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Melitz(2003)Outline1.Summary2.setupofthemodel3.FirmEntryandExit4.Closed-economyEqlm6.Open-economyEqlm7.ImpactofTrade8.Conclusions5.OverviewandassumptionoftheopeneconomymodelMelitz(2003)Summary1.Themodelshowshowtheexposuretotradewillinduceonlythemoreproductivefirmstoentertheexportmarket(whilesomelessproductivefirmstocontinuetoproduceonlyforthedomesticmarket)andwillforcetheleastproductivefirmstoexit.2.Itthenshowshowfurtherincreasesintheexposuretotradeleadtoadditionalinter-firmreallocationstowardsmoreproductivefirms.3.Thepaperalsoshowshowtheaggregateindustryproductivitygrowthgeneratedbythereallocationscontributestoawelfaregain,thushighlightingabenefitfromtradethathasnotbeenexaminedtheoreticallybefore.SummaryThepaperdevelopsadynamicindustrymodelwithheterogeneousfirmstoanalyzetheintra-industryeffectsofintltrade.Rigorousempiricalworkhasrecentlycorroboratedthisanecdotalevidence.BernardandJensen(1999a)(fortheU.S.)Aw,Chung,andRoberts(2000)(forTaiwan),Clerides,Lack,andTybout(1998)(forColombia,Mexico,andMorocco)allfindevidencethatmoreproductivefirmsself-selectintoexportmarkets.Aw,Chung,andRoberts(2000)alsofindevidencesuggestingthatexposuretotradeforcestheleastproductivefirmstoexit.Pavcnik(2002)directlylooksatthecontributionofmarketsharereallocationstosectoralproductivitygrowthfollowingtradeliberalizationinChile.Shefindsthatthesereallocationssignificantlycontributetoproductivitygrowthinthetradablesectors.Inarelatedstudy,BernardandJensen(1999b)findthatwithinsectormarketsharereallocationstowardsmoreproductiveexportingplantsaccountsfor20%ofU.S.manufacturingproductivitygrowth.Melitz(2003)ThepaperadaptsHopenhayn's(1992a)dynamicindustrymodeltomonopolisticcompetitioninaequilibriumsetting.general(Hopenhayn's(1992a,1992b)worktoexplaintheendogenousselectionofheterogeneousfirmsinanindustry;Hopenhaynonlyconsiderscompetitivefirms)thepaperprovidesanextensionofKrugman's(1980)trademodelthatincorporatesfirmlevelproductivitydifferences.SummaryMelitz(2003)5Melitz(2003)•2.1Demand–Preferences:CESutilitycontinuumofgoodsmassofavailablegoods,elasticityofsubstitutionbetweentwogoods–Define:aggregategood:aggregateprice:–Optimalconsumptionandexpenditure:2.setupofthemodel6Melitz(2003)2.2Supply–Thereexistsacontinuumoffirms,eachchoosingtoproduceadifferentvariety,withonefactor–labor.–Productiontechnology:fixedcost:productivity:–FOCoffirm’sprofitmaximizationproblemimplies:=1:commonwageratewhichimpliesconstantmarkup:andfirmprofit:–Revenueandprofitasfunctionsofaggregatevariables:Equations(3)-(6):moreproductivefirms(higher)willbebigger(largeroutputandrevenues),chargealowerprice,andearnhigherprofits.7Melitz(2003)2.3Aggregation–Eqlm:(1)amassoffirms(andgoods):(2)adistributionofproductivity:–Aggregate/Averageproductivity:–Otheraggregatevariables:–Otheraveragevariables:8Melitz(2003)•3.FirmEntryandExit–Toentertheindustry,firmsmustinvestafixedentrycost:–Afterentry,firmsdrawtheirproductivityfromacommondistn,withacumulativedistributionandsupportover.–Ifproductivityislow,thefirmeither(1)exitimmediately,or(2)produce,butfacesaprobofofabadshockineachperiodthatforcesittoexit.–Newentrants(includingunsuccessfulones)willhave,onaverage,lowerproductivityandahigherprobofexitthanincumbents.–Firm’svaluefunction:–Cutoffproductivityofproducingfirms:If,thefirmwillexitimmediately.9Melitz(2003)3.FirmEntryandExit–Eqlmproductivitydistnistheconditionaldistnofonwhereistheex-anteprobofsuccessfulentry.–Aggregateproductivityisafunctionofthecutoffproductivity:–Averagerevenueandprofit10Melitz(2003)•3.FirmEntryandExit3.1Zerocutoffprofit(ZCP)condition(afterentry):3.2Freeentry(FE)condition(beforeentry)-presentvalueoftheaverageprofitflow:-netvalueofentry:11Melitz(2003)4.Closed-economyEqlm12Melitz(2003)4.Closed-economyEqlm–Inastationaryeqlm:-numberoffirmsisstable:(ismassofnewentrants)-labormarketclears:laborforproduction:laborforentrycost:Thus-massofproducingfirms:4.1analysisoftheequilibrium-welfareperworker:(13)and(14):L(economysize)↑→M(varieties)↑→W(welfare)↑13Melitz(2003)---theexportmarketentrydecisionoccursafterthefirmgainsknowledgeofitsproductivity---wherebyunitsofagoodmustbeshippedinorderfor1unittoarriveatdestination---identicalcountries:inordertoensurefactorpriceequalizationacrosscountries---n+12countries)allcountriessharethesamewage,---Exporttoanyforeigncountryrequiresafixedcost:14Melitz(2003)•6.Open-economyEqlm–Timingofevents:Entrydecision(basedon)→productivity()isrevealed→productiondecision(basedon)andexportdecision(basedon)–Pricesfortwomarkets:–Revenuefortwomarkets:Combinedrevenue:15Melitz(2003)•6.Open-economyEqlm–Profitsfortwomarkets:whereisamortizedper-periodfixedexportcost.Combinedprofit:–Firm’svaluefunction:-cutoffproductivityforentry:-cutoffproductivityforexporting:bydefinition:≥–Conditionforpartitionoffirms:combinewithand(16)toget:-if,novariablecostcaninducethepartition.-if,itwillinducepartitionevenifnovariablecost(=1).16Melitz(2003)6.Open-economyEqlm–Eqlmdistnoffirms:-Eqlmdistnofproductivitylevelforincumbentfirms:-Ex-anteprobofsuccessfulentry:-Ex-anteprobthatonesuccessfulfirm