sector s at time t−1 (with total exports in the sector in that year indicated as French exports ). The variable MktAccess measures cost of s,t−1 st accessordemandsizeinforeignmarketsforfirmsinagivensectors, weightedbytheimportanceof Frenchfirmsinthatsectorinthepreviousyear. Themodelpredictsthatagoodexportopportunity should result in an increase in the average worker type and a further tightening of the acceptance 34The inclusion of French exports to country r does not affect the results. 36

set for an exporting firm, so we expect γ < 0 and γ(cid:48) > 0 for the case of MktAccess =Tariffs 1 1 srt srt Imports and the opposite when market access is measured as Imports or srt. srt Tariffs srt 3.6.1 Results Tables 11 and 12 report estimates of the coefficients in specifications (14) and (15) when market accessforafirminsectorsismeasuredbytotaldemandforimportsfacedbyanexporterinsectors as in equation (16). We do not present results for the case in which total import demand is deflated by the tariff faced by French exporters because they are very similar. Table 11 reports results on the average worker type; our coefficient of interest is positive and significant on all specifications. However, if evaluated at the mean of the market access measured by Imports , an exporter does srt not feature a higher average worker ability; only exporters in sectors with a degree of openness larger than the average will enjoy an effect on the average worker type. In Table 12, we find that the estimated coefficient γ(cid:48) is negative and significant in all speci- 1 fications, so that exporters seem to choose a less dispersed workforce in particular when having better access to foreign markets. The inclusion of firm type controls does not affect the magnitude and significance of this result. The coefficient on export status is negative and significant in all specifications. If evaluated at the mean of the market access measured by Imports , an exporter srt features worker variability that is lower by 3.4% of a sd than a non-exporter (which is in line with our previous quantifications). Tables 13 and 14 report estimates of the coefficients from specifications (14) and (15) when market access for a firm in sector s is measured by the average tariff faced by exporters in sector s. Only columns 4-6 of Table 13 report a negative coefficient γ - which is line with the prediction 1 - but not statistically significant. Table 14 reports very similar results to Table 12: better export market conditions as measured 37

by a lower tariff faced on the export market result in a tighter matching set for exporting firms. So, contrary to Table 13, the effect of export opportunities on the standard deviation of worker type seems more robust to the definition of market access. In particular, firms exporting in countrysector with mean market access (mean value equal to 5.58 in our sample) have a lower worker variability than non-exporters (13.7% standard deviation units), with such a gap increasing with the market access of the firm. We apply the IV strategy also to specifications (14) and (15). We predict export status using past export shares and country-sector specific tariffs; we interact our predicted variables with our two measures of market access (see the endogeneity section above for a more detailed discussion). Results of the IV strategy are reported in Tables A16-A19. The first 2 columns show the results of the IV strategy that uses the previous year export share, while columns (3)-(4) strengthen the validity of our instruments relying on t−3 firm-level export shares. Our results look robust when usingdemandshocksinforeignmarketstoproxyforthedegreeofopenness: theinteractionbetween export status and our proxy for market access is positive in Table A16 and negative in Table A17; the coefficients tend to lose their significance when adding more controls. Less robust are instead theresultsthatusetariffsasameasureofmarketaccess: thecoefficientsonourvariablesofinterests suggest that there does not seem to be a magnifying effect across exporters vs. non-exporters in more open sectors in addition to the difference accounted for by export status (Tables A18 and A19). 4 Implications for Matching Efficiency We have so far not discussed any welfare implications of the mechanism explored in this paper. Our model predicts that exporting firms tolerate less relative dispersion in worker type, but it does not analyze whether exporting and non-exporting firms’ choices result in a matching outcome that 38

is closer to the optimal one. In what follows, we propose revenue loss relative to the frictionless allocation as a measure of matching inefficiency and confirm that the revenue loss is lower for exporting and more productive firms. 4.1 Revenue Loss WechooseameasureofrevenuelossrelativetotheoptimalallocationasinEK.Foreachfirmϕand worker θ, we can construct a revenue loss relative to the optimum, which we also define L(ϕ,θ) = 1 (θα−ϕα)2. Theassumptionincreatingsuchameasureisthatintheoptimalallocation, aworker 2 of type θ would generate a revenue of θ2α and is allocated half of that revenue. Holding the type of the firm constant at ϕ, we sum the revenue loss, relative to the optimal level, for each possible worker type in the acceptance set. We then divide by the optimal revenue summed across the same range. We obtain the share of revenues lost relative to the optimum for a firm of type ϕ (and the workers in that firm’s acceptance range), which we define as RL(ϕ): (cid:82)u(ϕ) 1 (θα−ϕα)2dθ l(ϕ) 2 RL(ϕ) = (17) (cid:82)u(ϕ)(cid:2)1θ2α+ 1ϕ2α(cid:3) dθ l(ϕ) 2 2 The following proposition shows that such deviations from the optimal revenues are smaller for more productive firms. Proposition 2 The share of output lost relative to the optimal revenues, RL(ϕ), is decreasing in the type of the firm ϕ: 1. For any α, as c → 0, 2. For any c if α = 1 or α = 2 or α = 1. 2 Proof. See Appendix A.3. 39

Moreover, we have verified that this result holds for a very wide range of parameters. We have not been able to find instances in which proposition 2 does not hold, although a general proof is arduous due to many non-integer exponents in the expressions involved. This proposition is a comparison across firm types observed in a given equilibrium, so that, for example, we can use this proposition to compare revenue losses of an import-competing firm versus an exporting firm of the same original underlying productivity. The exporting firm will feature across all the possible matches in her matching set a lower share of revenue lost because of mismatch. This is a partial equilibrium result that we cannot employ to evaluate the overall welfare impact of trade opening because the two equilibria will feature different type distributions and therefore different shapes of the matching sets. In particular, if we want to compare autarky and trade equilibria, we can no longer assume that the distribution of types is uniform. If we start with a uniform distribution for firms and workers, only the distribution of worker types will remain unchanged, while the distribution of firms will be affected by the endogenous shock to revenues given by export opportunities andimportcompetition. Oncewemoveawayfromauniformdistributionandthetwodistributions of workers and firms are no longer symmetric, the analytical characterization becomes intractable. Tito (2015) builds a general equilibrium model where she introduces a second symmetric country and computes overall welfare changes. She finds that moving to autarky increases output losses, suggesting that the mechanism explored in this paper, exposure to exports, is a novel source of gains from trade, bringing the economy closer to the efficient allocation of workers to firms. 5 Conclusions Usinglinkedemployer-employeedatafromFrance,weshowthatexportersandnon-exportersmatch with sets of workers that are different. Exporters employ workers of higher average type and lower type dispersion. We rationalize this finding using a model of matching with search frictions in 40

which more productive firms and exporting firms match with better workers and tolerate a lower degree of dispersion among the workers employed. Inthispaper,wehavenotfullydiscussedtheconsequencesofourresultsintermsofwelfare. We showthattherevenuelossesofanexportingfirmaresmallerthanthelossesofanimport-competing firm of the same original underlying productivity. However, this is only a partial equilibrium result. In fact, the model features two counteracting effects. While newly exporting firms have higher incentives to tighten their matching range, non-exporting firms see their revenues decline because of import competition and therefore will see an increase in their normalized matching range. Hence the model is currently in a very simple partial equilibrium setup, which cannot be used for welfare analysis. We leave this interesting, but non-trivial, evaluation of welfare effects to future research. 41

References Abowd, J., Haltiwanger, J., & Lane, J. (2009). Wage structure and labor mobility in the united states. In The Structure of Wages: An International Comparison (pp. pp. 81–100). University of Chicago Press. Abowd, J., Kramarz, F., Lengermann, P., & P´erez-Duarte, S. (2004). Are good workers employed by good firms? a test of a simple assortative matching model for france and the united states. Unpublished Manuscript. Abowd, J. M., Creecy, R. H., & Kramarz, F. (2002). Computing person and firm effects using linked longitudinal employer-employee data. Technical report, Center for Economic Studies, US Census Bureau. Abowd, J. M., Haltiwanger, J., Lane, J., McKinney, K. L., & Sandusky, K. (2007). Technology and the demand for skill: An analysis of within and between firm differences. Technical report, National Bureau of Economic Research. Abowd, J.M., Kramarz, F., Lengermann, P., McKinney, K.L., &Roux, S.(2012). Persistentinterindustry wage differences: rent sharing and opportunity costs. IZA Journal of Labor Economics, 1(1), 1–25. Abowd, J. M., Kramarz, F., Lengermann, P., & P´erez-Duarte, S. (2003). Sorting workers between and within industries. Technical report, mimeo, February 2003, available at http://cep. lse. ac. uk/seminarpapers/28-02-03-KRA1. pdf. Abowd, J. M., Kramarz, F., & Margolis, D. N. (1999). High wage workers and high wage firms. Econometrica, 67(2), pp. 251–333. 42

Abowd, J.M., Kramarz, F., &Roux, S.(2005). Wages, mobilityandfirmperformance: Ananalysis using matched employee and employer data from france. Economic Journal. Abowd,J.M.,Kramarz,F.,&Roux,S.(2006). Wages,mobilityandfirmperformance: Advantages andinsightsfromusingmatchedworker–firmdata*. The Economic Journal,116(512),pp.F245– F285. Abowd, J. M., Kramarz, F., & Woodcock, S. (2008). Econometric analyses of linked employer– employee data. In The Econometrics of Panel Data (pp. pp. 727–760). Springer. Abowd, J. M., McKinney, K. L., & Vilhuber, L. (2009). The link between human capital, mass layoffs, and firm deaths. In Producer Dynamics: New Evidence from Micro data (pp. pp. 447– 472). University of Chicago Press. Amiti, M. & Cameron, L. (2012). Trade liberalization and the wage skill premium: Evidence from indonesia. Journal of International Economics, 87(2), pp. 277–287. Andrews, M., Schank, T., & Upward, R. (2006). Practical fixed-effects estimation methods for the three-way error-components model. Stata Journal, 6(4), 461. Atakan, A. E. (2006). Assortative matching with explicit search costs. Econometrica, 74(3), pp. 667–680. Becker, G. S. (1973). A theory of marriage: Part i. The Journal of Political Economy, pp. 813–846. Bernard, A., Eaton, J., Jensen, J., & Kortum, S. (2003). Plants and productivity in international trade. The American Economic Review, 93(4), pp. 1268–1290. Bustos, P. (2012). The impact of trade liberalization on skill upgrading evidence from argentina. Unpublished manuscript. 43

Card, D., Heining, J., & Kline, P. (2013). Workplace heterogeneity and the rise of west german wage inequality*. The Quarterly Journal of Economics, 128(3), pp. 967–1015. Carneiro, A., Guimar˜aes, P., & Portugal, P. (2012). Real wages and the business cycle: Accounting for worker, firm, and job title heterogeneity. American Economic Journal: Macroeconomics, 4(2), pp. 133–152. Costinot, A. & Vogel, J. E. (2010). Matching and inequality in the world economy. Journal of Political Economy, 118(4), pp. 747–786. Davidson, C., Heyman, F., Matusz, S., Sj¨oholm, F., & Zhu, S. C. (2014). Globalization and imperfect labor market sorting. Journal of International Economics, 94(2), pp. 177–194. Davidson, C., Matusz, S. J., & Shevchenko, A. (2008). Globalization and firm level adjustment with imperfect labor markets. Journal of International Economics, 75(2), pp. 295–309. Davidson,C.&Sly,N.(2012). Tradeandthelabormarket: Recentdevelopmentsandnewfrontiers. In M. Kreinin & M. G. Plummer (Eds.), Oxford Handbook on International Commercial Policy. Oxford University Press. Eaton, J., Kortum, S., & Kramarz, F. (2011). An anatomy of international trade: Evidence from french firms. Econometrica, 79(5), pp. 1453–1498. Eeckhout, J. & Kircher, P. (2011). Identifying sortingin theory. The Review of Economic Studies, 78(3), pp. 872–906. Feenstra, R. C. & Hanson, G. H. (1999). The impact of outsourcing and high-technology capital on wages: estimates for the united states, 1979–1990. The Quarterly Journal of Economics, 114(3), pp. 907–940. 44

Fr´ıas, J. A., Kaplan, D. S., & Verhoogen, E. (2012). Exports and within-plant wage distributions: Evidence from mexico. The American Economic Review, 102(3), pp. 435–440. Guimaraes, P. & Portugal, P. (2010). A simple feasible procedure to fit models with highdimensional fixed effects. Stata Journal, 10(4). Hagedorn, M., Law, T. H., & Manovskii, I. (2014). Identifying equilibrium models of labor market sorting. Technical Report 896. Helpman, E., Itskhoki, O., Muendler, M.-A., & Redding, S. (2015). Trade and inequality: From theory to estimation. Helpman,E.,Itskhoki,O.,&Redding,S.(2010). Inequalityandunemploymentinaglobaleconomy. Econometrica, 78(4), pp. 1239–1283. Kremer, M. & Maskin, E. (1996). Wage inequality and segregation by skill. National Bureau of Economic Research. Krishna, P., Poole, J. P., & Senses, M. Z. (2014). Wage effects of trade reform with endogenous worker mobility. Journal of International Economics, 93(2), pp. 239–252. Krugman, P. R. (1979). Increasing returns, monopolistic competition, and international trade. Journal of international Economics, 9(4), pp. 469–479. Melitz, M. J. (2003). The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica, 71(6), pp. 1695–1725. Naboulet, A. & Carlier, A. (2007). principal: N´egociations collectives et gr`eves dans le secteur marchand: en 2005, la moiti´e des entreprises dau moins 50 salari´es a n´egoci´e. 45

Sampson, T. (2014). Selection into trade and wage inequality. American Economic Journal: Microeconomics, 6(3), pp. 157–202. Shapley, L. S. & Shubik, M. (1971). The assignment game i: The core. International Journal of Game Theory, 1(1), pp. 111–130. Shimer,R.&Smith,L.(2000). Assortativematchingandsearch. Econometrica,68(2),pp.343–369. Smyth, G. K. (1996). Partitioned algorithms for maximum likelihood and other non-linear estimation. Statistics and Computing, 6(3), 201–216. Tito, M. D. (2015). Worker-Firm Matching in a Global Economy. PhD thesis. Torres, S., Portugal, P., Addison, J. T., & Guimar˜aes, P. (2013). The sources of wage variation: a three-way high-dimensional fixed effects model. Verhoogen, E. A. (2008). Trade, quality upgrading, and wage inequality in the mexican manufacturing sector. The Quarterly Journal of Economics, 123(2), pp. 489–530. Woodcock, S. D. (2008). Wage differentials in the presence of unobserved worker, firm, and match heterogeneity. Labour Economics, 15(4), 771–793. 46

Table 1: Rank Correlation Matrix, Proxies for Firms’ Types ψ AvgθAKM AvgθLW Dom Share VA pw Empl j j ψ 1 AvgθAKM -0.80 1 j AvgθLW 0.13 0.35 1 j Dom Share 0.01 0.08 0.20 1 VA per worker 0.001 0.05 0.13 0.64 1 Empl -0.01 0.06 0.12 0.78 0.72 1 ψ: Firms’ fixed effects, from the AKM decomposition. AvgθLW: average of the workers’ lifetime wages at firm j. j AvgθAKM: Averageofworkers’fixedeffectsbyfirm, fromtheAKMdecomposition, atfirmj j VA per worker: Average value added per worker, normalized by 4-digit industries. Dom Share: Average domestic market share at a 4-digit level. Empl: Average employment, normalized by 4-digit industries. Notes: Rank correlation between proxies of firm types. We do not report the p-values but all rank correlations are significantly different from zero. 47

Table 2: Measuring Sorting Patterns, Manufacturing Sectors (4) (5) (6) (7) ψ, Avg.Share, AvgθAKM AvgθLW j j NAF Industry Label No Firms ρ 1 p-val2 ρ 1 p-val2 S S 10 Food 9 -0.96 0.00 - - 11 Beverage 8 -1 - - - 12 Tobacco prods - - - - - 13 Textiles - - - - - 14 Clothing 270 -0.84 0.00 0.18 0.00 15 Leather/shoes - - - - - 17 Paper 1317 -0.85 0.00 0.14 0.00 18 Printing 1286 -0.86 0.00 0.14 0.00 19 Refining 402 -0.88 0.00 0.42 0.00 20 Chemical 666 -0.86 0.00 0.17 0.00 21 Pharma 780 -0.79 0.00 0.30 0.01 22 Plastics 2070 -0.76 0.00 0.13 0.00 23 Non-metallic prods 59 -0.64 0.00 0.13 0.33 24 Metalworking 1565 -0.72 0.00 0.33 0.00 25 Metal prods 1987 -0.83 0.00 0.25 0.00 26 Info/elec/opt 947 -0.82 0.00 0.27 0.00 27 Elec equip 595 -0.84 0.00 0.14 0.00 28 Machinery 5433 -0.81 0.00 0.21 0.00 29 Automotive 2898 -0.82 0.00 0.28 0.00 30 Other trans equip 126 -0.74 0.00 0.16 0.07 31 Furniture 969 -0.81 0.00 0.25 0.00 32 Other mfg 878 -0.71 0.00 0.13 0.00 33 Repairs 1197 -0.79 0.00 0.23 0.00 Manufacturing 23388 -0.80 0.00 0.20 0.00 1Spearman correlation coefficient. 2p-value from testing independence between the variables. Notes: Columns(4)-(5): Rankcorrelationandsignificancelevelbetweentheaverageworkertype,(AvgθAKM),andthefirmfixedeffect(ψ)fromanAKMdecomposition including a quartic polynomial in experience, a dummy for workers residing in Ile-de-France, time dummies and all the interactions with the gender dummy. Columns (6)-(7): Rank correlation and significance level between the average lifetime wage of workers, (AvgθLW), and the firm type, proxied by the average domestic market share in 4-digit sectors Avg.Share. 48

Table 3: Pooled Cross-Section Regressions: Average Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Export 0.142a 0.058a 0.060a 0.075a 0.036a 0.025c (0.012) (0.012) (0.012) (0.011) (0.011) (0.013) N.Occ 0.017a 0.033a 0.034a 0.013a -0.002 (0.002) (0.002) (0.002) (0.002) (0.002) logempl 0.114a 0.113a 0.118a (0.006) (0.006) (0.006) logdom.share 0.025a 0.004b 0.0033c (0.002) (0.002) (0.002) logVA per worker 0.166a 0.165a 0.105a (0.008) (0.008) (0.008) white share 0.526a (0.019) logN. Products 0.006c (0.003) Sector-Year y y y y y y Obs. 57,469 57,469 57,469 57,469 57,469 57,469 R2 0.136 0.201 0.188 0.213 0.236 0.301 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-Sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 49

Table 4: Pooled Cross-Section Regressions: Standard Deviation of Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Export -0.035a -0.017c -0.037a -0.052a -0.020b -0.020b (0.010) (0.010) (0.010) (0.010) (0.010) (0.009) N.Occ 0.031a 0.013a 0.010a 0.030a 0.025a (0.002) (0.002) (0.001) (0.002) (0.001) logempl -0.107a -0.108a -0.022a (0.005) (0.005) (0.004) logdom.share -0.008a 0.001 0.002 (0.002) (0.002) (0.001) logVA per worker 0.045a 0.043a 0.108a (0.006) (0.006) (0.005) white share 0.482a (0.013) logN. Products 0.013a (0.002) Avg Lifetime Wage -0.730a (0.009) Sector-Year y y y y y y Obs. 57,469 57,469 57,469 57,469 57,469 57,469 R2 0.062 0.089 0.067 0.068 0.092 0.542 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-SectionalRegressionsforfirmswithmorethan5workers,years1995- 2007. Different specifications in the columns. Standard errors, clustered at the levelofthefirm,arereportedinparentheses. Allspecificationsbutthefirstinclude a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 50

Table 5: Pooled Cross-sectional Regressions: Average Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: AKM worker fixed effect θAKM Export 0.079a 0.030 0.036 0.039 0.025 0.013 (0.027) (0.028) (0.028) (0.027) (0.028) (0.031) N.Occ. 0.014a 0.022a 0.022a 0.012a 0.001 (0.004) (0.004) (0.004) (0.004) (0.004) logempl 0.053a 0.055a 0.059a (0.013) (0.014) (0.014) logdom.share 0.007c -0.002 -0.003 (0.004) (0.004) (0.005) logVA per worker 0.060a 0.062a 0.014 (0.014) (0.015) (0.015) white share 0.421a (0.036) logN. Products 0.007 (0.009) Sector-Year y y y y y y Obs. 54,633 54,633 54,633 54,633 54,633 54,633 R2 0.020 0.027 0.026 0.027 0.028 0.040 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first includeaquadraticinthenumberofsampledworkerstocontrolfortheprecision of the left-hand side variable. 51

Table 6: Pooled Cross-sectional Regressions: Standard Deviation of Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: AKM worker fixed effect θAKM Export -0.036a -0.020c -0.039a -0.052a -0.029b -0.042a (0.011) (0.011) (0.011) (0.011) (0.011) (0.013) N.Occ. 0.029a 0.013a 0.010a 0.028a 0.025a (0.002) (0.001) (0.001) (0.002) (0.002) logempl -0.096a -0.096a -0.092a (0.005) (0.006) (0.006) logdom.share -0.007a 0.0004 -0.001 (0.002) (0.002) (0.002) logVA per worker 0.036a 0.035a 0.024a (0.007) (0.007) (0.007) white share 0.130a (0.016) logN. Products 0.010a (0.003) Avg Worker Type -0.086a (0.005) Sector-Year y y y y y y Obs. 54,633 54,633 54,633 54,633 54,633 54,633 R2 0.065 0.087 0.069 0.070 0.088 0.120 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. Avg Worker Type: average worker fixed effect, estimated by the AKM decomposition, by firm. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectionalRegressionsforfirmswithmorethan5workers,years1995- 2007. Differentspecificationsinthecolumns. Standarderrors,clusteredatthelevel of the firm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 52

Table 7: IV Regressions: Average Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Worker Type: Average Lifetime Wage θLW Variables Exp Share Exp Share t−1 t−3 Export 0.195a 0.047 0.146b 0.229a 0.059b 0.229a (0.027) (0.030) (0.065) (0.026) (0.030) (0.073) N.Occ. 0.007b -0.002 0.007b -0.002 (0.003) (0.003) (0.004) (0.004) logempl 0.137a 0.140a 0.139a 0.144a (0.011) (0.010) (0.012) (0.011) logdom.shared 0.006 0.005 0.006 0.004 (0.004) (0.003) (0.004) (0.004) logVA per worker 0.185a 0.117a 0.188a 0.123a (0.013) (0.013) (0.014) (0.014) white share 0.566a 0.571a (0.030) (0.031) logN. Products -0.033b -0.051a (0.016) (0.018) Sector-Year y y y y y y Obs. 16,072 16,072 16,072 13,217 13,217 13,217 R2 0.183 0.286 0.354 0.186 0.286 0.351 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. a significant at 1%, b significant at 5%, c significant at 10%. Notes: IV Regressions for firms with more than 5 workers, years 1995- 2007. Export status is instrumented using tariffs and the previous year export share in columns (1)-(3); columns (4)-(6) use the t−3 export share. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 53

Table 8: IV Regressions: Standard Deviation of Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Worker Type: Average Lifetime Wage θLW Variables Exp Share Exp Share t−1 t−3 Export -0.075a -0.081a -0.153a -0.085a -0.093a -0.158a (0.019) (0.029) (0.035) (0.023) (0.027) (0.058) N.Occ. 0.013a 0.027a 0.029a 0.022a (0.002) (0.003) (0.003) (0.002) logempl -0.093a -0.013a -0.101a -0.014c (0.009) (0.005) (0.011) (0.008) logdom.share 0.009a 0.010a 0.010a 0.010a (0.001) (0.001) (0.003) (0.002) logVA per worker 0.031a 0.101a 0.022b 0.096a (0.010) (0.005) (0.0105) (0.009) white share 0.465a 0.450a (0.015) (0.021) logN. Products 0.045a 0.045a (0.015) (0.014) Avg. Lifetime Wage -0.733a -0.726a (0.012) (0.015) Sector-Year y y y y y y Obs. 16,072 16,072 16,072 13,217 13,217 13,217 R2 0.058 0.064 0.544 0.055 0.079 0.54 Export: dummy=1 if firm exports. N.Occ.: numberofoccupations,basedon2-digitoccupationalcodesforFrance. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. a significant at 1%, b significant at 5%, c significant at 10%. Notes: IV Regressions for firms with more than 5 workers, years 1995-2007. Export status is instrumented using tariffs and the previous year export share incolumns(1)-(3); columns(4)-(6)usethet−3exportshare. Standarderrors, clusteredatthelevelofthefirm,arereportedinparentheses. Allspecifications but the first include a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 54

Table 9: Group-Weighted Regressions: Standard Deviation, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Export -0.012b -0.023a -0.026a -0.030a -0.022a -0.031a (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) N.Occ. 0.016a 0.012a 0.011a 0.016a 0.017a (0.001) (0.000) (0.000) (0.001) (0.001) logempl -0.023a -0.022a 0.025a (0.003) (0.003) (0.003) logdom.share -0.003a -0.000 -0.001 (0.000) (0.001) (0.001) logVA per worker -0.002 -0.001 0.117a (0.003) (0.003) (0.003) white share -0.150a (0.008) logN. Products 0.003c (0.002) Avg. Lifetime Wage 0.011a (0.001) Sector-Year y y y y y y Obs. 54,436 54,436 54,436 54,436 54,436 54,436 R2 0.037 0.072 0.069 0.068 0.072 0.108 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Group-weightedRegressionsforfirmswithmorethan5workers,years1995- 2007. The dependent variable is a weighted average of the standard deviations for managers,executives,andbluecollarworkers,usingasweightstheaverageemployment compositions of those groups within firm over time. Different specifications in the columns. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 55

Table 10: Pooled Cross-sectional Regressions: Inter-quartile Range, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Export -0.083a -0.010 -0.049a -0.073a -0.021 -0.024b (0.015) (0.015) (0.015) (0.015) (0.015) (0.012) N.Occ. 0.019a -0.012a -0.016a 0.016a 0.005a (0.002) (0.002) (0.002) (0.002) (0.002) logempl -0.178a -0.179a -0.068a (0.007) (0.007) (0.006) logdom.share -0.011a 0.003 0.004a (0.002) (0.002) (0.002) logVA per worker 0.084a 0.079a 0.142a (0.010) (0.010) (0.007) white share 0.789a (0.019) logN. Products 0.019a (0.003) Avg. Lifetime Wage -0.930a (0.016) Sector-Year y y y y y y Obs. 57,469 57,469 57,469 57,469 57,469 57,469 R2 0.056 0.094 0.062 0.066 0.099 0.493 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995- 2007. Different specifications in the columns. Standard errors, clustered at the levelofthefirm, arereportedinparentheses. Allspecificationsbutthefirstinclude a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 56

Table 11: Market Access Regressions: Average Worke Type, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Market Access*Export 0.014a 0.012a 0.011a 0.012a 0.013a 0.013a (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) Market Access -0.016a -0.014a -0.013a -0.012a -0.015a -0.018a (0.004) (0.004) (0.003) (0.004) (0.004) (0.003) Export -0.052 -0.078 -0.106b -0.114b -0.108b -0.168a (0.051) (0.050) (0.047) (0.050) (0.050) (0.050) N.Occ. 0.039a 0.015a 0.032a 0.035a -0.002 (0.002) (0.002) (0.001) (0.001) (0.001) logempl 0.125a 0.125a (0.005) (0.005) logdom.share 0.031a 0.004b (0.002) (0.002) logVA per worker 0.158a 0.096a (0.008) (0.006) white share 0.500a (0.024) logN. Products 0.008b (0.003) Sector1-Year y y y y y y Observations 44,728 44,728 44,728 44,728 44,728 44,728 R-squared 0.142 0.184 0.209 0.196 0.215 0.299 12-digit sector dummies. Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. Market Access: weighted-average - across destinations - of the demand faced by a given industry i (4 digit sector) at time t, where the weights are the share of world exports to that particular destination in that industry the previous year. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995- 2007. Differentspecificationsinthecolumns. Standarderrors,clusteredatthelevelof thefirm,arereportedinparentheses. Allspecificationsbutthefirstincludeaquadratic in the number of sampled workers to control for the precision of the left-hand side variable. 57

Table 12: Market Access Regressions: Standard Deviation of Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Market Access*Export -0.009a -0.009a -0.009a -0.009a -0.009a -0.009a (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) Market Access 0.011a 0.012a 0.011a 0.011a 0.012a 0.011a (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) Export 0.096b 0.089c 0.113b 0.096b 0.080c 0.094b (0.048) (0.047) (0.046) (0.048) (0.046) (0.041) N.Occ. 0.011a 0.031a 0.012a 0.010a 0.026a (0.001) (0.001) (0.001) (0.001) (0.001) logempl -0.107a -0.105a (0.004) (0.004) logdom.share -0.006a 0.002 (0.002) (0.002) logVA per worker 0.050a 0.033a (0.006) (0.005) white share 0.158a (0.018) Avg Lifetime Wage -0.104a (0.004) logN. Products 0.009a (0.003) Sector1-Year y y y y y y Obs. 44,728 44,728 44,728 44,728 44,728 44,552 R2 0.068 0.071 0.094 0.072 0.075 0.143 12-digit sector dummies. Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. Market Access: weighted-average - across destinations - of the demand faced by a given industry i (4 digit sector) at time t, where the weights are the share of world exports to that particular destination in that industry the previous year. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995- 2007. Differentspecificationsinthecolumns. Standarderrors,clusteredatthelevelof thefirm,arereportedinparentheses. Allspecificationsbutthefirstincludeaquadratic in the number of sampled workers to control for the precision of the left-hand side variable. 58

Table 13: Tariff Regressions: Average Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Weighted Tariff*Export 0.002 0.001 0.001 -0.001 -0.001 -0.004 (0.004) (0.003) (0.003) (0.003) (0.003) (0.003) Weighted Tariff 0.001 0.002 0.002 0.00395 0.006c 0.012a (0.004) (0.003) (0.003) (0.003) (0.003) (0.003) Export 0.128a 0.082a 0.045b 0.050b 0.071a 0.039c (0.023) (0.021) (0.020) (0.020) (0.021) (0.021) N.Occ. 0.039a 0.016a 0.033a 0.035a -0.002 (0.001) (0.002) (0.001) (0.001) (0.001) logempl 0.123a 0.124a (0.005) (0.005) logdom.share 0.031a 0.005a (0.002) (0.002) white share 0.512a (0.021) logVA per worker 0.161a 0.099a (0.008) (0.007) logN. Products 0.004 (0.003) Sector1-Year y y y y y y Obs. 48,280 48,280 48,280 48,280 48,280 48,280 R2 0.143 0.185 0.210 0.197 0.217 0.303 12-digit sector dummies. Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Weighted Tariff: weighted average - across destination - of tariff levels in a given industry i (4 digit sector) at time t, where weights are the share of world exports to that particular destination in that industry and year. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectionalRegressionsforfirmswithmorethan5workers,years1995-2007. Different specifications in the columns. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first include a quadratic in thenumberofsampledworkerstocontrolfortheprecisionoftheleft-handsidevariable. 59

Table 14: Tariff Regressions: Standard Deviation of Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Weighted Tariff*Export 0.007b 0.007b 0.007b 0.007b 0.006b 0.002 (0.003) (0.003) (0.003) (0.003) (0.003) (0.002) Weighted Tariff -0.013a -0.012a -0.012a -0.013a -0.011a -0.001 (0.003) (0.003) (0.003) (0.003) (0.003) (0.002) Export -0.059a -0.069a -0.037b -0.062a -0.073a -0.032b (0.017) (0.017) (0.017) (0.017) (0.017) (0.013) N.Occ. 0.011a 0.031a 0.013a 0.010a 0.025a (0.001) (0.001) (0.001) (0.001) (0.001) logempl -0.108a -0.022a (0.004) (0.003) logdom.share -0.007a 0.005a (0.002) (0.001) white share 0.480a (0.010) logVA per worker 0.047a 0.103a (0.006) (0.004) logN. Products 0.014a (0.002) Avg Lifetime Wage -0.727a (0.010) Sector1-Year y y y y y y Obs. 48,280 48,280 48,280 48,280 48,280 48,280 R2 0.068 0.071 0.094 0.072 0.074 0.550 12-digit sector dummies. Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. WeightedTariff: weightedaverage-acrossdestination-oftarifflevelsinagivenindustry i(4digitsector)attimet,whereweightsaretheshareofworldexportstothatparticular destination in that industry and year. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectionalRegressionsforfirmswithmorethan5workers,years1995-2007. Differentspecificationsinthecolumns. Standarderrors,clusteredatthelevelofthefirm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 60

A Appendix A.1 Proof of Decreasing Normalized Matching Range under the Assumption of a Homogeneous Revenue Function Assume that the revenue function f(θ,ϕ) is increasing, symmetric, supermodular, and homogeneous in θ and ϕ. A.1.1 Outside Options: Wages and Profits At the optimum, the marginal benefit from hiring a better worker has to equalize the marginal increase in wage: dw∗ ∂f(θ,ϕ) = dθ ∂θ Outside option for the worker is given by θ (cid:12) w∗(θ) = (cid:82) ∂f(t,x)(cid:12) dt ∂t (cid:12) 0 x=µ(t) where, because of symmetry, µ(t) = t. It is useful to use the following result relating the partial and total derivatives of f: (cid:12) (cid:12) df(θ,θ) ∂f(θ,x)(cid:12) ∂f(x,θ)(cid:12) = (cid:12) + (cid:12) dθ ∂θ (cid:12) ∂θ (cid:12) x=θ x=θ Again, symmetry implies that the two partial derivatives are identical: (cid:12) (cid:12) ∂f(θ,x)(cid:12) ∂f(x,θ)(cid:12) (cid:12) = (cid:12) ∂θ (cid:12) ∂θ (cid:12) x=θ x=θ 61

therefore, the wage w∗(θ) can be rewritten as θ w∗(θ) = (cid:82) 1df(t,t) dt = 1f(θ,θ) 2 dt 2 0 The profit function is derived residually as 1 π∗(ϕ) = f(ϕ,ϕ) 2 The matching range is defined by the set of θ that satisfies the following inequality: 1 1 f(θ,ϕ)− f(θ,θ)− f(ϕ,ϕ)+2c ≥ 0 2 2 A.1.2 Normalized Matching Range Let us normalize the matching range by the firm type ϕ: (cid:18) (cid:19) (cid:18) (cid:19) θ 1 θ θ 1 2c f ,1 − f , − f(1,1)+ ≥ 0 (A-1) ϕ 2 ϕ ϕ 2 ϕ Assuming that the function is well behaved and that (A-1) is satisfied with equality for only two u(ϕ) values of θ, we can study the behavior of the normalized upper bound u (ϕ) = and the 1 a(ϕ) l(ϕ) normalized lower bound l (ϕ) = . In particular, we are interested in proving the following 1 a(ϕ) proposition. Proposition A-1 The normalized matching range d (ϕ) = u (ϕ)−l (ϕ) is decreasing in ϕ. 1 1 1 Proof. Define normalized worker type as θ(cid:98)= θ and rewrite (A-1) with equality as a function of ϕ θ(cid:98): (cid:16) (cid:17) 1 (cid:16) (cid:17) 1 2c f θ(cid:98),1 − f θ(cid:98),θ(cid:98) − f(1,1)+ = 0 2 2 ϕ 62

We apply the implicit function theorem to study how θ(cid:98)varies with ϕ: (cid:16) (cid:17) (cid:16) (cid:17) ∂f θ(cid:98),1 dθ(cid:98) 1 df θ(cid:98),θ(cid:98) dθ(cid:98) 2c − − = 0 ∂θ(cid:98) dϕ 2 dθ(cid:98) dϕ ϕ2 Solving for dθ(cid:98), we find the following: dϕ 2c dθ(cid:98) ϕ2 = . (A-2) dϕ ∂f(θ(cid:98),1) − 1df(θ(cid:98),θ(cid:98)) ∂θ(cid:98) 2 dθ(cid:98) The sign of the denominator in (A-2) determines the sign of the derivative of interest dθ(cid:98). It is dϕ df(θ(cid:98),θ(cid:98)) convenient to rewrite as follows: dθ(cid:98) (cid:16) (cid:17) (cid:16) (cid:17)(cid:12) (cid:16) (cid:17)(cid:12) df θ(cid:98),θ(cid:98) ∂f x,θ(cid:98) (cid:12) ∂f θ(cid:98),x (cid:12) (cid:12) (cid:12) = (cid:12) + (cid:12) , dθ(cid:98) ∂θ(cid:98) (cid:12) ∂θ(cid:98) (cid:12) (cid:12) (cid:12) x=θ(cid:98) x=θ(cid:98) where by symmetry (cid:16) (cid:17)(cid:12) (cid:16) (cid:17)(cid:12) ∂f x,θ(cid:98) (cid:12) ∂f θ(cid:98),x (cid:12) (cid:12) (cid:12) (cid:12) = (cid:12) . ∂θ(cid:98) (cid:12) ∂θ(cid:98) (cid:12) (cid:12) (cid:12) x=θ(cid:98) x=θ(cid:98) We can therefore rewrite (A-2) as 2c dθ(cid:98) ϕ2 = . (cid:12) dϕ ∂f(θ(cid:98),1) ∂f(θ(cid:98),x)(cid:12) − (cid:12) ∂θ(cid:98) ∂θ(cid:98) (cid:12) x=θ(cid:98) The assumption of supermodularity of function f(·,·) implies that (cid:16) (cid:17) (cid:16) (cid:17)(cid:12) ∂f θ(cid:98),1 ∂f θ(cid:98),x (cid:12) (cid:12) > (cid:12) ∂θ(cid:98) ∂θ(cid:98) (cid:12) (cid:12) x=θ(cid:98) for θ(cid:98)< 1 and vice versa if θ(cid:98)> 1, which in turn implies that u 1 is decreasing in ϕ (case θ(cid:98)> 1) and l 1 is increasing in ϕ (case θ(cid:98)< 1). 63

A.2 Identification of Worker Type: Average Lifetime Wage Agents’ types are positively correlated with the average realization of their payoffs over their job spells. In particular, a more productive worker makes a larger contribution to revenues and tends to match with a better firm in the frictionless equilibrium, obtaining, on average, a higher payoffs. Following the model, we propose to identify the agents’ type using the average wage. In fact, there exists a well-defined relation. In fact, the average wage of a worker of type θ, 1 (cid:90) (θα+2 √ c)1/α(cid:20) θ2α θαyα y2α(cid:21) w¯(θ) = √ √ + − dy (θα+2 c) 1/α −(θα−2 c) 1/α (θα−2 √ c)1/α 4 2 4 θ2α θα (cid:104) (θα+2 √ c) α α +1 −(θα−2 √ c) α α +1(cid:105) (θα+2 √ c) 2α α +1 −(θα−2 √ c) 2α α +1 = + − 4 (cid:104) √ 1 √ 1(cid:105) (cid:104) √ 1 √ 1(cid:105) 2(α+1) (θα+2 c)α −(θα−2 c)α 4(2α+1) (θα+2 c)α −(θα−2 c)α In particular, if α = 1, θ2 c w¯(θ) = − 4 3 If the demand elasticity α and the search cost c were known, we could back up exactly the worker types. Inordertoprovethattheaveragewageisincreasinginθ,we’llbreaktheproofintotwoparts. First, it is trivial to prove that the outside option is increasing in the worker type. The second part of the proof will show that a worker of higher ability generates a larger surplus and obtains a 64

larger share of it. In the two-period model, under the assumption of a uniform distribution, (cid:82) l u (θ ( ) θ) s(θ,y)dy (cid:82) ( ( θ θ α α − + 2 2 √ √ c c ) ) 1 1 / / α α(cid:104) θα·yα− θ2 2 α − y2 2 α (cid:105) dy = √ √ (cid:82)u(θ) dy (θα+2 c) 1/α −(θα−2 c) 1/α l(θ) (cid:104) (cid:105)(cid:12)(θα+2 √ c)1/α y θα·yα − θ2α − y2α (cid:12) α+1 2 2(2α+1) (cid:12) (θα−2 √ c)1/α = √ √ (θα+2 c) 1/α −(θα−2 c) 1/α (cid:104) (cid:105)(cid:12)(θα+2 √ c)1/α y θα·yα− θ2α − y2α +αθα·yα + 2αy2α (cid:12) 2 2 α+1 2(2α+1) (cid:12) (θα−2 √ c)1/α = √ √ (θα+2 c) 1/α −(θα−2 c) 1/α (cid:104) √ 1+α √ 1+α(cid:105) (θα+2 c) α −(θα−2 c) α (3α+2)θα = −2c+α + √ 1 √ 1 (α+1)(2α+1) (θα+2 c)α −(θα−2 c)α 2 √ c (cid:104) (θα+2 √ c) 1+ α α +(θα−2 √ c) 1+ α α(cid:105) +α (2α+1) √ 1 √ 1 (θα+2 c)α −(θα−2 c)α The surplus is increasing for all α > 0. In fact, ∂ (cid:104) (θα+2 √ c) 1+ α α −(θα−2 √ c) 1+ α α(cid:105)  1+α 1 (θα+2 √ c)α 2 +(θα−2 √ c)α 2  ∂θ  (θα+2 √ c)α 1 −(θα−2 √ c)α 1  = αθα−1  α − α(cid:16) (θα+2 √ c)α 1 −(θα−2 √ c)α 1(cid:17)2   + +αθα−1   1 (θα+2 √ c)α 1 (θα−2 √ c)α 1 (cid:104) θ θ α α + − 2 2 √ √ c c + θ θ α α − + 2 2 √ √ c c (cid:105)  α (cid:16) √ 1 √ 1(cid:17)2  (θα+2 c)α −(θα−2 c)α (θα+2 √ c)α 1 (θα−2 √ c)α 1 (cid:104) θα+2 √ √ c + θα−2 √ √ c −2 (cid:105) = αθα−1+θα−1 θα−2 c θα+2 c (cid:16) √ 1 √ 1(cid:17)2 (θα+2 c)α −(θα−2 c)α and ∂ (cid:104) (θα+2 √ c) 1+ α α +(θα−2 √ c) 1+ α α(cid:105) (cid:34) (θα+2 √ c)α 1 +(θα−2 √ c)α 1 (cid:35) ∂θ  √ 1 √ 1  = αθα−1 √ 1 √ 1 + (θα+2 c)α −(θα−2 c)α (θα+2 c)α −(θα−2 c)α +αθα−1   1 (θα+2 √ c)α 1 (θα−2 √ c)α 1 (cid:104) θ θ α α + − 2 2 √ √ c c − θ θ α α − + 2 2 √ √ c c (cid:105)  α (cid:16) √ 1 √ 1(cid:17)2  (θα+2 c)α −(θα−2 c)α 65

are both positive. A.3 Relative Losses: Variation by Firm Type Proof of Proposition 2InordertoshowthatRL(ϕ)isdecreasinginϕ, itisconvenienttorewrite it as follows: (cid:104) (cid:105) 2(1+2α) (ϕα+b) 1+ α α −(ϕα−b) 1+ α α ϕα RL(ϕ) = 1− . (cid:110) (cid:104) (cid:105)(cid:111) 1+2α 1+2α 1 1 (1+α) (ϕα+b) α −(ϕα−b) α +ϕ2α(1+2α) (ϕα+b)α −(ϕα−b)α It is easy to verify that RL(ϕ) is decreasing if and only if N(cid:48)(ϕ) D(cid:48)(ϕ) > (A-3) N (ϕ) D(ϕ) where (cid:104) (cid:105) N (ϕ) = (ϕα+b) 1+ α α −(ϕα−b) 1+ α α ϕα, (cid:104) (cid:105) D(ϕ) = (ϕα+b) 1+ α 2α −(ϕα−b) 1+ α 2α +ϕ2α(1+2α) (ϕα+b)α 1 −(ϕα−b)α 1 and (cid:16) (cid:17) (cid:16) (cid:17) N(cid:48)(ϕ) = ϕα−1(α+1)ϕα (ϕα+b)α 1 −(ϕα−b)α 1 +α (ϕα+b) 1+ α α −(ϕα−b) 1+ α α (cid:104) (cid:16) (cid:17)(cid:105) D(cid:48)(ϕ) = ϕα−1(2α+1) (ϕα+b) 1+ α α −(ϕα−b) 1+ α α +2αϕα (ϕα+b)α 1 −(ϕα−b)α 1 (cid:104) (cid:105) +ϕα−1(2α+1)ϕ2α (ϕα+b) 1− α α −(ϕα−b) 1− α α We can now operate a change of variables as follows: 66

(cid:18) ϕα+b (cid:19) α 1 h = ϕα (cid:18) ϕα−b (cid:19) α 1 d = ϕα and substitute in inequality (A-3) to obtain the following inequality: (α+1)(h−d)+α (cid:0) h1+α−d1+α(cid:1) (2α+1) (cid:0) h1+α−d1+α+2α(h−d)+ (cid:0) h1−α−d1−α(cid:1)(cid:1) > . h1+α−d1+α h1+2α−d1+2α+(1+2α)(h−d) If we multiply each side by the two denominators and divide by (h−d), we obtain a simplified inequality: h1+2α−d1+2α h1+α−d1+αh1+2α−d1+2α (α+1) +(α+1)(1+2α)+α > (A-4) h−d h−d h−d (cid:34) (cid:35) (cid:18) h1+α−d1+α(cid:19)2 h1+α−d1+α (cid:18) h1−α−d1−α(cid:19)(cid:18) h1+α−d1+α(cid:19) (2α+1) +α + h−d h−d h−d h−d 1. For c → 0, using an approximation of h around d: h1+2α−d1+2α ≈ (1+2α)d2α, h−d h1+α−d1+α ≈ (1+α)dα, h−d h1−α−d1−α ≈ (1−α)d−α. h−d 67

We can therefore simplify inequality (A-4) as follows: (α+1)(1+2α)d2α+(α+1)(1+2α)+α(1+α)dα(1+2α)d2α > (cid:104) (cid:105) (2α+1) (1+α)2d2α+α(1+α)dα+(1−α)d−α(1+α)dα which further simplifies to (dα−1)2(dα+1) ≥ 0, which is verified for all α. 2. If we do not put any restrictions on the search costs, the proof simplifies for specific values of α. For α = 1, (cid:104) (cid:105) 2 (cid:0) h2+hd+d2(cid:1) +6+(h+d) (cid:0) h2+hd+d2(cid:1) > 3 (h+d)2+h+d 2 (cid:0) h2+hd+d2(cid:1) +6+(h+d) (cid:0) h2+hd+d2(cid:1) > 3 (cid:2) h2+2hd+d2+h+d (cid:3) (2+d+h)· (cid:2) 3+d2+(d+h)(h−3) (cid:3) > 0 Using the definition of h and d, (cid:34) (cid:35) (cid:18) b (cid:19)2 (cid:18) b (cid:19) b2 (2+2)· 3+ 1− +2· 1+ −3 = 4 > 0 ϕ ϕ ϕ2 68

• For α = 2, h5−d5 h3−d3h5−d5 3 +15+2· > h−d h−d h−d (cid:34) (cid:35) (cid:18) h3−d3(cid:19)2 h3−d3 (cid:18) h−1−d−1(cid:19)(cid:18) h3−d3(cid:19) 5 +2 + h−d h−d h−d h−d 3 (cid:0) h4+h3d+h2d2+hd3+d4(cid:1) +15+2 (cid:0) h4+h3d+h2d2+hd3+d4(cid:1)(cid:0) h2+hd+d2(cid:1) > (cid:34) (cid:0) h2+hd+d2(cid:1)(cid:35) 5 (cid:0) h2+hd+d2(cid:1)2 +2 (cid:0) h2+hd+d2(cid:1) − hd Using the definition of h and d, (cid:20) (cid:21) (cid:16) (cid:17)1/2 −2b4+4b2 3+2 1− b2 ϕ4 (cid:34) (cid:35) ϕ4 (cid:18) b2(cid:19)1/2 b2 ≥ 0 ⇔ 3+2 1− ϕ4 ≥ (cid:16) (cid:17)1/2 ϕ4 2 1− b2 ϕ8 ϕ4 Recalling that ϕ2 ≥ b, the inequality is always verified. • For α = 1, the expression simplifies to 2 b2 ≥ 0 ϕ under the assumptions on b. A.4 Numerical Simulation We simulate the model using the empirical distribution of worker and firm types to show that the properties of matching bounds are verified under this specification (see Figure A5 for the distribution of worker types and A6 for the distribution of firm types). Figure A1 shows the matching set of the economy when normalizing the aggregate price index to unity and assuming the search cost c = 0.01, the meeting rate ρ = 1, and the exogenous separation rate δ = 1. Using 69

the simulation results, we construct two measures of dispersions of worker types by firm, the length andthestandarddeviation35 ofthefirmmatchingset. FiguresA2andA3showthatbothmeasures are decreasing in firm type, when normalized by the average worker type. Figure A1: Matching Set for the Simulated Economy. For a given firm type ϕ, the matching set is [l(ϕ),u(ϕ)]. Figure A2: Standard Deviation of the Figure A3: Standard Deviation of the Matching Set by Firm Type, normalized Matching Set by Firm Type, normalized by the Average Worker Type (d (ϕ)) by the Average Worker Type 1 35In the empirical analysis, our preferred measure of dispersion is the standard deviation of the worker types by firm, since it is less sensitive to outliers. 70

A.5 Additional Empirical Results Figure A4: Distribution of Value Added per Worker in Exporting and Non-Exporting Firms Figure A5: Distribution of Individual Effects, Largest Connected Group 71

Figure A6: Distribution of Firm Effects, Largest Connected Group Figure A7: Variability in Wages: Comparison 72

Figure A8: Wage Changes by Wage Quartile (Source: DADS). Figure A9: Distribution of Firms by Number of Exporting Years (Source: EAE and Export Customs). 73

Table A1: Classification of CS Occupation into white and blue collar workers CS code White Collar Jobs 3 Executives and Higher Intellectual Professions 31 Health Professionals and Lawyers 33 Senior Official in Public Administration 34 Teachers, Scientific Professions 35 Information, arts and entertainment 37 Administrative and Commercial skilled workers 38 Engineers and technical managers 4 Intermediate Occupations 42 Teachers and related 43 Intermediate occupations, health and social work 44 Religious 45 Intermediate administrative professions in Public Administration 46 Intermediate administrative and commercial occupation in Enterprises 47 Technicians 48 Foremen, supervisors CS code Blue Collar Jobs 5 Clericals 52 Civilian Employees and officers in Public Service 53 Protective Services 54 Administrative Employees 55 Commercial workers 56 Personal services workers 6 Labourers 62 Qualified Industrial workers 63 Qualified craft workers 64 Drivers 65 Storage and Transport workers 67 Non-Qualified Industrial workers 68 Non-Qualified craft workers 69 Farm Workers 74

Table A2: Summary Statistics Mean Median Std Deviation Avg. Worker Type -0.04 -0.02 0.86 Std Dev. Worker Fixed Effects 0.62 0.52 0.41 Std Dev. Worker Fixed Effects, White Collars 0.55 0.47 0.36 Std Dev. Worker Fixed Effects, Blue Collars 0.50 0.36 0.41 Std Dev. Worker Fixed Effectsa 0.62 0.52 0.41 Std Dev. Worker Fixed Effects, White Collarsa 0.55 0.47 0.36 Std Dev. Worker Fixed Effects, Blue Collarsa 0.50 0.36 0.41 Num. Occupation 4.90 4.00 2.44 Domestic Market Share 0.03 0.01 0.08 Employment 290.48 134.00 715.65 Products 8.57 9.01 4.22 Share of Non Production Worker 0.34 0.29 0.25 Value Added per worker 70.76 45.71 161.35 aConditioning on a sample of firms with more than 5 sampled workers. Table A3: Summary Statistics: Market Access Shocks Mean Median Std Deviation Weighted Tariff 5.58 5.03 3.49 Market Access Shock 12.93 14.32 6.15 1 Market Access Shock 12.89 14.27 6.12 2 Weighted Tariff: Weighted average - across destination - of tariff levels in a given industry i at time t, where weights are the share of world exports to that particular destination in that industry and year. Market Access Shock : Weighted average - across destinations, ex- 1 cludingFrance-ofthedemandfacedbyagivenindustryiattimet, where the weights are the share of world exports to that particular destination in that industry the previous year. Market Access Shock : Weighted-average - across destinations - of 2 thedemandfacedbyagivenindustryiattimet,wheretheweights are the share of world exports to that particular destination in that industry the previous year. Table A4: Wage Inequality Decomposition Conditional Wage Components 1995 2007 Between-Firm 41.6% 37.2% Within-Firm 52.0% 57.7% Worker Observables 7.6% 4.7% Cov. observables-firm -1.3% 0.3% Note: WageVariancedecompositionfromaMincerianequation thatcontrolsforworkerobservables(in-firmtenure,gender,and occupation dummies) and firm fixed effects. 75

Table A5: Non-Exporting Spells Number of years Average spell Average number exporting of non-exporting in the sample 1 1.63 3.02 2 1.89 4.30 3 1.40 4.89 4 1.19 5.65 5 1.05 6.47 6 0.75 7.06 7 0.75 8.03 8 0.57 8.80 9 0.55 9.72 10 0.45 10.57 11 0.33 11.39 12 0.17 12.17 13 0 13 Notes: Average spells of non-exporting status and number of years in the sample by years of presence in foreign market. Table A6: Wage Changes when Moving to a New Job Wage Change Percentage Positive 54.82% Negative 45.18% Notes: Frequency of positive and negative wage changes for movers. 76

Table A7: Pooled Cross-sectional Regressions: Standard Deviation of Worker Type (only newly hired workers) (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Export -0.025 -0.048b -0.057a -0.063a -0.056a -0.057a (0.020) (0.020) (0.020) (0.020) (0.020) (0.017) N.Occ. 0.031a 0.024a 0.022a 0.030a 0.0198a (0.003) (0.002) (0.002) (0.003) (0.002) logempl -0.028a -0.031a -0.023a (0.007) (0.008) (0.006) logdom.share -0.0002 0.002 0.004c (0.003) (0.003) (0.002) logVA per worker 0.038a 0.038a 0.048a (0.010) (0.010) (0.008) white share 0.332a (0.019) logN. Products 0.018a (0.004) Avg. Lifetime Wage -0.444a (0.011) Sector-Year y y y y y y Obs. 14,971 14,971 14,971 14,971 14,971 14,971 R2 0.154 0.168 0.166 0.168 0.169 0.483 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-numberofexportedproducts(HS6codes). Thisvariableiszero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. Legend: a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995- 2007. Differentspecificationsinthecolumns. Standarderrors, clusteredatthelevel of the firm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the lefthand side variable. 77

Table A8: Pooled Cross-sectional Regressions: Standard Deviation of Worker Type (only current workers) (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Export 0.020b 0.010 0.002 -0.003 0.006 -0.014 (0.009) (0.009) (0.009) (0.009) (0.009) (0.010) N.Occ. 0.025a 0.020a 0.018a 0.024a 0.018a (0.001) (0.001) (0.001) (0.001) (0.001) logempl -0.032a -0.033a -0.017a (0.004) (0.004) (0.004) logdom.share -0.001 -8.06e−5 0.001 (0.001) (0.001) (0.001) logVA per worker 0.040a 0.041a 0.080a (0.005) (0.005) (0.005) white share 0.381a (0.013) logN. Products 0.011a (0.002) Avg. Lifetime Wage -0.447a (0.012) Sector-Year y y y y y y Obs. 40,579 40,579 40,579 40,579 40,579 40,579 R2 0.043 0.071 0.066 0.072 0.077 0.253 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-numberofexportedproducts(HS6codes). Thisvariableiszero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995- 2007. Different specifications in the columns. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the lefthand side variable. 78

Table A9: Pooled GLS Regressions: Average Worker Type (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Export 0.174a 0.047a 0.050a 0.072a 0.021b -0.009 (0.011) (0.010) (0.010) (0.010) (0.010) (0.012) N.Occ. -0.004 0.013a 0.019a -0.006b -0.009a (0.003) (0.002) (0.002) (0.003) (0.003) logempl 0.097a 0.085a 0.075a (0.007) (0.006) (0.006) logdom.share 0.032a 0.006a 0.004b (0.003) (0.002) (0.002) logVA per worker 0.177a 0.167a 0.103a (0.010) (0.009) (0.009) white share 0.559a (0.022) logN. Products 0.014a (0.004) Sector-Year y y y y y y Obs. 148,784 148,784 148,784 148,784 148,784 148,784 R2 0.181 0.253 0.244 0.268 0.289 0.360 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-numberofexportedproducts(HS6codes). Thisvariableiszero for non-exporters. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995- 2007. Differentspecificationsinthecolumns. Standarderrors,clusteredatthelevel of the firm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the lefthand side variable. 79

Table A10: Pooled GLS Regressions: Average Worker Type (1) (2) (3) (4) (5) (6) Variables Worker Type: AKM Fixed Effects θAKM Export 0.107a 0.030 0.026 0.035 0.018 -0.004 (0.025) (0.024) (0.024) (0.024) (0.025) (0.028) N.Occ. 0.007 0.011a 0.013a 0.007 0.0057 (0.005) (0.003) (0.003) (0.005) (0.005) logempl 0.028b 0.021 0.010 (0.014) (0.013) (0.014) logdom.share 0.012b 0.005 0.003 (0.005) (0.005) (0.005) logVA per worker 0.065a 0.060a 0.013 (0.017) (0.016) (0.016) white share 0.404a (0.037) logN. Products 0.011 (0.008) Sector-Year y y y y y y Obs. 79,689 79,689 79,689 79,689 79,689 79,689 R2 0.052 0.073 0.073 0.075 0.076 0.089 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first includeaquadraticinthenumberofsampledworkerstocontrolfortheprecision of the left-hand side variable. 80

Table A11: Pooled GLS Regressions: Standard Deviation of Worker Type (1) (2) (3) (4) (5) (6) Variables Worker Type: Average Lifetime Wage θLW Export -0.017 -0.017 -0.038a -0.050a -0.025b -0.035a (0.011) (0.012) (0.012) (0.012) (0.012) (0.010) N.Occ. 0.024a 0.012a 0.010a 0.024a 0.017a (0.003) (0.002) (0.002) (0.003) (0.003) logempl -0.055a -0.060a -0.004 (0.009) (0.008) (0.006) logdom.share -0.004 0.004c 0.006a (0.003) (0.002) (0.002) logVA per worker 0.037a 0.040a 0.095a (0.008) (0.009) (0.007) white share 0.508a (0.016) logN. Products 0.014a (0.003) Avg. Lifetime Wage -0.713a (0.012) Sector-Year y y y y y y Obs. 88,790 88,790 88,790 88,790 88,790 88,790 R2 0.099 0.119 0.108 0.111 0.123 0.553 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995- 2007. Different specifications in the columns. Standard errors, clustered at the levelofthefirm,arereportedinparentheses. Allspecificationsbutthefirstinclude a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 81

Table A12: Pooled GLS Regressions: Standard Deviation of Worker Types (1) (2) (3) (4) (5) (6) Variables Worker Type: AKM Fixed Effects θAKM Export -0.023c -0.026b -0.045a -0.054a -0.034a -0.043a (0.012) (0.013) (0.013) (0.013) (0.013) (0.014) N.Occ. 0.022a 0.011a 0.010a 0.021a 0.021a (0.003) (0.002) (0.002) (0.003) (0.003) logempl -0.048a -0.053a -0.056a (0.009) (0.008) (0.008) logdom.share -0.004 0.003 0.003 (0.003) (0.002) (0.002) logVA per worker 0.032a 0.035a 0.023a (0.008) (0.008) (0.008) white share 0.152a (0.020) logN. Products 0.005 (0.004) Avg Worker Type -0.092a (0.006) Sector-Year y y y y y y Obs. 79,689 79,689 79,689 79,689 79,689 79,689 R2 0.106 0.123 0.115 0.117 0.126 0.158 Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first includeaquadraticinthenumberofsampledworkerstocontrolfortheprecision of the left-hand side variable. 82

Table A13: Sectoral Rank Correlations (1) (2) (3) (4) (5) (6) (7) (8) Variables Rank Correlation Export 0.042a 0.029a 0.023b 0.017c 0.042a 0.037a 0.026a 0.027c (0.008) (0.010) (0.010) (0.010) (0.008) (0.014) (0.010) (0.014) logempl 0.009c 0.004 0.003 -0.001 (0.005) (0.005) (0.009) (0.009) logVA per worker 0.077a 0.075a 0.064a 0.064a (0.017) (0.017) (0.023) (0.024) Sector,Year y1 y1 y1 y1 y2 y2 y2 y2 Obs. 3,836 3,836 3,836 3,836 3,836 3,836 3,836 3,836 R2 0.041 0.042 0.049 0.049 0.195 0.195 0.198 0.198 12-digit sector dummies. 24-digit sector dummies. logempl: log-employment. logVA per worker: log-value added per worker. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Industry regressions, years 1995-2007. Standard errors, clustered at the sector-level, are reported in parentheses. Table A14: GLS Regressions: Sectoral Rank Correlations (1) (2) (3) (4) (5) (6) (7) Variables Rank Correlation Export 0.037a 0.033a 0.018b 0.024a 0.035a 0.011 0.022b (0.009) (0.009) (0.009) (0.009) (0.011) (0.007) (0.011) logempl 0.002 -0.004 -0.001 -0.008 (0.004) (0.004) (0.007) (0.007) logVA per worker 0.074a 0.078a 0.096a 0.100a (0.014) (0.015) (0.020) (0.021) Sector,Year y1 y1 y1 y1 y2 y2 y2 Obs. 3,812 3,812 3,812 3,812 3,812 3,812 3,812 R2 0.082 0.082 0.094 0.094 0.333 0.343 0.343 12-digit sector dummies. 24-digit sector dummies. logempl: log-employment. logVA per worker: log-value added per worker. a significant at 1%, b significant at 5%, c significant at 10%. Notes: Industryregressions,years1995-2007. Differentspecificationsinthecolumns. Standard errors, clustered at the sector-level, are reported in parentheses. 83

Table A15: IV Regressions: Standard Deviation of Worker Type, more than 5 workers (1) (2) (3) (4) (5) (6) Standard Deviation of Lifetime Wage, more than 5 Variables Exp Share Exp Share t−1 t−3 Second Stage Export -0.075a -0.102a -0.153a -0.085a -0.092a -0.158a (0.019) (0.020) (0.035) (0.022) (0.027) (0.057) First Stage Firm Tariff 0.120a 0.110a 0.043a 0.125a 0.101a 0.038a (0.005) (0.004) (0.001) (0.005) (0.004) (0.002) F-stat (First Stage) 528 551 599 668 588 243 Obs. 16,072 16,072 16,072 13,217 13,217 13,217 Firm Tariff: (inverse of) average applied tariff across industry-destination, weighted by the share of firm j exports to each industry-destination the previous period or at t−3. a significant at 1%, b significant at 5%, c significant at 10%. Notes: IV Regressions for firms with more than 5 workers, years 1995-2007. Differentspecificationsinthecolumns. Standarderrors,clusteredatthelevel ofthefirm,arereportedinparentheses. Allspecificationsbutthefirstinclude a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 84

Table A16: IV Market Access Regressions: Average Worker Type, more than 5 workers (1) (2) (3) (4) Worker Type: Average Lifetime Wage θLW Variables Exp Share Exp Share t−1 t−3 Market Access*Export 0.008 0.022a 0.007 0.015a (0.008) (0.006) (0.006) (0.005) Market Access -0.010 -0.027a -0.010c -0.022a (0.006) (0.005) (0.005) (0.004) Export 0.078 -0.169b 0.136 0.007 (0.108) (0.084) (0.086) (0.075) N.Occ. -0.003 -0.003 (0.002) (0.003) logempl 0.145a 0.150a (0.008) (0.009) logdom.share 0.005c 0.004 (0.003) (0.003) logVA per worker 0.111a 0.114a (0.009) (0.010) white share 0.562a 0.564a (0.025) (0.024) logN. Products -0.030a -0.046a (0.011) (0.013) Sector1-Year y y y y Obs. 14,883 14,883 12,028 12,028 R2 0.187 0.360 0.192 0.360 12-digit sector dummies. Export: dummy=1 if firm exports. N.Occ.: numberofoccupations,basedon2-digitoccupationalcodesfor France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. Market Access: weighted-average - across destinations - of the demand facedbyagivenindustryi(4-digitsector)attimet,wheretheweightsare theshareofworldexportstothatparticulardestinationinthatindustry the previous year. a significant at 1%, b significant at 5%, c significant at 10%. Notes: IV Regressions for firms with more than 5 workers, years 1995- 2007. Export status is instrumented using tariffs and the previous year exportshareincolumns(1)-(2);columns(3)-(4)usetariffsandthet−3 export share. Different specifications in the columns. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 85

Table A17: IV Market Access Regressions: Standard Deviation of Worker Type, more than 5 workers (1) (2) (3) (4) Worker Type: Average Lifetime Wage θLW Variables Exp Share Exp Share t−1 t−3 Market Access*Export -0.029a -0.005 -0.018a -0.001 (0.006) (0.004) (0.005) (0.003) Market Access 0.030a 0.005 0.020a 0.001 (0.005) (0.003) (0.004) (0.003) Export 0.342a -0.075 0.169b -0.146a (0.083) (0.053) (0.071) (0.051) N.Occ. 0.020a 0.022a (0.002) (0.002) logempl -0.011b -0.011c (0.005) (0.006) logdom.share 0.013a 0.013a (0.002) (0.002) logVA per worker 0.094a 0.088a (0.006) (0.006) white share 0.465a 0.450a (0.016) (0.018) Avg. Lifetime Wage -0.733a -0.728a (0.013) (0.014) logN. Products 0.044a 0.045a (0.008) (0.010) Sector1-Year y y y y Obs. 14,883 14,883 12,028 12,028 R2 0.058 0.545 0.058 0.544 12-digit sector dummies. Export: dummy=1 if firm exports. N.Occ.: numberofoccupations,basedon2-digitoccupationalcodesfor France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. Market Access: weighted-average - across destinations - of the demand facedbyagivenindustryi(4-digitsector)attimet,wheretheweightsare theshareofworldexportstothatparticulardestinationinthatindustry the previous year. a significant at 1%, b significant at 5%, c significant at 10%. Notes: IV Regressions for firms with more than 5 workers, years 1995- 2007. Export status is instrumented using tariffs and the previous year exportshareincolumns(1)-(2);columns(3)-(4)usetariffsandthet−3 export share. Different specifications in the columns. Standard errors, clustered at the level of the firm, are reported in parentheses. All specifications but the first include a quadratic in the number of sampled workers to control for the precision of the left-hand side variable. 86

Table A18: IV Tariff Regressions: Average Worker Type, more than 5 workers (1) (2) (3) (4) Worker Type: Average Lifetime Wage θLW Variables Exp Share Exp Share t−1 t−3 Weighted Tariff*Export -0.004 0.009b -0.004 0.010a (0.004) (0.004) (0.004) (0.004) Weighted Tariff -0.005 -0.008 -0.009c -0.013a (0.006) (0.005) (0.005) (0.005) Export 0.214a 0.173a 0.273a 0.271a (0.037) (0.052) (0.033) (0.055) N.Occ. -0.003 -0.003 (0.002) (0.003) logempl 0.146a 0.150a (0.008) (0.008) logdom.share 0.007b 0.007b (0.003) (0.003) logVA per worker 0.110a 0.560a (0.009) (0.023) white share 0.558a 0.114a (0.024) (0.010) logN. Products -0.031a -0.045a (0.011) (0.013) Sector1-Year y y y y Obs. 15,160 15,160 12,305 12,305 R2 0.187 0.360 0.193 0.360 12-digit sector dummies. Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. WeightedTariff: weightedaverage-acrossdestination-oftarifflevelsin a given industry i (4-digit sector) at time t, where weights are the share of world exportsto that particular destination in that industryand year. a significant at 1%, b significant at 5%, c significant at 10%. Notes: IV Regressions for firms with more than 5 workers, years 1995- 2007. Export status is instrumented using tariffs and the previous year export share in columns (1)-(2); columns (3)-(4) use tariffs and the t−3 export share. Different specifications in the columns. Standard errors, clusteredatthelevelofthefirm, arereportedinparentheses. Allspecificationsbutthefirstincludeaquadraticinthenumberofsampledworkers to control for the precision of the left-hand side variable. 87

Table A19: IV Tariff Regressions: Standard Deviation of Worker Types, more than 5 workers (1) (2) (3) (4) Worker Type: Average Lifetime Wage θLW Variables Exp Share Exp Share t−1 t−3 Weighted Tariff*Export -0.006 0.001 -0.008b -0.001 (0.004) (0.003) (0.004) (0.002) Weighted Tariff 0.006 -0.003 0.016a 0.002 (0.006) (0.003) (0.005) (0.003) Export -0.104a -0.143a -0.163a -0.161a (0.035) (0.038) (0.031) (0.042) N.Occ. 0.020a 0.022a (0.002) (0.002) logempl -0.008 -0.008 (0.005) (0.006) logdom.share 0.013a 0.012a (0.002) (0.002) logVA per worker 0.096a 0.091a (0.006) (0.006) white share 0.468a 0.453a (0.015) (0.018) Avg. Lifetime Wage -0.739a -0.732a (0.012) (0.014) logN. Products 0.046a 0.043a (0.008) (0.010) Sector1-Year y y y y Obs. 15,160 15,160 12,305 12,305 R2 0.063 0.548 0.063 0.548 12-digit sector dummies. Export: dummy=1 if firm exports. N.Occ.: number of occupations, based on 2-digit occupational codes for France. logempl: log-employment. logVA per worker: log-value added per worker. logdom.share: log-domestic market share, at the 4-digit sector level. white share: share of non-production worker. logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters. Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm. WeightedTariff: weightedaverage-acrossdestination-oftarifflevelsin a given industry i (4-digit sector) at time t, where weights are the share of world exportsto that particular destination in that industryand year. a significant at 1%, b significant at 5%, c significant at 10%. Notes: IV Regressions for firms with more than 5 workers, years 1995- 2007. Export status is instrumented using tariffs and the previous year export share in columns (1)-(2); columns (3)-(4) use tariffs and the t−3 export share. Different specifications in the columns. Standard errors, clusteredatthelevelofthefirm, arereportedinparentheses. Allspecificationsbutthefirstincludeaquadraticinthenumberofsampledworkers to control for the precision of the left-hand side variable. 88