No2025-17–November2025

WorkingPaper

CEpii

SectoralLinkagesandtheImpact

ofImmigrationonExportPerformance

AmandineAubry&AnthonyEdo

Highlights

Thispaperstudieshowimmigrantsinintermediatesectorsaffectdownstreamexportperformance.

Wedevelopatheoreticalmodelinwhichasector’sexportsdependnotonlyonitsownimmigrantworkforcebutalsoonimmigrantlaborininput-supplyingsectors.

Weshowthatincreasesinimmigrantemploymentinthesesectorsraiseexportsinconnecteddownstreamindustries.

RESEARCHANDEXPERTISE

ONTHEWORLDECONOMY

CEPIIWorkingPaperSectoralLinkagesandtheImpactofImmigrationonExportPerformance

Abstract

Thispaperstudieshowimmigrantsinintermediatesectorsaffectdownstreamexportperformance.Wedevelopatheoreticalmodelinwhichasector’sexportsdependnotonlyonitsownimmigrantworkforce,butalsoonimmigrantlaborininput-supplyingsectors.UsinganewdatasetonU.S.input–outputfrom2003-2017,weshowthatincreasesinimmigrantemploymentinthesesectorsraiseexportsinconnecteddownstreamindustries.Thiseffectoperatespartlythroughimprovedproductionefficiencythatlowersupstreaminputcosts.Bylinkinglabormigrationtoproductionnetworks,weidentifyanewchannelthroughwhichimmigrationshapescomparativeadvantageininternationaltrade.

Keywords

Immigration,Trade,SectoralLinkages,IntermediateSectors.

JEL

F22,F16,J61,O31.

WorkingPaper

CEpii

ISSN2970-491X

EdItoRIAldIRECtoR:AntoInEBou?t

CEPIIWorkingPaper

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?CEPII,PARIS,2025

November2025

Centred’étudesprospectives

etd’informationsinternationales

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CEPII(Centred’étudesProspectivesetd’InformationsInternationales)isaFrenchinstitutededicatedtoproducingindependent,policy-orientedeconomicresearchhelpfultounderstandtheinternationaleconomicenvironmentandchallengesintheareasoftradepolicy,competitiveness,macroeconomics,internationalfinanceandgrowth.

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Allrightsreserved.Opinionsexpressedinthispublicationarethoseoftheauthor(s)alone.

RESEARCHANDEXPERTISE

ONTHEWORLDECONOMY

2

3

CEPIIWorkingPaperSectoralLinkagesandtheImpactofImmigrationonExportPerformance

SectoralLinkagesandtheImpactofImmigrationonExportPerformance*

AmandineAubry?,AnthonyEdo?

1Introduction

Moderneconomiesoperateasintricateproductionnetworks,whereshocksinonesec-torripplethroughothers(

CarvalhoandTahbaz-Salehi

,

2019

).Immigration,meanwhile,reshapeslocallabormarketsandproductionefficiency(

LewisandPeri

,

2015

;

Dustmann

andSchnberg,

2025

).Althoughpriorresearchhighlightstheimportanceofsectorallink-agesfortrade(

CaliendoandParro

,

2014

;

BaqaeeandFarhi

,

2024

),littleisknownabouthowimmigrationinteractswiththeseproductionnetworkstoaffectdownstreameconomicoutcomes.Thispaperinvestigatesthisdimensioninthecontextofthemigrationexportnexus,askinghowimmigrantemploymentininput-producingsectorsaffectstheexportperformanceofdownstreamindustriesthroughsectorallinkages.

Therelationshipbetweenimmigrationandexportshasbeenstudiedextensively,moti-vatedbytheparallelgrowthofinternationaltradeandcross-bordermigration.Beginningwiththeseminalcontributionsof

Gould

(

1994

)and

HeadandRies

(

1998

),thisliteraturefindsthatimmigrationenhancestradeandbooststheexportperformanceofhostcoun-

*Theusualdisclaimersapply.WearegratefultoMetteFoged,TorstenJaccard,SbastienJean,GianlucaSantoni,AndrSesboandCamiloUmana-Dajudfortheirinsightfulcomments.WethanktheparticipantsattheXIImeetingoninternationaleconomics,the14thAnnualConferenceonImmigrationinOECDCoun-tries,theinternationaltradeseminarattheJaumeIuniversity,theCoLablunchworkshopattheUniversityofCopenhagen,theCREM-CREST-SMART'sworkshop.

?UniversitdeCaenNormandie,CNRS,CREMUMR6211,F-14000Caen,France.E-mail:

amandine.

aubry@unicaen.fr

.

?CEPII,ICM,IZA.E-mail:

anthony.edo@cepii.fr

.

CEPIIWorkingPaperSectoralLinkagesandtheImpactofImmigrationonExportPerformance

4

tries.

1

Moststudiesemphasizemigrationnetworksasthecentraltransmissionmech-anism,wherebyimmigrantslowerbilateraltradecostsbyfacilitatinginformationflows.Asecondchanneloperatesthroughproductivitygainsinducedbyimmigration,whichreduceproductioncostsandimproveexportcompetitiveness(

Mitaritonnaetal.

,

2017

;

Ottaviano

etal.

,

2018

;

Mahajan

,

2024

).

Thepresentpapercontributestotheliteraturebyintroducinganewmechanismthroughwhichimmigrationcanenhanceexportperformance.Productivitygainsfromimmigrationarenotconfinedtothesectorsthatemployimmigrantlaborbutcanpropagatethrough-outdownstreamindustriesviainput-output(I-O)linkages.Specifically,immigrantsinup-streamsectorscanhelpreduceinputcosts,therebyimprovingtheexportperformanceofdownstreamsectors.Toformalizethisidea,wedevelopatheoreticalframeworkthatchar-acterizeshowproductivityeffectsfromimmigrantlaborpropagatethroughtheproductionnetwork.Thisframeworkalsoincorporatesthestandardnetworkmechanismwherebyimmigrantsreducebilateraltradecosts,allowingustoanalyzemultiplechannelsofthemigration–traderelationshipwithinaunifiedmodel.Specifically,ourtheoreticalframeworkextendsthemodelof

CaliendoandParro

(

2014

)byincorporatingimmigrationasafac-torthataffectsbilateraltradecosts,following

AubryandRapoport

(

2019

),andproductioncosts,consistentwithempiricalevidencefrom

Mitaritonnaetal.

(

2017

);

Ottavianoetal.

(

2018

);

Mahajan

(

2024

).Tomodelhowimmigrantlaborgeneratesproductivitygainsandhowtheydiffuseacrosssectors,webuildontheknowledgediffusionframeworkof

Cai

etal.

(

2022

).Thisapproachallowsustoformalizethreedistinctchannelsthroughwhichimmigrationaffectsexportswithinaunifiedframework:(i)anetworkchannel,whereimmi-grantsreducebilateraltradecostswiththeircountryoforigin;(ii)aproductivitychannel,whereimmigrationraisesproductivityinthesectortheywork;and(iii)asectoralspilloverchannel,whereimmigrationinupstream(i.e.input-providing)sectorsenhancesproduc-tivity,therebyloweringinputcostsfordownstreamsectors.Toourknowledge,noexistingstudyhasjointlymodeledthenetworkandproductivitychannels,orincorporatedsectorallinkagesinanalyzingtheimmigration–traderelationship.

Ourtheoreticalmodelyieldsatestableempiricalspecification,whichweestimateusingI-Odata.Specifically,weconstructanenrichedI-Omatrixbycombiningthe2002DetailedBenchmarkI-OAccountswithdatafromtheAmericanCommunitySurvey(ACS)andtheU.S.Census.Thesedataallowustomapdetailedeconomiccharacteristicsforeachsec-torwithintheproductionnetworkandtomeasureimmigrantpenetrationinbothupstreamanddownstreamindustries.Wethenexploitsectoralvariationsfrom2003to2017toesti-matetheimpactofimmigrationinintermediatesectorsontheexportperformanceoffinal

1See,e.g.,

PeriandRequena-Silvente

(

2010

);

FelbermayrandToubal

(

2012

);

Andrewsetal.

(

2017

);ParsonsandVzina(

2018

);

AubryandRapoport

(

2019

);

Baileyetal.

(

2021

);

CardosoandRamanarayanan

(

2022

);

Oreficeetal.

(

2025

).Seealso

Gencetal.

(

2012

)forameta-analysis,and

Hatzigeorgiouand

Lodefalk

(

2021

)forareviewoftheliterature.

CEPIIWorkingPaperSectoralLinkagesandtheImpactofImmigrationonExportPerformance

5

manufacturingsectors.

Toensurethatourestimatesarenotbiasedbythenon-randomallocationofimmi-grantsacrosssectors,weconstructshift-shareinstrumentsbasedonthehistoricaldis-tributionofimmigrantsbycountryoforiginacrosssectors(

AltonjiandCard

,

1991

;

Card

,

2001

).Specifically,weusethe1980U.S.Censustoconstructapredicteddistributionofimmigrantsacrosssectorsfortheperiodunderstudy.Ourinstrumentalvariable(IV)strategyreliesonthefactthatthecurrentpenetrationofimmigrantsinsectorsispartlydeterminedbythepresenceofpreviousmigrantsinthesesectors(

PatelandVella

,

2013

),whilethe1980distributionshouldbeuncorrelatedwithcontemporaneoussectoralshocks.Wevalidatethisapproachthroughaseriesofpre-trendtests.

Ourempiricalresultsshowthatariseintheimmigrantworkforceinintermediatesec-torsimprovestheexportperformanceofdownstreamsectors,consistentwiththesectoralspillovermechanism.TheIVestimatesindicatethata1%increaseinimmigrantem-ploymentinthetwomainintermediatesectorsofagivenfinalsectorraisesitsexportsbyapproximately1.2%.Inlinewiththetheoreticalpredictions,wefindevidencethatimmigrantlaborfacilitatestheadoptionofimprovedproductionprocessesinintermediate

sectors,loweringinputcostsfordownstreamexporters.

Wealsofindthatalargerimmigrantworkforceinagivensectorenhancesitsownexportperformance.Thisfindingisconsistentwith

Mitaritonnaetal.

(

2017

);

Ottaviano

etal.

(

2018

)whoshowthatimmigrationboostsregionalexportperformance.Bycontrast,ourcross-sectoralestimatesdonotshowrobustevidenceofnetworkeffects.Anincreaseinthenumberofimmigrantsfromagivenorigincountryemployedinagivensectorisnotsystematicallyassociatedwithhigherexportsfromthatsectortothatcountry.

Insum,ourfindingshighlightanewdimensionofthemigration–exportnexus:im-migrantsinupstreamsectorscanenhancetheexportcompetitivenessofdownstreamindustriesbyimprovingefficiencyandreducingproductioncosts.Ourpaperthusbridgestheliteratureonimmigration,trade,andproductionnetworks,providingaframeworkforunderstandinghowimmigrationshocksaffecttheeconomythroughsectorallinkages.

Theremainderofthepaperisstructuredasfollows.Section

2

describesthedataandprovidespreliminaryevidenceonthecorrelationbetweenimmigrantpenetrationinkeyinputsectorsandtheexportperformanceofdownstreamindustries.Section

3

providesatheoreticalframeworkthatrationalizesthispositivecorrelation.Section

4

outlinestheempiricalspecificationandidentificationstrategy.Section

5

presentsthemainempiricalresults,whileSection

6

exploresakeymechanismthatexplainsourmainempiricalfinding.Finally,Section

7

concludes.

CEPIIWorkingPaperSectoralLinkagesandtheImpactofImmigrationonExportPerformance

6

2DataandDescriptiveEvidence

Thissectiondescribesthedataandmethodologyusedtoconstructthemainvariables,andpresentsstylizedfactsonsectorallinkagesandimmigration.Toanalyzehowimmi-grantsinintermediatesectorsaffecttheexportperformanceoffinalsectors,weconstructadatasetlinkinganI-Omatrixtotradeandeconomicvariables.Specifically,wecom-pilesector-leveldataontrade,employment,innovation,andpricesfrommultiplesources,standardizingallvariablesaccordingtothe2002NorthAmericanIndustryClassificationSystem(NAICS).

2.1Data

DataonExports.Exportdataaretakenfrom

Schott

(

2008

)andreportedatthe6-digitNAICSlevel.Weaggregatethemtothe4-digitlevelbysummingexportvaluesacrosscorresponding6-digitsectors.Toensurecomparability,wemapthe2007and2012NAICSrevisionsbacktothe2002classificationusingofficialcrosswalks.Werestricttheanalysistothemanufacturingsectorduetoits“tradablenature”.Manufacturingaccountedfor92%ofU.S.exportsoverthe2003–2017period.

2

Exportvaluesaredeflatedto2015U.S.dollarsusingtheWorldBankGDPdeflator(

WorldBank

,

2020

).

DataonSectoralLinkages.Sectorallinkagesaremeasuredusingthe2002DetailedBenchmarkI-OAccountsfromtheBureauofEconomicAnalysis(BEA).Thismatrixre-portsthevalueofeachcommoditypurchasedbysectorsasinputforproduction.Following

Acemogluetal.

(

2016

),weusetheI-Omatrixthatpredatestheanalysisperiodtoavoidpotentialendogeneitywithrespecttosubsequentmigrationflowsandeconomicoutcomes.Thus,BEAI-Oindustriesaremappedto2002NAICScodesusingBEA’scrosswalks,withimputationbasedonEconomicCensussalesdatawhenindustriesspanmultipleNAICSsectors.Themappingisnontrivial,assomeI-OindustriesspanmultipleNAICSsectors,requiringimputationofdataattheNAICSlevel.WeperformthisimputationusingsalesfromtheEconomicCensuspublishedbytheU.S.CensusBureau.

AppendixB1

providesadditionaldetailsontheimputationprocedure.

TheBEAI-Oclassificationandcorrespondingcrosswalktableswereupdatedin2007and2012,coincidingwithrevisionstotheNAICSclassification.Toharmonizesectoraldefinitionsovertime,weadoptatwo-stepprocedure.First,wealignthedatacodedwithI-OclassificationstotheNAICSsystemineffectduringeachsubperiod:the2002NAICSfor2003–2006,the2007NAICSfor2007–2011,andthe2012NAICSfor2012–2017.

2Thetradabilityofnon-manufacturingindustrieshaschangedovertime.However,manufacturingstillrepresentedthevastmajorityoftotalU.S.exportsin2018(89%).

7

Second,wemapthe2007and2012classificationsbacktothe2002NAICSusingofficialcrosswalks,ensuringconsistencyacrosstheentiretimeseries.

DataonEmployment.WemeasureimmigrantemploymentusingtheACS,whichpro-videsindividual-levelinformationonbirthcountry,laborforcestatusandsectorofactivity.Werestrictthesampletoindividualsaged16–64intheworkforce,anddefineimmigrantsasforeign-bornworkers.ToalignACSindustrycodeswiththe2002NAICSsystem,weapplyBEAcrosswalks.SincesomecensusindustriesmaptomultipleNAICSsectors,weallocateworkersacrossNAICSsectorsusingrelativeemploymentsharesfromtheBLS(see

AppendixB2

fordetails).Toharmonizesectoraldefinitionsovertime,wefollowthesamemethodologydescribedabove.

Ourmainvariableofinterestisthesizeoftheimmigrantworkforceinthe“intermediateindustry”ofmanufacturingsectors.Specifically,wedefinethe“intermediateindustry”asthetwolargestinput-supplyingsectorsin2002(regardlessofwhethertheybelongtoman-ufacturing)linkedtoagivenexportingmanufacturingsector,andthentakethelognumberofforeign-bornworkersinthesetwoinputsectorstoconstructourmainimmigrationvari-able.

3

Weusethetwolargestinputsectorsfortwomainreasons.First,thenumberofinput-supplyingsectorsvariessubstantiallyacrossmanufacturingindustries(rangingfrom75to137).Includingallsupplierswouldmaketheanalysissensitivenotonlytochangesinimmigrantemploymentbutalsotodifferencesinsectoralcoverage,whichcouldconfoundtheresults.Byconsistentlyselectingthetwolargestsuppliers,weavoidcompositionalvariationandmaintaincomparabilityacrossindustries.Second,focusingonthetoptwoinput-supplyingsectorscapturestheunevendistributionofinputvalueacrosssuppliersforagivenmanufacturingsector.Inthisregard,Figure

1

showsthedistributionofintermedi-atesuppliersforarepresentativemanufacturing(exporting)sector,rankedbythevalueofinputspurchasedbythatsector.Thelargestsupplieralone(top1%)accountsfornearly29%ofthetotalinputvalue,andthetwolargestinputsectorstogetheraccountforslightlymorethan40%ofthetotal.Finally,weshowthatourresultsremainrobustwhentheim-migrantworkforceismeasuredinthetopthreeinputsectorsofagivenfinalsector,whichtogetherrepresentroughlyhalfofthetotalinputvalueacrossallinputsectors.

DataonInnovationandPrices.Weusetwodatasourcestoexaminehowimmigrationshockspropagateacrosssectors.First,werelyontheBusinessResearchandDevelop-mentandInnovationSurvey(BRDIS),conductedbytheU.S.CensusBureaufrom2008to2016.Thisnationallyrepresentativeannualsurveycollectsinformationonfirms’researchanddevelopmentactivities.Wefocusonwhetherfirmsreportedengagingininnovationandthetypeofinnovationundertaken.Dataareavailablefortheyears2008-2011and2014-2016.Aswiththecalculationofimmigrantpenetrationinthe“intermediateindustry”,

3Usingthe2002I-Otable,werankinput-supplyingsectorsbythevalueoftheirsalestoeachmanufac-turingsectorandretainthetoptwosuppliers.

CEPIIWorkingPaperSectoralLinkagesandtheImpactofImmigrationonExportPerformance

8

weaggregateresponsesacrossthetwomaininput-supplyingsectorsofeachexportingsectortoconstructanindicatorofinnovationintensity.

Second,weuseoutputpricedataoverthe2003-2017periodfromtheIndustryEco-nomicAccountspublishedbytheBEA.Weapplythesamemethodologydescribedearliertomatchthesedatatothe2002NAICSclassificationviatheI-Otable.Wethencomputeaveragelogpricesforthetwomainintermediatesectorsofeachexportingsectorusingannualchain-typepriceindexesforgrossoutput(seasonallyadjusted).Tosmoothshort-termvolatilityinoutputprices,weaveragepricesoverthree-yearintervals.Eachyearisreassignedtothemidpointofitscorrespondingwindow(e.g.,2003–2005isrecodedas2004,and2015–2017as2016).Wethencomputethemeanlogoutputpriceforeach“intermediateindustry”andtimeinterval,usingthesameaggregationapproachasfortheimmigrantvariable.Thisprocedureyieldsfivenon-overlappingperiods:2004,2007,2010,2013,and2016.

2.2StylizedFactsonTrade,ImmigrationandInputSectors

Ourfinaldatasetspans15years(2003to2017)andincludes744-digitmanufacturingindustriesand115countriesoforigin.AsshowninTable

1

,theaverageexportvaluepersectorshowsanupwardtrend,alongsidearisingshareofforeign-bornworkersinbothmanufacturingandintermediatesectors,indicatingagrowingrelianceonimmigrantlabor,particularlyinfinalsectors.

4

Understandingthesetrends,particularlytheroleoflaborandtradeinproduction,re-quiresexamininghowmanufacturingsectorsareinterconnected.Toillustratetheselink-ages,Figure

2

documentsakeystylizedfactabouttheU.S.productionnetwork,showingthatamongthe20largestsupplierstomanufacturingsectors,asmallnumberofhubindustriesdominateintersectorallinkages.Theleftpanelshowsthat10hubsgeneratein-termediateinputsalesbetween$50billionand$200billion,whiletherightpanelhighlightsthat13ofthe20largestsuppliersprovideinputstomorethan60ofthe74manufactur-ingsectors.Thus,ahandfulofdominanthubssustainmanymanufacturing-exportingindustries,whiletherestofthenetworkconsistsofsmaller,lessconnectedsuppliers.

5

Figure

3

showssubstantialvariationinemploymentacrossinputsectors,withlittlecor-respondencetotheirimportanceintermsofinputvalue.Forexample,sectorssuchas“WholesaleTrade”,“TruckTransportation”and“CropProduction”accountformanyimmi-grantworkers,whileotherkeyintermediatesuppliers,like“ManagementofFirms,”employ

4These115countriesaccountfor97%oftotalexportvalueinthesample.

5“ManagementofFirms”and“WholesaleTrade”emergeascriticalsuppliers:theformeristheleadinginputproviderfor16manufacturingsectors,whilethelatterholdsthatrolefor8ofthe74sectorsinoursample.

CEPIIWorkingPaperSectoralLinkagesandtheImpactofImmigrationonExportPerformance

9

relativelyfew.Figure

3

alsoshowsthatthesectoraldistributionofimmigrantstendstomirrorthatofnatives,indicatingthatsectorswithhigh(orlow)employmentlevelshavesimilarproportionsofbothgroups.

Motivatedbythedifferentiatedroleofintermediatesectors,weexaminethecorrelationbetweenimmigrantemploymentinthetwomaininputsectors(i.e.ourmeasureofim-migrationpenetrationininputindustries)andtheexportperformanceofthedownstreammanufacturingsectorstheysupplyoverthe2003–2017(Figure

4

).Theunitofobservationisasector–yearcell.Exportsandimmigrantsupplyshocksaremeasuredasresidualsfromregressionsonsectorandyearfixedeffects.Thus,bothvariablescapturedeviationsfromasector’saverage,netofcommonperiodshocks.Figure

4

revealsastrongposi-tivecorrelation,suggestivethatexportgrowthishigherinsectorslinkedtointermediateindustriesexperiencinglargerincreasesinimmigrantemployment(estimatedcoefficient0.32,standarderror0.13).Thisfindingsuggeststhatimmigrationmayinfluenceexportsthroughitsimpactontheproductionprocessofexportedgoods.Theremainderofthepaperexploresthisrelationshipindepth,testingitsrobustnessandprovidingaframeworkthatexplainshowimmigrationshapestradethroughproductionnetworks.

3TheoreticalFramework

WedevelopapartialequilibriummodelbasedontheRicardiantrademodelof

Caliendo

andParro

(

2014

),incorporatingsectoralheterogeneityandI-Olinkages,whiledrawingontheendogenousgrowthmodelof

Caietal.

(

2022

)toformalizetheimpactofimmigrationontotalfactorproductivity(TFP).Thismodelallowsustoendogenizethreekeymechanismsthroughwhichforeign-bornworkerscanenhanceexportperformance.First,weformalizethereductioninbilateraltradecostsarisingfromthepresenceofimmigrantsineachsec-tor,oftenreferredtoasthenetworkeffect.Second,wemodeltheeffectofimmigrationonTFPwithinthesectorswhereimmigrantsareemployed,capturingthedirectproductivitygainsonexportperformance(productivityeffect).Third,andmostimportantly,weintro-duceapropagationchannelthroughwhichproductivitygainsinintermediatesectorsaretransmittedtodownstreamsectorsviaininputprices.

Weassumethatallmarketsareperfectlycompetitive.ThereareNcountriesandJsectorsineachcountry.Wedenotecountriesbyiandnandsectorsbyjandk.

3.1PreferencesandConsumer’sDecisions

Ineachcountryn,thereisameasureLnofrepresentativeconsumerswithincomeWn,whomaximizethefollowingutilityfunction:

CEPIIWorkingPaperSectoralLinkagesandtheImpactofImmigrationonExportPerformance

10

whereCistheconsumptionofacompositegoodproducedinsectorj.

6

Thepref-erenceparameters,α,measuretheshareofexpenditureongoodC.Weassumethat .Laborsupplyisexogenousandweassumethateachindividualconsumesherincomeentirely.

7

Theutilityfunctionismaximizedsubjecttothefollowingbudgetconstraint:

wherePdefinesthepriceofthecompositegoodCproducedinsectorjandconsumedincountryn.ThedemandfunctionforthecompositegoodCderivedfromthefirst-orderconditionofthemaximizationproblemis:

3.2Firm’sDecisions

Acontinuumofintermediategoodsωj∈[0,1]areproducedineachsectorj.Theefficiencyofproductiondiffersacrosscountriesandsectors.Wedenotez(ωj)theefficiencyofproducinggoodωjincountryn.Twotypesofinputsareusedfortheproductionofωj;labor,(l(ωj))andintermediategoodsfromeveryothersectork,(mj,k(ωj)).Agoodωjisproducedaccordingtothefollowingconstant-returns-to-scaletechnology:

whereγj+Σ=1γj,k=1.

8

Theparameterγj,k≥0istheshareofintermediategoods

6Thesubscriptsdenotethecountryandthesuperscriptsdenotethesector.Whenevertherearetwosubscripts,theleftmostonecorrespondstothedestination.

7See

Aubryetal.

(

2016

)foradetaileddiscussionofthisassumption.

8UsingI-Otablesfrom2002and2012,wefollow

CaliendoandParro

(

2014

)inassessingthestabilityofinputsharesbycomputingthecorrelationofsharesovertime.Wefindanaveragecorrelationof0.90forU.S.manufacturingsectors,consistentwith

CaliendoandParro

(

2014

),whoreportsimilarresultsacross26

CEPIIWorkingPaperSectoralLinkagesandtheImpactofImmigrationonExportPerformance

11

fromsectorkusedintheproductionofgoodωjinsectorj,andtheparameterγjistheshareofvalueadded.

Thecostminimizationproblemfacedbyeachproducerdeterminesheroptimalunitcostofproduction.Sinceeachgoodωjisproducedunderconstantreturnstoscaleandmarketsareperfectlycompetitive,theunitcostofproducingωjis:

,(5)

wherecdenotesthecostofabundleofinputsandisdefinedas:

whereWisanominalwageindexpaidinsectorj,p(ωk)isthepriceofagoodωkproducedinsectorkincountrynandBjisaconstantandequalsΠ=1(γj)-γj(γj,k)-γj,k.

Equation(

6

)capturessectoralinterdependencies:thecostoftheinputbundledependsonwagesandonthepricesofallintermediategoodsintheeconomy.Consequently,achangeintheproductioncostofanysectork,suchasalaborshockinducedbyimmi-gration,indirectlyaffectsallsectorsthatuseitsgoodsasinputs.Inthisway,Equation(

6

)formalizeshowshockspropagateacrosssectorsthroughinputprices.

Producersinsectorjoperateunderperfectcompetitionandpurchaseintermediateproductsωkfromthelowest-costsupplier.TheysupplyQ,thetotalquantitydemandedforbothfinalconsumptionandasanintermediateinputintheproductionofothergoods.Qisan

Ethier

(

1982

)aggregatorgivenby:

whereσj>0istheelasticityofsubstitutionacrossgoodswithinsectorj,andr(ωj)isthedemandofgoodsωj.TheoptimaldemandofgoodsωjisdeterminedbythecostminimizationsubjecttoEquation(

7

)andisdefinedas:

wherePisapriceindexdefinedas:

countrie