WTO-The Impact of Geopolitical Conflicts on Trade,Growth,and Innovation-report (2022-07-06)（英文）行业资料

WorkingPaperERSD_____________________deOrganizationhandStatisticsDivision_____________________GEOPOLITICALCONFLICTSONTRADEGROWTHANDINNOVATIONsyofCaliforniaSanDiegoManuscriptdate10June2022______________________________________________________________________________sitingscholarsandistheproductofprofessionalresearchsoftheWTOoritsMembersnortheofficialpositionofanystaffmembers.Anyerrorsarethefaultoftheauthor.21IntroductionOpenmarketsandfreetradehavebeenabasictenetoftheinternationalorderemergingoutofWorldWarII.Overthatperiod,alargeconsensusregardingtheneedtoreducetradecostsandprioritizegainsfromtradeledtoacontinuousdeepeningoftheinternationaltraderegime.TheEuropeanUnionenlargedeastwardsandmanycountriesjoinedtheWorldTradeOrganization(WTO),includingRussia,thecenter-of-gravityoftheformerSovietbloc.AtthesametimeChina,displayedspectaculargrowthrates,integratedtoworldmarkets,andwasrecognizedasamarketeconomybyalsojoiningtheinternationaltradesystem.However,thelastdecadehaswitnessedthebeginningofabacklashagainstglobaltradeintegration.PoliticalscientistsconjecturethattheemergenceofChinaasanewsuperpoweragainstanincumbentU.S.mightleadtostrategiccompetitionbetweenthesecountries—oneinwhichgeopoliticalforcesandthedesiretolimitinterdependencetakeprimacyoverwin-wininternationalcooperation1.RisingsupportforpopulistandisolationistpartiesinmanyWesterncountriespointstowardsthesamedirection2.Additionally,the2022WarinUkraineandthesubsequentstrongretaliationoftheEuropeanUnion,theUnitedStates,andtheiralliesagainstRussiasuggestthattheinternationaleconomicorderbasedonopenmarketsandexpandedglobalizationcouldbereplacedbyamorefragmentedinternationaleconomicsystem.Usingthesefactsasmotivation,thispaperaimstodeterminethepotentialeffectsofincreasedandpersistentlarge-scalegeopoliticalconflictsontrade,economicgrowth,andtechnologicalinnovation.Someoftheadverseeffectsarewell-known.Increasedtradebar-riersdecreasedomesticwelfareandgainsfromtradebyshiftingproductionawayfromthemostcost-efficientproducersandleavinghouseholdswithalowerleveloftotalconsumption.Canonicaltrademodelscapturethisstaticresultthroughthefactthatwelfareispropor-tionaltothedegreeoftradeopenness(Arkolakis,Costinot,andRodr´ıguez-Clare2012)3.However,someofthemainconcernsofpolicymakersandpractitionersregardingpo-tentiallydetrimentaleffectsoflimitingtradeareabstractedawayinstandardmodels.Forinstance,thesemodelstypicallyassumeafixedtechnologydistributionfordomesticfirms,therebylimitinggainsfromtradetostaticgains.Thisassumptionrendersitimpossibletoaddressoneofthemostimportantlong-termconsequencesofcontinuedgeopoliticalcon-flictsorrecedingglobalization—namely,reducedtechnologyandknow-howspilloversthathappenthroughtrade.Inordertorealisticallyassesstheimpactoftradeconflictsonglobalinnovation,webuildamulti-sectormulti-regiongeneralequilibriummodelwithdynamicsector-specificknowledgediffusion.AsinBueraandOberfield(2020),wemodelthearrivalofnewideasasalearningprocessofproducersinacertaincountry-sector.Byengagingininternationaltrade,i.e.importingintermediateinputs,domesticinnovatorshaveaccesstonewsourcesofideas,whosequalitydependsontheproductivityofthecountriesandsectorsfromwhichtheysourceintermediates.1SeeWei(2019)andWyne(2020)forareviewofthedebateamongrespectivelyChineseandAmericanscholarsabouttheshiftinforeignpoliciestowardseachother.2Forevidenceoftheimpactoftradeshocksontheriseofpopulistpartiestopower,seeColantoneandStanig(2018).3Thisistrueofallcanonicaltrademodels.AsArkolakis,Costinot,andRodr´ıguez-Clare(2012)show,Armington(1969),Krugman(1980),EatonandS.Kortum(2002),andMelitz(2003),albeitdifferentinmotivation,areisomorphicandsummarizegainsfromtradebysomevariationoftheexpressionGα(πii)e,whereπiiisdomestictradeshareandεistheelasticityoftradeflowswithrespecttotradecosts.3Inourmodel,ideadiffusionismediatedbytheinput-outputstructureofproduction,suchthatbothsectoralintermediateinputcostsharesandimporttradesharescharacterizethesourcedistributionofideas.Innovationissummarizedbydescribingproductivityindifferentsectorsasevolvingaccordingtoatrade-shareweighted-averageoftrade-partnerssectoralproductivities.Thisprocessiscontrolledbyaparameterwhichdeterminesthespeedofdiffusionofideas,whichwecalibrateusinghistoricaldata.Productivitythusevolvesendogenouslyasaby-productofmicro-foundedmarketdeci-sions—i.e.,anexternalitythatmarketagentsaffectwiththeirbehaviorbutdonottakeintoaccountwhenmakingdecisions.Inthisframework,theoutbreakoflarge-scaletradeconflictswillhavespillovereffectsonthefuturepathofsectoralproductivitiesofallcoun-tries.Changesintradecostsinducetradediversionandcreation,which,inturn,impactproductivitydynamicsinawaythatisnotinternalizedbyagents.Aftercharacterizingthemodel,weuseittoperformpolicyexperimentsinthecontextofheightenedgeopoliticalconflicts.Weexplorethepotentialimpactofa“decouplingoftheglobaleconomy,”ahypotheticalscenariounderwhichtechnologysystemswoulddivergeintheglobaleconomy.WedividetheglobaleconomyinaWesternblocandanEasternblocbasedondifferentialscoresforeignpolicysimilarity.First,wesimulateincreasedtradecostsarisingfromgeopoliticalcircumstances,whichincreasefrictionsprohibitivelyifonecountrywantstotradewithanotheroneoutsideitsbloc.Alternatively,wesimulateascenarioofaglobalincreaseintariffs,inwhichallcountriesmovefromcooperativetariffsettinginthecontextoftheWTOtonon-cooperativetariffsetting.Nicita,Olarreaga,andSilva(2018)estimatetoincreaseglobaltariffs,onaverage,by32percentagepoints.Forsimplicity,weusethisaveragenumberasareferenceandweassumethatcountriesindifferentblocsraisetariffsagainstcountriesintheotherblocbysuchaverageamount.Ouranalysisleadstofivemainfindings.First,amulti-sectorframeworkexacerbatesdiffusioninefficienciesinducedbytradecostsrelativetoasingle-sectorone;weexplorethisissueboththroughtheoryandsimulations4.Second,weshowthattheprojectedwelfarelossesfortheglobaleconomyofadecouplingscenariocanbedrastic,aslargeas12%insomeregions;andarelargestinthelowerincomeregionsastheywouldsuffermostfromreducedtechnologyspilloversfromricherareas.Third,thedescribedsizeandpatternofwelfareeffectsarespecifictothemodelwithdiffusionofideas.Inadynamicsettingwithdiffusionofideaswelfarelossesarelargeranddisplaymorevariation.Fourth,ifoneofthemiddleincomeregions,LatinAmericaandCaribbean(LAC),wouldswitchfromthehigher-incomeWesternbloctothelowerincomeEasternbloc,itswelfarecostsofdecouplingwouldbesignificantlyhigher.Thisexperimentillustratesthatpolicymakersinlow-andmiddle-incomecountrieswouldfacedifficultdecisionsifdecouplingwouldaggravate.Fifthandfinally,thewelfarecostsofdecouplingonlyinelectronicequipment,thesectorwheredecouplingisalreadytakingplace,wouldbemuchsmallerthanunderfulldecoupling,albeitsizeable,rangingfrom0.4_1.9%.Wemakefourmaincontributionstotheliterature.First,webuildamulti-sectormodeloftheglobaleconomywithBertrandcompetition,profits,andtechnologyspilloverswhichcanbesolvedrecursivelythatpermitsassessingrealistictradepolicyexperiments.Second,wecalibratethestrengthofthediffusionoftechnologiesthroughtradewithatightfitbetweensimulatedandhistoricalGDPgrowthrates.Third,weexaminethelong-runeffectsofreal-4Beforeconductingsimulationswiththemulti-sector,multi-regionmodelcalibratedtoreal-worlddata,weexplorethediscrepancybetweenactualandoptimallevelsofideadiffusionThiscomparisonshowsthattomaximizethetotaldiffusionofideas,tradesharesmustbeattheiroptimalpointineverysector.4worldpolicyexperimentsrelatedtothedecouplingoftheglobaleconomy.Last,wedrawinsightsfromthePoliticalScienceliteratureinordertoincorporategeopoliticalconflictsintoaworkhorsetrademodel.Ourmodelbuildsontheworkthatevaluatestheimpactoftradeoninnovationandshowsthattradeopennesscanincreasethelevelofdomesticinnovation,particularlyonthesingle-sectormodelofBueraandOberfield(2020).Comparedtopreviouswork,wepresentarecursivemodelwithintermediatelinkages;calibratethestrengthofthediffusionofideastotargethistoricalGDPgrowthratesacrossallregions;andexplorediffusioninefficienciesinamulti-sectorsetting.RelatedLiterature.Ourpaperiscloselyrelatedtotheliteraturethataddsdynamicstotrademodelsbyincorporatingknowledgediffusionchannels.TheearliestexplorationsofthistopicgobacktoEatonandS.Kortum(1999),whodevelopedamulti-countrydynamicmodelinwhichfirmsinnovatebyinvestinginresearchanddevelopment(R&D)andknowledgediffuses,aftersomelag,toothermarkets.Inthismodel,diffusionhappenedsomewhatmechanically,wasunrelatedtotradeandeventuallyreachedallcountries5.Morerecently,Alvarezetal.(2013)combinedtheEatonandS.Kortum(2002)RicardianmodeloftradewithanideadiffusionprocessfirstpresentedbyS.S.Kortum(1997).Im-portantly,theauthorsconjecturedthatthediffusionprocessisproportionaltothequalityofmanagersoffirmswhoseproductreachagivendestinationmarket.Ideasflowfromonemarkettoanotherinproportiontothetradelinkagesbetweenthem.Therefore,impedi-mentstotradehavenotonlystatic,butalsodynamiccosts—astheydecreaseknowledgediffusion.OurmodelisalsocloselyrelatedtotheonedescribedbySantacreu,Li,andCai(2017),whoextendedtheoriginalmodelbyEatonandS.Kortum(1999)incorporatinglag-diffusiondynamicsintoamulti-sectorframework.Santacreu,Li,andCai(2017)buildamulti-sectormodeloftrade,innovation,andknowledgediffusion,exploringhowthewelfaregainsfromtradeareaffectedbyknowledgediffusionthroughtheirimpactonchangesincomparativeadvantage.Theyshowthatthewelfaregainsarelargerwithendogenousknowledgediffusionbecauseexistingspecializationpatternstendtogetreinforcedbyknowledgediffusion.Therearethreemaindifferencesbetweentheirworkandours.First,ourmodelempha-sizesthenexusbetweentradeandideadiffusion,whereasSantacreu,Li,andCai(2017)modeltechnologyspilloversasbeingindependentoftheamountoftrade(orotherendoge-nousvariableslikeFDIormigration).Additionally,whiletheycalibrateknowledgespilloverswithdataonpatentcitation,wecalibratethestrengthofthediffusionofideasbasedonthefitbetweenactualandsimulatedhistoricalGDPgrowthrates.Third,thepapershaveadifferentfocus:wefocusonconcretepolicyquestionsandexplorehowtheeffectofpotentialtradepolicychangesareaffectedbytheinclusionofideasdiffusioninthemodel;whiletheyhighlighthowpatternsofcomparativeadvantagechangewithtechnologyspillovers.Organization.Thispaperisorganizedasfollows.InSection2wepresentthemodel,detailingproduction,demand,andconsumptionoftheglobaleconomy.Wealsodescribethedynamicevolutionofproductivitiesindifferentregionsandsectors.InSection3wedecribethediscrepancybetweentheactualandoptimaldiffusionofideasinamulti-sector5Indifferentiatedvarietiestrademodels,knowledgediffusionshowsupinpaperslikeRomer(1990),Rivera-BatizandRomer(1991),Rivera-BatizandRomer(1991)andGrossmanandHelpman(1989).Inthetext,wefocusonpapersthatincorporateknowledgediffusiontoRicardianmodels,whichistheclassofmodelsthatthispaperfallsin.5framework.InSection4wediscussthecalibrationofthemodelandunderpintheexaminedpolicyexperiments.InSection5wepresenttheresultsofourmainpolicyexperimentsandsomealternativesimulations.Finally,weconcludeinSection6summarizingthekey2EnvironmentTimeisdiscreteandindexedbyteT.TherearedeDregionsintheglobaleconomy,whichcovereverypartoftheworldeconomy,eitherasastand-alonecountry,oraregionalaggregateofcountries.Ineachregion,therearemultipleindustriesieI.2.1DemandIneachregiondandeachperiodtarepresentativeagentmaximizesCobb-Douglasprefer-encesoverconsumptionofgoodsindifferentsectorsieI,q:max)κ{q}i年zs.t.Lκ=1i年zLpq<(1_sd,t)Yd,ti年zYd,t=wd,tyd,t+rd,tkd,t+Td,t+LΠi年z(1)Yd,tisgrossincomedeterminedbywd,t,yd,t,thewageandmeasureofworkers;rd,tkd,t,capitalincome;Td,t,transfers;andΠ,profits.Wesetsd,ttobetheexogenoussavingsrate.Hence,weabstractfromintertemporaloptimizationasdiscussedfurtherbelowinthesubsectiononmarketclearing.Savingsareusedtofinanceinvestmentasdiscussedbelow.ThispreferencestructureimpliesthefollowingdemandfunctionforgoodsinsectorieI:q=Theaggregatepriceindexsatisfies:P,t=K.Πi年z(p)κWithK=Πi年z(κ)去κ,aconstant.(2)(3)2.2ProductionTherearemanyproducersofdifferentvarietiesωofeachcommodityi.Firmsareendowedwithanidenticaltechnologyandcombinefactorsofproductionf,tandintermediateinputsmtoproducevarietyq,t(ω):q,t(ω)=z,t(ω)|(Ψ)(f,t)pl+(Ψ)(m)pl]pi一l(4)6Thecostoftheunitinputbundle,c,isafunctionofthepricesoffactorsofproduction,pf,t,andpricesofcommoditiesusedasintermediates,p:c=|Ψ(pf,t)1去ρi+Ψ(p)1去ρi卜l一pi(5)Firmscombinefactorsofproduction(f,t)andintermediatecommodities(m)accord-ingtothefollowingsub-productionfunctions:f,t=┌(Ψ,)kl+(Ψ,lt)yl┐ui一l(6)m=(Ψ)(q)ului一l(7)Thefirstaggregatorcombinescapital,kd,t,andlabor,yd,t,asfactorsofproduction,whilethesecondoneusessectoralcommoditiesqasintermediateinputs.2.3SupplyofFactorsofProductionThesupplyofthethreefactorsofproductionchangesovertime.Theyareperfectlymobileandthushaveauniformpriceacrosssectors.Foreachcountry,anexogenouspathofendowmentsoflaborisimposedbasedonexternalprojectionsfromtheUnitedNationsandtheInternationalMonetaryFundasdescribedinthedatasectionbelow.Aggregatecapital,kd,t,isafunctionofcapitalinthepreviousperiod,kd,t去1,deprecia-tion,δ,andinvestment,ind,t,evolvingaccordingtothefollowinglawofmotion:kd,t=(1_δd)kd,t去1+ind,t(8)ThereisaninvestmentsectorthatcombinesdifferentsectoralcommoditiesqwithLeontieftechnologyunderperfectcompetition:ind,t=min,,...,、(9)Hence,thedemandforanyparticularinputiandthepriceoftheaggregateinvestmentgoodare,respectively:q=χind,t(10)p=Lχp(11)i年zWeassumethattheratioofaregion’stradebalancetoitstotalincomeisfixed.Ab-stractingfromothercomponentsofthecurrentaccount,thecapitalaccountisequaltothetradebalance.Assumingafixedtradebalanceratio(relativetoincome)thusimpliesthattheinvestmentrateisequaltothesavingsrate.Hence,inequilibriumwehave:Lpind,t=sd,tYd,t(12)i年z7minminns,2.4InternationaltradeConsumers,investorsandfirmsdemandsectoralcommoditiesqbyamountsqqandq,respectively.Alocalproducersourcethecheapestlandedvarieties{q(ω):ωe[0,1]}fromallcountriesseDandproducesthesectoralcommodityaccordingtothefollowingtechnology:qqgldgjl(13)ThepriceofcommodityjeIthussatisfies:p,1]p(ω)1去σjdω┐ll一gj(14)Tradehappensthroughdemandforvarietiesusedasinputsintheproductionofsectoralgoodsq.Thesegoods,inturn,areusedintwodifferentways:asintermediateinputsintheproductionofvarietiesandinvestmentgoods;andinfinalconsumption.Letx(ω)bethelandedunitcostofsupplyingvarietyωofcommodityieIproducedinsourceregionseDanddeliveredtoregiondeD:x(ω)==(15)wheretmaregrossimporttaxes,whichcanbesourceanddestinationspecific;τd,t21arebilateralicebergtradecosts;andz,t(ω)isthefirm’sproductivity.Thelastequalityfollowsfromdefining=tm.τd,t.casthelandedinputbundlecosts.SincevarietiescanbesourcedfromeveryregionseDconsumersindestinationregiondeDwillonlybuyvarietyωfromthesourcewiththelowestlandedprice.FollowingBernardetal.(2003),producersengageinBertrandcompetition.Foreachcountry,orderfirmsk=[1,2,...]suchthatzs,t(ω)>zs,t(ω),....Ifthelowest-costproviderofthevarietyωtocountrydeDisaproducerfromcountryseD,thepriceindsatisfies:zs,t(ω)è2MCof2ndmostproductivefirmfromsAssumption1(Productivitydraws).WefollowthecanonicalEatonandS.Kortum(2002)assumptionthatandtakez,t(ω):A×D×I×Ω-R+tobetherealizationofani.i.d.ran-domvariable,whereAisthesetofstatesoftheworld.ProductivityisdistributedaccordingF,t(z)=exp{_λz去θi}(17)Thecountry-specificFr´echetdistributionhasaregion-commodity-specificlocationpa-rameterλ,whichdenotesabsoluteadvantage(betterdrawsforallvarieties),andasector-speccificscaleparameterθi,whichgovernscomparativeadvantage(higherθiimpliesless8variabilityinproductivityandlowerpotentialfordiversificationaccordingtocomparativeadvantage).WeshowintheAppendixthatpricesinthedestinationregiondeDwillbe,respectively:p=Γ1(Φ)去whereΓ1isaconstant6;Φ=|s年pλ()去θi.Asthereareinfinitelymanyvarietiesintheunitinterval,bythelawoflargenumbers,theexpenditureshareofdestinationregiondeDongoodscomingfromsourcecountryseDconvergestotheirexpectedvalues.πd,tdenotesexpendituresofconsumersinregiondeDongoodscomingfromregionseDasashareoftheirtotalexpenditureoncommodityieIandisgivenby:d,tπd,t=λ(d,t)去θd,tSectoralcommoditiescanbeusedbothforfinalconsumptionandasintermediateinputs.Giventheassumptionsabove,π,whichistheexpenditureongoodscomingfromstobeusedasintermediateinputsinsectoriofcountrydasashareoftotalexpendituresofthatsectorongoodsfromsectorjisequaltothetradesharesforfinalconsumption,i.e:(Ai,j)π=π.InthepresenceofBertrandCompetition,weshowintheAppendixthatsourcefirmsrealizeaprofitwhichisproportionaltothetotalexpenditureofdestinationcountries.Inparticular,profitsare:Π=πd,te;withithe=pqe=Leag年{c,in,m}2.5MarketClearingIneverregion,factormarketsmustclear,suchthattheuseofeachfactorofproductionsummedoverallsectorsieIinregionseDbyproducersofvarietiesmustequalitssupply:Lk,t=ks,Ly=ys,t(21)i年zi年zThemainequilibriumconditionsare|D|.|I|expenditureequationsthatsatisfy:e=πη,.η,,.ei+Lπ.╱κ.(1_sd,t)Yd,t+e、(22)d年pThefirstlineofequation(22)denotesthepurchasingbyfirmsofintermediateinputs.πisthetradeshareofsinvarietiesdemandedbytheproducerofsectoralgoodjin6Specifically,Γ1=′1一+/、┐9i]Γ、,whereΓ(．)istheGammafunction9regiond;ηisthecostshareofsectorjinthetotalintermediateexpenditureuseinsectori;ηisthecostshareofintermediatesintotalcostinsectori;andeisthetotalcostpayments7.Thesecondlinerepresentsexpenditurerelatedtotheuseofvarietiesintheproductionofsectoralgoodsforfinalconsumptionandforinvestmentgoods.κistheCobb-Douglasparameterthatdenotesexpenditureshareinsectoriasafractionoftotalfinalgoodsexpenditures.Pricesoffactorsofproductionareproportionaltotheiruseandtotalcost.Sincefactorsareusedineverysector,weaggregateoversectorstocalculateaggregatepaymentstoeachfactorofproduction:ws,tys,t=η.η..πd,t.ers,tks=η.η..πd,t.ewhereηisthecostshareofvalueaddedintotalcost;and,foreachfactorofproductionne{y,k},ηisthecostshareoffactornintotalexpenditureonfactorsofproduction8.Thegovernmentcollectstariffsandothertaxesanddirectsthemtotherepresentativehouseholdaslump-sumtransfers:Td,t=πd,teRecallingthatprofitsareΠ=|d年pπd,tecompletesallelementsnecessarytocharacterizedomesticincome:Ys,t=ws,tys,t+rs,tks,t+Ts,t+LΠj年zOurmodelischaracterizedbyasequenceofstaticequilibriasatisfyingtheequilibriumequationsineachoftheperiodst.Solutionsinthedifferentperiodsarerelatedintwoways.First,thecapitalstockinperiodtisdeterminedbyinvestmentinperiodtandthecapitalstockinperiodt_1(plusdepreciation)asspecifiedinequation(8).Second,thecountry-sector-specifictechnologyparametersλchangeovertimeasspecifiedinequation(24)below.Weabstractfromintertemporaloptimizationofconsumption,imposinginsteadafixedsavingsrate.Thismakesthemodelcomputationallymoretractableandleadstoamorestraightforwardinterpretationofthesimulationresults.Wefocusonthelong-runeffectsofdecouplingoftheglobaleconomyfrom2020to2040andnotontheeffectsofdecoupling7Thecostsharesare,respectivelly:η=Ψ(p)1┐ui/(Ψ(pm)1┐pi/(Ψ(pf,t)1┐pi+Ψ(pm)1┐pi).8Onceagain,themathematicalexpressionsfortheΨ(pf,t)1┐pi/(Ψ(pf,t)1┐pi+Ψ(p)1┐pi);and,foreach=k~4Ψ(p,t)1┐ui)and=costsharesare:η=factorofproductionn∈{e,k},η=Ψ(pn)1┐vi/g~|e,k}Ψ(pq,t)1┐vi,withpnstandingforthepriceoffactorn.onthetrajectoryfollowedbytheeconomyto2040.However,abstractingfromintertempo-raloptimizationimpliesthatpotentialeffectsthroughchangesinsavingsratesoncapitalaccumulationarealsoabstractedfrom9.2.6DynamicinnovationUnlikeinthestandardEatonandS.Kortum(2002)modelorintheBertrand-competitionversiondevelopedinBernardetal.(2003),weassumethateachregion’slocationparameterevolvesovertime.EachcommodityieIandeachcountrydeDhasadifferentperiod-specificproductivitydistributionF,t(z).Ourmodelfollowsastrandoftheliteraturewhichmodelsideasdiffusionthroughrandommatchesbetweendomesticandforeignmanagers10.SeminalexamplesofthisworkincludeJovanovicandRob(1989)andS.S.Kortum(1997).Morerecently,Alvarezetal.(2013)exploredhowideadiffusionisintertwinedwithtradelinkages.LikeBueraandOberfield(2020),weassumethatamanagerdrawsnewinsightsasaby-productofsourcingabasketofinputs.Weextendthisframeworktoamodelwithdiffusionofideasinamulti-sectorcontextandsolveitinarecursivefashionthatpermitsforward-lookingassessmentofpolicyexperiments.Theideadiffusionmechanismismediatedbytheinput-outputstructureofproduction,suchthatbothsectorcostsharesandimporttradesharescharacterizethesourcedistributionofAssumption2(Ideaformation).Newideasarethetransformationoftworandomvari-ables,namely:(i)originalinsightso,whicharriveaccordingtoapowerlaw:Ot(o)=Pr(O<o)=1_αto去θ;(ii)derivedinsightsz\,drawnfromasourcedistributionG(z).Aftertherealizationofthosetworandomvariables,thenewideahasproductivityz=o(z\)β,whereoistheoriginalcomponentofthenewidea,z\isthederivedinsight,andβe[0,1)newideasiftheirqualitydominatesthequalityoflocalvarieties.Therefore,foranyperiod,domestictechnologicalfrontierevolvesaccordingto12:F,t+∆(z)=F尸z)2×╱1_\tt+∆\ατz去θ(z\)βθdG(z\)dτ、Pr{productivity<zPr{productivity<zatt}←今Pr{nobetterdrawsin(t,t+∆)}Lemma(GenericLawofMotion,BueraandOberfield2020).GivenAssumption2,if,foranyt,F,t(z)isFr´echetwithlocationparameterλ=|oατ|(z\)βθidG(z\)dτand9Theassumptionofafixedtradebalanceimpliesthatthecapitalstockisalsonotaffectedbypotentialchangesinthecapitalbalanceinresponsetoshocks.However,theinternationalfinanceliteraturesuggeststhatstandardopeneconomymodelswithintertemporaloptimizationhavegeneratedcounterfactualpredic-tionsonthedirectionofcapitalflowsbetweendevelopedandemergingcountriesinthe1990sand2000s.Capitalwasflowingonnetfromemergingtodevelopedeconomiesinsteadofcapitalflowingtotheemergingeconomieswithhighergrowthratesaspredictedbythestandardmodels.10Foradetailedreviewofthisliterature,seethecomprehensivereviewchapterpublishedbyBueraandLucas(2018).11Asmentionedearlier,ourworkiscloselyrelatedtoSantacreu,Li,andCai(2017),whoextendS.S.Kortum(1997)toamulti-sectorframework.Wedifferinthattheymodeldiffusionashappeningseparatelyfromtrade,ratherthanasatrade-externality.12Herewesimplyusethefactthato=X(X\)┐8andnotethat,givenaninsightX\,atanymomenttthearrivalrateofideasofqualitybetterthanXisPr(O>o)=Pr(O>X(X\)┐8)=αtX┐9(X\)89.WethenintegrateoverallpossiblevaluesofX\.scaleparameterθi,theformerevolvingaccordingtothefollowinglawofmotion:∆λ=αt\(z\)βθidG(z\