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Working Paper Series

Whatever it takes to save the planet?

Central banks and unconventional

green policy

Alessandro Ferrari, Valerio Nispi Landi

Disclaimer: This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB.

No 2500 / December 2020

Abstract

Westudy theef fectsofatemporaryGreen QE,dened asa policy thattemporarilytilts thecentral bank'sbalance sheetto ward greenbonds,i.e.bondsissuedby rmsin non-pollutingsectors. To this purpose, wemer geastandard DSGEframe workwithan environmental model.Inourmodel,detrimental emissions producedby thebro wnsector increasethestockof pollution.W end thatthe imperfect substitutability betweengreen andbro wnbonds isanecessarycondition forthe effecti veness ofGreen QE. Underthe assumptionof imperfectsubstitutability ,we pointout thefollowingresults. Atemporary in reducingthe stockof pollution,if pollutantsare slow-mo vingv ariabless uchas atmosphericcarbon. The welfaregains ofGreenQEare positiv eb utsmall. Welf aregainsincreaseifthe owofemissions negativelyaffectsalsothe utilityofhouseholds.

Keywords

: CentralBank, MonetaryPolic y, QuantitativeEasing,ClimateChange

JEL Codes

: E52,E58, Q54

ECB Working Paper Series No 2500 / December 20201

Non-technical summary

In thethe lastdecades global temperaturehas beenw orryinglyincreasing. Abroadconsensusin thesci- entic communityrelates theglobal warming tohuman activity, specicallyto theemission ofgreenhouse gases.Recently ,aglobalmo vement against climatechangehasbeenraisinga warenessamongthe public opinion, renovatinganurgenc yto actforpolicymak ers.Some commentatorsha ve beencallingalsocentral banks toplay arole inaddressing thechallenge ofclimate change.It hasbeen argued thatcentral banks should extendtheasset purchaseprogram, theso calledquantitati ve easing,to nancein vestment ingreen sectors. Quantitativeeasinghas beendesignedfollowing theGreat Recession,and ithas beenexpanded after theoutbreak ofthe recentpandemic. Isquantitati ve easingtar getedto sectorsthatdonotpollutean effectiveinstrumenttoaddress theclimate challenge? Tothis purpose,we dev elopan analyticalframeworksuitedto studythe economicand environmental

effectsof theso called“Green QE",i.e. anasset purchasesprogram targeted togreen sectors.In ourmodel,

there aretw osectors:agreen sector, whichdoes notpollute; abrownsector ,whose productionincreases CO

2emissions. Inour framew ork,theowofdetrimental emissionsraises thestockofpollution, whichin

turn reducesthe productivity oftheeconomy, ultimatelydepressing consumption. Our analysissho wsthatGreenQE reducespollution onlyif thereis afriction prev entingbanks tofully exploitarbitrage betweenbonds issuedby thegreen sector (greenbonds) andbond issuedby thebrown sector (brownbonds).This frictionmak egreen andbro wnbondsimperfectsubstitutes. We caninterpret this frictionas are gulationor asanelev atedde greeof publica warenessontheclimatechange issuethat create pressureson thebanking sectorto holda giv enshare ofgreen bonds.W ecalibratethemodelusing parameters standardin themacroeconomic literature.En vironmentalparameters arecalibrated following the benchmarken vironmental-economicmodel.Underthe assumptionof costlyarbitrage forbanks, we carry outthe following experiments. First, westudy thetransmission mechanismof atemporary GreenQE thatdoes notincrease central bank'stotal assets:the centralbank nancesthe purchaseof greenbonds byselling brown bonds.W e showthat thispolic yinstrument isaneffecti ve toolin reducingdetrimental emissions,butitlesspowerful in affectingthestockof pollution. Whenthe centralbank unexpectedlysellsbro wnbonds tob uygreen bonds onnancial markets, nancingcostsofthe brown sectorincrease, nancingcost ofthe greensector decrease: productionin thebro wnsector islower, andemissions fall. Giventhatpollutionfollo wsa slow lawof motion,the reductionin theo wof emissionis notable tosignicantlyaffect thestock ofpollution.

ECB Working Paper Series No 2500 / December 20202

Second, weanalyse thetransmission mechanismof atemporary GreenQE thatdoes increasecentral bank'stotal assets:the centralbank buys greenbonds byissuing liabilities.Wecompare thisscenario with a market-neutralQE.BothQE policiesboost economicacti vity, thusraising theo wof emissions.Inthe Green QEscenario, theincrease intheow ofdetrimental emissionsis signicantlylower. Inboth scenarios, the stockof pollutionis barelyaf fected. Third, weanalys ethewelfare effects ofdeployingGreen QEduringaneconomic expansion. Wend that thecentral bankshould increasesubstantially thecomposition ofgreen assetsin responseto higher emissions. Overallwelfare gainsarepositi vebut small. Fourth,we show thatwelfareg ainsof GreenQEaresubstantially higheriftheo wof detrimental emissions negativelyaffectstheutilityfunction ofhouseholds. Webelie vethatclimatechangeis aserious issuewith effects thatcentral bankscannot ignore.Our anal- ysis pointsout whatGreen QEcan andcannot achiev e.G reenQE isable totemporarilyreducedetrimental emissions. GreenQEis lessef fectiv ein affectingthestockofpollution,whichfollo wsa slowlaw ofmotion. Nevertheless,someca veats shouldbekeptwellin mind.In ourmodel GreenQEisneutral inthe long-run, as othermonetary policy tools.Howev er, thereareotherpotentialchannelsthatweareignoring,through which GreenQE mayha ve permanenteffects.Welea ve thestudyofthese channelstofutureresearch.

ECB Working Paper Series No 2500 / December 20203

1 Introduction

Can centralbanks playan activeroleingreening theeconomy? Theaim ofthis paperis toenrich the debate onthe roleof centralbanks inghting climatechange throughthe lensof aformal model. To this purpose, wemer getheworkhorse DSGEframe workwithan environmental model:inthissetup,westudy the macroeconomicand welfare consequencesoftheso called"Green Quantitativ eEasing" (GreenQE), dened asa centralbank' spurchase ofbondsissuedby rmsin non-pollutingsectors. In thelast few yearsthescienticcomm unityhas beenincreasing itsw arningsonthef actthat “planet

Earth isf acingclimateemergenc y"(

Ripple etal.

,2017;Ripple etal. ,2020). Thew arningsofscientists

havebeenattracting interestamong thepublic opinion,and sev eraldemonstrations hav etak enplace allover

the world,oftenled byinuential environmental activists .Scientist sarguethat theclimatecrisisisclosely

linkedto excessi veconsumptionoftheadvancedeconomies, whichfeature thegreatest per-capita emissions of greenhouseg as.Thisfact establishesa challengingtrade-offfor policy makers, whoha vethehard task to mitigatetheadv erseconsequences ofclimatechangewithout jeopardizingeconomic growth. Climate changeis thestandard example ofa negativ ee xternality, whichshouldbeaddressedbyan appropriate Pigoviantax.

1However,climatechangeisnot achallenge thatcan bes olved inthe short-

term. Asar guedbyCarney(2015), climatechange isa “tragedyof thehorizon", becauseits impactlies well beyondthehorizon ofmost actors.While thepolitical costsof enactingen vironmentalre gulationand raising eco-friendlytax esmustbef acedin theshort term,theassociatedwelf areand politicalg ainsare likelyto emerge onlyinthemedium-long term,suggesting thatpolitical economicsar gumentsmay play an importantrole. Asan anecdotale xample,the FrenchGo vernmentwas forcedto postponethe increase

in theeco-tax onfuel, afterse veral protestsby thesocalled“Yellow Vests". Ifgo vernments arenot ina

good positionto raisetax es,independent institutionssuchascentral banksmay bebetter placedto face the

climate changechallenge. The goalof thispaper isto studythe issuethrough aDSGE model.In thelast decade,DSGE models havebeencommonly usedto analyzethe effects ofQE, denedas anasset purchaseprogramofthe central bank targetedtopublic orpri vate bonds(

Curdia andW oodford

,2011;Gertler andKaradi ,2011;Chen et al. ,2012;Gertler andKaradi ,2013;Burlon etal. ,2018). DSGEmodels hav ebeenalsousedtostudy the effectsofen vironmental policies:Heutel(2012),Annicchiarico andDi Dio(2015), andBarrage(2020) are applicationsof thebenchmark environmental setupof Nordhaus(2008), whichincludes aneconomic 1 Forinstance, thisis theviewby Rogoff(2019).ECB Working Paper Series No 2500 / December 20204 and ageoph ysicalsector.In thesemodels, productionincreases CO

2emissions, whichin turnaf fecttotal

factorproducti vityoftheeconomy .Our modelis theresultofmer gingthe DSGEframe work ofGertler and Karadi(2011), designedto studyQE, withthe environmental modelof Heutel(2012), designedto study environmentalpolicies ov erthebusinesscycle. Unlikethe previous economic-environmentalliterature, wedistinguishbetweentw oproductionsectors: the brownsector, whoseproductiongeneratesdamaging emissions;a greensector ,whose productionis not polluting. Thisassumption allows ustodistinguishbetween bondsissued bygreen rms(green bonds)and bonds issuedby brown rms(brownbonds). Bondscan beboughtbypri vate banksand bythe centralbank. A leverageconstraintprev entsbanks tofullyexploitthearbitrage opportunitybetween bondsand deposits from households:in equilibrium,there isa spreadbetween thebond andthe depositinterest rate. Wedene GreenQE asa policy thattilts thecentral bank'sbalancesheet tow ardthe greensector .W e distinguish betweentw otypesofGreen QE:a Green QEthat doesnot changethe sizeofcentralbank' s balance sheet;a GreenQE thatincreases thesize ofcentral bank's balancesheet. Itis wellkno wnthat QE can workonlyif Wallace Neutralityis broken.AsWallace(1981) pointsout, theequilibrium pathof output and pricesis independentfrom centralbank' sbalance sheetpolicies, unlessthereissomething specialin centralbank'sintermediation.Inourmodel, QEdoesaffectproduction,because thecentralbank,asopposed

to privatebanks,doesnot face le ve rageconstraints.Ifthe centralbanktemporarilyexpandsitsbalancesheet

by increasingholding ofgreen andbro wnbonds, banksreduce theirleverage, creditspread goesdo wn, and outputgro ws.Thisisthe mechanismat theheart ofGertler andKaradi (2011). Ifgreen andbro wn bonds areperfect substitutesfor banks,when thecentral banktemporarily tiltsthe portfoliocomposition to greenbonds andk eepsconstant totalassets,productionin bothsectors isnot affected. Without further assumptions, eveninamodel whereQE works, thisbalance-sheet neutralGreen QEis notabletoaf fect neither totalproduction nordamaging emissions.The intuition relieson ano-arbitrage condition.Ifbonds issued bythe greenand thebro wnsectors areperfect substitutesforbanks,t heirreturns mustbe identical as well.In thiscase, theportfolio rebalancingof thecentral bankdetermined byGreen QEis fullyof fset by arebalancing ofpri vate banksintheoppositedirection. Underthis scenario,Green QEonly impliesa transaction betweenpri vatebanksandthecentral bank,with nomacroeconomic oren vironmentalef fect. As aresult oft hesame intuition,aGreenQE thatincreases thesize ofcentral bank's balance sheethas the same effectsofa market-neutral QE. In orderto explore theroleofGreen QE,we make greenand brown bondsimperfect substitutes.W e do soby introducinga quadraticcost whenev era bankchanges thecompositionofitsportfoliowith respect

ECB Working Paper Series No 2500 / December 20205

to thesteady-state lev el.

2Underthis hypothesis,banksare notable tofully exploit arbitrageopportunity

between greenand brown bonds.Wesho wthat theshareof bank'sgreenbonds outof bank's totalassetsis a positivefunctionofthe spreadbetween greenand brown bonds:the higherthe interestrate paidby green bonds relativelytobrown bonds,the morebanksinv estin thegreen sector. Havinga modelsuited tostudy GreenQE, weperform foure xperiments. First, wesimulateatemporaryGreenQEshock.Whenthecentralbanktemporarilyincreasesits shareof

green bonds,k eepingconstanttotalassets, theinterest ratepaid bygreen (brown) rmsdecrease (increase).

Banks arenot ableto fullye xploitthe arbitrageopportunity ,becausechangingthe assetcomposition is costly: aspread betweenbro wnand greeninterestratesopens up.Green rmsf acea lower interestrate, increase capitaland raiseproducti on.Bro wnrmsface higherinterestrateand cutproduction: detrimental emissions arelo weranddecreasethe stockof atmospheric carbon.The productione xternalityis reduced

and totalf actorproductivityincreases. Fromaquantitativ eperspecti ve, GreenQE iseffectivein reducing

detrimental emissions.Ho wever,theeffectsonthetotal stockof pollutionandthuson TFPare negligible. Our calibration,that weborro wfrom Nordhaus(2008) andHeutel(2012), impliesthat atmosphericcarbon followsa highlypersistent process:gi ven thatthe GreenQEshockistemporary, emissions arelo weronly

in theshort run,bringing abouta tiny reductionin thestock ofpollution.Moreo ver ,the marginal TFPg ain

of reducingpolluti onisalmost0 closeto thesteady state:this resultshinges onthe smallTFP losscaused by pollutionin themodel byNordhaus(2008), ifsteady-state pollutionis setto currentv alues. In oursecond experiment wesimulatean increasein centralbank'stotal assets (aQE shock)compar - ing twodifferent scenarios.Intherst scenario,we assumethat centralbank' spurcha sesrespect market neutrality.In thesecond scenario, weassume thatQEisentirely targeted togreen bonds.W esho wthat the differencebetweenthe two scenariosis quantitatively mildboth formacroeconomic variablesandpol-

lution. Inaddition, ev enifQEisentirelytar getedto greenbonds, itse xpansionaryef fectalsoboostsbro wn

production inthe rstperiods, driving aslightly higherriseinpollution. Third, wedesign aT aylorrule forGreenQE,assuming thatthe fractionof central bank's greenassets endogenously respondto brown production.Wesimulate apositi veTFPshock, comparingthe responseof the economywith andwithout theGreen QErule. We ndag ainthat GreenQE isabletomitig ateemissions, butthe quantitativ eimpactonpollutionisne gligible. Fourth,we mov etothenormative sideand wesho wthreeadditionalresults.First,we computethe 2

This frictionis usede xtensivelyin DSGEmodels, inorder tomak edif ferentassets imperfectsubstitutes (seeforinstance

Benigno

,2009andCurdia andW oodford,2011.)ECB Working Paper Series No 2500 / December 20206 constant taxon brown productionthat makesthesteady stateof themodel equalto thesteady-state ofa social-planner economy.Thetax is0:4%, reectingthelo wsteady state-statepollutioncostin thebaseline calibration: byincreasing thecost ofpollution, weget amuch highertax. We cannotdo thise xercise with Green QE,because asother monetarypolic yinstruments, inour modelGreenQEhas noef fectin thesteady

state. Second,we computenumerically theconstant taxthat optimizeswelf arein aneconomy hitby positiv e

and negativeTFPshocks.Theoptimalconst anttax isin linewith thepre viousexercise. Third,we compute numerically theparameter ofthe GreenQE rulethat maximizes welfare aftera positiv eTFPshock.This parameter governstheelasticity ofGreen QEtobrown production.W end thatthe centralbank should aggressivelyrespondto brown production,though netwelfareg ainsare extremely small. The bottomline ofour studyis thata temporaryGreen QEis ableto affect detrimentalemissions inthe brownsector ,butit hassmalleffects onthe stockof pollution.The mainreasonisthat climatechange and pollution arestructural problems,while atemporary GreenQE isan instrumentthat playsa rolealong the business-cycle,asother monetarypolic ytools: atemporary GreenQEstrugglesto affect aslo w-moving stock pollutantssuch asatmospheric carbon,the maingreenhouse gas. Indeed,we alsosho wthat GreenQE

yields higherwel faregainsifwe increasethedecayrate ofpollution. Nev ertheless,there aresome important

caveatsthatshould bek eptwell inmind. Wehav emodeled atemporary asopposed toapermanent Green QE: thelattercould setthe stagefor aperm anentlo wersize ofthe brown sector.Ev enifinmost DSGE models monetaryneutrality holdsin thelong run,we believ ethat thecentral bankmay stillbeableto permanently affectthebeha viorof economicagents,throughincenti ves andmoral suasionto inv estmore in thegreen sector. Monetarypolicycould alsoinduce greenrmstoin vest morein R&D:as far asR&D investmentincreaseslong-run TFP, monetarypolic ymayhav ea permanentpositive effect onthegreen sector.Moreo ver,atemporaryGreenQEmay stillbe usefulalong atransition froma steadystate withhigh emissions toa steadystate withlo wemissions. We leavethese considerationsto featureresearch. Weaim atb uildinga bridgebetweentwo different streamsof theliterature. First,ourpaperts inthe literature studyingthe effect ivenessofQEinDSGEmodels.Thisliterature hasourished in theaftermath of the GreatRecession,when centralbanks aroundthe world hitthe zero-lower boundand startedtoimplement large-scaleasset purchases.Curdia andW oodford(2011) computecentral bank's optimalbalancesheet policyi naNew Ke ynesianmodelwithtw otypesofhouseholds(borrowers andsa vers). Gertler andKaradi 2011
) andGertler andKaradi (2013) analyzethe macroeconomicef fectsand thedesirabilityofthe FED balance sheet'spolicy inaDSGEmodel augmentedwith abanking sector. Inthese threepapers, central

bank'slending tothe priv atesector isaneffective policy toreduce thecredit spread.Chen etal. (2012)ECB Working Paper Series No 2500 / December 20207

estimate amedium-scale DSGEmodel withnancial marketsegmentation, ndingthatthesecond FED LargeScale AssetPurchase Programhad very limitedef fectson outputandination.Burlon etal. (2018) study theinteraction betweenthe EurosystemAsset PurchaseProgramme andmacroprudentia lpolic y, ina large-scalemodel forthe euroarea. Second, ourpaper tsin theliterature studyingclimate-related issuesin DSGEmodel s.Fischer and Springborn(2011),Heutel(2012), andAngelopouloset al.(2013) studyen vironmentalpoliciesinan RBC model, whileAnnicchiarico andDi Dio(2015) analyzethese policy toolsinamodel withnominal rigidi- ties.Chan(2020) explorestheinteraction betweenstandard macroeconomicpolicies (scaland monetary) with carbontaxation. Barrage(2020) studiesthe interaction ofcarbontaxes withother standarddistor -

tionary taxes.Inthese papers,the climate/pollutione xternalityis anincreasing functionof totaloutput:

the externalityeithera ffects totalfactorproductivity(as inNordhaus,2008), orenters directlythe utilityof

households. Usinga stock-ow- fundmodel,(

Dafermos etal.

,2018) assessthe nancialand globalw arm- ing implicationsof GreenQE. Unlike (

Dafermos etal.

,2018), weuse amicrofunded DSGEmodel tostudy Green QE:with respectto bothstreams ofthe literature,to thebest ofour knowledge weare therst to analyze thispolic ytoolina DSGEmodel. The restofthe paperis org anizedas follows. Section2presentsthemodel.In Section3 weanalyzethe transmission channelof GreenQE. InSection 4we carryout awelf areanalysis. InSection 5we perform some robustnesschecks.Section 5concludes.

2 Model

Wemer gethenancialaccelerator framew orkof Gertler andKaradi (2011) withthe environmental modelof Heutel(2012), whichin turnis asimplied version ofNordhaus(2008).3UnlikeGertler andKaradi (2011) andHeutel(2012), ourmodel featurestw oproduction sectors:abrown sector ,which generatesa pollution externalityaf fectingtotalfactor productivity; agreensector, whichdoesnotgenerate any externality . 4Two differentse ctorsarecrucialto distinguishbetween greenbonds andbro wnbonds. Greenand brown rms sell theirgoods toa continuumof intermediaterms. Theserms operatein monopolisticcompe titionand are subjectto price-adjustmentcosts. Anal good-rmcombines thedif ferentiatedintermediate goodsto produce anal good.The nal isgood isboughtbyhouseholds forconsumption andby capitalproducers, 3

The majordif ferencebetweenthetwoen vironmentalmodelsisthe following. InHeutel(2012) allthe variables, including

pollution, revertinthelong-run inthe steadystate: thismodel isappropriate forc ycleanalysis. Nordhaus(2008) isa growth model

with asteady growth pathforpollution:this modelis bettersuited foranalysis ofstructural policiesand their long-termimpact.

4InHeutel(2012) allrms generatethe pollutione xternality. Inour model,onlybrownrmspollute. ECB Working Paper Series No 2500 / December 20208

which transformi tinphysical capital.Households canbe eitherw orkers ingreen andbrownrms,or bankers.Bank ers,collectdepositfrom householdsand grantloans togreen andbro wnrms. Inwhat follows,we layout theoptimization problemsof allthe agentsof themodel. We leav ethe fulllist of equations tothe Appendix.

2.1 Households

There isa continuumof householdsof measureunity .In any period,a fraction1fof householdsare workers,afraction fare bankers.Every bankerstaysbank erinthene xtperiod withprobability: ine very period(1)fbankersbecome work er.Itisassumedthat(1)fworkersrandomlybecome bankers and theproportion remainsunchanged. Eachbank ermanages abank andtransfersprotsto households.

Differenthouseholds completelyshare idiosyncraticrisk: thisassumption allows touse therepresentati ve

household framework. The representativehouseholdsolves thefollo wingoptimizationproblem: max f c t;ht;dtg1 t =0E 01 X t =0 t c1t1h1+' t1 +'! s:t: c t+dHt=rt1 tdHt1+wthttt+ t; wherectdenotes consumptionof the nalgood; htdenotes hoursw orked;dHtis thesum ofbank deposits d tand publicbonds dPt: bothassets aree xpressedin realtermsandyield anominal interestrate rt;wtis hourly realw age;tis CPIgross inationrate; ttdenote lump-sumtax es;tare protsfrom ownership of rms andnet transfersfrom bankers. First-orderconditions read: h tct=wt(1) c t=Et c t+1r t t +1 :(2)

2.2 Final-goodrms

The representativenal-good rmuses thefollo wingCES aggregatorto producethe nalgoodyt: y t= 1 0 y t(i)"1" di ""1 ;(3)ECB Working Paper Series No 2500 / December 20209 whereyt(i)is aninterme diategoodproducedby intermediaterm i, whoseprice ispt(i). Theproblem of the nal-goodrm isthe following: max y t;fyt(i)gi2[0;1]p tyt 1 0 p t(i)yt(i)di s:t y t= 1 0 y t(i)"1" di ""1 whereptis theCPI. Thisproblem yieldsthe followingdemandfunction 8i: y t(i) =ytpt(i)p t :(4)

2.3 Intermediate-goodrms

There isa continuumof rmsinde xedbyiproducing adif ferentiatedinputusingthe following linear function: y t(i) =yIt(i);(5) whereyItis aCES aggreg atorofgreenproductionyGtand brownproductionyBt: y

It(i) =

(1)1 yGt(i) 1 +1 yBt(i) 1 1:(6) In orderto choosethe optimalinput combination,intermediaterm isolvesthe following intratemporal problem: max yBt;yGt (1)1 yGt(i) 1 +1 yBt(i) 1 1 p

GtyGt(i) +pBtyBt(i) =Yt(i);

whereYt(i)isa givenlevel ofproduction;pGtandpBtare theprice ofgreen andbro wnproduction respec- tively,bothexpressed relativ elytotheCPI. Theproblemyieldsthefollowing demandfunctions: y

Gt(i) =(1 )pGtp

It y

It(i)(7)

y

Bt(i) =pBtp

It y It(i);(8)ECB Working Paper Series No 2500 / December 202010 wherepIt=h (1)pGt 1 +pBt 1 i11 is thereal marginal costof therm. Firms operatein monopolisticcompetition, sothe yset pricessubject tothedemandof thenal good rm ( 4 ). Firmipays quadraticadjustment costsACt(i)in nominalterms, whenev eritadjuststhegrowth of itsprice pt(i)with respectto thebenchmark lev el: AC t(i) =P2 pt(i)p t 1(i) 2 p tyt:

Firmi'sintertemporal maximizationproblem reads:

max fp t(i)g1 t =0E 0( 1X t =0 tt 0" pt(i)p t "pt(i)p tpIt y tP2 pt(i)p t 1(i) 2 y t#) wheretis themar ginalutilityofhouseholds. Ina symmetricequilibrium, thisproblem yieldsthe standard

Phillips Curve:

t(t) =Ett+1 tt+1(t+1)yt+1y t P p It"1" :(9)

2.4 Greenandbr own rms

Green andbro wnrmsproducean outputgood thatis usedas aninput byintermediate rms.Green rms use thefollo wingfunctiontoproduce yGt: y

Gt=AtkGt1

hG(1) t;(10) wherekGtandhGtare capitaland laborused inthe greensector; Atis totalf actorproductivity, whichis endogenous. Weexplain indetailwhatdri ves totalf actorproducti vityinSection2.7. Greenrms issue bondsbGtto nancecapital expenditure: b

Gt=qtkGt;(11)

whereqtis theprice ofthe capitalgood. Thebond ise xpressedin realterms andpay areal interestraterGt. Green rmsb uycapitalfromcapital producers,which inturn buy backnon-depreciated capitalfrom green rms. Inperiod t, protsGtof greenrms aregi ven by: Gt=pGtyGtwthGtrGktkGt1;(12)ECB Working Paper Series No 2500 / December 202011 where r

GktrGtqt1(1)qt(13)

is therental rate ofcapital forgreen rms.First orderconditions forgreen rmsread: w thGt= (1)pGtyGt(14) r

GktkGt1=pGtyGt:(15)

The brownsectoris modeledanalogously andit comprisesthe following equations: y

Bt=AtkBt1

hB(1) t(16) w thBt= (1)pBtyBt(17) r

BktkBt1=pBtyBt(18)

b B t=qtkBt(19) r

Bkt=rBtqt1(1)qt:(20)

2.5 Capitalpr oducers

Capital producersb uyoutputproducedby nal-goodrms andnon-depreciated capitalfrom intermediate rms, inorder toproduce physical capital.Capital isthenpurchasedby greenand brown rms.Capital producers solvethefollo wingproblem:quotesdbs_dbs46.pdfusesText_46

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