亚开行-数字金融能否推动低碳转型？来自中华人民共和国的证据（英）

ADBIWorkingPaperSeriesCANDIGITALFINANCEPROMOTELOW-CARBONTRANSITION?EVIDENCEFROMTHEPEOPLE’SREPUBLICOFCHINAXingGeandTomokiFujiiulyAsianDevelopmentBankInstituteXingGeisajointtrainingPhDstudentatXi'anJiaotongUniversityandSingaporeManagementUniversity.TomokiFujiiisAssociateDean(UndergraduateCurriculum)andAssociateProfessorofEconomicsattheSchoolofEconomics,SingaporeManagementUniversity.TheviewsexpressedinthispaperaretheviewsoftheauthoranddonotnecessarilyreflecttheviewsorpoliciesofADBI,ADB,itsBoardofDirectors,orthegovernmentstheyrepresent.ADBIdoesnotguaranteetheaccuracyofthedataincludedinthispaperandacceptsnoresponsibilityforanyconsequencesoftheiruse.TerminologyusedmaynotnecessarilybeconsistentwithADBofficialterms.Discussionpapersaresubjecttoformalrevisionandcorrectionbeforetheyarefinalizedandconsideredpublished.TheWorkingPaperseriesisacontinuationoftheformerlynamedDiscussionPaperseries;thenumberingofthepaperscontinuedwithoutinterruptionorchange.ADBI’sworkingpapersreflectinitialideasonatopicandarepostedonlinefordiscussion.Someworkingpapersmaydevelopintootherformsofpublication.TheAsianDevelopmentBankrefersto“China”asthePeople’sRepublicofChina.tedcitationGe,X.andT.Fujii.2023.CanDigitalFinancePromoteLow-CarbonTransition?EvidencefromthePeople’sRepublicofChina.ADBIWorkingPaper1399.Tokyo:AsianDevelopmentBankInstitute.Available:/10.56506/FMXX6317Pleasecontacttheauthorsforinformationaboutthispaper.Email:gexing@,tfujii@.sgAsianDevelopmentBankInstitutegasekiBuildingthFloor3-2-5Kasumigaseki,Chiyoda-kuTokyo0-6008,JapanTel:+81-3-3593-5500Fax:+81-3-3593-5571URL:E-mail:info@©2023AsianDevelopmentBankInstituteGeandFujiiADBIWorkingGeandFujiiAbstractUsingpaneldataofcitiesinthePeople’sRepublicofChinafrom2011to2019,thispaperanalyzestheimpactofdigitalfinanceonlow-carbontransitionderivedfromasuper-efficiencyslacks-basedmeasuredataenvelopmentanalysis.Wefindthatdigitalfinancepromoteslow-carbontransition,andthisfindingisrobustwithrespecttothechoiceofsample,potentialpresenceofmeasurementissue,choiceofstudyperiod,presenceofotherpolicies,andpotentialendogeneity,amongothers.Thisimpact,atleastinpart,isthroughincreasedgreeninnovations.Wealsofindevidenceforimpactheterogeneityacrosslocationsandbytheleveloflow-carbontransition.Thispaperprovidespolicyimplicationsforthelow-carbontransitionoftheregionfromadigitalfinanceperspective.Keywordsdigitalfinancelowcarbontransitiongreeninnovationslacks-basedmeasureelopmentanalysisJELClassificationG20,Q54,Q55GeandFujiiADBIWorkingGeandFujiiContents1.INTRODUCTION 12.LITERATUREREVIEW 33.DATA,METHODOLOGY,ANDEMPIRICALMODEL 43.1DataSources 43.2MeasurementofLow-CarbonTransition 43.3MeasurmentofDigitalFinanceandControlVariables 73.4SpatialDistributionofKeyVariables 83.5EmpiricalModel 94.EMPIRICALRESULTS 94.1BaselineResults 94.2RobustnessChecks 104.3GreenInnovationasaChannelofImpact 155.IMPACTHETEROGENEITY 176.CONCLUSIONSANDPOLICYIMPLICATIONS 18REFERENCES 19APPENDIX 23GeandFujiiADBIWorkingGeandFujii11.INTRODUCTIONWiththedevelopmentofinformationtechnology,digitalfinance—whichreferstotheuseofdigitaltechnologiesintheprovisionoforaccesstofinancialservices—hasgrownrapidlyinrecentyears.Digitalfinanceisanimportantfactorinfluencingtheeconomy,finance,andenergy(Zhang,Jin,andWang2015)andmayenableahigherlevelofconsumptionandpromoteinclusivedevelopment,forexample,throughincreasedavailabilityofloansforsmallandmedium-sizedenterprisesandvulnerablegroups.Digitalfinancehasalsocontributedtogreeninnovationandreducedpollution(MengandZhang2022;ZhangandLing2022).Digitalfinancecanbeexpectedtoplayanimportantroleinlow-carbontransition,orashifttowardsloweremissionsofpollutants(Chen2012).Thisisbecausethekeydriveroflow-carbontransitionisgreeninnovation,whichrequiressubstantialfinancialsupportfromthefinancialsector.Nevertheless,theimpactofdigitalfinanceonlow-carbontransitionhasbeenunderexploredintheexistingliterature.Thisstudyfillsthisresearchgap.Digitalfinancemayaffectlow-carbontransitionbycontributingtogreeninnovationthroughtheprovisionoffundingforgreenandcleanprojects.Thisispossible,sincedigitalfinancemayabsorbfundsfromlong-tailgroups,1therebyreducingborrowingcostsforfirmsandindividualsandfacilitatinggreeninnovationprojectswithpotentiallyhighrisksandlongpaybackcycles,whicharetypicallyexcludedfromtraditionalfinance.Ourfindingsareindeedconsistentwiththerelevanceofgreeninnovation.Thereareatleastthreeadditionaltheoreticalchannelsthroughwhichdigitalfinancecanaffectlow-carbontransition.First,digitalfinanceincludessomeecologicalrestorationprojects(suchasAlipay’sAntForest),whichaimtoencouragethepublictoreducecarbonemissions.Second,digitalfinancefacilitatesthegreenconsumptionofdisadvantagedgroupsbyprovidingthemwithfundsthatcontributetolow-carbontransition.Finally,digitalfinancebreaksthroughtimeandspaceconstraintsandreducestransactioncostsforconsumption.Whilethesethreechannelsarepotentiallyimportant,theanalysisofthesechannelsisbeyondthescopeofthispaperduetothelackofavailabledata.Thediscussionabovemerelysuggeststhepossiblecausalchannelrunningfromdigitalfinancetolow-carbontransition,andwhetherdigitalfinanceindeedinfluenceslow-carbontransitionisanempiricalquestion.Thus,weexplorethisquestionusingpaneldatafrom283citiesinthePeople’sRepublicofChina(PRC)between2011and2019.TherearethreeimportantreasonswhywestudycitiesinthePRC.First,thePRCisthesecondlargesteconomyandthelargestdevelopingcountryintheworld.Further,thePRCisalreadyhighlyurbanizedwith63%ofthepopulationlivinginurbanareasin2020.GiventhenumberoflargecitiesinthePRCandthecontinuingtrendofurbanization,citiesinthePRCareofinteresttostudy.Second,thePRCisthelargestcarbonemitterintheworld,accountingformorethan30%oftheworld’scarbonemissionsfromfossilfuelsandindustrybutwithoutaccountingforlandusechange,accordingtotheGlobalCarbonAtlas.Finally,citiesarethebasicunitforpolicyimplementationinthePRCandplayavitalroleinreachingpeakcarbonemissions.With70%ofglobalcarbonemissionscomingfromcities,citiesarealsorelevanttotheanalysisofgreentransitionbothinsideandoutsideofthePRC.1Thelong-tailgroupreferstoindividualsorsmallbusinesseswithrelativelysmallfinancialassetsbutlargenumbers.GeandFujiiADBIWorkingGeandFujii2Measuringdigitalfinanceandlow-carbontransitioniscriticalinthisstudy.Forthemeasurementoftheformer,thispaperemploysthePekingUniversityDigitalFinancialInclusionIndexofChina(PKU_DFIIC),whichprovidesanoverallindexfordigitalfinanceaswellasitssubindicesforcoveragebreadth,usagedepth,anddigitizationlevel.Tomeasurelow-carbontransition,weusethetechnicalefficiencymeasurederivedfromunorientedslacks-basedmeasuredataenvelopmentanalysis(SBM-DEA)anditssuper-efficiencycounterpartwithundesiredoutputs.Thetechnicalefficiencymeasuretendstobehigherwhenacityusesfewerinputsandproducesmoredesiredoutputsandfewerundesiredoutputscomparetoothercities.Usingthesemeasures,weregressthelow-carbontransitiononthedigitalfinanceindexandothercontrolvariables.Thebaselineregressionresultsindicatethatdigitalfinancesignificantlyaccelerateslow-carbontransition.Thisconclusionisrobustwithrespecttotheexclusionofthefourdirect-administeredmunicipalities,exclusionofcertainoutliers,changesinthestudyperiod,andinclusionofpotentiallyconfoundingpolicies.Further,addressingthepotentialendogeneityofdigitalfinancebyatypeofshift-shareinstrumentvariable(SSIV)alsodoesnotchangetheresults.Wearguethatthisisaplausiblyvalidinstrument,becausetheinverseofthesphericaldistancebetweenacityandHangzhouispositivelycorrelatedwithdigitalfinanceontheonehandandtheinverseofthesphericaldistancebetweenacityandHangzhouislargelyirrelevanttothelow-carbontransitionontheother.Inaddition,basedontheapproachproposedbyConley,Hansen,andRossi(2012),thispaperfindsthatthepositiveeffectofdigitalfinanceonthelow-carbontransitionisrobustwithrespecttoamodestviolationoftheexclusionrestriction.Wethenanalyzethemechanismsthroughwhichdigitalfinanceinfluenceslow-carbontransition.Theresultsindicatethatdigitalfinancedriveslow-carbontransitionatleastinpartbypromotinggreeninnovation,whichincludesalltypesofinnovationsthatenabletheproductionofgoodsandserviceswhilereducingorremovingundesirableimpactsontheenvironmentandnaturalresources.Wealsoanalyzetheimpactheterogeneitywithrespecttovariouscitycharacteristics.ThisanalysissuggeststhatdigitalfinanceincitiestotheeastoftheHeihe–Tengchongline—ahypotheticallinethatextendsfromthecityofHeiheinthenortheasttothecityofTengchonginthesouthwest—promotedlow-carbontransition,butthisisnotthecaseforcitiestothewestofthisline.Wealsofindthatdigitalfinanceonlyfacilitateslow-carbontransitionincitiesabovethemedianlow-carbontransition.Therearethreeinnovationsinthispaper.First,previousstudiestypicallyignoredthepresenceofpotentialendogeneityconcerns.WeproposeanewtypeofSSIVfordigitalfinancedefinedastheproductbetweentheinverseofthesphericaldistancebetweenthecityandHangzhoumultipliedbythePRCdigitalfinanceindexforeachyear.Aselaboratedsubsequently,thisIVisplausiblyexogenousandourresultsarerobusttoamodestviolationoftheexogeneityoftheSSIV.Second,thispaperanalyzeswhethertheimpactofdigitalfinanceonlow-carbontransitionisheterogeneousacrosscitieswithdifferentlow-carbontransitionlevels,apointthathasalsobeenpreviouslyignored.Third,unlikepreviousstudies,thispaperoffersagranularanalysisofgreeninnovationasachannelthroughwhichdigitalfinanceaffectslow-carbontransitionbydividingitintolow-levelandhigh-levelinnovations.Thepaperisstructuredasfollows.Section2reviewstherelatedliterature.Section3presentsthedata,methods,andmodel.Section4showstheempiricalresultsandanalysis.Section5presentstheheterogeneityanalysis.Finally,Section6offersconclusionsandpolicyimplications.GeandFujiiADBIWorkingGeandFujii32.LITERATUREREVIEWThispaperisrelatedtothebodyofliteratureondigitalfinance.Intheearlyliterature,scholarsassessedtheimpactsofdigitalfinanceoneconomicoutcomes,suchasentrepreneurship(Xieetal.2018),economicgrowth(Qianetal.2020),andincomedisparityJietalMorerecentlystudieshaveexaminedtheenvironmentaleffectsofdigitalfinance.Forexample,Wan,Pu,andTavera(2023)findasignificantnegativerelationshipbetweendigitalfinanceandpollutantemissions.Fuetal.(2023)usedPRCprovincialdatatofindaninvertedU-shapedeffectofdigitalfinanceonenergyefficiency.Inparticular,thispaperaddstotheliteratureontheanalysisoftheimpactofdigitalfinanceoncarbonemissionsandgreeneconomyefficiency.DigitalfinancehasbeenfoundtoreducecarbonemissionsinthePRCbasedonprovincialdatabyZhaoetal.(2021)andcity-leveldatabyWangandGuo(2022).Wangetal.(2022)identifiedthatdigitalfinanceimprovesgreeneconomyefficiencybystrengtheningcreditconstraintsonhighlypollutingfirms.Thisstudyalsocontributestotheliteratureonthefactorsinfluencinglow-carbontransition.Existingstudieshaveexaminedvariousfactorsaffectinglow-carbonalindustrialagglomeration(Zhangetal.2019),technologicalinnovation(LiuandZhang2021),greeninnovation(ZhangandLiu2022),greenbonds(Sartzetakis2021),andgreencredit(Liuetal.2022b).Wecomplementthisliteraturebyexamininggreeninnovationasoneofthekeychannelsthroughwhichdigitalfinancepromoteslow-carbontransition.Thisstudyalsocarefullyconstructsameasureoflow-carbontransitionbyadoptingthe(super-efficiency)SBM-DEA.Thisisanimportantpointbecausethemeasurementcanpotentiallyaffectourresults.Weemploythe(super-efficiency)SBM-DEAwithundesiredoutputs,sinceitallowsustocomputethetotalfactorefficiency,takingintoconsiderationnotonlytheinputsanddesiredoutputsbutalsoemissions(undesiredoutputs).Thisisincontrasttosingle-factorefficiencymeasures,suchaspercapitacarbonemissions(Zhengetal.2019),percapitaenergyconsumption(Truong,Wiktor,andBoxall2015),andcarbonemissionsperunitGDP(Liuetal.2019).Sincesingle-factorefficiencycannotfullyreflectthemultipleoutcomesweareinterestedin,wearguethatthetotal-factorefficiencyintheDEAapproachismoresuitable.TheDEAapproachalsohasanadvantageoverparametricapproaches,suchasthestochasticfrontieranalysis,becausewedonotneedtoassumeaparticularformofproductionfunction.Someotherstudiesusetheindexsystemmethodtomeasurelow-carbontransition.Tanetal.(2017)usedtheentropyweightmethodtoconstructalow-carboneconomicindexthatreflectssevendimensionsof(i)economicdevelopment,(ii)energypattern,(iii)societyandlife,(iv)carbonandenvironment,(v)urbantransportation,(vi)solidwaste,and(viii)water.DengandYang(2019)appliedtheentropyweightmethodtoconstructanindustriallow-carbontransitionindexfromfivedimensionsof(i)resourcesaving,(ii)pollutionreduction,(iii)industrialupgrading,(iv)productivityimprovement,and(v)developmentsustainability.Sunetal.(2020)builtasustainabledevelopmentindicatorfromthethreedimensionsof(i)environment,(ii)energy,and(iii)economy,andevaluatedthesustainabledevelopmentperformanceofSouthAsia.Huangetal.(2022)adoptedentropy-weightedTOPSIStocomprehensivelyevaluatethelevelofgreenandlow-carbondevelopmentfromthethreedimensionsof(i)greenbenefits,(ii)low-carbonbenefits,and(iii)economicandsocialbenefits.Wealsoconsiderasimilarentropy-weightedindexasanalternativemeasureoflow-carbontransition,GeandFujiiADBIWorkingGeandFujii4eventhoughourpreferredmeasureoflow-carbontransitionisbasedonthe(super-efficiency)SBM-DEA.Asshownsubsequently,thecurrentstudyshowsthatdigitalfinanceaffectslow-carbontransitionthroughthechannelofgreeninnovation.Therefore,thispaperalsorelatestotheexistingstudiesthatfindapositiveimpactofdigitalfinanceongreeninnovation.Forexample,Liuetal.(2022a)findthatdigitalfinancepromotesgreeninnovationbyalleviatingfinancialconstraintsandincreasinginvestmentinR&D.Raoetal.(2022)discoverthatdigitalfinancefacilitatesgreeninnovationbyincreasingthefinancialliquidityoffirms.MengandZhang(2022)believethatdigitalfinancepromotesgreeninnovationbyenhancingregionalgreenfinancialservices.Whilewedonotanalyzehowdigitalfinanceaffectsgreeninnovation,thefindingsofthecurrentstudyareconsistentwiththesefindings.Thisstudyalsoaddstoagrowingbodyofliteratureontheimpactofgreeninnovationonlow-carbontransition.Greeninnovationisinlinewiththegoalofsustainabledevelopment(LiandLiao2020),asitemphasizesnotonlyeconomicbenefitsbutalsoenvironmentalandecologicalbenefits.Basedonsectoraldatafor17OECDcountriesfrom1975to2005,WurlodandNoailly(2018)findthatgreeninnovationreducesenergyintensity(theinverseofenergyefficiency).Xuetal.(2021)findapositiverelationshipbetweengreeninnovationandcarbonemissionperformance.Dongetal.(2022)detectimprovementincarbonemissionefficiencythroughgreeninnovationsusingPRCdata.Greeninnovationhasbecomeaneffectivemeanstopromotesustainabledevelopmentandlow-carbontransition(Yuetal.2021;LinandMa2022).Thecurrentstudycorroboratesthesefindings.3.DATA,METHODOLOGY,ANDEMPIRICALMODEL3.1DataSourcesThispaperstudied283citiesinthePRCfrom2011to2019duetodatalimitations.Therearefourmaindatasourcesfortheempiricalanalysisinthispaper.Weobtain(i)carbonemissiondatafromtheChinaUrbanConstructionStatisticalYearbookandtheChinaCityStatisticalYearbook;(ii)thedigitalfinanceindexfromthePKU_DFIIC;(iii)variablesongreeninnovationfromtheChineseResearchDataServicesPlatform(CNDRS);and(iv)variousothercity-levelvariablesobtainedfromtheChinaCityStatisticalYearbook.3.2MeasurementofLow-CarbonTransitionWemeasurelow-carbontransition(LCT)usingthetechnicalefficiencyintheunoriented(super-efficiency)SBM-DEAmodelwithundesiredoutputafterTone(2002).Here,webrieflydescribetheintuitionbehindtheSBM-DEAmodelandthenstepstakentocomputeLCT.TomotivatetheuseofDEA,notethatitisessentialtohaveeithermultipleinputsoroutputs,thelatterofwhichmaycontainundesirableones.Ifinsteadwehadjustoneinputandoneoutput,wecouldcreateatechnicalefficiencymeasurebytakingtheratioofoutputtoinput.Butthissimpleapproachdoesnotworkinamoregeneralsituationwithmultipleinputs,multipleoutputs,orboth.TheDEAallowsustoaddressthisissue.WhiletherearemanyvariantsofDEAmodels,wetypicallyconsiderabestlinearcombinationofdecision-makingunits(DMUs)anddeterminehowefficientagivenDMUisrelativetothisbestlinearcombination.Tofacilitateanintuitiveunderstanding,GeandFujiiADBIWorkingGeandFujii5letusconsideracasewherethereisonetypeofinputandtwotypesofoutputs,wherehigherlevelsofoutputsforagivenlevelofinputaremoredesired.InFigureA1,therearefourDMUslabeledfromAtoD,andeachpointrepresentsthecombinationofoutputsthatagivenDMUproducesfromaunitinput.ThekinkedlinethatgoesthroughDMUsA,B,andDiscalledthe“efficiencyfrontier,”sincethisrepresentsthesetofoutputsthatcanbeproducedfromalinearcombinationofefficientDMUs.InthetraditionalDEA,thetechnicalefficiencyismeasuredbyhowefficientlyaDMUproducesoutputsrelativetotheefficiencyfrontier.ThoseDMUsthatareontheefficiencyfrontierhaveaunittechnicalefficiencymeasureandthosewhicharenothaveatechnicalefficiencystrictlybelowunity.InFigureA1,thetechnicalefficiencyforDMUCcanbecomputedastheratioof0Cto0D.OnepotentialdisadvantageofthetraditionalDEAisthatitdoesnotallowustocreatearankingamongefficientDMUs.Thesuper-efficiencyDEAapproachovercomesthisissuebyrestrictingthelinearcombinationtothoseDMUsthatexcludetheDMUunderconsideration.Forexample,whenconsideringthetechnicalefficiencyofDMUD,weconsiderthelinearcombinationofDMUsAandB.InFigureA1,pointErepresentsthecombinationoftwooutputsthatcanbeattainedbyalinearcombinationofDMUsAandBthathasthesamemixofoutputsasDMUD.Therefore,thetechnicalefficiencyforDMUDinthesuper-efficiencyDEAwouldbetheratioof0Dto0E.Asthisexampleshows,thetechnicalefficiencymeasureinasuper-efficiencyDEAcanexceedunity.DEAandsuper-efficiencyDEAmodelshavebeenusedinawidevarietyofcontexts.OurapplicationinparticularrelatestotheapplicationstotheanalysisofproductioninefficiencyinthepresenceofundesirableoutputsbyWangandFeng(2015)andtheevaluationofurbanenvironmentalsustainabilitybyYuandWen(2010).Wetakeeachofthe283citiesineachobservationperiodinthedataasadecision-makingunit.Weconsiderthreeinputsoflabor,capital,andenergy,whicharerespectivelymeasuredbythenumberofemployeesinthecity(unit:10,000persons),thecity’scapitalstock(unit:10,000yuan)estimatedbytheperpetualinventorymethod,andthecity’selectricityconsumption(unit:10,000kWh).Wechoosecity’selectricityconsumptionbecausethereisahighcorrelationbetweenelectricityconsumptionandenergyconsumptioninthePRC.Thedesiredoutputistakentobethecity’srealGDPatconstantpricesin2000(unit:10,000yuan).Theundesiredoutputiscarbonemissionsinthecity(unit:10,000tons),whichiscalculatedbysummingthecarbonemissionsgeneratedfromelectricity,gas,LPG,transportation,andthermalenergyconsumption.2ThedetailsofthecalculationprocesscanbefoundinWuandGuo(2016).Themeasurementoflow-carbontransitionisdividedintotwosteps.First,wecalculatetheefficiencyscore6ctincitycinyeartusingtheSBM-DEAmodelwithundesirableoutputs,wherext,yct,andbctarethei-thinput,desiredoutput,andnondesiredoutput,respectively.Specifically,wesolvethefollowingminimizationprobleminEq.(1). 1−∑=1(sx,i⁄xt)6ct=min入c′t′,sx,i,sy,sb11+2(sy⁄yct+sb⁄bct)2Thispaperfocusesoncarbonemissionsfromtheproductionside.Duetotheunavailabilityofinter-cityinput–outputtables,itisunabletoaccuratelymeasurecarbonemissionsfromtheconsumptionsideofcities.GeandFujiiADBIWorkingGeandFujii6xt=∑入c′t′x′t′+sx,i,i=1,2,3s.t.(1)bct=∑入c′ts.t.(1)bct=∑入c′t′bc′t′+sbbwhere入c′t′istheweightforcreatingthelinearcombinationofDMUs,andsx,i,sy,sbareslackvariablesforthei-thinput,desiredoutput,andnondesiredoutput,respectively.Theseslackvariablesrespectivelyrepresenttheexcessofinputs,shortfallofdesiredoutputs,andexcessofundesiredoutputsrelativetothelinearcombinationofefficientDMUs.Therefore,theycanbeinterpretedasmeasuresofthedistancefromtheefficiencyfrontierinaparticulardimension.Itisstraightforwardtoverifythat6ctisunitywhenalltheslackvariablesareequaltozero.Whenatleastoneoftheslackvariablesisstrictlypositive,6ctisstrictlylessthanunity,indicatingthatcitycinyeartisinefficient.Next,wecalculatethesuper-efficiencyscoreyctforDMUsusingthesuper-efficientSBM-DEAconsideringundesirableoutputsinEq.(2). 1+∑=1(sx,i⁄xt)yct=min入c′t′,sx,i,sy,sb11−2(sy⁄yct+sb⁄bct)l≥∑c′t′≠ct入c′t′x′t′,i=1,2,3≤∑c′t′≠ct入c′t′yc′t′≥∑c′t′≠ct入c′t′bc′t′s.t.l=xt+sx,i(2)=yct−sy=bct+sb≥0where,l,,areefficiencyfrontiersexcludingDMUincitycinyeart,respectively.sx,i,sy,sbrepresentslackvariablesforthei-thinput,desiredoutput,andnondesiredoutput,respectively.Theseslackvariablesrepresentthereductionininputs,excessofoutputs,andreductioninundesiredoutputsrelativetothelinearcombinationofefficientDMUs.Putdifferently,ycttellsushowwellcitycinyeartdoescomparetootherefficientDMUs.SincetheslackvariablesforinefficientDMUsarezero,yctisequaltounityforinefficientunits.Therefore,weonlyneedtocomputeyctforefficientunits(i.e.,6ct=1)inpracticeandyctallowsustorankefficientDMUs.Tosolvetheminimizationproblemsineqs.(1)and(2),weusetheCharnes–Coopertransformationtoconvertitintoalinearprogrammingproblem.Forexample,weobtainthefollowingtransformationfromeq.(2):yct=min入c′t′,sx,i,sy,sb(t+∑=1(sx,i⁄xt))GeandFujiiADBIWorkingGeandFujii7txt+tsx,i≥∑c′t′≠ctt入c′t′x′t′,i=1,2,3tyct−tsy≤∑c′t′≠ctt入c′t′yc′t′s.t.tbct+tsb≥∑c′t′≠ctt入c′t′bc′t′(3)t−(sy⁄yct+sb⁄bct)=1Onceweobtaintheefficiencyandsuper-efficiencyscores,wetaketheirproducttoarriveatthefollowingmeasureoflow-carbontransitionLctct:Lctct=6ctyct=Lctct=6ctyct={yctif6ct=1.Lctctmeasureshowwellcitycinyearttransformsinputsintodesiredoutputswithoutproducingundesiredoutputs.Hence,ifLctctishigh,itmeansthatthecitycintimetcanproducemoreGDPandfewercarbonemissionswithfewerinputs(labor,capital,andenergy).3.3MeasurementofDigitalFinanceandControlVariablesTheprimaryindependentvariableofinterestinthisstudyisdigitalfinance(Df),whichisthedigitalfinanceinclusionindexfromthePKU_DFIICbyGuoetal.(2020)dividedby100torescale.ThePKU_DFIICindexisbasedonatotalof33underlyingindicators,whicharenormalizedtorangebetween0and100(andhencebetween0and1afterrescaling)inthebaseyearof2010andaggregatedusingtheweightsbyacombinationofthecoefficientofvariationandanal