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Carbon Pricing and the

Elasticity of CO2 Emissions

Ryan Rafaty, Georoy Dolphin, and Felix Pretis

Working Paper 21-33

October 2021

Resources for the Future i

About the Authors

Ryan Rafaty is a political scientist by training, whose ongoing research investigates

the design, sequencing, and comparative performance of climate change mitigation

policies under varied political and economic regimes. Ryan is a Postdoctoral

Researcher at Climate Econometrics, based at Nuield College, Oxford, where

he contributes to policy-focused knowledge exchange between climatology,

econometrics, and political science. He has a doctorate from the Department of Politics

at University of Cambridge, and is a Fellow at the Cambridge Centre for Environment,

Energy and Natural Resource Governance.

Georoy Dolphin is a postdoctoral fellow at RFF and PhD graduate from the

University of Cambridge Judge Business School, where he is an ailiate of the Energy

Policy Research Group. Georoy’s research interests span political economy, energy

& environmental economics and climate policy. His research aims to inform the

development of climate policy designs that are politically sustainable while being

environmentally eective.

Felix Pretis is an Assistant Professor in the Department of Economics at the University

of Victoria, British Columbia, and the co-director of the Climate Econometrics project

based in Nuield College. He is also a James Martin Research Fellow at the Oxford

Martin School, Programme for Economic Modelling at the Institute for New Economic

Thinking, and an Associate Member at Nuield College. His work has been funded by

a British Academy Postdoctoral Research Fellowship at the Department of Economics

at the University of Oxford. Pretis has served as a visiting researcher at the University

of California, Berkeley, at the Global Policy Lab and the Renewable and Appropriate

Energy Laboratory.

Carbon Pricing and the Elasticity of CO2 Emissions ii

About RFF

Resources for the Future (RFF) is an independent, nonprofit research institution in

Washington, DC. Its mission is to improve environmental, energy, and natural resource

decisions through impartial economic research and policy engagement. RFF is

committed to being the most widely trusted source of research insights and policy

solutions leading to a healthy environment and a thriving economy.

Working papers are research materials circulated by their authors for purposes of

information and discussion. They have not necessarily undergone formal peer review.

The views expressed here are those of the individual authors and may dier from those

of other RFF experts, its oicers, or its directors.

Sharing Our Work

Our work is available for sharing and adaptation under an Attribution-

NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) license. You

can copy and redistribute our material in any medium or format; you must give

appropriate credit, provide a link to the license, and indicate if changes were made,

and you may not apply additional restrictions. You may do so in any reasonable

manner, but not in any way that suggests the licensor endorses you or your use.

You may not use the material for commercial purposes. If you remix, transform, or

build upon the material, you may not distribute the modified material. For more

information, visit https://creativecommons.org/licenses/by-nc-nd/4.0/.

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CarbonPricingandtheElasticityofCO2EmissionsRyanRafaty,GeoffroyDolphin,andFelixPretisWorkingPaper21-33October2021ResourcesfortheFutureiAbouttheAuthorsRyanRafatyisapoliticalscientistbytraining,whoseongoingresearchinvestigatesthedesign,sequencing,andcomparativeperformanceofclimatechangemitigationpoliciesundervariedpoliticalandeconomicregimes.RyanisaPostdoctoralResearcheratClimateEconometrics,basedatNuffieldCollege,Oxford,wherehecontributestopolicy-focusedknowledgeexchangebetweenclimatology,econometrics,andpoliticalscience.HehasadoctoratefromtheDepartmentofPoliticsatUniversityofCambridge,andisaFellowattheCambridgeCentreforEnvironment,EnergyandNaturalResourceGovernance.GeoffroyDolphinisapostdoctoralfellowatRFFandPhDgraduatefromtheUniversityofCambridgeJudgeBusinessSchool,whereheisanaffiliateoftheEnergyPolicyResearchGroup.Geoffroy’sresearchinterestsspanpoliticaleconomy,energy&environmentaleconomicsandclimatepolicy.Hisresearchaimstoinformthedevelopmentofclimatepolicydesignsthatarepoliticallysustainablewhilebeingenvironmentallyeffective.FelixPretisisanAssistantProfessorintheDepartmentofEconomicsattheUniversityofVictoria,BritishColumbia,andtheco-directoroftheClimateEconometricsprojectbasedinNuffieldCollege.HeisalsoaJamesMartinResearchFellowattheOxfordMartinSchool,ProgrammeforEconomicModellingattheInstituteforNewEconomicThinking,andanAssociateMemberatNuffieldCollege.HisworkhasbeenfundedbyaBritishAcademyPostdoctoralResearchFellowshipattheDepartmentofEconomicsattheUniversityofOxford.PretishasservedasavisitingresearcherattheUniversityofCalifornia,Berkeley,attheGlobalPolicyLabandtheRenewableandAppropriateEnergyLaboratory.CarbonPricingandtheElasticityofCO2EmissionsiiAboutRFFResourcesfortheFuture(RFF)isanindependent,nonprofitresearchinstitutioninWashington,DC.Itsmissionistoimproveenvironmental,energy,andnaturalresourcedecisionsthroughimpartialeconomicresearchandpolicyengagement.RFFiscommittedtobeingthemostwidelytrustedsourceofresearchinsightsandpolicysolutionsleadingtoahealthyenvironmentandathrivingeconomy.Workingpapersareresearchmaterialscirculatedbytheirauthorsforpurposesofinformationanddiscussion.Theyhavenotnecessarilyundergoneformalpeerreview.TheviewsexpressedherearethoseoftheindividualauthorsandmaydifferfromthoseofotherRFFexperts,itsofficers,oritsdirectors.SharingOurWorkOurworkisavailableforsharingandadaptationunderanAttribution-NonCommercial-NoDerivatives4.0International(CCBY-NC-ND4.0)license.Youcancopyandredistributeourmaterialinanymediumorformat;youmustgiveappropriatecredit,providealinktothelicense,andindicateifchangesweremade,andyoumaynotapplyadditionalrestrictions.Youmaydosoinanyreasonablemanner,butnotinanywaythatsuggeststhelicensorendorsesyouoryouruse.Youmaynotusethematerialforcommercialpurposes.Ifyouremix,transform,orbuilduponthematerial,youmaynotdistributethemodifiedmaterial.Formoreinformation,visithttps://creativecommons.org/licenses/by-nc-nd/4.0/.CarbonPricingandtheElasticityofCO2EmissionsRyanRafaty,∗GeoffroyDolphin∗∗andFelixPretisManuscriptVersion:October19,2021WordCount:16,022(excludingappendicesandreferences)ABSTRACTWestudytheimpactsofcarbonpricingonCO2emissionsacrossfivesectorsforapanelof39countriescovering1990–2016.Constructingnewsector-levelcarbonpricedata,weimplementanovelapproachtoestimatethechangesinCO2emissionsassociatedwith(i)theintroductionofcarbonpricingregardlessofthepricelevel,(ii)theelasticityofemissionswithrespecttothepricelevel,and(iii)thepotentialresponseoffutureemissionstopossiblecarbonpricetrajectories.Usingasyntheticcontrolfactormodel,wefindthattheintroductionofcarbonpricinghasreducedgrowthintotalaggregate(national)CO2emissionsby1–2percentonaveragerelativetoimputedcounterfactuals,withmostabatementoccurringintheelectricityandheatsector.Exploitingvariationinobservedcarbonpricestoexplainheterogeneityintreatmenteffects,wedecomposetheaveragetreatmenteffectobtainedfromthesyntheticcontrolfactormodeltodistinguishthe∗ClimateEconometricsatNuffieldCollege,UniversityofOxfordandInstituteforNewEconomicThinkingattheOxfordMartinSchool∗∗ResourcesfortheFutureandEnergyPolicyResearchGroup,UniversityofCambridgeDepartmentofEconomics,UniversityofVictoria,ClimateEconometricsatNuffieldCollege,UniversityofOxford,andInstituteforNewEconomicThinkingattheOxfordMartinSchool2effectofmerelyintroducingacarbonpricefromtheeffectofthepricelevelitself.Wefindasmallandimpreciselyestimatedsemielasticityofa0.03percentreductioninemissionsgrowthperaverage$1/metrictonofCO2.Simulatingtheresponseoffutureglobalemissionstoseveralpossiblecarbonpricetrajectories,weconcludethatcarbonpricingalone,evenifimplementedgloballyatalevelequivalenttotheworld’scurrenthighestrecordedpriceinSweden,isunlikelytobesufficienttoachieveemissionreductionsconsistentwiththeParisclimateagreement.Keywords:CarbonPricing,CO2EmissionsElasticity,CarbonTaxEffects,EmissionsTradingEffects,ClimatePolicyImpactEvaluation,GeneralizedSyntheticControl,Emissions-WeightedCarbonPrice.JELClassifications:Q43,Q48,Q54,Q58,H23.31.INTRODUCTIONPricingcarbondioxide(CO2)emissions—viaacarbontax,emissionstradingsystem,orsomehybridscheme—haslongbeenrecommendedasanintegraland,inprinciple,cost-efficientwaytoreduceemissionsandmitigatetheadverseimpactsofclimatechange(BaumolandOates1988;Nordhaus1992;Metcalf2009;Cramtonetal.2017;Stern-StiglitzHigh-LevelCommissiononCarbonPrices2017).1Sincetheworld’sfirstcarbontaxeswereimplementedinFinlandandPolandin1990,anadditional28jurisdictionshaveadoptedthem.Similarly,sincetheEuropeanUnionestablishedtheworld’sfirstemissionstradingsystem(ETS)coveringCO2emissionsin2005,thenumberofcarbonmarketshasgrownto31,withthelatestadditionsinChina,theUnitedKingdom,andGermanyin2021.Carbonpricinginitiativesnowcoverone-fifthofglobalgreenhousegas(GHG)emissions,or12gigatons(Gt)ofCO2equivalentemissionsannually.TheseinitiativesraisedpublicrevenuestotalingUS$53billionin2020(WorldBank2021).However,behindtheproliferationandpopularizationofthecarbonpricingparadigmisagreatuncertaintyoveritsroleinclimatepolicy.Criticsandendorsersalikeconcedethat“optimal”pricingschemesthatarecost-efficientandenvironmentallyeffectiveintheorymaybepoliticallyunfeasibleinpractice(Rosenbloometal.2020a;Stiglitz2019).Aclashofparadigmspersistsregardingwhatthismeansinpracticalpoliticalterms(Rosenbloometal.2020b;vandenBergh1TheoptimalcarbonpriceistypicallydefinedinrelationtoanidealobjectivefunctionthatsetsthecarbontaxrateequaltothemonetizeddamagesassociatedwithemittinganadditionaltonofCO2,referredtoasthe“socialcostofcarbon”(SCC)(GillinghamandStock2018).However,globalSCCestimatescanbeUS$10/tCO2toUS$1,000/tCO2andaboveduetotheuncertaintiesinherentindamagefunctionestimationandalternativeethicalparameters(Adler2017).Forpolicymakersseekingguidanceinsettingtheoptimalpricelevel,theunwieldyrangeofSCCestimatesisunhelpful.Thishaspromptedsomeeconomicpolicymakerstoadvanceatarget-basedapproach,wherebytheappropriatepricepathisonethatminimizesthecostofachievingadesiredquantityofCO2reductionsoveragivenperiod(Hepburn2017).4andBotzen2020).Underthe2015ParisAgreement,195countriescommittedtomitigateagainstdangerouslevelsofclimatechangethiscenturybymaintainingglobalaveragesurfacetemperaturesbelow1.5–2°Crelativetopreindustrialconditions,butthiswouldnecessitateareductioninglobalemissionsofaround50percentby2030relativeto2020(UNEP2019).2IntheEconomists’StatementonCarbonDividends(2019),whichclaimstobethelargestpublicstatementinthehistoryoftheeconomicsprofession,carbonpricingishailedasthetoolofchoicetoachievethesereductionsatthe“scaleandspeedthatisnecessary”.3AccordingtotheStern-StiglitzHigh-LevelCommissiononCarbonPrices(2017),explicitcarbonpricesintherangeof≥US$40–80/tCO2by2020and≥US$50–100/tCO2by2030willbe“indispensable”toachievingtheParisAgreementgoals,albeitwiththeprovisothattheyarecombinedappropriatelywithcomplementarypolicies.4However,suchassessmentshavereliedonexantecalibratedmodelprojectionswithlimitedempiricalcorroboration.Forcontext,currentcarbonpricesrangefrom<$1/tCO2inPolandandUkraineto$137/tCO2inSweden(innominalterms),andnearlyhalfofallcoveredemissionsworldwidearepricedatlessthan$10/tCO2(WorldBank2021).5Globally,theaverage(emissions-weighted)carbonpriceisaround$3/tCO2(Dolphinetal.2020),equivalenttoaddingapproximatelyUS$0.03pergallonofgasoline(€0.009perliterofpetrol).2Thisisanecessarybutinsufficientcondition.Afurtherrequirementisthatglobalemissionsdeclinetonetzerobyaround2050–2070.Anyirreduciblepositiveemissionswouldneedtobeoffsetbyarangeofnegativeemissionstechnologies,noneofwhichareapanaceaandallofwhichfaceconsiderablebiophysicallimits,uncertainlong-termcosts,andpoliticalcoordinationchallenges(Griscometal.2017;Hepburnetal.2019;ChatterjeeandHuang2020;Smithetal.2016).3Thestatement(2019)includesamongitssignatories3,589US-basedeconomists,fourformerchairsoftheFederalReserve,27NobelLaureateeconomists,and15formerchairsoftheCouncilofEconomicAdvisers.4AsStiglitz(2019)cautions,carbonpricepathswillinevitablyvaryacrossheterogeneoussociopoliticalandeconomiccontextsand,critically,“thereisnopresumptionthatacarbontaxalonecansufficetoaddressoptimallytheproblemofclimatechange”(emphasisinoriginal).5AsofMay2020.Allmonetaryunitsthroughoutthisstudyarein2015USdollars.5EmpiricalevaluationsoftheimpactofimplementedcarbonpricesonCO2emissionshavebeenmixed,inconclusive,and,untilrecently,strikinglyscarce.WereportthemainempiricalfindingsandevaluationmethodsofpreviousstudiesinSection3.Ourkeytakeawayfromthisburgeoningevaluationliteratureisthatthefragmentarynatureoftheevidenceprecludessystematicinferenceaboutthelikelyresponseofemissionstocarbonpricingacrossspaceandtime.AswedescribeinSection4,thepaucityofcross-countryempiricalassessmentsispartlyafunctionofthelackofstandardizedcarbonpricedataadjustedtoaccountforvariationinindustryexemptions,rebates,andsectoralcoverage.Buttheempiricalneglectcanalsobeattributedtotheconsiderableidentificationchallenges,summarizedsuccinctlybyMildenberger(2020):Carbonpollutionlevelsaresooverdeterminedbydiverseeconomicandsocialforcesthatretrospectivecausalidentificationofpolicyimpactsremainsdifficult.Economistshaveofferedevaluationsofsomepolicies,buttheseestimatesaredifficulttocompareacrosscountriesandtime.Norcanwereliablytranslatesimplepolicycontentmetrics,likeanationalcarbonpricelevel,intounitsofcarbonpollutionreduced.Evenidenticalcarbonpriceshavedifferenteffectsbasedonvariationinsectoralcostexposureandsectoraldifferencesintheelasticityofcarbon-dependentactivities.Motivatedbysimilarconcerns,wepresentaviableempiricalmodelingapproachthatlargelyovercomestheseidentificationchallenges.Untilrecently,thepersistentlackofstandardizedcarbonpricingdatahascompelledresearcherstorelypredominantlyonquasi-experimentalmethodstoestimategeneric“treatmenteffects”ofcarbonpricingwithoutspecifyingtheinitialpricelevelanditssubsequentevolutionoverthetreatmentperiod.Ineffect,essentialinformationaboutthedynamicsandfunctionalformoftherelationshipbetweenthepricelevelandemissionsisignoredoromittedperforce.Thishasprecludedpursuingconventionaleconomicinterestinestimating6empiricalelasticities(inthiscase,ofemissions,withrespecttoheterogeneouscarbonpricelevelsobservedacrosscountries,sectors,andtime).Furthermore,whentreatmenteffectsorelasticitiesareestimated,thefocushasremainedontheirstatisticalratherthaneconomicsignificance,withfewempiricallygroundedstudiesassessingwhetherpricingissufficienttoachievegovernments’emissionsreductioncommitments.Thepracticalconsequenceisthatpolicymakersandthepublicstillknowlittleabouttheenvironmentaleffectivenessofoneofthecorepillarsofclimatepolicy.6Weconstructanoveldatasetcomprisingaverage(emissions-weighted)carbonpricesacrossfivesectorsforapanelof39countriesthatimplementedacarbonpriceduring1990–2016(and164othercountriesthatdidnot),combinedwithemissionsdatafrom1975–2016.Weaimtoanswerthreequestions.First,doespricingcarbonreduceemissions?Inotherwords,whatistheeffectoftheintroductionofcarbonpricingonCO2emissions,irrespectiveofthepricelevel?Second,doesthepricelevelmatter(dohighercarbonpricesleadtogreaterreductions)?Third,iscarbonpricingsufficienttoachieveinternationalemission-reductiontargets?Wereporttwosetsofestimatedeffectsforeachsector.First,weestimatetheaveragetreatmenteffectofintroducingacarbonpriceirrespectiveofthepricelevel.Toovercomechallengesinidentifyingtreatmenteffectsusingconventionaldifference-in-differences(DiD)andsyntheticcontrolapproaches,weapplytreatmentevaluationmethodsaccommodatingstaggeredadoption(Xu2017;Atheyetal.2018)andcontrolforunobservedtime-varyingheterogeneityusing6Althoughmuchoftheacademicclimateeconomicsdiscoursehasfocusedonestimatingthesocialcostofcarbon(withaviewtodesigningsociallyoptimalcarbonpricingschemes),governmentdiscoursehasshiftedtowardamoretarget-basedapproachsincetheParisAgreement.Forexample,countriesaccountingfortwo-thirdsofglobalemissionshaveannouncedcommitmentstoachieve“net-zero”CO2emissionsbymidcenturyorshortlythereafter,raisingthequestionofwhethercarbonpricingcanplausiblyachievethedeclaredgoalsand,ifnot,whatroleitoughttoplayinthebroaderpolicymix.7interactivefixedeffects(Bai2009).Forcompleteness,wealsoreportestimationresultswhenusingconventionaltwo-wayfixedeffects(TWFE)andinteractivefixedeffects(IFE)estimators.Wefindthattheaveragetreatmenteffectimpliesastatisticallysignificant1.5percentagepointreductioninaggregate(national)CO2emissionsgrowthrelativetoimputedcounterfactualemissions.Notably,significantlygreateraveragetreatmenteffectshavebeengeneratedintheelectricityandheatsector(–2.5percentagepointsrelativetothecounterfactual).Second,wealsoproposeanewapproachtoestimatingelasticitiesfromcounterfactualestimatorssuchasthosebasedonsyntheticcontrolmethods.Specifically,weestimatethe(semi)elasticityofemissionswithrespecttothecarbonpricebyassessingwhetherheterogeneityintreatmenteffects(estimatedinthefirststage)canbeexplainedbyvariationinthetreatmentintensityprovidedbycarbonpricingschemesobservedwithinandbetweencountriesovertime.Inaddition,wereportelasticityestimatesusingsimpleTWFEandIFEmodelsoftheemissionsresponsetothepricelevel.Unlikepreviousempiricalstudiesevaluatingcarbonpricingimpacts,weexplicitlyestimatethedistincteffectsofmerepolicyintroduction(regardlessofthepricelevel)versuseffectsattributabletothepricelevelitself.Wefindthatthe(semi)elasticityeffectisnegativebutimpreciselyestimatedformostsectors.Medianestimatesforaggregateemissionssuggestareductionofaround0.03percentforeachadditional$1/tCO2,albeitwithhighuncertainty;theseresultsareonlystatisticallysignificantforthemanufacturingsector(–0.16percentforeachadditional$1/tCO2).Accountingforpossibleintroductioneffects,ourresultsshowthatthepriceeffectonCO2emissionsislowerthanfoundinpreviousstudies.Thissuggeststhatmerelyintroducinganynonzerocarbonpricereducesemissions,whereashigherpricelevels(asobservedsofar)yieldonlymarginallylargerreductions.Conversely,omittingintroductioneffectsfrommodelsoftheimpactofcarbonpricingmayleadtobiasedestimatesoftheemissionelasticity.To8explaintheseresults,weproposethattheestimatedintroductioneffectmayelicitchangesinrealizedCO2emissionsbyalteringexpectationsaboutthefuturestringencyofemission-reductionpolicies.Thisimpactisintrinsicallylinkedtohoweconomicagentsperceivethepolicyuponintroduction.7Third,toassesswhethercarbonpricingissufficienttoachievestatedemission-reductiontargets,wecombineourestimatesoftheintroductioneffectsandemissionselasticitieswithclimatemodelprojectionsofCO2emissionsfromseveralindicativereferencescenariostostudytheemissionsabatementpotentialofdifferenthypotheticalpricingschemesoverthenextthreedecades.Ouridentificationstrategyattenuatesmultiplepossiblesourcesofcarbon-priceendogeneityinthefollowingways:first,byincludingrelevantcontrolvariablesknowntoinfluencenationalproclivitiestointroduceacarbonprice8,thelevelofthecarbonprice,andCO2emissions;second,byusingfixedweightswhenconstructingtheemissions-weightedcarbonpriceseries,sothatthecomputedprices(andassociatedexemptions)areindependentofinterannualchangesinsectoralenergyuseandcarbonintensities;lastly,byallowingforamultifactorerrorstructureandapplyingtheprincipalcomponentsapproachofBai(2009)toapproximateunobservabletime-varyingcommonfactorswhicharecontrolledforinourbaselinemodelspecifications(forestimatingbothaveragetreatmenteffectsandsemielasticities).7Forinstance,LinnandLi(2014)provideevidencethatconsumersrespondmorestronglytochangesingasolinetaxesthanchangesingasolineprices.Oneexplanationtheyputforwardisthatconsumersperceivetaxesasmore“stable”(whethertheyactuallyareisadifferentquestion).AlthoughtheevidencepresentedinLinnandLi(2014)isbasedonmarginalchangesintaxrates(andretailfuelprices),itseemsplausibletoexpectsimilareffectsupontheinceptionofnewpolicyinstruments.8Includingcontrolssuchasthevalue-addedofsector-specificeconomicactivitiestoGDP,andweatheranomaliesquantifiedasheatingandcoolingdegreedays.9Thereportedresultsarerobustacrossestimationmethods(syntheticcontrols,TWFE,IFE),awiderangeofmodelspecifications(includingseparatelyassessingcarbontaxandtradingschemes),andadditionalequilibriumcorrection(EC)specificationsthataccommodateglobalstochastictrendsaffectingCO2emissions.Wearriveatanimportantresult:carbonpricingatcurrentobservedlevels,evenifimplementedglobally,isunlikelytoachieveemissionsreductionsatthescaleandspeednecessarytoachievethecommitmentsoftheParisAgreement—orevensubstantialreductionsatall.Achievingtherequisitelevelofemissionreductionsrequiresglobalcarbonpricingwithnear100percentemissioncoverageandinexcessof$250/tCO2.Itisunlikelythatcarbonpricingwillreachsuchhighaveragelevelsglobally,butthefactthattheintroductionofpricingdoesreduceemissionsmeansthatitremainsoneofmanyimportantinterventionstotackleanthropogenicclimatechange.Inparticular,ourfindingsareconsistentwiththeviewthatjurisdictionscouldachieveconsiderableemissionsreductionsbyintroducingcarbonpricingmechanismsinsectorsthatarenotcurrentlysubjecttosuchpolicies.Afterdescribingthecoreelementsofcarbon-pricingtheorythatinformourempiricalinvestigation(Section2)andreviewingempiricalevidencefrompreviouscarbon-pricingimpactassessments(Section3),wedescribethestandardizedsector-levelcarbonpricedataweconstructedtoestimateemissionselasticities(Section4).Wethenexplainouridentificationstrategy,baselinemodelspecifications,andmultistageestimationprocedure,summarizingateachstagetheassociatedcountry-andsector-levelresultsacross24modelspecifications(Section5).Afterdescribingtheestimationprocedureforsimulatingthepotentialresponseoffutureemissionstoseveralpossible10pricepathsandsummarizingtheprojectedimpacts(Section6),weconcludewithreflectionsontheoverallpolicyimplicationsofourfullsetofresults(Section7).2.CO2PRICES,MARGINALABATEMENTCOSTS,ANDEMISSIONSAnthropogenicCO2emissionsareprimarilyaby-productoftheproductionprocessincertain“dirty”sectorsoftheeconomy,whichimplicitlydefinesapollutiondemandscheduleforthatsector.9ThequantityofCO2emissionsgeneratedbythesesectorsdependsprimarilyontheirabsolutesize,thecostofavailableCO2abatementtechnologies,andtheexplicitandimplicit(shadow)priceofemissions.Therefore,foragivensetofCO2abatementtechnologies(assumingastaticmarginalabatementcostcurve),achangeinthecarbonpriceisexpectedtoinducechangesinthesizeand/oremissionsintensityofthepollutingsectors,resultinginachangeinCO2emissions“demanded”bythosesectors.10ThedemandscheduleforarisingcarbonpriceisdownwardslopingandreflectsthediminishingmarginalvaluethattheeconomyplacesonunitsofCO2.Thisgenericschemaprovidesthetheoreticalfoundationofourempiricalinvestigation.Theempiricaldiscussionrequiressomeclarificationregardingthefunctionalformoftherelationship.First,thepollutiondemandschedulecanbereinterpretedasamarginalabatementcost9.Thepollutiondemandscheduleindicatestheresponseofasector’semissionstoagivenpriceofemittingeachunitofCO2.10.Underconditionsofuncertaintyaroundthedemandschedule,thequantityofCO2emissionreductionsassociatedwithagivencarbonpricewilldependonthetypeofpolicyinstrumentthelegislatureorregulatoryagencychooses.Astrictlypositivepricesignalshould,inprinciple,triggerCO2abatementactivity.However,ifthemarginalproductofabatementisboundedabove,thenitislikelythatfirmsandindividualswillonlyundertakeabatementactivitiesifthecarbonpriceisaboveacertainthreshold(CopelandandTaylor2003).TheavailableevidencereviewedinSectionIII,however,suggeststhatcarbonpriceshavetriggeredatleastsomeCO2abatement.11schedule:giventhatthedemandscheduleprovidesinformationaboutthemarginalwillingnesstopayforemissions,italsoconstitutes—whenreadintermsofCO2abatement—themarginalcosttotheeconomyofrestrictingemissions.TheoreticaldiscussionsoftherelationshipbetweenCO2emissionsandtheirpriceoftenassumethatitisnonlinear(Nordhaus1993).Thatis,atlevelsofemissionsclosetoaneconomy’sbusinessasusual(BAU)emissions,pricingCO2atagivenratewillresultinrelativelylargeemissionreductions,ceterisparibus.ButatemissionlevelsfarfromBAU,asimilarincreaseinpricewillgeneratelessCO2abatement(astheeasierandcheaperabatementoptionshavealreadybeenexploited).StudiesofCO2abatementoptionshave,however,foundthemarginalabatementcostcurvesforspecificjurisdictionsorregionstobemostlylinearatlowcarbonprices,withcostsrisingsteeplyonlytowardtheendofthecurve(GoulderandHafstead2017).EmpiricalCO2demandschedulesthereforeappeartobemuchflatterthantheoreticallyassumed,atleastatthehistoricallyimplementedcarbonpricelevelsconsideredherein(seeSectionIV).ThishasimportantimplicationsfortheempiricalrelationshiptobeexpectedbetweencarbonpricesandassociatedchangesinCO2emissionlevels.Wetakethistosuggestthat,fortheperiodanalyzedhere,theappropriatemodelspecificationmaybelinear.WereturntothequestionoffunctionalforminAppendixCwithmisspecificationtestsofourbaselinemodelformulation;ultimately,thetestscorroborateourinitialconjecturethatnonlinearrelationsareabsentornondetectableintheshortsampleandinsignificantathithertoobservedcarbonpricelevels.Weconcludethatalinearspecificationisappropriate.123.EVIDENCEFROMPREVIOUSEVALUATIONSStudiesinvestigatingtheresponseofCO2emissionstoacarbonpricefallintotwobroadcategories:(i)exanteprojectionstypicallybasedoninput-outputmodels,computablegeneralequilibrium(CGE)models,orlargeintegratedassessmentmodels(IAMs);and(ii)expostevaluationsusingobservationaldata,typicallybasedonquasi-experimental,instrumentalvariable(IV),orpanelregressionmethods.Moststudiesareintheformercategory,generatingpolicy-responseestimateswhosewiderangeislargelyareflectionofaprioriassumptionsregardingoutputandpopulationsizeinbaselinescenarios,futuretechnologycosts,andotherunknownparameters,includingthepriceelasticityofCO2emissionsitself(forarangeofperspectives,see,e.g.,Barronetal.2018;Fawcettetal.2014;GoulderandHafstead2017;Edenhoferetal.2010;Mercureetal.2016;EllermanandBuchner2008).11Ourstudyisconcernedprincipallywithretrospectivepolicyevaluation,sowefocusonexpostmethodshenceforth.Incontrasttosimulation-basedassessments,expostevaluationshaveremained—untilrecently—comparativelyscarceandrarelypresentelasticityestimatesorcounterfactualprojectionsofemissions,despitetheirpotentialtoprovidemorerobustevidenceaboutreal-worldpolicyimpactsthancanbeobtainedviatheoreticalconsiderationsorexanteprojectionsalone(see,e.g.,discussionsinOECD1997;Andersen2004;EkinsandBarker2001;Cropperetal.2018).Consistentwiththisview,arecentassessmentofBritishColombia’scarbontaxinCarboneetal.(2020)findsthatthesignandmagnitudeofthepolicycoefficient(s)estimatedviaareducedform11Thegeneraltendencytorelyonexantemodelsisunderstandablegiventhedata-relatedchallengesofempiricalcarbonpricingevaluations(seeSectionIII),thescarcityofreal-worldcarbonpricinginitiativesuntilthepastdecadeorso,andthegrowinginterestofpolicymakersinacquiringreasonableprojectionsofthelikelyenvironmentalandmacroeconomicimpactsofcarbonpricingproposalsoverthecomingdecades.13econometricpolicy-responsemodelcorrespondcloselywiththosederivedfromalargeCGEmodel,suggestingthattheformerarenotdistortedbygeneralequilibriumeffectsandcanprovideempiricalevidencethatinformssubsequentparametrizationofthestructuralmodel.TheavailableevidencesummarizedinTableIhasbeenmixedandsomewhatinconclusive.Nevertheless,wecaninferafewbasicfactsfromthisliterature:(i)existingemissionsresponseestimatesareheterogeneousacrossregionsandsectors,anditremainsdifficulttodrawsystematiccomparisonsofpolicyimpactsacrossspaceandtime;(ii)ingeneral,expostevaluationsdetectlessCO2abatementthanexantestudies(butwehesitatetomakeanysystematiccomparisonsgiventhefragmentarynatureoftheavailableevidence;forrecentmeta-analysesofthecarbon-pricingevaluationliterature,seeGreen(2021)andLilliestametal.(2021));and(iii)researchersaspiringtoattributechangesinemissionstocarbonpricinginstrumentshavetypicallyadoptedaquasi-experimentalapproachusuallybasedontraditionalDiDorsyntheticcontrolestimators,whichrestrictthepolicyvariabletoabinaryspecification.Asafinalnoteconcerningtheevaluationliterature:tothebestofourknowledge,onlyonestudy,Bestetal.(2020),hasattemptedtoestimateemissionselasticitiesinacross-countrypanelusingstandardizedcarbonpricedata,albeitoverashortertimehorizon.12However,itdoesnotestimatecounterfactualemissions,relyinginsteadoncausalinferencebasedoncorrelationalevidencefromTWFEpanelregressionswithnumerouscontrols.13Furthermore,itdoesnotdifferentiatebetween12Bestetal.(2020)useOECDdataon“effectivecarbonrates,”buttheavailabletimehorizonisshort(2012–2017).13TheincludedcontrolvariablesareGDPpercapitagrowth,populationgrowth,thenetgasolinetax,fossilfuelsubsidies,scoresforenergyefficiencyandrenewableenergypolicies,andabinarydummyindicatingthepresence/absenceoffeed-intariffs.14introductionandpriceeffects(whichcanbiaselasticityestimates,aswefindinSection5),nordoesitassesstheestimatedeffectsizesinrelationtoemission-reductiontargets.TableI.EmpiricalevaluationsofimplementedcarbonpricesandassociatedCO2emissionreductionsStudyJurisdiction(s)PeriodEstimatorPolicyinstrumentOutcomevariableChangeinemissionsoverentireperiodChangeinemissionsperyearAbrelletal.(2011)EU2005–2008PropensityscorematchingforpricedandunpricedfirmsEUETSCO2emissionsgrowthrate(firmlevel)–3percentin’07/’08relativeto’05/’06(–6percentforfirmswithgreatestdecreaseinfreeallocation)N/AGloaguenandAlberola(2013)EU2005–2012PropensityscorematchingEUETSCO2emissions–10percent(100MtCO2)upperboundN/ABelandJoseph(2015)EU2005–2012Arellano-BondIVwithlagsasinstrumentsEUETSElectricityandindustrysectorCO2emissions33to41MtCO2over8yearsduetoETS,or–12percentfromtotalN/ADechezleprêtreetal.(2018)EU2005–2012DiDEUETSCO2emissions(plantlevel)–6percentduringPhaseI(2005–2007)and–15percentduringPhaseII(2008–2012)–2percentduringPhaseIand–3percentduringPhaseII15BayerandAklin(2020)EU1990–2016GSCmethodwithIFEmodel(syntheticcontrolgroupcomposedofunpricedsectors)EUETSSector/industryCO2emissions(energy,metals,minerals,chemicals,andaggregateforpricedsectors)–7.5percent(–1.2Gt)onaggregateacrosspricedsectorsfrom2008–2016N/AKlemetsenetal.(2016)Norway2001–2013DiDEUETSCO2emissions(plantlevel)SignificantreductionsonlyduringPhaseII(2008–2012)N/ADussaux(2020)France2014–2018Regression-basedcounterfactualinferenceCarbontaxManufacturingsectorCO2emissionsN/A–5percentin2018Wagneretal.(2014)Germany1995–2010DiDEUETSCO2emissions(plantlevel)–20percentduringPhaseIINASchäfer(2019)Germany2005–2015Regression-basedcounterfactualEUETSElectricitysectorCO2emissions<6percentoftotalemissions;for2005–2007:reductionof10.5–31.4MtCO2;–2.0percentemissionintensity(firsttradingperiod),–2.9percent(secondtradingperiod),–1.2percent(years1–3ofthirdtradingperiod)Timetrendleadsto–.5percentofemissionsintensityp.a.JaraiteandDiMaria(2016)Lithuania2003–2010DiDEUETSCO2emissions(plantlevel)InsignificantInsignificant16MetcalfandStock(2020b)EU1990–2018PanelOLSwithLPmethodandpanelSVARCarbontaxesGrowthrateoftotalCO2emissions(countrylevel)–4to–6percentover6yearsfora$40/tCO2taxcovering30percentofCO2emissionsN/AMurrayandManiloff(2015)RGGIstates(US)1991–2012PanelOLSwithsimulatedcounterfactualRGGUCO2emissions–24percentrelativetocounterfactualMartinetal.(2014)UnitedKingdomTwo-stageleastsquaresIVUKClimateChangeLevyManufacturingsectorCO2emissions(plantlevel)–7.3percentN/AAbrelletal.2020UnitedKingdom2013–2016ML-basedcounterfactualinferenceUKCarbonPriceSupportElectricitysectorCO2emissions(highfrequencyplant-leveldata)–6.2percentN/AGugleretal.2020UnitedKingdom2012–2016RDiTUKCarbonPriceSupportElectricitysectorCO2emissions(highfrequencyplant-leveldata)–26.2percentN/ALeroutier(2018)UnitedKingdomSyntheticcontrolmethod(donorpoolcomposedofEUcountries)UKCarbonPriceSupportElectricitysectorCO2emissions(highfrequencyplant-leveldata)–49percentN/AAndersson(2019)Sweden1960–2005DiDandsyntheticcontrolCarbontax(transportsector)TransportsectorCO2emissionsN/A–6.3percentperyearonaverage(1990–2005)LinandLi(2011)Denmark,Finland,Netherlands,Norway,SwedenInceptionto2008DiDCarbontaxesTotalpercapitaCO2emissionsN/A–1.7percentdeclineingrowthrateinFinlandonly17RiversandSchaufele(2015)BritishColumbia1990–2011PanelmodelregressionwithsimulatedcounterfactualCarbontaxProvince-levelCO2emissionsfromgasolineconsumptionrelativetotherestofCanada–2.4Mt(over4years)–0.6MtLawleyandThivierge(2018)BritishColumbia2001–2012(2008–2012treatmentperiod)DiDCarbontaxProvince-levelCO2emissionsfromgasolineconsumptionrelativetotherestofCanada–1.13percentto–4.87percent(5years)<–0.97percentErutkuandHildebrand(2018)BritishColumbia1991–2015DiDCarbontaxCO2emissionsfromgasolineconsumptionrelativetotherestofCanada–0.26percentto10.3percent(5years)<–2percentPretis(2019)BritishColumbia1990–2016DiD,syntheticcontrol,andbreakdetectionCarbontaxAggregateandsectoralCO2emissions–19percent(DiD)and–3to–15percent(synth)forroadtransportCO2emissions(2008–2016)+$5/tCO2increase→–1percentreductioninroadtransportemissionsBestetal.(2020)42countries2012–2017Cross-sectionalandpanelregressionswithmanycontrols“Effectivecarbonrate”includingtaxesandETSsGrowthrateofroadtransportCO2emissionsandaggregateemissionsofallnonroadsectors–2percentrelativetocountrieswithoutaprice–.03percentfora€1/tCO2priceincreaseRunstandThonipara(2020)Sweden1990–2016DiDandsyntheticcontrolCarbontaxEmissionsintheresidentialbuildingssector–200–800kgpercapitainresidentialbuildingsN/A18Colmeretal.(2020)France(EUETS)1996–2012DiDETSEmissionsandemissionsintensityinmanufacturingsectorN/A–8.2percentrelativetounregulatedfirmsand–10.7percentemissionsintensityofvalueadded4.EMISSIONS-WEIGHTEDCARBONPRICEDATAEconomictheoryhaslongrecommendedusingasingle,uniformpricesignaltoreduceCO2emissionsatminimalcost,14providedthatthepublicauthoritycancrediblycommittoanescalatingpricepath(ordecliningemissionscap)andassumingtheabsenceoftransactioncosts.15Contraryto“first-best’”theory,practicalexperienceshowsthatgovernmentsareroutinelyconstrainedbydomesticpoliticaleconomyconstraintsthatinhibitoptimalcarbonpricing,andthetransactioncostsofimplementingandsustainingcarbonpricinginstrumentsinsomesectorsarefarfromtrivial.14TheexternalityassociatedwitheachtonofCO2emittedtotheatmosphereisthesameregardlessofitssource(i.e.,country,sector,ortechnology).Therefore,assumingapolicymakerwantstosetthecarbonpriceequaltothemonetizeddamagesfromemittinganadditionaltonofCO2,anydeparturefromasingle,economywidepricesignalwillinevitablyintroducedistortionsbetweensectorsand/ortypesofconsumers.Followingthese“first-best”policyprescriptions,theIntegratedAssessmentModels(IAMs)citedbytheIntergovernmentalPanelonClimateChange(IPCC)assumethatimplementedcarbonpricesaremoreorlesseconomywide.15Iftransactioncosts(e.g.,ofmonitoringandverifyingemissions)arepositive,thenoptimalcoveragemaynotbe100percent.Inthatcase,emissionsshouldbeincludedonlyifthemarginalbenefitintermsofenhancedcostefficiencyoutweighsthemarginalcostofmonitoringandverifyingemissions.IfonlyCO2emissionsarecovered,variousstrategicpointsexistatwhichfossilfuels,forexample,canbepricedupstream,midstream,ordownstreamtominimizetransactioncosts.However,technicaldifficultiesinhibitimplementingschemescoveringothergreenhousegases,soitmightbesuboptimaltoaimfor100percentcoverageofGHGemissions.19FromtheUnitedStatesandBraziltoIndiaandRussia,thelargestcarbon-exposedbusinesseshaveinvestedinlobbyingactivitiesandtacticalrent-seekingtopreventcarbonpricing(MengandRode2019;Stokes2020;Mildenberger2020;Martus2019;Gershkovich2019;Senguptaetal.2019;Grubb2014;Helm2010;Jenkins2014).Notably,thisincludestheorganizedoppositionofpeakbusinessassociationsrepresentingindustriesotherthanfossilfuels,whichareexposedtocarboncostsindirectlythroughextensivesupplychainlinkages(Coryetal.2020).Inlargecoal-producingcountrieswithinordinatelymoney-drivenpoliticalsystems,suchastheUnitedStatesandIndia,theroleofcampaigncontributionsduringmultibillion-dollarelectioncyclescannotbediscountedasaconsiderabledeterrentagainstraisingclimatepolicyasacentralcampaignissue(Fergusonetal.2013;ChamonandKaplan2013).Beyondheedingtheconcernsofdomesticindustry,politiciansofnearlyallideologicalstripeshavebeencautiouslyreluctanttorousecivicoppositionfromtax-aversevoterstoanysalientriseinconsumerenergypricesthatmightbeattributedtoacarbonpricingscheme.Suchdistributionaleffects,sometimesrealbutoftenexaggeratedorcontrived,accountforpersistentlylowpricesandcoverage(Grubb2014;Helm2010;Jenkins2014;Dolphinetal.2020).Hence,carbontaxesandETSshavetypicallybeenimplementedinalimitednumberofsectorsandattenuatedbyindustryexemptions,rebates,andomittedfuels(MetcalfandWeisbach2009;Martinetal.2014b;Edenhoferetal.2014;OECD2018).Itisthusunsurprisingthatgovernmentshavesoughttoreduceaggregateemissionsbyemployingadiversemixofpolicyinstruments,16thecombinedenvironmentalimpactofwhichcouldbesimilartoasinglehigher(andmoreblunt)carbonpricebutwhichmayfacelessindustryresistance.Furthermore,theuseofmultiplepolicy16Examplesincludeproductstandards,buildingregulations,emissionlimitsforpowerplants,renewableenergyauctions,R&D,grantsandsubsidies,publicinfrastructureinvestments,andproductbans.20instrumentsmaybeintendedtoachievemultiplepolicyobjectivessimultaneously(e.g.,governmentshavealsocitedgoalsofsupportingR&Dandindustrialpolicyinnascentgreentechnologiesandreducingairpollution).Theobservedpatternisconsistentwiththeprinciple,popularizedbyTinbergen(1952),thatweneedatleastasmanypolicyinstrumentsasmarketfailurestobecorrected.17Climatechangeneednotbetheonlymarketfailure.Thishasintroducedamajorimpedimenttoeconomywide(letalonecross-country)empiricalevaluationsofprice-inducedCO2emissionsabatement.Coefficientestimatesbasedonnominalpricedataareonlyrobustandcomparableifemissionscoverageisassumedtobeconsistentacrossunitsandtime,18whichiscompoundedbytherelativelyshorttime(<5years)coveredbyavailablecarbonpricedatasources(OECD2018;WorldBanketal.2018;WorldBank2021).Weovercomethisimpediment19bycompilingemissions-weightedcarbonprice(ECP)dataatasectorlevelforapanelof39countriesfrom1990to2016.TheECPdatahavebeenupdatedfromtheoriginalaggregate(economywide)CO2pricespresentedinDolphinetal.(2020).Weapplythesamemethodologytoobtainnotonlytheaggregate(economywide)ECPseriesbutalsosector-levelCO2pricesfor(i)electricityandheat,(ii)manufacturing,(iii)roadtransport,and(iv)commercialandresidentialbuildings.TheECPineachsectorkofeachcountryiiscomputedusing17InthehypotheticalsituationwhereapolicymakerwantstoachieveonlythegoalofreducingaggregateCO2emissions,perhapsnootherpolicyrivalsacarbontaxintermsofitstheoreticalcapacitytocovertheentiretyofemissionsgeneratedbyaneconomyviaasingle,encompassingpolicyinstrument.18AstheWorldBanketal.(2018)emphasize:“Pricesarenotnecessarilycomparablebetweencarbonpricinginitiativesbecauseofdifferencesinthesectorscoveredandallocationmethodsapplied,specificexemptions,anddifferentcompensationmethods.”Followingstandardpractice,WorldBanketal.(2018)presentdataonnominalcarbonprices,whichdonottakeintoaccountthesecross-nationaldifferences.19Indoingso,weavoidaparticulartypeofviolationofthe“stable-unit-treatment-value”assumption,arequiredassumptionwhenusinganyquasi-experimentalestimatorwithinthepotentialoutcomesframework(see,e.g.,thediscussioninFrölichandSperlich2019).21coverageandpriceinformationatthesector-fuellevel,incombinationwithsector-fuelCO2emissionsdata.AsummaryofthecomputationprocedureispresentedinAppendixA,andafullmethodologicaldescriptionisavailableinDolphinetal.(2020).Tothebestofourknowledge,theECPdataconstitutethefirstcentralizedandsystematicassessmentprovidingaconsistentdescriptionofcarbonpricesthatsimultaneouslyprovidespricelevelinformationdisaggregatedatthesectorlevel,extendsbackto1990toincludepriceinformationfortheearliestcarbontaxpolicies,andaccountsforasmanysector(-fuel)exemptionsasaccuratelypossible.AmajorbenefitoftheECPisthatitenablesaconsistentbasisformeasuringtheprice-inducedincentivetoreduceaggregateCO2emissionscross-nationally,makingcarbonpricestrulycomparableforpaneleconometricpurposes.20GiventhatECPdatawasunavailableuntilrecently,previousexpostevaluationswerelimitedtoestimatingtreatmenteffectsthatcapturetheimpactofpolicyimplementationirrespectiveoftheCO2pricelevel.21Thisstudygoesonestepfurtherandestimatesnotonlythegenerictreatmenteffectbutalsoemissionselasticitieswithrespecttothelevelandyearlychangeofprices.OurmainresultsuseourECPdatacombiningemissionstradingschemesandcarbontaxes.Weconsiderresultsdisaggregatedbyschemetype(ETSorcarbontax)insection5.3.2andAppendixF.20Dolphinetal.(2020)originallydevelopedtheECPdataandmethodologytoidentifythedeterminantsofcarbonpriceadoptionandstringency(i.e.,ECPasadependentvariable);weusetheECPforthefirsttimeasanindependentvariable.21Thefewstudiesincorporatingempiricalinformationoncarbonpricelevelswithinaquasi-experimentalevaluationframeworkwereconfinedtoone(orafew)jurisdictions(e.g.,Andersson2019;Pretis2019).22Table2highlightsthedisparitybetweennominalandemissions-weightedcarbonprices.Forexample,Sweden’snominalpricewas$130/tCO2in2015,butitsaverageECP(accountingforexemptionsandcoveragerestrictions)wasapproximately$76/tCO2.Likewise,Switzerland’shighestnominalpricein2015was$50/tCO2,butitsaverageECPwasunder$15/tCO2.Amoregranularlookattheheterogeneityanddispersionofcarbonpricelevelsandcoverageovertimeisprovidedviatime-seriesheatmapsinFigure1.EquippedwiththeECPdata,weproceedinSection5todescribeouridentificationstrategy,baselinemodelspecifications,andmultistageestimationprocedure,presentingtheresultsofeachestimationstagealongtheway.23TableII.Nominalvs.Emissions-WeightedCarbonPricesinSelectedJurisdictions,2015(US$/tCO2)NominalCO2priceEmissions-weightedCO2pricePercentdifferenceDenmark2621.38–17.8Finland6445.14–29.5France168.77–45.2Germany105.80–42Ireland2217.21–21.8Italy94.70–47.8Japan21.34–37.8NewZealand54.53–9.4Norway52520SouthKorea97.66–14.9Sweden130114.80–11.69Switzerland6217.70–71.45UnitedKingdom2814.57–47.96Note:Allpricesarein2015US$.NominalcarbonpriceinformationisobtainedfromWorldBankandEcofys(2015)andbasedonthehighestnominalpriceleviedwithinthejurisdictionin2015,withoutaccountingforsectoral,industrial,orfuel-specificexemptions.TheECPvaluesarebasedontheaverage(economywide)CO2pricelevel.24FigureI.CarbonPriceCoverageandStringencyAcrossCountriesandSectors(1990–2016)Note:Color-codedtilesindicateacarbonpricinginitiative(taxand/orETS)inagivenyear,withdarkertilesreflectinghighercarbonpricelevels(2015US$/tCO2).Basedonemissions-weightedcarbonpricedataupdatedfromDolphinetal.(2020)forsectoralanalysis.255.ESTIMATINGTHEIMPACTSOFCARBONPRICINGUsingsector-levelobservationsonemissions,wefirstestimatetheaveragetreatmenteffectonthetreatedoftheintroductionofcarbonpricingonthegrowthrateofCO2emissions(irrespectiveofthepricelevel)usingTWFE,IFE,andgeneralizedsyntheticcontrolmethodsforpolicyevaluationunderstaggeredadoption(multipletreatedunitsintroducethepolicyatvaryingpointsintime)(Xu2017;Atheyetal.2019;seeSection5.1).UsingECPdata,wequantifythesemielasticityofCO2emissionswithrespecttothecarbonpricelevel,allowingforbothintroductionandpriceeffects.Weproposeanewapproachtoestimateelasticitiesfromcounterfactualestimators(specifically,syntheticcontrols)bydecomposingvariationinthetreatmenteffectusingvariationinthetreatmentintensityprovidedbydifferentlevelsofcarbonpricing(Section5.2).5.1TheAverageEffectofIntroducingaCarbonPrice(AverageTreatmentEffect)Tounderstandthenetimpactoftheintroductionofcarbonpricingirrespectiveofthepricelevel,wefocusonthesector-specificaveragetreatmenteffectonthetreatedonthegrowthofCO2emissions.WefirstconsiderasimpleTWFEmodel,whichweexpandtoanIFEspecificationandageneralizedsyntheticcontrolmodeltoaddressconcernsaroundestimatingtime-varyingandheterogeneoustreatmenteffects.Asastartingpoint,weconsiderasimpleTWFEmodelofCO2emissionsgrowthincountryi,sectork,andyeart:26Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝛿𝛿𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜏𝜏𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡,(1)forcountries𝑖𝑖∈1,2,…𝑁𝑁𝑐𝑐𝑐𝑐,𝑁𝑁𝑐𝑐𝑐𝑐+1,…,𝑁𝑁,sectors𝑘𝑘∈𝑘𝑘𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚,𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒_ℎ𝑒𝑒𝑒𝑒𝑒𝑒,𝑘𝑘𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏,𝑘𝑘𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟,𝑘𝑘𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,where𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡isatreatmentindicatordenotingthepresenceorabsenceofacarbonpriceattime𝑡𝑡,and𝛿𝛿𝑘𝑘denotestheparameterofinterest—thesector-specifictreatmenteffect,capturingthechangeinemissionsattributedtothecarbonpriceconditionalonitsintroduction.Country-sectorindividualfixedeffectsaregivenby𝜉𝜉𝑖𝑖,𝑘𝑘,year-sectorfixedeffectsaregivenby𝜏𝜏𝑘𝑘,𝑡𝑡,and𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡denotesunobservedidiosyncraticmeanzeroshocks.Wecontrolforqobservedtime-varyingcovariates𝑥𝑥′=[𝑥𝑥′1,…,𝑥𝑥′𝑞𝑞]′,includingthecountry-levelpopulationgrowthrate,growthinrealaggregateGDP(anditssquare),andgrowthinsector-levelGDP(anditssquare)whereavailable.22Weinvestigateawiderangeofspecificationsinrobustnesschecks(SectionV.4),includingpopulation-weightedheatingandcoolingdegreedays(HDD,CDD),ascontrolvariablestocapturetheimpactofweatheronenergydemandandemissions(Mistry2019).TheTWFEmodelin[1]includescountry-sectorandyear-sectorfixedeffects;however,theremaybeamyriadofunobservedcommonshocksexpressedaslatentcommonfactorsandaffectcountriesandsectorsdifferently.Wethereforeexpand[1]toanIFE(Bai2009)wherewetreattherlatentcommonfactors𝐹𝐹𝑡𝑡andcountry-sectorspecificfactorloadings𝜆𝜆𝑖𝑖,𝑘𝑘′asIFEparameterstobeestimatedasameansofcontrollingforunobservedheterogeneity:22Additionalcovariatesincludedinthesector-levelmodelsincludemanufacturingGDP,transportGDPfortransportemissions,andservicesandretailGDPforbuildingemissions(UNCTAD2020a).SeeAppendixBforasummaryofallobservedcovariatesincludedinthemodelspecifications.27Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝛿𝛿𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜆𝜆𝑖𝑖,𝑘𝑘ʹ𝐹𝐹𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡(2)The(𝑟𝑟×1)vectorFt=[𝐹𝐹1𝑡𝑡,…,𝐹𝐹𝑟𝑟𝑟𝑟]′denotesunobserved(latent)commonfactorsthatmaybecorrelatedwithΔlog(𝐶𝐶𝐶𝐶2),𝐷𝐷,and𝑥𝑥′;λi,k=[λ𝑖𝑖,𝑘𝑘,1,…,λ𝑖𝑖,𝑘𝑘,𝑟𝑟]′isan(𝑟𝑟×1)vectorofunknownheterogeneousfactorloadings.𝐹𝐹𝑡𝑡mayrepresentcommonshocks(e.g.,internationalclimateaccords,pandemics,financialcrises),unobservablenationaltrends(e.g.,motivationtomitigateclimatechange),co-movementsinthevolatilityofinternationalcoal,oil,andgasprices,theconfluenceofdeindustrializationinOECDcountriesandrapidindustrializationinAsia,downward-slopingtechnologylearningcurves(e.g.,solarPV,wind,andbatterystorage),orcross-sectionallycorrelatedclimatictrends(e.g.,theeffectofwarmertemperaturesonenergydemand).Wearefacedwithmultipletreatedcountriesimplementingcarbonpricingschemesatdifferenttimesandpotentiallyexhibitingdistinctpretreatmenttrends.ConventionalTWFEandIFEestimatorsrelyontherestrictiveassumptionofparalleltrendsintheoutcomesoftreatedandcontrolunits.Further,bothbasespecificationsoftheTWFEandIFEmodelsin[1]and[2]arerestrictiveintermsofheterogeneityandstabilityofthetreatmenteffects.Theeffectofcarbonpricingonemissionsgrowthmaydifferbycountryandbenonconstantovertime.Toallowforheterogeneityandtime-varyingtreatmenteffectsandrelaxtheparalleltrendsassumption(andavoidproblemsofestimatingtreatmenteffectsinstaggeredadoptionsettings;see,e.g.,Goodman-Bacon2021,deChaisemartinandD’Haultfoeuille2020,Bakeretal.2021,CallawayandSant’Anna2020),weemployrecentdevelopmentsincounterfactualestimationwithstaggeredadoption.Specifically,weapplythegeneralizedsyntheticcontrolestimatorproposedbyXu(2017)basedonpanelIFEmodels(Bai2009).Intuitively,thisapproachusesthepretreatmentperiodtoestimatean28IFEmodelthatisusedtoprojectanuntreatedcounterfactualforthetreatedunits.WealsoreportresultsusingthematrixcompletionestimatorofAtheyetal.(2018)inourrobustnesschecks.WemodeltheCO2emissionsgrowthrateinsectorkofcountryiattimetusinganIFEmodelthatcanbewrittenasΔlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜆𝜆𝑖𝑖,𝑘𝑘ʹ𝐹𝐹𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡(3)forcountries𝑖𝑖∈1,2,…𝑁𝑁𝑐𝑐𝑐𝑐,𝑁𝑁𝑐𝑐𝑐𝑐+1,…,𝑁𝑁,sectors𝑘𝑘∈𝑘𝑘𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚,𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒_ℎ𝑒𝑒𝑒𝑒𝑒𝑒,𝑘𝑘𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏,𝑘𝑘𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟,𝑘𝑘𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,wherethetreatmenteffect,𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡,maybeheterogeneousoveriandpotentiallytimevarying,capturingthechangeinemissionsattributedtothecarbonpriceconditionalonitsintroduction.Thebaselinemodelspecificationincludesunitfixedeffects,𝜉𝜉𝑖𝑖,𝑘𝑘,whichenterthemodeladditively,andfactorsFcapturepotentialcommonlatenttrends.Ourbasemodelincludesbothunitandtimefixedeffects,andweassesstherobustnessofourresultstothechoiceoffixedeffectsinSection5.3.Bai(2009)showsthatwhenTislargeandofcomparablesizetoN,ashere,leastsquaresestimationofmodel(1)isrobusttoserialcorrelationandheteroskedasticitiesofanunknownformintheidiosyncraticerrors.23AsinBai(2009),wemakenoassumptionaboutwhether𝐹𝐹𝑡𝑡and𝜆𝜆𝑖𝑖,𝑘𝑘′haveazeromeanorareindependentovertime.𝐹𝐹𝑡𝑡mayaffectCO2emissionsonly,butitalsomaycorrelatewithtreatmentassignment𝐷𝐷,thecarbonpricelevel𝑝𝑝𝑖𝑖,𝑘𝑘,and/ortheobservedcontrolvariables𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡′.Thefactorloadings,𝜆𝜆𝑖𝑖,𝑘𝑘′,capturetheheterogeneouseffectsthatthecommonfactorsgenerateineachcountryandsector.Although𝐹𝐹areunobservedandtheirtruenumber,r,isunknownwhen23Thiscontrastswithfirst-generationfactormodelswhereinthelackofidentificationiswellknown.29estimating𝛽𝛽(andviceversa),wecanimposeaninitialestimateofrandproceedtojointlyestimate𝛽𝛽̂,𝐹𝐹�,and𝛬𝛬̂bysolvingtheleastsquaresobjectivefunctionsinBai(2009)untilthesumofsquaredresidualsisiterativelyminimized.24Tocapturethe(potential)multidimensionalityofthefactorstructurewithoutoverfitting,weuseanalgorithmtoselecttheoptimalnumberoffactors(between1–3)foreachmodeliterationusingthecross-validationproceduredescribedinXu(2017).Models(1–3)canaccommodatethetheoreticalschemadescribedinSection2,wherethequantityofCO2emissionsgeneratedbyeachsectorinagivenyeardependsprimarilyonthesector’sabsolutesize,thecostofavailableCO2abatementtechnologies,andtheexplicitandimplicit(shadow)priceofemissions.Werequire,however,somefurtherassumptions.ASSUMPTION1.Theidiosyncraticerrors,𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡,areindependentofthepolicytreatment,conditionalontheobservedcovariates,latentfactors,andfactorloadings,𝔼𝔼�𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡�𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡,𝑥𝑥𝑖𝑖,𝑗𝑗,𝑡𝑡,ft,λi,k�=𝔼𝔼�𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡�𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡,ft,λi,k�=0.Thisstrictexogeneityassumptionisneededinorderforthecarbonpricingtreatmenteffect,𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡,tobeidentifieddespitethepresenceofunmeasuredcountry-specificconfounders,includingtheunknownCO2-equivalentshadowpricesignal,endogenoustechnicalchange,andothertime-varyingidiosyncrasiesspecifictoeachjurisdiction.Assumption1permitsthetreatmentindicator𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡tobecorrelatedwith𝑥𝑥𝑖𝑖,𝑗𝑗,𝑡𝑡andft.24SeeBai(2009)forafullmethodologicaldescription.30ASSUMPTION2.Transitoryshocksin𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡arecross-sectionallyindependent,suchthatanyunobservedcommonfactorsandheterogeneitiesthathaveasubstantivebearingonemissionsinmodel(1)arecapturedorcloselyapproximatedbytheadditive(timeandunit)fixedeffects𝜏𝜏𝑡𝑡and𝜉𝜉𝑖𝑖,𝑘𝑘,orthemultiplicativefactorstructure,𝜆𝜆𝑖𝑖,𝑘𝑘′𝑓𝑓𝑡𝑡.Totheextentthatthisassumptionholds,theIFEestimatoreffectivelyobviatesendogeneityconcernsrelatedto(potential)presenceofunobservedcommonfactorsandtime-varyingheterogeneitycorrelatedwiththeobservedcovariates(Bai2009).Underanalogousassumptions,theIFEestimatorhasbeenusedtomitigatecross-sectiondependenceandendogeneitybiasesinstudiesestimatingtheeffectsofspilloversonprivatereturnstoR&D(Eberhardtetal.2013)anddivorcelawreformsondivorcerates(KimandOka2014),amongothers.GobillonandMagnac(2016)provideMonteCarloevidenceshowingthattheconventionalDiDestimatorisgenericallybiasedinthepresenceofcommonerrorcomponents,whereasthesyntheticcontrolmethodperformsrelativelywellunderspecificconditionsandtheIFEestimatorusuallyproducestheleastbias.ASSUMPTION3.Theabsolutesizeofeachsector𝑘𝑘∈𝑘𝑘𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚,𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒_ℎ𝑒𝑒𝑒𝑒𝑒𝑒,𝑘𝑘𝑏𝑏𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢,𝑘𝑘𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟,𝑘𝑘𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡isindependentofthecarbonprice.Wecapturethesizeofthesectorbycontrollingforsector-levelGDPgrowth,totalGDPgrowth(andtheirsquarestoallowfornonlinearrelationships),andpopulationgrowth,whicharedenotedby𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡′inequation(1).Tosatisfystrictexogeneity,werequirethatsector-levelandtotalGDPgrowthareinvarianttointroducingthecarbonpriceandthepricelevelitself.Thereislittleevidencethatcarbonpriceshaddiscernibleimpactsoncountries’GDP,positiveorotherwise.Thesimulation31evidenceinGoulderandHafstead(2017)andtheempiricalevidenceinMetcalfandStock(2020;2020b)reassureusthatanyinferableimpactofacarbonpriceonGDPislikelytobenegligible,atleastwithrespecttothehistoricallyobservedpricelevelsconsideredhere.Thisassumptionisplausiblefortheperiodunderconsideration,butitmightbeviolatedinthefutureifmorestringentcarbonpricesareimplemented.WethereforealsoreportresultsomittingGDPgrowthascontrolsinSection5.3.Further,wenotethatMetcalfandStock(2020)show,usinglocalprojections,littleevidenceoffeedbackofemissionsorGDPonthecarbonpricelevel(or,byextension,theintroductionofpricingitself).WefollowXu(2017)inextendingtheIFEestimatorofBai(2009)tothequasi-experimentalframeworkusingsyntheticcontrols(Abadieetal.2010,2015;BillmeierandNannicini2013).Theresultinggeneralizedsyntheticcontrolmethodcanbeunderstoodasabias-correctedversionoftheIFEestimatorthatcanaccommodatebothcross-sectionalandtemporalheterogeneityinthetreatmenteffects.Inafirststep,theIFEmodelisestimatedusingonlycontrolgroupdata.Havingobtainedafixednumberoflatentfactors,factorloadingsareestimatedforeachtreatedcountrybylinearlyprojectingtheirpretreatmentoutcomesontothespacespannedbythesefactors.Inafinalstep,thecounterfactualsfortreatedunitsareestimatedbasedonthosefactorsandfactorloadingsobtainedinthepreviousstep.Liketheoriginalsyntheticcontrolmethod,countriesinthedonorpoolareweightedusingpretreatmentoutcomesinthetreatedcountryasthebenchmark.Theimputedcounterfactualsfortreatedcountriesareestimatedusingcross-sectionalcorrelationsbetweentreatedandcontrolgroupcountries.2525TheGSCmethoddiffersfromtheconventionalsyntheticcontrolapproachinthatitemploysdimensionreductiontosmoothvectorsforthecontrolgrouppriortoreweighting(Xu2017).32Toestimatecounterfactualemissions,weextendourdatasetfurtherbackto1975or1980,basedondataavailability.Iftheweightsassignedtoeachcontrolunitsuccessfullyproduceasyntheticcontrolgroupthatcloselypredictsthetreatedunit’sCO2emissionsduringthepretreatmentperiod,wecanhavegreaterconfidencethattheposttreatmentcounterfactualcanserveasacrediblebaselinetoassesstheeffectofthecarbon-pricingintervention.Testsof“notreatmenteffect”basedonsyntheticcontrolscanbeextremelyoversized(andthusmisleadinglyrejected)ifnonstationarityisignored(MasiniandMedeiros2020),sowefocusonspecificationsinfirstdifferences(growthratesofCO2emissions).UnitroottestsconfirmthatobservedCO2emissionlevelsareI(1)nonstationarybutbecomestationaryinfirstdifferences(seeAppendixC).Todifferentiatebetweenlevelandgrowtheffects,weintroducelagsoftheemissionsgrowthrate;theirsignallowsustodeterminewhetherpricingaffectedprimarilythegrowthorlevelofCO2emissions.Ourmodel(3)usingtheIFEestimator(Bai2009)inageneralizedsyntheticcontrolframework(Xu2017)yieldsestimatesofthesector-,country-,andtime-specifictreatmenteffects𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡.Wereporttheaveragetreatmenteffectovertreatedcountriesforeachsectorandeachperiodas𝐴𝐴𝐴𝐴𝑇𝑇𝑡𝑡,𝑘𝑘�=1𝑛𝑛𝑇𝑇𝑇𝑇𝑘𝑘,𝑡𝑡�𝛿𝛿̂𝑖𝑖,𝑘𝑘,𝑡𝑡𝑖𝑖∈𝑇𝑇𝑇𝑇(4)where𝑛𝑛𝑇𝑇𝑇𝑇𝑘𝑘,𝑡𝑡isthenumberoftreatedcountriesineachsectorandyear,andtheoverallaveragetreatmenteffectforeachsectorisgivenbytheweightedaverageof𝐴𝐴𝐴𝐴𝑇𝑇𝑡𝑡,𝑘𝑘�overalltreatedperiods.Weconductinferenceon𝐴𝐴𝐴𝐴𝑇𝑇𝑡𝑡,𝑘𝑘and𝛿𝛿̂𝑖𝑖,𝑘𝑘,𝑡𝑡usinganonparametricbootstrap.26The“base”26Allmodelsareestimatedusingthegsynth(XuandLiu2018)andlfe(Gaureetal.2013)packagesinRforarangeofspecificationstoassesstherobustnessoftheresults(seeSection5.3forrobustnesschecks).33specificationreportedhereincludesIFEandadditivetwo-way(countryandtime)fixedeffects,restrictsthetreatedcountriestothosewithpretreatmentdataspanningaminimumof15years,requirescountriesinthecontrolgrouptohaveaveragepopulation,realGDP,andemissionslevelsatleastashighasthelowestaverageinthetreatmentgroup,allowsfor1–3commonfactors(determinedusingcross-validation),andrequiresatleastfiveyearsoftreatment.Forcompleteness,wealsoreporttheestimatesobtainedusingtheTWFEandIFEmodelsin(1)and(2).Weinvestigateawiderangeofmodelspecificationsinourrobustnesschecks(Section5.3).5.1.1Results:TheAverageEffectofIntroducingaCarbonPrice(AverageTreatmentEffect)EstimationresultsshowthattheintroductionofcarbonpricingresultedinasignificantdecreaseinthegrowthrateofCO2emissions(TableIIIandFigureII)relativetotheestimatedcounterfactual.TheaveragetreatmenteffectovertreatedcountriesandperiodsestimatedusinggeneralizedsyntheticcontrolssuggeststhatgrowthintotalCO2emissionsisroughly1.6percentagepoints(SE=0.8points)lowercomparedtotheestimatedcounterfactual.Resultsatthesectorlevelindicatethatemissionsgrowthis2.8percentagepoints(SE=1.3points)lowerforelectricityandheat,1.4percentagepoints(SE=1.7points)lowerformanufacturing,0.5percentagepoints(SE=1.6points)lowerforroadtransport,and1.1percentagepoints(SE=1.1points)lowerforbuildings.Theseresultsarerobustacrossawiderangeofmodelspecificationsandestimationmethods(seeSection5.3forrobustnesschecks);AppendixDreportsTWFEandIFEestimates.FigureIVshowstheestimatedtreatmenteffectsforeachtreatedcountrybysector.Strikingly,treatmenteffectsdonotappeartovarymuchoverobservedpricelevels,aninitialfindingthatwe34investigatefurtherinSection5.2onelasticities.Fornow,wesimplynotethattheostensibleinvarianceofestimatedcountry-sectortreatmenteffectstothecountry-sectoraveragecarbonpricelevelseemstocontradictconventionalwisdom,whichassumesthathigherpricesshouldleadtodiscernablylargerquantitiesofavoidedemissionsonaverage,ceterisparibus.OurestimationresultssuggestthattheintroductionofcarbonpricingprimarilyaffectsthegrowthrateofCO2emissionsratherthanthelevel.Visualinspectionofthetime-varyingtreatmenteffectsshowsapersistentdifferencebetweentheobservedandcounterfactualgrowthrate,ratherthanaone-offchange(whichwouldcorrespondtoalevelchange).WefurtherestimatetheTWFE(1)andIFE(2)modelsincludinglagsofthetreatmentindicator.Iftheeffectwasonthelevelratherthanthegrowthrate,wewouldexpectopposite-signedcoefficientsonthecontemporaneousandlaggedtreatmentdummy,whichdoesnotoccur,supportingtheinterpretationthatcarbonpricingprimarilyimpactsemissionsviagrowthratherthanleveleffects(seeAppendixD).35TableIII:AverageTreatmentEffectsoftheIntroductionofCarbonPricing[DependentVariable:𝚫𝚫𝐥𝐥𝐥𝐥𝐥𝐥(𝐂𝐂𝐂𝐂𝟐𝟐)𝒊𝒊,𝒌𝒌,𝒕𝒕]TotalElectricityandheatManufacturingRoadtransportBuildingsATT–0.016(0.008)[p=0.05]–0.028(0.013)[p=0.03]–0.014(0.017)[p=0.44]–0.005(0.016)[p=0.65]–0.011(0.011)[p=0.42]Δlog(GDP)0.40207(0.45619)–0.59072(1.0307)–0.47818(1.59878)–0.03008(0.49753)–1.81785(2.35302)Δlog(GDP)2–0.00495(0.01871)0.0443(0.04288)0.03174(0.06822)0.01849(0.02258)0.08496(0.09644)Δlog(population)0.39359(0.15253)0.22088(0.24974)–0.06424(0.53198)0.22569(0.18432)1.37189(0.56168)Δlog(servicesGDP)NANANANA0.9296(1.01796)Δlog(servicesGDP)2NANANANA–0.03912(0.0515)Δlog(manfacturingGDP)NANA1.65345(0.69482)NANAΔlog(manfacturingGDP)2NANA–0.06557(0.03841)NANAΔlog(transportGDP)NANANA0.13592(0.1421)NA36Δlog(transportGDP)2NANANA–0.0013(0.00861)NAΔlog(heatingdegreedays)NANANANANAΔlog(coolingdegreedays)NANANANANAr11111𝑁𝑁𝑇𝑇𝑇𝑇17161667𝑁𝑁𝐶𝐶𝐶𝐶2927272140Specification#11112Note:Bootstrapstandarderrorsareshowninparentheses,withthebootstrapp-valuefortheATTreportedinsquarebrackets.Section5.3showsresultswithheatingandcoolingdegreedays.TableVpresentsspecifications;wereportresultsusingspecification#2forthebuildingssectortoensureasufficientnumberoftreatedcountries.37FigureII.GeneralizedSyntheticControlEstimatesofAverageTreatmentEffectsNote:Leftpanelsshowobserved(solid)andcounterfactual(dashed)changeinlogemissionsbysector.Rightpanelsshowtheestimatedtreatmenteffectsasthedifferencebetweenobservedandcounterfactual,withtheestimateoftheaveragetreatmenteffectsandits95percentbootstrapconfidenceinterval(shaded).38FigureIII.AverageTreatmentEffectsonTreatedBySector:GeneralizedSyntheticControl(left),Two-WayFixedEffects(middle),andInteractiveFixedEffects(right)Note:Estimatesforbuildingssectorgivenforspecification#2.39FigureIV.AverageOverallTreatmentEffectsandBetween-CountryVariationinTreatmentEffectsBySectorandOverAverageObservedCarbonPriceLevelsNote:Panelsshowthedistributionofaveragetreatmenteffectsofeachtreatedunitplottedagainsttheaveragecarbonpricelevelsfordifferentsectors.Averagetreatmenteffects(acrosstreatedunits)obtained40fromthegeneralizedsyntheticcontrolanalysisareshownasbarswiththe95percentbootstrapconfidenceinterval(shaded).415.2TheEffectoftheCarbonPriceLevel(Semielasticity)TheestimatedaveragetreatmenteffectsindicatethattheintroductionofcarbonpricingresultedinadecreaseinthegrowthofCO2emissions.However,itisnotclearwhetherhigherpricelevelsresultinlargeremissionreductions.Merelyintroducinganynonzerocarbonpricemightdrivetheapparentreductionsbyalteringexpectations(seee.g.,Friedetal.2020).Werefertothisasthe“introductioneffect.”Aconcernisthatsimpletreatmenteffectestimates,𝛿𝛿̂𝑖𝑖,𝑘𝑘,obtainedusingTWFE,IFE,orthegeneralizedsyntheticcontrolapproach,donotallowustodifferentiatebetweentheemissionreductionsstemmingfromtheintroductioneffectversusfromagivenpricelevel(thepriceeffect).Toassesswhetherhigherpricelevelsleadtolargerreductionsinemissionsrequiresanestimateofthe(semi)elasticityofemissionswithrespecttothe(emissions-weighted)carbonprice.Wedecomposethetreatmenteffectintointroduction(𝑎𝑎𝑖𝑖,𝑘𝑘)andprice(𝑏𝑏𝑘𝑘)effectstoestimatetheemissionselasticitywithrespecttothecarbonprice.The(potentiallyheterogeneousandtime-varying)treatmenteffect,𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡(𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡=Δlog(𝐶𝐶𝑂𝑂2)𝑖𝑖,𝑘𝑘,𝑡𝑡𝐷𝐷𝑖𝑖,𝑡𝑡=1−Δlog(𝐶𝐶𝑂𝑂2)𝑖𝑖,𝑘𝑘,𝑡𝑡𝐷𝐷𝑖𝑖,𝑡𝑡=0),capturesthedifferenceinemissionsgrowthresultingfromintroducingcarbonpricing,relativetothe“nopolicy”counterfactual.Thetreatmenteffectispotentiallyafunctionofasector-specificintroductioneffect(𝑎𝑎𝑖𝑖,𝑘𝑘),semielasticitywithregardtothecarbonprice(𝑏𝑏𝑖𝑖,𝑘𝑘),andthepricelevelitself(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡):𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡=𝑓𝑓(𝑎𝑎𝑖𝑖,𝑘𝑘,𝑏𝑏𝑖𝑖,𝑘𝑘,𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡)(5)42Weconsideralinearmodelfor𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡estimatingsector-specificeffects:𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡=𝑎𝑎𝑘𝑘+𝑏𝑏𝑘𝑘×𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡(6)Here,𝑎𝑎𝑘𝑘denotestheeffectofintroducinganycarbonpriceinsector𝑘𝑘,anditcapturestheimpactonexpectationsgeneratedbytheintroductionofacarbonprice,regardlessofthepricelevel.Ourmainparameterofinterestis𝑏𝑏𝑘𝑘,denotingthe(semi)elasticityofCO2emissionswithrespecttothecarbonprice,𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡.If𝑏𝑏𝑘𝑘isnegative,thenahighercarbonpricewouldleadtolargerreductionsinemissionsbeyondmereintroductioneffects.Naturally,amyriadofpossibleextensionsexist,allowingtheintroductionandpriceeffectstovaryoveri,orfordifferentfunctionalforms,suchasincludinglagsofpricestocapturepotentialgrowthinsteadofleveleffects.WeexpandtheTWFE,IFE,andsyntheticcontrolmodelstoestimateboththeintroductionandpriceeffects.ThisisstraightforwardfortheTWFEandIFEmodels.Weconsiderheterogeneityoveriaswellastemporal-dynamiceffectstodifferentiatebetweenlevelandgrowtheffectsinourrobustnesschecks.Weproposeanovelapproachtoestimateelasticitiesandintroductioneffectsfromcounterfactualestimators(i.e.,thesyntheticcontrolmodelhere)inSection5.2.1.FortheTWFEandIFEmodels,wesubstituteourexpressionfor𝛿𝛿𝑖𝑖,𝑘𝑘,𝑡𝑡fromequation(6)intoequation(1),resultingin𝛥𝛥𝑙𝑙𝑙𝑙𝑙𝑙(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝑎𝑎𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡+𝑏𝑏𝑘𝑘(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡)+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜏𝜏𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡(7)43andintoequation(2),resultingin𝛥𝛥log(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝑎𝑎𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡+𝑏𝑏𝑘𝑘(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡)+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜏𝜏𝑘𝑘,𝑡𝑡+𝜆𝜆𝑖𝑖,𝑘𝑘ʹ𝐹𝐹𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡(8)Models(7)and(8)thusincludecountry-sectorspecificdummyvariablescapturingtreatedcountriesposttreatment(withcoefficients𝑎𝑎𝑘𝑘denotingtheintroductioneffects),andcountry-sectorspecificdummyvariablesinteractedwiththecarbonpricelevels(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡),andassociatedcoefficients𝑏𝑏𝑘𝑘denotingtheemissionssemielasticitieswithregardtotheprice.Bestetal.(2020)estimatedmodelscomparabletotheTWFEmodelincludingthepricelevelonly(i.e.,equation(7)butwiththeintroductioneffectterm,𝑎𝑎𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡,removed)butdidnotaccountforpossibleintroductioneffects.Thisrisksconfoundingtheintroductioneffectwiththepriceeffect.Thus,omittingtheintroductioneffecttermmaybiastheestimateoftheemissionselasticity,bk.Todifferentiatebetweenimpactsontheemissionslevelversusgrowthrateandtestforpotentiallaggedpriceeffects,wealsoestimateTWFEmodel(7)andIFEmodel(8)includinglagsof𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡(seeAppendixD).Toestimateelasticities,werequiretheadditionalexogeneityassumptionforthelevelofcarbonpricing:ASSUMPTION4.ThelevelofthecarbonpriceattimetisindependentofΔ𝑙𝑙𝑙𝑙𝑙𝑙(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡,…,𝑡𝑡−𝐿𝐿,conditionalonthesetofobservedregressors,additivefixedeffects,andestimatedfactorstructure𝜆𝜆𝑖𝑖,𝑘𝑘′𝑓𝑓𝑡𝑡.44Inotherwords,weassumethatchangesinthecarbonpricearestrictlyexogenous.Thisassumptionisarguablyreasonable,asmanypricingschemeshavecommittedchangesinadvance,andpricechangesareunlikelytobedrivenbycontemporaneousgrowthinCO2emissions.27Severalconsiderationssupportthisassumption.First,economistshaveexplicitlyrecognizedthelongtimelagsbetween(uncertain)CO2emissionsoutcomesandpoliticallyinitiatedadjustmentstothecarbontaxrate(ortheemissionscapforcarbonmarkets).Tomitigatetheuncertaintyaboutpolicyefficacycreatedbythesetimelags,Hafsteadetal.(2017),Metcalf(2020)andrelatedstudieshaveproposedmethodsofredesigningcarbonpricingschemessothattheyincludebuilt-inprice-adjustmentmechanismsthatrespondtounanticipatedemissionsoutcomes,therebyprovidingassurancethatcarbonpricelevelscanbepreemptivelyadjustedinaccordancewithspecificemission-reductiontargets.Tothebestofourknowledge,suchautonomousCO2price-adjustmentmechanismshaveyettobeadoptedinanyjurisdiction.28Furthermore,wehavenotidentifiedasinglecasewherepolicymakershavemanuallyadjustedthecarbontaxrate(oremissionscap)asacontemporaneousresponsetounanticipatedchangesinemissions.29Intheirbroadmacroeconometricanalysis,MetcalfandStock(2020)detectlittletonoevidenceoffeedbackbetweenCO2emissions(orGDP)andthelevelofthecarbonprice.InETSs,theissueofsimultaneityismorecomplex.EconomictheorywouldsuggestapriorithattheCO2permitpriceshouldrespondtooverachievementorunderachievementofemissions27AnalternativetotheIFEmodelherewouldbetousethelocalprojectionmethodinMetcalfandStock(2020;2020b).28TheMarketStabilityReserveintheEUETScomesclosetoanautonomousprice-adjustmentmechanism,butthisisscheduledfor2023onwardanddoesnotaffecttheperiodconsideredinthisstudy.29OnepossibleexceptionisAustralia,inwhichthefederalgovernmentrepealedacarbontaxin2014thathadbeenimplementedjusttwoyearsearlier,arguablyinresponsetothetaxhavingimposedsubstantivepolicycostsoncarbon-exposedindustry.However,forourpurposes,thiscaseposesnoproblemanddoesnotviolatestrictexogeneity,astheyearofthetaxrepealsimplymarkstheendofthetreatmentperiod.45abatementwithrespecttothecapsetbyregulators.However,acompellingbodyofempiricalevidenceindicatesthatoccasionalboutsofvolatilityandnonstationarityinCO2permitpricesintheEUETSsince2005havepredominantlybeenafunctionofexogenousevents—unanticipatedregulatorychangesandpolicyannouncementsregardingtheallocationandbankingofallowances—andtheCO2permitpriceispoorlypredictedbymarketfundamentals,negativedemandshocks,orlaggedemissions(Kochetal.2014,2016;Friedrichetal.2019).Theseregulatoryeventsor“shocks”30arebestunderstoodastheproductofprotractednegotiationswithemissions-intensiveandtrade-exposedindustries—oftenresultinginsubstantialovercompensation(Grubb2014;Martinetal.2014b)—ratherthancontemporaneousresponsestooverachievementorunderachievementunderthecap.Forextendedperiods,theEUcarbonmarkethasbeenstationaryatlowCO2prices,onlyoccasionallyundergoingperiodsofvolatilityinresponsetopoliticallydetermined(ratherthan“emissionsdetermined”)changesintheexpectationsofmarketparticipants,atleastfortheperiodconsideredinourstudy.3130Forexample,Friedrichetal.(2019)modelEUETSpricevolatilityinresponsetotheMarch2018amendmentpassedbytheEuropeanCommission,whichannouncedplanstocancelexcessallowancesfrom2023onwardunderaMarketStabilityReserve.AnothermajorregulatorychangetotheEUETS,theintroductionofthelinearreductionfactor,ismodeledinBockletetal.(2019).31OurargumentrelatestoakeypointinSims(1983):“[t]hefactthatsomeeffectsofapolicyactionoccurthrougheffectsonexpectationsdoesnotnecessarilyimplythatonemustexplicitlyidentifytheparametersofexpectation-formationmechanismstoobtainmodelsthatcorrectlyprojecttheeffectsoftheaction.”465.2.1ElasticityEstimatesUsingTreatmentEffectsfromSyntheticControlsItisstraightforwardtomodifytheTWFEandIFEmodelstoallowforintroductionandpriceeffectsandthenestimatethesemielasticitywithregardtothecarbonprice,butthesemodelsstillpotentiallysufferthesamechallengesastheoriginalsin(1)and(2),includingheterogeneoustreatmenteffects,nonparalleltrends,andstaggeredadoption.Ideally,wecouldusethesyntheticcontroltreatmentestimatesfrom(3)whenestimatingelasticitiesandintroductioneffects.Inthissection,weproposeanovelapproachtoestimatingelasticitiesusingtreatmenteffectestimatesobtainedfromcounterfactualestimators,suchassyntheticcontrolandrelatedmethods.Fewstudieshaveestimatedelasticitiesdirectlyfromthetreatmenteffectsobtainedfromcounterfactualestimators.DubeandZipperer(2015)andCengizetal.(2019)arenotableexceptions.Theauthorsestimateelasticitiesusingmultipletreatmentestimates(obtainedviasyntheticcontrolmethods—oneforeachtreatedunit32inDubeandZipperer)scaledbythemagnitudeoftreatmenttoassesswhetherchangesinunemploymentcanbeattributedtothemagnitudeofchangesinminimumwages.Theirapplicationfocusessolelyonexistingminimum-wagepolicies,thusavoidingthechallengeofseparatingintroductionfrompriceeffects.Ourproposedapproachistomodelvariationinthecountry-specifictreatmenteffectsusingobservedvariationinthecarbonpricelevelswithinandbetweencountriesovertime.Specifically,weassesswhetherheterogeneityoveri(andt)intheestimatedtreatmenteffect𝛿𝛿̂𝑖𝑖,𝑘𝑘,𝑡𝑡obtainedusing32CombiningmultiplesyntheticcontrolestimatestoconductinferenceonanaveragetreatmenteffectisanapproachthatalsobeenappliedbyIsaksen(2020)forpollutantemissionsandGobillonandMagnac(2016)forunemployment.47syntheticcontrols(asinSection5.1)canbeattributedtovariationinobservedcarbonpricesandtheirinterannualtrajectoriesoverrelevanttreatmentperiods.Weestimatethiselasticityusingbothbetween-andwithin-countryvariation.5.2.1.1ElasticityEstimatesUsingBetween-CountryVariationToestimatethe(semi)elasticityofCO2emissionsgrowthwithrespecttothecarbonpriceusingbetween-countryvariation,wemodeltheestimatedsector-specifictreatmenteffectfromthesyntheticcontrolmodel(3)foreachcountryiaveragedovertime33,𝛿𝛿̂̅𝑖𝑖,𝑘𝑘,asafunctionoftheaveragecarbonpricelevel𝑝𝑝̅𝑖𝑖,𝑘𝑘ofcountryi:𝛿𝛿̂̅𝑖𝑖,𝑘𝑘=𝑎𝑎𝑘𝑘+𝑏𝑏𝑘𝑘𝑝𝑝̅𝑖𝑖,𝑘𝑘(9)where𝛿𝛿̂̅𝑖𝑖,𝑘𝑘=1𝑇𝑇𝑡𝑡𝑡𝑡,𝑖𝑖,𝑘𝑘∑𝛿𝛿̂𝑖𝑖,𝑘𝑘,𝑡𝑡𝑇𝑇𝑡𝑡𝑡𝑡,𝑖𝑖,𝑘𝑘𝑡𝑡=1,and𝑝𝑝̅𝑖𝑖,𝑘𝑘=1𝑇𝑇𝑡𝑡𝑡𝑡,𝑖𝑖,𝑘𝑘∑𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡𝑇𝑇𝑡𝑡𝑡𝑡,𝑖𝑖,𝑘𝑘𝑡𝑡=1,with𝑏𝑏𝑘𝑘denotingtheparameterofinterest:thechangeintheaveragesector-leveltreatmenteffect(i.e.,changeinthegrowthrateofCO2emissions)inresponsetoa$1increaseintheaverageemission-weightedcarbonprice.ThisapproachiscloselyrelatedtoCengizetal.(2019),whoscaletheirminimum-wagetreatmenteffectsbytheleveloftheminimumwage.Theequivalentapproachinoursettingwouldbetoset𝑎𝑎𝑘𝑘=0inmodels(7)and(8)andthenestimate𝑏𝑏𝑘𝑘bydividing𝛿𝛿̂̅𝑖𝑖,𝑘𝑘33𝑇𝑇𝑡𝑡𝑡𝑡,𝑖𝑖,𝑘𝑘inthedescriptionjustafterequation(9)isthenumberoftreatmentyearsinsector𝑘𝑘ofcountry𝑖𝑖.48by𝑝𝑝̅𝑖𝑖,𝑘𝑘.However,wecannotruleoutnonzerointroductioneffects,andthuswedonotimposethezero-interceptrestrictioninequation(9).Giventhevariationinthetreatmentlength(thenumberofyearscarbonpriceshavebeeninforce),countrieswithshortertreatmentperiodsmightexhibithighervarianceintheirtreatmenteffects.Toaccountforthispotentialheteroskedasticity,weestimate(9)usinganestimatorweightedbytreatmentlength:𝛿𝛿̂̅∗𝑖𝑖,𝑘𝑘=𝑎𝑎𝑘𝑘𝑥𝑥0,𝑖𝑖,𝑘𝑘∗+𝑏𝑏𝑘𝑘𝑝𝑝̅∗𝑖𝑖,𝑘𝑘,(10)wheretheweightedvariablesaregivenby𝛿𝛿̂̅∗𝑖𝑖,𝑘𝑘=�𝑙𝑙𝑖𝑖,𝑘𝑘𝛿𝛿̂̅𝑖𝑖,𝑘𝑘,𝑥𝑥0,𝑖𝑖,𝑘𝑘∗=�𝑙𝑙𝑖𝑖,𝑘𝑘,𝑝𝑝̅∗𝑖𝑖,𝑘𝑘=�𝑙𝑙𝑖𝑖,𝑘𝑘𝑝𝑝̅∗𝑖𝑖,𝑘𝑘,with𝑙𝑙𝑖𝑖,𝑘𝑘denotingthetreatmentlengthforsectorkintreateduniti.Toalleviateconcernsaboutsingleoutlyingcountriesdistortingtheestimates,weestimate(10)usinganoutlier-robustMMestimator(KollerandStahel2011).34Toconductinferenceon𝑏𝑏𝑘𝑘,webootstrap(10)bysamplingntreatobservations(wherentreatreferstothenumberoftreatedcountriesinthesample)fromthebootstrapsamplesobtainedusingthegeneralizedsyntheticcontrolestimatorfromSection5.1.Forexample,inasampleof22treatedcountries(ntreat=22),wesampleonetreatmenteffectforeachcountry1,000timesfromtheoriginalbootstrapdrawsandestimatethisrobustweightedregressionwith22observations1,000timestoapproximatethedistributionof𝑏𝑏𝑘𝑘.Ourmodelshere,(9)and34ImplementedusingtheRpackagelmrobust.49(10),implicitlyassumethattheintroductioneffect𝑎𝑎𝑖𝑖,𝑘𝑘isidenticalforallcountries.Wenextrelaxthisassumptionwhenconsideringthewithin-countryestimatoroftheimplementationelasticity.5.2.1.2ElasticityEstimatesUsingWithin-CountryVariationUsingbetween-countryvariationtoestimatethesemielasticityofCO2emissionswithrespecttothecarbonpricedoesnotcontrolforcountry-specificcharacteristicsthatmightleadtoheterogeneousintroductioneffects.Thismodelassumesthatthepureintroductioneffectcapturedby𝑎𝑎𝑖𝑖,𝑘𝑘isthesameforallcountriesi.Wethereforealsoestimatetheeffectofthecarbonpriceontheestimatedtreatmenteffectusingwithin-countryvariationofthecarbonpricelevel,allowingustocontrolforcountryfixedeffectsoftheintroductionofcarbonpricing.Weestimateafixedeffectspanelmodelofthecountry-yearspecifictreatmenteffectsforeachsectorgivenin(10):𝛿𝛿̂𝑖𝑖,𝑘𝑘,𝑡𝑡=𝑎𝑎𝑖𝑖,𝑘𝑘+𝑏𝑏𝑘𝑘𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡(11)where𝑎𝑎𝑖𝑖,𝑘𝑘arecountryfixedeffectscapturingthe(potentiallyheterogenous)country-specificintroductioneffectsofcarbonpricing.Wefurtherestimate(11)includingthefirstlagofthecarbonpricetotestwhetheranypriceeffectworksthroughfirstdifferencesratherthanlevels.Weformallytestheterogeneityoftheintroductioneffectsandpriceeffectsusingtestsofpoolabilityofthefixedeffects(𝑎𝑎𝑖𝑖,𝑘𝑘=𝑎𝑎𝑘𝑘∀𝑖𝑖)andcoefficients(𝑏𝑏𝑖𝑖,𝑘𝑘=𝑏𝑏𝑘𝑘∀𝑖𝑖).Weconductinferenceon𝑏𝑏𝑘𝑘in(11)byestimatingthepanelmodel1,000timesusingeachbootstrapdrawofthetreatmenteffect𝛿𝛿̂𝑖𝑖,𝑘𝑘,𝑡𝑡obtainedfromthegeneralizedsyntheticcontrolestimatorinSection5.1.505.2.2Results:TheEffectofthePriceLevel(SemielasticitywithRespecttotheCarbonPrice)Thepointestimateoftheemissionsemielasticitywithrespecttothecarbonpriceisnegativeformostsectorsbutimpreciselyestimated.TableIVshowsthebetween-countryandwithin-countryestimatesoftheimplementationsemielasticity,withFigureVplottingthecountry-levelaveragetreatmenteffectsagainstaveragecarbonpricelevelsusedtoderivethebetween-countryestimatesoftheimplementationsemielasticity.Theresultssuggesta0.07percentreductioninthegrowthrateoftotalCO2emissionsfora$1/tCO2increaseintheaveragecarbonprice.However,the95percentbootstrapconfidenceintervalincludeszero,from–0.4to+0.2percentperdollar.Modelresultsassessinglevelversusgrowthrateeffectsusinglaggedpricesinthewithin-countrymodel(andtheTWFEandIFEestimates)arereportedinAppendixD,primarilysupportinganeffectofthelevelof,ratherthanchangein,theprice.Theresultsarerobusttothechoiceofestimationmethod;themainresultsusingthegeneralizedsyntheticcontrolmodelarenearlyidenticaltothoseobtainedusingtheTWFEandIFEmodels.35ThenullhypothesesthatthecarbonpricecoefficientsandfixedeffectsarehomogeneousovercountriesandthereforepoolablearebothrejectedonlyinthecaseofthemodelofmanufacturingCO2emissions.36NotethatthemodelofmanufacturingCO2emissionsistheonlyonewithreallylargeestimatesforthesemielasticity(particularlyforthewithin-countryestimate)inTableIV,35ThenumberoffactorsintheIFEmodelischosentomatchthenumberoffactorsdeterminedusingcross-validationintheestimationoftheassociatedsyntheticcontrolfactormodelfromSection5.1.36InTableIV,thenullhypothesisthatfixedeffectsarepoolableisalsorejectedforthemodeloftotalaggregateemissions,whereaswecannotrejectthenullhypothesisthatcarbonpricecoefficientsarepoolableinthismodel.51suggestingthatasmallnumberofcountriesmaybedrivingtheresults.WeexplorethispossibilityfurtherinrobustnesschecksinSection5.3byestimatingthemodelofmanufacturingemissionsinECform;AppendixEpresentstheresults.OurresultsshowingsubstantialtreatmenteffectsbutsmallanduncertainelasticityestimatessuggestthattheintroductioneffectaccountsformuchofthechangeinCO2emissionsgrowthinresponsetotheintroductionofcarbonpricing.Thisholdstrueforboththebetween-andwithin-countryestimatorswhenusingsyntheticcontrols(TableIVandFigureV)andTWFEandIFEestimates(AppendixDandFigureV).AsFigureV(panelb)shows,thetreatmenteffectsdonotvarymuchwiththelevelofthecarbonprice(thisalsoholdswhenincludingcountrieswithmuchhighercarbonprices,suchasSwedenandNorway—seespecification#6plottedinFigureD1inAppendixD).Merelyintroducingcarbonpricingappearstoresultinemissionsreductionsand,atcurrentobservedpricelevels,additionalreductionsinemissionsinresponsetohigherpricelevelsaremarginal.Thecorollaryisthatnotcontrollingforintroductioneffects(i.e.,omitting𝑎𝑎𝑖𝑖,𝑘𝑘andmodelingCO2growthsolelyasafunctionofcarbonprices)likelybiasesestimatesoftheemissionselasticities.ThisisapparentinFigureV(panelb),whereallowingforintroductioneffectsshowsnoresultingchangeintheestimatedtreatmenteffectacrosspricelevels.However,notallowingforintroductioneffectsisakintoforcingtheintercepttobezero(intherelationshipbetweentreatmenteffectsandpricelevels).ThedashedlineinpanelbofFigureVshowstherelationshipbetweentreatmenteffectsandpricelevelswhentheinterceptisomitted:theslope(thesemielasticity)isnotablysteepercomparedtothatwhenallowingforintroductioneffects.Thismayexplainwhywefind52smallerelasticityestimatesthanearlierstudies(e.g.,Bestetal.2020),includingthoseusingfueltaxratesasproxiesforcarbonpricing(e.g.,DavisandKilian2011).53FigureV.SemielasticitywithRespecttoCarbonPriceLevelsbySectorNote:Panel(a):generalizedsyntheticcontrol(left),two-wayfixedeffects(middle)andIFE(right)modelsacrosssectors.Estimatesforthebuildingssectorgivenforspecification#2.Lightshadingreportselasticitieswhenomittingintroductioneffects(denotedas“nointro”).Panel(b)showshowomissionofintroductioneffectsbiasestheestimatesofemissionelasticitieswithregardtocarbonpricing.54TableIV.SemielasticitywithRespecttotheCarbonPrice[DependentVariable:𝚫𝚫𝚫𝚫𝚫𝚫𝚫𝚫(𝐂𝐂𝐂𝐂𝐂𝐂)𝒊𝒊,𝒌𝒌,𝒕𝒕]TotalElectricityandheatManufacturingBuildingsRoadtransportSemielasticity(between-country)–0.033percent(–0.41percent,0.303percent)0.002percent(–0.506percent,0.3percent)–0.192percent(–0.773percent,0.432percent)0.012percent(–0.117percent,0.152percent)0.028percent(–0.195percent,0.23percent)Semielasticity(within-country)0.001percent(–0.279percent,0.344percent)0.093percent(–0.102percent,0.276percent)–0.258percent(–0.672percent,0.11percent)0.001percent(–0.178percent,0.089percent)–0.045percent(–0.201percent,0.173percent)𝑁𝑁𝑇𝑇𝑇𝑇17161667Ftestforpoolabilityofcarbonpricecoefficientp=0.645p=0.943p=0.005p=0.905p=0.984Ftestforpoolabilityoffixedeffectsp=0.009p=0.71p=0.012p=0.518p=0.744Specification#11112Note:The95percentbootstrapconfidenceintervalisshowninparentheses.555.3RobustnessoftheResultsWeconsiderarangeofmodelspecificationsfortheestimatedtreatmenteffectsandsemielasticitiesandseparatetheeffectsofemissiontradingschemesfromthoseofcarbontaxes.5.3.1RobustnesstoModelSpecificationFigureVIshowsestimatesoftheaveragetreatmenteffectandsemielasticityobtainedusinggeneralizedsyntheticcontrols(andmatrixcompletion)foreachofthefivesectorsacross15modelspecificationssummarizedinTableV.Wevarytheminimumnumberofpretreatmentandposttreatmentobservations,criteriaforcontrolvariablesusedtoselecttheunitsinthedonorpool(averagelevelofemissionsandallobservedcontrolvariablesmustbeatleastaslargeastheminimum,or25thpercentile,fortreatedunits),andforcedadditivefixedeffectspecificationsintheIFEmodel.Wealsovarythesetofcontrolvariablesacrossspecifications:omittingGDPgrowthtoalleviatepotentialconcernsofGDPgrowthitselfbeingaffectedbycarbonpricingandincludingHDDandCDDtocontrolforweatherfluctuation.Toassesswhetherresultsaresensitivetoourchosenestimator,weincludeadditionalspecificationsbasedonthematrixcompletionestimatordevelopedinAtheyetal.(2018).3737Atheyetal.(2018)showthatthegeneralizedsyntheticcontrolestimator(basedontheIFEmodel)andtheirproposedMCestimatorbelongtoageneralclassofmatrixcompletionmethodsbasedonmatrixfactorization.Whereasthesyntheticcontrolapproachminimizesthesumofsquarederrorsgivenafixednumberoflatentfactors,theirMCestimatordeterminestherankofthemissingcounterfactualmatrixusingnuclearnormpenalization.TheMCapproachemployscross-validationtoselectthepenaltyterm,𝜆𝜆,forregularization,similartothegeneralizedsyntheticcontrol(withIFE)approachtoselectingtherankofcommonfactors(Xu2017).Mostimportantlyforthisstudy,bothestimatorsaccommodatestaggeredadoptionacrossmultipletreatedunits.5657TableV.ModelSpecificationsforRobustnessAnalysisSpec.ID#Min.treatedyearsMin.pretreatmentyearsDonorpoolquantilesStartyearFixedeffectsEstimatorObservedcontrolvariables1(base)51501980two-wayIFEsoc_econ201501980two-wayIFEsoc_econ352001980two-wayIFEsoc_econ4515nomin1980two-wayIFEsoc_econ55150.251980two-wayIFEsoc_econ651501975two-wayIFEsoc_econ751501980unitIFEsoc_econ851501980noneIFEsoc_econ921501980two-wayIFEsoc_econ1051501980two-wayIFEsoc_econ_weather1151501980two-wayIFpop_only1251501980two-wayMCsoc_econ13515nomin1980two-wayMCsoc_econ145150.251980two-wayMCsoc_econ1551501975two-wayMCsoc_econNote:Basespecificationshowninmainresultssectioncorrespondstospecificationnumber=1(shadedingrey).“Donorpoolquantiles”referstorestrictionsoncountriesincludedinthecontrolgroup;“0”indicates58thattheiraveragelevelsofemissions,GDP,population,andallothercovariatesmustbeequaltoorgreaterthantheminimumlevelsinthetreatedunits;“nomin.”indicatesthatnolimitsareimposed;and“0.25”indicatesthattheiraveragelevelsforeachvariablemustexceedthe25thpercentileofeachvariableinthetreatedunits.“Startyear”referstothesamplestartdate,“socioeconomic”referstoinclusionofGDP,sector-levelGDP,andpopulationcontrolvariables;and“weather”referstoinclusionofpopulation-weightedheatingdegreedaysandcoolingdegreedays.Estimatesoftheaveragetreatmenteffectsandelasticitiesarerobustacrossspecifications.Withrespecttoaggregate(economywide)emissions,theaveragetreatmenteffectiscenteredarounda–1.5percentagepointchangeinthegrowthrateofemissions,whereasemissionssemielasticityisaround–0.03percentperaverageemissions-weighteddollarofCO2pricing.SeveralaspectsoftherobustnessanalysispresentedinFigureVIarenoteworthy.First,ourestimatesarerobustexcludingGDPasacontrolvariable,whichalleviatestheconcern—discussedinSection5.1—thatthecarbonpricemightaffectemissionsvis-à-visitspotentialimpactoneconomicoutput.Second,includingHDDandCDDyieldsasignificantincreaseintheATTandmarginalsemielasticitypointestimatesforthebuildingssector,withaconsiderablenarrowingofthe95percentbootstrapconfidenceintervals.Thisfindingisconsistentwiththewell-establishedempiricalliteraturedemonstratingthesubstantialimpactofweathervariationonenergydemand(Mistry2019)andindicatesthatourpreferredspecificationsforthebuildingssectorshouldbenumber10.Third,ourestimatesarerobusttothechoiceofcounterfactualestimator:generalizedsyntheticcontrolwithIFEormatrixcompletion.Fourth,althoughelasticitiesareimpreciselyestimated,thebootstrapconfidenceintervalsshowlongnegativetailsinmanyspecifications,makingincreasesinemissionsinresponsetocarbonpricingunlikely.59Asafurtherrobustnesscheck,weestimatepanelECmodelsforeachsectorthatincludesanytreatedcountry𝑖𝑖𝑇𝑇𝑇𝑇∈1,2,…𝑁𝑁𝑇𝑇𝑇𝑇,withasufficientlylongtreatedperiod𝑡𝑡𝑇𝑇𝑇𝑇∈𝑡𝑡1,…≥𝑡𝑡23withrespecttocarbonpricinginsectork.AppendixEprovidesasummaryofthesespecificationsandresults.Estimatingthesemodelsallowsustocheckforpotentialcointegratingrelationsandaveragelong-runeffectsthatmaybemutedbyourmainmodelspecificationsinfirstdifferences.TheECspecificationalsoallowsustofurtherinvestigatetheresultsfromSection5.2,whereFtestsindicatedthatthecarbonpricecoefficientandfixedeffectsarenotpoolableforthemodelofmanufacturingemissionsand,moreover,thatfixedeffectsmaynotbepoolableforthemodeloftotalemissions.Morespecifically,astherelativelylargeimplementationsemielasticitiesestimatedinthemanufacturingsectormaybedrivenbyasmallnumberofcountries,wecanusetheECspecificationtocheckifanyofthecountrieswitharelativelylongtreatmentperiod(Finland,Sweden,andPoland)inthemanufacturingsectoraredrivingthisresult.ThisintuitionisconfirmedinAppendixE:Finlandaccountsforthelargesemielasticityofmanufacturingemissions.Werejectthenullhypothesisof“nocointegration”forthemodelsoftotalandmanufacturingemissionsbutcannotrejectitforothersectors.AsshowninAppendixE,theaveragelong-runeffectsofanadditional$1/tCO2area0.2–0.6percentreductioninthegrowthrateoftotalCO2emissionsandmanufacturingemissions,respectively.5.3.2ComparingEmissionsTradingandCarbonTaxSchemesThemainestimateswereportrefertotheintroductionofanycarbonprice,whetheracarbontax,ETS,orsomehybridscheme.WerepeatouranalysisforcarbontaxesandETSsinisolation,wherewerestrictthesetofcountriesinthecontrolgrouptothosewithoutanypricingschemeatall(toensurecleancontrolgroups).FiguresVIIandVIIIshowtheresultswhenconsideringthecarbon-60tax-onlyandETS-onlytreatmenteffectsandelasticitiesinturn,withfullestimationresultsinAppendixF.Withrespecttoaggregate(economywide)emissions,theaverageETS-onlytreatmenteffectiscenteredarounda-1.5percentagepointchangeinthegrowthrateofemissions(roughlyequivalenttotheestimatedATTofcarbonpricingregardlessofthepolicytype),andtheETS-onlyemissionssemielasticityisclosetozero(-0.01percentperaveragedollarofcarbonpricing).Theaveragecarbon-tax-onlytreatmenteffectissimilarlycenteredarounda-1.5percentagepointchangeinemissionsgrowth,whereastheassociatedemissionselasticitycannotbeestimatedbasedoninsufficientin-sampleobservations.Overall,thedistinctionbetweenETSandcarbontaxeffectsseemssominisculeastobesubstantivelyirrelevant.SubstantivelyimportantdistinctionsbetweenETSandcarbontaximpactsarediscernableonlyatthesectorlevel.Specifically,wefindthatthemajorityofETS-inducedemissionsabatementoccurredintheelectricityandheatandmanufacturingsectors,whereemissionstradingelicitedsignificantlygreaternegativeeffectsonemissionsgrowthrelativetothe(relativelyfew)carbontaxschemesthathavebeenappliedinthesesectors.Bycontrast,themajorityoftax-inducedemissionsabatementoccurredintheroadandbuildingssectors,withsignificantlygreateremissionsreductionsthanweregeneratedviaemissionstrading,alesscommonlyusedformofcarbonpricinginthesesectors.ThisislikelydueinlargeparttotherelativelyhighadministrativecostsandadditionalmonitoringrequirementsofimplementingETSsforroadandbuildingssectorsatthenationallevel,ascomparedtocarbontaxes,whichcanbeappliedrelativelyseamlesslytothecarboncontentofpurchasedfuels.Weconcludethattheostensibledifferencesinthesector-specificemissionsresponsetothesetwomainformsofcarbonpricingareprobablymereartifacts61oftherelativeeasewithwhicheachcanbeappliedtotherelevantsectors,ratherthananyintrinsicdifferenceinenvironmentalefficacyperse.FigureVI.62AverageTreatmentEffectsandSemielasticities(UsingSyntheticControlsandBetween-CountryVariation)Across15ModelSpecifications63FigureVII.CarbonTax–OnlySample:AverageTreatmentEffectsandSemielasticities(UsingSyntheticControlsandBetween-CountryVariation)Across15ModelSpecifications64FigureVIII.ETS-OnlySample:AverageTreatmentEffectsandSemielasticities(UsingSyntheticControlsandBetween-CountryVariation)Across15ModelSpecifications656.SIMULATINGTHEEMISSIONSRESPONSETOFUTUREPRICEPATHSPolicymakershavelongsoughttheanswertothequestionofwhatchangesinemissionscanbeexpectedinresponsetoaspecificcarbonpricingscheme;thisisparticularlypressingduetotheinternationalcommitmentsundertheParisAgreement.Morerecently,severalgovernmentshaveissuedstatements(Japan),submittedlegislativeproposals(Canada,EU)orenactedlaws(UK,NewZealand)committingtonet-zeroemissionsbymidcentury(ClimateActionTracker2021).Manyeconomistshavehailedcarbonpricesasthetoolofchoicetoimplementsuchemissionreductionsatthe“scaleandspeedthatisnecessary”(Economists’StatementonCarbonDividends2019).However,theseclaimsweremadewithlittleempiricalevidencetosupportthem.Usingourestimatesoftheimplementationandmarginalsemielasticities,wesimulatetheimpactofcarbonpricingonprojectedemissionstoassesswhetheritislikelytobesufficienttoachievereductionsattherequiredscaleandspeed.Wecompareemissionsundercarbonpricingtono-pricingscenariosusingprojectedCO2emissionsfromtheSharedSocioeconomicPathways(SSPs),asetofreferencescenariosfrom2005to2050(Riahietal.2017).38Weconsiderahypotheticalglobalcarbonpriceintroducedin2021.Wesimulateprojectedtotal(tot)emissionsaslog(𝐶𝐶𝐶𝐶2�)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡=log(𝐶𝐶𝐶𝐶2�)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡−1+∆log(𝐶𝐶𝐶𝐶2�)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡,(12)for𝑡𝑡=2006,…,210038SSPemissionspathwaysareavailablefromtheSSPdatabasehostedattheIIASAwebsite:(https://tntcat.iiasa.ac.at/SspDb/dsd?Action=htmlpage&page=about)andprovidedin10-yeartime-steps.WeinterpolatetheSSPprojectedemissionslinearlytoanannualfrequencytomatchourestimatesoftheimplementationandmarginalsemielasticities.66withtheinitialvaluelog(𝐶𝐶𝐶𝐶2�)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡=2005providedbythe2005levelofemissionsintheSSPscenarioandtheprojectedchangeinemissionsgivenbyΔlog�𝐶𝐶𝐶𝐶2��𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡=Δlog(𝐶𝐶𝐶𝐶2)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡,𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵+Δlog(𝐶𝐶𝐶𝐶2)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡,𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃(13)whereΔlog(𝐶𝐶𝐶𝐶2)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡,𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵istheCO2emissionsgrowthrategivenintheSSPreferencescenarioandΔlog(𝐶𝐶𝐶𝐶2)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡,𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃istheemissionsgrowthinahypotheticalcarbonpricingscenario.Weconsidertwoapproachestoprojecttheimpactofpricingonemissions.Inthefirst,wespecifythepolicyimpactonthegrowthrateassolelytheaveragetreatmenteffectonthetreated:Δlog(𝐶𝐶𝐶𝐶2)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡,𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃=𝛿𝛿̂̅𝑡𝑡𝑡𝑡𝑡𝑡(14)where𝛿𝛿̂̅𝑡𝑡𝑡𝑡𝑡𝑡istheaveragetreatmenteffectonthetreatmentestimatedusingsyntheticcontrolsforemissionsaggregatedacrosssectors.Thus,thecounterfactualsimulationusing(11,REF)projectsthechangeinemissionscombiningtheaverageintroductioneffectsandtheaveragein-samplepricelevel(around$3/tCO2).Inthesecondsetofscenarioprojections,wedecomposethetreatmenteffectintotheestimatedintroductionandpriceeffects:Δlog(𝐶𝐶𝐶𝐶2)𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡,𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃=𝑎𝑎�𝑡𝑡𝑡𝑡𝑡𝑡+𝑏𝑏�𝑡𝑡𝑡𝑡𝑡𝑡𝑝𝑝𝑡𝑡(15)67where𝑏𝑏�𝑡𝑡𝑡𝑡𝑡𝑡istheestimatedsemielasticityusingbetween-countryvariationfromSection5.2,𝑝𝑝𝑡𝑡,𝑡𝑡𝑡𝑡𝑡𝑡denotesthecarbonpriceattimetduringtheprojectedtreatedperiod(2021–2050)and𝑎𝑎�𝑡𝑡𝑡𝑡𝑡𝑡istheinterceptinourmodelusedtoestimatetheelasticity.Takentogether,𝑎𝑎�𝑡𝑡𝑡𝑡𝑡𝑡+𝑏𝑏�𝑡𝑡𝑡𝑡𝑡𝑡𝑝𝑝𝑡𝑡correspondtoourmodeloftheaveragetreatmenteffect.Theelasticityandintroductionestimatesaretakenfromthebaselinemodelspecification(1)summarizedinTable6.Themodelin(12)allowsustosimulatetheimpactofanyhypotheticalpricepath𝑝𝑝𝑡𝑡.Wesimulatetheuncertaintyrangearoundprojectedemissionsbysamplingoverthebootstrapdrawsofthetreatmenteffect𝛿𝛿̂̅𝑡𝑡𝑡𝑡𝑡𝑡,pricecoefficient,𝑏𝑏�𝑡𝑡𝑡𝑡𝑡𝑡,andintroductioneffect(intercept),𝑎𝑎�𝑡𝑡𝑡𝑡𝑡𝑡.Weimplicitlyassumethattheseparametersremainconstantovertheprojectedperiodand,therefore,thatnogradualphase-inofeffectsornonlinearitiestakeplace.Granted,itisnotguaranteedthattheemissionselasticitywillbeconstantorthedemandfunctionwillbesmoothandcontinuousintothefuture;asrenewableenergyresourcesbecomecheaperthanfossilfuelsinagrowingnumberofsectorsandmarkets,economiesmayreachaninflectionpointwherethepriceelasticityofemissionsshiftsupwardasdemandforfossilfuelsplummets.Parameterconstancyisastrongsimplifyingassumption,butanyvariationinemissionsthatoccursduetotime-dependencyofpolicyeffectslikelyfallswellwithinthealreadywiderangeofsimulatedoutcomes.Uncertaintyaboutthephasinginoftreatmenteffectsislikelydwarfedbytheuncertaintyintheparameterestimates.Thefollowingsimulationsareperhapsoptimisticintheshortrun,becausetheyassumepricesaffectemissionsimmediately.68Figure9showsprojectedemissionsfortheSSP2referencescenario(commonlyreferredtoasthe“middle-of-the-road”scenario)togetherwithhypotheticalcarbonpricepaths.39Thefirstscheme(purple)introducesaconstantemission-weightedpriceof$8/tCO2(themedianacrossallcurrentschemes).Asecondschemesimulatesaninitial$20/tCO2pricethatincreasesby$5/tCO2peryearuntilreaching$100/tCO2(green).Athirdsimulatesaconstant$250/tCO2price(red).Eventhoughthesemielasticityisimpreciselyestimated,themedianprojecteddifferenceinemissionssuggestsa35percentreductioninthelevelofCO2emissionsby2050forthe$8constantpricingscheme.Itiscriticaltonotethatthisisrelativetothereferencescenario,andevena35percentreductionintheemissionslevelrelativetotheSSP2baselinecorrespondstoonlyalittleover10percentemissionsreductionrelativeto2020(bottompanelinFigure6).Thewideuncertaintyrangeofprojectedemissionsimpliedbythebootstrapintervalsshowswecannotbecertainofcarbonpricingguaranteeinglarge-scaleemissionreductions(the25–75percentinterquartilebootstraprangesareshownasshadedfortheconstant$8and$250pricingschemes).Ourconclusionisthatachievingamedianprojectedemissionsreductionof50percentby2030relativeto2020usingonlycarbonpricingseemsallbutimpossible.Projectedmedianemissionchangesinresponsetoa$20/tCO2carbonpricethatisrampedupby$5peryearuntilreachingto$100resultina15percentreductionby2030and40percentby2050.Withoutpersistenceinemissions,achievingthedesiredreductionwouldlikelyrequireaglobalemission-weightedeconomywidecarbonpriceinexcessof$250/tCO2(redpricingschemeinFigureIX,withveryhighuncertainty).Thisseemsfaroutsidetherealmofpoliticalfeasibility.39Frickoetal.(2017)offersafulldescriptionoftheSSP2scenarioanditsunderlyingassumptions.69FigureIX.GlobalCO2EmissionsRelativetoReferenceScenario(SSP2,“MiddleoftheRoad”)UsingEmpiricalEstimatesoftheEmissionsResponsetoCO2PricingNote:Toppanelshowstheprojectedemissions,withthereferencescenarioinblackandmedianhypotheticalemissionsfordifferentpricingschemes:constant$8(purple);initial$20andincreasinguntilreaching$100(green);andconstant$250(red).Themiddlepanelshowsthepercentagedifference707.CONCLUSION:POLICYIMPLICATIONSFewquestionsareaspressingtodayinthearenaofclimatepolicyastheeffectivenessofcarbonpricingatreducingemissions,giventhepreponderantpreferencefor(oratleastpromotionof)market-basedapproachesatnumerousgovernmentministries,NGOs,carbon-intensivecorporations,OECD,IMF,WorldBank,andUNFCCC.Ourretrospectiveevaluationcontributestoafullerunderstandingofthisquestion,basedonanovelapproachtoestimatingchangesinCO2emissionsassociatedwith(i)theintroductionofcarbonpricingirrespectiveofthepricelevel,(ii)theeffectofcarbonpricingconditionalonthepricelevel,and(iii)theresponseoffutureemissionstopossiblecarbonpricepathsbasedonourempiricalestimatesofaveragetreatmenteffectsandemissionselasticities.Consistentacrossarangeofmodelspecifications,carbonpricinginstrumentshavereducedtheannualgrowthrateofCO2emissionsby1–2.5percentagepointsonaveragerelativetocounterfactualemissions,withmostabatementoccurringintheelectricityandheatsector(whereestimatesoftheaveragetreatmenteffectreachupto–6percentagepointsinsomespecifications).Theresponseofemissionstoahigherpricelevelisimpreciselyestimatedinallsectors,withthepotentialexceptionofmanufacturing.Negativepointestimatesforthesemielasticityarecenteredarounda0.1percentreductioninthegrowthrateoftotalemissionsforeachadditional$1/tCO2tobaselineineachyear,andthebottompanelshowsthepercentagedifferencefromthereferencescenarioin2020.Shadedbandsdenotea25–75percentbootstrapinterquartilerangeforthepurpleandredschemes.TheParisAgreementtargetofa50percentreductionrelativeto2020by2030isindicatedbythereddiamond.71androughly0.2percentinthemanufacturingsector.Thissuggeststhatmerelyintroducingcarbonpricing(evenatlowlevels)canreduceemissionsgrowth.However,perhapsonlymarginaladditionalreductionscanbeachievedathigherpricelevelsfortherangeofpricescurrentlyobservedinsample.Forexample,inresponsetocarbonpricing,NewZealand—withanaveragepriceofaround$6dollarspermetrictonofCO2intheelectricityandheatsector—reducedemissionsbyaround3percentagepoints,andSwitzerland,withamuchhigheraveragecarbonpriceof$36,experiencedasimilar3percentagepointreductioninemissionsgrowth.BasedonoursimulationsofpotentialfutureCO2emissionsreductionsinresponsetoalternativecarbonpricepathsupto2050,weconcludethatemissionsareunlikelytodeclinetolevelsconsistentwithParisclimatetargetsgivenplausiblelevelsofcarbonpricinginthedecadesahead,absentcomplementary(nonpricing)policiesandsubstantialpublicinvestmentstodeploygreentechnologiesandinfrastructure.Ourestimatesof(semi)elasticitiesindicatethatemissionsmaybesubstantiallylessresponsivetothelevelofthecarbonpricethansuggestedbypreviousempiricalstudies,whereasperhapsthemereintroductionofcarbonpricingsendsasignalthatleadstoreductionsinemissions.Theenergydemandelasticitiesassumedinenergy-climatemodels,forexample,typicallyfallbetween–0.3and–0.7—seediscussionsinMadleneretal.(2011),Websteretal.(2008),andParry(2020).Bycontrast,our(implied)energydemandelasticityestimatescenteraround–0.18forelectricityandheat,buildings,andtheeconomyasawhole.40Fortheroadtransportsector,Sterner(2007)reports40Thisiscalculatedbasedonourestimateoftheaveragemarginalsemielasticitybycomputingtheeffectofa$1/tCO2priceincreaserelativetoanaveragepriceof$8/tCO2insample.Thesameholdsforthesubsequentestimatereportedinthisparagraphforthepriceelasticityofgasolinedemand.72globallyaveragedgasolinepriceelasticitiesofaround–0.7basedonestimatesfromEuropeandtheUnitedStates,andtheestimatesinDahl(2012)areclosertoabout–0.25onaverage.Our(implied)gasolinepriceelasticityestimatescenteraround–0.25.Weaddacaveat:ourimpliedelasticityestimateshereassumethatthe(carbon)-priceelasticityofenergydemandisequivalenttothegenericpriceelasticityofenergydemand.IfinsteadoneweretoassumethattheCO2-priceelasticityisaroundthreefoldgreaterthanthegenericpriceelasticity,assuggestedinseveralrecentstudies,41thenthedisparitybetweenourestimatesandthoseofpreviousempiricalstudieswouldbeevengreater.Severalconsiderationsleadustoconcludethatoursignificantlylowerelasticityestimatesarenotmereartifactsofstatisticalnoisebutratherindicativeofpoignantempiricalrealities.1.Thedifferencebetweenourestimatesandearlierresultscouldpartlystemfromourexplicitdifferentiationbetweenintroductionandpriceeffects.Ifwedonotallowforintroductioneffects,thismaybiastheelasticityestimateswithrespecttocarbonprices.2.Relyingonempiricalestimatesofenergydemandelasticitiesbasedondatafromthe1980sandearliermayleadresearchersandpolicymakerstounderestimatetheextenttowhichenergydemandhasbeenshiftingtowardrelativelyfast-growingandlessprice-responsiveproductsandregions.423.Policy-responsemodelsofCO2emissions(bothexanteandexpost)havetendedtopoorlycapturetheinertiaofinfrastructurelock-in.4341See,forexample,Andersson(2019).42See,forexample,theevidenceforworldoildemandinDaragayandGately(2010).43See,forexample,theanalysisinAvneretal.(2014)ofurbanvs.ruralresponsestocarbonpricingundervaryingdensitiesofmasspublictransportinfrastructure.734.Ourempiricalevaluationisthefirsttoexplicitlyaccountforcross-countryandtemporalvariationincarbonpriceexemptionsacrossdifferentsectorsandindustries.Theimportanceofthiscanbeseenwhenconsideringthatgovernmentsmaybeincentivizedto“offload”highercarbonpricesontosectorsandindustriesthatareeither(i)relativelypriceinelasticbutabletobearthepolicycostsduetorelativelylesscarbonexposure;or(ii)highlypriceelasticbuthavealreadyundergonecriticalprocessesofdecarbonizationintheyearsprecedingtheintroductionofcarbonpricing.44Takentogether,theseconsiderationsshouldcastdoubtonthenotionthatthepriceelasticityofenergydemandshouldbestableovertime,animplicitassumptionofoursimulationexercise.Instead,emissionselasticitiesarelikelytobeafunctionofnotonlythepriceofemissionsbutalsotheinitialstateintheevolutionaryprocessofcomplexenergy-technologicalsystemstowhichthepriceisapplied(Mercureetal.2014;Grubb2014).Asaconsequence,weemphasizethatanyconclusionsdrawnfromoursimulationexercise,althoughtheyarebasedonempiricallygroundedandup-to-dateelasticityestimates,arelimitedbyanirreducibleelementofuncertainty.Ourassessmentcorroboratesseveralbestpracticesforoptimizingcarbonpricingreformsthathavebeenidentifiedelsewhere.First,carbonpricesareunderminedthemoretheyarevolatileinterannually;theirenvironmentalefficacytendstobeenhancedwhentheyareonacredibleupwardtrajectory,whichhasbeenrarebutcanbereinforcedthroughbuilt-inprice-adjustmentmechanisms(Hafsteadetal.2017;Metcalf2020).Alternatively,policymakersmayattempttopriceCO2emissionsatveryhighlevelsinitiallytobettercaptureclimateexternalitiesunderconditionsofuncertainty,whichmaycounterintuitivelyimplyadecliningCO2pricepathovertime(Daniel44Forexample,DenmarkandGermanyunderwentmultidecadeprocessesofenergysystemtransformationinresponsetotheoilpriceshocksofthe1970s,asdiscussedinGrubbetal.(2017)andelsewhere.74etal.2019).Suchanexperimentwouldbeintriguing,butitseemsunlikelytopassmusterwithoutsubstantialrevenuerecyclingintheearlyphasetocounteractanyregressiveimpactsonindividualswhosecarboncostexposurecomprisesasalientshareoftheirhouseholdincome(Klenertetal.2018).Second,despitecompellingargumentsthatmightleadpolicymakerstoprefercarbonpricingschemesthatstrategicallytargetasmallnumberofindustriesorsectorswithsignificantintersectorallinkages(Kingetal.2019),thoseoptingforsuchanapproachshouldrecognizethatthediscrepancybetweencurrentcoveragelevelsandthosethatarelikelyneededtocomplywith1.5–2°Cclimatetargetsremainsstark.Thus,additionalregulationsthatimplicitlypriceCO2emissionsorpublicgreeninvestmentsthatreducethecostsofalternativeswillbeneededtoincentivizedecarbonizationwhereveranexplicitandsufficientlyhighCO2priceisabsent.Underatargetedcarbonpricingscheme,exemptionsforemissions-intensiveindustriesshouldstillbeeliminatedtothegreatestextentpossible,includingintheimplicitformofunpricedcarbonembodiedininternationallytradedgoods(Moranetal.2018);norshouldgreaterrelianceonnonpricingclimatemeasuresdistractpolicymakersfromtheneedtoeliminatefossilfuelsubsidiesthatfunctionasanegativecarbonprice,aboutthree-quartersofwhichgloballyareduetodomesticfactorsthatarealterableviaenergypricingreforms(Coadyetal.2019).Climatepolicies,whenstrategicallytargetedandcombined,maybehighlysynergistic(Farmeretal.2019;Grubb2014;Mercureetal.2014).Carbonpricingstillhasthepotentialtobeapowerfultoolcontributingtoemissionreductions,butitisnopanacea.75APPENDIXA.COMPUTINGECPSTocomputetheemissions-weightedcarbonprice(ECP),thefollowinginformationisrequired:(i)thecoverageofthecarbonpricingpolicy(volumeofCO2emissionstowhichthepriceapplies),(ii)verifiedtotalCO2emissionsineachjurisdiction,and(iii)thenominalemissionsprice(/tCO2).Thisinformationiscollectedatthesector-fuellevel.SectoraldisaggregationfollowstheguidelinesoftheInternationalPanelonClimateChange(IPCC2006).Themainanthropogenicsourcesofnational(territorial)CO2emissionsareincludedbasedonthreeIPCCsourcecategories:“FuelCombustionActivities—SectoralApproach”(category1A);“FugitiveEmissionsfromFuels,GasFlaring,andVenting”(category1B);and“IndustrialProcessesandProductUse,IncludingCement”(category2).Thesecategoriesaccountedfor92and72percentoftotalglobalCO2andGHGemissions,respectively,in2012(IEA2018;UNFCCC2018).Informationpertainingtothefuels,sectors,andquantityofemissionstowhicheachcarbonpricingpolicyinstrumentapplieswithineachcountryisfromvarioussources,includingprimarylegislation,theOECDDatabaseonInstrumentsUsedforEnvironmentalPolicy(OECD2020),customsagencies’documentation,academicjournalarticles,andpolicyassessmentreports(forafulllist,seehttps://github.com/g-dolphin/WorldCarbonPricingDatabase).VerifieddataontotalCO2emissionsineachjurisdictionisderivedfromIEA(2018).Informationaboutnominalemissionprices(taxrateorallowanceprice)isfromdifferentsourcesdependingonthetypeofpolicyinstrumentandparticularjurisdiction.Forcarbontaxes,werelyontheIEA’sannualEnergyPricesandTaxespublication,jurisdictions’budgetproposals,andprimaryand76secondarylegislativeacts(forexhaustiveinformationondatasourcesforCO2pricesinETSsandcarbontaxschemes,seehttps://github.com/g-dolphin/WorldCarbonPricingDatabase).Withthisinformation,theemissions-weightedcarbonprice(ECP)canbecomputedatthesectorandeconomywidelevels.Formally,theECPofsector𝑗𝑗ofcountry𝑖𝑖inyear𝑡𝑡canbeexpressedasECPi,t,j=∑�τi,t,j,k�qi,t,j,ktax+qi,t,j,kets,tax�+pi,t,j,k�qi,t,j,kets+qi,t,j,kets,tax��kqi,t,jCO2(A1)whereτi,t,j,kisthecarbontaxrateapplicabletofuel𝑘𝑘,qi,t,j,ktaxisthequantityofCO2emissionscoveredbyataxonly,pi,t,j,kisthepriceofanemissionpermit,qi,t,j,ketsisthequantityofCO2emissionscoveredbyanemissionstradingsystem(ETS),qi,t,j,kets,taxisthequantityofCO2emissionscoveredbybothanETSandacarbontax,andqi,t,jCO2isthetotalquantityofCO2emissionsinsector𝑗𝑗ofcountry𝑖𝑖inyear𝑡𝑡.ShouldasectorbecoveredbyonlyoneofthetwopolicyinstrumentsandallCO2emissions(i.e.,allofitsfuelsarecovered),theECPi,t,jwouldcollapsetoeitherτi,t,jorpi,t,j.AneconomywideECPisthencomputedasaweightedaverageofthesectoralcarbonrates.Theweightscorrespondtothequantitiesofemissionssubjecttoeachindividualcarbonrate,suchthat77ECPi,t=�ECPi,t,jγi,t,jj,(A2)whereγi,t,jrepresentstheCO2emissionsofsector𝑗𝑗asashareoftotalCO2emissionsineachjurisdiction(i.e.,qi,t,jCO2qi,tCO2�).AllpricesareexpressedinUSdollarsatconstant2019prices.ToensurethatthecomputedECPlevelsarenotbiasedbyinterannualchangesinCO2emissionsthatmaybeaconsequenceofthepolicyitself,allyearsareweightedusingemissionsdataoftheyearbeforethepolicywasintroduced.Forcountry-levelECP,thismeansthattheweightsarebasedonemissionsintheyearbeforethecarbonpricingpolicyinanysectoroftheeconomy.Forsector-levelECP,weightsarebasedonemissionsintheprecedingyearforthatsector.WhenconsideringpricesarisingfromETSandtaxschemesseparately,weightsarebasedonemissionsintheyearprecedingtheintroductionofanypricingscheme.78APPENDIXB.DATASUMMARYTableB1.SummaryofObservedCovariatesCovariatesUnitSourceCO2emissions:total(economywide),electricityandheat,manufacturing,roadtransport,andbuildings(commercialandresidential)MilliontonsofCO2(MtCO2)IEA(2018)Emissions-weightedcarbonprice:total(economywide),electricityandheat,manufacturing,roadtransport,andbuildings(commercialandresidential)USdollarspertonCO2(constant2015prices)UpdatedfromDolphinetal.(2020)GDP:total,manufacturing,transport,andservicesUSdollars(millions,constant2015prices)UNCTAD(2020a),basedonUnitedNationsDESAStatisticsDivision,NationalAccountsMainAggregatesDatabasePopulationsizeAbsolutevalueinthousandsUNCTAD(2020b),basedonUnitedNationsDESAPopulationDivision,WorldPopulationProspects:The2019Revision79Degreedays:heating,coolingPopulation-weighted(18.3°Cbasetemperature)Mistry(2019)80APPENDIXC.DIAGNOSTICSANDMISSPECIFICATIONTESTSOurmodelspecificationsareinformedbydiagnostictestsforcross-sectiondependence,commonfactors,unitroots,andpanelcointegration.First,westronglyrejectthenullhypothesisofcross-sectionindependence(andweakcross-sectiondependence)oftheerrorsforourbaselinemodelwhenvariablesareinlevels,butwecannotrejectthenullwhenthemodelisspecifiedinfirstdifferences.Hence,differencingnotonlyeliminatesserialcorrelationoftheerrorsbutalsoallaysconcernsaboutcross-sectiondependence.UsingtheunitroottestsdevelopedinImetal.(2003)andPesaran(2007),wecannotrejectthenullhypothesisthatthecovariatescontainunitrootsforallpanels,butwerejectthenullwhenvariablesareinfirstdifferences.Thus,allvariablesareintegratedoforderI(1).Thenullhypothesisthatadditive(timeandunit)fixedeffectsaresufficientisstronglyrejectedatthe1percentlevelusingtheHausman-typetestinBai(2009).Thenullhypothesisthatthedimensionalityofcommonfactorsequalszeroisstronglyrejectedatthe1percentlevel,regardlessofwhetherthefactorsareassumedtobeI(0)orI(1)(Bai2009;Kneipetal.2012).Wedeterminetheoptimalnumberoffactorstobe2–5dependingonthesectorandmodelspecification,basedonthedimensionalitytestcriteriaproposedinAhnandHorenstein(2013),Kneipetal.(2012),andBaiandNg(2002).4545AlltestsarecomputedusingphttinR.81Todistinguishbetweencommonandidiosyncraticcomponentsoftheresiduals(BaiandNg2004,2010),weapplythePANNICAtestingproceduredescribedinReeseandWesterlund(2016);TableC.1presentstheresults.TheprocedurecombinesthestrongsmallsampleperformanceofthetestsdevelopedinPesaran(2006)withtheflexibilityregardingordersofintegrationforcommonandidiosyncraticerrorcomponentsasinthetestsfromBaiandNg(2004,2010).Theresultscorroboratethepresenceofmultiplecommonfactors.Whenvariablesareenteredinlevels,wefailtorejectthenullhypothesisoffewerunitrootsthancommonfactors,suggestingglobalstochastictrends.Butwhenvariablesareinfirstdifferences,wedonotdetectunitrootsintheremainingfactors.Furthermore,werejectthenullhypothesisofaunitrootintheidiosyncraticerrorsofallcountriesusingtheBaiandNg(2010)tests.Hence,alltestsconsistentlysuggestthatnonstationarityisdrivenentirelybycommonerrorcomponents,whereasstationarityisattainedinthefirst-differencedmodelconditionalontheobservedregressors.Thisnaturallyleadstotestsforcointegration.WeapplythoseproposedbyWesterlund(2007)tothebaselinespecificationforthemodeloftotalaggregateCO2emissions.TableC.2presentstheresults.Bootstrapcriticalvaluesofthesetestsarerobustinthepresenceofcommonfactors.Westronglyrejectthenullhypothesisofnocointegrationatthe1percentlevel.82TableC1.PanelAnalysisofNonstationarityinIdiosyncraticandCommonComponents(PANIC)CommonfactorsUnit-specificresidualskMQcMQfPaPbPMSBlog(CO2_total)32–24.089–10.935–12.486(0.000)–5.166(0.000)–2.12(0.017)log(CO2_industry)4–39.428–38.999–21.91(0.000)–8.806(0.000)–3.468(0.0003)log(CO2_electricity)6–46–42–31.885(0.000)–11.271(0.000)–3.99(0.000)log(CO2_road)6–46–42–23.952(0.000)–8.203(0.000)–2.824(0.0024)Notes:WeapplytheiterativeestimationprocedureofBaiandNg(2004)toobtainMQcandMQf,,whicharemodifiedversionsofthe“corrected”Qcand“filtered”QftestsinStockandWatson(1988),wherekdenotesthenumberofindependentstochastictrendsdrivingthecommonfactors.Thenullhypothesisofbothtestsiskunitrootsinthecommonfactors;wereportonlytheteststatisticsforiterationswhereitcannotberejected.Fortheidiosyncratic(unit-specific)component,wecomputethethreeteststatisticsfromBaiandNg(2010):PMSBisapanel-modifiedSargan–Bhargavatestthatdoesnotrequireestimationofp,thepooledautoregressivecoefficientoftheunit-specificerrors.Thenullhypothesisofallthreeunit-specifictestsisthatallunitsarenonstationary,whichwestronglyreject.AllteststatisticsarecomputedusingxtpaniccainStata,withthankstoSimonReeseforhelpfulinput.83TableC2.TestsforPanelCointegration[Dependentvariable:𝚫𝚫𝚫𝚫𝚫𝚫𝚫𝚫(𝑪𝑪𝑪𝑪𝑪𝑪)𝒊𝒊,𝒌𝒌,𝒕𝒕]𝐺𝐺𝜏𝜏𝐺𝐺𝛼𝛼𝑃𝑃𝜏𝜏𝑃𝑃𝛼𝛼–6.127(0.000)6.067(1.000)2.458(0.993)2.384(0.991)Note:Bootstrapp-valuesbasedon1,000replicationsareshowninparentheses.Criticalvaluesoftheteststatisticsarerobustinthepresenceofcommonfactors.TheoptimallagandleadlengthforeachseriesisselectedusingtheAkaikeinformationcriterion.Thelong-runvarianceisbasedonsemiparametricestimationusingtheBartlettkernel.84APPENDIXD.ADDITIONALESTIMATIONRESULTSD.1Two-WayFixedEffectsandInteractiveFixedEffectsResultsD.1.1TreatmentEffectEstimatesWereportthefullsetofresultswhenestimatingtreatmenteffectsusingTWFEandIFEmodels.TableD1.1.1showstheestimationresultsoftheTWFEmodelin(1);TableD1.1.2showstheestimationresultsoftheIFEmodelin(2).ThenumberoffactorsintheIFEmodelischosentomatchthenumberoffactorsdeterminedusingcross-validationinthesyntheticcontrolfactormodel.TWFEstandarderrorsareclusteredatthecountrylevel.IFEstandarderrorsarederivedusing500bootstrapdraws.Theestimationresultsarecomparabletothosefromgeneralizedsyntheticcontrolmethods,thoughthelattergenerallyexhibitlowerestimationuncertainty.Todifferentiatebetweengrowthandleveleffectsweexpandmodels(1)and(2)tofurtherincludealaggedtreatmentindicatorintheTWFEmodel:Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝛿𝛿0,𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡+𝛿𝛿1,𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡−1+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜏𝜏𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡(D1)andtheIFEmodel:Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝛿𝛿0,𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡+𝛿𝛿1,𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡−1+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘(D2)85+𝜏𝜏𝑘𝑘,𝑡𝑡+𝜆𝜆𝑖𝑖,𝑘𝑘ʹ𝐹𝐹𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡IftheintroductionofcarbonpricingaffectsthelevelofCO2emissionsratherthanthegrowthrate,weexpectthechangeinthatratetobetransitoryandthecoefficient𝛿𝛿0,𝑘𝑘onthecontemporaneoustreatmentvariabletohavetheoppositesignfromthecoefficient𝛿𝛿1,𝑘𝑘onthelaggedtreatmentvariable.TablesD1andD2alsoreportestimationresults,showinglittleevidenceoflevelratherthangrowtheffects.Thecoefficientsarepredominantlynotoppositesigned.TableD1.TWFEResults:AverageTreatmentEffectsTotalElec.&HeatManufacturingRoadtransportBuildingsIntroduction–0.006(0.007)[p=0.37]0.006(0.011)[p=0.58]–0.019(0.011)[p=0.1]–0.003(0.033)[p=0.93]–0.002(0.016)[p=0.89]–0.025(0.031)[p=0.43]–0.011(0.01)[p=0.28]–0.002(0.019)[p=0.92]–0.014(0.01)[p=0.2]–0.005(0.025)[p=0.86]L1.IntroductionNA–0.014(0.013)[p=0.28]NA–0.018(0.033)[p=0.59]NA0.025(0.031)[p=0.42]NA–0.01(0.018)[p=0.57]NA–0.011(0.023)[p=0.65]𝑛𝑛𝑇𝑇𝑇𝑇2323202024247722𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠1,7681,7681,6131,6131,6881,688937937472472Specification#1111111111TableD2.IFEResults:AverageTreatmentEffectsTotalElec.&HeatManufacturingRoadtransportBuildings86Introduction–0.0147(0.0072)[p=0.11]0.0047(0.0129)[p=0.71]–0.0205(0.0112)[p=0.09]–9e-04(0.0313)[p=1]–0.0049(0.0169)[p=0.97]–0.0267(0.0315)[p=0.41]–0.0071(0.0114)[p=0.58]–0.0258(0.0313)[p=0.38]–0.0308(0.0118)[p=0]–0.0453(0.0252)[p=0.12]L1.IntroductoonNA–0.0219(0.0141)[p=0.2]NA–0.022(0.032)[p=0.5]NA0.0246(0.0298)[p=0.31]NA0.0219(0.0292)[p=0.42]NA0.0167(0.0286)[p=0.57]𝑛𝑛𝑇𝑇𝑇𝑇2323202023236622𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠1,8721,8721,6921,6921,8721,8721,0081,008504504r1111111111Specification#111111111187D.1.2ElasticityEstimatesWereporttheelasticityestimatesobtainedusingTWFE(D1.2.1)andIFE(D1.2.2).WeshowtheestimationresultsallowingforbothanintroductionandapriceeffectandalsoreporttheestimationresultswhenintroductioneffectsareomittedandmodelsareestimatedincludingsolelythecarbonpriceintheTWFEmodel:Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝑏𝑏𝑘𝑘(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡)+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜏𝜏𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡(D3)andtheIFEmodel:Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝑏𝑏𝑘𝑘(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡)+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜏𝜏𝑘𝑘,𝑡𝑡+𝜆𝜆𝑖𝑖,𝑘𝑘ʹ𝐹𝐹𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡(D4)TWFEstandarderrorsareclusteredatthecountrylevel.IFEstandarderrorsarederivedusing500bootstrapdraws.Todifferentiatebetweenlevelandgrowtheffects,wealsoestimateversionsincludingthelagofthecarbonpriceintheTWFEmodel:Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝑎𝑎𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡+𝑏𝑏0,𝑘𝑘(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡)+𝑏𝑏1,𝑘𝑘(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡−1𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡)+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜏𝜏𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡(D5)andtheIFEmodel:88Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝑎𝑎𝑘𝑘𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡+𝑏𝑏0,𝑘𝑘(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡)+𝑏𝑏1,𝑘𝑘(𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡−1𝐷𝐷𝑖𝑖,𝑘𝑘,𝑡𝑡)+𝑥𝑥𝑖𝑖,𝑘𝑘,𝑡𝑡ʹ𝛽𝛽+𝜉𝜉𝑖𝑖,𝑘𝑘+𝜏𝜏𝑘𝑘,𝑡𝑡+𝜆𝜆𝑖𝑖,𝑘𝑘ʹ𝐹𝐹𝑘𝑘,𝑡𝑡+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡(D6)Ifthelevelofthecarbonpriceprimarilyaffectsthelevel(ratherthanthegrowthrate)ofCO2emissions,weexpectthecoefficientonthecontemporaneouspricevariabletohavetheoppositesigntothecoefficientonthelaggedprice.LagresultsareshowninTablesD3andD4.89TableD3.TWFEResults:IntroductionandPriceEffectsTotalElec.&HeatManufacturingRoadtransportBuildingsIntro–3e-04(0.0093)[p=0.98]-–0.0067(0.0204)[p=0.75]–0.0248(0.0231)[p=0.29]––0.0158(0.0098)[p=0.12]––0.009(0.0254)[p=0.73]–Price–9e-04(5e-04)[p=0.09]–0.001(0)[p=0.04]–8e-04(9e-04)[p=0.35]–0.001(0)[p=0.04]–0.002(0.0015)[p=0.18]–0.001(0.001)[p=0.32]3e-04(1e-04)[p=0.01]0(0)[p=0.79]–2e-04(7e-04)[p=0.76]0(0)[p=0.03]𝑛𝑛𝑇𝑇𝑇𝑇2323202024247722𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠1,7141,7141,5591,5591,6881,688937937472472Spec.#1111111111TableD4.IFEResults:IntroductionandPriceEffectsTotalElec.&HeatManufacturingRoadtransportBuildingsIntroduction–0.0089(0.009)[p=0.44]––0.0157(0.0195)[p=0.4]–0.0239(0.0227)[p=0.25]––0.0115(0.0419)[p=0.41]––0.0456(0.027)[p=0.01]–Price–8e-04(6e-04)[p=0.2]–0.0013(5e-04)[p=0.04]–3e-04(8e-04)[p=0.82]–8e-04(4e-04)[p=0.12]–0.0022(0.0015)[p=0.19]–0.0012(0.0011)[p=0.38]2e-04(0.0027)[p=0.46]0(8e-04)[p=0.99]7e-04(0.0015)[p=0.23]–7e-04(0.001)[p=0]𝑛𝑛𝑇𝑇𝑇𝑇2323202023236622𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠1,8721,8721,6921,6921,8721,8721,0081,008504504r1111111111Specification#111111111190TableD5.TWFEResults:LagPricesTotalElec.&HeatManufacturingRoadtransportBuildingsIntro–0.001(0.009)[p=0.91]–0.0069(0.0081)[p=0.4]–0.0143(0.0251)[p=0.57]–0.0263(0.0223)[p=0.24]0.0338(0.028)[p=0.23]0.0075(0.0209)[p=0.72]–0.0157(0.0098)[p=0.12]–0.015(0.0098)[p=0.14]–0.0091(0.0253)[p=0.72]–0.0124(0.0222)[p=0.58]Price–9e-04(6e-04)[p=0.12]––0.001(9e-04)[p=0.29]––0.002(0.0015)[p=0.18]–2e-04(4e-04)[p=0.72]––7e-04(0.0011)[p=0.55]–L1.price1e-04(6e-04)[p=0.83]–1e-04(6e-04)[p=0.9]7e-04(0.001)[p=0.47]5e-04(0.001)[p=0.64]–7e-04(0.0013)[p=0.56]–8e-04(0.0012)[p=0.54]1e-04(5e-04)[p=0.79]3e-04(2e-04)[p=0.1]6e-04(0.0012)[p=0.62]–1e-04(7e-04)[p=0.92]𝑛𝑛𝑇𝑇𝑇𝑇2323202023236622𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠1,7141,7141,5591,5591,6881,688937937472472Spec.#1111111111TableD6.IFEResults:LagPricesTotalElec.&HeatManufacturingRoadtransportBuildingsIntro–0.0042(0.0096)[P=0.78]–0.0071(0.0086)[P=0.49]–0.0224(0.0275)[P=0.34]–0.0281(0.0217)[P=0.19]0.0418(0.0288)[P=0.16]0.0115(0.0206)[P=0.55]–0.0112(0.064)[P=0.38]–0.0135(0.0272)[P=0.28]–0.0467(0.0281)[P=0.03]–0.0524(0.0147)[P=0]Price–5E-04(6E-04)[P=0.4]––5E-04(0.001)[P=0.77]––0.0022(0.0016)[P=0.17]––5E-04(0.0051)[P=0.27]––0.0012(0.0027)[P=0.46]–L1.price–0.001(8E-04)[P=0.33]–0.0011(7E-04)[P=0.24]7E-04(0.0011)[P=0.49]5E-04(0.0011)[P=0.55]–0.0014(0.0012)[P=0.34]–0.0014(0.0011)[P=0.32]9E-04(0.0024)[P=0.13]4E-04(0.0019)[P=0.18]0.0025(0.0015)[P=0.22]0.0012(7E-04)[P=0.05]𝑛𝑛𝑇𝑇𝑇𝑇2323202023236622𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠1,8721,8721,6921,6921,8721,8721,0081,008504504𝑟𝑟111111111191Spec.#111111111192D.2AdditionalResultsUsingSyntheticControlsWithin-countryestimationresultsofthepanelmodeloftreatmenteffectsasafunctionofthepricelevelallowingforlevelorgrowtheffectsthroughtheinclusionoflaggedcarbonprices.Table2.1reportstheestimationresults.IfcarbonpricesaffectthelevelofCO2emissionsinsteadofthegrowthrate,weexpectthecoefficientoncontemporaneouspricestohavetheoppositesigntothecoefficientonlaggedprices.Thereislittleevidencesupportingleveleffects,thecoefficientsarenotgenerallyoppositesigned,andwhenthepointestimatesexhibitstheoppositesign,theeffectsarenotstatisticallydifferentfromzero.TableD7.Country-YearSpecificTreatmentEffectsfromPanelModelAllowingforLevelorGrowthEffectsTotalElectricityandheatManufacturingRoadtransportBuildingsP𝑡𝑡0.001(0.003)–0.002(0.001)–0.005(0.006)–0.001(0)–0.002(0.001)P𝑡𝑡−10.001(0.002)0.001(0.001)–0.007(0.005)0(0)0.003(0.001)𝑁𝑁𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠1711621623821Spec#1111193FigureD1.TreatmentEffectEstimatesforSpecification#694APPENDIXE.TESTINGFORLONG-RUNEFFECTSINEQUILIBRIUMCORRECTIONMODELWeestimatethefollowingpanelequilibriumcorrection(EC)modelforeachtreatedcountry𝑖𝑖𝑇𝑇𝑇𝑇∈1,2,…𝑁𝑁𝑇𝑇𝑇𝑇,thathashadasufficientlylongtreatedperiod𝑡𝑡𝑇𝑇𝑇𝑇∈𝑡𝑡1,…≥𝑡𝑡23withrespecttocarbonpricinginsectork:Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡=𝛼𝛼𝑖𝑖,𝑘𝑘+𝛽𝛽0,𝑖𝑖.𝑘𝑘𝐸𝐸𝐸𝐸log(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡−1+𝛽𝛽1,𝑖𝑖,𝑘𝑘Δ𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡+𝛽𝛽2,𝑖𝑖,𝑘𝑘𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡−1𝛽𝛽3,𝑖𝑖,𝑘𝑘Δlog(𝑥𝑥ʹ)𝑖𝑖,𝑘𝑘,𝑡𝑡+𝛽𝛽4,𝑖𝑖,𝑘𝑘log(𝑥𝑥ʹ)𝑖𝑖,𝑘𝑘,𝑡𝑡−1+𝜔𝜔0,𝑖𝑖,𝑘𝑘𝐶𝐶𝐶𝐶log(𝐶𝐶𝐶𝐶2)��𝑖𝑖,𝑘𝑘,𝑡𝑡−𝐿𝐿+𝜔𝜔1,𝑖𝑖,𝑘𝑘𝐶𝐶𝐶𝐶Δ𝑝𝑝̅𝑖𝑖,𝑘𝑘,𝑡𝑡+𝜔𝜔2,𝑖𝑖,𝑘𝑘𝐶𝐶𝐶𝐶𝑝𝑝̅𝑖𝑖,𝑘𝑘,𝑡𝑡−𝐿𝐿+𝜔𝜔3,𝑖𝑖,𝑘𝑘𝐶𝐶𝐶𝐶Δlog(𝑥𝑥ʹ)��𝑖𝑖,𝑘𝑘,𝑡𝑡+𝜔𝜔4,𝑖𝑖,𝑘𝑘𝐶𝐶𝐶𝐶log(𝑥𝑥ʹ)��𝑖𝑖,𝑘𝑘,𝑡𝑡−𝐿𝐿+∑π0,𝑖𝑖,𝑘𝑘Δlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡−𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖,𝑘𝑘+∑π1,𝑖𝑖,𝑘𝑘Δ𝑝𝑝𝑖𝑖,𝑘𝑘,𝑡𝑡−𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖,𝑘𝑘+∑π2,𝑖𝑖,𝑘𝑘Δ𝑥𝑥ʹ𝑖𝑖,𝑘𝑘,𝑡𝑡−𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖,𝑘𝑘+𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡,(E1)where𝑝𝑝istheECP,thebarsindicatecross-sectionaveragesofthevariables,𝜔𝜔1,𝑖𝑖,𝑘𝑘𝐶𝐶𝐶𝐶,…,𝜔𝜔4,𝑖𝑖,𝑘𝑘𝐶𝐶𝐶𝐶aretheunknowncoefficientsforthecross-sectionaverages,andthesuperscript𝑆𝑆𝑆𝑆𝑆𝑆indicatesthatthenumberoflagsoffirst-differencedvariables(whichmaybeheterogeneousof𝑖𝑖)areselectedusingageneral-to-specificlagtruncationprocedure.46WeinvestigatecointegrationbetweenthevariablesbyassessingtheECcoefficient𝛽𝛽0,𝑖𝑖,𝑘𝑘in(E.E1).Specifically,wecomputetheunweightedmean-groupECcoefficientas46Foreachcountryi,thelargestlagofeachvariableinfirstdifferences(upto𝑡𝑡−2)isdroppedifitisinsignificantatthe10percentlevel,andthentheselectionprocedureisrepeateduntilthelargestlagsofthevariablesinfirstdifferencesaresignificant(ifany).95∑(𝛽𝛽0,𝑖𝑖,…𝑁𝑁,𝑘𝑘,…𝐾𝐾𝑖𝑖)𝑁𝑁⁄andobtaintheaveraget-statisticandcorrespondingp-valuebasedonthecriticalvaluesinGengenbachetal.(2016).Todeterminewhetherthelong-runaverageemissionssemielasticity(withrespecttothecarbonprice)issignificantlydifferentfromzero,wecomputethelong-runaveragecoefficientas𝜚𝜚=−(�(𝜔𝜔1,𝑖𝑖,𝑘𝑘,…𝜔𝜔𝐶𝐶,𝑖𝑖,𝑘𝑘𝑖𝑖,𝑘𝑘)�(𝜔𝜔0,𝑖𝑖,𝑘𝑘)𝑖𝑖�)(E2)wherethestandarderror,𝑇𝑇�statistic,andp-valuearecomputedusingtheDeltamethod.47Toassesswhetheraugmentingtheequationwithcross-sectionaveragesofthevariablesiseffectiveatremovingcross-sectiondependence,weapplythetestofweakcross-sectiondependencedevelopedinPesaran(2015)tothedependentandindependentvariablesandmodelresiduals.ConsistentwithKapetaniosetal.(2011)andChudikandPesaran(2015),wefindthataddingasufficientnumberoflagsofcross-sectionaverages,𝐿𝐿𝐶𝐶𝐶𝐶=𝑇𝑇^1/3−1,inmodel(9)isapowerfulmeansofresolvingcross-sectionaldependence(seeCDtestsinTableE.1,confirmingthattheresidualsarecross-sectionallyindependent).The𝑇𝑇�statisticinTableE.1leadsustorejectthenullhypothesisofnocointegrationatthe1percentlevel.Theaveragelong-runcoefficientissignificant.47WecomputetheequilibriumcorrectionmodelsandassociatedmisspecificationtestsviaxtcaecinStata.96TableE1.AverageLongRunSemielasticity(Dependentvariable:𝚫𝚫𝚫𝚫𝚫𝚫𝚫𝚫(𝑪𝑪𝑪𝑪𝑪𝑪)𝒊𝒊,𝒌𝒌,𝒕𝒕,inpanelmean-groupequilibriumcorrectionmodel]TotalManufacturingRoadtransportAveragelongrunsemielasticity–1.57percent(0.4)–0.6percent(0.2)–2.55percent(1.39)[–.0529,0.0018]𝛽𝛽0,𝑖𝑖.𝑘𝑘𝐸𝐸𝐸𝐸–1.058(.432)–1.104(.372)–.6107(0.283)Shortrunmarginalsemielasticity–1.06percent(0.82)–0.32percent(0.15)–0.76percent(0.77)Treatedcountries253Treatedobservations50119Totalobservations129CountriesusedtocomputeCA393939RMSE0.01190.02830.0121PanelEC𝑇𝑇�testforlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡−1–4.480[p≤0.01]–7.141[p≤0.01]–3.574[p≤0.05]CDtestforlog(𝐶𝐶𝐶𝐶2)𝑖𝑖,𝑘𝑘,𝑡𝑡–5.116(0.000)7.549(0.000)0.387[p=0.699]CDtestfor𝜖𝜖𝑖𝑖,𝑘𝑘,𝑡𝑡1.6[p=0.109]1.757[p=0.079]–0.612[p=0.540]Note:Allmean-groupcoefficientsarecalculatedasunweightedmeansofthecountry-specificestimates.StandarderrorsinparenthesesarederivednonparametricallyfollowingPesaranandSmith(1995).The95percentconfidenceintervalsforelasticityestimatesareinbrackets.𝛽𝛽0,𝑖𝑖.𝑘𝑘𝐸𝐸𝐸𝐸97denotesthespeedofequilibriumadjustment;thepanelEC𝑇𝑇�statisticteststhesignificanceofthecointegratingrelationship;RMSEistherootmeansquarederror;and“CDtest”referstothePesaran(2015)testforweakcross-sectiondependence,underthenullhypothesisofcross-sectionindependence.98APPENDIXF.ASSESSINGHETEROGENEITYOFEFFECTSINEMISSIONTRADINGVERSUSCARBONTAXSCHEMESWeprovidetheestimationresultswhenthemodelsarelimitedtoETSorcarbontaxes(relativetotheoverallcarbonpricingresultsregardlessofthenatureofthepricingschemereportedinthemaintext).WhenestimatingthetreatmenteffectsandsemielasticitiesforcarbonpriceineitherETSorundercarbontaxschemes,welimitpotentialcontrolcountriestoincludeonlythosewithoutanycarbonpricingschemetoensurecleancontrolgroupsinallspecifications.Forexample,acountrythatoperatesacarbontaxschemeisnotincludedasapotentialcandidateforthecontrolgroupwhenassessingtheimpactofintroducinganETS.TablesF1andF2showtheestimationresultsforETS-onlytreatments;TablesF3andF4showresultsforcarbontax–onlytreatments.99TableF1.EstimatingETS-SpecificImpactsTotalElectricityandheatManufacturingRoadtransportBuildingsATT–0.018(0.017)[p=0.07]–0.032(0.018)[p=0.03]–0.014(0.018)[p=0.48]–0.005(0.004)[p=0.27]NAΔlog(GDP)0.40424(0.65553)–0.68713(0.98872)–0.49469(1.66986)–0.74685(0.76339)NAΔlog(GDP)2–0.00539(0.02634)0.04767(0.042)0.03252(0.07279)0.04412(0.03003)NAΔlog(population)0.38441(0.1639)0.10163(0.25968)–0.06342(0.41497)0.36537(0.43272)NAΔlog(servicesGDP)NANANANANAΔlog(servicesGDP)2NANANANANAΔlog(manfacturingGDP)NANA1.68059(0.76086)NANAΔlog(manfacturingGDP)2NANA–0.06737(0.04254)NANAΔlog(transportGDP)NANANA0.5378(0.46355)NAΔlog(transportGDP)2NANANA–0.01834(0.02164)NAΔlog(heatingdegreedays)NANANANANAΔlog(coolingdegreedays)NANANANANA100r1111NA𝑁𝑁𝑇𝑇𝑇𝑇1012151NA𝑁𝑁𝐶𝐶𝐶𝐶27252712NASpecification#1111NA101TableF2.EstimatingETS-SpecificImpactsTotalElectricityandheatManufacturingRoadBuildingsElasticity(between-country)–0.004percent(–0.942percent,0.712percent)–0.015percent(–1.324percent,1.463percent)–0.246percent(–1.475percent,0.984percent)NANAElasticity(within-country)0.019percent(–0.629percent,0.563percent)0.126percent(–0.096percent,0.367percent)–0.294percent(–0.736percent,0.094percent)NANA𝑛𝑛𝑇𝑇𝑇𝑇(between-country)101215NANA𝑛𝑛𝑇𝑇𝑇𝑇(within-country)101215NANAFtestforpoolabilityofpricecoefficientsp=0.681p=0.931p=0.005NANAFtestforpoolabilityofintroductioneffectsp=0.012p=0.497p=0.016NANASpec.#111NANA102TableF3.EstimatingTax-SpecificImpactsTotalElectricityandheatManufacturingRoadtransportBuildingsATTNANANA–0.007(0.017)[p=0.54]–0.03(0.014)[p=0.02]Δlog(GDP)NANANA–0.04219(0.45828)–2.07581(1.91964)Δlog(GDP)2NANANA0.01941(0.02164)0.08036(0.06945)Δlog(population)NANANA0.22258(0.18995)1.45328(0.87253)Δlog(servicesGDP)NANANANA1.94165(1.35541)Δlog(servicesGDP)2NANANANA–0.07451(0.0569)Δlog(manfacturingGDP)NANANANANAΔlog(manfacturingGDP)2NANANANANAΔlog(transportGDP)NANANA0.13622(0.12511)NAΔlog(transportGDP)2NANANA–0.00145(0.00802)NAΔlog(heatingdegreedays)NANANANANAΔlog(coolingdegreedays)NANANANANArNANANA11𝑁𝑁𝑇𝑇𝑇𝑇NANANA52103𝑁𝑁𝐶𝐶𝐶𝐶NANANA2112Specification#NANANA11104TableF4.EstimatingTax-SpecificImpactsTotalElectricityandheatManufacturingRoadtransportBuildingsElasticity(between-country)NANANA0.032percent(–0.063percent,0.1percent)0.059percent(–0.159percent,0.193percent)Elasticity(within-country)NANANA–0.015percent(–0.146percent,0.074percent)–0.063percent(–0.215percent,0.191percent)𝑛𝑛𝑇𝑇𝑇𝑇(between-country)44496𝑛𝑛𝑇𝑇𝑇𝑇(within-country)NANANA96FtestforpoolabilityofpricecoefficientsNANANAp=0.074p=0.98FtestforpoolabilityofintroductioneffectsNANANAp=0.743p=0.744Spec.#22222105106SUPPLEMENTARYMATERIALThedataandRcoderequiredtoreplicatethemodelresultsinthisstudywillbemadeavailableuponrequestandbeaccessibleonlineuponfinalpublicationofthemanuscript.107ACKNOWLEDGEMENTSForthoughtfulfeedbackatvariousstagesofthispaper’sdevelopment,wewishtothankDavidHendry,ThomasSterner,MichaelGrubb,GibMetcalf,ThomasFerguson,RichardCarson,MoritzSchwarz,SamRowan,AndrewMartinez,BentNielsen,TommasoProietti,andSimonJohnBlack.SupportfromClimateEconometrics(NuffieldCollege,UniversityofOxford),theOxfordMartinProgramonthePost-CarbonTransition,andtheEnergyPolicyResearchGroup(UniversityofCambridge)isgratefullyacknowledged.PreviousversionsofthispaperwerepresentedattheHarvardSeminarinEnvironmentalEconomicsandPolicy,FirstResearchConferenceoftheCarbonPricingLeadershipCoalition(NewDelhi),22ndDynamicEconometricsConference(Oxford),FourthConferenceonEconometricModelsofClimateChange(Milan),andEconomicsDepartmentSeminarSeriesatUniversityofRome“TorVergata.”108REFERENCESAbadie,A.,Diamond,A.,andHainmueller,J.2010.SyntheticControlMethodsforComparativeCaseStudies:EstimatingtheEffectofCalifornia’sTobaccoControlProgram.JournaloftheAmericanStatisticalAssociation105(490):493–505.————2015.ComparativePoliticsandtheSyntheticControlMethod.AmericanJournalofPoliticalScience59(2):495–510.Abrell,J.,Kosch,M.,andRausch,S.2020.HowEffectiveWastheUKCarbonTax?—AMachineLearningApproachtoPolicyEvaluation.WorkingPaper19/317bis,CenterofEconomicResearchatETHZurich.Abrell,J.,NdoyeFaye,A.,andZachmann,G.2011.AssessingtheImpactoftheEUETSUsingFirmLevelData.BruegelworkingpaperNo.2011/08.Adler,M.,Anthoff,D.,Bosetti,V.,Garner,G.,Keller,K.,Treich,N.2017.Priorityfortheworse-offandthesocialcostofcarbon.NatureClimateChange(7):443–449.Ahn,S.C.andHorenstein,A.R.2013.EigenvalueRatioTestfortheNumberofFactors.Econometrica81(3):1203–1227.Andersen,M.S.2004.VikingsandVirtues:ADecadeofCO2Taxation.ClimatePolicy4(1):13–24.Andersen,M.,Dengsoe,N.,andPedersen,A.2000.AnEvaluationoftheImpactofGreenTaxesinNordicCountries.Copenhagen,Denmark:TheNordicCouncil(TemaNord).Andersson,J.J.2019.CarbonTaxesandCO2Emissions:SwedenasaCaseStudy.AmericanEconomicJournal:EconomicPolicy11(4):1–30.Athey,S.,Bayati,M.,Doudchenko,N.,Imbens,G.andKhosravi,K.2018.MatrixCompletionMethodsforCausalPanelDataModels.NationalBureauofEconomicResearch,WorkingPaperNo.25132.109Avner,P.,Rentschler,J.,andHallegatte,S.2014.CarbonPriceEfficiencyLock-InandPathDependenceinUrbanFormsandTransportInfrastructure.WorldBank,PolicyResearchWorkingPaper6941,1–26.Bai,J.2009.PanelDataModelswithInteractiveFixedEffects.Econometrica77(4):1229–1279.Bai,J.,Kao,C.andNg,S.2009.PanelCointegrationwithGlobalStochasticTrends.JournalofEconometrics149(1):82–99.Bai,J.S.andNg,S.2002.DeterminingtheNumberofFactorsinApproximateFactorModels.Econometrica70:191-221.Bai,J.,andNg,S.2004.APANICAttackonUnitRootsandCointegration.Econometrica72(4):1127–1177.Bai,J.,andNg,S.2010.PanelUnitRootTestswithCross-SectionDependence:AFurtherInvestigation.EconometricTheory26(4).Baker,A.,Larcker,D.F.andWang,C.C.2021.HowMuchShouldWeTrustStaggeredDifference-In-DifferencesEstimates?EuropeanCorporateGovernanceInstitute–FinanceWorkingPaperNo.736/2021,RockCenterforCorporateGovernanceatStanfordUniversityWorkingPaperNo.246,AvailableatSSRN:https://ssrn.com/abstract=3794018Barron,A.R.,Fawcett,A.A.,Hafstead,M.A.,McFarland,J.R.andMorris,A.C.2018.PolicyInsightsfromtheEMF32StudyonU.S.CarbonTaxScenarios.ClimateChangeEconomics9(01):1840003.Baumol,W.J.,andOates,W.E.1988.TheTheoryofEnvironmentalPolicy(2ndedition).CambridgeUniversityPress.110Bayer,P.,andAklin,M.2020.TheEuropeanUnionEmissionsTradingSystemReducedCO2EmissionsDespiteLowPrices.ProceedingsoftheNationalAcademyofSciences117(16):8804–8812.Bel,G.,andJoseph,S.2015.EmissionAbatement:UntanglingtheImpactsoftheEUETSandtheEconomicCrisis.EnergyEconomics49:531–539.Best,R.,Burke,P.J.,andJotzo,F.2020.CarbonPricingEfficacy:Cross-CountryEvidence.EnvironmentalandResourceEconomics:1–26.Billmeier,A.,andNannicini,T.2013.AssessingEconomicLiberalizationEpisodes:ASyntheticControlApproach.ReviewofEconomicsandStatistics95(3):983–1001.Bocklet,J.,Hintermayer,M.,Schmidt,L.,andWildgrube,T.2019.ThereformedEUETS-IntertemporalEmissionTradingwithRestrictedBanking.EnergyEconomics84,104486.Callaway,B.andSant’Anna,P.H.,2020.Difference-in-DifferenceswithMultipleTimePeriods.JournalofEconometrics.CDIAC(CarbonDioxideInformationAnalysisCenter).2017.FossilFuelCO2Emissions:Global,Regional,andNationalAnnualTimeSeries(1751–2014).OakRidge,TN:OakRidgeNationalLaboratory,U.S.DepartmentofEnergy.Carbone,J.C.,Rivers,N.,Yamazaki,A.,andYonezawa,H.2020.ComparingAppliedGeneralEquilibriumandEconometricEstimatesoftheEffectofanEnvironmentalPolicyShock.JournaloftheAssociationofEnvironmentalandResourceEconomists7(4):687–719.Cengiz,D.,Dube,A.,Lindner,A.,andZipperer,B.2019.TheEffectofMinimumWagesonLow-WageJobs.QuarterlyJournalofEconomics134(3):1405–1454.111Chamon,M.andKaplan,E.2013.TheIcebergTheoryofCampaignContributions:PoliticalThreatsandInterestGroupBehavior.AmericanEconomicJournal:EconomicPolicy:1–31.Chatterjee,S.,andHuang,K.W.2020.UnrealisticEnergyandMaterialsRequirementforDirectAirCaptureinDeepMitigationPathways.NatureCommunications11(1)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