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AutomationandWelfare:TheRoleofBequestsandEducation
PreparedbyManukGhazanchyan,AlexeiGoumilevski,
andAlexMourmouras
WP/24/11
IMFWorkingPapersdescriberesearchin
progressbytheauthor(s)andarepublishedto
elicitcommentsandtoencouragedebate.
TheviewsexpressedinIMFWorkingPapersare
thoseoftheauthor(s)anddonotnecessarily
representtheviewsoftheIMF,itsExecutiveBoard,
orIMFmanagement.
2024
JAN
NAr
rARY
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©2023InternationalMonetaryFund
WP/24/11
AutomationandWelfare:TheRoleofBequestsandEducation*
PreparedbyManukGhazanchyan,AlexeiGoumilevski,andAlexMourmouras
AuthorizedfordistributionbyAlexMourmouras
January2024
IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.
ABSTRACT:Thispaperexaminesthewelfareeffectsofautomationinneoclassicalgrowthmodelswithandwithoutintergenerationaltransfers.Inastandardoverlappinggenerationsmodelwithoutsuchtransfers,improvementsinautomationtechnologiesthatwouldlowerwelfarecanbemitigatedbyshiftsinlaborsupplyrelatedtodemographicsorpandemics.Withperfectintergenerationaltransfersbasedonaltruism,automationcouldraisethewell-beingofallgenerations.Withimperfectaltruism,fiscaltransfers(universalbasicincome)andpublicpoliciestoexpandaccesstoeducationopportunitiescanalleviatemuchofthenegativeeffectofautomation.
JELClassificationNumbers:E13,E62,D64
Keywords:
Automation;Aging;Altruism;FiscalPolicy;Education;OverlappingGenerations
Authors’E-MailAddresses:
mghazanchyan@;
agoumilevski@im
;
amourmouras@
口ManukGhazanchyanisanEconomistintheWesternHemisphereDepartment,AlexeiGoumilevskiisaSeniorScientificComputingEngineerintheInformationandTechnologyDepartment,andAlexMourmourasisDivisionChiefintheAsiaPacificDepartment.
*Presentedatthe28thInternationalConferenceonComputinginEconomicsandFinanceinDallas,Texas,June17-19th,2022.Wethankconferenceparticipantsfortheirusefulcomments.WearealsogratefultoPeterRangazas,MarinaMendesTavares,andJeremyCliftfortheinsightfulcommentsthatshapedourpaper.
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Contents
I.Introduction 1
II.RelevantLiterature 3
III.AutomationandWelfareinOverlappingGenerationModels 5
B.IntroducingaOne-Timetax 9
C.K&SModelwithaBequest 11
D.K&SModelwithBequestandEducation 14
1.PrivateEducation 15
2.PublicEducation 17
IV.ArtificialIntelligence 22
A.K&SModel 22
IV.Conclusions 26
Appendices 27
AppendixA.K&SModelwithBequest 27
AppendixB.ReplicatingKotlikoffandSachs(2012) 31
AppendixC.RobustnessChecks 31
A.References 34
I.Introduction
Automationhasacceleratedinrecentdecades,drivenbyongoingimprovementsincomputingandinformationtechnologiesandassociatedcostreductions.Machinesinawideningrangeofindustriesperformincreasinglycomplextasks,poweredbysophisticated,networkedsoftware.Theaccelerationinautomationanditseconomy-widediffusioninblue-andwhite-collaroccupationsalikeiscreatingnewemploymentcategoriesbutisalsocontributingtowideninginequalityandfuelingdemandforgovernmentpoliciestoreverselong-termincomelossesoflabor.Thislong-standingpromiseandconcernsarevividlyillustratedbythelatestbreakthroughinArtificialIntelligenceinvolvinggenerative,pretrainedtransformers.
Lookingahead,whilethepaceofautomationislikelytocontinue,itseffectsmaybemitigatedbyoffsettingforces.Populationsareagingalmosteverywhere.Intheadvancedeconomies,theworking-agepopulationhasstartedshrinkingforthefirsttimesinceWorldWarII(Spence,2022).Globally,thepopulationofworkingageisexpectedtocontinuetogrowuntilabout2040,buttheratiooftheworkingagepopulationtothetotalisalreadydecliningglobally(Chart).InthecaseofChina,forexample,theworking-agepopulationisexpectedtoshrinkbyafifthoverthenext30years.AsGoodhartandPradhanstress,ourageisoneofdemographicreversalinwhichthe“longglutofinexpensivelaborthathadkeptpricesandwagesdownfordecades,isgivingwaytoaneraofworkershortages,andhencehigherprices”.
Recurringglobalpandemicsalsoadverselyaffectlaborsupply,eitherbydepressinggrowthinthelaborforcedirectly(AIDSpandemic),orindirectlybyreducingtheparticipationofolderworkersandothersincontact-intensiveoccupations(pandemicrelatedtoCovid-19).Intheabsenceofmasssouth-north
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migration,robotsmayturnouttobeessentialinmeetingmoreoftheneedsoftheelderlyandreversedeclinesinaggregateoutputandwelfare1.
Thispaperexaminesthecombinedwelfareeffectsofautomationandlowerlaborsupplyusingneoclassicalgrowthmodelswithandwithoutintergenerationaltransfers.Itbeginsbyreplicatingaversionofthewell-knownresultofKotlikoffandSachs(K&S,2012)thataone-timeimprovementinthetechnicalefficiencyofmachinesendsupimmiseratingallfuturegenerations.Thisstrikingresultreliesontwocrucialassumptions.First,machinesareverygoodsubstitutesforunskilledlaborthroughouttheeconomy,sothatimprovedautomationendsupdisplacingworkersandloweringwagesacrosstheboard.Second,therearenooperativeintergenerationaltransfersofanykind,sothattheownersofcapitalendupconsumingtheentirewindfallfromtheimprovementsinautomationduringtheirlifetime(ageneration,roughlythirtyyears).Thepositiveshocktotheefficiencyofmachinesdoesnotraisesaving,depressesinvestmentinphysicalandhumancapital,andsetsinmotionanever-endingcycleofdecliningwelfare.Governmentpolicyisthereforeneededtospreadthiswindfallmoreequitablyacrossfuturegenerations.K&Sconsiderwealthtaxes,inparticularsocializingaportionoftheeconomy’scapitalstockthatallowsthegovernmenttofinanceasustainableincomestream(universalbasicincome)forallfuturegenerations.Resortingtocompulsionisessentialwhengenerationsareselfish,precludinganysortofvoluntaryintergenerationaltransfers.
Infact,privateintergenerationaltransfersaresubstantial,withabouthalfofallhouseholdsplanningtoleaveestates(LaitnerandJuster,2017).Thefirstobjectiveofthepaperistoreassessthewelfareeffectsofautomationinthepresenceofintergenerationaltransfers,bothbequestsandprivatelyandpubliclyfundedschooling.InaversionoftheK&Smodelwithoperativebequests,wefindthatintergenerationaltransfersarepositiveinequilibriumifthestrengthofaltruismexceedsacertainthreshold,mitigatingthenegativeeffectsofautomation.Butwhileitiscomfortabletoknowthatthegainsfromautomationmaybepassedtofuturegenerationswithouttheneedtonationalizecapital,thismodelofperfectaltruismisalsoextreme:manyfamiliesineachgenerationcannotmakeefficienttransferstotheirchildren.
Whatisneededisamorebalancedmodel,onethatfeaturesheterogeneitybothwithinandacrossgenerations,withsomehouseholdsmakingefficientbequestsandothersstuckinacornersolution.WeassesswhetherautomationisimmiseratinginaversionofK@Smodelthatincorporatespurealtruism,andinGlommandRavikumar’smodel(G&R,1992)inwhichparentsmakeinvestmentsintheschoolingoftheirchildren.Westudyhowfiscalandeducationalpoliciescanbestraisewelfare,byalleviatingfinancingconstraintsinthefinancingofhumancapitalinvestmentsandrestoringequalityofopportunity.SimilarresultsobtaininaversionofthemodelusedbyIvanyna,MourmourasandRangazas(2018)inwithtwotypesofhouseholds(thepoor,whoarebequest-constrained)andtherich(whoareunconstrained).
Thepaperthenturnstoananalysisofacombinedshockinvolvingajumpinautomationandasimultaneousreductioninlaborsupplydrivenbydemographics.Asexpected,strengtheningaltruisticbondsraisebequestsandhumancapitalinvestmentsoftheyoung,providinganadditionalstimulustoeconomicgrowth.Inaddition,governmenttransfersoftaxrevenueleviedontherichcanimprovethe
1Businessleadershavealsomadeaconnectionbetweenautomationandagingrecently.OneexamplewastherecentarticleinFortunebyIBMCEO,ArvindKrishnaherehepointstodecliningpopulationstocalmfearsaboutA.I.takingjobs.Hefurtheraddedthat
ultimately“thereisgoingtobejobcreation”withA.I.,asjobswillalsobeaddedinareaswithmorevaluecreation.
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welfareofthepoorandreduceinequalitywithinandacrossgenerationswhenaltruisticlinksbetweengenerationsareweak.
II.RelevantLiterature
Theliteratureonautomationanditseconomicimpactisevolving,withsomeearlierstudiesfromGordon(2012),Cowen(2011),AcemogluandRestrepo(2017,2018),SachsandKotlikoff(2012,2015),Ford,(2015);Freeman,(2015)amongstpessimists,andBrynjolfssonandMcAfee(2014),Autor(2014,2015)amongtheoptimists.Thekeyissueiswhetherautomationreplaceslaborshareandemploymentthroughreplacementofroutinetasksofever-increasingscopeandcomplexityorwhether,onnet,itincreaseslaborparticipationbycreatinghigh-payingjobsinemergingnewoccupations.SomegloomyscenariosforlaborresultingfromartificialintelligenceandsimultaneousautomationbreakthroughsaredescribedinBostrom(2014).Graetzet.al.(2018)examinedtheeconomiccontributionofmodernindustrialrobotsin17countriesfortheperiod1993-2007.
Contrarytothepessimisticview,theseauthorsfoundthattheincreasinguseofrobotsraisedtheannualgrowthofGDPandlaborproductivityby0.37and0.36percentagepoints,respectively.Authorsconcludethatthoserobotsdidnotsignificantlyreducetotalemployment,althoughtheydidreducelow-skilledworkers’employmentshare.Gaaitzenetal.(2020)studiedtheeffectsofadaptationofindustrialrobotsandoccupationalshiftsbytaskcontentinthethirty-sevencountriesfortheperiodfrom2005to2015.Theauthorsfoundthatincreaseduseofrobotsisassociatedwithpositivechangesintheemploymentshareofnon-routineanalyticjobsandnegativechangesintheshareofroutinemanualjobs.Ofcourse,enhancingpolicyincludingR&Dandtheregulatoryplatformsinbothprivateandpublicsectorstosupportdigitaltechnologiesiskeytoimproveproductivity.Whilethe2020-22pandemichelpedtoacceleratethedigitaltransformation,manysectors–includingthepublicsector–arelagging,andhenceconcernsabouttheeffectsofautomationonemploymentwillpersist(Spence,2022).
OnlyafewstudiesexaminedtheeffectofautomationandpopulationagingonthelabormarketasidefromtheclassicalworkbyFreyandOsborne(2017)focusingontheprobabilityofautomationaffectingvariousjobsandoccupations.OneoftheearlieststudiesonautomationandpopulationagingwasbyAcemogluandRestrepo(2017),wheretheauthorsexaminedtherelationshipbetweeneconomicgrowth,populationaging,andautomationatthecountrylevel.
Phiromswad
etal(2022)isamongstthemostrecentstudiestofocusonthoseeffectsbutalsoontheinteractioneffectsofautomationandpopulationagingonthelabormarket.ConsistentwithpreviousliteratureincludingwithGraetzandMichaels(2018)theauthorsfoundstrongevidencethatautomationnegativelyaffectsemploymentgrowthholdingotherfactorsconstant.Theyalsofoundstrongevidencethatthedisaggregatedmeasuresofage-relatedabilitiesaffectemploymentgrowthbutnottheaggregatemeasure.Asexpectedandconsistentwithfindingsthatautomationisstillevolvinginaffectinghighvaluejobs,theauthorsfindthatwithoccupationswithlowscoreonboththeage-appreciatedcognitiveabilityaswellage-depreciatedphysicalability(suchasproductionoccupationsandfoodpreparationandservingrelatedoccupations),thenegativeeffectofautomationonemploymenttendstobestrongest.However,foroccupationswithahighscoreinbothage-appreciatedcognitiveabilityaswellasage-depreciatedphysicalability(suchasprotectiveserviceoccupationsandhealthcarepractitionersandtechnicaloccupations),thenegativeeffectofautomationonemploymenttendstobeweakest.
Aghion-Jones-Jones(2017)studytheimplicationsofartificialintelligenceforeconomicgrowthinlightofreconcilingevolvingautomationwiththeobservedstabilityinthecapitalshareandpercapitaGDPgrowthoverthepastcentury.Theauthorscreatesufficientconditionstogenerateoverallbalanced
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growthwithaconstantcapitalsharethatstayswellbelow100percent,evenwithnearlycompleteautomation.Inotherwords,whileBaumol’scostdiseaseleadstoadeclineintheshareofGDPassociatedwithmanufacturingoragriculture(oncetheyareautomated),thisisbalancedbytheincreasingfractionoftheeconomythatisautomatedovertime.TheauthorsalsostudytheeffectsofintroducingA.I.intheproductiontechnologyfornewideasandthepossibilitythatA.I.couldgeneratesomeformofasingularity,wheretheauthorsneverthelessclaimthattheBaumolthemeherealsoremainsrelevant:evenifmanytasksareautomated,growthmayremainlimitedduetoareasthatremainessentialyetarehardtoimprove.
Pizzinelliandothers(forthcoming)examinetheimpactofArtificialIntelligence(AI)onlabormarketsinbothAdvancedEconomies(AEs)andEmergingMarkets(EMs).TheauthorsproposeanextensiontoastandardmeasureofAIexposure,accountingforAI'spotentialaseitheracomplementorasubstituteforlabor,wherecomplementarityreflectslowerrisksofjobdisplacement.Thentheyanalyzeworker-levelmicrodatafromtwoAEs(USandUK)andfourEMs(Brazil,Colombia,India,andSouthAfrica),revealingsubstantialvariationsinunadjustedAIexposureacrosscountries.TheauthorsfoundthatwhileAIposesrisksoflabordisplacementduetotaskautomation,italsoholdspromiseinitscapacitytoenhanceproductivityandcomplementhumanlabor,especiallyinoccupationsthatrequireahighlevelofcognitiveengagementandadvancedskills.TheauthorsalsofindthatAEsmayexpectamorepolarizedimpactofAIonthelabormarketandarethuspoisedtofacegreaterriskoflaborsubstitutionbutalsogreaterbenefitsforproductivity.
Theextentandformofvoluntaryintergenerationaltransfersisdictatedbythestrengthofintergenerationalaltruismandisanimportantconsiderationinmacroeconomicsthatisrelevantforourpaper.Kotlikoff(2001)providesanexcellentsurveyofkeyworksontheroleofintergenerationalaltruism,includingempiricalfindings—forexample,theresultsofAltonjiandHayashi(1994)whichareconsistentwiththepurealtruismtheory.Acloselyrelatedareaofresearchconcernstheformofhumancapitalinvestments,specificallytherationalebehindeducationorotherbequestsinkind.RazinandRosenthal(1990)showthatfamilytaxationasaresponsetoinformationasymmetrybetweenaparentandachildcouldreducetheneedforgovernmentinterventionandtaxation.HoodandJoyce(2017)provideanexcellentupdatetotheempiricalrelevanceofaltruism.OurpaperismostcloselyrelatedtoMichel,Thibault,andVidal(2004),whostudytheeffectsofaltruismandfiscalpoliciesongrowthinanoverlappinggenerationsmodelinthetraditionofDiamond,andtoGlommandRavikumar(1992)whostudybequestsintheformofhumancapitalinvestmentsinchildren.Westudyprivatelyfundedschoolingforfamilieswithoperativebequestsandpubliclyfundededucation.
Wefindthatgovernmentspendingoneducationpromoteeconomicgrowth.Theseconclusionsaresupportedbyavastvolumeofresearchthatlinkindividuals’educationattainmenttoeconomy-wideprosperity.FabrizioCarmignani(2016)studiedeffectsofgovernmentexpendituresoneducationtoeconomy.AuthorusedtheWorldBank'sWorldDevelopmentIndicatordatabasedataon151countriesfor2000-2010years.Heconcludedthat“increaseineducationexpenditureby1pointofGDPincreasesGDPgrowthby0.9percentagepoints”.Gheraia,Zouheyretal.(2021)investigatedrelationshipbetweenthecostofeducationandeconomicgrowthintheKingdomofSaudiArabiafortheperiod1990-2017.Authorsfoundthatinthelongruntheriseineducationalexpenditureby1%wouldleadtoanincreaseineconomicgrowthby0.89%.SimilarresultswereobtainedbyYahya,Mohdetal.(2012).Authorsanalyzedthelong-runrelationshipandcausalitybetweenthegovernmentexpenditureineducationandeconomicgrowthinMalaysiafortheperiod1970to2010.Theyconcludedthateconomicgrowthispositivelycorrelatedwithfixedcapitalformation,laborforceparticipationandexpenditureineducation.RegardingGrangercausality,theeducationalexpenditure
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istheshort-termGrangercauseofeconomicgrowthandviceversa.MehmetMercanaetal.(2014)performedcointegrationanalysisbetweentherealgrossdomesticproductandtotalexpensestotheeducationforthecaseofTurkeyfortheperiod1970-2012.AuthorsusedAutoregressiveDistributedLagmodelwithboundstesting.Authorsfoundthat1%increaseineducationexpensesincreaseseconomicgrowthby0.3%.
III.AutomationandWelfareinOverlappingGenerationModels
A.AnAnalyticalTool:TheK&SModel(2012)
Webeginwithasimplemodelfeaturingtwoperiod-livedoverlappinggenerations(OLG).Eachperiodt=1,2,…thepopulationconsistsofyoungandoldhouseholds.Theyoungareendowedwithoneunitofinelasticallysuppliedunskilledlabor.Theyconsumepartofthisincomeandinvesttherestinphysicalcapital(machines,M)andintheirownhumancapital(skilledlabor,S).Machinesandhumancapitalareperfectsubstitutesinsavingportfolios.Inthesecondperiodoflife,householdsrenttheirmachinesandskillsinperfectlycompetitivemarkets,consumingallinterestandprincipal.GrossoutputQisaconstantelasticityofsubstitution(CES)productionfunctionoftheeconomy-widestocksofM,L,andS:
Q=Q(N(uM,L),S)(A.1)
MandLcombineinaCESproductionfunctionwithelasticityεMLtoproduceanintermediateproductN,andNandScombineinaCESproductionfunctionwithelasticityεSNtoproducethefinaloutputQ.Theparameteruisaparametermeasuringthetechnicalefficiencyofmachinery.Ariseinuisapuretechnicaladvance.KotlikoffandSachs(KS,2012)examinewhetherariseinucanreduceeconomicwellbeing,anoutcometheyrefertoas“im-mesmerizingproductivity.”
CompetitivefirmshireM,L,andStothepointwheretheirmarginalproducts(denotedasQifori=M,L,andS)equaltheirmarketwages:Qi=wi.FollowingK&Sthepartialderivativeofwagewithrespecttoproductivityuis,
dln(QL)⁄dln(u)=[εSN−θεML]⁄εML(A.2)
whereθistheshareofskilledlaborintheeconomy,equalto(Qs∗S)⁄Q.Weseethatariseinmachine’sproductivityreducestheunskilledwageifεML>εSN⁄θ.Thus,“im-mesmerizing”productivityismorelikelyif:
.Substitutabilityofmachinesandunskilledlaborishigh(εMLlarge)
.Substitutabilityofintermediategoodsandskilledlaborislow(εSNsmall)
.Theshareofskilledlaborinfinaloutputishigh(θhigh)
BelowwepresenttheoreticalunderpinningsfortheK&Sconclusions.Notethattheincomeoftheyoung,It,iscomprisedofwageswt,partofwhichisinvestedinmachinesandhumancapital.Income
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β
=ct
whenold,It+1,comesfromtheownershipofmachinesandacquiredskills.Thelifetimebudgetconstraintsofgenerationbornatt,whoareyounginperiodtandoldatt+1are:
It=Ltwt=ct+svt(A.3)
It+1=tMt+1+tst+1=Dt+1(A.4)
Herectistheconsumptionwhenyoung,Dt+1isconsumptionwhenold,andsvtissaving,whichisinvestedinmachinesandskills:
svt=Mt+1+st+1(A.5)
Thisallocationofsavingsismadeunderperfectforesighttomaximizeutility,sothatinvestmentinmachinesandskillsarechosentoequalizemarginalproductsofMandStothegrossinterestrateintheeconomy:
Rt=t=t=1+rt(A.6)
HereRtisthegrossrateofreturnandrtistheinterestreturnonmachines.Combiningequations(A.3-4),weget:
ct+D1=It(A.7)
Lifetimeutilityforahouseholdbelongingtogenerationtis:
U=βlog(ct)+(1−β)log(Dt+1)(A.8)
Parameterβisthetimediscountfactor.Itisrelatedtothepatienceoftheagentaboutconsumption-largerβmeanstheagentispredisposedtoconsumemoreduringyouth.Theutilitymaximizingchoicesofconsumptionmustsatisfythefirstordercondition,
1−β
Dt+1
Rt
(A.9)
Turningtotheproductionsideoftheeconomy,wefollowK&SwhopostulateaCobb-DouglasproductionfunctionforfinalgoodsassembledusingskilledlaborSandanintermediateinputN:
Q(N,s)=ANas1−a
(A.10)
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TheintermediatefactorNisalinearcombinationoflaborLandmachinesM,meaningthatthesetwoprimaryfactors,machinesandlaborareperfectsubstitutes.
N=L+u1M(A.11)
Hereuisthetechnicalefficiencyofmachinery.Highervaluesofu1indicateimprovementsinautomation.Themarginalproductsofthefactorsare,
QL=Aa(N⁄s)a−1
QM=Aau1(N⁄s)a−1
Qs=A(1−a)(N⁄s)a
Assuming“perfectforesight”,QM=Qs,weget,
aus=(1−a)N
and
QM=Qs=Aau1a−1
wt=Aa()a−1
(A.12)
(A.13)
(A.14)
Solvingsavingsequation(A.5),noarbitrageassumption(A.6),firstordercondition(A.9),andusingequationforintermediateproduction(A.11),wecanderive:
ct=βLtwt
(A.15)
Dt+1=(1−β)RtLtwt
svt=(1−β)Ltwt
Mt+1=asvt−(1−a)Lt⁄u1
st+1=(1−a)svt+(1−a)Lt⁄u1
MachinesMtandskillsstareproportionaltosavingsandincrease/decreasewithgrowthofproductivityfactoru,respectively.
Weareinterestedintheeffectsontheeconomyofdifferentcombinationsofshockstoproductivityandlabor,especiallyinthepossibilityofimmiseratingequilibriaovertimeinwhichinequalitywithinandacrossgenerationsrises.
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PropositionA1:Improvementsinautomationbenefittheownersofcapital(theinitialoldgeneration)andlowerthewelfareofallsubsequentgenerationsofworkers.Apositiveshockintheefficiencyofmachinesleadstohigherconsumptionandincomeoftheold.Itsimultaneouslylowersthewageincomesofunskilledworkersandlowerstheirlifetimeconsumptionandutility.Intergenerationalinequalityrises.
BelowweassumethatCobb-Douglasproductionfunctionhasweightsa=0.74onlaborand0.26onmachinesandβ=0.5onskills.ThissetupproducestheresultsinFigure1.InFigure1weassumethatproductivityunexpectedlyrisesby35%inperiodt=3whilelaborsupplyremainsthesame.Inthethirdperiod,MandNareunchangedbecauseoftheproductivityshock,astheyweredeterminedbythesavingdecisionsoftheyounginthefirstperiod.Thecurrentwageofunskilledworkers(i.e.,theearningsoftheyoungofgeneration3)declinesfrom2.82to2.61astheresultoftheriseinu1.ThereturnsonMandSbothrises,andtheoldgeneration(thatownsbothMandS)experiencesaboominincomewhileyounggenerationexperiencesabust.Consumptionoftheoldriseswhileconsumptionandsavingoftheyoungdeclines.ThispushesdownthefuturecapitalstocksofMandS.Byperiod5theeconomyreachesanewequilibriumcharacterizedbylowerwages,lowerskills,lowerM,andhighertotaloutputthaninthebaseline.Theratioofearningsofskilledworkersrelativetounskilledworkers,ws/wl,ispermanentlyraisedfrom1to1.35.
FollowingK&S,wetraceshowtheimplicationsofimprovedautomationforlifetimeutilityacrossgenerations.Theutilityofgeneration3isslightlybelowthatofgeneration1,aswageshavedeclinedwhilethereturnsonsavinghaveincreased.Yettheutilityofgenerations4andlaterishigherthanthebaselineutility.Youngunskilledworkerslosefromtheriseinmachineproductivity.Theproductionofgeneration3soarsasthisgenerationbenefitsfromhighreturnstobothMandS.Theanticipatedcaseproducesslightlydifferentbutqualitativelysimilarresults.
Forpiece-wiseconstantproductivityu1thesevariablesarepiece-wiseconstant.Consumptionreaches
stationarylevelwhenct=Dt+1,orwhen(1−β)Rt=β.Thissetsconditionfortotalfactorproductivity,A=1−a.Itinverselydependsonproductivityfactoru1.
Figure1.TimedependenceofvariablesforSachsandKotlikoffsettings.Atp
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