IMF-寻找工资增长：对“新机器时代”的政策回应（英）

SearchingforWage

Growth:Policy

Responsestothe“New

MachineAge”

AndrewBerg,EdwardF.Buffie,MariarosariaComunale,

ChrisPapageorgiou,Luis-FelipeZanna

WP/24/3

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progressbytheauthor(s)andarepublishedto

elicitcommentsandtoencouragedebate.

TheviewsexpressedinIMFWorkingPapersare

thoseoftheauthor(s)anddonotnecessarily

representtheviewsoftheIMF,itsExecutiveBoard,

orIMFmanagement.

N

Ar

2024

JAN

AR

©2024InternationalMonetaryFund

WP/24/3

IMFWorkingPaper

InstituteforCapacityDevelopmentandResearchDepartment

SearchingforWageGrowth:PolicyResponsestothe“NewMachineAge”

PreparedbyAndrewBerg,EdwardF.Buffie,MariarosariaComunale,

ChrisPapageorgiou,Luis-FelipeZanna

AuthorizedfordistributionbyAndrewBergandChrisPapageorgiouJanuary2024

IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicit

commentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseofthe

author(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.

ABSTRACT:Thecurrentwaveoftechnologicalrevolutionischangingthewaypolicieswork.Thispaper

examinesthegrowthanddistributionalimplicationsofthreepolicieswhen“robot''capital(abroaddefinitionofrobots,ArtificialIntelligence,computers,bigdata,digitalization,networks,sensorsandservos)isintroducedinaneoclassicalgrowthmodel.1)cutstothecorporatetaxrate;2)increasesineducationspending;and3)

increasesininfrastructureinvestment.Wefindthatincorporating“robot''capitalintothemodeldoesmakeabig

differencetopolicyoutcomes:thetrickle-downeffectsofcorporatetaxcutsonunskilledwagesareattenuated,andtheadvantagesofinvestmentininfrastructure,andespeciallyineducation,arebigger.Basedonour

calibrationsgroundedonnewempiricalestimates,infrastructureinvestmentandcorporatetaxcutsdominateinvestmentineducationina"traditional"economy.However,inaneconomywith“robots”theinfrastructure

investmentdominatescorporatetaxcuts,whileinvestmentineducationtendstoproducethehighestwelfaregainsofall.Thespecificresults,ofcourse,maydependontheexactmodelingofthetechnologicalchange,butourmainresultsremainvalidandcanprovidemoreaccuratewelfarerankings.

RECOMMENDEDCITATION:AndrewBerg,EdwardF.Buffie,MariarosariaComunale,ChrisPapageorgiou,Luis-FelipeZanna.2024.“SearchingforWageGrowth:PolicyResponsestothe“NewMachineAge””,IMFWorkingPaperNo.2024/3.

JELClassificationNumbers:E23,E25,O30,O40

Keywords:

Technologicalchange;ArtificialIntelligence;robots;growth;incomedistribution;fiscalpolicy;publicinvestment;education

Author’sE-MailAddress:

WORKINGPAPERS

SearchingforWageGrowth:

PolicyResponsestothe“NewMachineAge”

PreparedbyAndrewBerg,EdwardF.Buffie,MariarosariaComunale,ChrisPapageorgiou,Luis-FelipeZanna

1

1TheviewsexpressedinthispaperarethoseoftheauthorsanddonotnecessarilyrepresentthoseoftheIMForIMFpolicy.

EdwardF.BuffieisattheDepartmentofEconomics,IndianaUniversity.WethankPaulGagglforhisguidanceoncodesandreplication.WethankJieminRen,JohnRalyea,andSanghamitraWarrierMukherjeeforcomments.

I.INTRODUCTION

Stagnantrealwageshavebecomeacentral,problematicfeatureofseveraladvancedcoun-tries—mostnotablytheUnitedStates—inrecentdecades.Whilethecausesarevarious,advancesintechnologyandparticularlyautomationofroutinetaskshavebeenidentifiedasamajorfactor.Inthispaperwelookspecificallyatabroaddefinitionofthesetechnologies,wecallit“robot”,asanumbrellacoveringnotonlyrobotsperse,butalsoincludingArtificialIntelligence(AI),computers,bigdata,digitalization,networks,sensorsandservosthatareem-phasizedintheliteratureonthe“newmachineage”.Expertopinionalsoholdsthat,soonerorlater,anewwaveofinnovationassociatedwithever-fastercomputers,moreeffectivemachinelearningandgenerative-AI(gen-AI)algorithms,andpervasivedigitalizationwillusherinanewindustrialrevolutionwithevengreatermacroeconomicrepercussions(andinitialindica-tionsarethatthesemaylooksomewhatdifferentcomparedtoourbroaderdefinition).

1

Therecentspreadingofadvancedgen-AItechnologies,especiallyafterthereleaseofChatGPTbyOpenAIinNovember2022,alreadystartedanewdebateonimpactofthesetechnologiesonthelabormarket.

Themacroeconomicliteratureonthenewindustrialrevolution,includingourownearlierwork,investigatestheimplicationsofimprovementsintechnologyforgrowth,labormarkets,andthedistributionofincome.Inthispaperweaskadifferentquestion,namely:Howdotheeffectsofpolicydifferintheneweconomywiththis“robot”capital?

2

Employingavariantofthemodelin

Berg,Buffie,andZanna

(2018),weanalyzetheimpacton

growthandthedistributionofincomeofthreepolicies:cutsinthecorporatetaxrate,increasesineducationspending,andincreasesininfrastructureinvestment.Themodelfeatureslow-skillworkerswholivecheck-to-check,capitalistsandhigh-skillworkerswhosaveandinvest,andourbroad“robot”capitalthatdiffersfromtraditionalcapitalinbeinghighlysubstitutablewithlow-skilllaborinproduction.

3

Moreover,weseparateoutinformationandcommunication

1Exposuretogenerative-AI(gen-AI)ishighlyheterogeneousacrossindustries,occupationsandjobtitles.Re-centempiricalstudiesshowthatgainsfromgen-AIaccrueprimarilytolower-skilled,lower-paidworkers(

Bryn-

jolfsson,Li,andRaymond

(2023))andthatgen-AIadoptiontendstoflattenfirms’hierarchicalstructures,in

-

creasingworkersinjuniorpositionsanddecreasingworkersinmiddlemanagementandseniorroles(

Babinaand

others

(2023))

.

2

KorinekandStiglitz

(2018)discusspolicyissues,particularlywithrespecttototechnologyandtransfers,at

agenerallevel.Thereislittleornoformalexamination,however,ofhowrobots,AI,andrelatedtechnologieschangethewaytheeconomyrespondstopolicies.

AcemogluandRestrepo

(2019a)focusonpolicytowards

technologyitself.

Acemoglu,Manera,andRestrepo

(2020)isanimportantrecentexception,analyzingimpli

-cationsoftheU.S.taxcodeforemployment,wages,thelaborshare,andautomation.TheyfindthattheU.S.

taxsystemisbiasedagainstlaborandinfavorofcapital,increasinglysoinrecentyears.Morerecently

Korinek

(2023)analyzedaframeworktoevaluatetheimpactofatechnologicalinnovation,includingLargeLanguage

Models(LLMs)examples,onlabordemandandinequality,findingthattheseeffectsdependonboththepricingstrategiesofinnovatorsandtheinstitutionalstructureoftheeconomy.

3

CaselliandManning

(2019)analyzehowimprovementsintechnologyaffectrealwagesinthelongrun.They

donotanalyzethetransitionpathtothenewsteadystate.Theirproductionfunctionisverygeneralbutassumes

2

technology(ICT)capitalfromtherestandwelookatelasticitiesofsubstitutioninthiscontext.AnimportantcontributionofthispaperistoexamineempiricallyaproductionfunctionwithICTcapital,comparingthemeritsofdifferentspecifications.Theempiricalexerciseprovidessupportforthespecificationthatwearguedinearlierworkisapriorithemostplausible.WeshowthatICTcapital—a(poor)proxyfor“robots”,tobesure—isdifferentinitsrelationshiptootherfactorsofproductioncomparedtotherestofequipmentcapital.Failingtotakethisintoaccountgivesthewrongresults.

Thedominantthemerunningthroughourresultsisthatrobots(andAI)indeedcanmakeabigdifferencetohowpolicieswork;oldtheoreticalassumptionsandbenchmarkmodelsneedtoberevisitedandearlierempiricalworktakenwithsomecautions.

Basedonourcalibrations,inthecaseofcorporatetaxcuts(CTC),standardCobb-DouglasandCESmodelsreadilydeliverstandardresults:alowertaxrateencouragescapitaldeepening,themarginalproductoflaborrisesasaresult,andrealwagesincreaseequally(inpercent)forlow-andhigh-skillworkers.If,instead,weassumethat“robot”capitalishighlysubstitutablewithlow-skillworkers,thenlong-runGDPgrowthishigherby1–2percentagepoints,buttheskillpremiumrisessharply:theincreaseinthehigh-skillwageequalsorexceedsGDPgrowthwhilethelow-skillwageincreasesverylittleorevendeclines.

Infrastructureinvestment(II)followssimilarpatterns:unskilledwagesriselessandskilledwagesmoreas“robot”capitalbecomesmoresubstitutablewithunskilledlabor.ComparedtoCTC,laboracrosstheskillspectrumbenefitsmore.Forratesofreturninlinewithempiricalestimates,theprivatecapitalstockincreasesmorethanwiththecomparableCTC;evenunderpessimisticassumptionsaboutthereturntoinfrastructure,strongcrowding-inofprivatecap-italliftsGDPgrowth3-4percentagepointsabovethatwiththeCTC.ThelargerincreaseinunskilledwageswithIIrelativetoCTCbecomesmoresalientas“robot”capitalbecomesmoresubstitutablewithunskilledlabor:withCTC,thelow-skillwagemayfall;withII,itincreasessubstantiallyinallruns.

Evenstarkerimplicationsofnewtechnologies,andbiggercontrastswithCTC,emergeforinvestmentineducation(IE).Wageinequalityislower,andgrowthhigher,dramaticallysowithmorehighlysubstitutable‘robot”capital.IEgivesanespeciallystrongboosttoaccumulationof“robot”capital,duetoboththelargedecreaseinunskilledlaborthatcompeteswithitandtheincreaseinthesupplyofcomplementaryskilledlabor.Strikingly,inthegreatmajorityofrunswhere“robot”capitalishighlysubstitutablewithlow-skilllabor,traditionalcapitalincreases2-5timesasmuchaswithCTC.

Thesepositiveresultsinformmanyofourwelfareresults.Attheinitialequilibrium,thereturnoninfrastructureandthepre-taxreturnonprivatecapitalbothequal10percent,whilethereturn

onlyonetypeofcapital,thusmissingoutonmanyimportantinteractionsoftraditionaland“robot”capitalwithdifferentdegreesofsubstitutabilitywithdifferenttypesoflabor.

3

oninvestmentineducationis7percent.Theprivatetimepreferencerateequals6percent.Consequently,thereistoolittleinvestmentinalltypesofcapital.Thesocialwelfarefunctionallowspolicymakerstodiscountthefuturelessheavilythantheprivatesectorand/orvalueincomeofthepoormorethanincomeofthenon-poor.Whenpolicymakersdoneither,theymaximizewelfareoftherepresentativeprivateagent.

4

Becausethethreepolicieshaveverydifferenteffectsonaggregatecapitalaccumulationandrealwages,thewelfarerankingsaresensitivetothesocialdiscountfactorandweightondistri-butionalobjectives,aswellastheparametersoftheproductionfunction.Oneresult,however,iscompletelyrobust:IIalwaysdominatesCTC.Thisresultisacorollaryoftheaforementionedpositiveresults.BecauseIIstronglycrowdsinprivatecapital,italwaysincreasestheaggregatecapitalstock(inclusiveofinfrastructure)andthelow-skillwagemorethanCTC.HenceitisalwaysmoreeffectivethanCTCinreducingunderinvestmentandincreasingrealincomeofthepoor.TheresultsforIEarelessrobust.Inapartialequilibriumsetting,thelow(direct)returnonIE(7vs.10percentforprivatecapitalandinfrastructure)doomsittolastplaceinthewelfareranking.Thisisalsothecaseingeneralequilibriumwhenthesocialwelfarefunctionisthesameasthewelfarefunctionoftherepresentativeagent.Theword“same”isimportant.SinceIEincreasestheaggregatecapitalstockandthelow-skillwagemuchmoreinthelongrunthantheothertwopolicies,itspositioninthewelfarerankingchangesdramaticallywhenpolicymakersdiscountfuturegainslessheavilythantheprivatesectorandcaremoreaboutwelfareofthepoorthanwelfareoftherepresentativeagent.Inourpreferredcalibration,forex-ample,IEbeatsCTCwhenthesocialdiscountfactoristwobasispointshigherthantheprivatediscountfactor;whenthesocialdiscountfactoris140basispointshigher(0.957vs.0.943),italsobeatsII.Andifrealincomeofthepoorentersthesocialwelfarefunctionwithasmallpositiveweight,IEbeatsbothCTCandIIevenwhenpolicymakersapplythesamediscountfactorastheprivatesector.

Theelasticitiesofsubstitutionbetweenthevariousfactorsofproductionplayacriticalroleinouranalysis,particularlybetween“robot”capitalandlow-skilledlabor.Thenoveltyofourspecification,notablytheintroductionof“robot”capitalasadistinctfactorofproductionmea-suredbyICTcapital,meansthatempiricalestimatesfromtheliteraturearenotdirectlycom-parable.Weextractdataonthecapitalandlaborstocks,andwagesandratesofreturn,thatcorrespondtoourproductionfunction.Wetheninfertheelasticitiesimpliedbythisdataforourspecification,aswellasfortwoalternativeplausibleCESproductionfunctionswithdiffer-entnestingstructures.Wefindthatourpreferredspecificationisthemostempiricallyplausible,andforboththebaselineandthealternativespecifications,theelasticityofsubstationbetween“robot”capitalisabove2andhigherthantheotherelasticities,lendingbroadsupporttothemostimportantassumptionwemakeinthispaper.

4Ourmodelhaspoorandnon-pooragents.Thereferencetothe“representativeagent”meansthatonlyaggre-gateconsumptionentersthewelfarefunction.

4

Therestofthepaperisorganizedasfollows.InSectionsIIandIII,welayoutthemodelandcalibrateittothedatafortheU.S.SectionIVdiscussestheextenttowhichcertainchoicesinthespecificationofthemodelanditscalibrationconditionourresults.Italsoreportstheempiricalexerciseandthesubsequentestimatedvaluesfortheelasticitiesofsubstitution.InSectionV,weanalyzethethreepolicyexperiments:corporatetaxcuts,investingininfrastructure,andinvestingineducation.Foreachexperiment,weprovideanalysisofthelongrun—includinganalyticalresults—andthetransitionpathtothenewsteadystate.WealsorankthewelfaregainsgeneratedbythepoliciesinSectionVI.SectionVIIconcludes.

II.THEMODEL

Weintroduceacorporateprofitstax,internationalcapitalflows,andinvestmentininfrastruc-tureandeducationintothemodeldevelopedby

Berg,Buffie,andZanna

(2018).Toisolatethe

effectsofeachpolicychange,transferpaymentstocapitalistsandhigh-skillworkerspayforchangesinthecorporatetaxrateandininfrastructureandeducationinvestment.

5

A.Technology

CompetitivefirmsproduceasinglegoodusingtraditionalcapitalKt,“robot”capitalZt,in-frastructurecapitalGt−1,high-skilllaborSt,andlow-skilllaborLt.TheproductionfunctionisQt=G1F[H(St,Kt),V(Lt,Zt)],whereF(•),H(•),andV(•)arelinearlyhomogeneousCESaggregatesoftheirrespectiveinputs.Tofacilitatethederivationofanalyticalresults,webypasstheproductionfunctionandworkwiththefirm’sunitcostfunction:

Ct=,(1)

where

ft=[ew,σ2+(1−e)rz,t1−σ2]1/(1−σ2)

and

ht=[gw,σ3+(1−g)rk,t1−σ3]1/(1−σ3)

aresub-costfunctionsdualtothecompositeinputsH(•)andV(•);σ1denotestheelasticity

ofsubstitutionbetweenHandV;σ2correspondstotheelasticityofsubstitutionbetweenlow-

5Becausethecapitalists/high-skillworkersfacetheusualintertemporalbudgetconstraintandlaborsupplyis

fixed,thesechangesintransfersinthemselveshavenobehavioraleffects.Ifthegovernmentweretofinancethepolicieswithreductionsintransferstolow-skilledhand-to-mouthworkers,therewouldbefirst-ordereffectsontheirconsumptionbut,withfixedlaborsupply,nogeneralequilibriumeffects;overall(pre-tax)inequalitywouldnotchange.

5

skilllaborLtand“robot”capitalZt;σ3istheelasticityofsubstitutionbetweenhigh-skilllaborStandtraditionalcapitalKt;wl,tandws,tarethewagesoflow-andhigh-skilllabor;andrk,tandrz,taretherentalratesfortraditionalcapitaland“robot”capital.

Thecostfunctionin(

1

)isnolesscumbersomethanthecorrespondingproductionfunction.Itisnotnecessary,however,tomanipulate(

1

)whenderivinganalyticalresults.Weemployin-steadthecompactspecificationCt=C[h(ws,t,rk,t),f(wl,t,rz,t)]/G1andinvokewell-knownformulasthatlinkthederivativesofthecostfunctiontothesubstitutionelasticitiesandfactorcostshares.

Flexiblefactorpricesensurethatdemandequalssupplyforeachprivateinput,whilethesupplyofinfrastructureisdeterminedbypublicinvestment.UsingShepherd’slemma,themarket-clearingconditionsmaybewrittenas:

Kt=Chhrk,Zt=Cffrz,(2)

and

Lt=Cffwl,

St=Chhws,

(3)

whereCh,Cf,hrk,frz,fwl,andhwsarepartialderivatives.LtandStareperfectlyinelastic.Underthissimplifyingassumption,asinglevariable,thewage,measurestheimpactofpolicyonincomeoflow-orhigh-skillworkers.

Utilizationofthetwocapitalinputsissubjecttothefollowingadding-upconstraint:

Ka,t−1=Kt+Zt,(

4)

whereKa,t−1,theaggregatecapitalstock,ispredetermined.AlthoughKtandZtarefreetojump,theydonotdoso.Inthescenariosweanalyze,traditionalcapitalisneverdismantledandinstantaneouslyconvertedintorobots.BothcapitalstocksbehaveasstatevariablesbecauseonthetransitionpaththeydependsolelyonKa,t−1

.6

6Wheninvestmentineducationorinfrastructureincreases,KtandZtdependonKa,t−1,St−1,andGt−1.ButSt−1andGt−1arealsopredeterminedstatevariables.

6

Pricealwaysequalsunitcostasperfectcompetitionpreventsfirmsfromearningsupranormalprofits.

7

Hencethefollowingzero-profitconditionholds:

t−1

1=C(ws,t,rk,t,wl,t,rz,t).

Gη

(5)

B.Preferences

Thepoorest40percentofU.S.householdslivecheck-to-check.Weequatethisgroupwithlow-paid,low-skillworkersLt,whoconsumealloftheirincomewl,tLteachperiod.

Capitalistsandskilledworkersarerichenoughtosaveandcanborrowintheworldcapitalmarketattheinterestrateit.TheylivetogetherpeacefullyinarepresentativeagentwhochoosesconsumptionCt,aggregateinvestmentIa,t,and“robot”capitalZttomaximize

U=βt,

subjectto

Ct+Ia,t+Γ(Ia,t,Ka,t−1)+(1+it−1)Bt−1

Ka,t

=ws,tLs,t+Tt+Bt+[rz,t(1−xt)+δxt]Zt+[rk,t(1−xt)+δxt](Ka,t−1−Zt),(6)

=Ia,t+(1−δ)Ka,t−1,(7)

whereβ=1/(1+ρ)isthediscountfactor;ρisthepuretimepreferencerate;τisthein-tertemporalelasticityofsubstitution;δisthedepreciationrate;Btisforeigndebt;Ttislump-sumtransfers/taxes;andxtisthetaxoncorporateprofits(netofdepreciation).Inthebudget

constraint(

6

),

v

2

−δ)2Ka,t−1

Γ(Ia,t,Ka,t−1)=

capturesadjustmentcostsincurredinchangingtheaggregatecapitalstock.

PertheMaximumPrinciple,thefirst-orderconditionsforanoptimumconsistof

Ct−1/τ=λ1,t,

rk,t=rz,t=rt,

(8)

(9)

7Thisisasimplificationassumption,withthecaveatthattechnologicalrevolutionsmaycausemarkupstoriseforsomegoodsandimperfectcompetitioninthelabormarketduetoincreasingmarketpowermayalsoleadtofallingrealwages.

7

λ1,t[1+v-δ)]=λ2,t,(10)

andtheco-stateequations

λ1,t=β(1+it)λ1,t+1,(

11)

λ2,t=βλ2,t+1+βλ1,t+1l(rt+1-δ)(1-xt+1)+-δ)2],(12)

whereλ1,tandλ2,taremultipliersattachedtotheconstraints(

6

)and(

7

).Equations(

11

)-

(12)canbeconsolidatedintotwofamiliarEulerequations.Onanoptimalpath,consumption

satisfies

1/τ=β(1+it)(13)

andinvestmentadjustssothattheafter-taxcapitalrental,netofdepreciationandadjustmentcosts,continuouslyequalstheinterestrate:

=1+it.(14)

(rt+1-δ)(1-xt+1-δ)+-δ)2

Therepresentativesaverviewstheworldmarketinterestrateasparametricwhensolvingtheiroptimizationproblem.Intheaggregate,however,U.S.borrowingislargeenoughtoinfluencei.Fortheanalysisthatfollows,afull-blowntwo-countrymodeloftheworldeconomywouldbeoverkill.Weassumesimply

8

it=ρeµ

whereρ=（1β)istheprivatetimepreferencerateassociatedwiththediscountfactorβ

andBcorrespondstotheinitialvalueofBt—thevalueattheinitialsteadystate.WhentheU.S.borrowsmore(Bt>B),itpushesitaboveρbyanamountthatdependsontheslopeofthesupplycurveforexternalloans.Thelimitingcasesµ→~andµ→0correspondtotheclosedeconomyandanopeneconomythatfacesafixedworldmarketinterestrate,respectively.

WeincorporateanopencapitalaccountinthemodelnottoberealisticbutrathertoproperlyjointhedebatebetweenproponentsoftheCTCanditsdetractors.TheproponentscontendthattheCTCwillstimulateaquick,largeincreaseininvestmentthankstocapitalinflowsthatkeep

8Thespecificationin(

15

)iscommoninopeneconomymodels.See

Turnovsky

(1997)and

UribeandSchmitt-

Grohe

(2017)

.

8

increasesintheinterestrate“relativelysmall.”

9

Criticsofthetaxcutdisputethis,assertingthat,becauseofthesheersizeofitseconomy,theU.S.cannotattractlargecapitalinflowswithout“drivingupinterestratesworld-wide”(

Krugman

(2017)).Varyingμ

in(15)toaccommodate

differentviewsabouttheelasticityofcapitalflowsallowsustofaithfullyrepresentthedebateintheliterature.

C.TheGovernmentBudgetConstraint

Cutsintransferpaymentstocapitalistsandhigh-wageskilledworkerspayforreductionsinthecorporateincometaxandforadditionalinvestmentsineducation(Is,t)andinfrastructure(Ig,t).

10

Thisiscapturedbythefollowinggovernmentbudgetconstraint:

Tt=xt(rt−δ)Ka,t−1−Ig,t−Is,t.(16)

D.PublicInvestmentinInfrastructureandEducation

Thelawofmotionforinfrastructurecapitalis

Gt=Ig,t+(1−δg)Gt−1,(17)

whereδgisthedepreciationrate.Ig,t—apolicyvariable—jumpsonceatt=1.

PublicinvestmentinhighereducationIs,tincreasesthesupplyofeducationcapitalSu,taccord-

ingtothestockaccumulationequation:

Su,t=Is,t+(1−δs)Su,t−1,(

18)

whereδsisthedepreciationrate.Afixedinput-outputcoefficientφconnectstheincreaseinthe

supplyofeducationcapitaltothesupplyofhigh-skilllabor:

St=S+φ(Su,t−1−Su),(

19)

whereSandSucorrespondtotheinitialvaluesofStandSu,t—thevaluesattheinitialsteadystate.

9Seetheguestcolumnby

Feldstein

(2017)andtheopenletterfromninemacroeconomiststoTreasurySecre

-taryMnuchin,bothintheWallStreetJournalinNovember2017.

10WethussidestepthecontroversialdirectdistributionaleffectsoftherecentU.S.taxreform.

9

E.DebtAccumulationandtheCurrentAccountDeficit

SubstitutingforTtin(

6

)(andrecognizingthatrz,t=rk,t=rt)producestheaccountingidentitythatlinksdebtaccumulation(left-handside)tothecurrentaccountdeficit(right-handside):

Bt−Bt−1=it−1Bt−1+Ct+Ia,t+Ig,t+Is,t+Γ(Ia,t,Ka,t−1)−rtKa,t−1−ws,tSt,(

20)

or,equivalently,

Bt−Bt−1=it−1Bt−1+wl,tLt+Ct+Ia,t+Ig,t+Is,t+Γ(Ia,t,Ka,t−1)−Qt.(

21)

Thecurrentaccountdeficitequalsthedifferencebetweennationalspendingandnationalin-come.Notethatthesumwl,tLt+Ctequalsaggregateconsumptionin(

21

),sincelow-skillworkersLtconsumealloftheirincomeeachperiod.

III.CALIBRATIONOFTHEMODEL

Tocalibratethemodelforlargechanges,weassignvaluestostructuralparameters,theoldandnewtaxrates,andfactorcostsharesattheinitialsteadystate.ThecalibrationissummarizedinTable

1.

Thediscountfactor,thedepreciationrateforprivatecapital,theintertemporalelasticityof

substitution,andtheq-elasticityofinvestment(Ω)alltakeordinaryvalues

.11

Withrespecttotheotherchoices:

•DataonAI,industrialrobots,ICTcapital,etc.,isscarce,especiallygoingbeyondtheU.S.Wesettheincomeshareofthisbroad“robot”capitalat4percentasin

Edenand

Gaggl

(2018).ThistobeconsistentwiththeshareofICTcapitalintheaggregatecapital

stock.

12

Clearly,thisisonlyanapproximationtothesortsofnewtechnologiesdescribedintheintroduction.IndustrialrobotsorAIpersearenotincludedinICTcapital(seeforinstance

EdenandGaggl

(2018)andOnlineAppendixII).Ontheotherhand,notallICT

capitalsubstitutesforlow-skilllabor.

11ThevalueassignedtoΩpinsdowntheadjustmentcostparameterv.Thefirst-orderconditionforinvestment

is1+v（−δ)=q,whereq=andλ1andλ2aremultipliersattachedtotheconstraintsin(

6

)and(

7

).qis

Tobin’sq,theratioofthedemandpriceofcapitaltoitssupplyprice.Evaluatedatasteadystate,v=δ,where

Ω=.

12TheshareofICTcapitalintheaggregatecapitalstockis5.7percentextendingdatafrom

EdenandGaggl

(2018)to2020,whileisof11percentbasedonthedefinitionanddatareportedin

Nordhaus

(2015)

.

10

•Thetaxratexoldcombinestheeffectivemarginaltaxrateoncorporateprofitswiththetaxrateoncapitalincome.Theeffectivemarginalcorporateprofitstaxismuchlessthanthestatutoryrateof35percent.Ourguessis27percent.ThetaxrateoncapitalgainsanddividendsintheU.S.is15percentformostincomebracketsand20percentforthehighestbracket.Weusetheaverageofthetworates.Theoverallpre-2018taxrateisthusxold=1