异质性企业经典文献 melitz 2003年

异质性企业经典文献 melitz 2003年 EconometricaVol.71No.6November20031695–1725THEIMPACTOFTRADEONINTRA -INDUSTRYREALLOCATIONSANDAGGREGATEINDUSTRYPRODUCTIVITYBY MARCJ.MELITZ1Thispaperdevelopsadynamicindustrymodelwithheterogeneousrmstoanalyzetheintra-industryeffectsofinternationaltrade.Themodelshowshowtheexposuretotradewillinduceonlythemoreproductivermstoentertheexportmarketwhilesomelessproductivermscontinuetoproduceonlyforthedomesticmarketandwillsimul-taneouslyforcetheleastproductivermstoexit.Itthenshowshowfurtherincreasesintheindustry’sexposuretotradeleadtoadditio nalinter-rmreallocationstowardsmoreproductiverms.Thepaperalsoshowshowtheaggregateindustryproductivitygrowthgeneratedbythereallocationscontributestoawelfaregainthushighlightingabenetfromtradethathasnotbeenexaminedtheoreticallybefore.ThepaperadaptsHopenhayn’s1992adynamicindustrymodeltomonopolisticcompetitioninageneralequilibriumsetting.InsodoingthepaperprovidesanextensionofKrugman’s1980trademodelthatincorporatesrmlevelproductivitydifferences.Firmswithdifferentproductivitylevelscoexistinanindustrybecauseeachrmfacesinitialuncertaintycon-cerningitsproductivitybeforemakinganirreversibleinvestmenttoentertheindustry.Entryintotheexportmarketisalsocostlybuttherm’sdecisiontoexportoccursafteritgainsknowledgeofitsproductivity.KEYWORDS:Intra-industrytradermheterogeneityrmdynamicsselection.1.INTRODUCTIONRECENTEMPIRICALRESEARC Husinglongitudinalplantorrm-leveldatafromseveralcountrieshasoverwhelminglysubstantiatedtheexistenceoflargeandpersistentproductivitydifferencesamongestablishmentsinthesamenarrowlydenedindustries.Someofthesestudieshavefurthershownthatthesepro-ductivitydifferencesarestronglycorrelatedwiththeestablishment’sexportstatus:relativelymoreproductiveestablishmentsaremuchmorelikelytoex-portevenwithinso-called―exportsectors‖asubstanti alportionofestab-lishmentsdonotexport.Otherstudieshavehighlightedthelargelevelsofresourcereallocationsthatoccuracrossestablishmentsinthesameindustry.Someofthesestudieshavealsocorrelatedthesereallocationswiththeestab-lishments’exportstatus.Thispaperdevelopsad ynamicindustrymodelwithheterogeneousrmstoanalyzetheroleofinternationaltradeasacatalystfortheseinter-rmreallo-cationswithinanindustry.Themodelisabletoreproducemanyofthemostsalientpatternsemphasizedbyrecentmicro-levelstudiesrelatedtotrade.Themodelshowshowtheexposuretotradeinducesonlythemoreproductivermstoexportwhilesimultaneouslyforcingtheleastproductivermstoexit.Boththeexitoftheleastproductivermsandtheadditionalexportsalesgainedby1ManythankstoAlanDeardorffJimLevinsohnandElhananHelpmanforhelpfulcommentsanddiscussions.Thismanuscripthasalsobenetedfromcommentsbytheeditorandtwoanony-mousreferees.FundingfromtheAlfredP.SloanFoundationisgratefullyacknowledged.16951696MARCJ.MELITZthemoreproductivermsreallocatemarketsharestowardsthemoreproduc-tivermsandcontributetoanaggregateproductivityincrease.Protsarealsoreallocatedtowardsmoreproductiverms.Themodelisalsoconsistentwiththewidelyreportedstoriesinthebusinesspressdescribinghowtheexposuretotradeenhancesthegrowthopportunitiesofsomermswhilesimultaneouslycontributingtothedownfallor―downsizing‖ofotherrmsinthesamein-dus trysimilarlyprotectionfromtradeisoftenreportedtoshelterinefcientrms.Rigorousempiricalworkhasrecentlycorroboratedthisanecdotalevi-dence.BernardandJensen1999afortheU.S.AwChungandRoberts2000forTaiwanandCleridesLackandTybout1998forColombiaMexicoandMoroccoallndevidencethatmoreproductivermsself-selectintoexportmarkets.AwChungandRoberts2000alsondevidencesug-gestingthatexposuretotradeforcestheleastproductivermstoexit.Pavcnik2002directlylooksatthecontributionofmarketsharereallocationstosec-toralproductivitygrowthfollowingtradeliberalizationinChile.Shendsthatthesereallocationssignicantlycontributetoproductivitygrowthinthetrad-ablesectors.InarelatedstudyBernardandJensen1 999bndthatwithin-sectormarketsharereallocationstowardsmoreproductiveexportingplantsaccountsfor20ofU.S.manufacturingproductivitygrowth.Clearlytheseempiricalpatternscannotbemotivatedwithoutappealingtoamodeloftradeincorporatingrmheterogeneity.Towardsthisgoalthispa-perembedsrmproductivityheterogeneitywithinKrugman’smodeloftradeunderm onopolisticcompetitionandincreasingreturns.ThecurrentmodeldrawsheavilyfromHopenhayn’s1992a1992bworktoexplaintheendoge-nousselectionofheterogeneousrmsinanindustry. Hopenhaynderivestheequilibriumdistributionofrmproductivityfromtheprotmaximizingdeci-sionsofinitiallyidenticalrmswhoareuncertainoftheirinitialandfutureproductivity.2ThispaperadaptshismodeltoamonopolisticallycompetitiveindustryHopenhaynonlyconsiderscompetitivermsinageneralequilib-riumsetting.3Acontributionofthispaperistoprovidesuchageneralequilib-riummodelincorporatingrmheterogeneitythatyetremainshighlytractable.Thisisachievedbyintegratingrmheterogeneityinawaysuchthattherel-evanceofthedistributionofproductivitylevelsforaggregateoutcomesiscompletelysummarizedbyasingle―sufcient‖statistic—an averagermpro-ductivitylevel.Oncethisproductivityaverageisdeterminedthemodelwith2Oneofthemostrobustempiricalpatternsemergingfromrecentindustrystudiesisthatnewentrantshaveloweraverageproductivityandhigherexitratesthanolderincumbents.Thissug-geststhatuncertaintyconcerningproductivityisanimportantfeatureexplainingthebehaviorofprospectiveandnewentrants.3Montagna1995alsoadaptsHopenhayn’smodeltoamonopolisticcompetitionenvironmentinapartialequilibriumsettingbutconnestheanalysistoastaticequilibriumwithnoentryorexitandfurtherconstrainsthedistributionofrmproductivitylevelstobeuniform.Althoughitisassumedthatonlythemoreproductivermsearningpositiveprotsremainintheindustryinfutureperiodsthepresentvalueoftheseprotowsdoesnotenterintotherms’entrydecision.IMPACT OFTRADE1697productivityheterogeneityyieldsidenticalaggregateoutcomesasonewithrep-resentativermsthatallsharethesameaverageproductivitylevel.Thissimplicitydoesnotcomewithoutsomeconcessions.TheanalysisreliesontheDixitandStiglitz1977modelofmonopolisticcompetition.Althoughthismodelingapproachisquitecommoninthetradeliteratureitalsoexhibitssomewell-knownlimitations.Inparticulartherms’markupsareexogenouslyxedbythesymmetricelasticityofsubstitutionbetweenvarieties.AnotherconcessionisthesimplicationofthermproductivitydynamicsmodeledbyHopenhayn1992a.Neverthelessthecurrentmodelpreservestheinitialrmuncertaintyoverproductivityandtheforwardlookingentrydecisionofrmsfacingsunkentrycostsandexpectedfutureprobabilitiesofexit.AsinHopen-hayn1992atheanalysisisrestrictedtostationaryequilibria.Firmscorrectlyanticipatethisstableaggregateenvironmentwhenmakingallrelevantdeci-sions.Theanalysisthenfocusesonthelongruneffectsoftradeontherelativebehaviorandperformanceofrmswithdifferentproductivitylevels.AnotherrecentpaperbyBernardEatonJensonandKortum2000henceforthBEJKalsointroducesrm-levelheterogeneityintoamodeloftradebyadaptingaRicardianmodeltorm-speciccomparativeadvantage.Bothpaperspredictthesamebasickindsoftrade-inducedreallocationsal-thoughthechannelsandmotivationsbehindthesereallocationsvary.InBEJKrmscompetetoproducethesamevariety—inclu dingcompetitionbetweendomesticandforeignproducersofthesamevariety.Thisdeliversanendoge-nousdistributionofmarkupsafeaturethatismissinginthispaper.BEJKalsoshowhowtheirmodelcanbecalibratedtoprovideagoodttoacombinationofmicroandmacroUSdatapatterns.Comparativestaticsarethenobtainedbysimulatingthisttedmodel.TheBEJKmodelassumesthatthetotalnum-berofworldvarietiesproducedandconsumedremainsexogenouslyxedandreliesonaspecicparameterizationofthedistributionofproductivitylevels.Incontrastthecurrentpaperallowsthetotalrangeofvarietiesproducedtovarywiththeexposuretotradeandendogenouslydeterminesthesubsetofthosevarietiesthatareconsumedinagivencountry.Despiteleavingthedis-tri butionofrmproductivitylevelsunrestrictedthemodelremainstractableenoughtoperformanalyticalcomparisonsofsteadystatesthatreectdifferentlevelsofexposuretotrade.Althoughthecurrentmodelonlyconsiderssym-metriccountriesitcaneasilybeextendedtoasymmetriccountriesbyrelyingonanexogenouslyxedrelativewagebetweencountries.4Inthismodeldiffer-encesincountrysize—holdingtherelativewagexed—onlyaffecttherelativenumberofrmsandnottheirpr oductivitydistribution.Thisstraightforwardextensionisthereforeomittedforexpositionalsimplicity.4ThisassumptionisalsomadeinBEJK.SeeHelpmanMelitzandYeaple2002foranexten-sionofthecurrentmodelthatexplicitlyconsiderstheasymmetriccountrycasewhentherelativewageisdeterminedviatradeinahomogeneousgoodsector.1698MARCJ.MELITZOnelastbutimportantinnovationinthecurrentpaperistointroducethedynamicforward-lookingentrydecisionofrmsfacingsunkmarketen-trycosts.Firmsfacesuchcostsnotjustfortheirdomesticmarketbutalsoforanypotentialexportmarket.5Thesecostsareinadditiontotheper-unittradecoststhataretypicallymodeled.Bothsurveyandeconometricworkshavedoc-umentedtheimportanceofsuchexportmarketentrycosts.DasRobertsandTybout2001econometricallyestimatethesecostsaverageoverU.S.1Mil-lionforColombianplantsproducingindustrialchemicals.Aswillbedetailedlatersurveysrevealthatmanagersmakingexportrelateddecisionsaremuchmoreconcernedwithexportcoststhatarexedinnatureratherthanhighper-unitcosts.FurthermoreRobertsandTybout1977aforColombiaBernardandJensen2001fortheU.S.andBernardandWagner2001forGer-manyestimatethatthemagnitudeofsunkexportmarketentrycostsisimpor-tantenoughtogenerateverylargehysteresiseffectsassociatedwithaplant’sexportmarketparticipation.62.SETUPOFTHEMODEL2.1.DemandThepreferencesofarepresentativeconsumeraregivenbyaC.E.S.utilityfunctionoveracontinuumofgoodsindexedbyω:Uω ???qωρdω1/ρwherethemeasureoftheset??representsthemassofavailablegoods.Thesegood saresubstitutesimplying0ltρlt1andanelasticityofsubstitutionbe-tweenanytwogoodsofσ1/1? ?ρgt1.AswasoriginallyshownbyDixitandStiglitz1977consumerbehaviorcanbemodeledbyconsideringthesetofvarietiesconsumedasanaggregategoodQ?Uassociatedwithanaggre-gate pricePω ???pω1??σdω11??σ15Sunkmarketentrycostsalsoexplainthepresenceofsimultaneousentryandexitinthesteadystateequilibrium.6Sunkexportmarketentrycostsalsoexplainthehighersurvivalprobabilitiesofexportingrms—evenaftercontrollingfortheirhighermeasuredproductivi ty.SeeBernardandJensen1999a2002forevidenceonU.S.rms.IMPACTOFTRADE1699TheseaggregatescanthenbeusedtoderivetheoptimalconsumptionandexpendituredecisionsforindividualvarietiesusingqωQpωP??σ2rωRpωP1??σwhereRPQω ???rωdωdenotesaggregateexpenditure.2.2.ProductionThereisacontinuumofrmseachchoo singtoproduceadifferentvari-etyω.ProductionrequiresonlyonefactorlaborwhichisinelasticallysuppliedatitsaggregatelevelLanindexoftheeconomy’ssize.Firmtechnologyisrep-resented byacostfunctionthatexhibitsconstantmarginalcostwithaxedoverheadcost.Laborusedisthusalinearfunctionofoutputq:lfq/??.Allrmssharethesamexedcostfgt0buthavedifferentproductivitylevelsindexedby??gt0.Forexpositionalsimplicityhigherproductivityismodeledasproducingasymmetricvarietyatlowermarginalcost.Higherproductivitymayalsobethoughtofasproducingahigherqualityvarietyatequalcost.7Re-gardlessofitsproductivityeachrmfacesaresidualdemandcurvewithcon-stantelasticityσandthuschoosesthesameprotmaximizingmarkupequaltoσ/σ??11/ρ.Thisyieldsapricingrulep??wρ??3wherewisthecommonwageratehereafternorm alizedtoone.Firmprotisthenπ??r????l??r??σ??fwherer??isrmrevenueandr??/σisvariableprot.r??andhenceπ??alsodependontheaggregatepriceandrevenueasshownin2:r??RPρ??σ??14π??RσPρ??σ??1??f57Giventheformofproductdifferentiationthemodelingofeithertypeofprod uctivitydiffer-enceisisomorphic.1700MARCJ.MELITZOntheotherhandtheratiosofanytworms’outputsandrevenuesonlyde-pendontheratiooftheirproductivitylevels:q??1q??2??1??2 σr??1r??2??1??2σ??16Insummaryamoreproductivermhigher??willbebiggerlargeroutputandrevenueschargealowerpriceandearnhigherprotsthanalesspro-ductiverm.2.3.AggregationAnequilibriumwillbecharacterizedbyamassMofrmsandhenceMgoodsandadistribution????ofproductivitylevelsoverasubsetof0?.InsuchanequilibriumtheaggregatepricePdenedin1isthengivenbyP?0p??1??σM????d??11??σUsingthepricingrule3thiscanbewrittenPM1/1??σp????where?????0??σ??1????d??1σ??17????isaweightedaverageofthermproductivitylevels??andisindependentofthenumberofrmsM.8Theseweightsreecttherelativeoutputsharesofrmswithdifferentproductivitylevels.9????alsorepresentsaggregateproduc-tivitybecauseitcompletelysummarizestheinformationinthedistributionofproductivitylevels????relevantforallaggregatevariablesseeAppendix:PM11??σp????RPQMr????QM1/ρq?????Mπ????whereR?0r??M????d??and??0π??M????d??representaggre-gaterevenueorexpenditureandprot. ThusanindustrycomprisedofMrmswithanydistributionofproductivitylevels????thatyieldsthesameav-erageproductivitylevel????willalsoinducethesameaggregateoutcomeasanindustrywithMrepresentativermssharingthesameproductivitylevel??????.8Subsequentconditionsontheequilibrium????mustofcourseensurethat????isnite.9Usingq??/q??????/????σsee6????canbewrittenas??????1?0????1q??/q????????d??.????isthereforetheweightedharmonicmeanofthe??’swheretheweightsq??/q????indextherms’relativeoutputshares.IMPACTOFTR ADE1701Thisvariablewillbealternativelyreferredtoasaggregateoraverageproduc-tivity.Furthernotethat??rR/Mand??π?/Mrepresentboththeaveragerevenueandprotperrmaswellastherevenueandprotlevelofthermwithaverageproductivitylevel??????.3.FIRMENTRYANDEXITThereisalargeunboundedpoolofprospectiveentrantsintotheindustry.Priortoentryrmsareidentical.Toenterrmsmustrstmakeaninitialinvestmentmodeledasaxedentrycostfegt0measuredinunitsoflaborwhichisthereaftersunk.Firmsthendrawtheirinitialproductivityparameter??fromacommondistributiong??.10g??haspositivesupportover0?andhasacontinuouscumulativedistributionG??.Uponentrywithalowproductivitydrawarmmaydecidetoimmediatelyexitandnotproduce.Ifthermdoesproduceitthenfacesaconstantacrossproductivitylevelsprobabilityδineveryperiodofabadshockthatwouldforceittoexit.Althoughtherearesomerealisticexamplesofsevereshocksthatwouldconstrainarmtoexitindependentlyofproductivitysuchasnat-uraldisastersnewregulationproductliabilitymajorchangesinconsumertastesitisalsolikelythatexitmaybecausedbyaseriesofbadshocksaffect-ingtherm’sproductivity.Thistypeofrmlevelprocessi sexplicitlymodeledbyHopenhayn1992a1992b.Thesimplicationmadeinthismodelentailsthattheshapeoftheequilibriumdistributionofproductivity????andtheex-antesurvivalprobabilitiesareexogenouslydeterminedbyg??andδ.Ontheotherhandtherangeofproductivitylevelsforsurvivingrmsandhencetheaverageproductivitylevelareendogenouslydetermined.11Importantlythissimpliedindustrymodelwillneverthelessgenerateoneofthemostrobustempiricalpatternshighlightedbymicro-levelstudies:newentrantsincludingthermswhoseentryisunsuccessfulwillhaveonaveragelowerproductivityandahigherprobabilityofexitthanincumbents.Thispaperonlyconsiderssteadystateequilibriainwhichtheaggregatevari-ablesremainconstantovertime.Sinceeachrm’sproductivityleveldoesnotchangeovertimeitsoptimalperperiodprotlevelexcludingfewillalsore-mainconstant.Anenteringrmwithproductivity??wouldthenimmediatelyexitifthisprotlevelwerenegativeandhenceneverproduceorwouldpro-duceandearnπ???0in everyperioduntilitishitwiththebadshockandis10Thiscapturesthefactthatrmscannotknowtheirownproductivitywithcertaintyuntiltheystartproducingandsellingtheirgood.Recallthatproductivitydifferencesmayreectcostdifferencesaswellasdifferencesinconsumervaluationsofthe good.11Theincreasedtractabilityaffordedbythissimplicationpermitsthedetailedanalysisoftheimpactoftradeonthisendogenousrangeofproductivitylevelsandonthedistributionofmarketsharesandprotsacrossthisrange.1702MARCJ.MELITZforcedtoexit.Assumingthatthereisnotimediscounting12eachrm’svaluefunctionisgivenbyv??max0?t01??δtπ??max01δπ??wherethedependenceofπ??onRandPfrom5isunderstood.Thus????inf??:v??gt0identiesthelowestproductivitylevelhereafterreferredtoasthecutofflevelofproducingrms.Since.