收斂一致增長預(yù)測中的氣候損害

10490

2023

June2023

ClimateDamagesin

Convergence-ConsistentGrowthProjections

TonyHarding,JuanMoreno-Cruz,MartinQuaas,WilfriedRickels,SjakSmulders

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CESifoWorkingPapers

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CESifoWorkingPaperNo.10490

ClimateDamagesinConvergence-ConsistentGrowthProjections

Abstract

Projectionsofclimatechangedamagesbasedonclimate-econometricestimatessuggestthat,withoutmitigation,globalwarmingcouldreduceaverageglobalincomesbyover20%towardstheendofthecentury(Burkeetal.,2015).ThisfiguresignificantlysurpassesclimatedamagesinIntegratedAssessmentModels(IAMs).Forexample,globalclimatedamagesobtainedwiththeseminalDICEmodelarejusta7%reductioninoutput(Nordhaus,2018).Here,weshowthatthediscrepancybetweentheprojectionscanberesolvedbyaccountingforgrowthconvergenceinaclimate-econometricapproachthatisconsistentwiththemacroeconomicmodelsunderlyingmostIAMs.Byre-estimatingtheglobalnon-linearrelationshipbetweentemperatureandcountry-leveleconomicgrowth,ourconvergence-consistentprojectionsrevealthatunderanunmitigated

warmingscenario,globalclimatedamagesamountto6%.

JEL-Codes:O400,O440,Q540,Q550,Q560.

Keywords:climatechange,economicsgrowth,convergence,integratedassessmentmodels.

TonyHarding

HarvardUniversity,Cambridge/MA/USA

tonyharding@

MartinQuaas

GermanCentreforIntegrativeBiodiversity

Research(iDiv)Halle-Jena-Leipzig/Germany

martin.quaas@idiv.de

JuanMoreno-Cruz

UniversityofWaterloo/ON/Canada

juan.moreno-cruz@uwaterloo.ca

WilfriedRickels

KielInstitutefortheWorldEconomy

IfWKiel/Germany

wilfried.rickels@ifw-kiel.de

SjakSmulders

TilburgUniversity/TheNetherlands

J.A.Smulders@uvt.nl

WethankReyerGerlaghandMauricioRodriguezAcostafortheircommentsandfeedback.

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1Introduction

Estimatingthefutureeconomicconsequencesofclimatechangeiscrucialfordevelopinge?cientclimatepolicies.IntegratedAssessmentModels(IAMs)serveasastandardtoolforformulatinge?cientclimatepolicypathwaysbyweighingthecostsofclimatepoliciesagainstthecostsofclimatedamages.Forinstance,theUnitedStatesInteragencyWorkingGroupontheSocialCostofGreenhouseGases(IWG,2021)employsthreepeer-reviewedIAMstocalculatethesocialcostofthreegreenhousegases(GHGs).Theseestimatesarethenappliedinregulatoryimpactanalysestoinformoptimalemissionsabatement

strategies(Aldyetal.,2021).

IAMstypicallyincorporateneo-classicalgrowthmodels,utilizingthebestavailabledatafromphysicalandeconomicsciencestoestablishrelationshipsbetweeneconomicproduction,climatechange,climatepolicycosts,andclimatechange’simpactsoneconomicactivity.Thesemodelsemployaneoclassicalproductionfunctioncharacterizedbyexogenoustechnicalchangeanddiminishingreturnsofcapital.Therateoftechnicalchangepinsdownthelong-rungrowthrateofincome,whichisindependentofproductivitylevelsorinvestmentrates.Asclimatechangereducesaggregateproductivity,the(averageandmarginal)productivityofcapitalsubsequentlydeclines.Thisleadstolowerinvestmentandalowerfuturecapitalstock.Becauseofdiminishingreturnstocapital,theendogenousreductioninthefuturecapitalstockcausestheaverageproductivityofcapitaltoconvergebacktooldlevels.Asaresult,outputlevelsarepermanentlylowercomparedtoascenariowithoutclimatechange,butthegrowthrateisonlytemporarilylower,convergingbacktotheoldlevelinthelongrun.Onlysteadyproductivitygrowth

throughongoingtechnicalprogresscandrivelong-runcapitalandoutputgrowth.1

IAMshavebeendevelopedsincethelate1980s.Inthemeantime,climatechangehascontinuedtoprogressintherealworld,withobservableimpactsoneconomiesworldwide.Recentclimate-econometricapproachesleveragethisdatatoempiricallyestimateclimatechangedamagefunctionsandprojectfutureclimatechangedamages(e.g.,Burkeetal.,2015,2018).However,theseapproachesdonotdirectlyapplytheneoclassicalgrowthmodelofIAMstothedataand,speci?cally,theydonotaccountfortheconvergencee?ectsinherentinneoclassicalgrowthmodels.Withthemutedconvergencee?ectsintheseprojections,climatechangehaspersistentdi?erentiale?ectsonincomeacrosscountiesandleadstoa

strongdivergenceineconomicincomesacrosscountries,resultinginpronouncedwinnersandlosers.

Thispaperpresentsaclimate-econometricapproachthatenhancestheempiricalestimationandprojectionsofclimatechange’smacroeconomicimpacts,aligningthemmorecloselywiththetheoreticalmodelsunderpinningIAMsandthemethodsemployedinthebroaderempiricalgrowthliterature(Barro

andSala-iMartin,1992;Temple,1999;JohnsonandPapageorgiou,2020).Byadoptingthefoundational

1SomerecentIAMsconsiderthatclimatechangecouldhavealastinge?ectoneconomicgrowth,suchasthroughalterationsininnovationrates(e.g.,Gerlagh,2023).Inthispaper,ourprimaryfocusisongeneratingempiricalestimatesofclimateimpactsthatalignwiththeunderlyingeconomictheoryofthemostprevalentIAMs.Intheconclusion,wediscussthepossibilityoffutureworktoexploreestimatesconsistentwithmorerecentIAMmodelframeworks.

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Solow-Swanmacroeconomicgrowthmodel,wederiveaconvergence-consistentequationforestimatingtheimpactsofclimateindicators–temperatureandprecipitation–oneconomicgrowthrates,usingcountry-leveldata.Subsequently,weapplyourempiricalestimatestoprojecteconomicdamagesfromclimate

changethroughoutthe21stcenturyunderthewidely-usedhigh-emissionsscenarioRCP8.5.

Wecon?rmpreviousevidenceforanon-lineare?ectoftemperatureoneconomicoutputlevels.How-ever,unlikepreviousstudies,wedonot?ndevidenceofenduringimpactsoneconomicgrowth.Whenprojectingeconomicdamagesfromclimatechanges,weratherobservethatincorporatingconvergencee?ectsconsiderablydiminishesclimatedamages.Whereaspriorestimatesindicatethatclimatechangewillreduceglobalaverageincomesbyapproximately20%,ourcentralspeci?cationindicatesareductioninglobalaverageincomescloseto6%.Thisreconcilesthediscrepanciesinclimatedamagesbetweentheclimate-econometricapproachandtheIAMliterature.Moreover,accountingforconvergencecon-siderablynarrowstherangeofcountry-leveleconomicgrowthratesprojectedfortheendofthecentury,indicatingthatclimatechangehaslessofanimpactoninter-countryincomeinequalitythanpreviously

found.

Thispaperaddstothegrowingbodyofliteratureonempirically-basedestimatesofclimate’simpactoneconomicgrowthusingclimate-econometricmethods(Delletal.,2014).Speci?cally,itaddressesacrucialopenquestionconcerningwhetherclimatechangea?ectsincomelevelsorratherincomegrowthrates(Burkeetal.,2015;KalkuhlandWenz,2020;Newelletal.,2021).Mostcloselyrelatedtothispaperis(Delletal.,2012),whoestimatethee?ectoftemperatureandprecipitationoneconomicgrowthand?ndthatrisingtemperaturesreduceeconomicgrowthinpoorercountries.Ourstudybuildsonthispaperbyconsideringnon-lineare?ectsoftemperatureandprecipitationoneconomicgrowthandapplyingtheresultingestimatestoprojectionsofclimatedamages.Includingnon-lineare?ectsofclimatevariables,wecannotcon?rmthepreviousevidenceforapersistentgrowthe?ect.Additionally,weemphasizethe

importanceofaccountingforconvergencee?ectswhenapplyingestimatesinprojections.

InSection2,webuildonaconciseneo-classicalgrowthmodelandderiveanempiricalmodel,factoringinconvergence,toestimatethemacroeconomicclimatedamages.InSection3,wedetailthedatautilizedintheempiricalestimationprocess.InSection4,wepresentour?ndings.Finally,inSection5,wedraw

ourconclusions.

2Estimatinggrowthe?ectswithconvergence

2.1Neoclassicalmacroeconomicgrowthandconvergence

TheSolow-Swanmodelrelatesaggregateoutputtolaborandcapitalinputsthroughaconstant-returns-

to-scaleCobb-Douglastechnology.Inthelong-run,themodel?ndsthattheeconomyunderconsideration

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reachesasteady-statewhereper-capitaoutputisdescribedby2

u(s):=ln=lnA(0)+gs+lng_ln(n+g+5)+e(1)

whereu(s)isthenaturallogarithmofper-capitaoutputinyears,istheper-capitaoutput,gisthesavingsrate,nispopulationgrowth,gislabor-productivitygrowth,aistheproductionelasticityofcapital,and5isthecapitaldepreciationrate.ThetermA(0)representsallexogenous,non-economic,sourcesofproductivity.AlreadyMankiwetal.(1992,p.5)emphasizesthat“theA(0)termre?ectsnot

justtechnologybutresourceendowments,climate,institutions.”

Thisstandardequationpredictsthatlong-runincomelevelsvaryacrosscountrieswithA(0),g,a,g,n,and5.However,thepredictionforlong-runincomegrowthissimplyg,independentofalltheotherdeterminants.Thismeansthatshockstotheeconomieshavenopermanentgrowthe?ectsunlessthey

permanentlya?ectthetrendproductivitygrowthrate.

Ifapermanentincreaseintemperaturelowersproductivitylevelspermanently,pre-shockcapitalstockscannolongerbesustainedandinvestmentfalls.Inthelong-run,lowercapitalstocklevelsrestorepre-shockreturnstoinvestment.Afterthisadjustmentprocess,theoutputlevelsarepermanentlylower,butthegrowthrateisbacktotheoldlevel.Wheneverthereismorecapitalthanjusti?edbytheproductivitylevels,thereturnstoinvestmentarelow,andgrowthissloweddownuntilthecapitalstockhasadjustedtoproductivitylevels.Onlysteadyproductivitygrowththroughongoingtechnicalprogress

candrivelong-runcapitalandoutputgrowth.

InDICEandmostotherIAMs,itisbyassumptionthatclimateimpactsproductivitylevels,butnotthelong-runtrendoftechnologicalchange.Consequently,thelong-rungrowthrateisnota?ectedbyclimate.However,theabsenceoflong-rungrowthe?ectspredictedbyneoclassicalgrowththeorycanandneedstobeempiricallytested.ThisrequiresamoredynamicapproachthanEquation(1).Theworkhorsedynamicequationtoestimatethedeterminantsofgrowthandlong-runlevelofpercapita

incomeincountryifromtimes_1tosisthe‘convergenceequation’(Acemoglu,2009,Section3.2):

?ui,t=gi_A(ui,t__1_u,t__1)

(2)

whereui,tisthenaturallogarithmofpercapitaincomesothattheleft-handsiderepresentspercapita

incomegrowth,u,t=u,0+gisisthelong-runexponentialgrowthpathtowhichactualincomeuitis

converging,andA>0measuresthe‘speedofconvergence’(Temple,1999),whichisproportionalto

1_a,i.e.theproductionelasticityofinputsotherthancapitalintheproductionfunction.3Decreasing

returnstoman-madecapitalimply1_a>0.Heregt,A,andu,0needtobeestimatedfromobservable

2The(discrete-timeCobb-Douglas)SolowmodelcanbepresentedbyproductionfunctionY=Kα(AL)1_αandcapitalaccu-mulationfunction?K=sY-δK.InAppendixC.1weshowhow(1)and(2)canbederivedfromthesetwoequations.

3De?ningzit=yit-ytasthedeviationofactualincomefromtrendincome,wecanwrite(2)aszit=(1-λ)zi,t__1,whichshowsthatzit→0i.e.yit→ytwhent→__,providedl1-λl<1.

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determinants,includingclimatevariables;combinedwithobservedincomeui,ttheypredictthegrowth

process.

Themodelallowsfortwosourcesofgrowth.First,gicaptureslong-runtrendgrowthandisdrivenby

continuousproductivityimprovements.Changesintrendgrowthgipermanentlya?ectincomegrowth.

Second,deviationsfromthetrend,ui,t_u,t,temporarilya?ectgrowth.Thiscapturesconvergence

growth.Afallinactualincomewithoutanycorrespondingchangeintrendgrowthcreatestemporarily

fastergrowthsothattheeconomygraduallyreturnstotheoldgrowthpath.Similarly,anincreasein

thetrendlevelofincome,u,0,createsonlytemporarilyfastergrowthsothattheeconomyconvergesto

incomeatahigherlevelbuteventuallygrowsattheold-growthrate.

This,inturn,suggeststwochannelsbywhichchangesinclimatecouldimpacteconomicgrowth.Ifchangesinclimatea?ectgi,thelong-rungrowthtrend,thesechangeswillhavepermanente?ectsoneconomicgrowthbychangingsteady-stategrowthrates.Impactsongrowthrateswouldbethecaseifclimatechangespermanentlyimpacteddeterminantsoflong-runeconomicgrowth,suchastherateofinnovation.Ifclimatechangesonlyimpactoutputlevels,suchasthroughachangeinproductivity,thiswillonlyhaveatransitorye?ect.Inthelong-run,convergencepressureswillreturngrowthtothe

steady-state.Thepaceatwhichthisoccursdependsonthespeedofconvergence,A.

WeanalyzethesetwochannelsinamannerconsistentwiththeoryfollowingtheapproachofBondetal.(2010)toestimatebothtransitoryandpermanentgrowthe?ectsofclimate.Toderivethecorresponding

empiricalmodel,we?rstrewriteEquation(2)as

?ui,t=_Aui,t__1+βkti,t,k+7i(s)+ni+ei,t(3)

k

whereAmeasuresthespeedofconvergence,ti,t,kdenotesexplanatoryvariableskthatmaydeterminegrowth,7i(s)arecountry-speci?ctimetrendfunctionsrepresentingtheratesofsteady-stategrowth,niarecountry-speci?cinterceptsrepresentinginitialconditions,andei,tisanerrorterm.Foranalyzingthedeterminantsofmacroeconomicgrowth,thecoe?cientsonti,t,kareofmaininterest.Thisapproachhasbeenusedtoanalyzeexplanatoryvariablessuchaspopulationgrowth,humancapital,orinvest-ment.Here,ourinterestisthepartiale?ectofclimate,soweuseclimatevariables—temperatureand

precipitation—astheexplanatoryvariables.

If|1_A|<1,t7i(s)=71is+72i,andexplanatoryvariablesti,t,k–includingclimatevariables–reachsteady-statevaluessuchthateventuallyti,t,k=ti,k,then,underthisspeci?cation,thecountry-

speci?cpercapitaincomeconvergestoanexponentialgrowthpathwithgrowthrate

gi=.

Notice,thissteady-stategrowthratedoesnotdependonclimate.Thus,whilechangesinclimatecan

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a?ecteconomicgrowth,thelevelsofclimatevariables,oncestabilized,donotmatterforthesteady-stateexponentialgrowthpath.Changesinclimateinthismodelonlyhavetransitoryimpactsoneconomic

growthascountriesadjusttoanewsteady-stategrowthpathatthesamesteady-stategrowthrate.

Noticealsothatincomeconvergestoanexponentialgrowthpathonlyifthe(country-speci?c)timetrends7i(s)arebounded,i.e.atmostlinearlyincreasing(inabsolutevalue)withs.Thus,forconsistencywiththeunderlyingtheoreticalframework,whenempiricallyestimatingEquation(3),itisimportantthatanycountry-speci?ctimetrendsbebounded.Insomepreviousempiricalanalysesofthegrowthe?ectsofclimate,estimateshaveusedunboundedtimetrends.Forexample,Burkeetal.(2015)estimatequadraticcountry-speci?ctimetrends.Thisassumptionimpliesthatcountrieswillneverconvergetoasteady-stategrowthpath.Inourempiricalestimates,reportedbelow,weratherestimatelinearcountry-speci?ctime

trends.4

Next,wederiveanempiricalmodelthatallowsustoestimatepersistentimpactsofclimateoneconomicgrowth.Tothisend,werewriteEquation(3)asalevelsequation,take?rstdi?erences,and

addadditionallaggedlevelsoftheexplanatoryvariablesti,t,k.Thisgives

?ui,t=(1_A)?ui,t__1+βk?ti,t,k+9kti,t__1,k+?7i(s)+?ei,t(4)

Againconsiderasteady-state,whereexplanatoryvariablesremainstable,ti,t,k=ti,k.If|1_A|<1,

andt7i(s)=71is+72i,country-speci?csteady-stategrowthratesaregivenas

gi=+.

UnlikeforEquation(3),heresteady-stategrowthratesareafunctionoftheexplanatoryvariables,notablyclimatevariables.Speci?cally,thesteady-stategrowthratedependsonthecoe?cients9kofthelaggedexplanatoryvariablelevels.Bycontrast,thecoe?cientsβkofthe?rst-di?erencedexplanatoryvariablesinEquation(4)thuscapturethetransitorygrowthe?ectsofchangesinclimate,asinEquation(3).ByestimatingEquation(4),whichincludescoe?cientsforbothe?ects,wecantestwhetherclimatemattersforlong-runeconomicgrowthorifchangesinclimateonlyhaveatransitorye?ectonincome

levels.5

Delletal.(2012)alsofollowthisestimationapproach,however,foreconometricestimatesinthetextoftheirpapertheyassumeA=0,i.e.theyabstractfromconvergence.Intheappendixoftheirpaper,theytestrelaxingthisassumptionand?ndthat?xingA=0doesnotbiasthecoe?cientsonclimate

variablesintheirestimates.So,theyopttoexcludetheconvergenceterminthetext.Whereasexcluding

4Toconsideranalternativenon-linearcountry-speci?ctimetrendspeci?cation,intheAppendixweconsideramore?exiblebutstillboundedspeci?cationgivenasγi(t)=γi1t+γ2ite__(t__t0).

5Kahnetal.(2021)useanautoregressivedistributedlag(ARDL)speci?cationsimilartoEquation(4)exceptthattheyexcludethelevelclimatevariableterms.Byexcludingthelevelterms,theycanonlycapturetheimpactsofclimateoneconomicoutputlevels,notthelong-rungrowthe?ects.

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theconvergencetermdoesnota?ecttheidenti?cationofthee?ectsofchangesinclimateongrowth,ithasimportantimplicationsinprojectionsoflong-rundamagesfromclimatechanges,asweshowbelow.Inshort,byignoringconvergencepressuresbyexcludingtheconvergenceterm,allgrowthe?ectsbecome

long-rune?ectswhenusingtheestimatesinprojections.

2.2Climate-growthe?ectsintheliterature

InIAMs,suchasDICE,climatechangereducesaggregateproductivityand,byconstruction,doesnota?ectlong-runeconomicgrowth.Whenclimatechangesa?ectgrowthrates,theimplicationsforoptimalclimatepolicyaresigni?cantlydi?erent(MooreandDiaz,2015).Itisanempiricalquestionwhether

climatehasshort-runorlong-rune?ectsongrowth,andassuchitcannotbeansweredbyanIAM.

Overthepastdecadetherehasbeenanexpandingclimate-econometricsliteratureapplyingcross-sectionalandpaneldataestimationmethodstoidentifyhowchangingclimatevariablesa?ecteconomicoutputandgrowth.Theliteratureprovidesmixedevidenceforlevelversusgrowthe?ects.Delletal.(2012)providesevidencethattemperatureimpactscountry-leveleconomicgrowthonlyinpoorcountries.Burkeetal.(2015)providesfurtherevidenceofthegrowthe?ectsoftemperature,highlightingthatthee?ectisnon-linearduetodi?erencesinclimateratherthanincome.Usingalow-pass?ltertoseparatelongerandshorterfrequencytemperature?uctuations,Bastien-OlveraandMoore(2021)?ndthatlongertemperatureanomaliescana?ectgrowthasmuchasshorteranomalies.Theyarguethatthisisindicativeofpersistente?ectsofclimatechange.Ontheotherhand,KalkuhlandWenz(2020)andNewelletal.(2021)provideevidencethattemperatureimpactsGDPlevels,buttheydonot?nde?ectsonthegrowth

rate.

Estimatesfromthisclimate-econometricsliteraturearefrequentlyusedtoprojecttheimpactsoftheclimateoutsidethetheoreticalframeworkofIAMsbyupdatingcountry-levelsocioeconomicprojectionstoaccountforclimateimpacts(Burkeetal.,2015,2018;Di?enbaughandBurke,2019;KalkuhlandWenz,2020;Newelletal.,2021).However,theseempiricalestimatesdonotaccountfordiminishingreturnstocapitalthatboundthelong-runimpactsofclimatechange,asinEquations(3)and(4).Below,weshowhowaccountingforsuchconvergencee?ectscanmeaningfullyguideprojectionsoftheeconomicimpacts

ofclimatechanges.

3Data

Weusethesamecountry-leveleconomicandclimatedataforourempiricalanalysisasBurkeetal.(2015).ThedataoneconomicgrowthcomesfromtheWorldBankandcoverstheyears1960to2010(WorldBankGroup,2012).Theclimatedatacomesfrommonthlygriddedinterpolatedweatherstationdata

(WillmottandMatsuura,2012).Themonthlygriddedclimatedataisaggregatedtothecountry-level

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usingpopulationweightsandthentotheannualfrequencytakingtheaverageofmonthlytemperaturesandthesumofmonthlyprecipitation.Recentempiricalclimateeconometricsanalyseshaveconsideredalternativedatasetstoaddressvariouspotentialissuesorinnovations.Forexample,someanalyseshaveturnedtosub-nationaleconomicgrowthdata(Damaniaetal.,2020;KalkuhlandWenz,2020)orcon-sideredalternativeeconomicvariables(LettaandTol,2019).Otheranalyseshaveconsideredalternativesourcesofclimatedata,suchasusingreanalysisdatatoaddressweatherstationbias(Au?hammeretal.,2013).Hereourmaininterestistoassessthee?ectsofusingaconvergence-consistentgrowthmodelasthebasisforeconometricanalysisofclimateimpacts.Tothisend,weletthedataoverlapwithBurke

etal.(2015)asmuchaspossibletoensurecomparabilitywithpreviousworkonthistopic.

4Results

4.1Convergence-ConsistentRegressionResults

Hereweestimatearelationshipbetweenclimateandeconomicactivitybasedonthepastglobalex-periencewithclimatechange.Speci?cally,weestimateEquations(3)and(4)tostudythee?ectsofaccountingfortheoretically-foundedconvergenceandthepersistenceofclimateimpactsoneconomicgrowth.Forclimatevariablesti,t,k,thereisnotheoreticalguidanceontheappropriatefunctionalformorwhichclimatevariablesshouldbeincluded.Weopttouselinearandquadratictermsofcountry-leveltemperatureandprecipitationtoallowfornon-linearitiesintherelationshipbetweenclimateandeconomicgrowth.6,7Weestimateasingleglobalrelationshipbetweenclimatevariablesandeconomicgrowth.But,ofcourse,itispossiblethisrelationshipdependsonotherfactors,suchasthelevelofeconomicdevelopment(Delletal.,2012).So,inonemodelspeci?cation,weseparatelyestimatee?ectsforrichandpoorcountries,allowingfordi?erentiale?ectsacrosslevelsofdevelopment.ThisfunctionalformapproachisconsistentwithBurkeetal.(2015)andDelletal.(2012).Table1showstheresults

acrossmodelspeci?cations.

First,incolumns(1)–(3)ofTable1weestimateEquation(3)imposingtheassumptionthatthereisnoconvergence,i.e.A=0.Acrosscolumns(1)–(3),wechangethecountry-speci?ctimetrendspeci?cationfromnotrends,tolineartrends,toquadratictrends.Theseestimatesre?ecttheestimatesofDelletal.(2012)andBurkeetal.(2015)andprovideabenchmarkforcomparison.Inparticular,estimatesin

column(3)ofTable1areidenticaltoBurkeetal.(2015)’sestimateincolumn(1)ofExtendedData

6Lackofvariationinclimatechanges,whichoccuronthescaleofdecades,makesempiricalidenti?cationdi?cult.Thus,we

followtheliteratureinusingvariationsinweather,measuredasannualtemperatureandprecipitationasaproxy.Identi?cationrestsontheassumptionthatannualdeviationsintemperatureandprecipitationwithincountriesareexogenous(Delletal.,2014).

7Weonlyconsidertemperatureandprecipitationasexplanatoryvariablestocapturethemarginale?ectofclimateasadeterminantofgrowth.Itisofcoursepossiblethatclimatecouldinteractwithotherdeterminantsofeconomicgrowth,suchaspopulationgrowthorhumancapitalformation.Futureworkcouldexploreinteractionsbetweenclimateandothersuchdeterminantsofeconomicgrowth.

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Table1,theirbenchmarkspeci?cation.Asareminder,byleavingouttheconvergenceterm,allclimate

e?ectsare,byconstruction,permanentgrowthe?ects.

Acrosscolumns(1)–(3)ofTable1we?ndstatisticallysigni?cantevidencethattemperaturehasanon-linearimpactoneconomicgrowth.Ourresultsindicatethatifacoldcountryexperiencesamarginallywarmeryear,itwillexperienceaboostineconomicgrowth,ceterisparibus.Andifawarmercountryexperiencesamarginallywarmeryear,itwillexperienceaslowdowninitseconomicgrowth,ceterisparibus.Thisisconsistentwithexistingevidenceofanon-lineare?ectoftemperatureonavarietyofeconomicfactors,suchasagriculturalyields,laborsupply,andmortality(SchlenkerandRoberts,2009;Gra?ZivinandNeidell,2014;Carletonetal.,2022).Incolumn(2)weestimateEquation(3)withlinearcountry-leveltime-trends.We?ndalowerpeakgrowthtemperatureandincreasedmagnitudeofthemarginale?ectsathighandlowtemperatures.Incolumn(3)wereproducetheestimatesofBurkeetal.(2015)whichincludesquadraticcountry-leveltimetrends.We?ndthecoe?cientestimatesforclimatevariablesaresimilartothoseincolumn(2).However,asaquadratictrendisunboundedandinconsistentwithourtheoreticalframework,weonlyreportthemhereforcomparisonwiththepreviousliteratureandfocusoncolumn(2)inthetext.Acrosstheseempiricalspeci?cations,we?ndnoevidenceofa

statisticallysigni?cante?ectofprecipitationoneconomicgrowth.8

Next,incolumns(4)–(5)ofTable1weestimateEquation(3)withtheconvergenceterm,i.e.relaxingtheassumptionλ=0.Thisestimatingequation,asdiscussedabove,onlycapturestransitorygrowthe?ectsofclimate.Inthelong-run,convergencepressuresrestorecountry-levelgrowthratestothesteady-statelevel,sochangesinclimateonlya?ectthelevelofoutput.Incolumn(4)wedonotincludecountry-speci?ctimetrends,i.e.weimpose71i=0.Incolumn(5)weestimatelineart