【国际清算银行】气候明斯基时刻和内生金融危机-2025.3

BISWorkingPapersNo1248

ClimateMinskymomentsandendogenousfinancialcrises

byMatthiasKaldorfandMatthiasRottner

MonetaryandEconomicDepartment

March2025

JELclassification:E32,E44,G20,Q52,Q58.

Keywords:Climatepolicy,financialstability,financialcrises,transitionrisk,non-linearities.

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ISSN1020-0959(print)

ISSN1682-7678(online)

ClimateMinskyMomentsandEndogenousFinancialCrises*

MatthiasKaldorfDeutscheBundesbank

MatthiasRottner

BankforInternationalSettlements,

DeutscheBundesbank

March13,2025

Abstract

Howdoesashiftinclimatepolicyaffectfinancialstability?Wedevelopaquanti-tativemacroeconomicmodelwithcarbontaxesandendogenousfinancialcrisestostudyso-called“ClimateMinskyMoments”.Byreducingassetreturns,anaccel-eratedtransitiontonetzeroinitiallyelevatesthecrisisprobabilitysubstantially.However,carbontaxesenhancelong-runfinancialstabilitybydiminishingtherel-ativesizeofthefinancialsector.Quantitatively,thenetfinancialstabilityeffectisonlynegativeforhighersocialdiscountrates.Eventhen,thewelfareeffectsof“ClimateMinskyMoments”are,atmost,second-orderrelativetotherealcostsandbenefitsofanacceleratedtransition.

Keywords:ClimatePolicy,FinancialStability,FinancialCrises,TransitionRisk,Non-Linearities.

JELclassification:E32,E44,G20,Q52,Q58

*matthias.kaldorf@bundesbank.de,matthias.rottner@bundesbank.de.

WethankMarkusBrunnermeier,EmanueleCampiglio,FrancescaDiluiso,SampreetGoraya,NikoJaakkola,JochenMankart,BenoitMojon,SimonScheidegger,HernanSeoane,ThomasStoerk,ourdis-cussantsJorgeAbad,BarbaraAnnicchiarico,VolhaAudzei,DanielMonteiro,MariaSolePagliari,andAnnaStraubinger,andparticipantsintheAnnualResearchConference2024bytheEuropeanCommis-sion,MannheimQuantitativeMacroWorkshop,NASMacroeconomicImplicationsofDecarbonizationWorkshop,7thannualmeetingofCEBRA’sIFMprogram,ESCBResearchClustersClimateChangeandFinancialStability,GreenFinanceResearchAdvances2024,CzechNationalBankWorkshoponFinancialStabilityandMacroprudentialPolicy,andtheresearchseminarsoftheBankforInternationalSettlements,BankofEngland,DeutscheBundesbank,EuropeanCentralBank,NGFS,UniversityofBolognaandUniversityofSt.Gallenfortheircommentsandsuggestions.TheviewsexpressedhereareourownanddonotnecessarilyreflectthoseoftheBankforInternationalSettlements,theDeutscheBundesbank,ortheEurosystem.

1

1Introduction

Doesthenetzerotransitionincreasefinancialfragilityand,ifso,byhowmuch?An-sweringthesequestionsiscrucialforfinancialregulationoverthenextdecades,whichmaybecharacterizedbyashiftawayfromemission-intensivetechnologies.Ambitioustaxesoncarbonemissionswouldnegativelyaffectthemacroeconomyandassetpricesbytriggeringasharpandpermanentdropintheproductivityofemission-intensiveassets.Climatepolicycouldthengiveriseto“ClimateMinskyMoments”,inwhichasuddenreductioninassetpricesraisestheconcernthatfinancialintermediariesareunabletorepaydepositors,triggeringafinancialcrisis.1However,asnocountryhasyetintro-ducedsufficientlystringentclimatepolicies,evaluatingtherelevanceof“ClimateMinskyMoments”forfinancialstability,themacroeconomy,andwelfareusinghistoricaldataispracticallyinfeasible.

Againstthisbackground,wedevelopanonlinearquantitativemacroeconomicmodelwithendogenousfinancialcrisesandcarbontaxestostudythethreatof“ClimateMin-skyMoments”.Ourmodeliscenteredonthenotionthatfinancialintermediariesarerun-proneinthespiritofDiamondandDybvig(

1983

)andiscalibratedtohistoricalmomentsforthefinancialsector.Specifically,thepossibilityofasystemicrunonthefinancialsystemisfullyendogenousanddependsonthemacro-financialenvironment.BasedontheseminalworkbyNordhaus(

2008

),themodelfeaturescarbonemissionsintotheproductionprocess,carbontaxes,andendogenousemissionabatement.Usingourmacro-finance-climatemodel,weevaluatehowaclimatepolicythatreachesnetzerocarbondioxideemissionsby2050-consistentwiththeParisAgreement-affectsfinan-cialstability,macroeconomicaggregates,andwelfare,bothintheshort-andlong-run.Evaluatingendogenousfinancialinstabilityaddsanewelementtotheongoingdebateonfinancialstabilityinthecontextofclimatepolicy.2Wethenexaminehowthethreatof“ClimateMinskyMoments”impactswelfare,comparingittothepotentialcostsandbenefitsofthenetzerotransition.

Thetwokeybuildingblocksofourframeworkarethefinancialsectorwithendogenousfinancialcrisesandfirms’emissionabatement,whichdependsonclimatepolicy.FinancialintermediariesaresubjecttoanendogenousleverageconstraintbasedonAdrianandShin

(2014

)andNu~noandThomas(

2017

).AddingriskshocksinthespiritofChristianoetal.

(2014

)introducestime-variationintotheleverageconstraint.Thefinancialsectorthenfacesoccasionalruns,drivenbydepositors’state-dependentwillingnesstorolloverintermediaries’liabilities,similartoGertleretal.(

2020

).Therefore,theprobabilityofsuchaself-fulfillingrundependsonthefinancialsector’sleverageandthepriceofcapital,whichisdirectlyaffectedbyclimatepolicy.

1Theterm“ClimateMinskyMoments”wascoinedbyCarney(

2016

)inthespiritofMinsky(

1977

).

2Thecurrentdebateonfinancialstabilityimplicationsofclimatepoliciescentersaroundnegativecreditsupplyeffects,whileabstractingfromfinancialcrises.

2

Climatepolicyentersthemodelthroughtheproductionsector.Firmsemitcarbondioxideduringtheproductionprocess.Unabatedemissionsaretaxedbythefiscalauthor-ity,butweallowforcostlyabatement,whichreducesfirms’emissionintensity(Nordhaus,

2008

).Emissionabatementcostsandthecarbontaxjointlydriveawedgeinthemarginalproductofcapitalthatmonotonicallyincreaseswiththecarbontax(Heutel,

2012

),suchthatabatementcostshaveanegativewelfareeffectbyreducinghouseholdconsumption.Globaltemperaturesarelinkedtocumulatedemissionsandinflictutilitylossesonhouse-holdsinthespiritofAcemogluetal.

(2012

),suchthatcarbontaxesincreasewelfarebycurbingglobaltemperatureincreases.3WeembedthisframeworkinaNewKeynesiangeneralequilibriumsetup,whichimprovesthemodel’sfittomacro-financialdynamicsandallowsustostudytheroleofcentralbankpoliciesinthecontextofclimatepolicy-inducedfinancialfragility.

Climatepolicyaffectsfinancialstabilitythroughtwoopposingmechanisms.Increasingthecarbontaxreducesthemarginalproductofcapital.Thisreducesthemarketvalueofassetsheldbythefinancialsector,whichendogenouslytightensthefinancialsector’sleverageconstraint.4Theresultingdownwardpressureonassetpriceselevatesthelike-lihoodofarunonthefinancialsector:theprobabilityof“ClimateMinskyMoments”increases.Ontheotherhand,byreducingthemarginalproductofcapital,highercarbontaxesreducetheincentivestoaccumulatecapital.5Consequently,lesscapitalneedstobeabsorbedduringacrisis,whichstabilizestheassetpriceandincreasesfinancialstability:theprobabilityof“ClimateMinskyMoments”decreases.Whichoftheseopposingmech-anismsdominatesisaquantitativequestion.Therefore,wematchthemodeltosalientfeaturesoffinancialcyclesandthemacroeconomiceffectsofclimatepolicy.Solvingourmodelinitsnonlinearspecificationwithglobalmethodsallowsustocalculatethecrisisprobabilityduringthetransitiontonetzero.Ouranalysisrevealsthatbothmechanismsmatterbutatdifferenttimehorizons.

Weshowthatthenetzerotransitioncomeswithanelevatedcrisisprobabilityintheearlystagesofthetransition.Toquantifythefinancialstabilityeffects,wecomparethecurrenttrajectorytoastringentpolicypathalignedwiththeParisAgreement.Forthecurrenttrajectory,weextrapolatethehistoricalreductioninglobalemissionintensitiesobservedbetween1990and2023,whichimpliesthatnetzerowouldbereachedin2090.Inourbaselinecalibration,fullabatementrequiresacarbontaxofaround140dollars

3Inourbaselinemodel,weabstractfromnegativefeedbackfromhigherglobaltemperaturestothemacroeconomyandfinancialstabilitythroughaphysicalriskchannel.Thissimplificationallowsustoattributeallfinancialstabilityconsequencestothetimepathofabatementcostsandpermitsananalyticallycleanwelfaredecomposition.Inanextensionwithphysicalrisk,weshowthatthekeypositiveandnormativeimplicationsofClimateMinskyMomentsdonotdependonthisassumption.

4Jungetal.

(2024

)showthatambitiousclimatepolicyinducesloanportfoliolossesbetween1and6%forUSbanks.Moregenerally,institutionalinvestorsareawarethatambitiousclimatepolicyhasdetrimentaleffectsonassetvalues(Kruegeretal.,

2020

).

5Kaenzig(

2023

)providesevidencethatpositivecarbontaxshocksdecreaseaggregateinvestment.Bertholdetal.

(2023

)showthatsuchpositivecarbonshocksalsotightenfinancingconditions.

3

pertonofcarbondioxide($/tCO2).TheParis-alignedtransitioninsteadassumesthattheclimatepolicysuddenlyshiftsin2025toataxpathdesignedtoreachfullabatementalreadyin2050.ThispathisconsistentwiththeParisAgreement,implyingthatglobalsurfacetemperatureswillnotincreasebymorethan2。Cbytheendofthecentury.Thesuddenshiftontoasteepercarbontaxpathcanrendertheinitialfinancialsectorleverageandsizeunsustainable:the(annualized)crisisprobabilityincreasesinitiallytoalmost3%intheParis-alignedtransition,whilethecrisisprobabilityisonly2.1%inthecurrenttrajectory.Thus,weobserveasubstantialinitialincreaseinfinancialfragility.Thecrisisprobabilitythenslowlydeclinestoitslowerlong-runlevel,whichisreachedshortlyafter2050Paris-alignedpath,whileitisonlyreachedaround2090onthecurrenttrajectory.

Assessingthelong-runimplications,weshowthatpermanentlyhighercarbontaxesenhancefinancialstability.Thereasonbehindthisperhapssurprisingresultisthatthereislesscapitalaccumulationifcarbontaxesarehigh.6Thefinancialsectorissmallerandlessleveragedinthelong-run,whilehouseholdsarewillingtoabsorbalargershareofthecapitalshockifintermediariesfacedeleveragingpressures.Ourmodelcapturesapositiverelationshipbetweencapitalaccumulationandthedemandforfinancialservices.ThisnotiongoesbackatleasttoRobinson(

1952

),whosummarizedtheideaas”whereenterpriseleads,financefollows”.Asaconsequence,intermediariescandeleveragemoreeasilyinacrisiswithouthavingtosellcapitalatfiresaleprices.Thiseffectivelyincreasesresilienceinthefinancialsector.Theprobabilityofafinancialcrisisdeclinesfromaround2.0%inthelong-runequilibriumwithoutclimatepolicyto1.4%inthelong-runequilib-riumwithfullabatement.NotethattheParis-alignedtransitionprofitsearlierfromthisreducedfinancialstabilitythanthecurrenttrajectory.

Ournon-linearmodelrevealsthatamonotonictransitionpathcanhavenon-monotonicfinancialstabilityeffects.Todeterminethenetfinancialstabilityeffectoftheseopposingmechanisms,weintroduceametricoffinancialstabilitythatsummarizestheoccurrencesofcrisesalongdifferenttransitionpaths.TheexcesscrisisprobabilityisdefinedasthediscounteddifferencebetweenthecrisisprobabilityundertheParis-alignedtransitionandthecurrenttrajectory.Asinallclimatepolicyassessments,choosingtheappropriatediscountrateforfuturefinancialstabilitygainsisahighlynon-trivialnormativeissue.Wedonottakeastandontheappropriatesocialdiscountrateandcomputetheexcesscrisisprobabilityoverareasonablerangeofdiscountrates.Theexcesscrisisprobabilityispositiveforsufficientlyhighsocialdiscountrates,astheelevatedcrisisprobabilityintheshortruntriggeredbythesuddenshiftonastringentcarbontaxpathdominates.Notably,theexcesscrisisprobabilityturnsnegativeifthesocialdiscountrateexceeds1.5%perannum.Iffuturefinancialstabilitygainsassociatedwithlesscapitalaccumula-tionarenotdiscountedtooheavily,ambitiousclimatepolicypositivelyaffectsfinancial

6WeshowinAppendix

D.1

thatthenegativerelationshipbetweencapitalaccumulationandcarbontaxesemergesinvariousmodelclassescommonlyusedinassessingclimatepolicies.

4

stability.Thisrejectsthenotionofanunambiguoustrade-offbetweenfinancialstabilityandclimatepolicyobjectives.Thetimepatternof“ClimateMinskyMoments”impliedbyourmodelbearsastrikingresemblancetothetimepatternofcostsandbenefitsofambitiousclimatepolicyactionmoregenerally.

Atthesametime,ourresultsalsoraisethequestionofhowrelevant“ClimateMinskyMoments”arewhencomparedtotheconsumptionandoutputlossesassociatedwithabatementcostsandtemperatureincreases.Usingourstructuralmodel,webenchmarkthewelfarerelevanceof“ClimateMinskyMoments”againsttherealcostsandgainsofatransitiontonetzero.First,wedemonstratethatthewelfaregainsof“ClimateMinskyMoments”areinverselyrelatedtotheexcesscrisisprobabilityandarepositive(negative)foralow(high)discountrate.However,ourmodelshowsthatthewelfareeffectsof“ClimateMinskyMoments”aredwarfedbythecostsofswitchingtoemission-freetechnologies.Forexample,assumingahighsocialdiscountrateof4%p.a.,“ClimateMinskyMoments”reducewelfarebyaround0.008%,whileabatementcostsreducewelfarebyslightlymorethan1%.Thereasonisthatthenegativeimpactonfinancialstabilityislimitedandrelativelyshort-lived,evenforambitiouscarbontaxpaths.Therefore,itcomesaslittlesurprisethatthewelfareeffectsof“ClimateMinskyMoments”aresecond-orderrelativeanddonotsubstantiallyaffectthekeytrade-offbetweenlossesfromabatementcostsandtemperaturegains.

Reassuringly,thelikelihoodof“ClimateMinskyMoments”andtheirassociatedwelfareresultsareveryrobusttoreasonablevariationsintheclimateblock.Specifically,wediscusshowthefollowingdimensionsaffectourfindings:a)physicalriskassociatedwithglobalwarming,b)technologicalchangedirectedatemissionreductionactivities,c)trendgrowththataffectsclimatecosts,d)variousmodificationstotheproductionsector,suchasagreen-browntwo-sectorstructureoramodelwithenergyasproductioninput,e)fiscalpolicythatfeaturesabatementsubsidies,f)theyearatwhichnetzeroisreached,g)non-linearcarbontaxpaths,h)highercostofabatementeffort,andi)thecostofglobalwarming.Thewelfarerelevanceof“ClimateMinskyMoments”remainsatmostsecond-orderineithercase.Takentogether,ourresultspushbackdecisivelyonthenotionthatfinancialstabilityconcernsareavalidreasontodelaythenetzerotransition,irrespectiveofthesocialdiscountrate.Ourresultsinsteadindicatethat“ClimateMinskyMoments”concernsseemamanageablerisk,regardlessoftheexactdetailsoftheproductionsector,climatepolicy,andtheclimateblock.

Asafinalstep,weevaluatethepotentialtomitigatefinancialstabilityconcernsfur-therusingthecentralbank’stoolkit.Inparticular,westudytheroleofmacroprudentialpolicyandmonetarypolicythroughthelensofourquantitativemodel.Notably,thefinancialcycleisacrucialdriverofthefinancialstabilityeffectsassociatedwithstringentclimatepolicies.Specifically,theshort-runfinancialstabilityandwelfareimpactofstrin-gentclimatepoliciesdependcruciallyontheinitialconditions.Ifthefinancialsectoris

5

highlyleveredupbeforetheswitchtoaParis-alignedtransition,thecrisisprobabilityissubstantiallyhighercomparedtoasituationwithlessleverage.Therefore,thebuild-upofmacroprudentialspaceortheimplementationofclimatepoliciesduringaperiodofstrongfinancialfundamentalsallowstomitigatethelikelihoodof“ClimateMinskyMoments”substantially.

Regardingmonetarypolicy,weshowthatanexpansionarymonetarypolicystancecansoftentheinitialimpactofambitiousclimatepolicyandthecrisisprobabilitybyloweringthefundingcostsofthefinancialsector.Conversely,contractionarymonetarypolicyexacerbatesfinancialfragilityattheonsetofthetransition.Wemodelthemonetarypolicystancebyadeterministicwedgeintheinterestraterule.Contractionarymonetarypolicyhasaquantitativelygreaterimpactforthesamesizeofthewedge,makinganoverlytightmonetarypolicymorecostlythananoverlylooseone.Thisimpliesthatmonetarypolicyshouldnot“leanagainstthetransition”-aswedenoteacontractionarymonetarypolicystanceinresponsetotheshiftontheParis-alignedpath.Thereasonisthatitistoolatetocontainfinancialfragilityatthispoint.

RelatedLiterature.Ourpaperisconnectedtothefast-growingliteraturethatusesfully-fledgedDSGEmodelswithclimatepolicyandfrictionsinthefinancialsector(e.g.,Diluisoetal.,

2021

;Annicchiaricoetal.,

2023

;Carattinietal.,

2023a

;ComerfordandSpiganti,

2023

;FrankovicandKolb,

2024

;NakovandThomas,

2023

;Airaudoetal.,

2024

).Closelyrelated,Carattinietal.(

2023b

)demonstratethatcarbontaxescannegativelyaffectfinancialintermediaries’networthandinduceacreditcrunch.Giovanardietal.

(2023

)andGiovanardiandKaldorf(

2023

)modelidiosyncraticdefaultandrisk-takinginthefirmandbankingsector.Barnett(

2023

)showshowfinancialfrictionscangiverisetofiresalesofcarbon-intensiveassets.Ourpaperdiffersfromthesestudiesasweexplicitlyconsiderthesystemicdimensionofclimatepolicy,i.e.,implicationsforfinancialstabilityattheaggregatelevel.ByincorporatingthepossibilityofrunsintoaclimateDSGEmodel,wecanstudytheroleofclimatepolicyfortheendogenousoccurrenceoffinancialcrises.

Toincorporatethepossibilityof“ClimateMinskyMoments”,webuildonthere-centadvancementsinthemacro-financeliteraturethatincorporatedendogenousfinan-cialcrisesinmacroeconomicmodels,asinBrunnermeierandSannikov(

2014

),GertlerandKiyotaki(

2015

),Boissayetal.(

2016

),MoreiraandSavov(

2017

),andAmadorandBianchi(

2024

).Ourmacro-financemodelblockbuildsuponRottner(

2023

),whichcom-binespro-cyclicalleveragedynamicswithself-fulfillingruns,asinGertleretal.(

2020

),toreconcilekeyfeaturesoffinancialcycles.7Ourpapercontributestothisliteraturebyincorporatingtheroleofclimatepolicyinthistypeofmodel.

7Theframeworkfeatures,forinstance,”creditboomsgonebust”dynamics(SchularickandTaylor,

2012

)andthevolatilityparadox(BrunnermeierandSannikov,

2014

).

6

Wealsorelatetotheliteratureontheinteractionsbetweenfinancialstabilityandclimatepolicythatusesanalyticallytractablemodels.Jondeauetal.(

2021

)addresstheriskoffiresalesofemission-intensiveassets.D¨ottlingandRola-Janicka(

2023

)analyzejointlyoptimalclimateandfinancialpolicyinthecontextofourpaper.Ourcontributionistobuildaquantitativemodel,whichopensupthepossibilityofexaminingtheimpactofdifferentclimatepoliciesonfinancialstabilitythroughaquantitativelens.

Analternativeapproachtakenbyseveralregulatorsisclimatestresstests.Acharyaetal.

(2023

)provideasummaryandoutlookforclimatechangestresstests.SpecificexamplesareJungetal.

(2024

)andIMF(

2022

),whoevaluatetheeffectsofspecificclimatechangescenariosontheloanportfoliofortheUSandUK,respectively.Brunettietal.

(2022

)reviewclimatestresstestresultsconductedinseveraljurisdictions.Bydesign,stresstestscannotuncoverpositivefinancialstabilityeffectsofthetransition,astheyabstractfromthefinancialsector’sdeleveragingincentivesalongthenetzerotransition.Incontrast,bytakingageneralequilibriumperspective,wecanfullyendogeneizetheresponsesofthedifferenteconomicagentsduringthetransitiontonetzero.Italsoopensupthepossibilityofawelfareanalysistobenchmarkthewelfareimpactof“ClimateMinskyMoments”againstcostsandbenefitsofthenetzerotransitionintherealsector.

2Model

Themodelconsistsofthreebuildingblocksrelatedtocarbonemissionsandclimatepolicy,thefinancialsector,andthemacroeconomy,respectively.TheclimateblockfollowstheframeworkofHeutel(

2012

),inwhichfirmsemitcarbondioxidethatcontributestoglobaltemperatureincreases.Emissionsaresubjecttoacarbontax,butfirmscanundertakeacostlyabatementefforttoreducetheiremissions.ThefinancialsectorfollowslargelythesetupofRottner(

2023

),whichembedsanendogenousleverageconstraint(AdrianandShin,

2014

;Nu˜noandThomas,

2017

)inamodelwithendogenousfinancialcrisesasinGertleretal.

(2020

).ThisrepresentationoffinancialfragilityandclimatepolicyisembeddedintoanotherwisestandardNewKeynesiansetup.

Production,Emissions,andCarbonTaxesWefirstdescribetheproductionsector,whichisthepartofthemodelwherecarbondioxideemissionsandtaxesenter.Perfectlycompetitive(intermediate)goodproducersuseaCobb-Douglastechnologytoproduce

outputYtusingcapitalKtandlaborLtasinputs:Yt=AK-1L-α.Theyemitcarbon

dioxideduringtheproductionprocess.Firmsaresubjectto(potentiallytime-varying)emissiontaxesτtc.WefollowHeutel(

2012

)inassumingthatemissionsareproportionaltoproductionYt,butcanbeabatedatacost.Denotingtheabatementsharebyηt,totalemissionsarethereforegivenby(1-ηt)Ytwhilethetotalcarbontaxpaidinperiodtisgivenbyτtc(1-ηt)Yt.Carbontaxrevenuesarerebatedtohouseholdsinalumpsum

7

fashion.8Abatementcostsareproportionaltooutput:

withb1,b2>0.Sinceemissionandabatementcostsareproportionaltooutput,theoptimalabatementeffortsolvesanintra-periodper-unitcostminimizationproblem:

n(1-ηt)τtc+b2b1η2+1.Theoptimalabatementeffortηisgivenby

.(2)

Theabatementeffortisincreasinginthecurrentcarbontaxandiscappedbyone,i.e.,wedonotallowforthepossibilityofnetnegativeemissions.9Sinceclimatepolicydirectlyaffectstheaccumulationandpricingofcapitalinourmodeleconomy,itishelpfultodefinethepolicy-inducedwedgeintothereturnoncapital.Pluggingintheoptimal

abatementeffortηintotheabatementcostfunction,ξt+1summarizesallexpensesper

unitofcapitalfromcarbontaxationandabatement:

TherealizedreturnoninvestmentisgivenbyR=[(1-δ)Qt+Zt]/Qt-1.Takingthe

priceoftheintermediategoodptasgiven,thefirst-orderconditionsforcapitalandlaborcanbeexpressedas:

and(4)

Sinceemissionsandabatementcostsareproportionaltototaloutput,thecarbontaxdoesnotaffecttheoptimalcapitalshareintheproductionfunctionbutinsteaddepressestotalfactorproductivity.

TemperatureandClimateDamagesEmissionsarelinkedtoeconomicdamagesthroughincreasesinglobaltemperatures.Followingtheclimateeconomicsliterature,carbonemissions(1-ηt)Ytaccumulateintoastockofatmosphericcarbondioxide,whichwecanmapintotemperaturechangesfollowingFernandez-Villaverdeetal.(

2024

).Specif-

8Wealsoconsideramodificationinwhichcarbontaxrevenuessubsidizefirms’abatementcosts.

9Analternativeinterpretationisthatfirmsswitchtoanemission-freebutlessproductivetechnology(seealsoComerfordandSpiganti(

2023

)andthereferencestherein).ηtwouldthenmeasurethenumberoffirmsthatoperatetheemission-freetechnology.Underthisinterpretation,itisreasonabletoassumethatsometechnologies,suchasaviation,cement,orsteelproduction,areverycostlytooperateinanemission-freefashion.Atthemacroeconomiclevel,thiswouldalsogiverisetoaconvexrelationshipbetweencarbontaxesandtheaggregatereturnonassets.

8

ically,theglobaltemperaturechangerelativetopre-industriallevels,∆Tt三Tt-T1850,ispositivelyrelatedtocumulatedemissionsEt三correspondstocumulatedemissionsuptothelastperiodbeforethe(potential)policychange.FollowingFernandez-Villaverdeetal.(

2024

),weapproximatethisrelationshipby:

∆Tt=ΨCCREt.(5)

Tomapglobaltemperatureincreasesintoeconomicdamages,weassumethattempera-turechangesinflictautilitylossD(∆Tt)asinAcemogluetal.,

2012.

Utilitylossesarequadraticintheglobaltemperatureincreaserelativetopre-industriallevels:

D(∆Tt)=γD(∆Tt)2.(6)

Suchquadraticlossfunctionsarecommonlyusedinintegratedassessmentmodels,forexampleNordhaus(

2008

).Thekeyadvantageofthisspecificationisthatitallowsustocleanlycomparethewelfarecostsof“ClimateMinskyMoments”relativetootherbenefitsandcostsofcurbingglobalwarmingwithout