IRLE IRLE WORKING PAPER #104-16 March 2016 Firms and Labor Market Inequality: Evidence and Some Theory David Card, Ana Rute Cardoso, Joerg Heining, and Patrick Kline Cite as: David Card, Ana Rute Cardoso, Joerg Heining, and Patrick Kline. (2016). “Firms and Labor Market Inequality: Evidence and Some Theory”. IRLE Working Paper No. 104-16. http://irle.berkeley.edu/workingpapers/104-16.pdf irle.berkeley.edu/workingpapers Firms and Labor Market Inequality: Evidence and Some Theory David Card, Ana Rute Cardoso, Joerg Heining, and Patrick Kline∗ March 2016 Abstract We review the literature on (cid:28)rm-level drivers of labor market inequality. There is strong evidence from a variety of (cid:28)elds that standard measures of productivity (cid:21) like output per worker or total factor productivity (cid:21) vary substantially across (cid:28)rms, even within narrowly-de(cid:28)ned industries. Several recent studies note that rising trends in the dispersion of productivity across (cid:28)rms mirror the trends in the wage inequality across workers. Two distinct literatures have searched for a more direct link between thesetwophenomena. The(cid:28)rstexamineshowwagesarea(cid:27)ectedbydi(cid:27)erencesinemployerproductivity. Studiesthatfocuson(cid:28)rm-speci(cid:28)cproductivityshocksandcontrolforthenon-randomsortingofworkers to more and less productive (cid:28)rms typically (cid:28)nd that a 10% increase in value-added per worker leads to somewhere between a 0.5% and 1.5% increase in wages. A second literature focuses on (cid:28)rm-speci(cid:28)c wage premiums, using the wage outcomes of job changers. This literature also concludes that (cid:28)rm pay setting is important for wage inequality, with many studies (cid:28)nding that (cid:28)rm wage e(cid:27)ects contribute approximately 20% of the overall variance of wages. To interpret these (cid:28)ndings, we develop a model whereworkplaceenvironmentsareviewedasimperfectsubstitutesbyworkers,and(cid:28)rmssetwageswith somedegreeofmarketpower. Weshowthatsimpleversionsofthismodelcanreadilymatchthestylized empirical (cid:28)ndings in the literature regarding rent-sharing elasticities and the structure of (cid:28)rm-speci(cid:28)c pay premiums. ∗WeareextremelygratefultoRa(cid:27)aeleSaggioforassistanceinpreparingthispaper,andtoDavidGreenforhelpfulsuggestions onanearlierdraft. Cardosoacknowledges(cid:28)nancialsupportfromtheSpanishMinistryofEconomyandCompetitiveness(Severo Ochoa Programme forCentres of Excellence in R&D grant SEV-2015-0563) and the Research Council of Norway (Europe in Transitionfundingschemeproject227072/F10atESOP). 1 Does where you work determine how much you earn? In the standard competitive labor market model (cid:28)rms take market wages as given and (cid:28)rm-speci(cid:28)c heterogeneity in(cid:29)uences who is hired, but not the level of pay of any particular worker. The pervasive in(cid:29)uence of this perspective is evident in major reviews of the wage inequality literature (Katz and Autor, 1999; Goldin and Katz, 2009; Acemoglu and Autor, 2011), which focus almost exclusively on the role of market-level skill prices in driving inequality trends.1 This view stands in stark contrast to the Industrial Organization literature, which typically models markets as imperfectly competitive (Tirole, 1988; Pakes, 2016). Though economists seem to agree that part of the variation in the prices of cars and breakfast cereal is due to factors other than marginal cost, the possibility that wages re(cid:29)ect anything other than skill remains highly controversial. The growing availability of matched employer-employee datasets has created new opportunities to disen- tanglethee(cid:27)ectsofworkerand(cid:28)rmheterogeneityonwageinequality. Nevertheless,manyofthefundamental issues that economists have long debated about di(cid:27)erences in the characteristics of the workers at di(cid:27)erent 2 (cid:28)rms, and the nature of the jobs at di(cid:27)erent workplaces, carry over to these new datasets. This review summarizes what has been learned so far from these new datasets about the importance of (cid:28)rms in wage setting, and what challenges remain. Ourstartingpointisthewidelyaccepted(cid:28)ndingthatobservablysimilar(cid:28)rmsexhibitmassiveheterogene- ityinmeasuredproductivity(e.g.,Syverson,2011). Anaturalquestioniswhethersomeoftheseproductivity di(cid:27)erences spill over to wages. The prima facie case for such a link seems quite strong: a number of recent studies show that trends in aggregate wage dispersion closely track trends in the dispersion of productivity acrossworkplaces(Dunneetal.,2004;Faggio,Salvanes,andVanReenen,2010;Barthetal. 2016). However, theseaggregaterelationshipsarepotentiallydriveninpartbychangesinthedegreetowhichdi(cid:27)erentgroups of workers are assigned to di(cid:27)erent (cid:28)rms. Two distinct literatures attempt to circumvent the sorting issue using linked employer-employee data. The (cid:28)rst literature studies the impact of di(cid:27)erences in (cid:28)rm productivity on the wages of workers. The resulting estimates are typically expressed as (cid:16)rent-sharing(cid:17) elasticities. The (cid:28)ndings in this literature are surprisingly robust to the choice of productivity measure and labor market environment: most studies that control for worker heterogeneity (cid:28)nd wage-productivity elasticities in the range 0.05-0.15, though a few older studies (cid:28)nd larger elasticities. We also provide some new evidence on the relationship between wages and (cid:28)rm-speci(cid:28)c productivity using matched worker-(cid:28)rm data from Portugal. We investigate a number of speci(cid:28)cationissuesthatfrequentlyariseinthisliterature, includingtheimpactof(cid:28)lteringoutindustry-wide shocks, di(cid:27)erent approaches to measuring rents, and econometric techniques for dealing with unobserved worker heterogeneity. A second literature uses data on wage outcomes as workers move between (cid:28)rms to estimate (cid:28)rm-speci(cid:28)c pay premiums. This literature also (cid:28)nds that (cid:28)rms play an important role in wage determination, with a typical(cid:28)ndingthatabout20%ofthevarianceofwagesisattributabletostable(cid:28)rmwagee(cid:27)ects. Wediscuss some of the issues that arise in implementing the two-way (cid:28)xed e(cid:27)ects estimator of Abowd, Kramarz, and Margolis(1999)(hereafterAKM),whichisthemaintoolusedinthisliterature,andevidenceonthevalidity of the assumptions underlying the AKM speci(cid:28)cation. Wethenattempttoforgeamoredirectlinkbetweentherentsharingliteratureandstudiesbasedonthe AKM framework. Speci(cid:28)cally, we argue that the (cid:28)rm-speci(cid:28)c wage premiums estimated in an AKM model 1Thismarket-wideperspectiveisalsocommonineconomicmodelsofdiscrimination,whichtypicallyhavenorolefor(cid:28)rm- speci(cid:28)cfactorstoa(cid:27)ectthewagesoffemaleorminorityworkers(seee.g.,CharlesandGuryan,2008,2011). 2Manyoftheissuesabouttheinterpretationof(cid:28)rm-speci(cid:28)cwagesettingcloselyparallelissuesthatwereraisedintheearlier literature on industry-speci(cid:28)c wage premiums (cid:21) see e.g., Slichter (1950), Katz (1986), Krueger and Summers (1988), Gibbons andKatz(1992),KatzandSummers(1989),andMurphyandTopel(1990). 2 incorporate any rent-sharing e(cid:27)ect, while adjusting for observed or unobserved skill di(cid:27)erences between workers at di(cid:27)erent (cid:28)rms (which are absorbed by the estimated worker e(cid:27)ects in these models). Using data from Portugal we show that more productive (cid:28)rms pay higher average wage premiums relative to the outside labor market, but also tend to hire more productive workers. Indeed, we estimate that about 40% of the observed di(cid:27)erence in average hourly wages between more and less productive (cid:28)rms is attributable to the di(cid:27)erential sorting of higher-ability workers to more productive (cid:28)rms, underscoring the importance of controlling for worker heterogeneity. We then go on to investigate the extent of di(cid:27)erential rent sharing between more and less educated workers in the Portuguese labor market. We con(cid:28)rm that more productive (cid:28)rms have a larger share of highly-educated workers. Nevertheless, the wage premiums o(cid:27)ered by more productive (cid:28)rms to more- and less-educated workers are very similar, and the relative wage of highly educated workers is nearly constant across (cid:28)rms, consistent with the additive speci(cid:28)cation underlying the AKM model. In the (cid:28)nal section of the paper we develop a stylized model of imperfect competition in the labor market that provides a tractable framework for studying the implications of worker and (cid:28)rm heterogeneity for wage inequality. Our analysis builds on the static partial equilibrium monopsony framework introduced byJoanRobinson(1933)which, asnotedbyManning(2011), capturesmanyofthesameeconomicforcesas search models, albeit without providing a theory of worker (cid:29)ows between labor market states. We provide a microeconomicfoundationforimperfectlabormarketcompetitionbyallowingworkerstohaveheterogeneous 3 preferencesovertheworkenvironmentsofdi(cid:27)erentpotentialemployers. Thisworkplacedi(cid:27)erentiationcould re(cid:29)ect heterogeneity in (cid:28)rm location, job characteristics (e.g., corporate culture, starting times for work), or other factors that are valued di(cid:27)erently by di(cid:27)erent workers. Regardless of its source, such heterogeneity makes employers imperfect substitutes in the eyes of workers, which in turn gives (cid:28)rms some wage-setting power. Our model can be viewed as an adaptation of the standard random preferences model of consumer demand (e.g., Berry, 1994; Berry, Levinsohn, and Pakes, 1995; Pakes, 2016), with (cid:28)rms setting wages rather than prices. We presume, as in Robinson’s analysis and much of the Industrial Organization literature, that the (cid:28)rm cannot price discriminate based upon a worker’s idiosyncratic preference for the (cid:28)rm’s work environment. Hence, rather than o(cid:27)er each worker her reservation wage (e.g., as in Postel-Vinay and Robin, 2002), (cid:28)rms post a common wage for each skill group that is marked down from marginal product in inverse proportion to their elasticity of labor supply to the (cid:28)rm. We show that many well-documented empirical regularities can be rationalized in this framework. Firm heterogeneity in productivity a(cid:27)ects not only the (cid:28)rm size distribution, but also the distribution of (cid:28)rm-speci(cid:28)c wage premiums and the degree of sorting of di(cid:27)erent skill groups across (cid:28)rms. Conditions are provided under which log wages are additively separable into components due to worker and (cid:28)rm heterogeneity, as in the pioneering econometric model of AKM. Speci(cid:28)cally, we show that the (cid:28)rm-speci(cid:28)c wage premium will be constant across skill groups if di(cid:27)erent groups are perfect substitutes in production, or if di(cid:27)erent skill groups have similar elasticities of supply to the (cid:28)rm. Even under these con- ditions, however, the market-level wage gap between skill groups will re(cid:29)ect di(cid:27)erences in their employment distributions across more and less productive (cid:28)rms. Weconcludewithsomethoughtsonunresolvedempiricalandtheoreticalissuesintheliterature. Perhaps the most important empirical concern is the lack of quasi-experimental sources of variation in (cid:28)rm-speci(cid:28)c productivity or (cid:28)rm switching. While a few older studies attempt to leverage world prices (Abowd and 3Intheirreviewofmonopsonymodels,BoalandRansom(1997)refertothisasthecaseof(cid:16)classicdi(cid:27)erentiation(cid:17). 3 Lemieux, 1993) or product market innovations (Van Reenen, 1996) to identify rent sharing elasticities, most recent studies, while able to control for worker heterogeneity, have not compellingly isolated exogenous changes in productivity. On the theoretical side, an important issue is how far the insights from a simple static wage setting model carry over to frictional labor market settings. 1 Productivity, wages, and rent sharing A large empirical literature reviewed by Syverson (2011) documents that (cid:28)rms, like workers, exhibit vast heterogeneityinproductivity. Forexample,Syverson(2004)(cid:28)ndsthatthe90thand10thpercentilesoftotal factor productivity (TFP) among US manufacturing (cid:28)rms di(cid:27)er by an average factor of approximately two within 4-digit industries. Hsieh and Klenow (2009) (cid:28)nd even larger productivity gaps in India and China, with90-10TFP ratiosontheorderof(cid:28)ve. Whilethevariationinmeasuredproductivityprobablyoverstates the true heterogeneity in plant-level e(cid:30)ciency, there is also strong evidence in the literature that measured productivityconveysrealinformation. Forexample,measuredTFP isstronglycorrelatedwith(cid:28)rmsurvival (Foster, Haltiwanger, and Syverson, 2008). It is natural to wonder if these large productivity di(cid:27)erences lead to di(cid:27)erences in worker pay. In fact, an extensive literature has documented the existence of substantial wage di(cid:27)erences across plants and establishments (Slichter, 1950; Davis and Haltiwanger, 1991; Groshen, 1991; Bernard and Jensen, 1995; Cardoso, 1997; Cardoso, 1999; Skans, Edin, and Holmlund, 2009; Song et al., 2015) that are strongly correlated with basic measures of productivity. Nevertheless, economists have been reluctant to interpret these di(cid:27)erences as wage premiums or rents, since it has been di(cid:30)cult to know how unobserved worker quality di(cid:27)ers across plants. Recent studies, however, have documented some striking links between establishment level productivity andwagedispersion(Dunneetal.,2004;Faggio,Salvanes,andVanReenen,2010;Barthetal. 2016). Figure 1 plots results from Barth et al. (2016), showing remarkably similar trends in the dispersion of wages and productivityacrossbusinessestablishmentsintheUnitedStates. Takenatfacevalue,theparalleltrendsare consistent with a roughly unit elasticity of establishment wages with respect to productivity (see Barth et al.,2016,p. S71). Ofcourse,Figure1doesnottelluswhetherthecompositionoftheworkforceemployedat these establishments is changing over time. What appear to be more productive establishments may simply be establishments that hire more skilled workers, which is fully consistent with the standard labor market model in which all (cid:28)rms pay the same wages for any given worker. Amoredirectattackonthequestionofwhether(cid:28)rm-speci(cid:28)cproductivitydi(cid:27)erentialsfeedintodi(cid:27)erences inwagescomesfromtheempiricalliteratureonrent-sharing. AppendixTable1describes21recentstudiesin thisliterature. Thebasicideainthesepapersistorelatewagestosomemeasureofemployerpro(cid:28)tabilityor rents. Since di(cid:27)erentstudies use di(cid:27)erent measuresof rents, however, it isimportant to clarifyhow di(cid:27)erent choices a(cid:27)ect the estimated rent sharing elasticity that is reported in a given study. It is also important to clarify the role of heterogeneity in workers’ skills, which can confound estimation. Measuring rents For simplicity, we will work with a model with two types of labor, and ignore capital. De(cid:28)ne the pro(cid:28)ts earned by (cid:28)rm j as: π =VA −w L −w H , j j Lj j Hj j 4 where VA is value added, L and H represent employment of (cid:16)low skill(cid:17) and (cid:16)high skill(cid:17) labor at (cid:28)rm j, j j j and w and w denote the wages paid to the two types of labor. Assume that value added is produced Lj Hj by a linear technology: VA ≡R −M =P T ((1−θ)L +θH ) j j j j j j j where R represents sales, M represents the cost of materials and other intermediate inputs (e.g., energy), j j P is a potentially (cid:28)rm-speci(cid:28)c selling price index, T is an index of technical e(cid:30)ciency, and θ is an index j j of the relative e(cid:30)ciency of type H workers. Here P T represents total factor productivity (TFP ) which, j j j in the terminology of Foster, Haltiwanger and Syverson (2008), is also referred to as (cid:16)revenue productivity(cid:17) because it is the product of (cid:16)physical productivity(cid:17) T and product price P . We assume that TFP is the j j j driving source of variation that researchers are implicitly trying to model in the rent sharing literature. Letting N = L +H represent the total number of workers at the (cid:28)rm, value added per worker is j j j VAj = TFP q where q = (1−θ)Lj+θHj is the average quality of the (cid:28)rm’s workforce. The logarithm of Nj j j j Nj value added per worker is: (cid:18) (cid:19) VA ln j =lnTFP +lnq . N j j j Holding constant labor quality, value added per worker is therefore a valid index of TFP. When di(cid:27)erences inlaborqualityareignored(orimperfectlymeasured),however,therearetwoproblemswiththeuseofvalue added per worker as an index of productivity. The (cid:28)rst is that average wages at a (cid:28)rm will (in general) depend on average worker quality. A (cid:28)rm with higher quality workers will have higher value added per worker and higher average wages, leading to an upward bias in rent sharing models based on (cid:28)rm-wide average wages. The second is that value added per worker is more variable than TFP. This can lead to attenuation bias in speci(cid:28)cations that relate wages for a speci(cid:28)c subgroup of workers to value added per worker at the (cid:28)rm. Instead of using value added per worker, some studies use sales per worker as a measure of productivity. Assuming that intermediate inputs vary proportionally with revenues (i.e., M = m R ), sales per worker j j j can be decomposed as: (cid:18) (cid:19) R ln j =lnTFP +lnq −ln(1−m ), N j j j j which varies with TFP, labor quality, and the fraction of intermediate inputs in (cid:28)nal sales. Sales per worker has the same potential problems as value added per worker, plus the extra complication introduced by variation across (cid:28)rms in the fraction of intermediate inputs and services that are purchased rather than produced in-house. ManyrentsharingstudiesadoptthebargainingframeworklaidoutbydeMenil(1971),inwhichworkers 4 and the (cid:28)rm split a so-called (cid:16)quasi-rent(cid:17): Q ≡VA −wa L −wa H , j j Lj j Hj j where(cid:0)wa ,wa (cid:1)arethealternativewagesavailabletoworkersintheeventofabreakdowninnegotiations. Lj Hj Quasi-rent per worker is Qj = VAj −wa (1−s )−wa s where s = Hj gives the fraction of high-skilled Nj Nj Lj j Hj j j Nj 4Moststudiesintherecentliteratureignorethedeterminationofemploymentandalsoignorecapital. Svejnar(1986)presents an analysis that generalizes de Menil (1971) to allow for the optimal determination of employment. When the (cid:28)rm also has to select a capital stock prior to the determination of wages there is also a potential hold-up problem in the choice of capital (Grout,1984). Card,Devicienti,andMaida(2014)arguethatholdupdoesnotappeartobeamajorissueforItalian(cid:28)rms. 5 workers at the (cid:28)rm. The elasticity of quasi-rent per worker with respect to TFP is: ∂ln(NQjj) = VAj × ∂ln(VNAjj) +(cid:0)wa −wa (cid:1)wLajLj +wHajHj × ∂lnsj . ∂lnTFP Q ∂lnTFP Hj Lj Q ∂lnTFP j j j j j The (cid:28)rst term in this expression can be thought of as giving the (ceteris paribus) relative sensitivity of quasi-rents and value added to productivity shocks. Our reading of the literature suggests that the ratio of valueaddedtoquasi-rentsisaround2, sorentsharingstudiesthatusequasi-rentperworkerasthemeasure ofpro(cid:28)tabilityshouldtendto(cid:28)ndelasticitiesthatareaboutone-halfaslargeasstudiesthatusevalueadded per worker (or a direct measure of TFP). The second term in the expression captures skill upgrading which willtendtoaugmenttherelativesensitivityofquasi-rentstoproductivityshocksinproportiontothegapin alternativewagesbetweentypeH andLworkers. Thissuggestsboththatmultiplyingquasi-rentelasticities by 2 may yield a conservative adjustment and that value added based measures of productivity are less sensitive to neglected worker heterogeneity. A (cid:28)nal approach is to use pro(cid:28)ts per worker πj = VAj −w (1−s )−w s as the rent measure. An Nj Nj Lj j Hj j equivalent derivation yields: ∂ln(πj) VA ∂ln(VAj) w L +w H ∂lns Nj = j × Nj +(w −w ) Lj j Hj j × j . ∂lnTFP π ∂lnTFP Hj Lj π ∂lnTFP j j j j j Because pro(cid:28)ts are empirically not much di(cid:27)erent from quasi-rents, a reasonable adjustment factor is again around 2. As with quasi-rents, estimates based upon pro(cid:28)ts per worker are more sensitive to neglected worker heterogeneity than value added per worker. A Summary of the Rent Sharing Literature Table 1 synthesizes the estimated rent sharing elasticities from the 21 studies listed in Appendix Table 1, extractingoneortwopreferredspeci(cid:28)cationsfromeachstudyandadjustingallelasticitiestoanapproximate 5 value-added-per-worker basis. We divide the studies into three broad generations based on the level of aggregation in the measures of rents and wages. The(cid:28)rstgroupofstudies, whichincludestwoprominentpapersfromtheearly1990s, usesindustry-wide measures of pro(cid:28)tability and either individual-level or (cid:28)rm-wide average wages. The average rent sharing elasticity in this group is 0.16. A second generation of studies includes (cid:28)ve papers, mostly from the mid- 1990s, that use (cid:28)rm- or establishment-speci(cid:28)c measures of rents but measure average wages of employees at the workplace level. The average rent sharing elasticity in this group is 0.15, though there is a relatively wide range of variation across the studies. Given the likely problems caused by variation in worker quality, we suspect that most (cid:28)rst generation and second generation studies yield upward-biased estimates of the rent sharing elasticity. A third generation of studies consists of 15 relatively recent papers that study the link between (cid:28)rm- or establishment-speci(cid:28)c measures of rents and individual-speci(cid:28)c wages. Many of these studies attempt to control for variation in worker quality in some cases by studying the e(cid:27)ect of changes in measured rents on changes in wages. In this group the mean rent sharing elasticity is 0.08, though a few studies report rent sharing elasticities that are 0.05 or smaller. 5WeextractanIVestimatewhenoneisavailable,andconvertelasticitieswithrespecttopro(cid:28)tperworkerorquasi-rentper workertoavalueaddedperworkerbasisbymultiplyingby2. 6 Althoughsigni(cid:28)cantprogresshasbeenmadeinthisliterature,noneofthesestudiesisentirelysatisfactory. Veryfewstudieshaveclearexogenoussourcesofvariationinproductivity. Mostpapers(e.g.,Card,Cardoso, and Kline, 2016; Carlsson, Messina, and Skans, 2014; Guiso, Pistaferri, and Schivardi, 2005) rely on timing assumptionsaboutthestochasticprocessdrivingproductivitytojustifyusinglagsasinstruments. Anotable exception is Van Reenen (1996), who studies the e(cid:27)ects of major (cid:28)rm innovations on employee wages. He (cid:28)nds a very large rent sharing elasticity of 0.29 but this (cid:28)gure may be upward biased by skill upgrading on the part of innovative (cid:28)rms (cid:21) a concern he could not address with aggregate data. Other studies (e.g., Abowd and Lemieux, 1993; Card, Devicienti, and Maida, 2014) use industry level shocks as instruments for productivity. However, these instruments may violate the exclusion restriction if labor supply to the sector is inelastic since even fully competitive models predict that industry level shocks can yield equilibrium wage responses. Moreover, industry level shocks might yield general equilibrium responses that change worker’s outside options (Beaudry, Green, and Sand, 2012). Finally, with the move to matched employer-employee microdata, economists have had to contend with serious measurement error problems that emerge when constructing plant level productivity measures. It remains to be seen whether instrumenting using lags fully resolves these issues. Speci(cid:28)cation issues: a replication in Portuguese data To supplement the estimates in the literature and probe the impact of di(cid:27)erent design choices on the mag- nitude of the resulting elasticities we conducted our own analysis of rent sharing e(cid:27)ects using matched employer-employee data from Portugal. The wage data for this exercise come from Quadros de Pessoal (QP), a census of private sector employees conducted each October by the Portuguese Ministry of Employ- ment. Wemergethesedatato(cid:28)rm-speci(cid:28)c(cid:28)nancialinformationfromSABI(SistemadeAnalisisdeBalances 6 Ibericos) database, distributed by Bureau van Dijk. We select all male employees observed between 2005 and2009whoworkinagivenyearata(cid:28)rmintheSABIdatabasewithvalidinformationonsalesperworker for each year from 2004 to 2010, and on value added per worker for each year from 2005 to 2009. Panel A of Table 2 presents a series of speci(cid:28)cations in which we relate the log hourly wage observed for a worker in a given year (between 2005 and 2009) to mean log value added per worker or mean log sales per worker at his employer, averaged over the sample period. These are simple cross-sectional rent sharing models in which we use an averaged measure of rents at the employer to smooth out the transitory (cid:29)uctuations and measurement errors in the (cid:28)nancial data. In row 1 we present models using mean log value added per worker as the measure of rents; in row 2 we use mean log sales per worker; and in row 3 we use mean log value added per worker over the 2005-2009 period but instrument this with mean log sales per worker over a slightly wider window (2004-2010). For each choice we show a basic speci(cid:28)cation (with only basic human capital controls) in column 1, a richer speci(cid:28)cation with controls for major industry and city in column 2, and a full speci(cid:28)cation with dummies for 202 detailed industries and 29 regions in column 3. Twomainconclusionsemergefromthesesimplemodels. First,therentsharingelasticityissystematically 7 larger when rents are measured by value added per worker than by sales per worker. Second, the rent sharing elasticities from this approach are relatively high. Interestingly, the 0.20 to 0.30 range of estimates 6Businesses in Portugal are required to (cid:28)le income statements and balance sheet information annually with the Integrated SystemofCompanyAccounts. Thesereportsarepubliclyaccessibleandarecollectedby(cid:28)nancialservice(cid:28)rmsandassembled intotheSABIdatabase. WemergeSABIandQPusinginformationondetailedlocation,industry,(cid:28)rmcreationdate,shareholder equity,andannualsalesthatareavailableinbothdatasets. SeeCard,CardosoandKline(2016)formoreinformationonthe matchingprocess. 7Asimilar(cid:28)ndingisreportedbyCard,Devicienti,andMaida(2014)usingItaliandata. 7 is comparable to the range of the studies in the (cid:28)rst two panels of Table 1. Anobviousconcernwiththespeci(cid:28)cationsusedinPanelAisthattheyfailtofullycontrolforvariationin workerquality. Asdiscussedabove,thisislikelytoleadtoanupwardbiasintherelationshipbetweenwages and value added per worker. The speci(cid:28)cations in Panel B of Table 2 partially address this by examining the e(cid:27)ect of changes in (cid:28)rm speci(cid:28)c rents on changes in wages for workers who remain at the (cid:28)rm over the period from 2005 to 2009 (cid:21) a within-job or (cid:16)stayers(cid:17) design. We present three sets of speci(cid:28)cations of this design. The models in row 4 measure the change in rents by the change in log value added per worker. The models in row 5 use the change in log sales per worker. The models in row 6 use the change in value added per worker as the measure of rents, but instrument the change using the change in sales per worker over a 8 slightly wider interval to reduce the impact of measurement errors in value added. Relative to the cross-sectional models, the within-job models yield substantially smaller rent sharing elasticities. This di(cid:27)erence is likely due to some combination of unobserved worker quality in the cross- sectional designs (which leads to an upward bias in these speci(cid:28)cations), measurement error (which causes a larger downward bias in the stayer designs), and the fact that value added (cid:29)uctuations may include 9 a transitory component that (cid:28)rms insure workers against (Guiso, Pistaferri, and Schivardi, 2005). The discrepancy is particularly large for OLS models using sales per worker (compare row 2 and row 5 of Table 2): theelasticityforstayersisonlyaboutone-tenthaslargeasthecross-sectionalelasticity. Wesuspectthat measurement errors and transitory (cid:29)uctuations in annual sales are relatively large, and the impact of these factors is substantially magni(cid:28)ed in the within-job speci(cid:28)cations estimated by OLS. Given the presence of errors and idiosyncratic (cid:29)uctuations, we prefer the IV estimates in row 6, which point toward a rent sharing elasticity of approximately 0.06. An interesting feature of both the OLS and IV within-job estimates is that the addition of detailed industry controls reduces the rent sharing elasticity by 10-20 percent. Since these industry dummies absorb industry-wide productivity shocks that are shared by the (cid:28)rms in the same sector, we conclude that the rent sharing elasticity with respect to (cid:28)rm-speci(cid:28)c productivity shocks (which is estimated by the models in column3)issomewhatsmallerthantheelasticitywithrespecttosector-wideshocks(whichareincorporated in the elasticities in the models in column 1). If true more generally, this suggests that the use of industry- wide rent measures will lead to a somewhat larger rent sharing elasticities than would be obtained using (cid:28)rm-speci(cid:28)cproductivitymeasuresandcontrollingforindustry-widetrends. Asimilarconclusionisreported by Carlsson, Messina, and Skans (2014). Overall, we conclude from the studies in Table 1 and our own within-job estimates for Portugal in Table 2 that a plausible range for the elasticity of wages with respect to value added per worker is 0.05-0.15. Elasticities of this magnitude are clearly too low to rationalize the parallel trends of productivity dispersion andwagedispersionillustratedinFigure1. Whenwagescontainanemployer-speci(cid:28)crentpremium,however, wage inequality also depends on the degree of sorting of high- and low-skilled workers to more- and less- pro(cid:28)table employers, which as emphasized in Card, Heining and Kline (2013) can contribute to the trend in wage dispersion. 8Ifmeasurementerrorsinvalueaddedperworkerinyeartareuncorrelatedwitherrorsor(cid:29)uctuationsinsalesperworker inyearst+1andt−1,thentheuseofa(cid:16)bracketing(cid:17) instrumentwilleliminatethee(cid:27)ectofmeasurementerrorinvalueadded. Wesuspectthatthisisonlypartiallytrue,sotheIVapproachreducesbutdoesnotfullyeliminatethee(cid:27)ectoferrorsinvalue added. 9A third potential explanation is selection bias in the stayer models, induced by selecting a sample of job stayers. Results presentedinCard,CardosoandKline(2016,AppendixTableB10)suggestthisfactorisrelativelysmall. 8 2 Firm Switching Whiletherent-sharingliteraturedocumentsastrongcorrelationbetween(cid:28)rmpro(cid:28)tabilityandpay,aparallel literature (cid:28)nds that workers who move between (cid:28)rms (or establishments) experience wage gains or losses thatarehighlypredictable. Inthissectionweprovideanoverviewofrecent(cid:28)ndingsfromthisapproachand discuss some of the major issues in this literature. In the next section we discuss how the (cid:28)rm-speci(cid:28)c wage premiums estimated by studies of (cid:28)rm switching are related to measures of (cid:28)rm pro(cid:28)tability, providing a link between the rent sharing and (cid:28)rm switching literatures. AKM Models IntheirseminalstudyoftheFrenchlabormarket,AKMspeci(cid:28)edamodelforlogwagesthatincludesadditive e(cid:27)ects for workers and (cid:28)rms. Speci(cid:28)cally, their model for the log wage of person i in year t takes the form: lnw =α +ψ +X(cid:48) β+ε it i J(i,t) it it where X is a vector of time varying controls (e.g., year e(cid:27)ects and controls for experience), α is a (cid:16)person it i e(cid:27)ect(cid:17) capturing the (time-invariant) portable component of earnings ability, the {ψ }J are (cid:28)rm-speci(cid:28)c j j=1 relative pay premiums, J(i,t) is a function indicating the employer of worker i in year t, and ε is an it unobserved time-varying error capturing shocks to human capital, person-speci(cid:28)c job match e(cid:27)ects, and other factors. The innovation in AKM’s framework is the presence of the (cid:28)rm e(cid:27)ects, which allow for the possibilitythatsome(cid:28)rmspaysystematicallyhigherorlowerwagesthanother(cid:28)rms. Speci(cid:28)cally, theAKM model predicts that workers who move from (cid:28)rm k to (cid:28)rm j will experience an average wage change of ψ −ψ , while those who move in the opposite direction will experience an average change of ψ −ψ (cid:21) a j k k j striking (cid:16)symmetry(cid:17) prediction that we discuss in more detail below. Estimates of AKM style models on population level administrative datasets from a variety of di(cid:27)erent countries have found that the (cid:28)rm e(cid:27)ects in these models typically explain 15-25 percent of the variance of wages (cid:21) less than the person e(cid:27)ects, but enough to indicate that (cid:28)rm-speci(cid:28)c wage setting is important for 10 wage inequality. One problem with this assessment is that the person and (cid:28)rm e(cid:27)ects are estimated with considerableimprecision, whichmeanstheexplanatorypowerof(cid:28)rmswilltypicallybesomewhatoverstated (cid:21) a problem that was also recognized in the earlier literature on industry wage di(cid:27)erentials (Krueger and Summers, 1988). Andrews et al. (2008) provide an approach to dealing with this problem that we discuss in more detail below. If di(cid:27)erent (cid:28)rms pay di(cid:27)erent wage premiums, the pattern of sorting of workers to (cid:28)rms will also matter for overall wage inequality. In particular, the variance of log wages is: Var(lnw ) = Var(α )+Var(cid:0)ψ (cid:1)+Var(X(cid:48) β)+Var(ε ) (1) it i J(i,t) it it +2Cov(cid:0)α ,ψ (cid:1)+2Cov(α ,X(cid:48) β)+2Cov(cid:0)ψ ,X(cid:48) β(cid:1) i J(i,t) i it J(i,t) it which includes both the variance of the (cid:28)rm-speci(cid:28)c wage premiums and a term re(cid:29)ecting the covariance 10Forexample,Abowd,Lengermann,andMcKinney(2003)(cid:28)ndthat(cid:28)rme(cid:27)ectscomprise17%ofthevarianceofUSwages. Card, Heining, andKline(2013)(cid:28)ndthatestablishmente(cid:27)ectsexplainbetween18%and21%ofthevarianceofthewagesof German men depending on the time period studied. Card, Cardoso, and Kline (2016) (cid:28)nd that (cid:28)rm e(cid:27)ects explain 20% of the variance of hourly wages for Portuguese men and 17% of the variance for women. Macis and Schivardi (2016) (cid:28)nd that (cid:28)rme(cid:27)ectsexplain15%ofthewagevarianceofItalianmanufacturingworkers. Finally,LavettiandSchmutte(2016)(cid:28)ndthat establishmente(cid:27)ectsexplain21%ofthevarianceofwagesofworkersintheformalsectorinBrazil. 9