Environmental Policy and Capital Movements The Role of Government Commitment

The Role of Government Commitment

Laura Marsiliani and Thomas I. Renström

Working Paper No. 31

October 2002

W. ALLEN

WALLIS

Institute of

POLITICALECONOMY

UNIVERSITY OF

ROCHESTER

EnvironmentalPolicyandCapitalMovements:

TheRoleofGovernmentCommitment*

LauraMarsiliani

W.AllenWallisInstituteofPoliticalEconomy,UniversityofRochester

ThomasI.Renström

W.AllenWallisInstituteofPoliticalEconomy,UniversityofRochester,andCEPRThispaperexplorestherelationshipbetweenenvironmentalprotectionandinternationalcapitalmovements,whentaxpolicyisendogenous(throughvoting).Atwo-periodgeneralequilibriummodelofasmallopeneconomyisspecifiedtocomparetheeffectsoftwodifferentconstitutions(commitmentornocommitmentintaxpolicy),aswellasincomeinequality.Underthecommitmentregime,theequilibriumischaracterisedbyalowerlabourtax,higherenvironmentaltaxandlesscapitalmovingabroadthanintheno-commitmentequilibrium.Furthermore,giventhedegreeofcommitment,moreequalsocietiesarecharacterisedbytougherenvironmentalpolicyandlesscapitalmovingabroad.

JELClassification:F2,H21,H23

Keywords:Environmentalpolicy,capitalmovements,time-inconsistentfiscalpolicy,incomeinequality,politico-economicequilibrium,humancapital.

Correspondenceto:LauraMarsiliani,W.AllenWallisInstituteofPoliticalEconomy,UniversityofRochester,109HarknessHall,Rochester,NY,14627,USA;email:msni@troi.cc.rochester.edu

*

WewishtothankWolframRichter,SjakSmulders,SimonVicaryandparticipantsattheSecondWorkshopon

\"EnvironmentalPolicy,CompetitivenessandtheLocationBehaviourofFirms\Maastricht,October1999andthePublicEconomicTheoryConference,Warwick,July2000,the54thIIPFConference,Seville,August2000,thefirstEURESCOConferenceon\"TheInternationalDimensionofEnvironmentalPolicy\Kerkrade,October2000,andTheRoyalEconomicSocietyAnnualConference,Durham,April2001forveryusefulcommentsonearlierversionsofthispaper.ThefirstauthorgratefullyacknowledgesfinancialsupportfromtheDutchScientificOrganisationNWO.Allerrorsandshortcomingsareourown.

1.INTRODUCTION

Policymakersoftenexpressconcernthatstrictenvironmentalprotectionwillleadtocapitalmovingabroadwithaconsequentdeteriorationofinternationalcompetitiveness,ariseinunemploymentandaslowdownofeconomicgrowth.Thisviewhasbeenreflectedintherecentpoliticaldebate.Forexample,theEuropeancarbon/energytaxproposaloftheearly1990sincludedtheexemptionofenergy-intensiveindustries,inordertopreservetheirinternationalcompetitiveness.Theproposalhasnotbeenimplementedyet,oneofthereasonbeingalikelylossincompetitivenessofEuropeancountries.Atthesametime,thedebateconcerningtheimplementationoftheNorth-American-Free-Trade-Agreement(NAFTA)focusedatalargeextentonthefearthatUSindustrieswouldrelocateinMexico,wheretheenvironmentalstandardsaremorelax.Furthermore,environmentalistsarguethatgovernmentsmayhaveincentivestorelaxenvironmentalpolicyinordertoattractforeigncapitalandthattheymayengageinaracetothebottominenvironmentalstandards.ThishasalsobeenloudlyclaimedbysomeinterestgroupsatthecongressoftheWorldTradeOrganisation,heldinSeattleinSeptember1999.

Economistshaveanalysedtheeffectsofenvironmentalpolicyeitheronthemovementsofcapitalacrossregionsoronthelocationbehaviouroffirms(seeJaffeetal.,1995,forausefulsurvey,andRauscher,1997andWilson,1996foranoverview).1Theexistingtheoreticalstudiestypicallyfindapositivecorrelationbetweenstringencyofenvironmentalpolicyandoutflowofcapitalorindustries.Inparticular,astudyofcapitalflowsandenvironmentalconcerninasmallopeneconomyhasbeenconductedbyBovenbergandvanderPloeg(1994).Theyfindthatstrongerpreferencesfortheenvironmentresultinareductioninoutputandcapitaldemand,whichinturncausescapitalflight.2

1

Inthispaperwedonotfocusondecisionsaboutfirms’orplants’locationbutwefocusoncapitalmovements,thatiswhetherindividualsinvestassetsathomeorabroad.Inthisrespectourpaperisdifferentfromtheliteratureonstrategicenvironmentalpolicyandplantlocation.Thetwoissuesarehowever,oftenmentionedtogetherinthepolicydebate.Fortheroleofgovernmentcommitmentonfirms’locationdecisions,seeUlphandValentini(2002).

2

Afewtheoreticalpapers,however,donotsupportapositivecorrelationbetweenstringencyofenvironmentalprotectionandcapitalflight.See,forexample,Rauscher(1995)whoclaimsthatifafirmusesacleanenvironment(ratherthanpollution)asafactorofproduction,strictenvironmentalstandardscanreduceproductioncosts,enhanceeconomicactivityandattractforeigncapital;andinataxcompetitionframework,withredistributiveconcerns,OatesandSchawb(1988)andWilson(1996).Inthispaperwewanttopointoutanotherreason,thatiseffectofgovernmentcommitment.

1

Incontrast,themajorityoftheexistingempiricalstudies,almostexclusivelyconcerningtheUS,findthatenvironmentalpolicytypicallyisnotsignificantinexplainingcapitalmovementsandfirms’migration.3

Thisrevealsthatstandardtheoreticalmodelsofenvironmentalpolicyandcapitalmovementsmayfailtocapturesomeimportantaspectsoftheproblemathand.Forexample,themajorityofthetheoreticalstudiesaresetupinastaticframework,whereasdynamicconsiderationsmayplayanimportantrole.Arelevantissueisatwhichdatetheenvironmentalpolicyisimplementedwithrespecttothehousehold’sdecisionsonconsumptionandinvestment(whichisnotanissueinastaticframework).Inadynamicsetup,whetherthegovernmentcanorcannotcommittotheenvironmentalpolicywillmakeaconsiderabledifference,duetothetime-inconsistencyproblem.4

Anotherfeatureofmostoftheexistingstudiesisthatonlyonepolicyinstrument,namelytheenvironmentaltax(orstandard),ismodelled.Wethinkitisimportanttoincorporateastandardsecond-bestframework,allowingfordistortionarytaxesaswell(seeamongothers,Sandmo,1975,andBovenberganddeMooij,1994).Furthermore,redistributiveconcernsfromrichtopoorindividualsmayplayanimportantroleinthegovernment’sdecisionaboutenvironmentalpolicy(seeOatesandSchwab,1988,andMarsilianiandRenström,2000a,b).

Moreover,observedpoliciesareendogenous,andthedecisionstakenbymajorityelectedindividuals.Onlyafewpapers(see,forexample,MarsilianiandRenström(2000a,b)modelenvironmentalandfiscalpolicyendogenously,throughvoting.Inademocraticsystem,individualshavethepossibilityofvotingonrepresentatives.Whetherthemajorityelectedcandidaterepresentsthepreferencesofthepoororrichpartofthepopulation,obviouslyinfluencesthepolicychoice.Infact,iftheenvironmentisanormalgood,poorerindividualsdemandlessofit(seeMarsilianiandRenström,2000b).

3

ForasurveyoftheexistingempiricalstudiesseeLevinson(1996).AnexceptionisListandCo(2000)whofindempiricalevidencefortheimpactofenvironmentalpolicyonfirms’locationbehaviour.

4

Agovernment’spolicyisdynamicallyinconsistentwhen,althoughbeingoptimalattheoutset,itisnotlongeroptimalatalaterdateevenifnonewinformationhasappeared.Thismeansthatthegovernmenthassomeincentivetochangeitsplans(seetheseminalpaperbyKydlandandPrescott,1977,andforanapplicationtoenvironmentalpolicy,seeMarsilianiandRenström,2000a).

2

Inthispaper,wewanttoexaminetherelationshipbetweenthedegreeofcommitmentinpolicy,environmentalprotection,andcapitalmovements.Ourmaininterestishowadifferentdegreeofcommitmentinfluencesenvironmentalprotectionandcapitalimports,whenbothareendogenous.Wetaketheviewthatgovernmentsadopttheoptimalpolicygiventheconstitution(i.e.givencommitmentornocommitment),andverifiesunderwhichcircumstanceshigherenvironmentaltaxesgohandinhandwithcapitaloutflow,whenbothareendogenous.Furthermore,ratherthanfocusingonagovernment’sincentiveforchangingonepolicyinstrument(suchasenvironmentalpolicy)wefocusontheincentivesrelatedtotheentiretaxsystem.

Wedevelopamodelthatisrichenoughforanalysingthisquestion.Indoingsowewouldneed(atleast)twoperiods(tocaptureintertemporaldecisions),andweneedasecond-bestframework(tomodeldistortionarytaxation).5Weintroducethesecondbestbyanalysinganeconomywithheterogeneousindividuals,rulingoutindividual-specificlump-sumtaxes.Finally,policyisendogenisedbylettingindividualsvoteonrepresentatives,andthemajority-electedrepresentativeimplementsherpreferredpolicy.Tocapturethedegreeofcapitalflow,wepresentanopeneconomywhereindividualsownassetsdomesticallyandabroad;thedomesticassetsarerentedtofirms.Consequently,capitaloutflowisgivenbythedifferencebetweenthestockoftotalassetsandcapitalinvestedindomesticproduction.

Specifically,individualsdifferintheirlearningabilitiesandthiswillmakethemspenddifferentamountsoftimeonlearning,andtherebyaccumulatedifferentamountsofhumancapital,whichinturnwillgiverisetowagedifferentials.FirmsareperfectlycompetitiveandemployaCRStechnologyinphysicalcapital,humancapitalandemissions.Wewillconsiderataxsystemconsistingofalinearlabourtaxandanenvironmentaltax(ataxonfirms’emissionsthatgeneratespollutionexternalities).Thetaxreceiptsareusedforprovisionofalump-sumtransfer.Individualsvoteoncandidatesandthemajorityelectedcandidateimplementsherpreferredfiscalpolicy.Throughoutthepaperwerefertothesecondbestwhenagovernmentcancommittofuturetaxpolicy,andthethirdbestwhenitcannot.

5

Thetime-inconsistencyproblemisafeatureofsecond-bestanalysis(itneverarisesinthefirst-best).Theymayariseeitherinone-personeconomiesiflump-sumtaxesareruledout,orinmany-personeconomiesifindividual-specificlump-sumtaxationisimpossible.Inbothcasestheproblemarisesiftheelasticitiesofthetaxbasesaredependentonwhenthepolicydecisionistaken.

3

Weshowthatthecommitmentandtheno-commitmentequilibriumdiffer.Thereasonisthatatime-inconsistencyprobleminlabourtaxationarises.Whenthegovernmentcancommittoalevelofthefuturelabourtax,ittakesintoaccountthatahigherlevelofthetaxcausesindividualstoswitchfromlabourtostudy-time.Ifthegovernmentcanreoptimiseinthefuture,theindividualshavealreadyinvestedinhumancapitalandthatstockisfixed.Theindividualsonlychangetheirlaboursupply.Theelasticityofthelabourtaxbaseis(expectedly)smaller.Thus,labourisovertaxedinthethirdbest(whenthegovernmenttakesthetaxdecisionaftertheindividualshavechosentheirinvestmentinhumancapital),becauselaboursupplyinefficiencyunitsislesselastic.

Furthermore,wefindthatchangingtheconstitutionfromdiscretiontocommitmentmakestheoptimalenvironmentaltaxgreaterandatthesametimereducescapitaloutflow.Thencommitmentintaxpoliciesresultstobeafactorwhichcanexplainanegativecorrelationbetweenenvironmentalprotectionandcapitaloutflow.Thereasonisthattheefficiencygaininmovingtocommitmentincreasestheconsumptionpossibilitiesofallgoods,andiftheenvironmentisanormalconsumptiongood,themajorityelectedrepresentativetendstowanttoprovidemoreofit,i.e.implementingalargerenvironmentaltax.Atthesametimecapitaloutflowislessundercommitment.Thereasonisthatthelabourtaxissmaller,andhumancapitalinvestmentlarger.Thelargersupplyofhumancapitalincreasestheproductivityofphysicalcapitalandthereforetendstoretainphysicalcapitalathome.

Thispaperisstructuredasfollows.InSection2theeconomyisintroducedandtheassumptionsareformalised,andinSection3theeconomicequilibriumissolved.InSection4wecharacteriseindividuals’preferencesoverpolicy,underthevarioustimingassumptions.InSection5wesolvethreepolitico-economicequilibria:thefirstwhenelectionstakeplaceinthesecondperiodandthemajorityelectedindividualimplementspolicyinthesecondperiod,thesecondwhenelectionstakeplaceinthefirstperiod,butthemajorityelectedindividualcannotcommittofuturetaxation,andthethirdwhenelectionstakeplaceinthefirstperiodandthemajorityelectedindividualcancommit.Severalquestionsareofinterest.Doesastricterenvironmentalpolicygohandinhandwithcapitaloutflows,whenredistributiveconcernsplayarole?Andunderwhichconstitutions?Whatistheroleofinequality(intermsoflearningabilityandconsequentlyincomedistribution)fortheimplementationofastringentenvironmentalpolicy?Andhowdoesinequalityrelatetocapitalmovements?Section6concludesthepaper.

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2.THEECONOMY

Weshallspecifyaneconomywhichisrichenoughtoanalysetherelationshipbetweenenvironmentalpolicyandcapitalmovementsandthatformalisesthetime-inconsistencyproblem,butsimpleenoughtokeeptheanalysistractable.

Individualshavepreferencesoverperiod-oneconsumption,c0i,period-onetimespentlearninghi,period-twolaboursupply,li,period-twoconsumption,ci,andperiod-twoprovisionofcleanenvironment,(-x),wherexdenotespollution.Individualsareindexedbyiandcharacterisedbytheirlearningabilityparameterγi,whichisdistributedaccordingtothedistributionfunctionΓ(i).Thelabourproductivityoftheindividualinthesecondperiodishertimespentlearninginperiodonetimesherlearningability.Throughmostofthepaperweshallassumethatthemedian(second-period)productivityisnotgreaterthanthemean.6Furthermore,wenormalisethepopulationsizetounity.

Inthefirstperiodindividuali(withabilityγi)receivesalump-sumendowmentW0,

whichisusedforperiod-oneconsumption,andsavinginassetsai.Inthesecondperiod,theseassetscanbeinvestedbothdomestically(i.e.rentedasphysicalcapitaltodomesticfirms,withRtherentalpriceofcapital)andabroad(foreigninvestments).Thedifferencebetweentotalassetsandproductivecapitaldenotescapitaloutflow.Inthesecondperiod,theindividualsupplieslabour,andearnsthepre-taxwageratew,perunitofefficientlabour.Theafter-taxwageincomeplusalump-sumtransferfromthegovernment,T,andthereturnsonassetsareusedforconsumption.Thepriceofconsumptionisnormalisedtounity.Pollutionxisgeneratedbyproduction,whichtakesplaceinperiodtwo.Thegovernmentprovideslump-sumtransfersbytaxinglabourincomeatrateτl,andpollutionatrateτx.Theafter-taxwageisdenotedω.Inordertogaintractability,weassumespecificfunctionalforms.Thenextsectionstatestheseassumptions.

6

Thisimpliesanassumptiononthedistributionoflearningabilities,Γ.Seefurthersection3.

5

2.1.Assumptions

A1Individuals’preferences

Theutilityfunctionisassumedtobeoftheform

(1a)

wherethesecondperiodutilityis

(1b)

andwherehi,li≥0,ε>1,andtheparametersβ,andηarestrictlypositive.Leisurehasbeennormalisedto1andxdenotesaggregatepollution.Ψ′(x)>0,andΨ′′(x)≥0.A2Individuals’constraints

Theindividuals’budgetconstraintsare

(2a)(2b)

whereω≡(1-τl)wistheaftertaxwage.A3Production

AlargenumberoffirmsoperatewithaCobb-Douglastechnologyinphysicalcapital,labour(inefficiencyunits)andpollution.Productionyt,canthereforebecalculatedasiftherewasarepresentativefirmemployingaggregatelabourH,physicalcapitalkandemissionsx

(3)

where

(4)

A4Government’sconstraint

Thetaxreceiptsarefullyusedforlump-sumtransfers

(5)

6

A5Representativedemocracy

Thetaxrates,τtl,τtxand,consequently,thespendingdecisionaredeterminedbyamajorityelectedrepresentative,undereitherofthreeconstitutions:

(a)electionsareheldinperiod2,andthemajorityelectedrepresentativechoosetaxesbeforethechoiceonperiod-2laboursupplyandconsumptionistaken,andbeforetheallocationofassetsathomeandabroadaremade;

(b)electionsareheldinperiod1,andthemajorityelectedrepresentativechoosetaxesinperiod2,beforethechoiceonperiod-2laboursupplyandconsumptionistaken,andbeforetheallocationofassetsathomeandabroadaremade;

(c)electionsareheldinperiod1,andthemajorityelectedrepresentativechoosetaxesbeforebothperiod1andperiod2decisionsaretaken.Case(a)isreferredtoasnocommitment(thirdbest);Case(b)isreferredtoaspartialcommitment(thirdbest);Case(c)isreferredtoasfullcommitment(secondbest).

3.ECONOMICEQUILIBRIUM

Inthissection,theindividualandaggregateeconomicbehaviouraresolvedforgivenarbitrarytaxratesandpublicexpenditure.Wesolvethemodelrecursively,firstthesecondperiodequilibrium,thenthefirst.

3.1.Secondperiodindividualeconomicbehaviour

Maximisationof(1b)subjectto(2b)givestheindividuals’laboursupply

(6)

andindirectutility(uptoanadditiveconstant)

(7)

7

Wenoticethatthehighertheafter-taxsalaryis,thehigheristhelaboursupply.Individualswithmorehumancapital(largerhi)willsupplymorelabour(everythingelsebeingequal).Adirectpropertyofthepreferencesin(1)isthatallincomeeffectisremovedfromthelaboursupplyandcarriedovertoconsumption.Anincreaseinlump-sumallowancethereforemakestheindividualconsumemore,withoutchangingthelabourdecision.Inthesecondperiod,hiandaiareconstantandtakenasgiven.

3.2.Firstperiodindividualeconomicbehaviour

Maximisationof(1a)subjectto(2a)givesanindividual’schoiceofthelevelofhandaasfunctionofsecondperiodafter-taxwagerate,ω,andsecond-periodproductivity,

(8)(9)

Wenoticethatthereisatrade-offbetweentimespentstudyingandinvestmentinassets:ahigherrateofinterestcausesindividualstostudylessandtoinvestmoreinassets.Wealsoseethatthehighertheafter-taxwageis,thelongeristhetimespentlearning.Also,whatwillmatterfortheindividual’sattitudetowardsredistributionisnottheabilitytolearn,buttheproductivityinworkinthesecondperiod.Theproductivityinworkisγihi,whichisproportionaltoγi(1+ε)/(ε-1).Thisisthekeymeasurewewillrefertointherestofthepaper.3.3.Aggregateeconomicbehaviour

Thesecond-andfirst-periodaggregateeconomicbehaviourisgeneratedbyaggregatingtheindividuals’quantitiesobtainedinSections3.1and3.2respectively.Toobtaintheaggregatelaboursupply(inefficiencyunits),definedin(4),weintegrate(8)overthepopulationtoget

(10)

where

(11)

(12)

8

Thedifferencebetweenthesecondandfirstperiodsisthatinthesecondperiodindividualshaveinvestedintheirhumancapitalandassetsandconsequentlyhandaarefixed,whileviewedfromthefirstperiodhandaarefunctionsofthetaxes.γ˜isthe(1+ε)/(ε-1)thmomentoftheabilitydistribution,andislinearlyrelatedtotheaverageworkproductivity.Whetheranindividualearnsahigher/lowerwagerate(perhour)thanaveragedependswhethertheγisgreater/smallerthanunity.ratioγi(1+ε)/(ε-1)/˜3.4.Firms’behaviour

Thefirms’optimalityconditionwithrespecttok(i.e.Fk=R)givesoptimalk,andproduction,asfunctionsofxandH

(13)

where

(15)

Inthenextsection,weshallexaminepolicymakers’preferencesoverfiscalpolicy.

4.PREFERENCESOVERPOLICY

Anyindividualelectedintoofficewillchoosepolicytomaximiseherownutility,subjecttothegovernmentbudgetconstraint.Wethereforeneedtocharacterisehoweachtypewouldchoosepolicy.Policywillthenbeafunctionofthetypeinoffice,andwecanconstructavotingequilibrium(insection5)whereindividualsvoteovercandidates.

First,itismoreconvenientoptimisingwithrespecttotheafter-taxwage,ω,andtheamountofthepollutingfactor,x,used,ratherthanwithrespecttothetaxratesthemselves.Infact,inequations(6)-(11),(13)-(14)onlyωandxappear.Weonlyneedtorewritethegovernment’sbudgetconstraintintermsofthosequantities.Equation(5)canbewrittenas

(17)(16)(14)

ThetimingmattersonlytotheextentthatH(aggregateefficientsupplyofhumancapital)respondsdifferentlytochangesintheafter-taxwage,dependingonwhenthetaxdecisionistaken.Infact,thefirst-orderconditionswilltakethesameformunderthevariousassumptions

9

abouttiming.Thisisduetothefactthattheelectedindividualchoosesli(andai,hiifcommitment)aswellaspolicy,sothederivativesofli(andai,hiifcommitment)withrespecttopolicycanbeignored(bytheEnvelopecondition).Theproblemofahypotheticalcandidateisto

(18)

subjectto(17),(effectsonli,ai,andhicanbeignoredbytheEnvelopecondition).Thefirst-orderconditionsto(18)are

(19)

(20)

Theseconditionshavetobeevaluatedunderthedifferentassumptionsoftiming.Firstweclarifyhowtheydiffer.(a)Nocommitment

Anindividual,ifelectedinthesecondperiod,willtakethedecisionuponωandx,

˜.Optimalpolicywillbeafunctionoftheidentityofthegiventhequantityofh

˜,whichinturnisafunctionofωe(i.e.ofexpectedω).candidateandh(b)Partialcommitment

Anindividual,ifelectedinthefirstperiod,willtakethedecisionuponωandx,given˜.However,thechoiceofωandxhavetobecompatiblewiththethequantityofh

˜.Thisissobecauseindividualswillobservewhotheelectedexpectationsofωinh

candidateisalreadyinthefirstperiodandcanformexpectationsofωbasedontheidentityofthecandidate.Optimalpolicywillbeafunctionoftheidentityofthecandidateonly.(c)Fullcommitment

Anindividual,ifelectedinthefirstperiod,willtakethedecisionuponωandx,

˜.recognisingtheinfluenceonh

10

˜isgivenunderbothpartialandnocommitment,Sincefromthepolicymaker’spointofviewh

partialcommitmentcanbetreatedasnocommitmentfortimebeing.

Aggregatelabourinefficiencyunitsasafunctionofpolicycanbewritteninoneequation,withtheparametersreinterpretedunderthevarioustimingassumptions.Combining(10)and(11)wecanwrite

(21)

where

(22)(23)

Next,sinceallindividualshavethesameexpectations(regardlesstiming)wecanwrite

(24)

where

(25)

Differentiating(17)withrespecttoω,using(21),andinsertingthederivativeintothefirst-ordercondition(19)gives

(26)

Using(24)andrearranginggives

(27)

where

(28)

Also,substituting(27)into(21)gives

(29)

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˜θH-θ,and1-τl=ω/w,equation(27)gives(alsousing(15))Sincew=(1-α-µ)Ax

(30)

asthelabourtaxratepreferredbyindividuali.

Recallthatγˆiistheratioofindividuali’slabourproductivitytotheaveragelabourproductivity.Ifγˆiissmallerthanunitytheindividualearnslesswageperhourworkedthantheaverage.Sinceνtakesondifferentvaluesdependingonthetiming,thesameindividualprefersadifferenttaxrateunderdifferenttimingassumptions.Infact,sinceνislargerundernocommitmentthanundercommitment,thelabourtaxislargerundernocommitmentthanundercommitment.ThereasonisthatthetaxbaseHislesselasticundernocommitmentandthuswouldbeovertaxed.Wealsoseethat,giventhetiming,anindividualwithgreaterlearningabilitypreferstotaxlabourless.

Wewillnowmakeacompletecharacterisationofthechoiceofahypotheticalindividualinoffice.ThiswillinvolvesubstitutingforωH,asafunctionoftheidentityofthedecisionˆi>0undermakerandofx(equation(28)),into(19)andfinding∂x/∂γˆi.Itturnsoutthat∂x/∂γalltimingassumptions(seetheappendix).Since∂mi/∂γˆi>0,thenby(28)∂ω/∂γˆi>0,sothedecisionsaremonotoneinthedecisionmaker’slearningability.

Lemma1AssumeA1-A5,andconsiderahypotheticaldecisionmakerγˆ*.Thedecisionmaker’schoicewillbefunctionsofγˆ*withthefollowingproperties

(31)

andgivenanyγˆ*

τl(nocommitment)>τl(commitment).

Proof:Seetheappendix.

Wewillnowturntothecharacterisationofthevariouspolitico-economicequilibria,andexaminetheconsequencesoftimeinconsistencyonenvironmentalpolicyandcapitalmovements.

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5.POLITICO-ECONOMICEQUILIBRIA

Regardingvotingwehaveaone-dimensionalchoicespace(theidentityofthedecisionmaker).Wenowneedtoexaminetheindividuals’preferencesovercandidates(potentialdecisionmakers).Ifpreferencesovercandidatesaresinglepeaked,thenweknowthatthecandidatepreferredbythemedianindividualinthevotingdistributioncannotloseagainstanyothercandidateinabinaryelection.Denoteahypotheticaldecisionmakerbysuperscript*.SubstitutethepolicyfunctionsinLemma1intoindividuali’sindirectutility,toobtainanindirectutilityintermsofγˆ*.Thisindirectutilityhasthefollowingproperties

Lemma2AssumeA1-A5,thenindividuali’spreferencesovercandidates’γˆ*aresinglepeaked,withthemaximumattained

atγˆ*=ˆγiifnocommitment,

atγˆ*=(1+ε)/(2ε)+[(ε-1)/(2ε)]ˆγiifpartialcommitment,andγiiffullcommitment.atγˆ*=ˆProof:Seetheappendix.

Lemma3AssumeA1-A5,thentheeconomicequilibriumunderpartialcommitmentwithpolicymakerγˆ*coincideswiththeeconomicequilibriumunderfullcommitmentwithpolicymakerγˆ*′=(1+ε)/(2ε)+[(ε-1)/(2ε)]γˆ*.

Proof:Insertingγˆ*′inequation(30),andevaluatingundernocommitment(ν=ε),givesthesamelabourtaxaswheninsertingγˆ*inequation(30)andevaluatingunderfullcommitment(ν=(ε-1)/2).Ifthelabourtaxisthesameinbothequilibria,thenbyequation(20),alsothepollutionlevelxisthesameinbothequilibria.

QED

Lemma2impliesthatwehaveamedian-voterequilibrium,andthatwecancompletelycharacterisepolicymakinggiventheunderlyingdistributionofabilities.Thesinglepeakednessfollowsfromthemonotonicityinthepolicyvariableswithrespecttotheabilityofthedecisionmaker.

Lemma2alsoimpliesthatwhenindividualsvoteinthefirstperiod,buttheelectedpolicymakerimplementspolicyinthesecondperiod,theywillvotestrategicallyonarepresentativewithadifferent(higher)abilitythanthemselves.

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Proposition1AssumeA1-A5,theninpolitico-economicequilibrium,theeconomicequilibriumunderpartialcommitment(votinginperiod1,policydecisioninperiod2)coincideswiththeeconomicequilibriumunderfullcommitment(votingandpolicydecisioninperiod1).Thepolicymakerhasahigherabilityinthepartialcommitmentthaninthefullcommitmentequilibrium.

Proof:FollowsfromLemma1,2,3.

QED

Proposition1impliesthatduetostrategicvoting,theperiod-oneelectedrepresentativewillimplementthesamepolicyinperiod2,asaperiod-oneelectedrepresentativewouldhaveimplementedinperiod1.Thusthepartial-commitmentequilibriumwillcoincidewiththefull-commitmentequilibrium.7Sincethepartialcommitmentequilibriumcoincideswiththefullcommitmentequilibriumwewillnotdistinguishbetweenthemtwo.Wewillhenceforthonlyrefertocommitmentversusnocommitment.Proposition2AssumeA1-A5,theninpolitico-economicequilibriumthefollowingholds

(32)

ˆ*whereγˆ*isthemedian.Furthermore,givenanyγ

τl(nocommitment)>τl(commitment).

Proof:FollowsfromLemma1-2.

QED

Wenoticethatthewagetaxdecreasesintheproductivityofthedecisiveindividual.Thisisastandardresult,andiscausedbythefactthatalessproductiveindividualhasmoretogainfromredistributivetaxation.

Furthermore,labourisovertaxedwhennocommitmentispossible(i.e.inthethirdbest).Thisisbecauseoncetheindividualshaveinvestedintheirhumancapital,theelasticityoflaboursupplyinefficiencyunitswithrespecttotaxesislesselastic(atthatstage,itistoolatetospendmoretimelearning).Whencommitmentispossible,individualresponsesto

7

Wedonotexpectthisisageneralpropertythough,butisduetotheassumptionsregardingutilitiesand

technologies.Generallyoneshouldnotexpectallpolicyvariablestoexactlycoincide.Whenpolicyisone-dimensional,though,andthecandidatespaceisrich(continuous),thefullcommitmentandpartialcommitmentoughttocoincide.ThishappensindeedinPerssonandTabellini(1994).

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changesinwagesaregreater.Weseealsofrom(30)thatthegreaterthedifferencebetweenthemedianproductivityandtheaverage,thegreateristhedifferencebetweenthecommitmentandthenocommitmentsolution.Thus,inequality(intheformofskewnessofthedistribution)makesthetime-inconsistencyproblemmoresevere.

Finally,pollutioninabsolutetermsisincreasingintheproductivityofthedecisiveindividual.Thisissobecausethisindividualwishestotaxlabourless,inducingindividualstoaccumulatemorehumancapital,whichinturnmakespollutionmoreproductive.

Next,whenwemakeallindividualsidenticalwehavethefollowingresult:Corollary1

AssumeA1-A5.Ifallindividualsarethesame,thecommitmentandno

commitmentequilibriacoincide,andtheenvironmentaltaxisatthePigouvianlevel.Proof:Whenallindividualsarethesameγˆ*=1,andthelabourtaxiszeroregardlessoftiming.Equation(20)thengivesthePigourule(whichisthesameregardlessoftiming).

QED

Thus,weverifythatthereisnotime-inconsistencyprobleminthefirstbest.Thisisageneralproperty,sincethetime-inconsistencyproblemisonlyasecond-bestphenomenon.Inthefirstbestthewagetaxiszeroandanyfundinginadditiontotheenvironmentaltaxreceiptsisobtainedbylump-sumtaxation,-T.

Furthermore,wegetthefollowingresults

Proposition3AssumeA1-A5,thentotalemissions,theafter-taxwage,andproductionaresmallerundernocommitmentthanundercommitment.Forgivenlevelofcommitment,thelowertheabilityofthedecisiveindividualis,thelowerareemissions,theafter-taxwage,andproduction.

Proof:Seetheappendix.

Proposition4AssumeA1-A5,thenthepollutiontaxissmallerandtheratiobetweenemissionsandproductionisgreaterundernocommitmentthanundercommitment.Forgivenlevelofcommitment,thelowertheabilityofthedecisiveindividualis,theloweristhepollutiontax,andthehigheristheratioofemissionstoproduction.Proof:Seetheappendix.

15

Intuitively,undercommitmenttheconsumptionpossibilitiesaregreater;iftheenvironmentisanormalgood(whichisensuredbyadditiveseparabilityin(1b)),theefficiencygainsachievedinthesecondbest(incomparisontothethirdbest)meansmoreconsumptionoftheenvironment.Thisisachievedbytaxingpollutionmore.Furthermore,ifthelabourtaxissmall,investmentinhumancapitalislargeandthemarginalproductivityofemissionsislargetoo.Consequently,itisoptimaltoincreaseemissions,butnottotheextentthatx/yincreases.

Wewillnextaddressthequestionofcapitalmovements.Usingthedecisionrulesforindividuals’savingsasafunctionofthetaxeswecanstate:

Proposition5AssumeA1-A5.Thepolitico-economicequilibriumundernocommitmenthaslargercapitaloutflowthanthepolitico-economicequilibriumundercommitment.Forgivenlevelofcommitment,thelowertheabilityofthedecisiveindividualis,thelargeristhecapitaloutflow.

Proof:Sincetheafter-taxwageisgreaterundercommitment(orunderapolicymakerwithhigherability),individualsinvestlessinphysicalassets(andmoreinhumancapital),byequation(9).Sincedomesticfirms’capitaldemandisproportionaltoproduction(equation(13)),andproductionisgreaterundercommitment(orunderapolicymakerwithhigherability),domesticfirmscapitaldemandisgreaterundercommitment.Thus,thedifferencedomesticsavings-domesticcapitaluse,islessundercommitment(orunderapolicymakerwithhigherability).

QED

Intuitively,commitmentontheonehandincreasesthereturnsonhumancapital,whichinturnreducedomesticsavings,andontheotherhandincreasestheproductivityofcapital,overallattractingforeigncapital.

6.SUMMARYANDCONCLUSIONS

Wehavepresentedageneralequilibriummodelofenvironmentaltaxationandcapitalmovements.Themostimportantfeatureofthismodelisthatitexaminestheeffectsofdifferentconstitutions,thatiswhetherthegovernmentcanorcannotcommittofuturetaxpolicy.

16

Wehaveshownthatthecommitmentandtheno-commitmentequilibriadonotcoincide,sinceatime-inconsistencyprobleminlabourtaxationispresent.Itariseswhenindividualshavethepossibilityofchoosingthetimetheyspendlearning.Theyhavetoformexpectationsaboutthelabourtaxthegovernmentisgoingtoimposeinthefuture.Onceindividualshaveinvestedintheirhumancapital,thegovernmentistemptedtoraisethelabourtaxinordertoredistributefromhighearnerstolowearners.Individualsexpectingthiswillinvesttoolittleinhumancapital,andatthesametimelabourisovertaxed.

Wehavedemonstratedthatundercommitment(secondbest),thelabourtaxissmallerandtheenvironmentaltaxisgreaterthanundernocommitment(thirdbest).Intuitively,thereisaconflictbetweenenvironmentalandlabourtaxationandlump-sumtransfers.Ifthelabourtaxissmall,thedistortionscausedbythetaxsystemwillbesmallaswell.Inthiscase,themarginalutilityoftransfersislowerandthemedianvoterwillprefertoprotecttheenvironmentmore(bypayingahigherenvironmentaltax).Furthermore,undercommitment,theincreasingreturnsonhumancapitalreducedomesticsavingsandincreasetheproductivityofcapital,whichinturnsattractsforeigncapitalordiscouragescapitaloutflow.

Everythingelsebeingequal,societieswithmorecommitmentinfiscalpolicywouldhaveatougherenvironmentalpolicyandlesscapitaloutflow.Governmentsshouldavoidadiscretionaryfiscalpolicyiftheywanttoprotecttheenvironmentandatthesametimeattractforeigninvestment.Thus,thispaperprovidesuswithatheoreticalexplanationforwhynoempiricalevidencecangenerallybefoundofapositiverelationshipbetweenthestringencyofenvironmentalpolicyandcapitalmigration.

Inaddition,ouranalysishassuggestedthatthenon-committedtaxdiffersmorefromthecommittedone,thelargerthedifferenceinlearningabilitybetweenthedecisiveindividual(medianvoter)andtheaverageindividual.Thissuggeststhatthetime-inconsistencyproblembecomesmoreseverewhenthereismoreinequality(intermsofmean-mediandistance).Inthiscase,apoorerdecisiveindividualwillpreferahigherlabourtaxandalsohaveagreatermarginalutilityofprivateconsumptionandlump-sumtransfers,andthereforewillbelesswillingtoprotecttheenvironment;atthesametimecapitalproductivitydecreasesandcapitalmigratesabroad.Viceversa,amoreequalsociety,giventhelevelofcommitment,wouldhavetougherenvironmentalpolicyandlesscapitaloutflow.Thus,throughtheinequalitychannelwecanalsogeneratesanegativecorrelationbetweenenvironmentalpolicyandcapitaloutflow.

17

REFERENCES

Bovenberg,LansandRuuddeMooij(1994).\"EnvironmentalLeviesandDistortionary

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Bovenberg,LansandRickvanderPloeg(1994).\"GreenPoliciesandPublicFinanceina

SmallOpenEconomy.\"ScandinavianJournalofEconomics96(3):343-363.

Jaffe,AdamB.,StevenR.Peterson,PaulR.PortneyandRobertStavins(1995).

\"EnvironmentalRegulationandtheCompetitivenessofU.S.Manufacturing.\"JournalofEconomicLiterature,33:557-572.

Kydland,FinnE.andEdwardC.Prescott(1977).\"RulesRatherthanDiscretion:The

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Marsiliani,LauraandThomasI.Renström(2000a).\"Time-InconsistencyinEnvironmental

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Marsiliani,LauraandThomasI.Renström(2000b).\"Inequality,EnvironmentalProtection

andGrowth.\"CentERDiscussionPaper34/2000.

18

Oates,WallaceE.andRobertM.Schwab(1988).\"EconomicCompetitionAmong

Jurisdictions:EfficiencyEnhancingorDistortionInducing?\"JournalofPublicEconomics35:333-354.

Persson,Torsten,andGuidoTabellini(1994).\"RepresentativeDemocracyandCapital

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Rauscher,Michael(1995).\"EnvironmentalPolicyandInternationalCapitalMovements.\"

inKarl-GöranMäler(ed.),InternationalEnvironmentalProblems:AnEconomicPerspective,Amsterdam:Kluwer.

Rauscher,Michael,(1997).InternationalTrade,FactorMovementsandtheEnvironment,

OxfordUniversityPress,ClarendonPress.

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Wilson,John(1996).\"CapitalMobilityandEnvironmentalStandards:IsThereaTheoretical

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19

APPENDIX

ProofofLemma1

ˆi<0followsfromequation(30).Next,weonlyneedtoprovethat∂x/∂γˆi>0underFirst∂τl/∂γ

allassumptionsontiming.Thisissosince∂x/∂γˆi>0implies,(by(29)inthefullcommitmentandno-commitmentcases,andby(50)(below)inthepartialcommitmentcase),that∂ω/∂γˆi>0(noticethatby(28)∂mi/∂γˆi>0).Takingthepartialderivativeof(17)w.r.t.xgives

(33)

whichisthenumeratorin(20)(thesecondequalityfollowsby(14)).Next,thedenominatorin(20)maybewrittenasfollows(byusing(6))

(34)

wheretheequalityfollowsfrom(24).Thenthefirstordercondition(20)maybewrittenas

(35)

where

(36)

WetreatZasafunctionofγˆiandx:Z(ˆγi,x).Denotethederivativesbysubscripts.Wethenfindthesoughtderivativebydifferentiating(35)

(37)

WenowneedtofindthederivativesofZ.Firstwewillrewrite(36).Premultiply(27)byHanduse(14),thenwehavethefollowing

(38)

Next,

(39)

wherethefirstequalityfollowsbyusing(14)in(17),thesecondequalitybyusing(38),andthethirdequalitybyusing(28).Usingthelastequalityof(39)in(36)gives

(40)

20

Sofartheanalysisisvalidunderallassumptionsontiming.Wenowneedtoproceeddifferently,dependingonwhichtimingofeventsweassume.Webeginwiththeno-commitmentcase.

Undernocommitmentthelastperiod’slearningandsavingsaretakenasgiven,andonlytheidentityofthepolicymaker(aswellasherchoice)canvary.Herewehaveν=ε(by(23)),thenZn,wheresuperscriptndenotesnocommitment,(i.e.equation(40))becomes

(41)

wherethesecondequalityfollowsbyusing(28),andthethirdbyusing(38).Use(21),(29),˜,thenwehaveand(38)tosubstituteforF

(42)

Takethederivativeswithrespecttoxandγˆi,toobtain8

(43)(44)

Substituting(43)and(44)in(37)gives∂x/∂γˆi>0undernocommitment.

˜andσchangesasγUnderpartialcommitmentωeinhˆichanges.Whenγˆiisknownalsoωewillbeknown(andcoincideswithω).ThishastobetakenintoaccountindifferentiatingZ.Underfullcommitmentωeisunderthecontrolofthepolicymaker.Thetwocasescanbecapturedsimultaneously.Inbothcasesaiwillrespondtochangesintheidentityofthedecisionmaker.Combining(8),(6)and(24),andsubstitutinginto(9)gives

(45)

Noexpectationsonωisneededbecausethedecisionmakerwillbeknowninadvance.

8

N.B.undernocommitmentaiisinvariantwithrespecttopolicy,andvariesonlywithrespecttoidentityi.

Thederivative(44)isnegativesince∂ai/∂γi<0,whichfollowsfrom(9).

21

Substituting(45)into(36)gives

(46)

wheresuperscriptc,pdenotecommitment,partialcommitment,respectively.Substitutingfor˜accordingto(38)givesTaccordingtothesecondequalityin(39),andforF

(47)

orrearranged

(48)

Fullcommitmentimpliesν=(ε-1)/2,thenusing(28)in(48)weobtain

(49)

wheremi/(ωH)hasbeensubstitutedforbyusing(29).

Partialcommitmentimpliesthatωein(22)hastobereplacedbyω.Settingωe=ωin(22)andsubstitutinginto(29)gives(whereverνappearsitequalsεaccordingto(23))

(50)

whereσ0=γ˜(Rη2)-1/(ε-1).Setωe=ωin(22)andsubstituteinto(21),premultiplybothsidesbyω,andsubstituteforωontheright-handsidebyusing(50)toobtain(N.B.ν=ε)

(51)

In(48),using(28)toeliminatemiwhereitfirstappearsand(51)toeliminatemi/(ωH)wehave

(52)

Wearenowreadytotakethederivativesof(49)and(52),respectively.

22

DifferentiatingZc(i.e.(49))withrespecttoxandγˆigives

(53)

(54)

(54)followssinceZcisdeclininginmi,andmiisincreasinginγˆi.Then(37)impliesthat∂x/∂γˆi>0holdshereaswell.

FinallydifferentiatingZp(i.e.(52))withrespecttoxandγˆigives

(55)

(56)

whereη=(ε-1)/2.Then(37)gives∂x/∂γˆi>0.ProofofLemma2

Takingthederivativeofindividuali’sindirectutilityfunctionwithrespecttoγˆ*gives

QED

(57)

Thefirsttermistheindividual’sfirst-ordervariationwithrespecttoωtimesthechangeinωwhenγˆ*changes.Thesecondtermisthefirst-ordervariationwithrespecttoxtimesthechangeinxwhenγˆ*changes.Withnocommitment,andwithfullcommitment,thesefirst-ordervariationsarethosethattheindividualwouldfaceifshewasdecisive.Thepeakisreachedatγˆi=ˆγ*.Ifγˆ*<(>)γˆithefirst-ordervariationispositive(negative)duetothemonotonicityinωandxwithrespecttoγˆ*.Withpartialcommitment,thefirstordervariationsarenotthesameastheindividualwouldfaceifbeinginoffice(becauseofthedifferenceintiming).However,byreplacingwithγˆ*′=(1+ε)/(2ε)+[(ε-1)/(2ε)]ˆγi,thefirst-ordervariationsbecomethesame,andtheargumentaboveapplies.

23

QED

ProofofPropositions3-4

Intheno-commitmentcase,individualswillpredictωeaccurately.Tocharacterisetheequilibrium,ωehastobesubstitutedbyωinequation(22).Thiswillresultinequation(29),withν=(ε-1)/2intheexponents,butwithmievaluatedatν=ε(seeequation(50)).Then,inequation(29)theonlydifferencebetweentheno-commitmentandthecommitmentequilibriaisthattheformerisevaluatedatmibyusing(35),

(58)

since∂Z/∂mi<0.Sincemi

ν=ε

ν=ε

,andthelatteratmi

ν=(ε-1)/2

.Then,incomparingthe

twoequilibriaweuseequation(51)andperformcomparativestaticswithrespecttomi.First,

ν=(ε-1)/2

,miisgreaterundercommitment,andconsequently

xisgreaterundercommitment.

Next,sincethepollutiontaxis

(59)

weneedtoevaluatetheratioH/x.First,using(29),

(60)

Next,use(58)toobtain(N.B.ν=(ε-1)/2)

(61)

Therefore,∂(H/x)/∂mi>0,andH/xisgreaterundercommitment,implyingthatτxisgreater˜θH1-θ=Ax˜(H/x)1-θ,theresultonproductionundercommitment.FinallysinceproductionisAx

follows.Theresultontheafter-taxwagefollowsfrom(29).Theresultsregardingtheidentityofthepolicymakergothrough,sincemiisgreaterunderapolicymakerwithhigherability.

QED

24