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TheElasticityofSubstitution

BetweenSkilledandUnskilledLabor

InDevelopingCountries:ADirected

TechnicalChangePerspective

AlbertoBehar

WP/23/165

IMFWorkingPaperspasoJiqaJasaeJouin

dJo6Jassq(\uaeu\uoJ)s(enpeJaduqIisuap\o

aIioi\oomman\senp\oanoouJe6apaqe\a.

TheviewsexpressedinIMFWorkingPapersare

thoseoftheauthor(s)anddonotnecessarily

representtheviewsoftheIMF,itsExecutiveBoard,

orIMFmanagement.

2023

AUG

INTERNATIONALMONETARYFUND2

?2023InternationalMonetaryFund

WP/23/165

IMFWorkingPaper

WesternHemisphereDepartment

TheElasticityofSubstitutionBetweenSkilledandUnskilledLaborInDevelopingCountries:ADirectedTechnicalChangePerspective

PreparedbyAlbertoBehar*

AuthorizedfordistributionbyDingDing

August2023

IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.

ABSTRACT:Wedevelopamodelofendogenousskill-biasedtechnicalchangeindevelopingcountries.Theendogenousresponsetoariseinskillsupplycountersthetraditionalsubstitutioneffectanddampensitsroleinreducingwageinequality.Themodelre-enforcesconsensusestimatesoftheelasticityofsubstitutionbetweenmore/lesseducatedworkersbyreconcilingdispersedexistingestimates.Italsorationalizesestimatesthatwerehithertodeemedimplausibleormodel-inconsistent.Weproducenewestimatesfordevelopingcountrieswithanovelglobalpanel(findingvaluesatorjustabove2)andwithLatinAmericandatathatfacilitatesanalysisofdynamics(whichreduceestimatesto1.7-1.8).Wethereforeshednewlightonaparameterthatiscrucialforinequality,growth,andotherkeymacroeconomicquestions.

RECOMMENDEDCITATION:Behar,A.(2023),“Theelasticityofsubstitutionbetweenskilledandunskilled

laborindevelopingcountries:adirectedtechnicalchangeperspective”,IMFWP/23/165

JELClassificationNumbers:I20J23J24J31O15O33

Keywords:

Skill-biasedtechnicalchange;elasticityofsubstitution;skillpremium;inequality;growthaccounting

Author’sE-MailAddress:abehar@

INTERNATIONALMONETARYFUND3

WORKINGPAPERS

Theelasticityofsubstitutionbetweenskilledandunskilledlaborindevelopingcountries:adirectedtechnicalchangeperspective

PreparedbyAlbertoBehar

1

1Thisversion:August2023.Previousversion:December2009.IwouldliketothankMargaretStevens,CarloPizzinelli,andvariousseminarandconferenceparticipants.

2

1Introduction

Theelasticityofsubstitutionbetweenskilledandunskilledlabor,σ,iscrucialfordeterminingvariationsinincomewithinandacrosscountries.Bymakingskilledworkerslessscarcerela-tivetounskilledworkers,expandededucationcanreducewagedifferentialswithinacountry.Theeffectofsuchapolicydependsonσ.Alowervalueforσtendstoresultinabiggerreductionininequality,makingtheparametercrucialforstudiesofthepotentialcontribu-tionofincreasesinthesupplyofeducatedworkerstoreducingorcontaininginequality.1Inreverse,ahighervalueforσmeansthatanexogenouschangeinrelativefactorprices,suchasariseintheminimumwage,wouldhaveabiggereffectonthedemandforskilledandun-skilledworkers(Hamermesh,1993).2Oneargumentforwhyeducationshouldbesubsidizedbythestateisthattheremaybepositiveexternalitiestoeducation,whichcanbemeasuredbycomparingthereturnstoeducationestimatedwithmacroeconomicdatatothosefrommicroeconomicearningsfunctions.Suchcomparisonsrelyonσ(Teulins&vanRens,2008).Policy-makersoftenvieweducationalattainmentasawaytoimproveoverallincome,yetthegrowthaccountingliteratureincludesanunsettleddebateonhumancapital’simportance,inpartbecauseofsensitivityofresultstoσ.3σalsoinformsthepotentialforskill-biasingeffectsoftradeandtheeffectsofimmigrationonwages.4

Initialattemptstoestimatetheelasticityproducedwildlydispersedresults.Forexample,Freeman(1986)documentsvaluesofupto1000.Authorssubsequentlycoalescedaroundavalueofabout1.5attributabletoKatz&Murphy(1992)andre-enforcedbysubsequentstudies(Ciccone&Peri,2005).OneconcernisthattheseU.S.basedstudiesmaynotberepresentativeemergingmarketanddevelopingeconomies(EMDEs),whichtendtohavehigherinequalityandwhicharethefocusofthegrowthaccountingliterature.Havrenek,Irsova,Laslopova&Zeynalova(2022)(henceHILZ)notetheaverageofavailableestimatesishigherandthattherangeisconsiderable.Moreover,theyarguethatpublicationbiasexcludesmanyestimatesthataredeemedimplausiblyhighoroftheincorrectsign.Usingmeta-studymethodstocontrolforpublicationbiaspushestheaverageelasticityto10.Controllingforeconometricbiasinestimationbringsthisvaluebackdownpartiallyto3.7witha95%confidenceintervalofabout18.Forthesubsetofdevelopingcountries,theaverageelasticityis2.1withanintervalof3.

Theprimarycontributionofthispaperistoexplainhowawiderangeofestimatesthatincludesallegedlyimplausiblevalues,publicationbias(itscausesandconsequences),and

1Fernandez&Messina(2018),Manacordaet.al(2010).

2Thisstudyispartofabroaderbodyofworkoninputsubstitution.Karabarbounis&Neiman(2013)

explainpartoflabor’sdecreasingshareofincomeintermsofcheapercapitalandtheelasticityofsubstitutionbetweenlaborandcapital.

3Klenow&Rodriguez-Clare(1997),Hendricks(2002),Caselli(2005),Jones(2014),Caselli&Ciccone

(2019).

4Epifani&Gancia(2008),Thoenig&Verdier(2003),Borjas,Grogger&Hanson(2012).

3

econometricestimationbiascanbeeffectivelymitigatedbyreinterpretingthereduced-formempiricalrelationshipbetweentheskillpremiumandrelativeskillsupply.Weillustratethisusingexistingstudies.Anotherimportantcontributionisournewsetofestimatesfordevelopingcountries.

Thecanonicalapproachinthisliteratureisbasedonderivedrelativedemandcurvesthatproducearelationshipbetweentheskillpremium(inlogs)andtheratioofskilledtounskilledlabor(inlogs).Ourmaininnovationistoderivethisequationfromamodelincorporatingendogenousskill-biasedtechnicalchangesothat

skillpremium=(σ?2)?(relativeskillsupply),(1)

wherethecoefficient,β,onskillsupplyisσ?2,not?astraditionallyinferred.Under

thetraditionalusage,evenmodestdifferencesinβestimatesleadtolargevariationsinelasticityestimates.Evenmodestattenuationbias,whichartificiallypushesthecoefficientestimatetozero,haspotentiallylargeeffectsontheparameterofinterest.Formaltestsofstatisticalsignificancewiththenullhypothesisthatβ=0impliesavalueofinfinityforσ,whilepositivecoefficientestimatesareoutsidethefeasibleset.Thesefactorshavelikelycausedmanystudiestobediscarded.Incontrast,equation(1)formallypermitsacoefficientthatispositive,negativeorzerointermsofhypothesistestinginawaythatisusefultopolicymakers,produceslessuncertaintyinelasticityestimatesforuseinothermodels,softenstheimplicationsofbias,andconsequentlyreducestherisksofunnecessarilydiscardedstudies.

Tojustifyourproposedinterpretation,weuseamodelofendogenousskill-biasedtechnicalchange(SBTC)indevelopingcountries.Newtechnologiesdonotautomaticallyfavourskilledworkersandtherearemanyexampleswheretheydidn’t.AsmodelledinAcemoglu(1998)andKiley(1999)forrichcountries,ariseinthesupplyofskillsincreasesthemarketforskill-biasedmachines,makesitmoreprofitabletoproduceskill-biasedtechnologies,andraisestherelativeproductivityofskilledworkers.This“directedtechnicalchange”effectcounteractsthetraditionalsubstitutioneffect.Inthesemodels,largervaluesofσmakethedirectedeffectmorelikelytodominatethesubstitutioneffect.Themodelshelpexplainwhy,despiteasteadyriseinthesupplyofskilledworkersinrichcountries,wageinequalityincreased.

Caselli&Coleman(2006)arguethatdevelopingcountriesalsoapplytechnologiesac-cordingtotheirendowmentsusingasevidenceacross-countrypositivecorrelationbetweenrelativeskillsupplyandadoptionofskill-biasedtechnologies.Thissuggestsdirectedtechnicalchangeisrelevantfordevelopingcountriestoo.Inourmodel,σ>2meanswageinequalityriseswhileσ<2meansitfallsfollowingariseinrelativeskillsupply.Ourmodelalsoaccountsforthepossibilitythatdevelopingcountries,particularlymiddleincomecountries,absorbmoreskill-biasedtechnologiesifthosearethetechnologiesbeingproducedbydevel-

4

opedeconomies(Berman&Machin,2000,Raveh&Resheff,2016).Accordingly,ourpaperfitsintotheliteratureonthenatureoftechnologicalchange,whichhasbothpositiveandnormativeaspects.AsAtkinson(2015)notes,“Thedirectionoftechnologicalchangeshouldbeanexplicitconcernofpolicy-makers”.

Section2buildsaformalmodelwithanendogenousskillbiasoftechnicalchangeindevelopingcountriesandprovidesevidencethereof.Themodelyieldsthespecificationinequation(1).Section3showsthat,throughthisnewlens,existingempiricalestimatesaremoreconsistentwitheachother,morerobusttobias,andlesslikelytoproducecounterintu-itiveinterpretations,andmaythereforeresurrectsomeabandonedstudies.Section4appliestheframeworktonewdatawithafocusonEMDEs.Specifically,weconstructaglobalpaneldatasetthattoourknowledgeisunmatchedincountrycoverage.WealsousedatafromLatinAmerica,whichallowsustoinvestigatedynamiceffectsforthebroaderregion,focusonthehithertounderexploredCentralAmericaregion,andstudyBrazil.Fortheglobalsample,ourestimatedβcoefficientsareslightlypositive,whichwouldbetheory-inconsistentunderthetraditionalinterpretationbutimplyelasticitiesof2orslightlyhigher.ForourLatinAmericadata,ourestimatedβcoefficientsaregenerallyaroundzero,whichimpliestraditionalelasticitiesthatareverylargeorincorrectlysignedbutalternativelyimply,inourframework,σ≈2.Thedynamicapproachyieldsestimatesofσ=1.7?1.8.Section5derivesimplicationsandproposesextensionstoourresearch.

2Theory

Thissectiondescribesthemodel.Productionusesintermediatesproducedeitherwithskilledlaborandmultiplevarietiesofskill-complementarymachinesorunskilledlaborandmultiplevarietiesofmachinesthatcomplementunskilledlabor.Eachmachinevarietyisprovidedbyaholderofthelicencetothatmachine.Theskillpremiumisinfluencedbythesupplyofskilledlaborrelativetounskilledlaborandbythenumberofdifferentmachinesthatcomplementskilledlaborrelativetothenumberofdifferentmachinesthatcomplementunskilledlabor.Therelativenumberofskilledmachinesisdeterminedbytherelativesupplyofskillsandbytheglobalrelativeavailabilityoflicencesforpurchase.

2.1Thepopulationandlaborforce

TheeconomyhasaconstantpopulationL=1consistingofportionqskilledworkersand1?qunskilledworkers.Consumeri,skilledorunskilled,hasutilityfunction

∞

Uit=工Gih(1+r)?h+t,

h=t

(2)

5

whereGisoutputconsumed.Itislinearandpinsdowntheinterestrateatrforallt.Consumersearnwagesandtheprofitsfromanylicencestheymayhold.

2.2Production

TotaloutputoffinalgoodsisaCESaggregateoftwotypesofintermediate,asdescribedbythelinearlyhomogeneoustechnology:

e

Yt=[(y)+(y)]e?1

(3)

Finaloutputisproducedbyperfectcompetitorsusingtwointermediateinputspurchasedfromintermediatesproducers.?>0isthefiniteelasticityofsubstitutionbetweeninter-mediateinputs.Individualproducerstakethepriceoffinaloutput(unity)andpricesofintermediateinputsasgivenbeforechoosingtheiroptimalquantitiesofintermediates.Fortheeconomytobeinequilibrium,intermediatesmusthavepricespsandpusuchthat:

1

=()?e

(4)

BuildingonRomer(1990),intermediatesareproducedbyiperfectlycompetitivefirms,whereysusesskilledlabor,Lt,andTsdifferentmachineswhileyuusesunskilledlabor,L,andTudifferentmachines.Specifically,y=(Lt)1?αz1Xtandy=A(L)1?αz1Zt.

Xijtismachineinputoftypejusedbyfirmiatt.ItisthequantityofeachofTsmachines(capital)thatcomplementskilledlabor.Similarly,ZijtisthequantityofeachofTumachinescomplementingunskilledlabor.Capitaldepreciatesfullyineachperiod.A<1forunskilledlabormakesproductionafunctionofeffectiveunitsoflabor.WerefertoTsandTuasthenumberofskilledandunskilledmachines.

Thequantityofeachskilledmachinedemandedbyeachintermediatesproducerissuch

thatthemarginalproductofthemachineequalsitsprice.Firm-leveldemandforeachtype

1

ofskilledmachineisXijt=(α)1?αLt.

Thepriceofeachskilledmachine,p,issetbythefirmholdingthelicenceforthattypeofmachine.Technologyimportersmustreceiveexpostprofitstopersuadethemtoincurtheexantelicencecost.Wedescribetechnologyacquisitionbelowbut,oncethefixedcostofacquiringthelicencehasbeenincurred,itcosts1unitofYexportedtoimporteachmachine.

Theequationforfirm-leveldemandcanbeusedtoshowtheown-priceelasticityofdemandisforallmachinesofanytype.Thereforeeachmonopolistsetsaprofitmaximizingpriceofforallj,t.Fortheeconomyasawhole,wecanconditiondemandforskilledmachinesonthequantityofskilledlabor.Usingthefactthatfinalgoodsareproducedusingaconstant

6

returnstoscaletechnology,economy-widedemandforeachskill-biasedmachineis:Xt=α(p)qt

Similarly,economy-widedemandforeachunskilledmachineis:

Zt=Aα(p)(1?qt)

Economy-wideoutputofskilledandunskilledintermediatesis:

y=Ttsq?αX

y=TtuA1?α(1?qt)1?αZ

(5)

(6)

(7a)

(7b)

Asinmodelsofthisclass(Romer,1990),thereareconstantreturnstoincreasesinthevarietyofinputs.Thisiswhynewmachinetypeswillalwaysbeemployed.However,increasesinTsrelativetoTuorariseintheproportionofskilledworkers(q)willinducepriceadjustments.

2.3Pricesandwages

Anexogenouschangeintherelativeskillsupplywouldleadtoariseintherelativequantityofysproduced.By(4),thiswouldnecessitatearelativepriceadjustment.AchangeintheratioofTstoTuwouldalsorequirepricestochange.Aftersubstitutingfrom(5)and(6),combining(7)and(4),wecanwrite

pt≡()t1α=()1≡(TQ)1,(8)

whereT≡,Q≡andσ=?+α??αistheelasticityofsubstitutionbetweenskilledandunskilledlabor.In(8),weseeanegativerelationshipbetweentherelativepriceoftheskillintensivegoodontheonehandandtherelativenumberofskilledtechnologiesontheother.Producersofintermediategoodshirelaborsuchthatwageequalsmarginalrevenueproduct.Forequilibriumintheeconomy,relativewagesaregivenby:

Wt≡

=Ttpt=TtQ1

(9)

Equation(9)mirrorsthefindingsofAcemoglu(2002).Thefarrightoftheequationshowsrelativewagesareaffectedbytwothings.First,thestandardsubstitutioneffect,whereariseintherelativequantityofskilledlaborreducestherelativeskilledwage,ceterisparibus.Thiseffectoperatesthroughp:arelativeriseinskillsupplyleadstoarelativeriseinskilledintermediates,whichleadstoafallinpandhenceafallintherelativemarginalrevenue

7

productofskilledlabor.Second,relativetechnologies,theeffectofwhichcanbepositiveornegative.AriseinTraisestherelativephysicalproductivityofskilledlabor.However,ahigherTleadstolowerpandhencelowerW.Theneteffectdependsonσ,aswillbediscussed.Equation(9)describestheimportantdirectrelationshipbetweenwagesandtheskillsupply.Italsodescribestherelationshipbetweenwagesandtechnology.Thenextsectiondescribeshowtechnologyadoptionisendogenoustotheskillsupply.

2.4Technologyadoption

EmpiricalbackgroundBeforeproceedingwiththemodel,wepresentsomerelevantfactsontechnicalchangeindevelopingcountries.Mostcountriesdonotdeveloptheirowntechnologiesbutacquirethemfromabroadthroughimportsorotherformsoftechnologytransfer(Eaton&Kortum,2001;Savvides&Zachariadis,2005).Importantly,suchtechnicalchangeimportsneednotbeskill-biased.Caselli&Wilson(2004)findthatskill-abundantcountriesimportmachinesthataremorecomplementarywithskilledlabor.Gallego(2012)findsastronglinkbetweenthedegreeofskillupgradingintheU.S.andskillupgradinginChilethatisconsistentwiththeinternationaltransmissionofthebiasoftechnicalchange.RavehandReshef(2016)empiricallyshowthatsometypesofimportedcapitalaremorecomplementarytounskilledworkersandthuscanlowertheskillpremium.Fordevelopingcountries,itisthereforepertinenttomodeltechnologyacquisitionasapurchasefromabroadratherthanasaresultofR&Dandhomeproduction.

Moreimportantlyforthispaper,countriesdonotabsorbanynewmethodsautomatically,butconsiderdomesticfactormarketconditionsbeforechoosingappropriatetechnologies.Forexample,Knight(1979)notesthattheintroductionofthecolorbarrestrictedthesupplyofskillsinSouthAfricaandencouragedcapitalthatsubstitutedforskilledworkersandthattherelaxationofthecolorbarencouragedsubstitutionofmachinesforunskilledlabor.Ace-moglu&Zilibotti(2001)notethatmultinationalsmaketechnologiesavailabletotheirvariousdevelopingcountrysubsidiariesaccordingtotherelativeavailabilityofskilledworkers.Forexample,Kenyausedthehammermilltogrindmaizeratherthantherollermillbecauseofabundantunskilledlabor.InTanzaniaandThailand,anewmethodforproducingcanswasnotwidelyadoptedbecauseinsufficientskilledworkerswereavailabletoworkwiththem.Fransman(1985)presentscasestudiesofcountriesadaptingoverseastechnologiestolocalfactorsupplies,whileEsposito&Stehrer(2009)findeconometricsupportfortherelationship.Christenko,Martinaitis&Krˉuminas(2023)concudethattheBalticsexperiencedtechnolog-icalupgradingthatfavoredtheirabundantunskilledworkers.5

5Blum(2009)findevidenceconsistentwithtechnicalchangethatfavorsthemoreexpensivescarcefactor(Hicks,1963),whichmeansthatanincreaseinthesupplyofskilledlaborwouldhaveanamplifiednegativeeffectontheskillpremium.AsshowninBehar(2013),technologyadoptioncaneasilybeexpressedasafunctionoftherelativefactorshare,whichistheproductofrelativequantitiesandrelativeprices.Ifσ>1,

8

Thesimultaneouspresenceofmostlyskill-biasedR&Dindevelopedeconomiesandabun-dantunskilledlaborinEMDEsraisesquestionsonthe“appropriateness”oftechnologyforEMDEs(AtkinsonStiglitz,1969).6

ModellingtechnologyadoptionWiththisempiricalbackground,westartbyde-scribingthedecisionofapotentiallicenceholderwhetherornottoacquirealicenceforatechnologyfromabroad.7ItcostsoneunitofYexportedtoimportoneunitofamachinesuchthatthemarginalcostisunityforbothmachinetypes.ThecostofacquiringaskilledliceuceforaparticularskilledmachineXjisCsandthecostofalicenceforanunskilledmachineZjisCuunitsofYexported.Wewillassumedevelopingcountriesarebehindthetechnologyfrontierandarepricetakersinthetechnologymarket.However,thepriceofalicenceisinverselyrelatedtotheresearchfrontierreachedbyR&Dinthedevelopedworld.

Thatis,

Ct≡=≡t,

(10)

whereRistheskill-biasoftheworld’savailabletechnologiessuchthattherelativecostofimportingskilledtechnologiesisinverselyrelatedtoit.Atanytimet,theagentconsidersif

thevalueofthelicenceexceedsthecost.Thevalueisthediscountedpresentvalueofallfuture

profits.ThusthevalueofanyskilledlicenceattimetisVts=(Pi?1)Xt+i(1+r)?i.

1

RecallingPX=,using(5)anddefining?≡(1?α)α,theperperiodprofitfroma

licenceforaskilledmachineisπx=?(p)1?αqt.Therefore,thevalueofaskilledlicenceis:

Vts=?

Theprofitforanunskilledlicenceisπz=?(p)1?αA(1?qt)and

Vtu=A?

(11)

(12)

ariseinskillsupplyincreasesitsfactorshareandmakesskilledtechnologiesrelativelymorevaluable.Forσ<1,ariseinskillsupplyincreasesunskilledlabor’sfactorshareandmakesunskilledtechnologiesmorevaluable.

6Li(2020)suggestsithasbeenmorecostlyforMNCstoadapttoChina’sendowmentsthantosimplyusetheavailabledeveloped-countrytechnology.Diaoetal(2021)arguethatthislackofadaptedtechnologyhasheldbackemploymentinEthiopiaandTanzania.Incontrast,Okoye(2016)arguesthatitisdevelopingcountries’insufficientlyskill-biasedtechnologyadoptionthatisalargecontributortoproductivitygaps.

7Internationaltradeentersthismodelbutinastylizedway,namelydevelopingcountriesexportfinalgoodsandimporttechnology(licences)andcapital(machines).Weareinthiswaynotallowingfortheroleinternationaltradecanplayininfluencingtherelativepriceofskilledproductsandhencetheskillbiasoftechnologies,asdoneinBehar(2016).

9

sothattheratioofvaluesis:

[王]

Vt=A[王]

ForconstantvaluesofQandR,equation(13)canbesimplifiedto:

V=QσTσ

σ?1?1

(13)

(14)

2.5Steady-stateandcomparativestatics

Byfreeentry,Vs=CsandVu=Cusuchthat,insteadystate,

V=C

and

T=Qσ?1Rσ

(15)

(16)

Asanaturalextensionto(14),theratioofskilledtounskilledtechnologiesispositivelyrelatedtotherelativeskillsupplywhenσ>1.Moreover,byequation(9),wederivethefinalequationfortheskillpremium:

W=Qσ?2Rσ?1(17)

WeremarkthatthepreciseexponentonWcanbesensitivetofunctionalform.If,asisappropriateforoursmallopendevelopingcountrysetting,technologyisacquiredbypricetakersfromaninternationalmarket,weobtainthisparticularexponent,whichthenformsthebasisofoursimpleestimatingequation.8

Fromapolicyperspective,onecanconsiderareformthatreducesthecostsofacquiringeducation.Forexample,educationaccessexpandedmarkedlytonon-whitesinSouthAfricaaftertheendofApartheid(vanderBerg,2001)andtowomeninChina(Lavely,Zhenyu,Bohua&Freedman,1990).ElsewhereinAfrica,thespecificgovernmentobjectivewastheuniversalavailabilityofprimaryeducation(Knight&Sabot,1987)while,inTaiwan,ProvinceofChina,accesstohighereducationwascontrolledbythegovernment(Gindling&Sun,2002).IntheWestBankandGaza,therewerenohighereducationinstitutionsin1972but20bythemid1980s,sothesmallareawasquicklyfloodedwithcollegegraduates(Angrist,

8InrichcountrymodelsofR&DthesameexponentwouldapplyifthereareconstantreturnstoR&D.Increasingordecreasingreturnscanaffecttheexponentandhencethethresholdvaluesofσ.

10

1995).9

Differentiatingequation(17)yields:

dlogWdlogQ

?logWdlogT1

?logTdlogQσ

σ?11

=?

尸σ山、使尸σ山、使

=σ?1?

Technologyeffectsubstitutioneffect

=σ?2

(18a)(18b)

(18c)

Thesubstitutioneffectonthefarrightcomesfromconventionallabordemandtheoryandistheeffectempiricalstudiestypicallymeasure.However,thesubstitutioneffectmustbecomparedtotheeffectoperatingthroughachangeintechnologyimports.AriseinThastwoeffectsonwages.First,itincreasestherelative(physical)productivityofskilledlabor.Second,itincreasesys/yu,whichnecessitatesafallinpandthereforehasanegativeeffectontherelativemarginalrevenueproductofskilledlabor.Theneteffectonrelativewagesdependsonσ.Ifσ>1,ariseinTwillhaveapositiveeffectontheskillpremium,becausethesecondeffectisrelativelysmall.Analogously,theeffectofskillsupplyontechnologyadoptionhastwoeffectsandtheneteffectdependsonσ.Withreferencetoequation(14),ariseinskillsupplymakesthemarketforskilledtechnologiesmoreattractiveiffσ>1.Thereasonforthisisthattheincreaseinavailableskilledlabor,whichmakesskilledmachinesmoreattractive,alsoproducesareductioninskilledwages,whichmakesskilledmachineslessattractive.Forσ>1,thelattereffectissmallsothattheformereffectdominates.Conversely,σ<1meansrelativewagesadjustalot,sotheoveralleffectisthatmoreskilledlabormakesskilledmachineslessattractive.However,aswealreadymentioned,σ<1alsomeansthatareductioninThasapositiveeffectontheskillpremium.Therefore,thetechnologyimporteffectofskillsupplyonwagesis(strictly)positiveforanyσ1.

Algebraically,thisisconsistentwithAcemoglu(2002).Tomaketheargumentsmootherfromnowon,wewilltakeashort-cutandonlyconsiderσ>1(thiswillbeempiricallysupported)suchthatwecanrefertoariseinTandSBTCinterchangeablyandcansayariseinQleadstotheacquisitionofmoreskilledmachines.

WearemainlyinterestedinchangesinQ,butremarkthatthemodelcapturestherelativeskillbiasoftheglobaltechnologyfrontierbyR.Inequation(16),TrisesifthereisariseinRbecauseSBTCreducestherelativecostofaskilledtechnology,consistentwiththeviewthat“...developingcountriesmustbechoosingfromamenuofbestpracticesthatincludesanever-increasingpropo