Trade Reforms, Foreign Competition, and Labor Market Adjustments in the U.S.

BoardofGovernorsoftheFederalReserveSystem InternationalFinanceDiscussionPapers Number1095 December2013 Trade Reforms, Foreign Competition, and Labor Market Adjustments in the U.S. IlleninO.Kondo NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Networkelectroniclibraryatwww.ssrn.com.

Trade Reforms, Foreign Competition, and Labor Market Adjustments in the U.S. Illenin O. Kondo† Federal Reserve Board December 24, 2013∗ Abstract Using data on trade-induced displacements, this paper documents that locations facing more foreign competition in the U.S. have: higher job destructionrates,lowerjobcreationrates,andtherebyloweremploymentrates. Incontrasttostandardtradetheory,amodelwithvariablemarkupsandheterogeneous segmented labor markets is consistent with these facts. Foreign competition has a correlated effect on job destruction and job creation precisely because the most vulnerable locations also have lower productivity. Following an unexpected trade liberalization with limited mobility, employment sharply falls in the worse hit locations while welfare and employment increaseintheaggregate. Keywords: foreigncompetition,nonemployment,jobflows,spatialheterogeneity JELclassification: F16,F66,G64 IthankCristinaArellano,TimKehoe,andFabrizioPerrifortheircontinued,patient,andilluminatingadvice. Iam deeplygratefultomydiscussantsGeorgeAlessandria,JoelRodrigue,andJohnStevensfortheirexcellentcomments.IbenefitedfrominvaluablecommentsfromDavidAutor,WyattBrooks,RafaelDix-Carneiro,AlessandraFogli,JonathanHeathcote,SewonHur,MorrisKleiner,BrianKovak,LoganLewis,JohnRogers,GiselaRua,EdouardSchaal,KjetilStoresletten, OlgaTimoshenko,Kei-MuYi,andvariousseminarparticipantsattheClevelandFed,MinneapolisFed,Board,Minnesota, Clemson,Drexel,Northwestern,NUS,American,Vigo,MidwestTradeatMSU,SEDinSeoul,RMEITinBanff,andU.S. InternationalTradeCommission. IthankRobertTamurafortheU.S.stateproductivitydata. Thedataandprogramsused inthepaperareavailableonline.IgratefullyacknowledgetheUniversityofMinnesotaDoctoralDissertationFellowshipfor financialsupport.TheviewsexpressedhereinarethoseoftheauthoraloneandnotnecessarilythoseoftheFederalReserve System.Allerrorsandshortcomingsareminealone.∗Firstversion:November15,2011.†Email:kondo@illenin.com.

1 Introduction In international trade, the reallocation of production factors like labor is essential for the gains from trade. The effects of trade reforms therefore depend crucially on how labor is reallocated within and across labor markets. Even though labor markets are certainly geographic in nature, geographically segmented labor markets with unemployment have not been modeled in standard trade theory. Recent evidence,however,suggeststhatthelabormarketeffectsoftradeareunevenacross locations. In particular, Autor et al. (2013b) find that U.S. localities with higher import penetration also experience lower employment. In the aggregate, Dutt et al. (2009) show that trade openness is associated with increased employment using cross-country panel data. Hence, the empirical evidence suggests substantial within-countrydifferencesacrosslocations. Using a novel dataset on trade-induced job losses in the U.S., this paper documents that: localities facing more foreign competition experience a higher job destructionratebutalsoalowerjobcreationrate,whilepopulationadjustmentsare sluggish. In the Ricardian tradition, a trade model with heterogeneous segmented labor markets, unemployment, and endogenous variable markups is introduced. Spatialheterogeneityinproductivityandlabormarketsegmentationarefundamentaltounderstandtheuneveneffectsofforeigncompetition. Finally,thequantitative macroeconomicimplicationsoftradeliberalizationandforeignproductivitygrowth areevaluatedusingthemodel. Empirically, it is not obvious how to measure job losses induced by foreign competition. Consider, for instance, a shipment of electronic parts imported from ChinaarrivingattheportofLosAngeles,CA.Becauselocationsandplantsareheterogeneous, it is not trivial to determine how American workers at different plants and different locations across the country are affected by these imports. For example, the standard import penetration proxy ignores cross-sectional productivity differenceswithinanindustryandsupply-chainlinkages. Accordingtotheseproxies, two locations equally concentrated in the same industry are considered equally affected even if they substantially differ in productivity or supply chains. This paper uses a novel state-level panel dataset with a direct measure of job losses due to 2

foreign competition. The dataset is constructed using petitions data from the U.S. Department of Labor Trade Adjustment Assistance (TAA) programs since 1983.1 These federal programs carefully investigate all the establishment-level petitions submittedonbehalfofworkersthatweredeemeddisplacedduetoimportcompetition. Figure1: NonemploymentandimportcompetitionintheU.S. WV LA MS NM KY AL NY CA AK MI AR TN SC FL AZ IL TX WAGA OK OH OR PA ME NJ MTID IN NC HI NV DE MAVUAT MO W R Y I MD CT CO VTKS WI NNDH IA SMDN NE .p.a.w fo .tcp ni srekrow deyolpmenon 54 04 53 03 52 Import competition and nonemployment across states 1983 − 2009 0 .25 .5 .75 1 1.25 1.5 Trade Adjustment Assistance (TAA) certified workers per thous. w.a.p. Sources: March CPS and US DoL TAA programs. w.a.p. = working age population. This dataset sheds new light on foreign competition and labor markets outcomes. Figure1illustratesapositiverelationshipbetweentrade-inducedjoblosses and the average nonemployment rate across states.2 In fact, one extra worker displaced due to foreign competition is associated with an overall employment reduction by two to three workers. The reduced employment rate is found to result from both a rise in job destruction and a fall in job creation, while population adjustments are sluggish. These results are robust to state indicators, time indicators, 1Yotov (2007) and Uysal and Yotov (2011) previously used the underlying TAA petition data forindustry-levelandfirm-levelmeasures. Recently,Monarchetal.(2013)followedthesamefirmlevel matching approach. A location-specific measure is used in this paper because of the salient geographicnatureoflabormarkets. Margalit(2011)concurrentlyconstructedasimilarmeasurein thepoliticalscienceliteraturetostudyanti-incumbentvotingbehavior. 2Thenonemploymentrateistheunemploymentrateplusthenonlaborforceparticipationrate. 3

time-region interaction terms, panel-level autocorrelation, heteroskedasticity and various controls including the widely used import penetration proxies and unionization. These facts are explained using a trade model with heterogeneous firms and heterogeneouslabormarkets. Attheheartofthemodel,therearesomefirmswhich compete monopolistically (see Dixit and Stiglitz (1977)) and others which headto-head with their foreign rivals (see Dornbusch et al. (1977) and Bernard et al. (2003)).3 Inaddingsegmentedlocations,themaingoalistohavevariationinexposureto foreigncompetition. IntheRicardiantradition,thisisaccomplishedviaexogenous firm productivity differences across locations: locations differ in the productivity of their firms.4 Local nonemployment is obtained using random Leontief matching within each labor market and collective Nash bargaining. Workers direct their search and are allocated such that they are indifferent among these locations ex ante.5 Followinganunexpectedtradereform,consistentwiththedata,workerscan switchfirmswithintheirhomelabormarketsbuttheycannotchangelocation.6 Both cross-sectional productivity differences and variable markups are crucial toexplainthecorrelationsbetweentrade,andnonemploymentacrosslocations. Afteratradereform,firmsinthelessproductiveareasfacefiercerforeigncompetition andhavemorejoblossesbecausemanyoftheirlocalfirmsshutdown. Thesefirms shut down because their markups are already compressed and they cannot further reducethemtostaveoffcompetition. Fewerjobsarecreatedintheleastproductive areas because their firms are less likely to outcompete foreign rivals and become 3In the standard Melitz (2003) model, a model-based TAA-measure of foreign competition is zerosincefirmsdonotfacehead-to-headdirectcompetition: TAAinvestigatorswouldbeunableto findevidenceoftrade-inducedforeigncompetitionasacauseoflayoffs. 4This paper considers exogenous firm productivity differences for simplicity. See Glaeser and Maré(2001)andCombesetal.(2008)onagglomerationandworkerselectionacrosscities. 5This indifference condition is reminiscent of Lewis (1954), Harris and Todaro (1970), spatial equilibriummodelsfollowingRoback(1982),anddirectedsearchmodelssuchasLucasandPrescott (1974)andAlvarezandShimer(2011). 6Kennan and Walker (2011), Artuç et al. (2010), Dix-Carneiro (2013) estimate substantial interim switching and mobility costs. These findings are consistent with the sluggish population adjustments found in this paper, Autor et al. (2013b), Menezes-Filho and Muendler (2011), and Topalova (2007). The assumption of limited ex post mobility made here follows Helpman and Itskhoki(2010). 4

new exporters. Hence, the most vulnerable locations have both a higher job destructionrateandalowerjobcreationrate. In this model, more productive cities have larger firms, higher population, pay higher wages, and experience higher unemployment rates in the long run. In the long run, the least productive areas simply become ghost towns as their population vanish. In the medium run, when workers can switch employers but not locations, unemployment rates sharply rise in the least productive locations. The productivity channel is further corroborated using state productivity data from Turner et al. (2007)andTurneretal.(2008). Trade liberalization yields aggregate welfare gains along with large reductions in employment rate and earnings in the badly hit labor markets, when population adjustments are sluggish. This is because the ex ante spatial equilibrium ensures that most firms can tap into their local unemployment pool. However, these aggregatewelfaregainsdonotholdfollowinganunexpectedriseinforeignproductivity becauseeventhemostproductivelocationsareadverselyaffected. Thispapercontributestoagrowingliteratureatthenexusofinternationaltrade and labor economics. Topel (1986) and Blanchard and Katz (1992) made influential contributions on differential labor market dynamics across locations and workers. Topalova (2007) and Kovak (2013) study the impact of trade liberalization on migration and wages in India and Brazil respectively.7 Autor et al. (2013b) and Ebenstein et al. (forthcoming) conduct a thorough analysis of U.S. labor markets and trade. They document the worsening of labor market outcomes in localities andoccupationsthataremoreexposedtoimportcompetitionduetotheirindustrial composition.8 This paper extends these findings using geographic data on tradeinduceddisplacementsandjobflowsintheU.S. Davidsonetal.(1999)madeaseminalcontributionbyconsideringlaborsearch and matching frictions in international trade theory.9 Kambourov (2009), Artuç et 7Hasanetal.(2012)alsoinvestigatetradeprotectionandunemploymentacrossstatesinIndia. 8ArelatedliteratureinvestigatesthedeclineofAmericanmanufacturing. Alderetal.(2012)and Yoon(2012)considertheroleofunionizationandbiasedtechnicalchangeinthedeclineoftheRust Belt. SeeHolmesandSchmitz(2009)forareviewoftheliteratureoncompetitionandproductivity. PierceandSchott(2012)alsodocumentthattheeliminationoftradepolicyuncertaintywithChina in2000contributedtothesubsequentswiftdeclineofAmericanmanufacturing. 9Janiak(2006),EggerandKreickemeier(2009),Duttetal.(2009),MitraandRanjan(2010),and 5

al. (2010), Ritter (2012), Cos¸ar (2013), and Dix-Carneiro (2013) recently studied transition paths in dynamic models of trade and unemployment with sectoral and humancapitalheterogeneity. ThesemodelsassumethatautoworkersattheGeneral MotorsfactoriesinFlint,MIareinthesamelabormarketastheautoworkersatthe Ford factories in Louisville, KY. This paper introduces a trade and unemployment model with cross sectional productivity differences and geographically segmented labormarkets. This paper is closely related to Beaudry et al. (2012) who estimate a spatial equilibrium model with unemployment in which locations vary in industrial composition. Thispaperfeaturesatrademodelinwhichproductivitydifferencesacross locations and endogenous variable markups are crucial to account for the uneven effectsofforeigncompetitiononunemploymentacrosslabormarkets.10 Thispaperisstructuredasfollows. Section2empiricallyanalyzesforeigncompetitionandlabormarketoutcomesacrosstheUnitedStatesusingtheTradeAdjustment Assistance (TAA) petitions data. Section 3 develops a baseline trade and unemployment model with endogenous variable markups and heterogeneous segmented labor markets. Section 4 conducts two experiments: an unexpected trade reform as well as an unexpected increase in foreign productivity when mobility is limited. Section5concludes. 2 Evidence This section presents the main empirical findings on foreign competition and labor marketoutcomesacrosslocations. Thedatasetisbasedonestablishment-levelpetitionsfromtheU.S.TradeAdjustmentAssistance(TAA),individual-leveldatafrom Current Population Survey (CPS), job flows data in U.S. Census Business DynamicsStatistics(BDS),housingstartsfromU.S.CensusNewResidentialConstruction (NRC) database, and U.S. imports data combined with U.S. Census County Business Patterns (CBP). The data is aggregated yearly at the state level from 1983 to Felbermayretal.(2010),andHelpmanandItskhoki(2010)amongotherssubsequentlyintroduced nonemploymentinthebaselinemodelsofinternationaltrade. 10SeeNotowidigdo(2011)andMoretti(2011)forstudiesontheeffectsoflocalshocksonwages andlandpricesusingthespatialequilibriumframeworkofRoback(1982). 6

2009intoastate-levelpaneldataset.11 2.1 The Trade Adjustment Assistance (TAA) Petitions Data Instated in its current form as part of the Trade Act of 1974, the Trade Adjustment Assistance (TAA) for workers is a federal program that aims to support the professional transition of workers displaced due to foreign trade. Each petition includes information on the location of the establishment, the numbers of workers affected, thecertificationdecision,andthedateofimpact.12 Firms, unions, state unemployment agencies, or groups of workers can file a petition on behalf of a subset of workers at a given establishment. To establish the eligibility of the petitioning workers, federal investigators at the Department of Labor seek evidence that these workers were separated because of (a) import competition that led to decline in sales or production, (b) a shift in production to another country with which the United States has a trade agreement, or (c) due to loss of business as an upstream supplier or downstream producer for another producer that is TAA-certified. Certified workers are eligible to receive benefits suchastraining,incomesupport,jobsearchallowances,relocationallowances,and healthcareassistanceforuptotwoyears.13 Foreachpetition,federalinvestigatorsissuea“confidentialdatarequest”(CDR) for data such as sales history, sales of import-competing products, major declining customersandunsuccessfulbids. TheTradeAdjustmentAssistance(TAA)investigatorsalso havelegal powertoissue subpoenasif thecompanydoes notcomply to thedatarequest.14 2.2 Measuring Foreign Competition For every year t = 1983...2009 and for every state i in the U.S., import competition is measured as the ratio of all workers newly certified for Trade Adjustment 11Seeappendixandonlineprogramsfordetailsonthedataset. 12Allindividualpetitionsarepubliclyavailableatwww.doleta.gov. 13SeeDeckerandCorson(1994)andMagee(2001)andPark(2012)forpapersusingsurveydata onworkersreceivingTAAbenefitstoevaluatetheseprograms. 14AsampleCDRformisavailableonlineatwww.illenin.com/research/taa_cdr_article.pdf. 7

Assistance(TAA)relativetotheworkingagepopulation(w.a.p.): ∑ TAAcertifiedworkersi j,t TAAforeigncompetitioni ≡ plants j∈i t workingagepopulationi t Table 1 and Figure 1 show the typical order of magnitude of this TAA-based measure across states between 1983 and 2009. In 2009, a record 330,906 workers werecertifiedforTradeAdjustmentAssistance(TAA)acrossallstates.15 Table1: Summarystatistics(1983-2009) p10 p25 p50 p75 p90 TAAcertifiedworkers 0.03 0.17 0.43 0.88 1.64 (perthousandworkingagepopulation) TAApetitioningworkers 0.11 0.39 0.80 1.43 2.38 (perthousandworkingagepopulation) UnemployedminusUSaverage -2.24 -1.33 -0.35 0.79 1.99 (percentworkingagepopulation) In contrast, the standard import penetration proxies implicitly assume that two locations producing toys in the U.S. are equally impacted by the imports of toys from China. For example, the measure used in Autor et al. (2013b) - henceforth ADH-isaweightedaverageofnationalimportsusingthelocalindustrymix: employmentk ∆importsk ADHimportpenetrationi ≡ ∑ i,t ∗ US,t t employment employmentk industriesk i,t US,t (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) localindustrialmix nationalimports Figure 2 clearly illustrates a weak positive correlation between the standard import penetration proxy and the TAA-based measure, using within-year deciles across states of each variable. Unlike import penetration proxies, the TAA-based measureisdirectanditcancapturecross-sectionalproductivitydifferencesbetween ahypotheticalGMautocityandahypotheticalFordautocity.16 15Seetheappendixformapsandmoresummarytablesandfigures. 16TheweakcorrelationsuggeststhatadecompositionofTAA-basedjoblossesinindustry,loca- 8

Figure2: State-levelimportpenetrationandTAA-basedmeasure erusaem HDA gnisu eliced .gva 01 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 TAA measure decile 2.3 Foreign Competition and Labor Market Outcomes Theregressionbelowisestimatedtoassesstherelationbetweenimportcompetition andlabormarketoutcomesacrosstheU.S.: labormarketoutcomei =α + β × TAAforeigncompetitioni +γ·Zi + εi t t t t (cid:124) (cid:123)(cid:122) (cid:125) shareofnewlyTAAcertifiedworkers The variable “TAAforeigncompetitioni” is the share of working age workers cert tified by the Trade Adjustment Assistance (TAA) in state i during year t. The variables used as “labormarketoutcomei” are : (a) the share “notemployedi” of t t working age population workers who are not employed in state i as of the March CPS of the following year t+1; (b) the rate “jobdestructionratei” at which existing t jobsweredestroyedinstateiduringyeart;(c)therate“jobcreationratei”atwhich t newjobswerecreatedinstateiduringyeart;(d)theshare“pop. sharei”ofnational t tion, and firm effects using the ADH import penetration proxy at the commuting zone level is an importantquestion. Itisbeyondthescopeofthispaperandthereforeexploredseparately. 9

workingagepopulationresidinginstateiasof theMarchCPSint+1.17 ThesetofcontrolsZi includesthelagged“labormarketoutcomei ”,thelagged t t-1 “foreigncompetitioni ”,theshareofworkingageworkersdeniedbytheTradeAdt-1 justment Assistance (TAA), state indicators, year indicators, year and U.S. Census region indicators, the state log income per working age population, the state share of U.S. working age population. Additional controls include the state import penetration, the state unionization rate, the state Trade Adjustment Assistance (TAA) approval rate, the state new housing units started per working age population. The baseline sample is a balanced panel of 50 states spanning 27 years from 1983 and 2009. The estimation results are reported in Table 2. Increased foreign competition is correlated with reduced employment through higher job destruction and lower job creation, while population dynamics are sluggish.18 In fact, an extra worker separated (or at risk of being separated) due to foreign competition is associated with the overall employment falling by two to three extra workers relative to other locations. Naturally, one would be concerned about the ability of the Trade Adjustment Assistance (TAA) federal investigators to identify trade-induced displaced. First, if the TAA investigators were just using industry-level data, the import penetration proxy should be strongly correlated with the TAA measure. This does not appear to be the case as reported in Table 2 and in Figure 2. Furthermore, denied applicationsorapprovalratesarenotassociatedwithworseningorimprovinglabormarket conditions.19 ThefindingsreporteddonotholdwhentheimportpenetrationproxyisusedinsteadofthedirectTAAmeasure,asshowninthespecification(a2)ofTable2. The 17As found in the existing literature, the relationship with wages is not significant. Estimation resultsforwagesandotherlabormarketoutcomesarereportedintheappendix. 18The sluggish population dynamics echo the findings of Autor et al. (2013b) and Topalova (2007). Kleinetal.(2003)andMoseretal.(2010)alsodocumentsimilareffectsofexchangerate fluctuationsonjobflowsintheU.S.andinGermanyrespectively. 19The Reagan administration drastically revamped the TAA certification process (see Rosen (2006) ). That is the reason why the sample does not include the pre-Reagan reform era. Indeed, before1983,thedeniedcasesareassociatedwithworseninglabormarketsandcertifiedcaseshadan insignificanteffect. Incontrast, thefindingsreportedhereholdevenifsampleexcludestheperiod afterChina’saccessiontotheW.T.O.ortheGreatRecession. 10

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findings for the direct measure based on the Trade Adjustment Assistance (TAA) still hold after controlling for the import penetration proxy as shown in the specifications (a3), (b3), (c3), and (d3) of Table 2.20 The results are robust to controlling for unionization rates as well as local spillovers in the non-tradable sector using housingstartsdata. These findings reported above pose a challenge to existing models. Certainly, models with frictionless or centralized labor markets are not equipped to replicate these results and address related questions: why does foreign competition have a correlated effect of both job destruction and job creation? what are the consequences of the limited geographical mobility of workers in response to trade shocks? what are the welfare effects of the uneven effect of foreign competition across locations? These questions are addressed using a Ricardian model with heterogeneousfirms,variablemarkups,andsegmentedlabormarkets. 3 Trade Model with Segmented Labor Markets 3.1 Environment Thebaselineenvironmentconsistsoftwosymmetriccountries j=0,1populatedby a unit measure of families and firms.21 Each family is composed of L individuals allocated across a continuum of locations in their country. These locations vary in the exogenous productivity of their local firms. Within a given location, local firms vary in the degree of foreign competition they face. Local nonemployment is obtained using random Leontief matching of workers to firms and collective Nash bargaining. The population distribution is determined by the uncoordinated search forworkacrosslocations. Thereareinternationalicebergtransportationcostsτ.22 20Asdiscussedintheprevioussubsection,theimportpenetrationproxiesignoredifferencesacross firmsandlocationswithsimilarindustrialcomposition. Moreover,importpenetrationproxiessuffer fromaninherentdegrees-of-freedomproblem. ThisproblemissolvedwithfinergeographicgranularityasdiscussedinAutoretal.(2013b). Incontrast,theestimationwiththeTAAmeasureisdone atthestatelevelwithregion-timefixedeffects. 21Thissymmetryassumptionisrelaxedlater. 22This structure is similar to Alvarez and Shimer (2011) who consider a model with directed searchacrossmanyislandsandrandommatchingwithineachisland. 12

Preferences Following Helpman and Itskhoki (2010), each family has quasi-linear preferences over its homogeneous good consumption q and its composite good consumption 0 Q:U =q + 1Qη,whereQisaSpence-Dixit-Stiglitzaggregatoroverdifferentiated 0 η goods: ˆ (cid:18) (cid:19) σ σ−1 σ−1 Q≡ q(ν) σ dν M ∪H∪M 0 1 and0<η < σ−1 <1. σ Figure3: Asimpleoverviewofthemodel country 0 M 0 USA H cowboy hats widgets widgets foie gras H M 1 country 1 France The differentiated goods have two possible types, monopolistic or head-to-head, as illustrated in Figure 3. The monopolistic goods (“M−goods”) have no foreign counterpart and the producers of these goods are monopolistic competitors (e.g. American cowboy hat varieties and French foie gras varieties in the illustration). The head-to-head (“H−goods”) each have a domestic counterpart and a foreign counterpartthatareperfectsubstitutes(e.g. widgetvarietiesintheillustration). Taking the homogeneous good as numeraire, a household in country j faces a (cid:16) ´ (cid:17) 1 composite good price index P defined as: P ≡ p (ν)1−σdν 1−σ . A j j M ∪H∪M j 0 1 13

householdwithtotalincomeR fromearningsandprofitsoptimallychooses: j −ρ−η − η q (ν)= Q 1−ρ p (ν) −σ ∀ν and q = R −P 1−η =R −Q η j j j 0,j j j j j whereρ ≡ σ−1 ≡ 1. σ µ TechnologyandCompetition EachM−typeproducerisamonopolisticcompetitor. EachH−typeproducercompetesviasimultaneouspricesettingagainstauniqueforeigncounterpart.23 A model that includes only monopolistic competitors without direct foreign competitionwillfailtomatchthedatasimplybecauseitcannotgeneratejoblosses duetoforeigncompetition. Amodelwithoutmonopolisticcompetitors,ontheother hand, may overstate the effects of foreign competition on job losses and understate thegainsfromincreasedvarieties. An exogenous measure H of firms can produce (head-to-head) H−goods and the remaining measure M can produce (monopolistic) M−goods. There is a fixed unit measure of differentiated varieties (and firms) in each country. There are no fixed costs of entry or operation. The model is therefore a hybrid setup combining Chamberlinianmonopolisticcompetitionwithhead-to-headimperfectcompetition. Thesetwomodesofcompetitionarespecialcases(H=0andH=1respectively).24 Eachfirmφ isexogenouslyassigneditsvarietyν(φ)∈M ∪H∪M anditspro- 0 1 ductivity z(φ). Each head-to-head producer also has a randomly assigned foreign competitor. Each firm φ can produce its differentiated good ν(φ) using a linear 23This form of head-to-head competition is similar to Bernard et al. (2003) with the distinction that there is no domestic head-to-head competitor here. See Caliendo et al. (2013) for a closed economymodelwithmultiplelocationsanddomesticcompetition. 24Thecombinationofbothmonopolisticcompetitionandhead-to-headcompetitionresemblesthe model of mass production plants and boutique shops used by Holmes and Stevens (2010) in their studyofplantsizedistributionwithanapplicationtothetradeinwoodfurniture.Here,monopolistic firmsarenotnecessarilysmallernonexportingfirms.AlsoFreemanandKleiner(2005)showintheir studyofthe“lastAmericanshoemanufacturers”thatproductdifferentiationandindustrialrelations areadditionalchannelsofadjustment. StrategicproductdifferentiationwillmakeM/H endogenous. Thisexogenousmargindidnotsignificantlyaltertheresultsfromthismodelwhenthedifferentiation costsareproportionaltomonopolyprofits. 14

productiontechnology: y(φ)=z(φ) · (cid:96) where (cid:96) is the labor input and y is the output. The productivity z(φ) is assumed to be drawn randomly from a Pareto distribution with lower bound A ≡ 1 and shape parameters: Pr(z(φ)≤z)=1−z−s ≡F(z). Thefirmsinthehomogeneousgoodsectorarehomogeneous,competeperfectly andhaveasimplelineartechnology: y =(cid:96). 0 HeterogeneousLocationsandSegmentedLaborMarkets The main goal in defining locations is to have variations in foreign competition. In theRicardiantradition,alabormarketisdefinedsuchthatallthefirmsinthatlocationsharethesameproductivitylevel(z)andthesametype(M orH).25 Therefore, in each country, there are many H−type (head-to-head) towns and many M−type (monopolist)towns,inadditiontohomogeneousgoodtowns.26 There is still heterogeneity across firms within each H−type (head-to-head) town even though they share the same productivity. Figure 4 provides an illustration of these differences across and within locations. Firms collocated in the same H−type (head-to-head) town share the same productivity. Yet, they differ in their varieties and in the productivity of their head-to-head foreign competitors. Within an M−type (monopolist) town, firms share the same productivity and they each producedifferentvarieties.27 The economy is composed of a continuum of labor markets across which families assign their workers. Within each local labor market, workers are randomly matched with vacancies based on a Leontief matching function: firms fill all their vacanciesaslongastherearemoreworkerslookingforjobsthanvacancies.28 25Thestarkassumptiononcommonproductivitywithinalocationismadetotractablyhighlight the role of variable markups. At the other extreme, if locations did not vary in productivity, this modelwouldbeunabletoaddressthenonemploymenteffectsoftradeacrosslocations. 26Sincethehomogenousnumerairegoodisnottraded,itissimplyassignedaseparatetown. 27For simplicity, one can think of Texas towns and Pennsylvania towns making cowboy hats and widgets respectively. Certainly, a location maps more realistically to a labor market in the geography-industry-occupation-skillspace. 28TheLeontiefmatchingfunctionm(u.v)=min(u,v)hasnocongestionexternalities. 15

Figure4: Asimpleillustrationoflocations brown US widget 11 FR widget 11 (low) (med) (high) US widget 37 FR widget 37 (med) (low) black (low) low high prod. z med high prod. z cowboy hats locations widgets locations M country 0 H 0 USA At each plant, the workers bargain collectively with the firm over wages and productiondecisions.29 Theworkerscollectivelyhavebargainingpowerλ.30 Firms have to pay a hiring cost γ per hire. The union’s threat point is defined by a home production technology yielding b units of the numeraire good. It is convenient to interchangeablyidentifyaplantwithproductivityzby: c≡(γ+b)/z. Finally,thehomogeneoussectorissubjecttonohiringormatchingfrictions. 3.2 Characterization TheMonopolist(M−type)FirmProblem Consider a monopolist firm in country j with productivity z and supplying country j(cid:48). With(cid:96) j workers,thefirm-unionmatchgeneratesthefollowingsurplus: j(cid:48) 29Due to variable markups, plant-level bargaining by destination market makes the bargaining outcomemoretractable. 30Nash-bargaining provides a simple and tractable baseline to highlight how nonemployment is determined. Inthismodel,variablemarkupsarekeyforthecross-sectionaldistributionofemploymentandwages. Thealternativemultilateralbargainingï¿œlaStoleandZwiebel(1996)hasbeen usedinFelbermayretal.(2010)andHelpmanandItskhoki(2010). 16

(cid:32) (cid:33)1 (cid:16) (cid:17) 1 µ j j −(ρ−η) j j S z,(cid:96) =Q z(cid:96) −(b+γ)(cid:96) j(cid:48) j(cid:48) j(cid:48) j j(cid:48) j(cid:48) τ j(cid:48) (cid:124) (cid:123)(cid:122) (cid:125) (cid:16) (cid:17) revenuesRj z,(cid:96)j j(cid:48) j(cid:48) (cid:16) (cid:17) (cid:16) (cid:17) j j j j j j j The firm’s profit from this plant is: π z,(cid:96) =R z,(cid:96) −γ(cid:96) −w (z)(cid:96) j(cid:48) j(cid:48) j(cid:48) j(cid:48) j(cid:48) j(cid:48) j(cid:48) j j where w (z) is the wage paid to the workers. The wages w (z) and the plant size j(cid:48) j(cid:48) (cid:96) j aredeterminedthroughNash-bargainingwiththeworkers’unionbysolving:31 j(cid:48)  (cid:32) (cid:33)1 1−λ 1 µ maxQ −(ρ−η) z(cid:96) −γ(cid:96)−w(cid:96) · [(w−b)(cid:96)]λ j(cid:48) j w,(cid:96) τ j(cid:48) Since all costs are variable, the optimal outcome splits the maximal net surplus accordingto thebargaining power. Hence, thefirm-union producesthe monopolisticoutputandproportionallysplitsthenetsurplusgenerated. Thatis: j j p (c) =µτ c j(cid:48) j(cid:48) j w (c)−b =λ(µ−1)(γ+b) ≡w −b j(cid:48) M (cid:34) (cid:35)σ−1 (cid:96) j (c) =Q −ρ 1− − ρ η (cid:104) µ (γ+b) (cid:105)−σ (γ+b) ≡µ−σ(cid:96) j (c) j(cid:48) j(cid:48) j j(cid:48) τ c j(cid:48) j j j where τ c ≡ τ (γ+b)/z is the firm-union unit cost and (cid:96) (c) is the size correj(cid:48) j(cid:48) j(cid:48) spondingtothemarginalcostpricing(zeroprofits). TheM−type(monopolist)producersthereforechoosethestandardmarkuppricing rule that equalizes the marginal revenue and the marginal cost. Although more productivefirmsarelarger,itisimportanttonotethatthewagesareindependentof the firm productivity. This has been a standard result in environments with power revenuefunctions andlineartechnology.32 Thisproperty thatwagesdo notdepend on firm productivity implies that the M−type (monopolist) towns the same wage 31Forthemonopolist,castingtheproblemintermsofsize((cid:96))orpricesyieldthesameoutcome. 32SeeforexampleFelbermayretal.(2010)andHelpmanandItskhoki(2010). 17

and therefore the same equilibrium employment rate. Each worker extracts a share λ of the net markup (µ−1). Also, since there are no fixed cost of exporting, all M−typeproducersexportinthismodel. EmploymentRates Finally,giventherandomLeontiefmatching,anM−typelabormarketoffirmswith productivityzhasanemploymentratee (z): M j ∑ j(cid:48)=0,1 (cid:96) j(cid:48) (z) e (z)= M L (z) M where L (z) is the endogenous population of workers available in that town. The M expected earnings per worker W (z) in the town of an M−type producer with M productivityzthereforesatisfy: W (z)≡w ·e (z). M M M TheHead-to-Head(H−type)FirmProblem j Considerahead-to-headfirmincountry j thatishiring(cid:96) workerstosupplycounj(cid:48) try j(cid:48). Letzbethefirm’sproductivityandz˜beitsforeigncompetitor’sproductivity. Unlike a monopolistic firm, the firm has to set its price above its competitor’s zero profitprice(seeBernardetal.(2003)). Thefirmthereforesolves: (cid:34) (cid:18) (cid:19)1 (cid:35)1−λ max Q −(ρ−η) 1 z(cid:96) µ −γ(cid:96)−w(cid:96) · [(w−b)(cid:96)]λ w,(cid:96) j(cid:48) τ j j (cid:48) s.t. j 1−j p (z,(cid:96))≤ p (z˜) j(cid:48) j(cid:48) j π (z,(cid:96))≥0 j(cid:48) 1−j 1−j where p (z˜)=τ (γ+b)/z˜istheforeigncompetitor’smarginalcosttosupply j(cid:48) j(cid:48) country j(cid:48). Due to head-to-head competition, this H−type producer from country j supplies a country j(cid:48) if and only if it is the lowest unit cost supplier for that market: τ j (γ+b)/z< p 1−j (z˜). Conditional on supplying the market j(cid:48), the producer may j(cid:48) j(cid:48) 18

eitherbeatthecorner(constrained)orchoosetheunconstrainedmonopolistic(constantmarkup)price: (cid:110) (cid:111) j 1−j j p (c,c˜)=min τ c˜ , µτ c j(cid:48) j(cid:48) j(cid:48) (cid:124) (cid:123)(cid:122) (cid:125) µ j(c,c˜)×τ j c j(cid:48) j(cid:48) j The threat of being undercut induces variable markups µ (c,c˜)∈[1,µ] as the j(cid:48) firm seeks to maximize the net surplus shared with its workers. Less productive firms are more likely to have lower markups as they are more likely to face more productivecompetitors. Giventhenetsurplussharingoutcome,wagesarecommensuratetothevariable markup: (cid:16) (cid:17) j j w (c,c˜)−b=λ µ (c,c˜)−1 (γ+b) j(cid:48) j(cid:48) Therefore, wages are variable in contrast to the case of the monopolistic firms that do not face head-to-head competition. Less productive firms are also more likely to pay lower wages due to lower markups. Also, the more productive the competitor faced, the larger the firm because the lower markup translates into a higherdemandandlowermarkups: j (cid:104) j (cid:105)−σ j (cid:96) (c,c˜)= µ (c,c˜) ×(cid:96) (c) j(cid:48) j(cid:48) j(cid:48) The effect of the head-to-head competition on the firm behavior also depends on the level of frictions to international trade. In fact, as the tariff τ goes to infinity (autarky),theH−typeproducersareallinoperationandtheyallchargetheunconj strained monopolistic price: limµ (c,c˜) = µ. On the other hand, when trade is j τ→∞ frictionless,onlysomefirmschargethemonopolisticprice.33 Themodelthereforegeneratesrichpricing-to-marketmarkupsasshowninFigure5.34 Apoint(c,c˜)representsahead-to-headfirmlocatedinatownofproductiv- 33When µ <τ2,inparticularinautarky,tariff-protectedfirmspriceasmonopolistseventhough theydonotexport. 34Figure5illustratesthecasewhentradebarriersarelowenough(τ2<µ). 19

Figure5: Variablemarkupsacrossfirmsandlocations (cid:2020) (cid:2028)(cid:2020)(cid:1855) (cid:1855) (cid:2028)(cid:1855) (cid:2028) γ+b 1 (cid:1855) (cid:2028) FR everywhere (cid:2011)+(cid:1854) and US firms shutdown (cid:1855)= (cid:1878) γ+b erehwyreve tsiloponom SU )(cid:1855)(cid:2020)(cid:2028):(cid:1844)(cid:1832) |(cid:1855)(cid:2020) :(cid:1845)(cid:1847)( (cid:2011)+(cid:1854) (cid:1855)̃= (cid:1878)̃ unit cost (cid:1855)(location) of head-to-head firms in the U.S. )noitacol( (cid:1855)̃ tsoc tinu ecnarF ni smrif daeh-ot-daeh fo ity z=(γ+b)/c and facing a competitor with productivity z˜=(γ+b)/c˜. Hence, averticallinerepresentsahead-to-headtownofproductivityz. These variable markups are also the reason why productivity differences yield differences in foreign competition across locations: in the more productive locations, more firms outcompete their foreign competitors relative to the less productive locations. Hence, in less productive locations, more firms do not produce but shutdown altogether (see blue solid diamond region in Figure 5). Also, firms from lessproductivelocationsaremorelikelytoproducewithoutexporting. Thisregion is akin to the Ricardian non-tradable region and yields an extensive margin of new exporterswhentradebarriersfall(seegreengriddedregioninFigure5). Themodelalsogeneratesaregionofinternational“dumping”: firmschargethe 20

monopolistic price at home and the competitor’s marginal cost abroad (see solid colored region in Figure 5). This outcome could suggest “dumping” since the ratio of prices at home and abroad is larger than the iceberg transportation costs. This “dumping”regiononlydisappearsinthelimitcaseoffrictionlesstrade.35 EmploymentRates Basedontheseresults,atownofH−type(head-to-head)producerswithproductivityzhasanemploymentratee (z)satisfying: H ˆ ∑ (cid:96) j (z,z˜)dF (z˜) j(cid:48) H j(cid:48)=0,1 e (z)= H L (z) H j whereL (z)istheendogenouspopulationofthetownand(cid:96) (z,z˜)=0ifaproducer H j(cid:48) isoutcompeted. TheexpectedearningsperworkerW (z)inthattownsatisfy: H ˆ ∑ ω j (z,z˜)·(cid:96) j (z,z˜)dF (z˜) j(cid:48) j(cid:48) H j(cid:48)=0,1 W (z)≡ H L (z) H LaborAllocationacrossLocations Workers are allocated knowing the tariff, the town’s type (monopolistic or headto-head competition), and the local productivity. So, each family knows the distribution of wages and nonemployment rates across towns. Each family therefore allocates{L ,L (z),L (z)} suchthat: 0 M H z≥A ´ ´ L =L + L (z)dF (z)+ L (z)dF (z) 0 M M H H Inequilibrium,familiesmustbeindifferentacrosslocationstosendworkers. 35Astradebarriersfall,someofthefirmsinthis“dumping”regionbecomemonopolisticcompetitorsbothathomeandabroad:tradebarrierswerehurtingtheircompetitiveedgeabroad.Otherfirms inthisregionnowhavetochargethecompetitor’smarginalcostathomeinsteadthemonopolistic markup. 21

MarketClearing The market clearing condition for each differentiated good is trivially satisfied. Since hiring costs are paid in units of the homogeneous good, its market clearing conditionis: ´ ˜ (cid:16) (cid:17) j j L 0 =q 0 +γ· ∑ j(cid:48)=0,1 (cid:96) j(cid:48) (z)dF M (z)+ ∑ j(cid:48)=0,1 (cid:96) j(cid:48) (z,z˜)dF H (z˜)dF H (z) 3.3 Equilibrium Asymmetricequilibriumwithtariffτ is: (a)apriceindexP;(b)quantitiesq andQ; 0 (c)aggregateearningsW;(d)aggregateprofitsπ;(e)populations{L ,L (z),L (z)} 0 M H z≥A such that: (i) households solve their utility maximization given prices, profits and earnings; (ii) firms producing the differentiated goods solve their profit maximization problem given their productivity, their competition, and the aggregate consumption indexes; (iii) aggregate profits, aggregate earnings, and the price index are consistent with the firm decisions; (iv) all goods markets clear; and (v) the indifferenceconditionacrosstownsforlaborallocationholds. 3.4 Wages and Nonemployment across Locations Thefollowingpropertiesholdinequilibrium.36 Proposition1. Equalexpectedearnings. Expected earnings are equalized across all labor markets. Average income is also equalizedacrosslocationssinceallworkersreceiveanequalshareoffirmprofits. Proof. Thepropositiontriviallyfollowsfromthelaborallocationindifferencecondition. Given the quasi-linear preferences, the equilibrium indifference condition 36This model is quite tractable because of its block-recursive nature. Firms and households do notneedtocarryanycross-sectionaldistributions. Whilethemodelissimpleintermsoffirmand householdoptimizations,thegeneralequilibriumhastobenumericallycomputedbecausethenon trivialdoubleintegrationinvolved. 22

meansthatexpectedearningsareequalizedacrosslocations:37 (cid:40) W (z) ∀z s.t. L (z)>0 M M w = 0 W (z) ∀z s.t. L (z)>0 H H wherew = p =1isthewageinthehomogeneousregions. 0 0 In light of this proposition, greater vulnerability to foreign competition due to lowerproductivitydoesnotnecessarilymeanthatlabormarketoutcomesareworse exante. Moreover,exante,notransfersarerequiredacrosslocationstoequateconsumption allocations because the indifference condition makes it trivial. In others words, ex ante, transfers within a location are enough to implement the optimal consumptionallocationforeachindividual. Proposition2. Constantnonemploymentrateacrossmonopolisticlocations. Across monopolistic locations, more productive labor markets have higher total employment and population but workers earn the same wage and face the same nonemploymentrateaslessproductivemonopolisticlocations. Proof. The proof is based on Proposition 1 and the optimal firm decision. Wages are constant across monopolistic locations because markups are constant and the bargainingyieldsasimplenetsurplussharingrule. This proposition is important because it shows why, in this class of models, head-to-head competition can induce a non-degenerate distribution of employment rates across labor markets. In the absence of head-to-head competition, the distribution of nonemployment rate is degenerate because wages would be independent of firm productivity. Consequently, the wage determination rule assumed in this class of models or the constant markups are innocuous assumptions. However, the abstraction from multilateral bargaining is not problematic as long as the constant wageandproportionalnetsurplussharingresultshold. ThisisthecaseinHelpman andItskhoki(2010)andFelbermayretal.(2010)forexample. 37AsinHelpmanandItskhoki(2010), thefamilyinterpretationisessentialinthecaseofquasilinearpreferencesbutnotwhenpreferencesarehomothetic. 23

Proposition3. Differentnonemploymentratesacrosshead-to-headlocations. Across head-to-head locations, when there are no trade barriers, the more productive labor markets have higher employment, pay higher wages and thereby have highernonemploymentratethanlessproductivelabormarkets. Proof. The proof follows from Proposition 1 and the fact that expected markups andwagesinhead-to-headlocationsincreasewithlocalproductivity. This proposition characterizes the free trade long run equilibrium.38 In the extreme case of autarky, the distribution of markups and employment rates become j degenerate since limµ (c,c˜)= µ. In general, trade barriers (τ) interact with the j τ→∞ ideal markup (µ) to alter the entire distribution of markups as illustrated in Figure 5. Hence, the expected markups across head-to-head locations do not always fall withproductivity. 3.5 Equilibrium Labor Allocations The employment rate across monopolistic locations is degenerate and corresponds totheemploymentrateofthemostproductivehead-to-headlocations. Ontheother hand, the endogenous distribution of variable markups across locations also correspondstoadistributionofemploymentrates. Figure6showstheequilibriumemployment-to-populationacrosshead-to-head labormarketsforvariouslevelsoftradebarriers.39 ByProposition3,intheabsence of trade barriers, the nonemployment rate across head-to-head locations decreases withproductivity. However,themonotonicitydoesnotholdinthepresenceoftrade barriers. First, there is a kink at the marginal productivity level where all firms in a head-to-headlocationdonotexport. Abovethekink,aslightlylessproductivelocation has a higher employment rate because it faces tougher competition. Below the kink,theinfra-marginallocationexportsandhasahigheremploymentratebecause tradecostslowermarkupsabroad. Eventually,moreproductivelocationshavemore 38See the appendix for empirical evidence corroborating this relation between productivity and thenonemploymentrateinthelongrun. 39In the upper limit of autarky, the employment rate is constant since in all locations, all firms haveaconstantmarkup. SeeTable3fortheotherparametersusedintheillustration. 24

Figure6: TradeBarriersandEmploymentRate Local Employment Rate across Head−to−Head Locations 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 local firms’ unit cost etar tnemyolpme lacol Trade barriers τ = 1.67 Trade barriers τ = 1.53 Trade barriers τ = 1.25 Trade barriers τ = 1.00 firms charging higher markups. Therefore, the hump is an artifact of the changing composition of the endogenous markups. The kink and the hump naturally vanish intheabsenceoftradecosts. Furthermore,themodelpredictsthatmoreproductive locationshavehigheremploymentlevelsincetheirfirmsarelarger. 3.6 Long-Run Reallocation across Labor Markets When workers are mobile within and across labor markets, the most affected locations become ghost towns in the free trade equilibrium: their population vanish. As shown in Figure 7, some labor markets greatly expand and employ more workers than their original population.40 However, the full mobility assumption is at oddswiththeempiricalevidenceonmutedpopulationadjustmentstotradeshocks. Therefore, in the next section, worker mobility after a trade reform shock is restricted. 40The largest (proportional) firm expansions typically occur in the medium-sized locations that startexporting. ThisisreflectedinthekinkinFigure7. 25

Figure7: ReallocationofLaborwithFullMobility Hypothetical Employment Rate across Head−to−Head Locations 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 local firms’ unit cost etar tnemyolpme lacol Trade barriers τ = 1.67, with population for τ = 1.67 Trade barriers τ = 1.53, with population for τ = 1.67 Trade barriers τ = 1.25, with population for τ = 1.67 Trade barriers τ = 1.00, with population for τ = 1.67 4 Unexpected Trade Reform with Limited Mobility Consistent with the muted population adjustments in the data, workers are now assumed to be ex ante mobile across labor markets but not ex post as in Helpman andItskhoki(2010). Theexpostimmobilityassumptionmeansthatworkerscannot leavetheiroriginalhomelocationseventhoughtheymayswitchjobs. Theexanteindifferenceconditionacrosslocationsnolongerhastoholdexpost. Labor markets may still expand by tapping into their local pool of nonemployed workers. Anequilibriumwithlimitedworkermobilityisdefinedbelow. Themodel iscalibratedtostudytrade-inducedlabormarketadjustmentsacrosslocations. 4.1 Medium Run Equilibrium Post-Reform Givenaninitialequilibriumpopulationallocation{L ,L (z),L (z) : z∈Z}with 0 M H tariff τ, a symmetric medium run equilibrium with tariff τ (cid:98) is: (a) a price index P(cid:98); (b) quantities q (cid:98)0 and Q(cid:98); (c) earnings W(cid:98); and (e) aggregate profits π (cid:98) such that: (i) 26

households solve their utility maximization problem; (ii) firms solve their profit maximization problems; (iii) aggregate profits, aggregate earnings, employment rates,andthepriceindexareconsistent;(iv)allgoodsmarketsclear. 4.2 Calibration The limited mobility model is calibrated to quantify the effects of a trade liberalizationacrosslabormarketsintheU.S.TheArmingtonelasticityissettoσ =2.01 followingRuhl(2009). Theicebergtransportationcostbeforethereform ischosen tobeintherangeoftradecosts-includingobservedtariffsandnon-tariffbarriersdocumentedbyAndersonandvanWincoop(2004)fortheU.S. The Pareto distribution shape parameter is set to s = 2.05 to guarantee finite mean and finite variance, following Helpman and Itskhoki (2010). The elasticity of substitution with the outside good η is set to 0.25 < (σ−1)/σ to ensure that varieties are better substitutes for each other than for the homogeneous good. The bargaining power λ is set to 0.5 so the union and the firm have equal bargaining power. The fraction of firms subject to head-to-head foreign competition is chosen so that the average number of trade-induced displacements matches the data (0.7 workers percent of w.a.p.). The outside option parameter is chosen so that all local labor markets attract workers under full worker mobility. The other parameters are set to have a national nonemployment rate around 30 percent in free trade. The calibrationparametersaresummarizedinTable3. 4.3 Foreign Competition and Nonemployment To relate the model to the empirical findings, the import competition faced by a labor market is measured using a statistic akin to Trade Adjustment Assistance (TAA) certifications observed in the data: the number of workers in a given labor market that are displaced because of foreign competition. In the model, this is the fraction of local workers who lost their jobs after their plant shut down due to heightened head-to-head competition. This measure is equal to zero in non head- 27

Table3: Calibration Parameter Description Value H Fractionofhead-to-headfirms 0.01 M Fractionofmonopolistfirms 0.99 σ Armingtonelasticity 2.01 η Elasticityofsubstitutionofdifferentiatedgood 0.25 s Paretodistributionshape 2.05 λ Unionbargainingpower 0.50 b Outsideoption 1.00 γ Hiringcost 0.02 L Population 1.00 τ Icebergtransportationcostspre-liberalization 1.11 τ(cid:98) Icebergtransportationcostspost-liberalization 1.00 to-head labor markets.41 Figure 8 illustrates the relationship between the measure ofTAA-certifiedworkersandnonemploymentchanges. First, net changes in nonemployment maybe positive or negative depending on the productivity of the head-to-head labor markets. As indicated earlier, the non head-to-head labor markets correspond to a degenerate distribution at the point where trade-induced job losses are zero. Second, the reduced job creation explains the increased steepness of the curve in the locations experiencing the largest job destruction. Third, it is easy to observe that the elasticity of local nonemployment tolocaljoblossesduetoforeigncompetitionisslightlylargerthantwointheworst hit locations.42 The model therefore suggests that a selection bias in the petition process is needed to generate the measured elasticity of nonemployment to tradeinduceddisplacements. Astradebarriersfall,thefirmsinthemarginalexportinglabormarketsareable 41In the standard Melitz (2003) model and similar models with no direct competition, a TAAmeasureofimportcompetitionwouldalwaysbezerobecausethefirmsdonotshutdownbecause ofdirectforeigncompetition:TAAinvestigatorswouldbeunabletofindevidencefortrade-induced foreigncompetitionasacauseofthelayoffs. 42The model results are reported along the continuum of locations. These results can certainly be aggregated by statistical units called “states” where each state is a selection of locations with correlatedproductivity. Thecurrentexpositionissimplerandeasiertoconnecttothemechanismin themodel. 28

Figure8: ForeignCompetitionandNonemployment Change in Nonemployment across Head−to−Head Locations 11 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 local trade−induced job losses (TAA) etar tnemyolpmenon lacol ni egnahc to outcompete their foreign rivals in foreign markets, and thereby expand at the extensive margins. Less productive head-to-head locations lose most of their firms becausetheyare out-competed. Atthe otherextreme,themost productivehead-tohead labor markets are hardly affected by the fall in trade barriers as they behave as monopolists. These changes in markups and export participation drive changes labormarketoutcomesacrosslocations. The overall relationship for the employment rate is non monotonic due to the heterogeneity in markups and the correlation between lower productivity and vulnerabilitytoimportcompetition. Therelationshipisquantitativelyandqualitativelyrobusttothesizeoftheheadto-head sector (H).43 This is because the size of the head-to-head sector mainly affects the aggregate price index while the nonlinear effects are driven by the endogenous changes in variable markups illustrated in Figure 5. On the other hand, 43Infact, thecalibrationtargetisratherconservativesinceH ischosentomatchthenationwide averagefractionoftrade-displacedworkerscertifiedbytheTAA. 29

the elasticity of substitution σ is key for the magnitude of the elasticity of nonemploymenttotrade-induceddisplacements. 4.4 Welfare Gains and Limited Worker Mobility Both the model and the data indicate that import competition has large uneven effects on labor markets across locations. The model predicts overall aggregate welfaregainsandincreasedaggregateemploymentinthemediumrun,despitethelarge increase in nonemployment and the fall in earnings in the worst hit locations. The aggregateeffectsaresummarizedinTable4. Table4: EffectsofLimitedMobilityintheMediumRun Tradejoblosses Notemployed %∆Q %∆q %∆U 0 (per1,000) (percent) (diff. goods) (hom. good) (utility) Pre-reform 0.00 30.32 - - - Mediumrun 0.70 29.28 +7.02 -0.25 +1.69 Longrun 0.00 30.84 +7.03 -19.51 +1.37 Thesemediumrun(limitedmobility)welfaregainsareactuallynotsmallerthan the long run (full mobility) gains. While the differentiated good demand is lower, limitedmobilityreducesinefficienciesfromsearchfrictionsbyincreasingtheoverallemploymentlevel. Inthismodel,themainsourceofnonemploymentistheinefficiency from the directed search as opposed to matching frictions. Hence, limited mobilitypartiallyundoesthatinefficiencyasinHelpmanandItskhoki(2010). Whilefulllabormobilityensuredthatearningswereequalizedacrosslabormarkets, limited mobility induces a non-degenerate distribution of expected earnings. Thismediumrunearningsinequalityisasourceofincomeredistributionacrosslabor markets. In contrast, under full worker mobility, no redistribution across labor marketsisneededbecauseoftheindifferencecondition.44 44Welfaregainswouldbedifferentintheabsenceoffullinsuranceacrosslocations. Aricherand morecomplexmodelwithincompletemarketssuchasKruselletal.(2010)wouldbeneeded. The implicationsoflimitedinsuranceduringtradereformsgobeyondthescopeofthispaper. 30

setatsssorcasetamitsePFTgnisusemoctuOtekraMrobaL :5elbaT noitalupoP etaRnoitaerCboJ etaRnoitcurtseDboJ srekroWdeyolpmenoN →semoctuotekramrobaL 6d 4d 6c 4c 6b 4b 6a 5a 4a noititepmoCngieroF 610.0 500.0 332.1- ***694.1- 542.0- **984.1 526.2 - **918.2 srekroWdefiitreCAAT )832.( )510.( )387.( )135.( )710.1( )286.( )008.1( - )552.1( - - - - - - 05.812- - 40.56- 2srekroWdefiitreCAAT - - - - - - )71.613( - )10.712( ytivitcudorProtcaFlatoT 5000.0 - ***222.0 - ***761.0- - **339.2- **829.2- - PFTgoL )4100.( - )240.( - )160.( - )423.1( )023.1( - - - - - - - **964.0 **864.0 - 2PFTgoL - - - - - - )712.( )612.( slortnoCdradnatS seY seY seY seY seY seY seY seY seY emoctuodeggaL seY seY seY seY seY seY seY seY seY selbairavtnednepednideggaL seY seY seY seY seY seY seY seY seY srotacidniraeY seY seY seY seY seY seY seY seY seY srotacidnietatS seY seY seY seY seY seY seY seY seY srotacidninoigeR×raeY 5999.0 6999.0 7734.0 4565.0 6926.0 5294.0 6326.0 2536.0 8837.0 .qs-R 009 0531 009 0531 009 0531 009 009 0531 N folenapdecnalabasielpmasnoitamitseehT.setatsnoderetsulcerasesehtnerapnisrorredradnatstsuboR.leveltnecrep1dna,5,01ehttaecnacfiingisetoned***dna,**,*:etoN .0002otpuylnoelbaliavaerasetamitsePFTlevel-etatS.9002dna3891morfsraey72snapstahtsetats05eht 31

4.5 Evidence using Measured Cross-Sectional Productivity A fundamental ingredient in this model is the heterogeneity in productivity across locations: differences in trade-induced displacements are due to productivity differences across locations. In particular, the model predicts a nonlinear quadratic relation between productivity and nonemployment when population adjustments aremuted. These key tenants of the model are investigated using state-level data on Total FactorProductivity(TFP)estimatedbyTurneretal.(2007)andTurneretal.(2008). TheseTFPestimatesarederivedusingcarefullyconstructeddataonstate-levelsectoral inputs, especially physical capital, human capital, and land. The empirical estimationissimilartotheoneusedinSection2. TheresultsareshowninTable5. Alltheestimatedspecificationsincludestateindicators,yearindicators,year-region indicators,andlaggedvariables.45 In specifications (a5) and (a6) of Table 5, the nonlinear effects of productivity onnonemploymentratearecorroborated. Consistentwiththetheory,trade-induced displacementsarenolongersignificantwhenproductivityisaccountedforinspecification(a6). However,thequadraticeffectisnotsignificantwhenthetrade-induced displacements alone are used in specification (a4). This finding reinforces the possibilityofaselectionbiasinthepetitionsasnotedabove.46 Finally,productivityhasacorrelatedeffectsonjobcreationandjobdestruction. In specifications (b6) and (c6), the less productive locations create fewer new jobs and lose more existing jobs.47 Population dynamics remain muted in response to productivityinnovationsasshowninspecifications(d4)and(d6). Altogether, these findings reinforce the view that trade reforms unevenly affect locationsthroughpreexistingcross-sectionalproductivitydifferences. 45Incomeisnotincludedsinceitisstronglycorrelatedwithproductivity. 46Thelargeelasticityofnonemploymentratetotrade-displacementscanonlyberationalizedby thismodelwhenpetitionsmainlycomefromthehardesthitlocationsasshowninFigure8. 47Incontrastwithspecifications(b4)and(c4),theeffectsoftrade-induceddisplacedarenolonger significantonceproductivityisincluded. 32

4.6 Trade Reforms and Exogenous Growth : Similar Effects? In international trade, a fall in trade barriers and a growth in foreign productivity may have similar effects. For instance, Autor et al. (2013b) argue that the adverse labormarketeffectsofimportcompetitionfromChinaareduetoexogenousgrowth in China. In this subsection, the effects of an unexpected trade reform and an exogenousforeignproductivitygrowthinthismodelarecontrasted. To do so, an asymmetric free trade equilibrium is first computed by extending the symmetric setup in Section 3. The two countries are assumed to be different in their Pareto shape parameter. An unexpected productivity increase is then inducedinthespiritofthemediumrunequilibriumofSection4. Specifically,thetail parameter in the foreign country is reduced from 2.29 to the home economy’s tail parameter: 2.05. Thisrepresentsa10percentgrowthinaverageproductivityinthe differentiatedsectors. 48 Figure9: NonemploymentunderExogenousForeignGrowth Change in Nonemployment across Head−to−Head Locations 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 local trade−induced job losses (TAA) etar tnemyolpmenon lacol ni egnahc 48Foreigncompetitorsarerandomlyreassignedanewproductivityaccordingtothenewdistribution.Tradebarriersaresettoτ=1beforeandafterthechange.SeeTable3fortheotherparameters. 33

Figure 9 illustrates the net changes in nonemployment and trade-induced job losses across head-to-head labor markets when the foreign and less productive country experiences an exogenous growth in productivity in the absence of trade barriers. There is a systematic contraction across labor markets in the medium run. All domestic labor markets lose jobs due to the surge in foreign competition. Aggregate employment falls across the board as no new jobs are created. Unlike the trade reform case, the relationship is no longer nonlinear and the elasticity of local nonemployment to local job losses due to foreign competition is equal to one everywhere. Overall, these effects yield negative aggregate welfare effects in the advancedeconomyduetotheinducedfallinaggregateincome. Thisexerciseshowsthat,inthismodel,thelabormarketeffectsoftradereforms and foreign productivity are not identical in the cross-section or in the aggregate. Recent studies such as Autor et al. (2013a) have started exploring the identification of technology shocks and trade shocks across locations. This is certainly an important and a complex problem. For instance, in this model, trade openness endogenouslyamplifiescross-sectionaltechnologydifferences. 5 Conclusion This paper studies the labor market effects of trade-induced foreign competition across locations in the U.S. The impact of foreign competition on labor markets is documented using a novel dataset on the universe of establishment-level petitions for Trade Adjustment Assistance (TAA) in the U.S. over the last three decades. Increasedforeigncompetitioniscorrelatedwithreducedemploymentthroughhigher job destruction and lower job creation, while population dynamics are sluggish. Acrosslocations,anextraworkerseparatedduetoforeigncompetitionisassociated with the overall employment falling by two to three extra workers. These findings are robust to location fixed effects, time fixed effects, region and time interactions, importpenetration,constructionactivity,andunionization. ThispaperintroducesaRicardianmodelwithnonemployment,variablemarkups, and heterogeneous segmented labor markets. Both productivity differences across locations and endogenous variable markups are crucial to account for the uneven 34

effects of foreign competition on unemployment across labor markets. The model can rationalize the correlated effect of foreign competition on job destruction and job creation because the locations that are more vulnerable to foreign competition arepreciselythelessproductiveones. The model is used to estimate the welfare effects associated with the uneven effects of trade across locations. Some locations are severely affected while other locations gain from the reduction in trade barriers. However, aggregate welfare gainsfromtradereformsarenotlowerasaresultofreducedrelocationacrosslabor markets. In contrast, aggregate welfare effects can be negative in the case of an exogenous productivity growth in the foreign country since all labor markets lose workerswithoutcreatingnewjobsinthedomesticeconomy. Overall, this paper makes a contribution to the growing literature on tradeinduced labor market adjustments. Given the findings in this paper, future work on welfare effects of trade reforms should also focus on a richer set of labor market frictions and investigate technological change in negatively affected locations, firms, and workers. In light of the inequality induced by trade reforms, it is also important to study optimal transitional policies in the presence of heterogeneous workersandincompletemarkets. 35

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6 Appendix (For Online Publication) 6.1 Data Sources This section presents the main empirical findings on foreign competition and labor marketoutcomesacrosslocationsintheU.S.Thedatasetisbasedonestablishmentlevel petitions from the U.S. Trade Adjustment Assistance (TAA), individual-level data from the Current Population Survey (CPS), job flows data in the U.S. Census Business Dynamics Statistics (BDS), housing starts data in the U.S. Census New ResidentialConstruction(NRC)database,andU.S.importsdata. Thedataisaggregatedyearlyatthestatelevelfrom1983to2009toformastate-levelpaneldataset. TheMarchCPS For every year t = 1983...2009 and for every state, the following labor market outcomesareconstructed: unemployedperworkingagepopulation,notinthelabor forceperworkingagepopulation,notemployed(equivalently“nonemployed”)per working age population, and average unemployment duration. These measures are based on the public data from the Current Population Survey (CPS). In particular, this paper uses data from the Annual Social and Economic Supplement (ASEC) applied to the sample surveyed in March and assembled into the Integrated Public UseMicrodataSeriesbyKingetal.(2010). TheBusinessDynamicsStatistics For every year t =1983...2009 and for every state, the following job flows measures are used: jobs destruction rate, job creation rate, and net job creation rate. ThesemeasuresarecomputedfollowingDavis,HaltiwangerandSchuh(1998)and publicly available from theBusiness DynamicsStatistics (BDS).The BDSare created from the Longitudinal Business Database (LBD) by the U.S. Census Bureau. TheBDScontainannualseriesdescribingestablishment-levelbusinessdynamics. 42

ImportPenetrationData Autor et al. (2013b) use the years 1990, 2000, and 2007 at the commuting zone level. The state-level measure is computed here for each year between 1988-1997 and 1999-2005. The industry-country U.S. trade data used for the import penetration proxies comes from Schott (2008). The industrial mix comes from the U.S. CensusCountyBusinessPatterns(CBP)aggregatedatthestatelevel. TheTradeAdjustmentAssistance(TAA)PetitionsData This paper uses the petitions data from the Trade Adjustment Assistance (TAA) programs for workers to construct a direct measure of foreign competition at the state-level. Instated in its current form as part of the pivotal Trade Act of 1974, the Trade Adjustment Assistance (TAA) for workers is a federal program that aims to support the professional transition of workers displaced due to foreign trade. The measure of foreign trade competition is constructed using data on the number of workers certified by the federal investigators from the U.S. Department of Labor (DoL)tohavebeendisplacedbecauseofforeigntradefrom1983to2009. Firms, unions, state unemployment agencies, or groups of workers can file a petition on behalf of a group of workers at a given establishment to be eligible for Trade Adjustment Assistance (TAA) benefits. These benefits include: Trade Readjustment Assistance (TRA) for up to two years as long as the workers are enrolled intraining,incomesupportfortheworkerswhoarefindfullemploymentfollowing the trade-induced separations, job search allowances, relocation allowances, and healthcareassistance. To establish the eligibility of the petitioning workers, federal investigators at the Department of Labor seek evidence that these workers were separated because of (a) import competition that led to decline in sales or production, (b) a shift in production to another country with which the United States has a trade agreement, or (c) due to loss of business as an upstream supplier or downstream producer for anotherproducerthatisTAA-certified. Thispaperconstructsmeasuresoftrade-inducedforeigncompetitionusingdata on all establishment-level petitions filed under the program up to 2009. Data prior 43

to 1983 are excluded due to the lack of reliability of these data as a measure of import competition. Each petition includes information on the location of the establishment, the numbers of workers affected, the certification decision, and the dateofimpact.49 6.2 Descriptive Statistics by State Table6: TAAcertifiedworkersbystateperthousandofw.a.p. (1983-2009) State Average Minimum Maximum IQR AL 1.23 0.07 2.68 1.43 AK 0.93 0.00 6.02 1.07 AZ 0.33 0.03 1.47 0.27 AR 1.08 0.06 2.37 1.21 CA 0.25 0.03 0.74 0.23 CO 0.57 0.01 2.98 0.47 CT 0.44 0.04 1.01 0.47 DE 0.25 0.00 3.38 0.30 FL 0.13 0.04 0.29 0.13 GA 0.70 0.01 1.56 0.60 HI 0.06 0.00 0.70 0.08 ID 0.67 0.00 1.86 0.63 IL 0.45 0.02 1.87 0.38 IN 0.84 0.02 3.23 0.86 IA 0.38 0.00 2.10 0.49 KS 0.57 0.00 3.01 0.60 KY 0.91 0.02 2.56 0.84 LA 0.59 0.00 4.50 0.61 Overall 0.67 0.00 7.35 0.71 49Individualpetitionsarepubliclyavailableatwww.doleta.gov/tradeact/taa/taa_search_form.cfm 44

State Average Minimum Maximum IQR ME 1.32 0.43 2.66 1.09 MD 0.23 0.01 0.60 0.24 MA 0.58 0.05 1.63 0.34 MI 1.00 0.03 6.89 0.98 MN 0.47 0.01 2.05 0.33 MS 1.19 0.02 3.00 1.20 MO 0.74 0.06 1.33 0.46 MT 0.63 0.00 4.03 0.63 NE 0.24 0.00 0.94 0.47 NV 0.13 0.00 1.13 0.13 NH 0.59 0.00 1.88 0.65 NJ 0.54 0.13 1.07 0.41 NM 0.61 0.00 3.00 0.69 NY 0.39 0.07 0.74 0.20 NC 1.37 0.07 3.77 2.18 ND 0.57 0.00 5.66 0.48 OH 0.80 0.18 3.71 0.76 OK 0.74 0.01 2.14 0.47 OR 0.90 0.00 4.40 0.82 PA 0.95 0.14 2.44 0.44 RI 0.89 0.00 1.95 0.87 SC 1.10 0.02 2.78 1.65 SD 0.46 0.00 2.86 0.33 TN 1.31 0.22 2.68 1.03 TX 0.61 0.07 2.55 0.41 UT 0.64 0.07 3.43 0.53 VT 0.53 0.00 1.85 0.82 VA 0.63 0.10 1.97 0.36 WA 0.63 0.02 5.42 0.35 Overall 0.67 0.00 7.35 0.71 45

State Average Minimum Maximum IQR WV 0.62 0.05 2.06 0.61 WI 0.78 0.10 2.68 0.77 WY 0.87 0.00 7.35 1.12 Overall 0.67 0.00 7.35 0.71 6.3 U.S. TAA Series Ionlyusedatapost-1983duetotheunusualspikeinthethedatapre-1983. Significantchangesintheprogrampre-1983aredocumentedinRosen(2006). Inparticular,theauto-workersmisusedtheprogramandtheReaganadministrationultimately revampedit. Figure10: TotalTAA-certifiedWorkersintheU.S. 600000 550000 500000 450000 400000 350000 300000 250000 200000 150000 100000 50000 0 6791 7791 8791 9791 0891 1891 2891 3891 4891 5891 6891 7891 8891 9891 0991 1991 2991 3991 4991 5991 6991 7991 8991 9991 0002 1002 2002 3002 4002 5002 6002 7002 8002 9002 Total TAA certified workers 46

6.4 Standard Import Penetration Proxy For a given location i at a time t, the “China syndrome” measure used in Autor et al.(2013b)isanlocalimportpenetrationmeasure: employmentk ∆importsk ADHimportpenetrationi ≡ ∑ i,t ∗ US,t t employment employmentk industriesk i,t US,t (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) localindustrialmix nationalimports Table 8 shows the typical order of magnitude of this import penetration proxy across states between 1988 and 2005. State-level time series of the ADH and the TAAmeasuresarecomparedinFigure11. Table8: Summarystatistics(1988-2005) Variable p10 p25 p50 p75 p90 ChangeinChinaimportpenetration 0.12 0.25 0.56 1.38 2.70 in$000sperworker 6.5 Other Labor Market Outcomes SeeTable9foradditionallabormarketoutcomes. 6.6 Additional Model Outcomes Model predictions on medium-run earnings inequality and differences in employmentratesarepresentedin12. 6.7 Productivity and Long-Run Outcomes SeeTable10thelongruneffectsofproductivity. 6.8 Maps Figures13,14,and15showmapsoftheTAA-basedforeigncompetitionmeasure. 47

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Figure12: EarningsandEmploymentRatesafterTradeReform Earnings Inequality in Head-to-Head Locations 11..11 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 unit cost (c) noitalupop revo sgninrae latot Medium run Before reform Employment over Population in Head-to-Head Locations 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 unit cost (c) noitalupop revo tnemyolpme Before reform Medium run 50

Table10: LongRunLaborMarketOutcomesacrosstheUnitedStates Labormarketoutcomes→ NotEmployed Wages PopulationShare† inFiveYears inFiveYears inFiveYears TotalFactorProductivity LogTFP 0.909*** 23.05*** .004* (.233) (4.250) (.002) StandardControls Laggedoutcome Yes Yes - U.S.populationshare Yes Yes - Yearindicators Yes Yes - Stateindicators Yes Yes - R-sq. 0.2002 0.5408 .0993 N 900 900 900 Note:*,**,and***denotesignificanceatthe10,5,and1percentlevel.Robuststandarderrorsinparenthesesareclusteredonstates.Theestimationsampleisa balancedpanelofthe50statesfrom1983and2000.Alloutcomevariableareinlogexcepttheshareofw.a.punemployedandtheshareofw.a.p.notinthelaborforce. Wagesareusualhourlywagesadjustedfortop-codinganddeflatedusingthenationalPCEdeflator.Hoursworkedaretotalhoursworkedlastyear.†:Thepopulation dynamicsregressionisadifference-in-differenceestimationbecausethepopulationtimeseriesarenotstationary. 51

Figure13: Mapsofforeigncompetition 52

Figure14: Mapsofforeigncompetition 53

Figure15: Mapsofforeigncompetition 54