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Resource
and
Energy
Economics
j ou r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / r e e
Do
technology
externalities
justify
restrictions
on
emission
permit
trading?
夽
Enrica
De
Cian
∗,
Massimo
Tavoni
FondazioneEniEnricoMatteiandCentroEuro-MediterraneoperiCambiamentiClimatici(CMCC),Italy
a
r
t
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c
l
e
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n
f
o
Articlehistory:
Received27February2010
Receivedinrevisedform29May2012
Accepted31May2012
Availableonline15June2012
JELclassification: Q54 Q55 Q43 H23 Keywords: Energy-economymodelling Emissiontrading Technologyspillovers
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Internationalemissiontrading isanimportantflexibility mech-anism,butitsusehasbeenoftenrestrictedonthegroundthat accesstointernationalcarboncreditscanunderminethedomestic abatement effortreducingtheincentivetoinnovateand, even-tually,loweringthepaceofclimatepolicy-inducedtechnological change.Thispaperexaminestheeconomicsthatisbehindthese concernsbystudyinghowacaptothetradeofcarbonoffsets influ-encesinnovation,technologicalchange,andwelfare.Byusinga standardgameofabatementandR&D,weinvestigatethemain mechanismsthatshapetheserelationships.Wealsousea numer-icalintegratedassessmentmodelthatfeaturesenvironmentaland technologyexternalitiestoquantifyhowlimitstothevolume,the timing,andtheregionalallocationofcarbonoffsetsaffectclimate policycostsandtheincentivetoinvestininnovationand low-carbontechnologies.
Resultsindicate that,formoderatecapsontheamount trad-ableemissionspermitsandsufficientlyhightechnologyspillovers, globalinnovationandtechnicalchangewouldincreaseandthatthis additionalinnovativeeffortcouldleadtoeconomicefficiencygains. Thenumericalanalysisconfirmsthatwhenconstraintsareclose
夽ThispaperispartoftheresearchcarriedoutbytheSustainableDevelopmentProgrammeofFondazioneEnricoMattei.
FinancialcontributionfromthePLANETSprojectfundedbytheEuropeanCommissionunderthe7thframeworkprogrammeis
gratefullyacknowledged.Theusualdisclaimerapplies.
WewouldliketoespeciallythankProf.SjakSmuldersforthemanycommentsandsuggestionswhichhavehelpedto
consid-erablyimprovethismanuscript.
∗ Correspondingauthorat:FondazioneEniEnricoMattei,IsoladiSanGiorgioMaggiore,30124Venice,Italy.Tel.:+39041
2700450;fax:+390412700413.
E-mailaddress:[email protected](E.DeCian).
0928-7655/$–seefrontmatter©2012ElsevierB.V.Allrightsreserved.
to15%ofdomesticabatement,efficiencylossesaresmallbecause theyarepartlycompensatedbymoretechnologicalspilloversand lowerenergyprices.Underabroadrangeofparameters,restrictions arecostlyfortheconstrainedcountries,butalwaysbeneficialfor unconstrainedones.
©2012ElsevierB.V.Allrightsreserved.
1. Introduction
SincetheKyotoProtocol,theinternationaltradeofcarbonallowancesandcreditshasbeena fun-damentalelementtoensureflexibilityandcostefficiencyofclimatechangepolicies.International emissiontradinghasthepotentialtoreducecompliancecostsbecauseitallowsexploitinglowcost emissionreductionoptionsnomatterwheretheyarelocated.Regionalandsub-regionalcarbon mar-ketinitiatives,eitherregulatedorvoluntary,haveemerged,especiallyindevelopedcountries.1The exchangeofcarbonallowancesandcredits,especiallyattheinternationallevel,hasalsoraisedsome concerns.Ifnotwell-designed,cap-and-tradeschemesmightunderminetheenvironmental effective-nessofclimatepolicies,reduceinnovationincentives,andultimatelyhinderthedeploymentofclean technologies.Asamatteroffact,thelackofagreementontheimplementationproceduresoftheKyoto flexiblemechanismswasthecauseofthefailureofthenegotiationsintheHaguein2000.In2004, theEUlinkingdirectiveestablishedthepossibilitytousetheKyotocreditsintheEU-ETSwithoutany limit.DuringthesecondPhaseofemissiontrading,theEUCommissionsintroducedquantitativeand qualitativerestrictionsontheuseoftheseoffsets2(deSépibus,2008).Thisrevisionwasmeantto avoidapricecollapse,asobservedduringthefirstPhase.Anotherargumentwasthatemissiontrading couldreducetheincentivetoinnovate(Hourcadeetal.,1999).
Whenfacingthechoicebetweeninnovateorpurchasecarboncredits,apollutingcountrywould selectthecheapestoption(Driesen,2003).Ifpermitsarecheapercomparedtothecostofinvestingin mitigationoptionsatHome,thepossibilityoftradingcreatesanincentivetoshiftabatementabroad, reducingtotalcompliancecosts,butalsoloweringtheincentivetocarryoutinnovation.Considering thesearguments,mostcap-and-tradeschemesincludeceilingsontheuseofinternationalcarbon offsets.Iflimitstopurchasecreditsarenotlarge,economiclossesmightbemodestandtherefore itmaybeworthwhileoneconomicgroundstousethem(KarpandZhao,2009).Theselimitscould avoidhugefinancialtransfers,maketheagreementmoreappealingforindustrialisedcountries,and stimulateinnovation.
Theargumentinfavourofceilingsmightbereinforcedinasecond-bestworld.Unrestricted emis-siontradingalwaysgeneratesefficiencygainsinafirst-bestworldwhentheonlydistortionisglobal pollution(seeforexampleWeyantandHill,1999;Bohm,1999;Chanderetal.,2002;Richelsetal., 2007).However,inasecond-bestworldaddressingonlyoneofthevariousmarketdistortionswill notnecessarilyimprovewelfare(LipseyandLancaster,1956).Environmentaleconomicssuggeststhat multiplepolicyinstrumentsshouldbeemployed(Jaffeetal.,2003,2005;BennearandStavins,2007). Inpractice,however,designingseveralinstrumentscanbecomplicated,anddespitethevariousforms ofregulationusedtoday,amarket-basedsolutionaimedatpricingCO2iswidelyregarded(atleast
amongeconomists)asthemostefficientsolutionforthecaseofglobalwarming.
Theeconomicefficiencyofemissiontradinginthepresenceofvariousexternalitieshasbeen ana-lysedmostlyusingsimpleanalyticalmodels.However,hardlyanynumericalevaluationhasconsidered second-bestinteractionswithtechnologyexternalities.Mostsecond-bestquantitativeassessments haveexploretheroleofpre-existingdistortionarytaxes(Babikeretal.,2004;Paltsevetal.,2007; McKibbinetal.,1999).OnlyBuonannoetal.(2000)assesstheprosandconsofintroducingceilingsto emissiontradinginamodelwithendogenoustechnicalchange(ETC-RICE).Theyfindlittlesupportfor
1Forareviewofcap-and-tradeschemesaroundtheworldseeCapoorandAmbrosi(2009).
2Inthepaperwedonotdistinguishbetweentradeincarboncreditsandallowances,whichforthepurposeofouranalysis
quantitativerestrictions,whichhavenegativeimpactsonbothefficiencyandequity.Although quan-titativerestrictionsfostertechnologicalinnovation,itslong-runpositiveeffectsoneconomicgrowth arelowerthantheadditionaleconomiccosts.Theirmodeldoesnotincludeinternationalspilloversof knowledgeandexperienceandthereforeitunderestimatesthebenefitsoftechnologicalinnovation.
Adifferentissue,whichhowevercanultimatelyhavethesameeffectofreducingthevolumeof internationalcarbontrade,relatestothedifficultiesofputtinginplaceawell-functioninginternational carbonmarket.TheCleanDevelopmentMechanism(CDM)oftheKyotoProtocol,thelargestexisting internationalcarbonmarket,hasrevealedsevereproblemsconcerningmonitoring,creditverification, andqualitycertificationofprojects(WaraandVictor,2008).Aslongastheseproblemsarenotsolved, institutionalandadministrativeissueswilldelaytheestablishmentofaninternationalmarket.
Thegeneralquestionweaddressinthispaperiswhetherrestrictingthetradeofinternational carbonoffsetsisasecond-bestpolicyinthepresenceofenvironmental,technology,andeconomic externalities.Marketfailuresexistnotonlyintheprovisionoftheinternationalenvironmentalgood, suchasemissionreduction,but alsoinmarketsfor innovationandtechnologydiffusion.Climate policycaninducesecond-ordereffectsoninnovationandtechnicalchange,butitisdesignedtotackle theenvironmentalexternality,notthetechnologyone.Forthisreason,limitinginternationalemission tradingwouldleadtowelfarelossesinafirst-bestworld,butthismightnotbethecaseinasecond-best world.
Thepapermakesseveralcontributionstotheliterature.First,weuseastandardgameof abate-mentandR&Dwithtwoexternalities(environmentaldamageandinnovation)andtworegionsto evaluatetheimplicationsoflimitingcarbontradingoninnovationandwelfare.Thisprovidesnovel insightsontheinterplaybetweeninnovationandclimatepolicies.Second,weextendtheanalysis usingarichnumericalintegratedassessmentmodelthatfeaturesenvironmental,technology,aswell ascarbonleakagethroughinternationalenergymarkets.Thisallowstogenerateoneoftheeveryfew quantitativeestimatesoftheeconomicimplicationsoftraderestrictionsonemissionpermits.
Ourresultsindicatethatsomerestrictionsoninternationaltradingofemissionallowancescanbe justifiedwhentheonlyinstrumentavailabletopolicymakersisthatofacarbonmarket.Theanalysis showsthat,underplausibleassumptionsabouttechnicalchange,permittradingrestrictionleadsto moreglobalinnovationandthat,whenthelimitationismoderateandspilloverssufficientlyhigh,the efficiencylossescouldbesmallorevennegative.Specifically,whendealingwithaclimate stabili-sationpolicywheredevelopedcountriesinitiallytakeonthelargestobligations,limitingaccessto internationaloffsetswouldmakeabatementmorecostlygloballyandfortheOECDasawhole,but theefficiencylossesaresmallformoderatetradingrestrictions.Constrainingoffsetstoatmost15%of regionalabatement,approximatelyinlinewithwhatwasproposedintheEUandUS,wouldnotaffect welfareintheUS,thoughitwouldresultinalossforEurope.However,financialflowstodeveloping countrieswouldbesignificantlyreduced.Despitetherevenuelossonthecarbonmarket,non-OECD regionswouldbecompensatedbylowerenergypricesandhighertechnologicalspillovers,thelatter duetomoreinnovationbeingcarriedoutinconstrainedregions(OECD).Theseresultsareshownto berobusttoabroadsetofparametersregardingtheprocessoftechnologicalchangeandknowledge spillovers.
Theremainderofthepaperisorganisedasfollows.Section2discussestheconnectionsbetween R&D,spillovers,and permittraderestrictionsusingastandard modelwithmultipleexternalities. Section3introducesanumericalintegratedassessmentmodelandextendstheanalysistoamore generalset-up.Section4illustratesthemacroeconomicimplicationsoftheclimatepolicyunder dif-ferentcarbonmarketdesigns.Giventhecriticalroleoftechnologyexternalities,Section4explores thesensitivityofmajorresultstovariationsinkeyparameters.Section5concludesandaddssome policyconsiderations.
2. Restrictedpermittradeandtechnologicalchangeinastandardanalyticalframework
2.1. Contributionofexistingliterature
Anumberofstudieshaveinvestigatedhowmarketfailuresassociatedwithinnovationandthe dif-fusionoftechnologiesaffecttheoptimalenvironmentalpolicyandtheequivalencebetweendifferent
market-basedinstrumentssuchastaxandemissiontrading.Awell-knownresultisthat,when tech-nologyexternalitiesarenotinternalised,theoptimaltaxorthepermitpriceshouldbehigherthanthe Pigovianlevel.GolombekandHoel(2006)analysethewelfareimplicationsofcarbonpermittradeina second-bestworldwheretechnologyexternalitiesarenotinternalised.Theyfindthatthesecond-best optimumischaracterisedbymarginalcostsofabatementexceedingthePigoviantaxinallcountries. Atighteremissionrequirementisthusawayofcompensatingforthelackoftechnologypolicy.Ina follow-uppaper,GolombekandHoel(2008)findthatthepriceofcarbonshoulddifferacross hetero-geneouscountriesinthesecond-bestagreementandtheyconcludethatwhetheremissiontrading iswelfareenhancingornot,isanempiricalquestion.Gerlaghetal.(2009),usingamodelwithout spilloversbutwithfinitepatentlifetime,showthatthedifferencewiththePigoviantaxshouldmimic theoptimalresearchsubsidyortax.Infact,whenthetechnologyexternalityisnotregulatedbyan explicittargetedpolicy,theequilibriumlevelofinnovationtendstobelowerthanfirst-best(Golombek andHoel,2004,2005).AsrecentlypointedoutbyHealandTarui(2010),thisconventionalwisdom hingesontheassumedrelationshipbetweeninnovationandcoststructure.Thecrucialassumption isthattechnologyimprovementsreducemarginalabatementcosts.Bakeretal.(2008)discusshow abatementcostcurvescanchangeinmanydifferentwaysasaresultoftechnicalchange.Technical changecanactuallyleadtotheadoptionoftechnologieswithhighermarginalabatementcosts com-paredtotheoldones.Asexampleofabatementoptionswithadifferentcoststructure,HealandTarui (2010)discusstheapplicationofcarboncaptureandstorage(CCS)technologytocoalpower genera-tion.Contrarytorenewablesources,whichhavehighfixedcosts,butnearlyzerovariableones,CCSis characterisedbyhighvariablescoststhatincreasewiththeCO2price.HealandTaruishowthatwhen
technicalchangeleadstotheadoptionofatechnologywiththiscoststructure,theequilibriumR&D investmentsmightbelowerthanfirst-best,dependingalsoontheextentofinternationalspillovers.
Theexistingliteraturehasfocussedontheimplicationsofahighersecond-bestcarbonpriceon innovationandtechnologicalchange,butithasnotexploredthelinkbetweenrestrictionsonpermit trade,innovation,and welfare,which isthefocusofthispaper.Weaskthequestionwhether,in thepresenceofmultipleexternalities,restrictingthetradeofcarbonpermitscanbeasecond-best policyrecommendation,andifso,underwhichconditions.Theremainingofthissectionintroducesa standardsimultaneousgameofabatementandR&Dinvestments,whilethenextsectiongeneralises theanalysisbyusinganumericalgeneralequilibriumcalibratedmodel.
2.2. Amodelofinnovationandabatement
Consideratwo-regionmodelwhereeachcountrychoosesinvestmentsininnovation,x,and abate-ment,a.Bothregionshavethesameabatementcost,whichisanincreasingandstrictlyconvexfunction inabatement,Ca(X,a)>0,Caa(X,a)>0,butdecreasingintheleveloftotalknowledgestockX,CX(X,
a)<0,CXX(X,a)>0.InnovationinvestmentcostsaregivenbyG(x),whereGx>0,Gxx≥0.Thelevelof
knowledgestockintheHomeregiondependsonthesumofitsowninvestments(x)andthoseof theForeignregion(¯x): X=x+ ¯x,where∈[0,1]representstheextentofinternationaltechnology spillovers.Thatis,onlyafractionoftheR&Dinvestmentscarriedintheotherregionisappropriated domestically.Forcomparabilitywiththesecondpartofthepaper,weassumethatinnovationlowers marginalabatementcosts,CaX=CXa<0.Thismechanismisalsomaintainedinthenumericalmodel
usedinSection3,wheretechnicalchangereducesthecostsofcapital-intensivetechnologieswith verylowvariablecosts.3
Thefirst-bestParetolevelofinnovationinvestmentsandabatement{xp,ap}minimisesthetotal
socialcosts,includingenvironmentaldamageD,whichisafunctionoftotalemissions(orequivalently abatement,ifweassumeexogenousbaselineemissions),C(X,a)+G(x)+C( ¯X, ¯a)+G(¯x)+D(a+ ¯a).The firstorderconditions(FOCs)fortheHomeregionare:
x:Cx(Xp,ap)+Cx( ¯Xp,ap)+Gx(xP)=0 (1)
a:Ca(Xp,ap)=Da(ap+ ¯ap) (2)
Letusnowconsideracost-effectivepolicythatinternalisestheenvironmentalexternalitythrough aninternationalemissiontradingscheme,andinwhichregionsbehavenon-cooperativelyon inno-vation.Thesecond-bestleveloftechnologyinvestmentsandabatementinthecaseofnoconstraints (freetrade)ontheuseofcarbontrading,{xFT,aFT},isobtainedbyeachregionminimisingtheircosts,
includingthecostsofbuying(orprofitsofselling)CO2permitsatthepermitpricep,andtakingthe
otherregions’innovationexpendituresasgiven:p(a0− a)+C(X,a)+G(x).Theinitialendowmentof
abatementisequaltoa0intheHomeregionandto1− a0intheForeignone,wheretotalabatement
normalisedto1.ThisprocessleadstotheFOCs:
x:CX(XFT,aFT)+Gx(xFT)=0 (3)
a:Ca( ¯XFT,aFT)=pFT (4)
IftotalabatementissetsuchthatthemarginalabatementcostspequalsmarginaldamageD,then wehavethatxFT<xpif>0,sinceC
X(X,a)isincreasinginx.Thatis,whensettingthepermitpriceatthe
Pigouvianlevel,theinnovationlevelinthequotaschemewhereR&Dexpendituresaredeterminedina non-cooperativemannerislessthanoptimal.Toinducethefirst-bestlevelofinnovation,theemission quotaandtheresultingpriceneedtobemademorestringent.Thisisthestandardresulthighlighted inSection2.1.
Sincethefocusofthispaperistherelationshipbetweeninternationalpermittraderestrictionsand theincentivetoinvestininnovationwhenthereareinternationalspillovers,weconsiderthesame internationalquotaschemeasabove,butnowaddaconstraintonthenumberofemissionpermitsthat canbetraded.Wewanttounderstandwhethersuchrestrictionscanfostermoreglobalinnovation, andifsowhethertheyallowreducingthewelfaregapbetweenthefirstbestandthenon-cooperative solutions.Eachregionminimisestotalcostssubjecttotheadditionalconstraintthataminimumlevel ofabatement˛mustbeaccomplisheddomestically,aLIM≥˛.SupposetheHomeregionwillhaveto
abateatleast(aLIM=˛).TheFOCsthenbecome:
x:CX(XLIM,aLIM)+Gx(xLIM)=0 (5)
a:Ca(XLIM,aLIM)−=pLIM (6)
(aLIM−˛)=0 (7)
whereisthemultiplierassociatedwiththepermittradelimitintheHomeregion.Whenthe con-straintisbinding(aLIM=˛),themarginalabatementcostsacrossregionsarenolongerequal.Marginal
costsintheHomeregion,Ca(XLIM,˛)=pLIM+,becomelargerthanthoseintheForeignregion,where
theyequalthepermitprice,Ca( ¯XLIM, ¯aLIM)=pLIM.Atraderestrictionhasanambiguouseffectonthe
internationalpriceofcarbon.Ontheonehand,fewerpermitswouldbetraded,leadingtoalower inter-nationalprice.Ontheotherhand,alowerlevelofinnovationintheForeigncountrycouldincrease marginalabatementcostsandhencetheinternationalpriceofcarbon(seeLemma1).
Thebuyer(constrained)Homeregionwillincurintheextracostofraisingthedomesticeffortabove theefficientlevel,dependingonthestringencyofthetradeconstraint˛.Replacinga=˛and ¯a =1−˛ intheFOCsforinnovationandbytotallydifferentiatingthem,theeffectofmakingthepermittrading capmorestringentoninnovationisimmediatelyobtained.
Lemma1. Inatradableemissionquotasystemwhereregionsbehavenon-cooperativelywithrespectto theinnovationexternality,restrictingemissionpermitstradingincreasesR&DinvestmentsintheHome restrictedregiondx/d˛>0ifinnovationreducesmarginalabatementcosts,CaX<0.InnovationintheForeign
unrestrictedregionisnon-increasinginthetraderestriction,d¯x/d˛≤0.
Lemma1indicatesthat,aslongasinnovationlowersmarginalabatementcosts,CaX<0,arestriction
onpermittradeincreasesR&Dinvestmentsintheconstrainedregion.Becausethetotalamountof abatementisfixedto1,theotherregionwillreduceabatementandthereforeinnovationwilldecrease. Thepreciseeffectalsodependsontheextentofspillovers.Foragivenpermittraderestriction,the largerthemagnitudeofspillovers,thehighertheincreaseininnovationintheHomeregionandthe reductionintheForeignone.
GlobalinnovationwillincreaseiftheadditionalinvestmentintheconstrainedHomeregionis higherthanthereductionintheunconstrainedForeignone,(dx/d˛)+(d¯x/d˛)≥0,orequivalentlyif theinnovationintheconstrainedregionisconvexinthelevelofpermittraderestriction.Thefollowing propositionclarifiesthiseffect.
Proposition1.
a. Inatradableemissionquotasystemwhereregionsbehavenon-cooperativelywithrespecttothe inno-vationexternality,restrictingemissionpermitstradingincreasesglobalR&Dexpenditures,(dx/d˛)+ (d¯x/d˛)≥0,if: −C˛X( ¯XLIM,1−˛) Gxx(¯xLIM)+(1−)Cxx( ¯XLIM,1−˛) < −C˛X(XLIM,˛) Gxx(xLIM)+(1−)Cxx(XLIM,˛) (i) b.TotalR&DalwaysincreasesinthecornersolutioncaseofzeroR&Dinvestmentsintheunrestricted
Foreignregion(¯x =0).
Limitingtradeaffectsglobalwelfarethroughtwochannels.Bynotequalisingmarginalabatement costsacrosscountries,itgeneratesanefficiencyloss.BymodifyingtheincentivestoinvestinR&D,itcan generateinnovationbenefits.Corollary1summarisesthetrade-offbetweenthesetwomechanisms.
Corollary1. Foradeviationfromthefreetradeabatementallocationduetothetradingrestriction,total costsdecreaseif:
C˛(X,˛)−C˛( ¯X,1−˛) CX(X,˛) + CX( ¯X,1−˛) CX(X,˛) dx d˛+ d¯x d˛>0 (ii)
Conditions(i)and(ii)dependonthespecificationoftheabatementandinvestmentcostfunctions. Therelationbetweentechnicalchangeandthemarginalcostofemissionreductionisparticularly importantincondition(i).Ifthemarginalbenefitofinnovationincreasesinabatement, thenthe numeratorof(i),−CX˛,wouldincreaseinthetraderestriction.4ThisisthecaseinwhichR&Dpivots
downthemarginalabatementcostcurve,thusreducingmarginalabatementcostsespeciallyforhigh levelofabatement.Forexample,thinkofaR&Dprogrammethatleadstotheadoptionofa break-throughtechnologywithverylowvariablecosts.Eveninthiscase,though,condition(i)wouldbemet onlyifCXXandGxxdidnotchangeintheleveloftraderestriction.Forexample,aconstantGxxwould
implyGtobeeitherlinearorquadratic,whichispossiblyareasonableassumption.Butthismight notapplytoCXXRecallinfactthat,whileinnovationcostsGdependonlyoninnovation,Cdepends
oninnovationandabatement.Abatementandinnovationbothincreasewiththetraderestriction, buttheireffectonCXXhasanoppositesign.WhethertotalR&Dincreasesinthetraderestrictionwill
dependontheassumedfunctionalformsoftheabatementandtheR&Dcostfunctions.
Condition(ii)statestherequirementforaglobalwelfaregain.Welfaregainscanariseifthe effi-ciencyloss(firstterm)iscompensatedbytheinnovationgain(secondterm).Letusassumethatthe traderestrictionisamarginalonefromthefreetradeallocation(e.g.,˛ ∼= 0.5).Thenthefirsttermin(ii) iszero.Thesecondtermisrelatedtothechangeinglobalinnovation((dx/d˛)+(d¯x/d˛))butwithan additionalweight,CX( ¯X,1−˛)/CX(X,˛),whichmeasurestherelativereturntoinnovationbetween
ForeignandHome.Inthecaseoffullspillovers(=1),thisweightisequaltooneandthencondition (ii)collapsestocondition(i).Thatis,foramarginaldeviationfromfreetradeandfullspillovers,when totalinnovationincreases,costsdecrease.Costwouldalsodecreaseincaseofacornersolutionof zeroforeigninvestment(¯x=0),orifspilloversorreturntoinnovationweresufficientlyasymmetric andlargerforForeignthanforHome(<¯ or CX<CX).Thiscouldindeedholdifwewereto
iden-tifyForeignwithdevelopingcountrieswhicharedistantfromthetechnologyfrontier,somethingwe representintheintegratedassessmentmodelusedinSection3.
For<1andsymmetricregions,however,CX( ¯X,1−˛)/CX(X,˛)islessthanoneandcondition(i)is
anecessarybutnotsufficientconditionfor(ii),sincetheinnovationbenefitsintheForeignregion(for
4RememberthatC
2 3 4 5 6 7 8 9 0.95 0.85 0.75 0.65 0.55 0.45 Total innovaon Trade restricon, α
Fig.1.TotalR&Dexpendituresforthecaseofb=3andc=1,forrangingfrom0(upperline)to1(lowerline)withincrements
of0.1.Thehorizontalaxisplotsthelevelofpermittraderestriction˛from0.5(norestriction)to1.Theverticalaxisplotstotal
innovation.ThediamondsshowthetotallevelofinnovationintheParetocase,forthecorrespondingvalueof.
amarginaldeviationfromfulltrade)aresmallerthanatHome,duetotheincompleteappropriability ofinnovation.Moreover,whendeviationsfromfreetradearenotmarginal,theefficiencylossdue tothemisallocationofabatement(firsttermof(ii))wouldnolongerbeinsignificant.Thus,wecan expectpermittraderestrictiontoleadtowelfaregainsonlyforsmallconstraintsandsufficientlyhigh spillovers.WefurtherexplorethisresultinthenextsectionforagivenfunctionformofC(X,a). 2.3. Anumericalexample
Letusassumethatabatementcostisapowerlawfunctionofabatementandinnovation,andthat thecostofinnovationequalstheR&Dexpenditures:
C(X,a)= ˇab
(X+1)c and G(x)=x
withbandc(greaterthan0)controllingthecurvatureofmarginalabatementandinnovation.Thisis aquitegeneralfunctionalformwhichisoftenusedincalibratedmodels.
Solvingfortheoptimallevelofinnovationforbothregions(x, ¯x),itisstraightforwardtoshowthat, foraninteriorsolution,condition(i)issatisfiedwheneverb/(c+1)>1.Itisalsoeasilyshownthat thisinequalityisalwayssatisfiedifweassumeC(X,a)tobestrictlyconvex,thatisifCXXCaa−CXa2 >0.
Thatis,incondition(i),thestrictconvexityofC(X,a)ensuresthattheoptimallevelofinnovationinthe constrainedregionisalsoconvexinthelevelofthetraderestriction.Thus,theincreaseininnovation intherestrictedregionmorethancompensatesthedecreaseintheunrestrictedone,evenwhenthisis greaterthanzero.Ifb/(c+1)=1theresponsesinthetworegionsareequal,andthustotalinnovation isconstantintherestriction,untilthepointwhere ¯xgoestozero.
WepictoriallyshowtheimpactofpermittraderestrictionsontotalinnovationinFig.1(forˇ=100, b=3andc=1)fordifferentvaluesoftheinternationalknowledgespilloverparameter,.Thechart showsthat,asexpectedsinceb/(c+1)>1,totalinnovationincreasesinthetraderestriction.The increaseismilderforinteriorsolutionsthanforcornersolutions,whicharereacheddependingonthe levelofrestrictionandofknowledgespillover.Sinceforthechosensetofparametersacornersolution inwhich ¯x =0isachievedforalllevelsofspillover,forstringentenoughtradecapstotalinnovation eventuallyconvergestothesamevalue,giveninthechartbythelowerline.Convergenceisfasterfor higherspillovers.Themagnitudeofspilloversisalsoveryimportantfordeterminingthedifferencesin theinnovationeffortbetweenthenon-cooperativesolutionsandtheParetoones,showninthechart bythediamonds.Asexpected,theunrestrictednon-cooperativecasesyieldglobalR&Dexpenditures
9 10 11 12 13 14 15 16 17 18 19 0.95 0.85 0.75 0.65 0.55 0.45 Total costs
Traderestricon, α
Fig.2. Totalcostsforthecaseofb=3andc=1,forrangingfrom0(upperline)to1(lowerline)withincrementsof0.1.The
horizontalaxisplotsthelevelofpermittraderestriction˛from0.5(norestriction)to1.Theverticalaxisplotstotalcosts.The
diamondsshowthetotalcostsintheParetocase,forthecorrespondingvalueof.
thatarealwayslowerthantheParetoones.Thisgapdependsontheextentoftechnologyspillovers. ThedistancebetweenParetoandnon-cooperativeinnovationiszerowhentherearenoexternalities, =0.Fig.1representsthiscasebytheupperlineanddiamond,whichinfactareperfectlyaligned.As spilloversincrease,thegapbetweenthediamondandthecorrespondinglineincreasesanditreaches itsmaximumwhenspilloversarefull,representedinthechartbythelowerline.Traderestrictions,by fosteringmoreR&Dexpenditure,helptoclosetheinnovationgapwiththeParetosolution.Asevident fromthechart,iftradeissufficientlyrestricted,totalinnovationcanincreasebeyondtheglobally optimalParetolevel.
Asasecondrelevantquestion,weaskwhethersuchtraderestrictionscanbewelfareimproving. Asdiscussedintheprevioussection,restrictingthepossibilityoftradingpollutionpermitswould introducetwosourcesofinefficiency.First,itwouldshiftabatementawayfromtheoptimalallocation ensuredbytheequalisationofmarginalabatementcosts.And,itwouldrequireadditionalresources forR&Dexpenditure.However,bypartlyinternalisingtheinnovationexternality,thetradeceiling couldprovidewelfarebenefitsandreducethewelfaregapbetweenthedecentralisedoutcomeand thegloballyoptimalsolution.
Fig.2reportsthetotalcostsforvariousrestrictionsandspillovers(andagainforˇ=100,b=3and c=1).Onecannoticethatforhighlevelofspilloversandmildrestrictionsonpermittrading,thetotal costsarelowerthanfortheunrestrictedcase(˛=0.5).Thatis,thereappeartobecaseswherepermit traderestrictionsarewelfareenhancing,andthesecasesareinlinewithwhatstatedincondition(ii). Asexpected,thecostsremainalwayshigherthanintheParetocase(againrepresentedbydiamonds), sincetraderestrictionisnotthemostefficientwaytointernalisetheinnovationexternality. Nonethe-less,theresultisinterestingsinceitpointstopotentialefficiencygainsinducedbythesecond-best policyoflimitingpermittrading.
Summingup,inthissectionwehaveshownthatforcertainassumptionsregardingtheway tech-nicalchangeaffectsmarginalabatementcost,restrictionsontheamountoftradableemissionpermits canincreasethetotalinnovationeffort.Wehavealsoshownthatthisincreasedinnovativeeffortmight leadtopotentialeconomicefficiencygains,ifpermittraderestrictionsaremoderateandspillovers sufficientlyhigh.Intheend,theoveralleffectofrestrictingtradeontheregionalandtotalcostsof theclimatepolicydependsontheparameterisationofthevariousfunctions,especiallytheimpactsof innovationontheperformanceofabatingtechnology.Albeitdifficulttocharacteriseempirically,an integratedassessmentframeworkisneededtomovebeyondthelimitationsoftheanalysismadein thissection,especiallyforwhatregardstheroleofthedynamics,therepresentationofthetechnology spilloversandtechnologicalchange,issuesofleakageandotherpotentialeffectssuchastheimpacton
internationalenergymarkets.Totacklealltheseissuesinaunifiedframework,weturntoacalibrated generalequilibriummodel.Wefirstintroducethemodelandthescenarioset-up,andthenprovide complementaryinsightstotheonespresentedinthissection.
3. Afullyintegratednumericalanalysis
3.1. Modelstructureandsetupofthenumericalassessment
ThenumericalanalysisusestheWITCHmodel,5anenergy-economymodelthatfeaturesmultiple externalities.AfulldescriptionofthemodelcanbefoundinBosettietal.(2006,2009a).Herewe brieflydiscusshowtheexternalitiesarerepresentedinthemodel.
WITCHisadynamic,optimalgrowthmodelwithafocusontheenergysectorandonGHGmitigation options.Itconsistsof12aggregatedregions,denotedwithn.Oneofitsdistinguishingfeaturesis thegame-theoreticset-upthatallowsproducingtwodifferentsolutions.Themodelcanberunina cooperativemodewhichjointlymaximisesglobalsocialwelfareandinternalisesenvironmentaland economicexternalities,generatingafirst-bestoptimum.Inaddition,itcanprovidethedecentralised, ornon-cooperativesolution,byoptimisingthewelfareoftheindividualregions,takingasgiveneach otherregion’schoice.Thisisdonethroughaniterativeprocedure,whichiscapableofreproducingthe outcomeofanon-cooperative,simultaneous,openmembershipgamewithfullinformation,andthus achieveasecond-bestNashequilibrium.Withthissetting,itispossibletoexploretheconsequences ofdealingwithdifferentsourcesofmarketfailure.Themodelspecificallyincorporatestheclimate changeexternality,thetechnologyexternalityviainternationalknowledgeandexperiencespillovers, andcarbonleakagethroughinternationalenergymarkets.
Theclimateexternalityisaccountedforbyadamagefunctiondrivenbyglobalaveragetemperature, computedthroughasimplifiedclimatemodule.Thispaper,though,providesacost-effectiveanalysis ofaclimatepolicyaimedatstabilisingtheconcentrationsofgreenhousegasesintheatmosphereat agivenlevel,6essentiallyputtingacaponthecumulativeCO
2-eqemissions.Inthesamespiritofthe
precedingsection,weassumeglobalemissionreductionsareachievedthroughaninternationalcarbon market,whichisoperativefrom2020.FollowingtheUNFCCCdistinctionbetweenindustrialisedand developingcountries(intheprecedingsectionHome andForeignregion,respectively),OECDare allocatedstrictreductionsrequiringa90%cutofGHGsby2050comparedto2005levels.Developing countries(non-OECD)areallowedtoincreaseemissionsby20%which,comparedtothemodelbaseline projections,impliesareductionofalmost50%,7orofabout24GtCO
2,comparedto22GtCO2forthe
OECD.
Thetechnologyexternality,inWITCH, ismodelledviainternationalspilloversofknowledgeand experienceacrosscountries(Bosettietal.,2008).Themodelincludesanumberofdifferentlow-carbon mitigationoptions,tech.Ineachcountry,theirtechnologylevel(xtech,n,t)isdescribedbytheglobal
stockofenergyR&D(R&Dtech,n,t),whichmeasuresknowledge,andbythecumulativeinstalledcapacity
(CCtech,n)whichisaproxyofexperienceorLearning-by-Doing.Ateachpointintime,newideasadd
totheexistingR&Dstock,whichdepreciatesattherateı.Thegenerationofnewideasisdescribed bytheinnovationpossibilityfrontier,whichismodelledasaCobb-Douglascombinationbetween domesticinvestments(I R&Dtech,n,t),domesticknowledgestock(R&Dtech,n,t),andforeignknowledge
stock(SPILLtech,n,t):
R&Dtech,n,t+1=R&Dtech,n,t(1−ı)+IR&D˛tech,n,tR&D ˇ
tech,n,tSPILLεtech,n,t (8)
SPILLtech,n,t=
R&Dtech,n,t j∈OECDR&Dtech,j,t(
j∈OECDR&Dtech,j,t−R&Dtech,n,t) (9)
5Seewww.witchmodel.orgformodeldescriptionandrelatedpapers.
6Specifically530ppmofCO
2-eq,or3.5W/m2.
7Commitmentstartingdateshavealsobeendifferentiatedbetweendevelopedanddevelopingregions,witha10year-delay
innon-OECDregions.Weassumethatbeyond2050,allregionswillcooperatetoreachthelong-termstabilisationtargetand
The spillover term (SPILLtech,n,t) depends on the interaction between the countries’
absorp-tive capacity, measured by the ratio of the stock of the country to that of the frontier
R&Dtech,n,t/
j∈ OECDR&Dtech,j,t
,andthedistanceofeachregionfromthetechnologyfrontieritself
j∈ OECDR&Dtech,j,t−R&Dtech,n,t
.Thetechnologyfrontieriscalculatedasthetotalstockof knowl-edgeinOECDcountries.Thisformulationimpliesthatforeignknowledgecanbringsomebenefitsonly ifadomesticR&Dprogrammeisestablished.Knowledgespilloversarenotcompletelyfree,butthey requirededicatedinvestments.Inthenotationofthemodelusedintheprevioussection,thiscase correspondsto<1.8
Incontrast,spilloversofexperiencearecompletelyfreewithinthetimeframeofthemodel,which isoffiveyears,t=5.Worldcumulativeinstalledcapacityintechnologytechattimetiscomputedby addinginvestmentsinallregions(Itech,n,t):
CCtech,t+1=
tnItech,n,t (10)
Globallearningimpliesthatinvestmentsineachgivenregionequallycontributetheformationof aglobalstockofexperience,whichinturnaffectsinvestmentcostsinallregions,asdescribedinEq. (11).Inthenotationofthemodelusedintheprevioussection,thiscasecorrespondsto=1.Regarding themannertechnologylevel(xtech,n,t)impactsthemarginalcostofabatement(Cax),theWITCHmodel
distinguishesbetweentechnologicalchangefordecarbonisingtheenergysystemandforimproving energyefficiency.
Decarbonisationoccursbecauseahighertechnologylevelleadstolowerinvestmentcostsof low-carbontechnologies.Thisprocessisdescribedbyaso-calledtwofactorlearningcurveofthisform:
ICtech,n,t ICtech,n,0 =
R&Dtech,n,t−2 R&Dtech,n,0−c
CCtech,t CCtech,0−b
(11) ThetwoexponentsaretheLearning-by-Doing(LBD)index(−b)andtheLearning-by-Researching (LBR)index(−c).Theydefinethespeedoflearning.Moreprecisely,thelearningratios,definedasone minustheprogressratio,LBRratio=1−2−c;LBDratio=1−2−b,determinetherateatwhich invest-mentcostsdeclineeachtimethecumulativecapacityortheknowledgestockdoubles.Atwotime period(correspondingto10years)lagisassumedforR&D,tocapturetheinertiaofbringingresearch tothemarket.Sincethetechnologiesthataresubjecttolearningareassumedtobeofrenewabletype, theinvestmentcostscoincidewiththemarginalcosts.Inthisformulationtechnicalchangereducesthe marginalcostofabatement,asinthemodelpresentedinSection2,wheretheroleofthisassumption wasdiscussed.Energyefficiencyismodelledthroughimprovementsintheproductivityoftheenergyinput(ENn,t)
intheproductionofthefinalgoodsector.Theenergyknowledgestock(R&DEE,n,t)augmentsthe
quan-tityoffinalenergyservices(ESn,t)thatcanbeprovidedofeachgivenunitofphysicalenergy(ENn,t)
accordingtoaconstantelasticityofsubstitutionproductionfunction: ESn,t=
a1R&DEE,n,t+a2ENn,t
1/
(12) Finally,thelastchannelofinteractionacrossregionsisthatoftheinternationalenergyandcarbon market.InternationalpricesoffossilfuelsandCO2aredeterminedbytheequilibriumofdemandand
supplyatthegloballevel.Thus,differentdomesticabatementgoalsasaresultofconstraintsonthe amountofcarbontradingcanhaveanimpactonthepriceandtradeofsuchgoods.
Thestructureofthisnumericalmodelallowsustoconsiderthemostsalientfeaturesofthe cli-matemitigationpolicy,andtodosoinasecond-bestsetting.Althoughthismodelprovidesamuch richerframeworkthananalyticalonesandrepresentsastep-upoverstandardintegratedassessment modellingthatnormallyfeaturesonlytheclimateexternality,itmustnonethelessberecognisedthat itdoesnotthoroughlyrepresentasecond-bestworld.Forexample,nointernationaltradeofcapital
8Withtheparameterwegenerallydenotestheextentofspillovers,followingthenotationusedinSection2.InWITCHthis
Table1
Globalandregionalmacroeconomiccostsofclimatestabilisationpolicyunderthe“fulltradehypothesis.”Consumptionlosses
discountedat3%discountrate,2005–2100.
Consumption OECD Non-OECD World
2005US$Trillion 26.19 1.88 28.07 PercentageofBaUconsumption 1.68% 0.18% 1.07% Lossesaregrossofclimatechangedamages.Negativenumbersindicategains.
Table2
Internationalcarbonmarketunderfulltrade. Mktsize (GtCO2-eq) GtCO2-eq abated Internationally tradedabatement Carbonprice (2005 US$/tCO2) Mktvalue (2005US$ Billion) Mktvalue (%ofGWP) 2020 2.8 7 41% 4 11 0.02% 2025 3.0 14 22% 26 76 0.10% 2030 3.3 20 16% 58 193 0.22% 2050 7.1 46 16% 319 2260 1.74%
isassumedandpre-existingdistortionarytaxesandsubsidiesarenotaccountedforinthisexercise.
Ourmodelcapturesmarketfailuresrelatedtointernationalspilloversonlyintheenergysector,as
nogeneralpurposeR&Disassumed.Nolearningisconsideredforknown,yetpotentiallyimprovable
technologies,suchasnuclearpowerandcarboncaptureandstorage(CCS).Thus,thisexerciseprovides
anaccountofonlysomeofthemostrelevantsourcesofglobalinteraction.
3.2. Climatepolicyunderfullinternationalcarbontrading
Webeginbyevaluatingtheimplicationsofacost-effectivepolicyimplementedthroughan
inter-nationalquotaschemeinthecaseofnoconstraintsontheuseofcarbontrading(fulltrade).9 As
showninTable1,giventheregionalabatementcommitments,OECDcountriesfacethehighestcosts non-OECDcountriesslightlygainuntilmidcentury,mostlyduetopermitrevenues,butloseinthe long-term.
The1%globalfigurelieswithintherangereportedintheliterature(seeforexample,IPCC,2007; Ludereretal.,2009).Lowcostsareduetothescenariodesign,theassumptionofimmediate partici-pationandoffullflexibilityamonggreenhousegasesabatementoptions.Departurefromanyofthese assumptionsincreasescostssubstantially(Bosettietal.,2009b;Clarkeetal.,2009).
Withoutanyrestriction,countriesrelyontheinternationalcarbonmarket,andthissuggeststhatit isanimportantelementofeconomicflexibility.Table2showstheevolutionofthecarbonmarketover time.Theinitiallylowcarbonprice(duetotheassumptionofglobalparticipationandwidebasket ofGHGs)issuchthatthemarketvalueiscontainedattheoutset,butgrowssignificantlyovertime, drivenbytheconvexpathofthecarbonprice.Themarketsizeisalreadysignificantin2020,when almost3BilliontonnesofCO2(equaltoroughlyhalfoftoday’semissionsintheUS)areexchanged
internationally,enoughtorequiretheestablishmentofconsiderableinstitutionaland monitoring capacity.
However,aperfectlyfunctioninginternationalcarbonmarketisnotlikelybeavailablein2020. Recentnegotiationshaveshownthatissuesofmonitoringandverificationarequitecomplextobedealt withattheinternationallevel.Thelackofinstitutionalcapacity,reliablemonitoring,andverification systemsinsomecountriesmightdelayorfragmenttheestablishmentofaglobalmarket.Or,countries thathavealreadyimplementedemissiontradingschemes,suchastheEU,mightlimittheamountof internationalcreditsthatcanbeusedinthedomestictradingscheme.Theconsequencesofthesethree possibleoutcomesaredescribedinthenextsection.
9Fullcooperationisassumedtobesupportedbyafullyfledged,perfectlyfunctioning,internationalcarbonmarket,whichis
Table3
Regionalmacroeconomiclossesofclimatepolicywhentheuseofinternationaloffsetsisdelayed(“when”dimension).
Con-sumptionlossesdiscountedat3%discountrate,2005–2100.
OECD Non-OECD World
Fulloffsets 1.68% 0.18% 1.07%
From2030 1.81% 0.11% 1.12%
From2035 1.90% 0.08% 1.17%
From2040 2.26% 0.05% 1.37%
From2045 2.70% 0.08% 1.64%
Negativeentriesindicateconsumptiongains.
3.3. Delayed,fragmented,andconstrainedinternationalcarbontrade
Followingtheabovearguments,letusassumethattheestablishmentofaninternationalcarbon
marketisdelayedtoafuturedatebetween2030and2045(wenamethisthe“when”scenario).Table3
reportsconsumptionlosseswhenaccesstointernationaloffsetsisdelayedovertimeby10,15,20,or 25years.Postponingtheestablishmentofaninternationalcarbonmarketincreasesglobal macroe-conomiccostsmoderatelyfordelaysuntil2030–2035,butwaitinguntil2045raisesthepolicybillby about50%.ThisisdrivenbyadditionallossesinOECDregions.Instead,innon-OECDthe(moderate) consumptioncostsarehalved,reducingtheglobalpenalty.Welfareimprovementsintheseregions areasecond-bestresult,drivenbypositivetechnologyspilloversandlowerenergyprices.Theyalso dependontheassumptionthatnon-OECDcountriescommittomilderemissionreductionobjectives comparedtoOECD.
Whentradeisrestricted,moreexpensivemitigationoptionsareadopted,drivingupcompliance costs.10Withlimitedaccesstointernationaloffsets,OECDregionsfurtherdecreasetheirdemandof allfossilfuels(traditionalgas,coal,andoil),oilinparticular.ThereduceduseofoilinOECDcountries lowersitsinternationalprice,benefitingnon-OECDregions.Thiseffectisalsoknownasenergymarket effect,whichisoneofthepossiblesourcesofcarbonleakage.Asecondchannelthatisnotdiscussed inthispaperworksthroughchangesinterms-of-tradeandinternationalcompetitivenessof energy-intensiveindustries.11ThecontractionofoildemandinOECDcountriesisonlypartiallyoffsetby carbonleakageinnon-OECD,whichincreasestheoildemandby11%(onaverage)between2020and 2040.Fig.3,upperpanel,showsthatintheextremecaseofa2045delay,thesetwoeffectsresultina globaldemandcutbackof16%in2040.Theinternationalpriceisalmost4%lowercomparedtothefull tradecase.Itshouldbementionedthatmostoftheoilpricereductionoccurswhenimplementinga stabilisationpolicy,alreadyinthefreetradescenario,wheretheoilpricefallsbyabout30%in2050and 70%in2010comparedtothebaseline.Forthisreason,theadditionalpricereductionduetorestricted emissiontradeisrelativelycontained.
AsecondresponsetothetraderestrictionistoinvestmoreincleanR&Dandcarbonfreepower gen-erationtechnologies.ThisfindinggeneralisestheresultinProposition1.Aslongastechnicalchange reducesmarginalabatementcosts,permittradelimitsstimulateinvestmentsintechnologiessubject totechnologicalchange.Letusconsider,forexample,thedynamicsofinvestmentsinrenewable elec-tricity,whosemarginalcostdecreaseswiththeglobalcumulativecapacity,asdescribedinEq.(11).The globalpathofinvestmentsinwindandsolararedepictedinFig.3,bottompanel.Duringthetransition periodwithoutpermittrading(2020–2040),OECDinvestmentsinwindandsolarareraisedtomatch themorestringentabatementtarget(
∂
x/∂
˛>0).Investmentsinnon-OECDinitiallyremainatlevels comparableorslightlylowerthanthefulltradecase,buteventuallyincreaseaswell.Thispatternis duetothereductioninglobalinvestmentcostscausedbyadditionalinvestmenteffortintheOECD. Investmentsdropbelowthefulltradecaseonlyin2040,inanticipationoftheopeningtointernational10Weanalysetheseresultsforthemoststringentcaseinwhichtradestartsin2045.Theothercaseshavesimilar,butsmaller
magnitudeeffects.
11BurniauxandOliveira-Martins(2000)assessedtherelativecontributionofeachofthetwochannelsandconcludedthat
-5.00% -4.00% -3.00% -2.00% -1.00% 0.00% 1.00% -20% -15% -10% -5% 0% 5% 2040 2035 2030 2025 2020 2015 2010
Percentage change w.r.t. full trade
Percentage change w.r.t. full trade
World consumption International price (Rhs axis)
-4.25% -2.25% -0.25% 1.75% 3.75% 5.75% 7.75% -15 -10 -5 0 5 10 15 20 25 2010 2015 2020 2025 2030 2035 2040
Percentage change w.r.t. full trade
Difference w.r.t. full trade(US$ Billion)
Additional global investments Global investment cost reduction (RHS axis)
Fig.3. Internationaloilmarket(leftpanel)andrenewableelectricity(rightpanel)whendelayingtheuseofinternationaloffsets
to2045.
offsetsin2045,buttheyremainhigherthereafter.Theadditionalinvestmentcostreductionforwind andsolarinducedbythetraderestrictiondecreasesovertimebecauseofthedecreasingmarginal benefitsofinvestments,butnonethelessremainspositivethroughoutthecentury.Suchpath depen-dencieshelplowertheclimatepolicycostsinthelong-term,butrequireanadditionaleffortinthe beginning,whichismostlyfacedbydevelopedcountries.Asimilarresultisobservedforinvestments inenergyR&D,whichgloballyincreasethroughoutthecentury,butbyalargermagnitudeduring thetransitionperiodwithoutemissiontrading.Theglobalincreaseismostlydrivenbyadditional investmentsinOECDcountries.Non-OECDcountriesslightlyreducetheirR&Deffortinthe short-run,butincreaseitafter2035.Sincebothknowledgestockandnewinstalledcapacityinlow-carbon technologiesgenerateinternationalpositivespillovers,OECDadditionalinvestmentsreducemarginal abatementcostsinallotherregionsaswell.Inotherwords,theadditionalcostspaidbyOECDregions leadtoadditionalbenefitsinnon-OECD.
Anothersituationthatcouldariseisafragmentedinternationalcarbonmarket,atleastduring thetransitiontowardsmoreconsolidatedprocedures.AsnotedbyFrankel(2008),itcouldbethat theeligibilitytosellpermitsisrestrictedtocountrieswithgoodinternationalgovernanceratings,or thathavecommittedtoinvesttherevenueingreenprojects,orthathavedemonstratedabilityto abidetocommitments.Weanalysetheimplicationsofdelayingtheparticipationofthreegroupsof developingregionsthatintheglobalcarbonmarketwouldplaytheroleofnetsellers:EnergyExporting Regions(EEX:MiddleEastandNorthAfricaandRussia),DevelopingAsia(DA:ChinaandIndia)and RestofWorld(ROW:LatinAmericaandSub-SaharanAfrica).Inthisscenario,aninternationalmarket
Table4
Regionalmacroeconomiclossesofclimatestabilisationpolicywhenselectedregionsjoincap-and-tradein2045(“where”
dimension).Consumptionlossesdiscountedat3%discountrate,2005–2100.
OECD Non-OECD World
Fulloffsets 1.68% 0.18% 1.07%
DAjoinin2045 1.82% 0.12% 1.14%
ROWjoinin2045 1.73% 0.16% 1.10% EEXjoinin2045 1.73% 0.17% 1.10% Negativeentriesindicateconsumptiongains.
Table5
Regionalmacroeconomiclossesofclimatestabilisationpolicywhenlimitingtheuseofinternationaloffsetsuntil2045(“how much”dimension).Consumptionlossesdiscountedat3%discountrate,2005–2100.
OECD Non-OECD World
Fulloffsets 1.68% 0.18% 1.07%
20% 1.76% 0.14% 1.11%
15% 1.84% 0.12% 1.15%
10% 1.97% 0.11% 1.22%
0% 2.70% 0.08% 1.64%
Negativeentriesindicateconsumptiongains.
isassumedtoalreadyexistin2020,buttheaboveregionsjoinin2045(wenamedthisthe“where”
scenario).
Excludingeitherregionfromtheinternationalcarbonmarkethaslimitedeffectsonglobal
macro-economic costs (Table 4), essentially becausethe others compensate the absenceof a seller by
increasingsupply.Theonlycasethatleadstoavisibleadditionalglobalpenaltyistheexclusionof DevelopingAsia,whichcoversmorethan50%ofthedemandofpermits.Forexample,thepriceof carbonin2025woulddoubleifDevelopingAsiawerenotincludedinthemarket,whereasitwould increasebyonlyafewpercentagepointsifotherregionsweretodelay.Thisresultstemsfromthefact thatemergingeconomiessuchasChinaandIndiaareassumedtohostthelargestbaseofmitigation opportunities.ItalsoreinforcestheknownargumentthatanyclimatepolicyhastolookEasttobe effective.
Section3.2hasshownhowrapidtheexpansionofthecarbonmarketcouldbe(seeTable2).Itcould actuallymobilisehugefinancialresources.WefindthatthenetoutflowsfromtheOECDregionsto developingcountriescouldincreaseuptoUS$1.7Trillionin2050,morethan2%ofOECDGDPinthat year.Therefore,OECDcountriesfaceatrade-off.Ontheonehand,laissezfairwouldmaximise cost-effectivenessandcontaineconomiccosts.Ontheotherhand,itwouldentailsubstantialfinancialflows, whichmayunderminethewillingnessofindustrialisedcountriestocommit.Iftheclimateexternality weretheonlydistortionintheeconomy,restrictionstocarbontradewouldcreateawedgeinmarginal abatementcostsacrosscountries,reducingeconomicefficiency.However,sincetherearetechnology externalities,restrictingtrademightbeasecond-bestpolicyrecommendation.
Theremainderofthesectionexploresthiscase.Weassumethataninternationalcarbonmarket isalreadyestablishedin2020,butquantitativerestrictionsontheuseofinternationalcarboncredits areenforced(wenamethisthe“howmuch”scenario).Until2045,onlyafractionofabatementfrom 20,15,10,0%ofregionalabatement,canbemetthroughtheinternationalcarbonmarket.The0%case coincideswiththescenarioinwhichtradeispostponedto2045(the“2045”caseconsideredabove). ThestylisedanalysisinSection2alreadypointsoutthatrestrictingtradetendstocauseglobal effi-ciencylosses,unlesstherestrictionismildandspilloversaresufficientlyhigh(seeFig.2andCorollary 1).Table5confirmsthat,whenonlyafractionoftotalabatementineachregioncanbemetwith internationaloffsets,globalconsumptionlossesincrease.Amildrestrictionsuchas20%createscosts thatarecomparabletopostponingtradeto2030(1.12%consumptionloss).Tighterrestrictions(10%) havecostscomparabletopostponingtradetoatleast2035(1.17%consumptionloss).
Thedynamicsofregionalcostsdependsnotonlyontheinteractionsbetweentheeffectsoutlined before(energymarketandtechnologyspillovers),butalsoonthetradingpositionofeachregion.In
0 20 40 60 80 100 120 140 2030 2025 2020 $/tCO2e Europe USA Global
Fig.4.MarginalcostofcarboninEuropeandUSfora15%limitoninternationaloffsetsuntil2045,andglobalcarbonprice
whenthemarketisnotrestricted(Global).
theshort-term,netsellers(non-OECD)tendtolosebecauseofthecontractionofthemarketand,as aconsequence,ofthecarbonprice.Thenon-OECDregionssupplyisrationedandthereforetheyemit more.However,theyanticipatethatafter2045therewillbealagerdemandofpermitsandtherefore theystillkeepemissionsbelowtheinitialallocation.Throughoutthecentury,limitingtradeto10%of regionalabatementincreasesnon-OECDwelfarebyabout40%becauserevenuelossesonthecarbon marketareoffsetbytheenergymarketeffectsandtechnologyspillovers.
Theeffectonnetbuyers(OECD)dependsonwhetherthelimitisbindingornot.Whenthelimitis binding,theregionlosesbecausemoreexpensiveabatementoptionshavetosubstituteforimported credits.Ifthelimitisnotbinding,theregiongainsbecausecarbonpermitsarecheaper,pLIM<pFT.
Withoutanyceiling,andgiventhisallowancesdistribution,developedcountrieswouldfinditoptimal tobuybetween18and54%oftheirabatementontheinternationalmarket.Thisimpliesthatamild restrictionof20%isbindingformostdevelopedcountries,especiallyintheshort-runandinEurope. OnlytheUnitedStatesisrightatthelimit,andin2030the20%restrictionisnotbinding.12Asa consequence,becauseequivalentoffsetrestrictionsleadtorelativelymoreabatementinEuropeand otherOECDcountries,moreR&DandcleaninvestmentsareinducedoutsidetheUS.A15%limiton tradewouldraisethecostofcarbonsignificantlymoreinEuropethanintheUS,asshowninFig.4. IntheUS,the15%restrictionisbinding,butspilloversandtheenergymarketeffectscompensatethe additionalcosts,leadingtoshort-termwelfaregainsandonlytoa1%long-termadditionalpenalty.As aconsequence,theUSwouldhaveeconomicbenefitsfromimposingaslightlyhighercarbontaxand relyinglessoninternationaloffsets,providedEuropeandtherestofOECDwouldalsobewillingto adoptequallystringent(butwithahigherimpactonmarginalcostsofabatement)measures.Thislast conditionisimportantbecausetheUSwouldprofitfromthereductioninoilpricesandininvestment costsoflow-carbontechnologiesinducedbythetightercommitmentintherestofOECD,too.
Furtheranalysis13indicatesthatthetechnologyspillovereffectissomewhatlargerthantheenergy marketeffect,thoughinbothcasestheefficiencylossesaresmallcomparedtotheoverallpolicy costsshowninTable2byafewpercentagepoints.Thereasonforthisisthatthestringentclimate stabilisationpolicyconsideredinthispaperrequiresadrasticswitchoftheenergysystemfromafossil fuelbasedtoalow-carbononeeveninthecasewithfullaccesstointernationaloffsets.Thislimitsthe additionalroomforreductioninthepricesofenergyandlowcarbonfuelswhentradeisconstrained.
12ItisinterestingtonotethatBuonannoetal.(2000),inthedifferentpolicysettingoftheKyotoProtocolandwithadifferent
modelwithoutinternationaltechnologyspilloversfoundasimilarresultfortheUS.
13Wequantifythecontributionoftheenergymarketeffectandtechnologyspillovers,byconsideringthreevariationsofthe
15%scenarioinwhicheitherorbotheffectsareswitchedoff.Specifically,weranthreeadditionalsimulationsofthe15%trade
restrictioncaseinwhichwefixedthecostsofeitherfossilfuelsorlow-carbontechnologiescharacterisedbyspilloverstothe
ThetechnologyspilloverschannelisfoundtobehigherinOECDregions.Despitebeingclosertothe technologyfrontier,developedcountrieshavetocomplywithaverystringentdomesticcommitment (especiallywhentradeislimited)thatrequiresfastandmajorinvestmentsinlow-carbonmitigation options,suchaswindandsolar.Thus,thegainsofequalreductionofinvestmentcostsin renew-ables(givenbytheassumptionofgloballearningbydoing)benefitsdevelopedcountriesmorethan developingones.Onthecontrary,theenergymarketeffectislargerfornon-OECDcountries,which areconfrontedwithlessdemandingmitigationobligationsandcanprocrastinatetheconsumptionof fossilfuels.
4. Sensitivityanalysis
Thenumericalanalysisdescribedintheprevioussectionhasshownthat,whenthereare inefficien-ciesinothermarkets,limitingpermittradecanincreaseglobalinnovationandtechnologicalchange, leadingtopotentialefficiencygains.Welfareeffectstendtobenegativeinbuyerregions(OECD),but positiveinnon-OECD(seeforexampleTable5),becauseofloweroilpricesandhigher technologi-calspillovers,thelatterinducedbythemoreinnovationbeingcarriedoutintheOECDregions.The resultspresentedinSection3.2extendthevalidityofcondition(i)and(ii)toamoregenericframework characterisedbymultipleexternalitiesanddifferentabatementoptions.
Inthisremainingsectionwetestwhetherthenumericalresultsareidiosyncraticduetospecific parameterchoicesbyvaryingthemostrelevantcalibratedinputs.Wefocusthesensitivityanalysison theextentofinternationalknowledgespillovers(theparameterεinEq.(8))andtheimpactof inno-vationandexperienceontheperformanceofabatingtechnologies(theLBRandLBDindicesdenoted withtheparameterscandbinEq.(11)).Thesetwoparametersarekeybecausetheyaffecttheextent towhichknowledgeandexperiencereducemarginalabatementcosts,inournotationCax.
Itisimportanttostressthedifferentroleoftheextentofspilloversandthelearningrates.Spillovers ofexperiencearefree,orusingthenotationofSection2,is1.Learningisassumedtobeaglobal processthatreducestechnologycostsanywhereintheworld,nomatterwhereinvestmentsoccur.We assumetherearenobarrierstothediffusionofnewtechnologieswhich,oncecommercialised,canbe adoptedwithinthetimeframeoffiveyears.Incontrast,knowledgespilloversrequireR&Dcapacity atHomeand,usingthenotationofSection2,islessthan1.Inthesensitivityanalysiswevarythe extentofinternationalspilloversofknowledge(thevalueofεinEq.(8)),butnotthatofexperience spillovers.Forwhatconcernstheroleofexperience,weexploredtheimpactofdifferentdegreeof learning.
Theempiricalevidencethatguidestheselectionoftheparametervaluesforinternationalspillovers ofknowledgeisscarce,althoughanincreasingnumberofpaperssupporttheirexistence(starting fromGrossmanandHelpman,1991,tothemorerecentcontributionsofKeller,2004andVerdolini andGaleotti,2009).Inaddition,severalstudiessupportthehypothesisthatdomesticR&Deffortis neededtoabsorbinternationalknowledge(startingfromSchmookler,1966tothemorerecentworks byKeller,2004;Dechezleprêtreetal.,2008;Seresetal.,2009;VerdoliniandGaleotti,2009).Asa centralvalueinthemodel,weassumealowenoughvaluecomparedtothecontributionofdomestic investmentsandpastknowledgestock,ε=0.15.Toaccountfordiminishingreturns,thesumofthe elasticitiesofthethreeinputsinEq.(8)islessthanone.Thesensitivityanalysisonεcoversasufficiently largespectrumofvalues,from0.075(−50%)to0.22(+0.50%).Thelatterisaconsiderablyhighvalue, implyingacontributionlargerthanthat ofdomesticinvestments(0.18)andhalfthatofthepast knowledgestock(0.53).
ThelearningratiosinEq.(11)describetheeffectivenessofinnovationprecedingthebreakthrough (Learning-by-Researching,c)andofexperiencefollowingtheadoptionofthetechnology (Learning-by-Doing,b)atreducingthemarginalcostoftheabatingoption.Learning-by-Doingisglobal(=1) whereasLearning-by-ResearchingismostlydrivenbydomesticR&Dinvestmentsbecausethe con-tributionoftheinternationalpoolofknowledgeis only0.15.Theempiricalevidenceonlearning (by-Doing) rates spansrelativelywide ranges.On average, the costsof energy supply technolo-giesdeclineatratesof16±9%witheachdoublingincumulativeproduction(Weissetal.,2010). The value chosen in WITCHis lower than those typically estimated in single factor experience curvessincetechnologicalprogressresultsinpartfromdedicatedR&Dinvestments.Theliteratureon
Table6
Keyparametervaluesandsensitivityanalysis.Learningratios(LBRandLBD)andcontributionofspilloverstoknowledge
production(ε). Central[−50%to+50%] Literature LBR(parametercinEq.(11)) 0.13 0.13a [0.07–0.19] [0.07–0.19] [LBRm50–LBRp50] LBD(parameterbinEq.(11)) 0.1/0.14 0.16b [0.05–0.14]/[0.07–0.20] [0.03–0.25] [LBDm50–LBDp50]
InternationalknowledgespilloversSPILL(parameterεinEq.(8)) 0.15
[0.075–0.225] [SPILLm50–SPILLp50]
aVarioussources.ForspecificreferencesseeBosettietal.(2009a).
bWeissetal.(2010).
Learning-by-Researchingpointsatanaveragelearningrateof13%.Table6summarisesthecentral valueschoseninthemodelalongwiththerangeexploredinthesensitivityanalysis,whichcoversthe valuesreportedintheliterature(lastcolumn).
Therobustnessofournumericalresultstothesekeyparametersistestedbysimulatinganumber ofadditionalscenariosinwhichLBR,LBD,andSPILLareperturbedtothevalueindicatedinTable6. Wealsoanalysetheextremecasesinwhichtechnologicalexternalitiesareexcluded.Weconsiderthe fourceilingsontradeexaminedinSection3.2,namely0,10,15,and20%.Itshouldberecalledthat theselimitsareremovedafter2045,whenfulltradeisallowed.
Fig.5showstherelationshipbetweeninvestmentsininnovationandcleanenergytechnologies andpermittraderestrictions.Itconfirmsthepatternobtainedwiththesimplernumericalmodel,in Fig.1.LimitingtradeincreasesR&Dandinvestmentsintechnologiessubjecttotechnologicalprogress, foralltheparameterisationsconsidered.Fortraderestrictionsbetween20and15%,varying knowl-edgespillovershasmildimpactsoninnovationinvestmentsandallmarkersareclusteredaroundthe
0 50 100 150 200 250 300 20% 15% 10% 0% US$ B illio n s -d iff er ence comp ar ed to fu ll tr ade Traderestricon, α LBDp50 LBDm50 LBRp50 LBRm50 SPILLp50 SPILLm50 SPILLm25 SPILLp25 LBDp25 LBDm25 LBRm25 LBRp25 LBDm40 LBDp40 LBRm40 LBRp40 Central w/oLBD and LBR w/oLBD,LBR,SPILL
Fig.5. Technologicalchangeforatraderestrictionof20%,15%,10%and0%until2045,andforrangingparameters.Differencein
cumulativeinvestments(2005–2040)inenergyR&Dandrenewableelectricityrelativetothefreetradecase(Billions2005US$).
-20 -15 -10 -5 0 -2.50 -1.50 -0.50 0.50 1.50 2.50 Central LBDp50 LBRp50 LBRm50 SPILLp50 LBDp25 LBRm25 LBDm25 LBRp25 SPILLm50 SPILLm25 LBDm40 w/oLBD,LBR, SPILL w/oLBD andLBR LBRm40 LBDp40 LBRp40 LBDm50 SPILLp25 Disc ounted consumpon in OECD. Differenc e relave to the full trade case ( Trillions 2005U S$)
Discountedconsumpon in non-OECD. Difference relavetofull trade (Trillions2005US$)
Fig.6.Efficiencygainstraderestrictionsequalto20%(topmarkers),15%,10%,and0%(bottommarkers)forranging
param-eters.Lowerleftquadrant:worldwithouttechnologyexternalities.Lowerrightquadrant:differentparameterisationsofthe
technologymechanismsinthecalibratemodel.Differenceindiscountedconsumptionrelativetothefreetradecase(Trillions
2005US$).TrianglemarkersdenotesensitivityonLBDrates,diamondsonLBRrates,starsonSPILL.Greenmarkersdenotean
increaseintheparametervaluewhereaspinkadecrease.Thefouryellowdiamondsrepresentthecentralcase.Thebluecircles
arecasesinwhichspilloversareswitchedoff.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderis
referredtothewebversionofthearticle.)
centralvaluecase(yellowdiamond).Forthestricterlimitof0%,thechartshowsthatlarger incre-mentsininvestmentsoccurwhentheextentofspilloversisincreased(greenstars).Whentheextent ofspilloversislowercomparedtothecentralcase,technologyinvestmentsstillincrease,butbyaless amount.Thisisshownbythepinkstarslocatedbelowtheyellowdiamonds(centralcase).Limiting tradealwaysstimulatesglobalinvestmentsintechnologicalchange.Identifyingunderwhat condi-tionsthehighestincrementoccursiscomplicatedbythepresenceofseveraltechnologychannelsas wellastheothermechanisms,namelytheinternationalmarketofcarbonallowancesandoffossil fuels.
RegionalandglobalwelfareanalysisisillustratedinFig.6,whichshowstheeconomicefficiency gainsfromlimitedtrade.Moreprecisely,itshowsconsumptionchangesindiscountedUS$Trillion comparedtothefreetraderegime,forvariouscarbontraderestrictions.Positivenumbersaregains, indicatingthatconsumptionwithrestrictedtradeishigherthanwithfreetrade.Thevaluesonthe axesareconsumptionchangesforOECD(y-axis)andnon-OECD(xaxis).Togiveasenseofmagnitude, globalpolicycostsunderfreetradeamounttoaconsumptionlossof28US$Trillion(ofwhich1.88 innon-OECD, seeTable2).Thechartdepictstwodifferenthypotheticalworlds.In thelowerleft quadrant,aworldwithouttechnologyexternalitiesisshown.Inthelowerrightquadrant,different parameterisationsofthethreetechnologymechanismsincludedinthemodelarepresented.Efficiency gainsvarywithrangingtradelimits(vertically,fromthetopmarkerswhichrepresentthe20%limit tothebottommarkers,the0%limit)andoverthespaceofdifferentparameterisations(horizontally, fromthecasesofnoexternalitiesintheleftquadranttocaseswithdifferentparameterisationof externalitiesontheright).
In theabsenceoftechnologyexternalities, limitingthetradeofemissionpermitsworsensthe welfareinbothregions(leftquadrant).Thechartrepresentsthisbythetwosetsofmarkersnamed w/oLBD,LBR,SPILLandw/oLBDandLBR.Thesetwocasesillustratethehypotheticalsituationin whichtechnologicalchangeisfrozen14andtheonlymannertoreducemarginalabatementcostsisby improvingenergyefficiency.Wheninternationalspilloversareexcluded(w/oLBD,LBR,SPILL),energy efficiencycanonlybeincreasedbydomesticR&Dinvestments.Whenspilloversareincluded(w/oLBD andLBRcase),R&Dinvestmentsineachgivenregionaffectenergyefficiencyinotherregionsaswell,as describedinEq.(9).Thus,thedifferencebetweenthesetwosetsofmarkersgivesanindicationofthe welfareeffectassociatedwiththeunintendeddiffusionofknowledge.Inthepresenceoftechnology externalities,limitingpermittradealwaysbringsefficiencygainstonon-OECDcountries,butinduces efficiencylossestoOECDones(Fig.6,rightquadrant).Thisholdsforabroadenoughrangeofparameter values.
Globalwelfarearealwayshigherunderthefreetraderegime,suggestingthatthetechnology pos-itiveexternalityisnotenoughtooutweightheadditionalcostsofinnovationandtheefficiencyloss duetononequalisedmarginalabatementcosts.However,thenumericalanalysisinSection2.3points atcasesinwhichglobalgainsarepossible,especiallywhentraderestrictionsaremild.Fig.6shows that,whentheceilingis20%,theLBDm40andLBDm50casesarecharacterisedbyglobalwelfaregains. Thisresultisthecombinationofanumberofelements.First,the20%limitisbindingonlyforEurope whereasotherOECDcountries,namelytheUS,gainbecausecarbonpermitsarecheaper.Thissituation alsocreatesanincentivetoanticipateinnovationinChinaandLatinaAmerica,whicharethemajor sellersonthecarbonmarket.Inaddition,lowLBDratesarecompensatedforbyalargerinnovation effort.Whentheefficacyofexperiencetoreducetechnologycostsislow,asinthecasesLBDm#,more R&Dexpenditureisneededtocomplementthe(weaker)effectoflearning.Infact,whenLBDratesare lowtradelimitsincreasebreakthroughR&Devenmore.
Fig.6alsohighlightsthatthemagnitudeofwelfareeffectsvarieswiththenatureofthe exter-nalityconsideredandtheextentofspillovers.Thelargestimprovementsinnon-OECDarisewhen learningthroughexperienceismoreeffectiveatreducingmarginalabatementcosts(thegreen tri-anglemarkersdenotedwithLBDp#).HigherLBDratesimplythatthemarginalbenefitofagiven increaseinglobalinstalledcapacityislarger.HigherLBRrateshaveaverysimilareffect,butthe influ-enceonwelfareissmallerbecausetheextentofknowledgespilloversislessthanthatofexperience spillovers.VaryingthedegreeofR&Dspilloversisassociatedwithlimitedwelfareeffectsbecause ofthepartialappropriabilityofknowledge.Inaddition,thisperturbationchangesonlythedegree ofinternationalknowledgediffusion(ε),butitdoesnotmodifytheimpactonthecostsofabating technologies(Cax).
Allin all,policycostsvary significantlyacrossdifferentspecifications.Ifweconsiderthetwo extremecaseswithhighandlowLBDrates,globalconsumptioncostsunderfreetradealmostdouble, from0.79%to1.56%,anabsolutedifferenceofabout20US$Trillion(9US$Trillioninnon-OECD). Excludinginducedtechnicalchange(w/oLBD,LBR,SPILL)wouldincreaseglobalcoststo3.5%.Despite thesedifferences,theeffectoflesstradeoninnovationandwelfareisrobustacrossdifferent param-eterisations.
5. Someconcludingremarksandpolicyconsiderations
Thispaperexplorestherelationshipbetweentradeofcarbonallowances,theincentiveto inno-vate,technologydynamics,andeconomicefficiencywhenmultipleexternalitiesaresimultaneously considered.Usingastandardmodel,weidentifytheconditionsunderwhichrestrictionsonemission permittradingincreaseglobalinnovationandwelfare.Wethengeneralisetheanalysisusinga numer-icalintegratedassessmentmodelthatfeaturesmultipleexternalitiesandendogenoustechnological change.
Resultsindicatethatmildrestrictionstotheinternationaltradingofemissionallowancescanbe justifiedwhen emissiontradingis theonlyinstrumentavailabletopolicymakersandregionsact
0.50% 0.75% 1.00% 1.25% 1.50% 1.75% 2.00% 350 370 390 410 430 450 Consumpon lo ss (2005 -2100)
Cumulavetradedemissions
(GtCO2-eq 2005-2100)
Howmuch When Where
FullTrade 0% 2040 2035 2030 10% 15% 20% no China/India noEEX no ROW
Fig.7. Carbonmarketandglobalmacroeconomiccosts.Consumptionlossesdiscountedat3%discountrate.
non-cooperativelyoninnovation.Forcertainassumptionsregardingthewaytechnicalchangeaffects marginalabatementcost,restrictionsontheamountoftradableemissionpermitscanincreaseglobal innovationandtechnicalchange,leadingtoeconomicefficiencygains.Thesecondpartofthepaper considersaglobalstabilisationpolicyinwhichthedeveloped OECDcountriestakeonthelargest obligationsintermsofemissionreductionand,asaconsequence,arethemajorbuyersonthe inter-nationalcarbonmarket.Thenumericalanalysisshowsthatlimitingtheaccesstointernationalcarbon creditswouldmakeabatementmorecostlygloballyandfortheOECDasawhole.However,efficiency lossesaresmallformoderaterestrictionsthatlimittheuseofinternationaloffsetstoatmost15% ofdomesticregionalabatement.Internationalfinancialtransferwouldbesignificantlyreducedand moreinnovativeactivitywouldbeundertaken.Innon-OECDregions,therevenuelossesonthecarbon marketwouldbecompensatedbylowerenergypricesandhighertechnologicalspillovers.Thelatter isduetomoreinnovationbeingcarriedoutinconstrainedOECDregions.
Extensivesensitivityanalysisonthekeyparameterscontrollingtherateoftechnologicalchange andspilloversgeneralisesthevalidityoftheseresults. Forthewholespectrumofparameter val-uesanalysed,limitingpermittradealwaysbringsefficiencygainstonon-OECDcountries,provided therearetechnologyexternalities.Infact,whentheseareexcluded,bothdevelopedanddeveloping countrieswouldbeharmedbythebarrierstoemissiontrading.
Fig.7summarisestherelationshipbetweenthesizeofcarbonmarketandtheglobaleconomic costsoftheclimatepolicy.Whenmovingfromthefulltraderegimetothelimitingcaseofnopermit tradeuntil2045,thecostsoftheclimatepolicyincreasesquitesignificantly,byabout50%. How-ever,therelationbetweentradelimits andpolicycostsis quiteflatfor moderaterestrictions.A limitof15%(85%ofabatementmustbeachieveddomestically)wouldbecomparableto postpon-ingtradebetween2030and2035ortoexcludethelargersellerfromtrade.Thiswouldresultin aslightglobalefficiencyloss.Almostallpenaltiesthatarisefromtraderestrictionsarepaidbythe developedcountries,sincedevelopingcountriesarecompensatedbythepositiveexternalitiesof tech-nologicalchangeandenergymarketeffects.Afterexaminingtheeffectsonmacroeconomiccosts, financialflows,andinnovation,wecanconcludethatamoderatequantitativelimittotheuseof inter-nationaloffsets,suchasthe15%proposedinEuropeandintheUS,mightbeasecond-bestpolicy recommendation.
AppendixA.
ProofofLemma1. ReplacingthetradelimitinthefirstorderconditionsoftheHomeandForeign regions,a=˛and ¯a=1−˛,weobtain:
Homeregion
x:CX(XLIM,˛)+Gx(xLIM)=0 (a1)
a:Ca(XLIM,˛)−=pLIM (a2)
Foreignregion
x:Cx( ¯XLIM,1−˛)+Gx(¯xLIM)=0 (a3)
a:Ca( ¯XLIM,1−˛)=pLIM (a4)
BytotallydifferentiatingtheFOCsforinnovation–Eqs.(a1)and(a3)–weimmediatelyobtain theeffectoftighteningthetradepermitlimitoninnovation.Tosimplifythenotationwedropthe argumentofthecostfunctionsanddenotetheForeignregionwithabaroverthecostfunctions, CXX=CXX( ¯XLIM,1−˛),Gxx=Gxx(¯xLIM)andCX˛=CX˛( ¯XLIM,1−˛).15Usingthisnotationweobtain:
CXX+Gxx CXX CXX CXX+Gxx⎡
⎢
⎢
⎣
dx d˛ d¯x d˛⎤
⎥
⎥
⎦
= −CX˛ CX˛ApplyingCramer’srule,itcanbeshownthatinnovationintheHomeregionincreaseswiththe tradelimit: dx d˛= −CX˛(CXX+Gxx)−CXXCX˛ (CXX+Gxx)(CXX+Gxx)−(CXX)(CXX) >0 (a5)
becauseCX˛<0,CX˛<0,CXX(x,a)>0andGxx≥0,−CX˛(CXX+Gxx)−CXXCX˛≥0.Thedenominator
isalwayspositivebecause≤0,andthus(CXX+Gxx)(CXX+Gxx)>(CXX)(CXX).
Becausethetotalamountofabatementisgiven,theotherregionwillreducehisabatementeffort andthereforeinnovationwilldecreaseaccordingtoasimilarexpression:
d¯x d˛=
(CXX+Gxx)CX˛−(−CX˛)CXX
(CXX+Gxx)(CXX+Gxx)−(CXX)(CXX)
<0 (a6)
becauseCX˛<0,CX˛<0,CXX(x,a)>0andGxx≥0,hence(CXX+Gxx)CX˛+(CX˛)CXX<0.
ProofofProposition1a. Usingconditions(a5)and(a6)totalinnovationisgivenbythefollowing expression: dx d˛+ d¯x d˛= −CX˛(CXX+Gxx)−CXXCX˛ (CXX+Gxx)(CXX+Gxx)−(CXX)(CXX) + (CXX+Gxx)CX˛−(−CX˛)CXX (CXX+Gxx)(CXX+Gxx)−(CXX)(CXX)
Letusdefine=(CXX+Gxx)(CXX+Gxx)−(CXX)(CXX),where>0
dx d˛+ d¯x d˛= 1 ([GxxCX˛−CX˛Gxx]+[CXXCX˛−CX˛CXX]−[CXXCX˛−CX˛CXX]) Itfollowsthattotalinnovationincreases
dx d˛+
d¯x d˛>0
15NotealsothechangeinnotationfromC
X˛toCXatoemphasisethatweconsidermarginalvariationsinthetraderestriction,
