104902023June2023ClimateDamagesinConvergence-ConsistentGrowthProjectionsTonyHarding,JuanMoreno-Cruz,MartinQuaas,WilfriedRickels,SjakSmuldersImpressum:CESifoWorkingPapersISSN2364-1428(electronicversion)Publisheranddistributor:MunichSocietyforthePromotionofEconomicResearch-CESifoGmbHTheinternationalplatformofLudwigs-MaximiliansUniversity’sCenterforEconomicStudiesandtheifoInstitutePoschingerstr.5,81679Munich,GermanyTelephone+49(0)892180-2740,Telefax+49(0)892180-17845,emailoffice@cesifo.deEditor:ClemensFuesthttps://www.cesifo.org/en/wpAnelectronicversionofthepapermaybedownloaded·fromtheSSRNwebsite:www.SSRN.com·fromtheRePEcwebsite:www.RePEc.org·fromtheCESifowebsite:https://www.cesifo.org/en/wpCESifoWorkingPaperNo.10490ClimateDamagesinConvergence-ConsistentGrowthProjectionsAbstractProjectionsofclimatechangedamagesbasedonclimate-econometricestimatessuggestthat,withoutmitigation,globalwarmingcouldreduceaverageglobalincomesbyover20%towardstheendofthecentury(Burkeetal.,2015).ThisfiguresignificantlysurpassesclimatedamagesinIntegratedAssessmentModels(IAMs).Forexample,globalclimatedamagesobtainedwiththeseminalDICEmodelarejusta7%reductioninoutput(Nordhaus,2018).Here,weshowthatthediscrepancybetweentheprojectionscanberesolvedbyaccountingforgrowthconvergenceinaclimate-econometricapproachthatisconsistentwiththemacroeconomicmodelsunderlyingmostIAMs.Byre-estimatingtheglobalnon-linearrelationshipbetweentemperatureandcountry-leveleconomicgrowth,ourconvergence-consistentprojectionsrevealthatunderanunmitigatedwarmingscenario,globalclimatedamagesamountto6%.JEL-Codes:O400,O440,Q540,Q550,Q560.Keywords:climatechange,economicsgrowth,convergence,integratedassessmentmodels.TonyHardingHarvardUniversity,Cambridge/MA/USAtonyharding@hks.harvard.eduJuanMoreno-CruzUniversityofWaterloo/ON/Canadajuan.moreno-cruz@uwaterloo.caMartinQuaasGermanCentreforIntegrativeBiodiversityResearch(iDiv)Halle-Jena-Leipzig/Germanymartin.quaas@idiv.deWilfriedRickelsKielInstitutefortheWorldEconomyIfWKiel/Germanywilfried.rickels@ifw-kiel.deSjakSmuldersTilburgUniversity/TheNetherlandsJ.A.Smulders@uvt.nlWethankReyerGerlaghandMauricioRodriguezAcostafortheircommentsandfeedback.1IntroductionEstimatingthefutureeconomicconsequencesofclimatechangeiscrucialfordevelopingefficientclimatepolicies.IntegratedAssessmentModels(IAMs)serveasastandardtoolforformulatingefficientclimatepolicypathwaysbyweighingthecostsofclimatepoliciesagainstthecostsofclimatedamages.Forinstance,theUnitedStatesInteragencyWorkingGroupontheSocialCostofGreenhouseGases(IWG,2021)employsthreepeer-reviewedIAMstocalculatethesocialcostofthreegreenhousegases(GHGs).Theseestimatesarethenappliedinregulatoryimpactanalysestoinformoptimalemissionsabatementstrategies(Aldyetal.,2021).IAMstypicallyincorporateneo-classicalgrowthmodels,utilizingthebestavailabledatafromphysicalandeconomicsciencestoestablishrelationshipsbetweeneconomicproduction,climatechange,climatepolicycosts,andclimatechange’simpactsoneconomicactivity.Thesemodelsemployaneoclassicalproductionfunctioncharacterizedbyexogenoustechnicalchangeanddiminishingreturnsofcapital.Therateoftechnicalchangepinsdownthelong-rungrowthrateofincome,whichisindependentofproductivitylevelsorinvestmentrates.Asclimatechangereducesaggregateproductivity,the(averageandmarginal)productivityofcapitalsubsequentlydeclines.Thisleadstolowerinvestmentandalowerfuturecapitalstock.Becauseofdiminishingreturnstocapital,theendogenousreductioninthefuturecapitalstockcausestheaverageproductivityofcapitaltoconvergebacktooldlevels.Asaresult,outputlevelsarepermanentlylowercomparedtoascenariowithoutclimatechange,butthegrowthrateisonlytemporarilylower,convergingbacktotheoldlevelinthelongrun.Onlysteadyproductivitygrowththroughongoingtechnicalprogresscandrivelong-runcapitalandoutputgrowth.1IAMshavebeendevelopedsincethelate1980s.Inthemeantime,climatechangehascontinuedtoprogressintherealworld,withobservableimpactsoneconomiesworldwide.Recentclimate-econometricapproachesleveragethisdatatoempiricallyestimateclimatechangedamagefunctionsandprojectfutureclimatechangedamages(e.g.,Burkeetal.,2015,2018).However,theseapproachesdonotdirectlyapplytheneoclassicalgrowthmodelofIAMstothedataand,specifically,theydonotaccountfortheconvergenceeffectsinherentinneoclassicalgrowthmodels.Withthemutedconvergenceeffectsintheseprojections,climatechangehaspersistentdifferentialeffectsonincomeacrosscountiesandleadstoastrongdivergenceineconomicincomesacrosscountries,resultinginpronouncedwinnersandlosers.Thispaperpresentsaclimate-econometricapproachthatenhancestheempiricalestimationandprojectionsofclimatechange’smacroeconomicimpacts,aligningthemmorecloselywiththetheoreticalmodelsunderpinningIAMsandthemethodsemployedinthebroaderempiricalgrowthliterature(BarroandSala-iMartin,1992;Temple,1999;JohnsonandPapageorgiou,2020).Byadoptingthefoundational1SomerecentIAMsconsiderthatclimatechangecouldhavealastingeffectoneconomicgrowth,suchasthroughalterationsininnovationrates(e.g.,Gerlagh,2023).Inthispaper,ourprimaryfocusisongeneratingempiricalestimatesofclimateimpactsthatalignwiththeunderlyingeconomictheoryofthemostprevalentIAMs.Intheconclusion,wediscussthepossibilityoffutureworktoexploreestimatesconsistentwithmorerecentIAMmodelframeworks.2Solow-Swanmacroeconomicgrowthmodel,wederiveaconvergence-consistentequationforestimatingtheimpactsofclimateindicators–temperatureandprecipitation–oneconomicgrowthrates,usingcountry-leveldata.Subsequently,weapplyourempiricalestimatestoprojecteconomicdamagesfromclimatechangethroughoutthe21stcenturyunderthewidely-usedhigh-emissionsscenarioRCP8.5.Weconfirmpreviousevidenceforanon-lineareffectoftemperatureoneconomicoutputlevels.How-ever,unlikepreviousstudies,wedonotfindevidenceofenduringimpactsoneconomicgrowth.Whenprojectingeconomicdamagesfromclimatechanges,weratherobservethatincorporatingconvergenceeffectsconsiderablydiminishesclimatedamages.Whereaspriorestimatesindicatethatclimatechangewillreduceglobalaverageincomesbyapproximately20%,ourcentralspecificationindicatesareductioninglobalaverageincomescloseto6%.Thisreconcilesthediscrepanciesinclimatedamagesbetweentheclimate-econometricapproachandtheIAMliterature.Moreover,accountingforconvergencecon-siderablynarrowstherangeofcountry-leveleconomicgrowthratesprojectedfortheendofthecentury,indicatingthatclimatechangehaslessofanimpactoninter-countryincomeinequalitythanpreviouslyfound.Thispaperaddstothegrowingbodyofliteratureonempirically-basedestimatesofclimate’simpactoneconomicgrowthusingclimate-econometricmethods(Delletal.,2014).Specifically,itaddressesacrucialopenquestionconcerningwhetherclimatechangeaffectsincomelevelsorratherincomegrowthrates(Burkeetal.,2015;KalkuhlandWenz,2020;Newelletal.,2021).Mostcloselyrelatedtothispaperis(Delletal.,2012),whoestimatetheeffectoftemperatureandprecipitationoneconomicgrowthandfindthatrisingtemperaturesreduceeconomicgrowthinpoorercountries.Ourstudybuildsonthispaperbyconsideringnon-lineareffectsoftemperatureandprecipitationoneconomicgrowthandapplyingtheresultingestimatestoprojectionsofclimatedamages.Includingnon-lineareffectsofclimatevariables,wecannotconfirmthepreviousevidenceforapersistentgrowtheffect.Additionally,weemphasizetheimportanceofaccountingforconvergenceeffectswhenapplyingestimatesinprojections.InSection2,webuildonaconciseneo-classicalgrowthmodelandderiveanempiricalmodel,factoringinconvergence,toestimatethemacroeconomicclimatedamages.InSection3,wedetailthedatautilizedintheempiricalestimationprocess.InSection4,wepresentourfindings.Finally,inSection5,wedrawourconclusions.2Estimatinggrowtheffectswithconvergence2.1NeoclassicalmacroeconomicgrowthandconvergenceTheSolow-Swanmodelrelatesaggregateoutputtolaborandcapitalinputsthroughaconstant-returns-to-scaleCobb-Douglastechnology.Inthelong-run,themodelfindsthattheeconomyunderconsideration3reachesasteady-statewhereper-capitaoutputisdescribedby2y(t):=lnY(t)L(t)=lnA(0)+gt+α1−αlns−α1−αln(n+g+δ)+(1)wherey(t)isthenaturallogarithmofper-capitaoutputinyeart,Y(t)L(t)istheper-capitaoutput,sisthesavingsrate,nispopulationgrowth,gislabor-productivitygrowth,αistheproductionelasticityofcapital,andδisthecapitaldepreciationrate.ThetermA(0)representsallexogenous,non-economic,sourcesofproductivity.AlreadyMankiwetal.(1992,p.5)emphasizesthat“theA(0)termreflectsnotjusttechnologybutresourceendowments,climate,institutions.”Thisstandardequationpredictsthatlong-runincomelevelsvaryacrosscountrieswithA(0),g,α,s,n,andδ.However,thepredictionforlong-runincomegrowthissimplyg,independentofalltheotherdeterminants.Thismeansthatshockstotheeconomieshavenopermanentgrowtheffectsunlesstheypermanentlyaffectthetrendproductivitygrowthrate.Ifapermanentincreaseintemperaturelowersproductivitylevelspermanently,pre-shockcapitalstockscannolongerbesustainedandinvestmentfalls.Inthelong-run,lowercapitalstocklevelsrestorepre-shockreturnstoinvestment.Afterthisadjustmentprocess,theoutputlevelsarepermanentlylower,butthegrowthrateisbacktotheoldlevel.Wheneverthereismorecapitalthanjustifiedbytheproductivitylevels,thereturnstoinvestmentarelow,andgrowthissloweddownuntilthecapitalstockhasadjustedtoproductivitylevels.Onlysteadyproductivitygrowththroughongoingtechnicalprogresscandrivelong-runcapitalandoutputgrowth.InDICEandmostotherIAMs,itisbyassumptionthatclimateimpactsproductivitylevels,butnotthelong-runtrendoftechnologicalchange.Consequently,thelong-rungrowthrateisnotaffectedbyclimate.However,theabsenceoflong-rungrowtheffectspredictedbyneoclassicalgrowththeorycanandneedstobeempiricallytested.ThisrequiresamoredynamicapproachthanEquation(1).Theworkhorsedynamicequationtoestimatethedeterminantsofgrowthandlong-runlevelofpercapitaincomeincountryifromtimet−1totisthe‘convergenceequation’(Acemoglu,2009,Section3.2):∆yi,t=gi−λ(yi,t−1−y∗i,t−1)(2)whereyi,tisthenaturallogarithmofpercapitaincomesothattheleft-handsiderepresentspercapitaincomegrowth,y∗i,t=y∗i,0+gitisthelong-runexponentialgrowthpathtowhichactualincomeyitisconverging,andλ>0measuresthe‘speedofconvergence’(Temple,1999),whichisproportionalto1−α,i.e.theproductionelasticityofinputsotherthancapitalintheproductionfunction.3Decreasingreturnstoman-madecapitalimply1−α>0.Heregt,λ,andy∗i,0needtobeestimatedfromobservable2The(discrete-timeCobb-Douglas)SolowmodelcanbepresentedbyproductionfunctionY=Kα(AL)1−αandcapitalaccu-mulationfunction∆K=sY−δK.InAppendixC.1weshowhow(1)and(2)canbederivedfromthesetwoequations.3Definingzit=yit−y∗itasthedeviationofactualincomefromtrendincome,wecanwrite(2)aszit=(1−λ)zi,t−1,whichshowsthatzit→0i.e.yit→y∗itwhent→∞,provided1−λ<1.4determinants,includingclimatevariables;combinedwithobservedincomeyi,ttheypredictthegrowthprocess.Themodelallowsfortwosourcesofgrowth.First,gicaptureslong-runtrendgrowthandisdrivenbycontinuousproductivityimprovements.Changesintrendgrowthgipermanentlyaffectincomegrowth.Second,deviationsfromthetrend,yi,t−y∗i,t,temporarilyaffectgrowth.Thiscapturesconvergencegrowth.Afallinactualincomewithoutanycorrespondingchangeintrendgrowthcreatestemporarilyfastergrowthsothattheeconomygraduallyreturnstotheoldgrowthpath.Similarly,anincreaseinthetrendlevelofincome,y∗i,0,createsonlytemporarilyfastergrowthsothattheeconomyconvergestoincomeatahigherlevelbuteventuallygrowsattheold-growthrate.This,inturn,suggeststwochannelsbywhichchangesinclimatecouldimpacteconomicgrowth.Ifchangesinclimateaffectgi,thelong-rungrowthtrend,thesechangeswillhavepermanenteffectsoneconomicgrowthbychangingsteady-stategrowthrates.Impactsongrowthrateswouldbethecaseifclimatechangespermanentlyimpacteddeterminantsoflong-runeconomicgrowth,suchastherateofinnovation.Ifclimatechangesonlyimpactoutputlevels,suchasthroughachangeinproductivity,thiswillonlyhaveatransitoryeffect.Inthelong-run,convergencepressureswillreturngrowthtothesteady-state.Thepaceatwhichthisoccursdependsonthespeedofconvergence,λ.WeanalyzethesetwochannelsinamannerconsistentwiththeoryfollowingtheapproachofBondetal.(2010)toestimatebothtransitoryandpermanentgrowtheffectsofclimate.Toderivethecorrespondingempiricalmodel,wefirstrewriteEquation(2)as∆yi,t=−λyi,t−1+kβkxi,t,k+γi(t)+ηi+i,t(3)whereλmeasuresthespeedofconvergence,xi,t,kdenotesexplanatoryvariableskthatmaydeterminegrowth,γi(t)arecountry-specifictimetrendfunctionsrepresentingtheratesofsteady-stategrowth,ηiarecountry-specificinterceptsrepresentinginitialconditions,andi,tisanerrorterm.Foranalyzingthedeterminantsofmacroeconomicgrowth,thecoefficientsonxi,t,kareofmaininterest.Thisapproachhasbeenusedtoanalyzeexplanatoryvariablessuchaspopulationgrowth,humancapital,orinvest-ment.Here,ourinterestisthepartialeffectofclimate,soweuseclimatevariables—temperatureandprecipitation—astheexplanatoryvariables.If1−λ<1,limt→∞γi(t)=γ1it+γ2i,andexplanatoryvariablesxi,t,k–includingclimatevariables–reachsteady-statevaluessuchthateventuallyxi,t,k=xi,k,then,underthisspecification,thecountry-specificpercapitaincomeconvergestoanexponentialgrowthpathwithgrowthrategi=γ1iλ.Notice,thissteady-stategrowthratedoesnotdependonclimate.Thus,whilechangesinclimatecan5affecteconomicgrowth,thelevelsofclimatevariables,oncestabilized,donotmatterforthesteady-stateexponentialgrowthpath.Changesinclimateinthismodelonlyhavetransitoryimpactsoneconomicgrowthascountriesadjusttoanewsteady-stategrowthpathatthesamesteady-stategrowthrate.Noticealsothatincomeconvergestoanexponentialgrowthpathonlyifthe(country-specific)timetrendsγi(t)arebounded,i.e.atmostlinearlyincreasing(inabsolutevalue)witht.Thus,forconsistencywiththeunderlyingtheoreticalframework,whenempiricallyestimatingEquation(3),itisimportantthatanycountry-specifictimetrendsbebounded.Insomepreviousempiricalanalysesofthegrowtheffectsofclimate,estimateshaveusedunboundedtimetrends.Forexample,Burkeetal.(2015)estimatequadraticcountry-specifictimetrends.Thisassumptionimpliesthatcountrieswillneverconvergetoasteady-stategrowthpath.Inourempiricalestimates,reportedbelow,weratherestimatelinearcountry-specifictimetrends.4Next,wederiveanempiricalmodelthatallowsustoestimatepersistentimpactsofclimateoneconomicgrowth.Tothisend,werewriteEquation(3)asalevelsequation,takefirstdifferences,andaddadditionallaggedlevelsoftheexplanatoryvariablesxi,t,k.Thisgives∆yi,t=(1−λ)∆yi,t−1+kβk∆xi,t,k+kθkxi,t−1,k+∆γi(t)+∆i,t(4)Againconsiderasteady-state,whereexplanatoryvariablesremainstable,xi,t,k=xi,k.If1−λ<1,andlimt→∞γi(t)=γ1it+γ2i,country-specificsteady-stategrowthratesaregivenasgi=γ1iλ+kθkxi,kλ.UnlikeforEquation(3),heresteady-stategrowthratesareafunctionoftheexplanatoryvariables,notablyclimatevariables.Specifically,thesteady-stategrowthratedependsonthecoefficientsθkofthelaggedexplanatoryvariablelevels.Bycontrast,thecoefficientsβkofthefirst-differencedexplanatoryvariablesinEquation(4)thuscapturethetransitorygrowtheffectsofchangesinclimate,asinEquation(3).ByestimatingEquation(4),whichincludescoefficientsforbotheffects,wecantestwhetherclimatemattersforlong-runeconomicgrowthorifchangesinclimateonlyhaveatransitoryeffectonincomelevels.5Delletal.(2012)alsofollowthisestimationapproach,however,foreconometricestimatesinthetextoftheirpapertheyassumeλ=0,i.e.theyabstractfromconvergence.Intheappendixoftheirpaper,theytestrelaxingthisassumptionandfindthatfixingλ=0doesnotbiasthecoefficientsonclimatevariablesintheirestimates.So,theyopttoexcludetheconvergenceterminthetext.Whereasexcluding4Toconsideranalternativenon-linearcountry-specifictimetrendspecification,intheAppendixweconsideramoreflexiblebutstillboundedspecificationgivenasγi(t)=γi1t+γ2ite−1τ(t−t0).5Kahnetal.(2021)useanautoregressivedistributedlag(ARDL)specificationsimilartoEquation(4)exceptthattheyexcludethelevelclimatevariableterms.Byexcludingthelevelterms,theycanonlycapturetheimpactsofclimateoneconomicoutputlevels,notthelong-rungrowtheffects.6theconvergencetermdoesnotaffecttheidentificationoftheeffectsofchangesinclimateongrowth,ithasimportantimplicationsinprojectionsoflong-rundamagesfromclimatechanges,asweshowbelow.Inshort,byignoringconvergencepressuresbyexcludingtheconvergenceterm,allgrowtheffectsbecomelong-runeffectswhenusingtheestimatesinprojections.2.2Climate-growtheffectsintheliteratureInIAMs,suchasDICE,climatechangereducesaggregateproductivityand,byconstruction,doesnotaffectlong-runeconomicgrowth.Whenclimatechangesaffectgrowthrates,theimplicationsforoptimalclimatepolicyaresignificantlydifferent(MooreandDiaz,2015).Itisanempiricalquestionwhetherclimatehasshort-runorlong-runeffectsongrowth,andassuchitcannotbeansweredbyanIAM.Overthepastdecadetherehasbeenanexpandingclimate-econometricsliteratureapplyingcross-sectionalandpaneldataestimationmethodstoidentifyhowchangingclimatevariablesaffecteconomicoutputandgrowth.Theliteratureprovidesmixedevidenceforlevelversusgrowtheffects.Delletal.(2012)providesevidencethattemperatureimpactscountry-leveleconomicgrowthonlyinpoorcountries.Burkeetal.(2015)providesfurtherevidenceofthegrowtheffectsoftemperature,highlightingthattheeffectisnon-linearduetodifferencesinclimateratherthanincome.Usingalow-passfiltertoseparatelongerandshorterfrequencytemperaturefluctuations,Bastien-OlveraandMoore(2021)findthatlongertemperatureanomaliescanaffectgrowthasmuchasshorteranomalies.Theyarguethatthisisindicativeofpersistenteffectsofclimatechange.Ontheotherhand,KalkuhlandWenz(2020)andNewelletal.(2021)provideevidencethattemperatureimpactsGDPlevels,buttheydonotfindeffectsonthegrowthrate.Estimatesfromthisclimate-econometricsliteraturearefrequentlyusedtoprojecttheimpactsoftheclimateoutsidethetheoreticalframeworkofIAMsbyupdatingcountry-levelsocioeconomicprojectionstoaccountforclimateimpacts(Burkeetal.,2015,2018;DiffenbaughandBurke,2019;KalkuhlandWenz,2020;Newelletal.,2021).However,theseempiricalestimatesdonotaccountfordiminishingreturnstocapitalthatboundthelong-runimpactsofclimatechange,asinEquations(3)and(4).Below,weshowhowaccountingforsuchconvergenceeffectscanmeaningfullyguideprojectionsoftheeconomicimpactsofclimatechanges.3DataWeusethesamecountry-leveleconomicandclimatedataforourempiricalanalysisasBurkeetal.(2015).ThedataoneconomicgrowthcomesfromtheWorldBankandcoverstheyears1960to2010(WorldBankGroup,2012).Theclimatedatacomesfrommonthlygriddedinterpolatedweatherstationdata(WillmottandMatsuura,2012).Themonthlygriddedclimatedataisaggregatedtothecountry-level7usingpopulationweightsandthentotheannualfrequencytakingtheaverageofmonthlytemperaturesandthesumofmonthlyprecipitation.Recentempiricalclimateeconometricsanalyseshaveconsideredalternativedatasetstoaddressvariouspotentialissuesorinnovations.Forexample,someanalyseshaveturnedtosub-nationaleconomicgrowthdata(Damaniaetal.,2020;KalkuhlandWenz,2020)orcon-sideredalternativeeconomicvariables(LettaandTol,2019).Otheranalyseshaveconsideredalternativesourcesofclimatedata,suchasusingreanalysisdatatoaddressweatherstationbias(Auffhammeretal.,2013).Hereourmaininterestistoassesstheeffectsofusingaconvergence-consistentgrowthmodelasthebasisforeconometricanalysisofclimateimpacts.Tothisend,weletthedataoverlapwithBurkeetal.(2015)asmuchaspossibletoensurecomparabilitywithpreviousworkonthistopic.4Results4.1Convergence-ConsistentRegressionResultsHereweestimatearelationshipbetweenclimateandeconomicactivitybasedonthepastglobalex-periencewithclimatechange.Specifically,weestimateEquations(3)and(4)tostudytheeffectsofaccountingfortheoretically-foundedconvergenceandthepersistenceofclimateimpactsoneconomicgrowth.Forclimatevariablesxi,t,k,thereisnotheoreticalguidanceontheappropriatefunctionalformorwhichclimatevariablesshouldbeincluded.Weopttouselinearandquadratictermsofcountry-leveltemperatureandprecipitationtoallowfornon-linearitiesintherelationshipbetweenclimateandeconomicgrowth.6,7Weestimateasingleglobalrelationshipbetweenclimatevariablesandeconomicgrowth.But,ofcourse,itispossiblethisrelationshipdependsonotherfactors,suchasthelevelofeconomicdevelopment(Delletal.,2012).So,inonemodelspecification,weseparatelyestimateeffectsforrichandpoorcountries,allowingfordifferentialeffectsacrosslevelsofdevelopment.ThisfunctionalformapproachisconsistentwithBurkeetal.(2015)andDelletal.(2012).Table1showstheresultsacrossmodelspecifications.First,incolumns(1)–(3)ofTable1weestimateEquation(3)imposingtheassumptionthatthereisnoconvergence,i.e.λ=0.Acrosscolumns(1)–(3),wechangethecountry-specifictimetrendspecificationfromnotrends,tolineartrends,toquadratictrends.TheseestimatesreflecttheestimatesofDelletal.(2012)andBurkeetal.(2015)andprovideabenchmarkforcomparison.Inparticular,estimatesincolumn(3)ofTable1areidenticaltoBurkeetal.(2015)’sestimateincolumn(1)ofExtendedData6Lackofvariationinclimatechanges,whichoccuronthescaleofdecades,makesempiricalidentificationdifficult.Thus,wefollowtheliteratureinusingvariationsinweather,measuredasannualtemperatureandprecipitationasaproxy.Identificationrestsontheassumptionthatannualdeviationsintemperatureandprecipitationwithincountriesareexogenous(Delletal.,2014).7Weonlyconsidertemperatureandprecipitationasexplanatoryvariablestocapturethemarginaleffectofclimateasadeterminantofgrowth.Itisofcoursepossiblethatclimatecouldinteractwithotherdeterminantsofeconomicgrowth,suchaspopulationgrowthorhumancapitalformation.Futureworkcouldexploreinteractionsbetweenclimateandothersuchdeterminantsofeconomicgrowth.8Table1,theirbenchmarkspecification.Asareminder,byleavingouttheconvergenceterm,allclimateeffectsare,byconstruction,permanentgrowtheffects.Acrosscolumns(1)–(3)ofTable1wefindstatisticallysignificantevidencethattemperaturehasanon-linearimpactoneconomicgrowth.Ourresultsindicatethatifacoldcountryexperiencesamarginallywarmeryear,itwillexperienceaboostineconomicgrowth,ceterisparibus.Andifawarmercountryexperiencesamarginallywarmeryear,itwillexperienceaslowdowninitseconomicgrowth,ceterisparibus.Thisisconsistentwithexistingevidenceofanon-lineareffectoftemperatureonavarietyofeconomicfactors,suchasagriculturalyields,laborsupply,andmortality(SchlenkerandRoberts,2009;GraffZivinandNeidell,2014;Carletonetal.,2022).Incolumn(2)weestimateEquation(3)withlinearcountry-leveltime-trends.Wefindalowerpeakgrowthtemperatureandincreasedmagnitudeofthemarginaleffectsathighandlowtemperatures.Incolumn(3)wereproducetheestimatesofBurkeetal.(2015)whichincludesquadraticcountry-leveltimetrends.Wefindthecoefficientestimatesforclimatevariablesaresimilartothoseincolumn(2).However,asaquadratictrendisunboundedandinconsistentwithourtheoreticalframework,weonlyreportthemhereforcomparisonwiththepreviousliteratureandfocusoncolumn(2)inthetext.Acrosstheseempiricalspecifications,wefindnoevidenceofastatisticallysignificanteffectofprecipitationoneconomicgrowth.8Next,incolumns(4)–(5)ofTable1weestimateEquation(3)withtheconvergenceterm,i.e.relaxingtheassumptionλ=0.Thisestimatingequation,asdiscussedabove,onlycapturestransitorygrowtheffectsofclimate.Inthelong-run,convergencepressuresrestorecountry-levelgrowthratestothesteady-statelevel,sochangesinclimateonlyaffectthelevelofoutput.Incolumn(4)wedonotincludecountry-specifictimetrends,i.e.weimposeγ1i=0.Incolumn(5)weestimatelineartime-trends.Coefficientsonthesetrendsestimateγ1i.Forthetransitoryeffectsofclimateoneconomicgrowth,weagainfindsignificantevidenceinsupportofanon-lineareffectoftemperature,andwealsofindweaklysignificantevidenceofanon-lineareffectofprecipitation.Wefindthepeak-growthtemperatureinbothcolumns(4)and(5)arecomparabletothosefoundincolumns(2)and(3),ifslightlyhigher,thoughthemarginaleffectsathighandlowtemperaturesaredampened.9AsfoundbyDelletal.(2012),theseresultssuggestthatincludingtheconvergencetermhaslittleeffectontheprecisionoftheestimatesofclimate’sgrowtheffects.However,ithasimportantimplicationsfortheinterpretationofthecoefficientsandtheirimplicationsinprojectionsofdamagesfromclimatechangesaswewillexploreinthenextsubsection.Acrosscolumns(4)–(5),wefindthattheconvergenceterm,−λ,issignificant,negative,andoneplusthepointestimateislessthanoneinabsolutevalue.Thenegativepointestimatefor−λindicatesthatlowercurrentoutputleadstofastereconomicgrowth.Estimatinganabsolutevaluefor1−λoflessthan8AsdiscussedinDamaniaetal.(2020)thisislikelyduetotheaggregationofprecipitationmeasures,whichexhibitsignificantspatialvariation.9Thisisalsotrueforaquadratictimetrendwiththelaggedlogarithmicincometermthoughthisspecificationprohibitsconvergenceinterpretationduetobeingunbounded.9oneindicatessupportforconvergence.Ourpointestimatesareconsistentwithpreviousestimates,suchasthosebyLeeetal.(1998).InSupplementaryFigure7weplotestimatesforthelinearcountry-specifictrends’coefficientsforestimatesincolumn(5)ofTable1.Theseestimatesmeasurethesteady-stategrowthratesγ1iforeachcountry.Wefindthatover75%ofcountrieshaveasteady-stateannualgrowthofbetween0-5%,andthemajorityaround2-3%.Totestbothchannelsbywhichclimatecanaffecteconomicgrowth,bothlong-runandshort-run,incolumns(6)–(7)ofTable1weestimateEquation(4).Asareminder,coefficientsonclimatevariablefirstdifferencescapturetheshort-runimpacts,andcoefficientsonclimatevariablelevelscapturethelong-runimpacts.Column(6)isamoregeneralestimatingequationthanincolumn(5)byallowingforlong-rungrowtheffectsandbynestingthepreviousspecification.Butwefindthatthismoregeneralspecificationisconsistentwiththeshort-runonlyestimatesincolumn(5).Incolumn(7),weadditionallyexplorethepossibilityofdifferentialeffectsofclimatebetweenrichandpoorcountries.Letusfirstconsidertheshort-runimpactsofclimatecapturedbycoefficientsonthefirst-differencedclimatevariables.Asineachofourpreviousestimates,wefindsignificantevidenceofanon-linearrelationshipbetweentemperatureandeconomicgrowth.However,incolumn(7),estimatesareonlystatisticallysignificantforrichcountries.Comparedwithcolumn(5),wefindthatthepeakgrowthtemperatureislowerincolumn(6)andforpoorcountriesincolumn(7),butcomparableforrichcountriesincolumn(7).Weagainfindnosignificantevidenceinsupportofarelationshipbetweenprecipitationandeconomicgrowth.Next,letusconsiderthelong-runimpactsofclimatecapturedbythecoefficientsontheclimatevariablelevels.Wefindnostatisticallysignificantevidenceofalong-runeffect,neitherfortemperaturenorforprecipitation.10ThisfindingcontrastswithDelletal.(2012)whofindevidenceoflong-rungrowtheffects.11However,itisconsistentwithmorerecentresultsfromKalkuhlandWenz(2020)andNewelletal.(2021)whofindgreaterevidenceinsupportofclimatehavinganeffectoneconomicincomelevelsratherthanonlong-runeconomicgrowth.FortheestimatingEquation(4),theestimatedcoefficientforlaggedgrowthmeasures1−λ,oroneminustheconvergencerate.Convertingourestimates,wefindafasterconvergencerateforthismodelspecification,bothforthepooledmodelandforthemodelthatdistinguishesbetweenrichandpoorcountries,thanwhenestimatingEquation(3).However,thedifferenceinimpliedλestimatesbetweencolumns(5)and(6),whicharedirectlycomparableestimatingequation,isnotstatisticallysignificant.Again,ourestimatesfortheimpliedvalueofλareconsistentwithpreviousfindings,suchastheestimates10Intheappendixweconsideradditionallaggedclimateterms.Wefindadditionallagsdonotchangethisfinding.11Burkeetal.(2015)followtheapproachofDelletal.(2012)andincludelaggedclimatevariablestotestforshort-runversuslong-rungrowtheffects.Theyfindevidenceoflong-rungrowtheffects.Intheappendix,weanalyzetheirfindingsinthecontextofourgrowthframework.Whentheregressionincludeslaggedgrowthand,inparticular,laggedgrowthisinstrumentedtocorrectforendogeneity,wefindnoevidenceofalong-rungrowtheffect.10inBondetal.(2010).4.2ConvergenceConsistentProjectionsInthissection,weuseourempiricalestimatesfromtheprevioussubsectiontoprojectcountry-leveleconomicdamagesfromclimatechangeuntiltheendofthecentury.Weexploretheconsequencesofincorporatingconvergenceasguidedbyourtheoreticalframework.Toprojectcountry-levelclimatedam-ages,wefollowtheapproachoutlinedinBurkeetal.(2018).Specifically,webeginwithinitialprojectionsofcountry-leveleconomicgrowthforthe21stcenturyfromtheSharedSocio-economicPathways(SSPs)assumingthatclimatevariablesarestaticat2010levelsintheSSPs,xi,t,k=xi,2010,k,forallt(O’Neilletal.,2014).Thisrepresentsourbaselinescenariowithoutclimatechange.LetySSPi,tbetheprojectedincomepercapitawithoutclimatechangefromtheSSP.Then,wecanwritetheprojectionofper-capitaincomeincountryiastherecursiveequation:∆ySSPi,t=−λySSPi,t−1+kβkxi,2010,k+γi(t)+ηi.(5)SubstitutingthisintoEquation(3)andlettingyCCi,tbetheprojectedcountry-levelincomepercapitawithclimatechange,wefindthatthepathofprojectedincomeunderclimatechangecanbegeneratedrecursivelyasfollows∆yCCi,t=∆ySSPi,t−λ(yCCi,t−1−ySSPi,t−1)+kβk(xi,t,k−xi,2010,k),(6)whereclimatevariablesxi,t,kareobtainedfromtheclimatescenario.Similarly,foreconometricestimatesfollowingEquation(4),weprojectincomepercapitawithclimatechangebyrecursivelyapplying∆yCCi,t=∆ySSPi,t+(1−λ)(∆yCCi,t−1−∆ySSPi,t−1)+kβk∆xi,t,k+kθk(xi,t−1,k−xi,2010,k)(7)Equation(7)showsthatthegrowthprojectionswithclimatechangearethegrowthprojectionsfromtheSSPsadjustedfornotonlythedirectimpactsofclimatechangebutalsotheadditionalconvergenceeffectinducedbytheimpactsofclimatechange.12Thisconvergencetermisignoredinpreviousstudiesthatuseempiricalestimatestoprojectclimateimpacts,suchasBurkeetal.(2015).InAppendixC.2,wefurtherderiveanequationthatexpressesthelong-runeffectofclimatechangesonpercapitaincomewhenclimatevariablesreachanewsteady-state.WeusetheSSPsforourbenchmarkcountry-leveleconomicgrowthprojections.Here,wefocuson12Weassumethatourbaselinecountry-levelgrowthscenariosalreadyaccountforconvergencepressuresintheabsenceofclimatechanges.Figure4intheSupplementaryMaterialsshowsthechangesininter-countryincomeinequalityinthebaselinegrowthprojectionillustratedasLorenzCurvesin2010and2100.Thedeclineininequalityoverthecenturysupportsthisassumption.11SSP5,afossil-fueleddevelopmentscenariowithrapideconomicgrowth.IntheSupplementaryMaterials,wepresentresultsforalternativeSSPs.Whilequantitativeresultsvary,thequalitativetakeawaysarerobusttothedifferentSSPs.WeuseRCP8.5,theextremewarmingscenario,asourclimatechangescenarioforcomparabilitywithpreviousstudies(Burkeetal.,2015;KalkuhlandWenz,2020).Inthisscenario,themeanglobaltemperaturerisesaround3.6◦Coverthecentury.SupplementaryFigure5showsthechangeincountry-levelpopulation-weightedmeanannualtemperatures.InPanel(a)ofFigure1,weshowtheprojectionsofglobalaverageincomefortheSSPscenariowithoutclimatechange,andfortheRCP8.5climatechangescenarioacrossmodelspecificationsforcolumns(2),(4),and(5)fromTable1.13Ineachmodelspecificationprojectedaverageglobalincomesarelowerbytheendofthecenturywithclimatechangethanwithoutclimatechange.Thissupportsconcernsaboutthenegativeglobalimpactsofclimatechange.However,thereisvariationinprojectedincomesacrossmodelspecifications,rangingfrom$51,000/capitato$58,000/capitaattheendofthecentury(thisrangeisfromaround$35,000/capitato$70,000/capitaacrossallmodelspecificationsconsideredinthesupportingmaterialforSSP5).InPanel(b)ofFigure1weshowthedistributionofprojectedcountry-levelgrowthratesbytheendofthecentury.Immediatelyapparentarethedifferencesinthespreadofcountry-levelgrowthratesacrossmodelspecifications.First,considertheSSP5scenariowithoutclimatechange.Overthecentury,inthisbaselinescenario,country-levelgrowthslowsandconvergestoanannualgrowthrateofaround3%,whichisclosetoourempiricalestimatesofthesteady-stategrowthrateformostcountries(Figure7intheSupplementaryMaterials).Alternatively,considerthespreadincountry-levelgrowthratesattheendofthecenturyforthemodelspecificationofcolumn(2).Here,growthratesagainslow,butthespreadofprojectedcountry-levelgrowthratesincreasesovertime.Notably,lossestohottercountriesamplifyovertimeuntiltheirincomesareeventuallyshrinkingovertime.Thatis,theirgrowthratesbecomenegative.Thisisduetothelong-runpersistenceinthegrowtheffectsofclimateforthismodelspecification.Alternatively,whenaccountingforconvergenceeffectsinmodelspecificationsofcolumn(4)andcolumn(5),thespreadofcountry-levelgrowthratesshrinksovertimeandismoreconsistentwiththebaselineSSP5projection.InFigure2wecomparetheprojectedglobalaverageincomesinthebaselineSSPscenariowithoutclimatechangetoprojectionswithclimatechange,tomeasuretheglobaleconomiclossesfromclimatechange.Moreprecisely,wemeasurethelossesasthepercentagedifferenceinprojectedglobalaverageGDPpercapitabetweenthescenarioswithandwithoutclimatechange.Weagainfocusonmodelspecificationsforcolumns(2),(4),and(5)ofTable1toexaminetheeffectofaccountingforconvergence13Throughoutthissectionwepresentresultsonlyformodelspecificationsforcolumns(2),(4),and(5)fromTable1.ResultsforallmodelspecificationsreportedinTable1canbefoundintheSupplementaryMaterials.Inthetext,wefocusonthesemodelspecificationstocompareamodelspecificationsimilartothemodelinBurkeetal.(2015),buttheoreticallyconsistent,toacomparablemodelwiththeconvergenceterm.Wedonotshowresultsforthelong-runmodelspecifications,columns(6)-(7),becausewefindnoevidenceofpersistentgrowtheffectscapturedbythosemodels.12pressures.InPanel(a)weshowtheprojectedlossesfromclimatechangeagainsttime.Thisfigureshowsthataccountingforconvergencesignificantlyreducestheprojectedlossesfromclimatechange.By2100,forempiricalestimatesofcolumn(4)andcolumn(5),whichaccountforconvergence,wefindlossesfromclimatechangearearound6%to13%.Forempiricalestimatesofcolumn(2),whichdoesnotaccountforconvergence,wefindlossesfromclimatechangearearound16%.Thisresultfollowsbecauseinmodelspecificationsforcolumns(4)and(5),climatechange’sgrowtheffectsarenotaspersistentinthelong-run.Whileclimateimpactsreduceeconomicgrowth,convergencecounterstheseeffects,limitingthelong-runlossesinpercapitaincome.Theimplicationsofaccountingforconvergenceforthemagnitudeanddistributionoflong-runlossesfromclimatechangearealsoapparentatthecountrylevel.InFigure3weshowthecountry-leveldifferenceinGDPpercapitain2100betweenthescenarioswithandwithoutclimatechange.Forthecolumn(2)modelspecification,thespecificationwithoutconvergence,thenegativeimpactsofclimatechangearelargeandapparentforthehottertropicalcountries.Thereisalsoaconsiderablespreadinimpactsrangingfrom-95%to1,491%differenceinGDPpercapita.Thisimpliesaconsiderablerangeofwinnersandlosersfromclimatechange.Formodelspecificationsforcolumns(4)and(5),whichallowforconvergence,themagnitudeofimpactsandthespreadaresmaller,rangingfromjust-18%to22%.InPanel(a)ofFigure2theprojectionofglobaleconomiclossesunderthecolumn(2)specification,whichissimilartotheBurkeetal.(2015)specification,displaysaU-shapetowardstheendofthecentury.Thisshapesuggeststhatpeakeconomiclossesfromclimatechangewouldoccurin2090,afterwhichclimatedamageswouldstarttodecline.Neglectingconvergencethussuggeststhatthegainstoclimatechangewinners—duetopersistentpercapitagrowthwithoutconvergence—wouldstartdominatingthelossesofclimatechangelosersaround2090.Thus,failingtoaccountforincomeconvergenceoverestimatesmedium-runimpactsandunderestimateslong-termimpacts.IncorporatingconvergencepressuresisconsistentwiththeapproachusedbyIAMs.InPanel(b)ofFigure2wecomparetheeconomicdamagesofclimatechangebasedonprojectionsusingregressionestimatesformodelspecificationsforcolumns(2),(4),and(5)ofTable1totheresultsfromthreeofthemostcommonlyusedIAMsfordifferentmeanglobaltemperaturechanges.Theprojecteddamagesfromclimatechangeunderthecolumn(2)specification,whichisakintotheBurkeetal.(2015)specificationanddoesnotaccountforconvergence,greatlyexceedsdamagesobtainedfromtheIAMs,particularlyatmoderatetoextremetemperaturechanges.GlobalaverageincomelossesfortheIAMsrangefromaround2%to7%fora5◦Cincreaseintemperature,whereasincomelossesunderthecolumn(2)specificationareprojectedtobearound17%.FortheIAMs,themarginaldamagesofanincreaseintemperatureriseswithhighertemperatures.ThisconvexityinlossesforIAMsisconsistentwiththeexpectationthatthedamagesfromclimatechangewillincreaseconvexlywithdeviationsfromthepre-industrialstateofthe13climate.However,underthecolumn(2)specification,wefindthatthemarginalimpactofanincreaseintemperaturedecreasesathighertemperaturesbecausethegainsfromthewinnersoutweighthelossestothelosers.Onceweaccountforconvergence,asinmodelspecificationsforcolumns(4)and(5)ofTable1,projectedclimatedamagesaremuchclosertotheIAMresults,bothinshapeandinmagnitude.Ata5◦Cincrease,incomelossesforourcentralmodelspecificationincolumn(5)areclosetotheclimatedamageobtainedfromDICE,whichisareductionofoutputbyaround7%.5DiscussionClimate-econometricsplayanessentialroleinprovidinganempiricalfoundationforunderstandingthepotentialcostsofclimatechange.Whenestimatingand,moreimportantly,implementingtheseem-piricalapproaches,itiscrucialtoensureconsistencywithfundamentaleconomictheories,suchastheneoclassicalgrowththeorythatservesasthebasisforIntegratedAssessmentModels.Previousstudies,suchasBurkeetal.(2015),haveemployedeconometricestimatestoprojecttheeco-nomicimpactsofclimatechangeoverextendedperiods,forinstance,throughoutthe21stcentury.TheyreportclimatedamagessignificantlylargerthanthoseintraditionalIAMs.Inthispaper,wedemonstratethattheseprojectedmagnitudescanbereconciledbyadoptinganempiricalapproachconsistentwiththemacroeconomicmodelsunderlyingmostIAMs.Inparticular,weshowthatfactoringintheconvergencegrowtheffect,akeyfeatureofneoclassicalmacroeconomictheory,substantiallyreducestheprojectedlong-termimpactsofclimatechange.Amainresultfromourstudyisthatignoringgrowthconvergencemayleadtoartificiallyhighestimatesforthelong-termeconomicconsequencesofclimatechange.Drawingfromneoclassicalmacroeconomictheory,wederiveempiricalmodelstoestimatetheeco-nomicimpactsofclimateshocks,takingconvergenceintoaccount.Additionally,weproposeatestfordistinguishingbetweentransitoryimpactsoneconomicoutputlevelsandpersistentimpactsonunder-lyingsteady-stateeconomicgrowth.Ourempiricalregressionresultsrevealthat,whileaccountingforconvergencehardlychangesthepointestimatescapturingclimate’smacroeconomicimpact,ithassig-nificantimplicationsforassessingthelong-termeconomicconsequencesofclimatechange.ContrarytoDelletal.(2012),weuncovernoevidenceofpersistentlong-termgrowthimpacts.Ourestimatesrathersuggestthatclimateimpactsinthelong-runshouldonlyinfluenceincomelevels,butnoteconomicgrowthrates.Consequently,whenapplyingourfindingstoprojectionsofeconomicgrowthunderclimatechange,weobservethataccountingforconvergenceconsiderablymitigatesthedamagesfromclimatechange.Ignoringconvergence,asdoneinmostoftheclimate-econometricliterature,wefindaverageglobalincomelossesbytheendofthecenturythatreach16%.Allowingforconvergencereducestheselossestoaround6%.ThisestimateisinlinewithclimatedamagesinprominentIAMs,suchastheDICEmodel,whicharealsobasedonmacroeconomicmodelthatincludesdiminishingreturnstoman-madecapitaland14thusconvergence.Further,accountingforconvergenceinfluencestheimplicationsofclimatechange.Forinstance,withoutconvergence,thegainsexperiencedbythewinnersofclimatechangeeventuallysurpassthelossesincurredbythelosers;thus,fromautilitarianwelfareperspectiveclimatechangeisprojectedtobebeneficialinthelongrun,i.e.,startinginthe22ndcentury.Moreover,withoutconvergence,damagesareestimatedtobeconcaveinclimatedeviationsfrompre-industriallevels.Includingconvergencereversesbothfindingsandleadtoconclusionsmoreinlinewithexpectationsinformedbyenvironmental-macroeconomictheory:aggregatedamagesareconvexintheextentofclimatechangeandareprojectedtocontinuouslyincreaseovertimewithon-goingclimatechange.Despitethepanelapproachenablingthedisentanglementofhistorical,institutional,andtechnologicalcountry-fixedeffectsfromchangesinclimateconditions,ourempiricalapproachstillfacesfundamentallimitationsinherentinmostcurrentclimate-econometricapproaches.Forinstance,theapproachover-looksfeedbackfromtradeandpriceeffects,implyingthatcountrieslikeCanadaandRussiacontinuetobenefitfromclimatechangeastheirregionaltemperatureapproachestheoptimum,eventhoughtheremaybefewviabletradingpartnersleftintherestoftheworld.Consideringtheseeffects,theoverallimpactofclimatechangeoncountriesGDPmightdifferfromtheoneresultingfromthedirectclimateimpactswithinthecountry(Calzadillaetal.2013,Aaheimetal.2015).Moreover,whileourmodelalignsempiricalestimateswiththeconvergenceeffectintheneo-classicalmodelofeconomicgrowth,itdoesnotnecessarilycaptureallthemechanismsofmoreintricategrowthmodels.Weleavethesequestionsforfutureresearch.ReferencesAcemoglu,D.(2009).IntroductiontoModernEconomicGrowth.Princeton,NewJersey,USA:PrincetonUniversityPress.Aldy,J.E.,M.J.Kotchen,R.N.Stavins,andJ.H.Stock(2021).Keepclimatepolicyfocusedonthesocialcostofcarbon.Science373(6557),850–852.Publisher:AmericanAssociationfortheAdvancementofScience.Auffhammer,M.,S.M.Hsiang,W.Schlenker,andA.Sobel(2013).UsingWeatherDataandClimateModelOutputinEconomicAnalysesofClimateChange.ReviewofEnvironmentalEconom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pitation0.00867-0.00468/-0.00468(0.0107)(0.00962)/(0.00962)∆Precipitation2-0.002000.00277/0.00277(0.00302)(0.00221)/(0.00221)Growtheffects:Temperature-0.00113-0.00162/0.00445(0.00292)(0.00441)/(0.00728)Temperature20.00000952-0.0000281/-0.0000687(0.0000775)(0.000157)/(0.000159)Precipitation0.005900.00257/0.00513(0.00951)(0.0125)/(0.0154)Precipitation2-0.00253-0.00453/-0.00133(0.00256)(0.00296)/(0.00406)Convergence:Impliedλ0.04710.1920.3750.585/0.235(0.00758)(0.0109)(0.153)(0.193)/(0.184)MaxGDP/capitaGrowthTemp16.913.413.114.213.211.513.5/10.0Country-SpecificTimeTrendNoneLinearQuadraticNoneLinearNoneNoneObs.6584658465846187618760865963Rsq.0.1530.2190.286Adj.Rsq.0.1240.1700.221Allmodelsincludecountryandyearfixedeffects.StandardErrorsareclusteredatthecountrylevel.Columns(1)-(3)areestimatedusingordinaryleastsquares.Addressingendogeneity,columns(4)-(7)areestimatedinstrumentingforlaggedincomeorincomegrowthwithtwo-periodpriorlag.Forregressionswithlevelanddifferencedclimatevariables,maxGDP/capitatemperaturesarecalculatedusingthecoefficientsonthedifferencedvariables.Fortherich/poorspecification,maxGDP/capitatemperaturesisgivenforrich/poorcountries.Temperatureismeasuredin◦C.Precipitationismeasuredinµm/year.1891011122010204020702100YearGlobalGDP/capita(ln$/capita)ModelColumn2Column4Column5SSP(a)GlobalGDPpercapitaprojections−50510ModelCountryGrowthRate(%)ModelColumn2Column4Column5SSP(2010)SSP(2100)(b)Country-levelgrowthrates(2099)Figure1:GDPpercapitaprojections.(a)GlobalGDPpercapitaprojectionforSSP5andadjustedforclimatedamagesunderRCP8.5acrossempiricalspecificationsinTable1.(b)Box-plotsofprojectedcountry-levelgrowthratesforSSP5andadjustedforclimatedamagesunderRCP8.5acrossempiricalspecificationsinTable1.Forthebox-plots,thehorizontallineshowsthemedian,theboxshowstheinterquartilerange,andthewhiskersshowthe5to95percentilerange.−40−30−20−10010202010204020702100Year%changeinaverageGDP/capModelColumn2Column4Column5(a)Lossesovertime−30−20−10010203012345TemperatureChange(°C)%changeinaverageGDP/capModelColumn2Column4Column5DICEFUNDPAGE(b)LossesovertemperaturechangeFigure2:Globallossesfromclimatechange.DifferenceinprojectedaverageglobalGDPpercapitabetweennoclimatechangeandwithclimatechangeagainsttime(a)andagainsttemperaturechange(b)forempiricalspecificationsfromTable1andthreeIAMs.Temperaturechangein(b)isrelativetopre-industrialtemperature.BothfiguresareforSSP5.19(a)Column2(b)Column4(c)Column5Figure3:Country-levellossesfromclimatechange.Differenceinprojectedcountry-levelGDPpercapitabetweennoclimatechangeandwithclimatechangeintheyear2100.FiguresareforSSP5andempiricalspecificationsfromTable1.20AppendixAAdditionalDataFiguresSSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2100)SSP5(2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evelsteady-stategrowthratesforcolumn(5)empir-icalmodel.228.59.09.510.010.511.02010204020702100YearGlobalGDP/capita(ln$/capita)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(a)SSP18.59.09.510.010.511.02010204020702100YearGlobalGDP/capita(ln$/capita)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(b)SSP28.59.09.510.02010204020702100YearGlobalGDP/capita(ln$/capita)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(c)SSP38.59.09.510.02010204020702100YearGlobalGDP/capita(ln$/capita)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(d)SSP491011122010204020702100YearGlobalGDP/capita(ln$/capita)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(e)SSP5Figure8:Projections.Projectionsofaverageglobalincomeforeachmodel.23−50510ModelCountryGrowthRate(%)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(2010)SSP(2100)(a)SSP1−50510ModelCountryGrowthRate(%)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(2010)SSP(2100)(b)SSP2−50510ModelCountryGrowthRate(%)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(2010)SSP(2100)(c)SSP3−50510ModelCountryGrowthRate(%)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(2010)SSP(2100)(d)SSP4−50510ModelCountryGrowthRate(%)ModelColumn1Column2Column3Column4Column5Column6Column7SSP(2010)SSP(2100)(e)SSP5Figure9:Convergenceofgrowthrates.Boxplotofprojectedcountry-levelgrowthratesin2099foreachofthemodels.Horizontallinerepresentmedian,boxrepresentsinterquartilerange,andwhiskersrepresent5to95percentilerange.24−40−30−20−10010202010204020702100Year%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7(a)SSP1−40−30−20−10010202010204020702100Year%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7(b)SSP2−40−30−20−10010202010204020702100Year%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7(c)SSP3−40−30−20−10010202010204020702100Year%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7(d)SSP4−40−30−20−10010202010204020702100Year%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7(e)SSP5Figure10:ClimatedamagesovertimeGlobaldamagesofclimatechangeovertimemeasuredasper-centagedifferenceinglobalaverageincome.25−50−40−30−20−1001012345TemperatureChange(°C)%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7DICEFUNDPAGE(a)SSP1−50−40−30−20−100102012345TemperatureChange(°C)%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7DICEFUNDPAGE(b)SSP2−50−40−30−20−100102012345TemperatureChange(°C)%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7DICEFUNDPAGE(c)SSP3−50−40−30−20−10010203012345TemperatureChange(°C)%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7DICEFUNDPAGE(d)SSP4−50−40−30−20−100102012345TemperatureChange(°C)%changeinaverageGDP/capModelColumn1Column2Column3Column4Column5Column6Column7DICEFUNDPAGE(e)SSP5Figure11:ClimatedamagesovertemperatureGlobaldamagesfromclimatechangemeasuredaspercentagedifferenceinglobalaverageincomeversuschangeinglobalaveragetemperature26B.2Non-linearcountry-leveltimetrendsWeestimatethefollowingequationincludingnon-linear,butbounded,country-specifictimetrends.∆yi,t=−λyi,t−1+kβkxi,t,k+γ1it+γ2ite−(t−t0)/τ.(8)Thereisnogoodjustificationforusinganyspecificvalueofτ,whichcontrolstherateatwhichthenon-lineartimetrendtermapproaches0,soweconsiderarangeofpossiblevalues.Below,weplottheestimatedmarginaleffectsoftemperatureforeachoftheestimatedvaluesofτaswellasthecorrespondingprojectionsofclimatedamagesovertime.Itisclearthattheclimateimpactsaresensitivetotheτparameter.WefindthatthisisduetochangesintheestimatedtemperatureandprecipitationcoefficientswhenusinganIVregressionapproach.Forlowvaluesofτ,forwhichthenon-lineartermapproaches0morequickly,wefinddamagesaresimilartothelineartimetrendsmodel.Figure12:Marginaleffectsoftemperaturebyτvalue27Figure13:Globalcostsofclimatechangeovertimebytauvalue.CAdditionalTheoryandModelingC.1DerivingthesteadystateanddynamicsoftheSolowmodelThe(Cobb-Douglas)Solowmodelcanbepresentedandsolvedinafewlines.Letthetime-dependentvariablesY,K,L,Abeoutput,capital,laborinput(aswellaspopulationsize),andtechnology,respectively;andlettheconstantss∈(0,1),δ>0,α∈(0,1),g=∆lnA,andn=∆lnLbethesavingsrate,depreciationrate,productionelasticityofcapital,growthrateoftechnology,andgrowthrateofpopulation,respectively.OutputfollowsfromaconstantreturnsCobb-DouglasproductionfunctionY=Kα(AL)1−α.(9)Capitalaccumulatesaccordingto∆K/K=sY/K−δ.(10)Werewritethesetwoequationsintermsofthecapital-outputratioq≡K/Yandthelogofpercapitaincomey≡lnY/L.Usingthesedefinitionsintheproductionfunction(9)givesforpercapitaincomey=lnA+α1−αlnq.(11)28Takinglogsandfirstdifferencingtheproductionfunction(9),andsubstitutingthedefinitionofq,wefind∆lnq=(1−α)(∆lnK−n−g).In(10)weapproximate∆K/K≈∆lnKandsubstituteintheaboveequationtofind∆lnq=λ(q∗/q−1),(12)whereq∗≡s/(n+g+δ)andλ≡(1−α)(n+g+δ).Thisshowsthatthesteadystatevalueofqisq∗anditsadjustmentspeedisλ.Substitutingq=q∗into(11)gives(1)inthemaintext.Toderive(2),wenotethatforqclosetoq∗wehavethefirst-orderTaylorexpansionln(q∗/q)≈q∗/q−1,sothatwecanapproximate(12)by:∆lnq=λ(lnq∗−lnq).Substitutingthisresultintothefirstdifferenceof(11),wefind(2).C.2SSP-basedgrowthTheassumptionisthattheclimatevariablesarestaticatthe2010levelsintheSSPs,xitk=xi2010k,∀t.Thus,weadjustthecountry-leveleconomicgrowthineachyeartoaccountforchangesintheclimatevariablefromthe2010level.LetyCCbethepredictedvalue(forlogpercapitaincome)withclimatechangeandySSPthepredictedvaluewithoutclimatechangefromSSP:∆ySSPi,t=kβkxi,2010,k+γi(t)+ηi−λySSPi,t−1.Substitutingthisinto(3),wefind∆yCCi,t=∆ySSPi,t+kβk(xi,t−1,k−xi,2010,k)−λ(yCCi,t−1−ySSPi,t−1).ThisshowsthatthegrowthprojectionswithclimatechangearethegrowthpredictionsfromSSPadjustedfornotonlytheimpactofclimatechange,butalsotheadditionalconvergenceeffect,i.e.theadditionaltemporarygrowthbecausethelevelofincomeislower(orhigher)becauseofclimatechange.Solvingthedifferenceequation,wecanexpresstheclimateeffectonpercapitaincomeasyCCi,t−ySSPi,t=t−1s=0(1−λ)skβk(xi,t−1−s,k−xi,2010,k).29Ifclimatevariablesreachasteadystatexi,t,k→¯xi,k,thelong-runclimateeffectislimt→∞yCCi,t−ySSPi,t=1λkβk(¯xi,k−xi,2010,k).30C.3UnderstandingBHMLongrunspecificationFollowingtheapproachofDelletal.(2012),Burkeetal.(2015)testforlong-runorpersistentimpactsofclimateoneconomicgrowthbyusingadditionallags.FollowingtheAppendixofDelletal.(2012),Equation(4)canberewrittenas∆yi,t=(1−λ)∆yi,t−1+kβk∆xi,t,k+kθkxi,t,k+γi+∆i,t=(1−λ)∆yi,t−1+kβkxi,t,k−kβkxi,t−1,k+kθkxi,t,k+γi+∆i,t=(1−λ)∆yi,t−1+k(βk+θk)xi,t,k−kβkxi,t−1,k+γi+∆i,t=(1−λ)∆yi,t−1+kρtkxi,t,k−kρt−1kxi,t−1,k+γi+∆i,t.(13)Estimatingthisequationusingthelevelsofclimatevariables,ratherthanamixtureoflevelsandfirst-differencesonecantestforlong-rungrowtheffects,thatisθk=0,asρtk=−ρt−1k.Ifthecoefficientonthelaggedlevelclimatevariableisequalinmagnitudebutoppositeinsigntothecurrentperiodclimatevariable,thenclimatethereisnoevidencethatclimatehasapersistentimpactonlong-rungrowth.HereweestimatesuchamodelfirstusingtheBurkeetal.(2015)specificationandthenadjustingthemodelspecificationtomakethemodelconsistentwithours.TheregressionresultsareshowninTable2.Column(1)showstheresultsforaquadraticcountry-specifictimetrendandnolaggedgrowthterm.Consideringthecoefficientsonthecurrentandlaggedtemperatureterms,wecanrejectthenullhypothesisthatthecoefficientsareequalinmagnitudebutoppositeinsign.Thissuggeststhatthereisevidenceofthelong-runimpactsofclimateoneconomicgrowth.Inthenextcolumn,weaddlaggedgrowthandconsideronlyalinearcountry-specifictimetrend.Incolumn(3)weestimatethemodelinstrumentingforthelaggedgrowthterm.Finally,incolumn(4)weremovethecountry-specifictrends,givingamodelconsistentwithourtheory.Consideringthecoefficientsonthetemperaturetermsincolumn(4),thecurrentandlaggedtermsaresignificantlycloserinmagnitudeandwecannolongerrejectthenullhypothesisthattheirsumisstatisticallysignificantfromzero.Thisshowsthatafteradjustingthemodelspecificationtobeconsistentwiththeunderlyingtheoryandaccountforendogeneity,thepersistenceofclimateimpactsongrowthdisappears.31Table2:AdditionalRegressionResults(1)(2)(3)(4)∆yit∆yit∆yit∆yitTemperaturei,t0.01510.01360.01130.0119(0.00387)(0.00377)(0.00330)(0.00297)Temperaturei,t−1-0.00515-0.00929-0.0108-0.0131(0.00350)(0.00345)(0.00528)(0.00318)Temperature2i,t-0.000574-0.000550-0.000531-0.000557(0.000126)(0.000127)(0.000132)(0.000119)Temperature2i,t−10.0001930.0003460.0004630.000566(0.000106)(0.000107)(0.000209)(0.000119)Precipitationi,t0.01290.01090.01320.0146(0.0102)(0.00852)(0.00912)(0.00886)Precipitationi,t−10.004330.000680-0.00618-0.00867(0.0102)(0.0110)(0.0120)(0.0107)Precipitation2i,t-0.00432-0.00339-0.00414-0.00453(0.00260)(0.00192)(0.00229)(0.00217)Precipitation2i,t−1-0.00179-0.0001490.001230.00200(0.00258)(0.00317)(0.00365)(0.00302)∆yit−10.2380.4330.625(0.0401)(0.378)(0.153)MarginalEffectat5◦C0.00620.0023-0.0003-0.0010MarginalEffectat25◦C-0.0090-0.0059-0.0030-0.0006Country-SpecificTimeTrendQuadraticLinearLinearNoneObs.6,5196,4186,0866,086EstimationMethodOLSOLSIVIVAllmodelsincludecountryandyearfixedeffects.StandardErrorsareclusteredatthecoun-trylevel.Columns(1)-(2)areestimatedusingordinaryleastsquares.Columns(3)-(4)areestimatedinstrumentingforlaggedincomegrowthwithtwo-periodpriorlag.Marginaleffectsareevaluatedbysummingoverthelaggedcoefficientswhichisequivalenttoassumingastableclimate.Temperatureismeasuredin◦C.Precipitationismeasuredinµm/year.32