未來(lái)能源研究所-碳稅對(duì)實(shí)現(xiàn)美國(guó)巴黎協(xié)定目標(biāo)的宏觀經(jīng)濟(jì)影響（英文）-2021.5-57正式版

TheMacroeconomicEffectsofaCarbonTaxtoMeettheUSParisAgreementTarget

TheRoleofFirmCreationandTechnologyAdoption

AlanFinkelsteinShapiroandGilbertE.Metcalf

WorkingPaper21-14

May2021

TheMacroeconomicEectsofaCarbonTaxtoMeettheU.S.ParisAgreementTarget:TheRoleofFirmCreationandTechnologyAdoption

AlanFinkelsteinShapiroyGilbertE.Metcalfz

May19,2021

Abstract

Weanalyzethequantitativelabormarketandaggregateeectsofacarbontaxinaframeworkwithpollutionexternalitiesandequilibriumunemployment.Ourmodelincorporatesendogenouslaborforceparticipationandtwomarginsofadjustmentin-

uencedbycarbontaxes:(1)rmcreationand(2)greenproduction-technologyadop-tion.Acarbon-taxpolicythatreducescarbonemissionsby35percent|roughlytheemissionsreductionsthatwillberequiredundertheBidenAdministration’snewcom-mitmentundertheParisAgreement|andtransfersthetaxrevenuetohouseholdsgen-eratesmildpositivelong-runeectsonconsumptionandoutput;amarginalincreaseintheunemploymentandlaborforceparticipationrates;andanexpansioninthenumberandfractionofrmsthatusegreentechnologies.Intheshortterm,theadjustmenttohighercarbontaxesisaccompaniedbygradualgainsinoutputandconsumptionandanegligibleexpansioninunemployment.Critically,abstractingfromendogenousrmentryandgreen-technologyadoptionimpliesthatthesamepolicyhassubstantialadverseshort-andlong-termeectsonlaborincome,consumption,andoutput.Ourndingshighlighttheimportanceofthesemarginsforacomprehensiveassessmentofthelabormarketandaggregateeectsofcarbontaxes.

JELClassication:E20,E24,E62,H23,O33,Q52,Q55

Keywords:Environmentalandscalpolicy,carbontax,endogenousrmentry,greentechnologyadoption,searchfrictions,unemployment,laborforceparticipation

WethankGarthHeutelforveryusefulcommentsandsuggestions.Anyerrorsareourown.

yDepartmentofEconomics,TuftsUniversity,BrakerHall,8UpperCampusRoad,Medford,MA02155.

E-mail:Alan.FinkelsteinShapiro@.

zDepartmentofEconomics,TuftsUniversity,BrakerHall,8UpperCampusRoad,Medford,MA02155.

E-mail:Gilbert.Metcalf@.

Introduction

Thepotentialadverseeectsoftaxingcarbonemissionsonemploymentandaggregateeco-nomicactivityareacentralthemeincurrentdiscussionsofenvironmentalpolicyandregula-tion(OECD,2017;HafsteadandWilliamsIII,2019;MetcalfandStock,2020a,b).ThistopichastakenongreaterimportancewiththeBidenAdministration’sApril2021announcementoftargetingemissionreductionsof50to52percentfrom2005levelsby2030.1ThegrowinginterestinintroducingandbroadeningthescopeofcarbontaxesintheU.S.raisesthreeimportantquestions:Whatarethequantitativeeectsofthesetaxesonlabormarketsandmacroeconomicoutcomes?Howdochangesinrmentryandproduction-technologyadop-tionduetocarbontaxesshapethesemacroeconomicoutcomes?Finally,dotheshort-termeectsdierfromthelong-termeects?

Weaddressthesethreequestionsinageneralequilibriummodelwithlaborsearchfric-tionsandpollutionexternalities.Incontrasttoexistingstudies,ourframeworkincorporatestwoadditionalandinterrelatedmarginsofadjustmenttocarbontaxes:(1)rmcreation(subjecttosunkentrycosts)and(2)theabilityofrmstoadoptgreen(non-polluting)technologies(subjecttoxedcosts).Therationaleforincludingthesetwomarginsissim-ple:theregulatorycostsassociatedwithenvironmentalpolicynotonlyaectthelaborandcapitaldecisionsofexistingrmsandthedecisionsoveremissionsabatement|anintensivemarginofadjustmenttocarbontaxes|butalsotheincentiveofpotentialrmstoenterthemarketintherstplaceaswellastheserms’technology-adoptiondecisions|anextensivemarginofadjustmenttothesesametaxes.Atthesametime,bothrmentryandtechnologyadoptiondecisionscanin

uencelabormarketandmacroeconomicoutcomes.Critically,theinclusionofatechnologyadoptionmarginallowsustoconsiderpolicy-inducedendogenouschangesintheeconomy’sunderlyingtechnologicalcompositionofproduction(capturedbytheprevalenceofpollutingversusgreenproductiontechnologies).Byexplicitlyconsideringtheseimportantmarginsofadjustment,ourframeworkallowsforamorecomprehensiveassessmentofthelabor-marketandmacroeconomiceectsofcarbontaxes.

1WhiteHouseFactSheetonGreenhouseGasPollutionReductionTarget,April22,2021,available

at/brieng-room/statements-releases/2021/04/22/fact-sheet-president-biden-sets-2030-greenhouse-gas-pollution-reduction-target-aimed-at-creating-good-paying-union-jobs-and-securing-u-s-leadership-on-clean-energy-technologies/.

2

TheBidenAdministration’scommitmenttoreducinggreenhousegaspollutionby50to52percentfrom2005levelsby2030isanambitioustarget.BasedonmodelingintheU.S.EnergyInformationAdministration’s2021AnnualEnergyOutlook,emissionsin2030inEIA’sreference(nonewpolicy)casewillhavefallenbynearlyone-quarterfrom2005levels(4.583billionmetrictonsrelativeto2005emissionsof6billionmetrictons).Thus,emissionswillneedtofallanadditional35percentbetweennowand2030toachievetheBidenAdministration’sgoal.

Usingourmodelunderabaselinecarbon-taxschemedesignedtoreducelong-runemis-sionsby35percentwithcarbon-taxrevenuerebatedlump-sumtohouseholds,wendthatthispolicygeneratesmildpositivelong-runeectsonconsumption,output,andlaborforceparticipation;negligiblelong-runadverseeectsonunemployment;andalong-runincreaseinthenumberandshareofrmsthatadoptgreentechnologies.Moreover,thepositivelong-termeectsofcarbontaxesextendtothetransitionpathaswell.Indeed,thegradualincreaseincarbontaxesisaccompaniedbygreaterconsumptionandoutput,andaverylim-itedincreaseinunemployment.Thus,highercarbontaxeshavepositiveshort-andlong-termmacroeconomiceectsandnegligibledetrimentaleectsonthelabormarket.

Tohighlighttherelevanceofourndingsandstresstheimportanceofrmentryandgreen-technologyadoptiondecisions,wecompareourresultstothoseofasimplermodelthatabstractsfromthesetwoextensivemargins.Inthissimplermodel,thesamecarbon-tax-inducedreductioninemissionshasnon-trivialnegativeshort-andlong-termeectsonlaborincome,consumption,andoutput,aswellasstrongeradverseeectsonunemployment.However,thesedetrimentaleectsareatoddswithrecentempiricalevidencethatpointtopositiveoutputeectsfromcarbontaxes(MetcalfandStock,2020a,b).Therefore,ourframeworkisabletoreconcilethisevidence.Indoingso,wehighlighthowtechnologyadoptiondecisionsplayadecisiveroleingeneratingmutedadverselabor-marketeectsalongsidepositivemacroeconomicoutcomesinresponsetocarbontaxes.Atthesametime,ouranalysisshowshowchangesinrmentryinresponsetocarbontaxesplayakeyroleincontributingtotheshort-termexpansioninconsumptionascarbontaxesgraduallyincreasetoreachtheirhigherlong-termlevel.

Ourworkisrelatedtothegrowingtheoreticalliteratureonthelabormarketandmacroe-

3

conomiceectsofcarbontaxesandenvironmentalpolicy.Severalpapersinthisliteraturefocusonthelinkbetweenpollutionemissionsandbusinesscyclesfromapositivestandpoint,butabstractfromconsideringlabormarketoutcomesandthepotentialdierencesbetweentheshort-andlong-termaggregateeectsofcarbontaxes(thatis,thetransitionpathtoanenvironmentwithhighercarbontaxes).2Onlyrecentlyhastheliteraturestartedtoexploretherelationshipbetweenenvironmentalpolicy,macroeconomicoutcomes,andlabormarkets,includingunemployment(HafsteadandWilliamsIII,2018;AubertandChiroleu-Assouline,2019;FernandezIntriago,2020;GibsonandHeutel,2020;andCastellanosandHeutel,2021).Atthesametime,afewpapershavestudiedthelinkbetweenmarketstructure,rmentry,andenvironmentalpolicy(seeKreickemeierandRichter,2018;andAnnicchiarico,Corre-ani,andDiDio,2018).Anotherrecentstrandofworkexploreshowtechnologyadoptioninteractswithrmentryandexit(CoriaandKyriakopoulou,2018)and,separately,howenvi-ronmentalpolicyin

uencestheadoptionofgreentechnologies(Acemogluetal.,2016;Fried,2018).3Critically,noneofthesepapersconsiderthelinkbetweencarbontaxesandlabormarketoutcomes,whichlieatthecenterofouranalysis.ClosesttoourworkareAcemogluetal(2016),whoproposeaframeworkwherermschoosetoproduceusingeitheradirtyorcleantechnologyandinvestinresearchanddevelopment,HafsteadandWilliamsIII(2018),whouseatwo-sector(\dirty"and\clean")frameworkwithequilibriumunemploymentandndthatcarbon-tax-inducedreductionsinemissionsentailbothoutputandunemploymentcosts,andAnnicchiarico,Correani,andDiDio(2018),whouseaone-sectormodelwithendogenousrmentryandfrictionlesslabormarketsandndthatgreatercarbontaxesleadtoloweroutput,partlyvialowerrmcreation.OurndingsshowthattheadverseeectsfromcarbontaxesinbothHafsteadandWilliamsIII(2018)andAnnicchiarico,Correani,andDiDio(2018)dependcriticallyonwhetherrmscanadoptgreentechnologies.

Wecontributetotheliteratureonthelabormarketandmacroeconomicconsequencesofcarbontaxesinthreeways.First,whilethisliteraturehassteadilyexpanded,themajorityofmodelsfocusexclusivelyonunemploymentandthereallocationofworkersbetweensec-

SeeFischerandSpringborn(2011),Heutel(2012),AnnicchiaricoandDiDio(2015),Annicchiarico,Correani,andDiDio(2017),AnnicchiaricoandDiluiso(2019),andKhan,Metaxoglou,Knittel,andPapineau

(2019),amongothers.

3Forrecentworkonthelinkbetweenpollution,environmentalregulation,rmentry,andtrade,seeShapiroandWalker(2018).

4

torswithoutconsideringhowpolicychangesaectthesearchbehaviorofindividuals.4Theinclusionoflaborforceparticipationinourframeworkembodiesthislabor-supply-sidemar-gin.Second,thesesamestudiesabstractfromtheeectsofpolicychangesonlabormarketsandaggregateoutcomesvia(1)rmentryandexit,and(2)rms’decisionstoadoptgreentechnologies.Ourworkshowsthattheinteractionofthesemarginsplaysacrucialroleinshapingthequalitativeandquantitativeeectsofhighercarbontaxesonbothlabormar-ketoutcomesandaggregateeconomicactivityintheshortandlongterm,withtechnologyadoption|andthereforepolicy-inducedendogenouschangesintheeconomy’sunderlyingtechnologicalcompositionofproduction|playingadecisiveroleingeneratingpositiveag-gregateeectsfromcarbontaxes.Thislastndingis,tothebestofourknowledge,new,andstandsincontrasttothoseofexistingrelatedpapers,whichgenerallyndthatcarbontaxeshaveadverselabor-marketandmacroeects.Moreover,ourmodel-basedresultspro-videatheoreticalrationalebehindrecentempiricalevidenceonthepositivemacroeectsofcarbontaxes(MetcalfandStock,2020a,b).Finally,thecombinationofrmentryandexitandtechnologyadoptionwithfrictionallabormarketscontributestotheexistingliter-atureonmarketstructure,technologyadoption,andenvironmentalpolicy,whichabstractsfromtheimplicationsofadoptinggreentechnologiesonthelabormarket.Morebroadly,webringtogethertwoimportantmarginsofadjustmenttocarbontaxesthat,thusfar,havebeenstudiedinisolation,andshowthattheirinclusionplaysacentralroleinshapingthequalitativeandquantitativelabor-marketandmacroeconomicimplicationsofcarbontaxes.

Therestofthepaperisstructuredasfollows.Section2describesthemodel.Section3outlinesourcalibrationstrategyandpresentsthemainresultsfromourquantitativeanalysis.Section4concludes.

TheModel

Theeconomyiscomprisedofrms,agovernment,apopulationofunitmass,andarepre-sentativehouseholdwithameasureoneofhouseholdmembersthatownsallrms.Search

4TheonlyrecentexceptionisCastellanosandHeutel(2021),whoconsidersectorallaborforceparticipa-tion.

5

frictionsinthelabormarketgiverisetoequilibriumunemployment.Householdsconsume,makelaborforceparticipationdecisions,andinvestresourcesinrmcreationsothatrmentryisendogenous.Aswedescribeinmoredetailbelow,oncermsenterthemarket,theycanchoosethetechnologicalcompositionoftheirproductionprocess:oneofthetwopro-ductiontechnologiesavailabletothermgeneratesharmfulcarbondioxideemissionsasaby-productandissubjecttocarbontaxes,whiletheotheris\green"anddoesnotgeneratetheseemissions,butitsadoptionissubjecttoxedcostsofoperation.Revenuefromcarbontaxesistransferredlump-sumtohouseholds.

TheproductionandlabormarketstructureisanadaptationoftheframeworkinFinkel-steinShapiroandMandelman(2021)(henceforthFSM),whomodifytheproductionstruc-tureofthewell-knownGhironiandMelitz(2005)(henceforthGM)tradeframeworktocap-turetechnology-adoptionanditsimpactonlabormarketoutcomes.ThestructureinFSMhasrelevantfeaturesfortheanalysisofcarbontaxes,mainlytheinclusionoftechnology-adoptiondecisionsbyrms,endogenousrmentry,andjob-searchdecisionsbyhouseholdsviaendogenoussectorallaborforceparticipation.IncontrasttoFSM,weintroducepollu-tionexternalitiesandfocusonhowrms’decisionsoverentryandtechnologyadoptionarein

uencedbycarbontaxes.Withthismind,themodeldescriptionbelowfollowscloselythegeneralsetupinFSM.

2.1 FirmandProductionStructure

Thereisanunboundednumberofmonopolistically-competitivermentrantswhoseentryissubjecttoasunkentryresourcecost’e.Oncermsenter,theydrawtheiridiosyncraticproductivityafromacommondistributionG(a)withsupport[amin;1);wheretheresultinglevelofaremainsunchangeduntilthermexitswithexogenousprobability0<<1.Eachrmproducesasingleoutputvariety!basedona,whereyt(!)denotestheoutputofagivenrmproducingvariety!.Thus,intherestofthemodeldescription,werefertoarmproducingvariety!withproductivitylevelasimplyasrma.

Whenahouseholddecidestocreateanewrm,allitknowsistheproductivitydistribu-tion,G(a),butnottherm’srealizedproductivity.Uponenteringandincurringthesunkentrycost,thenewrm’sproductivitylevelisrealized,allowingittochooseoneoftwo

6

technologies.

Aregular(r)technologyisavailablethatgeneratescarbondioxide(harmful)emissions|emissionsforshort.Theseemissionsaresubjecttoacarbontaxbutcanbemitigatedviaexpendituresonemissionsabatement.Agreen(g)technologyisalsoavailablethatdoesnotgenerateemissions.Usingthegreentechnology,however,entailsincurringaxedresourcecost’gassociatedwiththeadoptionofthetechnology.AppendixA.1formallyshowsthatthereisanendogenousthresholdlevelofproductivitysuchthatrmswithrealizedpro-ductivitybelowthisthresholdchoosethertechnologyandrmswithrealizedproductivityabovethisthresholdchoosethegtechnology.Householdswillchoosetocreateanewrmbasedonthenewrm’sexpectedfutureprots,whichwilldependonthedistributionoftheproductivityparameteraandtheresultingtechnologythatisoptimalforthermtochoose.Thechoicetechnologymakesthemeasureofrmsineachcategoryendogenous.

Bothproductiontechnologiesrelyonlabor,whichissubjecttosearchandmatchingfrictions,andphysicalcapitalasinputs.Emissionsfromusingthertechnologyaddtotheeconomy’sstockofcarbondioxidepollutionthat,inturn,hasnegativeexternalitiesonproductionforallrmsintheeconomy,aswedetailbelow.

2.1.1 TotalOutput

"

TotaloutputisgivenbyYt=

yt(!)

"1

d!

"1

,whereisthepotentialmeasureof

!2

"

rmsintheeconomyand">1R

istheelasticityofsubstitutionacrossindividualoutput

1

varieties.Inturn,theaggregatepriceindexisPt

=

pt(!)1

"d!

.AsinGM,only

!2

1"

givenperiod.

asubsetofrmstareultimatelyactiveinany

R

2.1.2 FirmStructure

Inwhatfollows,weseparatetheproductionprocessfromtechnology-adoptionandpricingdecisionsbyintroducingintermediategoodsproducersandrmsthatusetheseintermediategoods.Thisfacilitatesthecomparisonofourframeworktorelatedmodelsthatabstractfromrmentryandtechnology-adoptionmarginswithoutaectingthegeneraleconomic

7

environment.5

FirmProtsandThresholdProductivityLevelAsnotedearlier,wecanthinkofarmaashavingaccesstotwopossibleproductionlinesthatdierintheirtechnology.Individualprotsfromproducingwiththertechnology,r;ty(a),aregivenby

y

hr;t(a)

mcr;t

iyr;t(a);

r;t(a)=

a

whileprotsfromproducingwiththegtechnology, g;ty(a),aregivenby

y

hg;t(a)

mcg;t

iyg;t(a)’g;

g;t(a)=

a

wherej;t(a)pj;t(a)=Pt,mcj;t,andyj;t(a)denote,respectively,therealoutputprice,therealmarginalcost,andthermoutputassociatedwithusingtechnologyj2fg;rg,and’gisthexedcostofg-technologyadoption.Firmaisindierentbetweenproductiontechnologieswhen

g;ty(ag;t)=r;ty(ag;t);

(1)

whereag;tisthethresholdidiosyncraticproductivitylevelabovewhichrmsadoptthegtechnology.6

OptimalPricingGiventheaggregationoftotalrmoutputinSection2.1.1,itiseasytoshowthatthedemandfunctionforrma’soutputisgivenbyyj;t(a)=(j;t(a))"Ytforj2fg;rg.Then,rmachoosesj;t(a)tomaximizej;ty(a)subjecttothedemandfunction

5Whilethisseparationofproductionfromtechnologyadoptioniscommoninthemacroeconomicslitera-ture,itmayseemunusualtoenvironmentaleconomists.Wenotethatwecouldequivalentlycharacterizetheproductionprocessasonewherermsusefactorsofproductiontoproduceanalgood.Firmsenter,learntheirproductivitylevel,andchooseaproductiontechnology(regularorgreen).Havinglearnedtheirpro-ductivitylevel,inequilibrium,theymatchthetechnologychoicetotheirproductivitylevelappropriately(asdiscussedbelow).Firmsusecapitalandlabortoproduceyt(a)withaconstant-returns-to-scaleproductionfunction.MarginalrevenueimpliedforintermediategoodsproducersinSection2.1.3belowsimplybecomesmarginalcostfornalgoodsproducersjustbelow.

SeeFSMforananalogousindierenceconditioninthecontextofrms’decisionstoadoptdigitaltechnologies,andZlate(2016)inthecontextofrms’decisionstooshoreproduction.Itcanbeshownthat

ifag;tisnotattheextremeendsofthesupportofthedistribution,thentheslopeofg;ty(ag;t)>r;ty(ag;t),forgandrrmsonlyintersectonce(atag;t).SeeAppendixA.1foraproof.

8

foryj;t(a).Theresultingoptimalrealpriceforrmaisgivenbyj;t(a)=

"

mcj;t

.

"1

a

EvolutionofFirmsDenotebyNtthemeasureoftotalactivermsandbyNe;tthemeasureofnewentrants.Then,theevolutionofthetotalnumberofrmsintheeconomyis

Nt=(1)[Nt1+Ne;t1]:

(2)

RecallingthatrmsdrawtheiridiosyncraticproductivityfromadistributionG(a)andthatag;tisthethresholdlevelofproductivityabovewhichrmsusethegtechnology,thenumberofrrmsNr;tisgivenbyNr;t=G(ag;t)NtandthenumberofgrmsNg;tisgivenby

Ng;t=[1 G(ag;t)]Nt.

FirmAveragesDenotebyear;ttheaverageidiosyncraticproductivitylevelofrrmsandbyeag;ttheaverageidiosyncraticproductivitylevelofgrms.Formally,theseaveragesare

1

1

givenbyar;t=

1

ag;t

a"

1dG(a)"

1andag;t

=

1

1a"1dG(a)

"1

.Then,

G(ag;t)a

1G(ag;t)

i

ag;t

yi

h

min

y

hNr;t

y

Ng;t

y

y

wecandeneaverageindividual-rmprotsas

=

+

where

(a

)

R

r;t

e

R

et

Nt

r;t

g;t

r;t

r;t

Nt

andy

y

(a

g;t

)areaverageindividual-rmprotsfromproducingwiththerandgtech-

g;t

g;t

e

e

e

e

e

e

e

nologies,respectively.Analogously,averagerealpricesandaverageindividual-rmoutput

aregivenbyer;t r;t(ear;t)andeg;t g;t(eag;t)andbyyer;t yr;t(ear;t)andyeg;t yg;t(eag;t),

respectively.Ofnote,asweshowinSection2.2,giventhatrms’idiosyncraticproductivityisrevealedonlyafterincurringasunkcostandenteringthemarket,rmcreationdecisionsarein

uencedby,amongotherfactors,theexpectedvalueofety.

2.1.3 IntermediateGoodsProducers

Thereisameasure1ofperfectly-competitiveproducersofintermediategoodsforrandgrms.Theseproducersusecategory-speciclabor,whichissubjecttosearchandmatchingfrictions,andcapital.Theproductionofintermediategoodsforrrmsgeneratespollutionemissionsetthataddtotheeconomy’sstockofpollutionxt(wherethisstockistakenasgivenbyrms).Wefollowtheliteratureandassumethatthestockofpollutionevolvesasxt=xxt1+et+erowt,0<x<1,whereerowtdenotesexogenousemissionsfromtherestoftheworld.Emissionsetaretaxed,butrrmscanmitigatetheseemissionsviaabatement

9

expenditures.Incontrast,theproductionofintermediategoodsforgrmsdoesnotgeneratepollutionemissionsandisnotsubjecttocarbontaxes.

Formally,intermediategoodsproducerschoosethenumberofvacanciesvg;tandvr;twhichareneededtohireworkerstoproduceeachcategoryofintermediategoods;thetotalamountofdesiredcapitalkt+1;thedesiredmeasureofgandrworkersng;tandnr;t;andthefraction

ofemissionsabatement ttomaximizeE0P1 tj0 isubjectto7

t=0 t

ti=[D(xt)mcr;tH(nr;t;kr;t) wr;tnr;t rvr;t tet t]

[D(xt)mcg;tF(ng;t;kg;t)wg;tng;tgvg;t]

[kt+1 (1 )kt];

theperceivedevolutionofeachcategoryofemployment

nr;t=(1%)nr;t1+vr;tq(r;t);

(3)

and

ng;t=(1%)ng;t1+vg;tq(g;t);

(4)

andtotalphysicalcapital

kt=kg;t+kr;t;

(5)

where tj0isthehousehold’sstochasticdiscountfactor(denedfurtherbelow),theterm

t

=

D(x

)H(n

r;t

;k

r;t

);

(6)

tt

isthetotalcostofabatingemissionsfromtheproductionofintermediategoodsforrrms,and

et=(1t)[D(xt)H(nr;t;kr;t)]1;

(7)

isthetotalamountofemissionsgeneratedbysuchproductionnetofabatement,where

>0,1;and0<1.Notethatboththecostofabatingemissions,t,andtheemissions

Recallthathouseholdsownallrms(andtaketheirprotsasgiven).Hencethejointprotmaximizationassumptionhere.

10

themselves,et,areafunctionoftheproductionofintermediategoodsforrrms.H(nr;t;kr;t)andF(ng;t;kg;t)areconstant-returns-to-scaleandincreasingandconcavefunctionsineachargument(weassumethataggregateproductivityisconstantandnormalizedto1).jandwj;tare,respectively,the

owcostofpostingvacanciesandtherealwageofworkersincategoryj2fg;rg,and0<<1isthecapitaldepreciationrate.8tisthetaxonemissionsandD(xt)isapollution-damagesfunctionthatisdecreasingintheeconomy’sstockofpollutionxtandtakenasgivenbyproducers.Assuch,anincreaseinpollutioneectivelyreducesoutputforagivenamountoflaborandcapital.Turningtotheevolutionofeachcategoryofemployment,0<%<1istheexogenousprobabilityofjobseparationandq(j;t)istheendogenousjob-llingprobabilityincategoryj,whichisafunctionofmarkettightnessj;t.Finally,wefollowthelabor-markettimingconventioninArseneauandChugh(2012)wherebylledvacanciesinperiodtbecomeproductiveinthesameperiod.

The rst-orderconditionsyieldanoptimalemissionsabatementrate t

(D(x

)H(n

r;t

;k

r;t

))=

1;

(8)

t

t

t

capitalEulerequations

1=Ett+1jt[D(xt+1)mcr;t+1Hkr;t+1

t+1ekr;t+1

kr;t+1+(1

)];

(9)

and

);

1=Ett+1jtD(xt+1)mcg;t+1Fkg;t+1+(1

(10)

aswellasstandardjobcreationconditionsforemploymentineachcategory

r

=2

D(xt)mcr;tHnr;t

tenr;t

3;

(11)

q()

r

r;t

4

nr;twr;t+(1

%)Ett+1jt

5

q(r;t+1)

and

wg;t+(1

%)Ett+1jtq(g;t+1)

q(g;t)=D(xt)mcg;tFng;t

;

(12)

g

g

Followingthemacroliteratureonendogenousrmentry,weassumethatthecapitaldepreciationrateandthermexitratearethesame.Introducingdierencesinrmexitandcapitaldepreciationratesdoesnotchangeourmainconclusions.

11

whereenr;tandekr;t,denotethemarginalincreaseinemissionsfromonemoreworkerandonemoreunitofcapitalintheproductionofintermediategoodsforrrms,respectively,andnr;tandkr;tdenotethemarginalincreaseintheresourcecostofemissionsabatementassociatedwithhavingonemoreworkerandonemoreunitofcapitalintheproductionofintermediategoodsforrrms,respectively.9

Intuitively,intermediategoodsproducersequatethemarginalcostofemissionsabatement|givenbytheresourcecostincurredasaresultofthemarginalincreaseinemissionsabatement|tothemarginalbenetofemissionsabatement|givenbythemarginaloutputgain(netofpollutiondamages)fromnothavingtopaythecarbontax.ThecapitalEulerequationsarestandard.Finally,thejobcreationconditionsequatethemarginalcostofpostingavacancyforeachcategoryofemploymenttotheexpectedmarginalbenetofdoingso.Inthecaseofpostingavacancytohireworkerswhoproduceintermediategoodsforrrms,producerstakeintoaccounttheregulationcostassociatedwithemissionsgenerationandthemarginalresourcecostofemissionsabatementassociatedwithhavingonemorerworker.Notethatthedamagesfrompollutionaecttheexpectedmarginalbenetofhiringworkersacrosscategories.

2.2 HouseholdsandFirmCreation

Thereisarepresentativehouseholdwithameasureoneofhouseholdmemberswhocanbeemployed,unemployedandsearchingforemployment,oroutsideofthelaborforce.House-holdsownallrmsandspendresourcestocreaterms.Inaddition,allproceedsfromtaxingemissionsfromtheproductionofintermediategoodsforrrmsaretransferredlump-sumtohouseholds.

Formally,householdschooseconsumptionct;themeasuresofsearchersinea