This  work  is  distributed  as  a  Discussion  Paper  by  the    

STANFORD  INSTITUTE  FOR  ECONOMIC  POLICY  RESEARCH    

     

SIEPR  Discussion  Paper  No.  15-­‐003    

 Designing  an  Optimal  'Tech  Fix'  Path  to  Global  Climate  Stability:  

       Integrated  Dynamic  Requirements  Analysis  for  the  'Tech  Fix'  

By  

                     Adriaan  van  Zon  and  Paul  A.  David  

   

Stanford  Institute  for  Economic  Policy  Research  Stanford  University    Stanford,  CA  94305            (650)  725-­‐1874  

   The  Stanford  Institute  for  Economic  Policy  Research  at  Stanford  University  supports  research  bearing  on  economic  and  public  policy  issues.  The  SIEPR  Discussion  Paper  Series  reports  on  research  and  policy  analysis  conducted  by  researchers  affiliated  with  the  Institute.  Working  papers  in  this  series  reflect  the  views  of  the  authors  and  not  necessarily  those  of  the  Stanford  Institute  for  Economic  Policy  Research  or  Stanford  University  

DesigninganOptimal'TechFix'PathtoGlobalClimateStability:IntegratedDynamicRequirementsAnalysisforthe‘TechFix’

By

*PaulA.David1,2andAdriaanvanZon2,3

1StanfordUniversity&AllSoulsCollege2UnitedNationalUniversity‐MERIT,Maastricht(NL)

3SBEUniversityofMaastricht(NL)

1stversion:28November20112ndversion:27November2012

3rdversion:15June2014Thisversion:10February2015

ABSTRACT

Thispaperanalyzestherequirementsforasocialwelfare‐optimizedtransitionpathtowardacarbon‐freeeconomy, focusing particularly on the deployment of low‐carbon technologies, and the roles ofengineeringupgradingofextantfacilities,anddirectedR&Dtoenhancingtheirproductivity. Thegoalineachcaseistoachievetimelysupply‐sidetransformationsintheglobalproductionregimethatwillavertcatastrophicclimateinstability,anddosoinamannerthatminimizesthesocialwelfarecostsofstabilizingthe levelof theatmospheric concentrationof greenhousegases (GHG).This “planning‐model” approachdeparts from conventional IAM exercises by dispensing with the need to make (generally dubious)assumptions about the macro‐level consequences of behaviors of economic and political actors inresponse to market incentives and specific public policy instruments, such as a carbon tax. It shiftsattention instead to the need for empirical research on critical technical parameters, and problems ofinter‐temporal coordination of investment and capacity utilization that will be required to achieve atimely,welfare‐optimizingtransition.Asuiteofheuristicintegratedmodelsisdescribed,inwhichglobalmacroeconomicgrowth isconstrainedbygeophysical systemwithclimate feedbacks, includingextremeweatherdamagesfromglobalwarmingdrivenbygreenhousegasemissions,andthethresholdlevelGHGconcentrationbeyondwhich theclimatesystemwillbe“tipped into”catastrophic runawaywarming. Avarietyoftechnologicaloptionsareidentified,eachcomprisinganarrayofspecifictechniquesthatshareadistinctiveinstrumentalroleincontrollingtheconcentrationlevelofatmosphericCO2. Thedevelopmentoflow‐carbontechnologiesthroughinvestmentinR&D,andtheirdeploymentembodiedinnewphysicalcapital formation, is explicitly modeled; as is the implementation of known engineering techniques to“upgrade”existingfossil‐fueledproductionfacilities.Thesocial‐welfareefficientexerciseoftheavailabletechnological options is shown to involve sequencing different investment and production activities inseparatetemporal“phases”that together formatransitionpathtoasustainable low‐carboneconomy—one inwhich gross CO2‐emissions do not exceed the Earth’s “natural” abatement capacity. Parametricvariationsofthe“tippingpoint”constraint inthesemodelswillpermitexplorationofthecorrespondingmodification in therequiredsequencinganddurationsof investmentandproduction in thephases thatformtheoptimaltransitionpath.Thepreliminarysolutions(usingmufti‐phaseoptimalcontrolmethods)expose important dynamic complementarities among technological options that are often presented assubstitutesbycurrentclimatepolicydiscussions.

JELcodes:Q540,Q550,O310,O320,O330

Keywords:globalwarming,tippingpoints,catastrophicclimateinstability,technologyfixoptions,R&Dinvestments,capital‐embodiedinnovations,optimalsequencing,IAMandDIRAMpolicydesignapproaches,multi‐phaseoptimalcontrol,sustainableendogenousgrowth

*Contactauthor:pad@stanford.edu  

   

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DesigninganOptimal'TechFix'PathtoGlobalClimateStability:IntegratedDynamicRequirementsAnalysisforthe‘TechFix’

1.OverviewandOrganizationofthePaper

OurmainpurposeinthesepagesistostimulatefreshthinkingaboutnothinglessthanthedesignofacoherentglobalprogramthatwouldmobilizethetechnicalandeconomicresourcesthatwillbeneededtoimplementeffectiveandtimelyactionsstabilizetheEarth’sclimate.Morespecifically,theconcernofthepaperfocusesonanalysingtherequirementsforasocialwelfare‐optimizedtransitionpathtowardalow‐carbonproductionregimethatwouldbebothviableandsufficienttoavertcatastrophicclimateinstability,andtherebypreservethefuturepossibilitiesofsustainabledevelopmentandcontinuingeconomicgrowth.

Tofixideasandbegintomakeanalyticalheadway,wedescribeasuiteofheuristic“integrated”modeloflong‐runmacroeconomicgrowth,i.e.,modelsinwhichendogenousgrowthisconstrainedbyfeedbacksfromthegeophysicalsysteminwhichtheglobaleconomicsub‐systemisembedded.Twoamongthefeedbackeffectsthatdirectlyconstraintheeconomicgrowtharemodeledexplicitly:firstly,thereisthepotentialforcontinuingemissionsofgreenhousegases(GHG)toraisetheleveloftheiratmosphericconcentration(measuredinCO2‐equivalentppmv),increasingradiativeforcingandcorrespondinglyelevatedmeantemperatureoftheEarth’ssurface,elevatedmoisturecontentoftheatmosphereand,consequentlymorefrequentratesofextremeweatherdamagestoinfrastructuresandlossesinproductivecapacity.Thesecond,andstillmoreseriousconstraintarisesfromrecognitionoftheexistenceofoneormoreclimate“tippingpoints”orthresholdsthatoncecrossedwouldinitiateaself‐reinforcing,“runawaywarming”processthatwouldbringinitstraincatastrophicdamagestohumanwelfareandwell‐being.

ApolicycommitmentthatembracesthePrecautionaryPrincipleandthereforeseekstoavertaglobalclimatedisasterwillbeseentobetantamounttoimposingahard“carbon‐budget”constraintontheoptimaltransitionpathtoastabilizedclimate.ThisfollowsfromdefiningacatastrophetippingpointintermsofacriticalthresholdlevelofCO2–eppmvintheatmosphere,which(giventhelattermeasure’sinitiallevel)servestofixthecumulativenetadditionsvolumeofGHGemissions,andhenceintheCO2‐equivalentatmosphericconcentrationofthosegases)thatdoesnotcrossthestipulatedthresholdleadingtocatastrophe.Thus,anyconjecturedcatastrophetippingpointsetsa“carbon‐budget,”andacorrespondingclimate‐stabilizingtransitionpaththatcanbeoptimized–ifitisfeasible,giventheotherconstraintsonthedynamicalreallocationofglobalresources.

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Asecondobtrusiverespectinwhichtheapproachtobedescribedheredeviatesfromthestyleofintegratedclimatepolicyassessmentmodeling(IAM)thathasbecomefamiliarinthefieldofenvironmentalandenergyeconomicsappliedtoclimatepolicyissues,1istobeseeninitsexplicitattentiontothetechnologicaltransformationsthatwillneedtobeeffectedinorderforaprogramofclimatestabilizationtosucceed.Ratherthanpositinganunchangingaggregateproductionfunctionfortheglobaleconomy,weproposetoconsideraportfoliooftechnologicaloptionscomprisingseveraldistinguishableclassesoflineartechniques,eachcharacterizedbyacommoninstrumentalroleincontrollingtheconcentrationlevelofatmosphericCO2.Thedevelopmentofalternative,low‐carbontechnologiesthroughinvestmentindirectedR&D,andtheirdeploymentembodiedinnewphysicalcapitalformation,areexplicitlymodeled,asareinvestmentsinimplementingknownengineeringtechniquesto“upgrade”existingfossil‐fueledproductionfacilities—loweringtheiraverageflowrateofCO2perunitofoutputandtherebyrenderingexistingcapitalstock“greener.”

Explicitmodelingofdistinctelementsinthearrayofavailableandlatenttechnologicaloptions,andtheassumptionthatthetechniquesinquestionmustbeembodiedinphysicalcapital(whetherinfrastructuralordirectlyproductiveassets)representanimportantrespectinwhichthepresentapproachdepartsfromtheleadingintegrated(policy)assessmentmodels’treatmentoftechnologicalchangesintheglobalproductionregime,whetherthroughthefurtherdiffusionofavailabletechniques(andthescrappingphysicalcapitalembodyingearliervintages),orthedevelopmentanddeploymentofrecenttechnologicalinnovations.2

Thesocial‐welfareefficientdeploymentoftheavailabletechnologicaloptionsisshowntoinvolvesequencingdifferentinvestmentandproductionactivitiesindistincttemporal“phases”eachofwhichsatisfythefirst‐orderconditionsforanoptimalcontrolsolution,andtakentogetherformatransitionpathtoasustainablelow‐carboneconomy—oneinwhichgrossCO2‐emissionsdonotexceedtheEarth’s“natural”abatementcapacity.Followingtheminimax‐regretcriterionfordecisionsaboutpolicyactions,welfareoptimizationofthetechfixprogrammustsatisfytheconditionthatthe

designachievesstabilizationoftheatmosphericconcentrationofCO2‐eqivppmvatalevel

1SeefurtherdiscussioninSect.4(below),especiallytheIAMmodelsfollowingandextendingtheparadigmaticDICEmodelofNordhaus(1993,2002,2007)andothercontributionstothisliteraturereviewedinKellyandKolstad(1999),andmorerecentlyinAckermanetal.(2009).

2The“technologicalportfolio”approachpresentedhere(basedonfunctionaldistinctionsamong“techniques”)isconsistentinspiritwithpreviousefforts(e.g.,Bosettietal.,2006,andothercontributionstothesamespecialissueofEnergyJournal)tocombinedetailed“bottomup”representationsofengineeringrealitiesintheenergysectorwith“topdown”modellingoftheglobalmacroeconomicandclimatesystems.Inordertoexplicitlyexaminetheimplicationsofswitchingbetweentechnologiesthatmustbeembodiedinphysicalcapital,wehavesacrificedengineeringdetailsforgreatercomputationaltractabilityoftheresultingmulti‐stageoptimalcontrolproblem.

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justbelowthespecified“catastrophetippingpoint.”GiventhecurrentatmosphericconcentrationofGHG,thisservestoimposeaconditionalnet“carbonemissionsbudget”constraintupontheoptimaltransitionpathcorrespondingtothespecified“catastrophetippingpoint”.Bysolvingthemodelforanarrayofalternativeconjecturedtipping‐point,itisthenpossibletoexplorethedynamicsofthealteredtechnologicalandinvestmentrequirementsthatwill(just)expendthebudgetbytakingtheindicatedtransitionpathstothecorrespondingstableclimate..

InterpretingapplicationofthePrecautionaryPrincipleas“minimaxregret”strategy,wouldprovideaformaljustificationforinvestigatingtherequirementsofwelfare‐optimaltransitionpathsthatwouldsufficetohaltnetadditionstotheatmosphericconcentrationofGHGsjustbeforethesystemcrossingaconjecturedcatastrophictipping‐point.3,isthatdoingsowouldeschewrelyinguponexpectedutilitymaximizingsolutions.Toobtainthelatterwouldcallforquantitativeassessmentsofthebalancebetweenfuturesocietalwelfarebenefitsandcosts.But,inthepresentincompletestateofscientificandeconomicunderstandingofthedynamicprocessesthatwouldbeinvolved,thoseassessmentsentailacceptinghighlydubiousquantitativeguessesregardingthetimedistributionandmagnitudesofmaterialdamagestopopulationsandproductivecapacitythatwouldentailcatastrophiclossesinutilityterms.Furthermore,ifthepossibilityofabruptandcatastrophicclimatechangesistobeexplicitlyacknowledged,italsowouldbenecessarytoacceptuncertainandhighlysubjectiveestimatesoftheprobabilitydistributionoftheGHGconcentrationlevelscorrespondingtothethresholdvaluesofvarious“tippingelements”intheEarth’sclimatesystem.

Thereis,however,andavailableattractivealternativetotheclassic“minimaxregret”strategyforrationalchoicedecisionsunderuncertainty,whichtypicallyisinvokedasaformalizationofthePrecautionaryPrinciplewhoseapplicationcouldaccountforhumanactorsobserveddeparturesfromthepredictionsimpliedbySavage’s(1951)postulated“sure‐thingprinciple.4AsformulatedbyLoomesandSugden(1982),

3Theminimax‐regretcriterionintroducedbySavage(1951)callsforchoosingtheaction(s)fromtheavailablesetthatwillminimizethemagnitudeof‘regret’associatedwiththeworstcasesocialwelfareoutcomes.Whentheoutcomevariablesareutilities(asisusualinwelfareanalysis),theminimax‐regretcriterionisbasedondifferencesinexpectedoutcomes,andthepresenceofuncertaintyrequiresassigning(subjective)probabilitiestoalternativeplausiblestatesoftheworld.TheworstcaseoutcomeofnottakingagivenprogramthatwouldstabilizetheclimatebeforereachinglevelkofMGTisthecastastrophiconsetofirreversible,self‐reinforcingglobalwarming–whichwouldexhypothesisensuefromexceedinglevelk.UnderanalternativestatethereisnosuchtippingpointbeforeoratMGTlevelk,andtheoutcomeoftakingtheactionisthewelfarelossoftheunnecessarystabilizationefforttostopthere.Ifthewelfareindexesarelinear,andthestatesoftheworldareindependentoftheactioninquestion,thenthisapproachisconsistentwithexpectedutilitytheory,wheresubjectiveprobabilitiesmaybeassignedtothestatesoftheworld,andthedecisioncriterionisthedifferencebetweentheexpectedpayofffornottakingandtakingthestabilizationaction.ThisapproachhasbeenimplementedbyCai,JuddandLontzek(2012b),LemoineandTrager(2012).But,aswillbeseen,onecanjustifyassertingthePrecautionaryPrinciplewithouthavingtoassignsubjectiveprobabilitiestothetippingpoint’sconjecturedlocations..

4SeeLoomesandSugden(1982),SlovicandTversky(1974),KahenmanandTversky(1979).

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thisapproachholdsthatarationalactorchosesbetweenactions(includingaparticularactionandinaction)soasthemaximizethemathematicalexpectationofmodifiedutility.Supposingthatexpectedmodifiedutilityistheobjectivefunctionmaximizedbyrationalactorsisjustifiedonthegroundsofsimplicityandconsistencywiththeempiricalevidenceofmostofthewelldocumentedbehavioraldeparturesfromtheconventionalframeworkofmaximizingexpectedutilityamongavailablechoices.5

Undertheassumptionthatthecurrentgenerationplacesavalueonfuturegenerations’welfare(conceivingofthelatterasasubjectivestateoffelicity),decisionstobetakeninthefaceofanuncertainexistentialthreat‐‐suchasthatofenteringintoanirreversiblecatastrophicstatethatwillentailextremedeprivationsforfuturegenerations‐‐mayweightcurrentsacrificesofutilityagainsttheprospectofmaintainingmorehopefulconditionsforfuturegenerations.Costlyactionsofthiskindwould,ineffect,sacrificethesubjectivefelicityofcurrentmaterialconsumptioninordertoavoidthesubjectiveinfelicityofcontemplatingthesituationthattheyhavemadeinadequatesacrificestoavertthe“hopeless”situationinwhichfuturegenerationswouldbeleftbymaterializationofthecatastrophicalternative.6

ThiswouldseemtocommenditselfastherationalapplicationofthePrecautionaryPrincipleinregardtodecisionsonactionsaimedatstabilizingtheEarth’sclimate.That,ofcourse,ispremisedonacceptingthepropositionsthat(i)thereexistoneormore“tippingpoints”intheatmosphereconcentrationlevelofGHG),and(ii)atleastoneofthesethresholdswouldbecrossedwithinthelifetimesofpresentmembersoftheworld’spopulation,unlessmajorcutsinthevolumeofGHGemissionsarenotbegunimmediately.Uncertaintiesabouttheextentofthematerialsacrificesofcurrenteconomicwelfarethataneffectiveprogramofthatkindwillentail–duetouncertaintiesandambiguitiesinthelocationofthetipping‐point(s),inthestatedependentdynamics

5Thisapproachproceedsfromtheviewthatpsychologicalexperiencesofregret(andrejoicing)cannotbeproperlyconceptualizedas“rational”or“irrational”–becausethey,likesorrowandjoyaresubjectivestates;theclassof‘objects’thatmaybetakentoproduceutilityisthusexplicitlyheldtoincludesubjectivestates(feelingsaboutamaterialstateoftheworld)aswellastheutilitydirectlyderivedfromthatworldstate.RatherthanfollowingKahenmanandTversky(1979,1981)bysuper‐imposingatheoryofsystematicbehavioralviolationsupontheexpectedutilitytheoryderivingfromvonNeumannandMorgenstern(1947),LoomesandSugden(1982)formulatea“modifiedutilityfunction”forthedecisionagent,inwhichincrementsordecrementsinutility(felicity)correspondingtotheexperiencedsensations(joyvs.regret)thatareassociatedwithcontemplationofthefactualandcounter‐factualoutcomesofconditionsthatactuallyhaveormighthavebeenachieved.Inotherwords,thisformulationassumesthatthedegreeofregret(orjoy)experienceddependsuponcomparisonoftheutilityof“whatis”with“whatmighthavebeen.”

6Beliefinthepossibilityof“abetterfuture”,oratleastafuturemoreviablethanthepresentundergirdsdeferralofgratification,andindividualbehaviors(saving,investing,acquiringknowledge)thatplaycriticalrolesintheaccumulationofproductivetangibleassets,aswellastheformationandmaintenanceofformalinstitutionsandsocialorganizationsthatstructurecooperationinthecollectivecreationofpublicgoods.Therefore,itisreasonabletoviewthewidespreadprospective“lossofhope”foraviablematerialfutureamongmembersofthehumanpopulationasposingagrave“existentialthreat”.

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oftheofEarth’sclimateunderconditionsofcontinuedwarming,andintheeffectivenesswithwhichbothpublicandprivateresourcereallocationplanscanbeimplemented,andcorrectedinmid‐course‐‐implyanon‐zeroprobabilitythatsomeofthesacrificeofthesocialwelfareoffuturegenerationswillbeperceivedtobe“excessive”orevenunnecessary.7

Ourapproachinexploringtherequirementsforoptimallydesignedtransitionstoastabilizedclimatethereforeproceedsfromthepositionthatinthecomparisonbetweenthetwocontemplatedsourcesofexpectedregret,thepreponderanceinthebalanceisoverwhelminglyonthesideofdecidinguponactionstoseektoavoidinadequatelystrongstabilizationmeasuresandtoacceptthehigherrisksofregretsassociatedwithhavingtakenactionsthatwillturnouttohavebeenunnecessarilycostly.Inotherwords,thisformulationassumesthatthedegreeofregret(orjoy)experienceddependsuponcomparisonoftheutilityof“whatis”with“whatmighthavebeen.”Decisionsthatmustbemadeinthefaceoftheexistentialthreatofenteringanirreversiblecatastrophicstate–recognitionofwhichwoulddeprivefuturegenerations(thatsharethedecision‐taker’snotionsofrationality)of“hope”forthepossibilityofallthingsconditionalonthesustainableexistenceofarecognizableformofcivilsociety.Preservationofthathopefulstateofwarrantsactionsentailingdegreesofmaterialsacrificethatwillnotcompromisetheviabilityofthefuturestateinwhichhopefulnesscanbemaintained.Costlyactionsofthiskindwill,ineffect,sacrificethematerialconditionsoftheviableworldlefttofuturegenerationsinordertoavertthehopelessnessofthecatastrophicalternative.

Itshouldalsoberemarkedherethat“excessiveprecaution”issubjecttocorrectioninsomemeasureonceithasbecomerecognized;andtherewouldremainscopeforarrangingsubsequentfurthercompensationforthoseinfuturegenerationsthathadbeenmostdamagedbyerrorsinpolicyplanningandimplementationfailures,rendingsuchremedialactionsanoptionforresourcereallocationandredistributivedecisionsbytheircontemporariesinthestabilizedandeconomicallysustainable(“green”)globalregimeofproduction.Thesameremedialoptions,however,willbeavailablewherefeasibleprecautionaryoptionsremaininadequatelyexploited.Ourapproachinexploringtherequirementsforoptimallydesignedtransitionstoastabilizedclimatethereforeproceedsfromtheviewthatincomparisonsbetweenthetwocontemplatedsourcesofexpectedregret,thepreponderanceinthebalanceisoverwhelminglyonthesideofdecidinguponactionscalculatedtoavoidinadequately

7Such“excessiveprecaution,”however,wouldbesubjecttocorrectioninsomemeasureonceithasbeeninitiated;aswellastosubsequentfurtheradjustmentbyfuturegenerationsthatmaybetterrecognizethescaleofcatastrophethathasbeenaverted.Thiscourseofactionwouldalsoprovidefurtheroptionsforresourcereallocationandredistributivedecisionsinthestabilizedandeconomicallysustainable(“green”)globalregimeofproduction.Thesameremedialoptions,however,arenotavailableinthecasewherefeasibleprecautionaryoptionsareinsufficientlyexploited.

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strongstabilizationmeasuresandtoaccepttheentailedhigherrisksofregretsassociatedwithhavingtakenprecautionsthatwillturnouttohavebeenunnecessary.8

Tostudytherequirementsofatimely(catastrophe‐averting)transition,weformulateasequenceofoptimalcontrolsub‐problemslinkedtogetherbytransversalityconditions,thesolutionofwhichdeterminestheoptimumallocationofresourcesandsequencingoftheseveralphasesimpliedbytheoptionsunderconsideration.Parametricvariationsofthetippingpointconstraintinthesemodelswillpermitexplorationofthecorrespondingmodificationintherequiredsequencinganddurationsofinvestmentandproductioninthephasesthatformtheoptimaltransitionpath.Thepreliminarysolutionsusingmulti‐phaseoptimalcontrolmethodsexposetheimportantdynamiccomplementaritiesamongtechnologicaloptionsthatareoftenpresentedassubstitutesbycurrentclimatepolicydiscussions.Further,the“planning‐model”approachdepartsfromconventionalIAMexercisesalsobyeschewingdubiousassumptionsaboutthebehaviorsofeconomicandpoliticalactorsinresponsetomarketincentivesandspecificpublicpolicyinstruments;itshiftsattentioninsteadtotheneedforempiricalresearchoncriticaltechnicalparameters.andproblemsofinter‐temporalcoordinationofinvestimentandcapacityutilizationthatwillberequiredtoachieveatimely,welfare‐optimizingtransition.

2.BackgroundandMotivation

ClimatechangeisnowconvincinglylinkedtoincreasingatmosphericconcentrationsofGHG(greenhousegases).9Amongthosewhohaveexaminedtherelevantscientificdatatherehasbeenagrowingconsensusthatthisposesaninter‐relatedhostofworrisomeproblems.Moreover,ratherthanconvenientlygoingaway,orbeinggraduallybeingaccommodatedbyadaptationsonthepartoftheworld’speoples,theseproblemsarelikelytogrowworse.Whileonmanyspecificpointsofclimatescienceuncertainties,doubtsanddisagreementpersist,theunderlyingphysicalandchemicalprocessesresponsibleforanthropogenic“greenhouseeffects”warmingtheEarth’surfacearefirmlygrounded,asistheaccumulatingmassofempiricalobservationsattestingtotheriseinmeanglobaltemperaturethathastakenplace

8ThegermofthefollowingargumentforembracingthePrecautionaryPrinciple,formulatedasthecaseforadoptingaminimaxregretstrategy,wasadvancedinaclimatepolicybriefpublishedontheeveofthe2009UNCopenhagenConference(seeDavid,etal.(2009:pp.2‐3).Intheinterim,theemergenceconsensusamongclimateandenvironmentalscientistsonthelikelyexistenceof“tippingpoints”initiatingabruptandcatastrophicalterationsofEarth’sclimate(furtherdiscussedinsection3.1,below),andtheabsenceofanysignificantgloballyconcertedactionsonrapidreductionofGHGemissions,hasrenderedonlymorecompellingthecasefordesigning(costly)policiesthatcouldrapidlystabilizetheatmosphericconcentrationofGHG.

9SeeIPCC(2007),”SummaryforPolicyMakers,”andtheSternReview(Stern,2006)foranextensiveoverviewofthecausesandconsequencesofclimatechange.

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duringthepasttwocenturies.10Together,thesefindingsfirmlyundergirdthescientificallyinformedwarningsabouttheconsequencesofcontinuing“businessasusual”basedonburningfossilfuels.

TherisinglevelsofmoisturethatwillaccompanythewarmingoftheEarth’ssurfaceinthetemperatelatitudescanbeexpectedtodrivemorefrequentandmoresevereweathercycles,bringingheavierprecipitation,strongerwindsandweather‐relateddamagestophysicalpropertyandlossesofhumanlife.Moreover,itismorethanconceivablethatatsomepointinthenotverydistantfuturecontinuingthecurrentrateofGHGemissionsandunimpededglobalwarmingwillusherinanageofcatastrophicallyabruptclimatechanges,characterizedbychaoticinstabilitiesinEarth’sclimates.11Thiswoulddrasticallycurtailthefractionoftheworld’scurrentpopulationthatwouldbeabletoachieveastateof“adaptivesurvival”preservingsubstantialresemblancestopresentstateofcivilization.

MitigatingenvironmentaldamagesfromCO2,methaneanddangerousparticulateemissionsbymoreextensivelydeployingknowntechnologies,andreplacingcarbon‐basedproductionsystemswiththosethatutilizenewandeconomicallyefficient“carbon‐free”technologies,aretwoobviouscoursesofactionthatmaybeabletoavertthesegrimfutureprospects.Togetherwithstillmoreradicaladaptationsthatpossiblymaybeachievedbygeo‐engineeringtocaptureandsequesterexistingatmosphericcarbonandmethane,theseformthecoreofthetechnologicaloptionswhosedevelopmentanddeploymentarethefocusofthisexploratoryexaminationofthedynamicsofafeasibleandtimelytransitiontoasustainablelow‐carbonglobaleconomy.

AprogramofpublicandprivateR&Dinvestmentsyieldingdirectedtechnicalchangesofthiskindshouldbeviewedasa“supply‐sidestrategy”inthecampaigntostabilizeglobalGHGconcentrationsataviablelevel.Theintentionofthispaperisgive“technologyfix”programofthatkinditswarrantedcentralplaceineconomicresearchonthedesignofpolicytomitigateCO2emissions.Thatwouldconstituteaquiteradicalreorientationofthediscussion,for,ontheoccasionsduringthepastdecadewhentechnologicalchangefiguredexplicitlyintheeconomicsliteraturedevotedtoclimatechangepolicy,itusuallyhasbeenpresentedasanancillaryandoptionalcomplementtoimplementing“carbonpricing.”Carbontaxes,orthe“capandtrade”schemesthathave

10SeeSolomonetal.,eds.(2007)onthephysicalbasisandscientificevidenceforIPCCconclusionsregardingglobalwarminganditssourcesinhumanactivity.“Climateskepticism”and“globalwarmingdenial”shouldnotbeconfusedwiththegenerallyacknowledgedscientificuncertaintiesthatstillsurroundthevaluessomekeyparametersinquantitativemodelsoftheprocessesinvolvedinanthropogenicglobalwarming‐‐e.g.,themagnitudeofthe“climatesensitivity”(linkingchangesinmeanglobalsurfacetemperaturetorelativegaininatmosphericGHGconcentration),andthecriticalleveloftemperaturegainthatwouldtriggerirreversiblerunawaywarmingandcatastrophicclimateinstability.Seefurtherdiscussionbelowanddetailsinfootnotes6‐7.

11Seee.g.,Alley(2000);Alley,Marotzke,Nordhaus,Overpecketal.,(2003);HallandBehl(2006),andfurtherdiscussioninSect.2.1(below).

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beenadvocatedasthemeansofcreatingaglobalmarketforcarbon‐emissionspermitsandderivativeinstruments,wouldworktomitigateCO2emissionsprimarilybyraisingthecurrentandexpectedfuturerelativepricesoffossilfuelsasasourceofenergy.Weretheytohavethateffect,thevolumeofdemandforgoodsandservices(e.g.,electricitysupply,transportation)thatwereespeciallycarbon‐intensiveintheirmethodsofproductionwouldbereducedbytheprivateoptimizingadjustmentsmadebyproducersandconsumersresponsetothealteredstructureofpricesofenergysourcesandcarbon‐intensivefinalgoodsandservices.12

Thatstrategyhasgainedbroadsupportamongeconomistsastheapproachthatmoredirectlyattackstherootcauseoftheglobalwarmingexternality‐‐namely,unregulatedandun‐pricedreleasesofCO2–whileleavingthechoiceofmitigationtacticstoagentsintheprivatesector.Anunfortunateconsequenceofthepreoccupationofeconomistswithassessingtheeffectivenessofcarbonpricingandtryingtogaugethewelfare‐optimalscheduleofcarbontaxesledtothedevelopmentofcomputationalmodelsthatglossoverthecomplicatedresourceallocationdynamicsofthetransitiontoalow‐carbonglobalregimeofproduction;and,insodoing,havedeflectedattentionfromthepotentiallygreaterroleofdirectedtechnologypolicyinitiativesbythepublicsectorthatwouldcombinetechnicalstandard‐settingwithdirectandindirectfundingsubsidies,andthepossibilitiesinstitutionalchangesthatwouldremoveexistingbarrierstorapidglobaldiffusionofeffective“greentechnologyinnovations.”

Consequently.itishardtopointtoabodyofpreviousintegratedanalysisdevotedtoassessingglobalclimatepolicydesignsthatconsideranarrayoftechnologicaloptionsinvolvinginvestmentindeployingavailableengineeringtechniquesthatwilllowerthecarbon‐intensityofexistingproductionfacilities,directedR&Dexpenditurestoenhancethecostcompetivenessandreliabilityofcarbon‐freeenergysources(vis‐à‐visfossilfuels),andadoptionsubsidestospeeddiffusionofinnovationsandtherealizationoffurtherincrementalimprovementsfromlearningunderfieldconditions.Butitisencouragingtonotethatacademicpapersthatdiscussedthepertinenceofendogenoustechnologicalchangeinthecontextofclimatepolicyhadbeguntoemergeevenbeforethedebacleoftheattemptatthe2009CopenhagenConferencestrengthenandexpandtoKyotoTreatyprotocols.13

12ThisaspectoftheenvironmentalandenergyeconomicsliteratureiswellrepresentedintheextensivereviewarticlebyAldy,Krupnick,Newelletal.(2010),which,intheconcisewordsofitsabstract“providesanexhaustivereviewofcriticalissuesinthedesignofclimatemitigationpolicybypullingtogetherkeyfindingsandcontroversiesfromdiverseliteraturesonmitigationcosts,damagevaluation,policyinstrumentchoice,technologicalinnovation,andinternationalclimatepolicy.”Theauthorsfocusfirstonthebroadissueofhowhighpolicyassessmentssuggestthenear‐andmedium‐termpricesetongreenhousegasemissionswouldneedtobe,bothundercost‐effectivestabilizationofglobalclimateandundernetbenefitmaximizationorPigouvianemissionspricing.Theythenturntodiscussionoftheappropriatescopeofregulation,questionsregardingpolicyinstrumentchoice,complementarytechnologypolicy,andinternationalpolicyarchitectures.”

13See,e.g.,Carraro,vanderZwaanandGerlagh(2003).Jaffe,NewellandStavins(2006)issalientamongthesepublications,asmuchforthecogencyofitsinsightsandargumentsasforthesparsenessofother

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Neithertheseearlyforaysintothisarea,norotherworkstoourknowledge,venturedtoexaminetherequireddynamicsequencingofdirectedR&Dandothertechnologypoliciesaffectingpublicandprivatesectorinvestmentsrequiredforatimelytransitiontoalow‐GHGemittingproductionregime,thepolicyissuethatisthefocusoftheresearchreportedhere.14

IthasbeensuggestedthatCO2emissionsmitigationachievedbytheintroductionofcarbon‐taxesor“cap‐andtrade”schemesfor“pricing”transferableemissionspermits,couldindirectlyachievewhatwouldotherwisehavetobeaccomplishedbymeansofsocialexpendituresforpublicresearchanddevelopmentprojectsandtaxsubsidiesforprivateinvestmentin“green”R&D,andpossiblyimplementingtheresultantinnovationsincarbonfreephysicalcapitalformation.15Theargumentisthattheeffectofraisingthecostofcarbon‐intensiveprocessesandproductstoproducersandconsumerswillbetostimulateproducers’demandsforoffsetting,carbon‐freetechnologiesandinduceincrementalprivatefundingofthesearchofthoseinnovativemethods.

Althoughthatisapossibility,sotooistheoppositeoutcome.Ifraisingcarbontaxesdoeseffectivelycurtaildemandforhighlycarbon‐intensiveproducts,theresult

contributionsinthisgenre.Theypointout(Ibid.,p.169)thatbecausetheU.S.andotherdevelopedcountrieshadnotbeenactivelypursuingsignificantenvironmentalpolicyintervention,“thereislittleenvironmentalpolicy‐inducedincentivetodeveloptechnologiesthatreducegreenhousegasemissions.Inthissecond‐bestsetting,policytofostergreenhousegas‐reducingtechnologymaybeoneofthemainpolicyleversavailableandcanbejustifiedoneconomicgroundssolongasithaspositivenetbenefits.”Thesamepassage,however,concludeswiththecaveatthatusing“technologypolicyasasubstitutefor,ratherthanacomplementtoenvironmentalpolicy”couldbeacostlyapproach‐‐implyingthatthepayofftoR&Dismoreriskythancountingontheresponsestoincreasesintherelativepriceoffossilfuels,andthatthepure“technologypush”approachsacrificesthepotentialbenefitsofinducedinnovationresponsesfromtheprivatesector.14InthewakeoftheSternReport(2007)andtheCopenhagenConferenceeconomicargumentsforgreaterpublicandprivateinvestmentinR&D,andsubsidiesforthediffusionofadvancedtechnologiesdirectedtoloweringCO2emissionsbeganappearingwithgreatermorefrequently–althoughthesetypicallyremainedunspecific.Earlystatementsproposinga“technologyfix”approachincludeArrow,Cohen,Davidetal.(2008),NelsonandSarewitz(2008),Klemperer(2007/2009),David(2009),David,Huang,SoeteandvanZon(2009),andHendry(2010).None,toourknowledge,venturetoexaminetherequireddynamicpathofdirectedR&DandcapitalformationembodyinginnovationsthatwouldlowertheglobalrateofGHGemissionsperunitofrealoutput,whichisthefocusofthepresentwork.SuchtheoreticalandcomputationalmodellingofendogenousandinducedtechnicalchangethathasbeenundertakentodatehaslargelyfollowingthepioneeringworkofGoulderandSchneider(1999),whichisnotedbelow.

15Amongthepioneeringeffortstoexaminethepropositionthatraisingthepriceofcarbonwouldinducebeneficialprivateinvestmentsintechnologicalinnovation,seetheworkingpapersbyNordhaus(1997),andGoulderandMathai(1998,publishedin2002).GoulderandSchneider(1999)carriedthislineofinquiryfartherbyusingacomputablemulti‐sectorgeneralequilibriummodeltoquantitativelyassesstheextenttowhichrealGDPcostsofimposingCO2abatementtaxeswouldbealteredbytheeffectsofendogenoustechnologicalimprovementsresultingfromR&Dinvestmentinducedbytheeffectofthetaxontherelativepricesofcarbonvs.non‐carboninputs.Thismodellingexercisedidnot,however,undertakeanevaluationoftheefficacyofthehypothesizedinducedtechnicalchangesintermsofthemagnitudeoftheabsoluteabatementoftheeconomy’saggregateemissionsrate.Morerecentexercisesinintegratedclimatepolicyassessmenthaveundertakentodoso,asisnoticedbelow(insection2).

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maywellbegenerallyadverseexpectationsaboutmarketgrowthandaconsequentweakeningofincentivesforR&Dinvestmentinallproductiontechniquesforinthoselinesofbusiness.16Moreover,commitmenttoafuturescheduleofrisingunittaxesonfossilfuelsmightwellhavetheperversefirst‐ordereffectofimmediatelydepressingthefuturevalueoffossilfueldepositsrelativetotheirpresentvalue‐‐ifthescheduledrateofincreaseinthe“carbontax”washigherthantheinterestrate.Underthatcondition,privateownersoftheresourcedepositswouldhaveanimmediateincentivetoraisetheresourceextractionrateinordertobringingforwardintimetheexploitationofthoseresourcedeposits,withtheconsequence(ceterisparibus)thatnear‐termpricesinthemarketsforcarbonfuelswouldbedepressed.17Eventhough,followingthatone‐timedrop,itwouldbeexpectedthatthepresentvalueofcarbondepositsinthegroundandtherelativemarketpriceofcarbonfuelswouldresumerisingattherateofinterest‐‐ascalledforbyHotelling’s(1931)analysis,therelativemarketpriceofcarbonfuelmightnotregainitspre‐taxregimelevelforsomeconsiderableperiodoftime.Duringthatinterval,atleast,theintendedmitigationofCO2emissionswouldbereversed,asalsowouldbethedirectionofsuchimpetusaswouldformerlyhavebeenimpartedtowardsinducedtechnicalinventionandinnovationaimedatsavingcarbon‐energyinputs.

Whetherornotthelong‐termeffectofahighandrisingcarbontaxeventuallywouldbesufficienttohaltthewithdrawaloffossilfuelsbeforefromtheknownreservesweretotallyexhausted(theoutcomethathascometobelabelledasthe“strong”formofGreenParadox,todistinguishitfrom“weak”forminwhichthereisatransientanti‐conservativeeffectonthepaceofresourceextraction),isamorecomplicatedanduncertainmatter,inwhichthedirectionoftheoverallenvironmentaleffectwouldturnonuponstillotherconditions.18Butinaworldinwhichoneshouldnotcountonfiscal

16Thequestioncannotbesettledontheoreticalgrounds,butseeGans(2009)foranalysisoftheconditionsunderwhichcarbon‐taxeswouldhaveaperverseeffectofdiscouragingcarbonemissions‐reducingtechnologyresearchandinnovation.Acemoglu,Aghion,Bursztynx,andHemous(2010/2012)exploretheconditionsforcarbontaxesinagrowthmodelwithenvironmental(carbonemissions)constraintsandendogenousdirectedtechnicalchangedrivenbyprivatesectorR&Dinvestmentsinducedbytheeffectsofanessentiallytransientcarbontax.Theyconcludethatwithasufficientlyhighelasticityofsubstitutionbetweenhighlycarbon‐intensityandlowcarbon‐intensityinputsinproduction,carbontaxescanswitchdirectedR&Dto“clean”(lowcarbonintensity)technologicalresearchandneednotbecontinuedindefinitely;thereisasimilarreinforcingrolefor“temporaryR&Dsubsidies”.Hourcade,PottierandEspagne(2011),however,shownthattheelasticityofsubstitutionrequiredtoproducetheseresultsinthe“illustrative”integratedclimatemodelpresentedbyAcemogluetal.(2010/2012)areimplausiblyhigh,bothfromtheengineeringviewpointandfromtheirimplicationsforthepriceelasticityofdemandforcarbonenergysources,whichareinconsistentwiththeavailableempiricalevidencefromthosemarkets.Inadditionthespecificationoftheclimatesysteminthe“illustrative”computationalmodelpresentedinthelatterpartofthispaperdepartsfromthestandardclimatesciencemodelsinawaythatleadstoseriousunderestimationofthecostsoftherequiredCO2mitigationstrategy—somuchsothatthecorrectedcomputationsvitiatetheauthors’policyconclusions.

17DiscussionofthelatterproblemwasbroachedfirstbySinn(2008,2009:pp.10‐13)whoprovidedalabel‐‐“TheGreenParadox”–underwhichatheoreticalliteraturesoondeveloped.See,e.g.,EdenhoferandKalkuhl(2010),Hoel(2010),Withagen(2010),vanderPloegandWithagen(2012).

18Amongconditionsthatwouldruleoutthe“strong”formoftheGreenParadox(see,esp.vanderPloeg(2010)andEdenhoferandKalkuhl(2010))include:(i)ahighleveloftheunittaxoncarbonextraction,(ii)marginalcostsofresourceextractionthatincreasedasaninversefunctionofthesizeofthe(unexhausted)

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andregulatoryinstrumentsbeingoptimallydesignedandconsistentlyusedbypoliticalauthorities,letalonebyassembliesorsovereignstates,thepossibilitiesofunintended“GreenParadox”outcomesshouldcautionagainstrelianceoncarbon‐pricingschemesasthe“bestpolicyresponse”tothethreatsposedbyglobalwarming.

Itseemspertinentherealsotonoticethatthedistinctiondrawnbetween“weak”and“strong”GreenParadoxesinthetheoreticalliteraturelosespracticalrelevancewhenthereisnoassurancethatglobalwarmingwillaffordhumanitysufficienttimetoevencomeclosetoexhaustingtheEarth’sknowndepositsoffossilfuel,asispre‐supposedbyallthemodelsthathavebeenusedtofindconditionsunderwhichthe“strong”formofGreenParadoxcouldorcouldnotberealized.

Aswillbeseenshortly(fromsection2.1,below),climatescientistsnowregardittobequitepossiblethatwealreadyhavearrivedatastatewhereaquitemodestfurthergainintheplanet’smeansurfacetemperaturecouldpushthegeo‐physicalsystempastacriticalclimate“tippingpoint,”initiatingaself‐reinforcingcascadeoftippingelementsthatwouldirreversiblyusherinanepochofcatastrophicclimateinstability.Thereisthuslittlecomfortintheknowledgethattheunintendedimmediateperverseboostintheratesofextractingandburningfossilfuel–broughtaboutbyresourceowners’wealth‐preservingreactionstotheprospectofhighandrisingfuturecarbontaxes‐‐mightbeonlyatransienteffect.BeforethatinitialimpulseboostingthevolumeofCO2haddissipated,thetrajectoryoftheclimatecouldhavebeenirretrievablyaltered.Itisinthatcontextthattheprecautionaryprincipleparadoxicallyservestoinveighagainstadvicetorelyexclusivelyuponsouncertainandpotentiallydangerousastrategyofcombattinggoalwarmingbypromisingafuture“rampingup”ofthecarbontaxrate.

Beyondthis,theforegoingreviewoftheworrisomepotentialdrawbacksofexclusiverelianceoncarbontaxesto“fixtheGHGemissionsexternality,”thereisstillgreatergroundsfordoubtsabouttheefficacyofthealternativeproposalthatgainedwidespreadpopularityamongenvironmentalandenergyeconomists–namely,downstreamcap‐and‐tradeschemes,whichpricetheemissionsfromburningcarbon,butnotthecarbonmaterialthatistheenergysource.

Itisnotatallobviousthatputtingapriceontheemissionsfromtheburningofhydrocarbonsnecessarilywouldsufficetoraisethecombinedpriceofthematerialanditscombustion,sothepossibilityofaperverserelativepricechangecannotbe

resourcedeposits,(iii)aunittaxthatwasnotscheduledtoincreaseatarateexceedingtheresourceowners’time‐discountrate,and(iv)wasadhocinnotbeingsetinaccordwithanoptimizedinter‐temporalprogramofresourceuse.Further,althoughnotconsideredinthetheoreticaljustcited,thepracticalvalueoftheanalyticaldistinctionbetweenthe“strong”and“weak”formoftheparadoxbecomesdubious,whenonerecognizesthatpositivefeed‐backeffectsfromtheriseinglobaltemperaturecausedby“transiently”acceleratedCO2emissionscouldalterthedynamicsoftheclimatesystemsufficientlytoinitiateaself‐reinforcing(“runaway”)processofwarming.Seesection2.1(below)forfurtherdiscussion.

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definitivelyruledout.19Bycontrast,theproposalofan“up‐stream”implementationofthecapandtrademechanism(seeRepetto2011)isadministrativelyattractivebecauseeffectiverestrictionofthevolumeoffossilfuelsavailablefrom“firstsellers”itwouldnecessarilyraisethecostofcarbon‐basedenergysources.Furthermonitoringandenforcementofthe“caps”wouldbegreatlysimplifiedbythelimitednumberof“firstsellers”andtheeaseofidentifyingthem–especiallyincomparisonwiththemyriaddownstreamusersthatwouldrequireCO2emissionpermits.Theoreticalanalystsoftheproblematicpossibilityofaperverse“GreenParadox”effectofrisingcarbonareagreedthattheanti‐conservationreactiononthepartofownersoffossilfueldepositswouldnotmaterializewereahighenoughadvaloremtaxratetobeimposedsoonerratherthanpromisedforthefuture.

But,asefficientandadministrativelyfeasibleasitmightbeforcentralgovernmentauthoritiesinthelargesteconomicstoquicklyimposecoordinatedtightregulatorycapsonfirstvendors,suchactionswouldbetantamounttodirectlyrestrictingextractionandimportationoffossilfuels.Thepoliticaleconomyofdomesticlegislationandinternationaltreatynegotiations,however,seemlikelytomilitatestronglyagainstpracticalimplementationofthisapproachtofixingthegreenhousegasexternality–bothpresentlyandforsometimetocome.Thatwouldseemtodepriveproposedup‐streamcap‐and‐trademechanismsofanypracticaladvantagevis‐à‐visthemorefamiliar“downstream”variety.20

Inthesecircumstancesitshouldberemarkedthatthepresentandlikelyfuturesocialandpoliticalresistancestostringentandenforceablecarbon‐pricingpolicies

19Thissourceofambiguityregardingtheeffectsofusingthe“capandtrade”mechanismtosetapositivepriceoncarbonemissions,itshouldbeemphasized,isquitedistinctfromtheconcernsaboutthepossibledisincentiveeffectsofcarbontaxes’negativeimpactsondemandsforcarbon‐intensivegoodsandservices–e.g.,thoserelyingheavilyonproductionprocessesusingenergysourcessuchascoal,oilandnaturalgas.Thetheoryofexhaustiblenaturalresourcepricing,followingtheclassicworkofHotelling(1931)tellsusthattheresourcevaluationmustriseattherateofinterest,andwithmarginalextractioncostsconstant,thepriceoftheflowofmaterialstradedinthemarketmustriseparipassuswiththatoftheresourcedeposit.Subsequenttheoreticalcontributionstoexhaustibleresourceeconomicshavepointedoutthatdownwardpressureexertedbyanticipationsofadvancesin“backstop”technologiespermittingsubstitutionofcarbon‐freeenergysources(and,moregenerally,moreenergy‐efficientproductionprocessinnovations)wouldlowerthelevelsfromwhichthemarketpricesofcoal,oilandnaturalgaswouldbetrendingupwards(seeHeal(1976),Dasgupta,HealandMajumdar(1978),DasguptaandHeal(1980)).Thiseffectwouldworktoslow,ifnottemporarilyhaltthediffusionofthoseinnovations.Whetherthemagnitudeofthefirst‐orderoffsetonpricesincarbonmarketswouldbelargeenoughtoperverselyneutralizetheintendedimpactofaglobalcap‐and‐tradescheme,orsolargeastotemporarilylowertheafter‐taxunitcostofburningcarbonfuels,isanempiricalquestion(obviouslyofpolicy‐relevance)thatdeservesmoreattentionthanithasreceived.Onfirstconsideration,itseemsthattheanswermustturnontheextentoftheanticipateddemanddisplacementinrelationtothesizeoftheresourcereservesthatcouldbeaccessedfromthemarketsinquestion.WearegratefultoLawrenceGoulderobservationthatthelatterconsiderationsmakethemagnitudeoftheoffset‐effectsgreaterinthecaseofhighqualityoilreservesthanitwouldbefortheworld’svastcoaldeposits.20Indeed,itseemmorethanlikelythatgovernmentregulationsbanningunlicensedfirstsalesoffossilcarbonsourcesofenergywouldbecharacterizedastantamounttostateexpropriationandcontrolofthoseformsofnaturalresourcewealth,andmetwithstrongpoliticaloppositionfrompowerfuleconomicinterestsintheWestasnothinglessthan“defactosocialization”oftheirprivatelyownedmineralwealth.

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mightbeweakenedweretherecrediblegroundsforanticipatingthattheeconomicwelfarecostsentailedinswitchingtoalternativeenergysourceswouldbesignificantreducedbyaconcertedmulti‐nationalprogramofdirectedtechnologicalinnovation.Seenfromthisangle,theattentionthateconomistshavepaidtothepotentialitythatraisingtherelativepriceoffossilfuelswouldinduce(private)investmentstoreducethecarbon‐intensityofproductionprocessesandfinalgoodsandservicesmayhaveputthepolicycartbeforethehorse.21Whilethedynamicsofthistechno‐politiconexuswillneedtobethoughtthroughcarefully,theargumentforsystematiceconomicanalysisofthepotentialroletechnologypoliciesineffectingatimely,climatestabilizingtransitiontoaviable“lowcarbon”globaleconomythereforecanrestinpartonthepossibletemporalasymmetryofcomplementary(orsuper‐modular)relationshipsbetweenthetwomajorpolicyapproaches.

Whenviewedinthatexpandedandexplicitlydynamicperspective,aprogramthatstartswith“techfix”maymakethatpolicyinitiativecomplementaryto(andnotasubstitutefor)fiscalandregulatoryinstrumentsdesignedtogetmarketpricesofcarbonfueltoreflecttheirmarginalsocialcosts.Thisconsiderationprovidesarationaleforaccordinggreaterattentiontotherequirementsofa“technologypush”strategythanithasreceivedinpreviousandcontemporaryeconomicresearchonclimatepolicydesignconceivedprimarilyindeterminingthelevelandtime‐profileofanoptimalglobal“carbontax”‐‐oritsequivalentimplementationbymeansofacrediblefuturescheduleforthestockofgloballyavailabletradablepermitstoemitCO2.

Thelatterconsiderationswarrantcloseattentiontothetechnologicalportfolioproblem,especiallyinviewoftheuncertainnatureofthetechnicalconstraintsonthepotentialperformanceimprovementsofthemultiplefossil‐fuelbasedtechniquesofenergygenerationandutilization.Therelevantconstrainshavetodonotonlywithphysicallimitationsonthescopebothforenhancingtheirrespectiveproductivities(byloweringthoseprocesses’carbon‐intensity),andfordirectlycurtailingtheratesatwhichtheyreleaseCO2andotherGHGsintotheatmosphere.EquallyrelevantaretheconstraintsuponthedistributionsofthemagnitudesandspeedswithwhichimprovementsinspecifictechnologiesorfamiliesofrelatedtechnologiescanbeantcitipatedtoflowfrompriordirectedR&Dexpenditures.Uncertaintiesofthesamesortsurroundthetechnicalconstraintsonraisingtheproductivityof“alternative”(non‐fossilfuelled)technologiesforgeneratingenergy.

21TheforceofthispointisnotvitiatedbypolicyargumentsthatrecognizethatpubliclysubsidizedR&Dmaywellbeneededtosupplementtheinducedresponseofprivateinnovation(see,e.g.,Acemoglu,Aghion,Bursztynx,andHemous,2012),because“free‐riding”ontheanticipatedexternalities(intheformofinformational“spill‐overs”)resultingfromR&Doutlaysislikelytoreducetheaggregatevolumeofthelatterinvestmentstoasociallysub‐optimal,whileracingforpatentprotectionandfirstmoveradvantageswouldtendtoproduceexcessR&Dcommitmenttoinventioninthecaseofsometechnicalareas.

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Analysisoftherequirementsofanexplicit“tech‐fix”approachtostabilizingtheglobalclimatethereforedemandsmorethanidentifyingasubsetofthearrayofavailabletechnologiesuponwhichCO2‐emissionsmitigatingmeasureshouldbefocused,howeverbroadtheresultingportfolioofselected“coretechniques”mightturnouttobe.Tobeuseful,theportfoliohastobespecifieddynamically.Notonlymustitbeconstructedsoastorenderfeasibleatleastonepathforthetimelytransitiontoaclimate‐stabilizingglobalproductionregime‐‐i.e.,characterizedbyzeronetadditionstotheatmosphericconcentrationlevelofGHGsinCO2‐equivalentppmv.Subjecttothatglobalconstraint,the“tech‐fix”pathshouldbedesignedtobe“socialwelfareoptimizing”,inthesensethatitwillminimizethewelfareburdenofthetransitionprocess,takingintoaccountthedamagesincurredbytheconsequencesoftherisingtemperature(s)ofEarth’slandandoceansurfacesuntilstabilizationhasbeenachieved.Timingdoesmatter:bothinregardtothesequencingofinvestmentsinresearchanddevelopmentactivitiesdirectedtoenhancingtheperformanceofspecifictechniquespriortotheirdeployment,andtothetimedistributionoftangibleinvestmentsthatwillbeneededinordertodeploythosetechnologiesthatmustbeembodiedinfixedcapitalstructuresandequipment,includingthenecessarysupportinginfrastructures.

3.Preliminariesformodellinga“TechFix”strategy’sdynamicrequirements

Allofthepreviouslymentionedsupply‐sideoptions,however,requirepayingexplicitattentiontomajorchangesinproductionsystemsand/orchangesinlife‐styleandconsumptionpatterns.Furthermore,toexplorethedynamicsoftransitionstowardsalesscarbon‐intensiveproductionregimeandtherolethatresearchpolicywouldhavetoplay,itisnecessarytoconsiderthetemporaldurationofR&Dactivitiesdirectedtoalteringtheperformancecharacteristicsofvariousclassesoftechnology,aswellasthedurationoftangiblecapitalformationprocessesrequiredbytechnologiesthatmustbe“embodied”innewphysicalplantandequipment.Suchquestionscanbemostusefullyexploredinthispaperwithintheframeworkofaheuristicmodelofendogenousglobaleconomicgrowth,whichistheresearchapproachpursuedhere..

Itisnolessessentialtobeginbyexplicitlytakingintoaccountthedynamicbehaviorofthegeophysicalsystemwithinwhichtheglobaleconomyisset.Thatlargerphysicalcontextquiteobviouslyimposesbothnaturalresourceandenvironmentalconstraintsupontheproductionregime,aswellasimpingingdirectlyuponhumanwelfare–inthisinstancethroughthecontinuinganthropogenicemissionsofgreenhousegasesandtheirdestabilizingimpactsuponglobalclimateandtheaccompanyingalterationofweatherpatterns.

3.1Climatesciencerealitiesandthegeophysicalsystemconstraints

TherearenowfirmscientificfoundationsforthegrowingconcernsthattoallowGHGemissionstocontinueatanythingclosetotheirpresentratemaysoonsetinmotionirreversiblerunawayglobalwarming,withpotentiallycatastrophicconsequencesfor

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globalecosystemsandforhumanlifeasweknowit.Thisconclusionhassurvivedthepersistingdoubtsvoicedbyadwindlingfringeofacademic“climatechangesceptics”andoutrightdeniersoftheseriousnessoftheproblemsthatcontinuedglobalwarmingwillpose.22

ThemassofevidenceprovidedbychemicalanalysisofthegasesinthedeepicecoresthathavebeenextractedfromArcticandmountainglaciersduringthepastdecade‐and‐a‐halfhasallowedclimatescientiststodocumentahistoryofabruptalterationsoftheEarth’sclimate(s)duringpre‐Holoceneepoch.TherecordpointstothepossibilitythatevenmodestglobalwarmingdrivenbycontinuedanthropogenicemissionsofGHGcouldtriggertheonsetofirreversibleglobalwarming,butaformofclimateinstabilitythatduringthemostrecenttransitionbetweenglacialandstadialepochsfeaturedaprolongederaof“climateflickering.”23Thislattertermreferstoaclimateregimecharacterizedbyhighfrequencyswitching(withperiodicitiesasshortas3to5years)betweenmarkedlywarmerandcooleraveragetemperatures‐‐thelatterdifferingbyasmuchashalfthe12oC.rangebetweenthelowestandhighestextremesrecordedduringEarth’sglacialandstadialepisodes.ThepossibilityofcatastrophicstatechangeofthatsortunderminesthesanguinesuppositionsthatthecontinuedemissionsofCO2wouldsimplyresultinasmoothtransitiontoawarmerglobalclimatetowhichhumansocietieswouldbeabletosuccessfullyadapt.

22DespitetheevidencepresentedbySolomonetal.(2007),doubtshavebeenraisedaboutconclusionthatthewarmingtrendobservableduringthesecondhalfofthe20thcenturyresultedfromradiativeforcingduetohumanactivities.ThesedoubtsarerootedincriticismofIPCCmodelsofgeneralclimatecirculationmodels(GCMs)onaccountoftheirpoorperformanceinpredictingthehighfrequencyandhighrelativeamplitudevariationsinglobalclimateduringthepast50‐60years.See,e.g.,Scarfetta(2011)andreferencesthereinforstudiesshowingthatthelattervariationscanbemoreaccuratelypredictedbystatisticallyfittingharmonic(Fourierseries)regressionmodelsthatcombineindicatorsofmultipleastronomicalcycleswithdifferingfrequencies.Suchresearch,however,shedsscantlightonthedynamicsofthephysicalforcingprocessesthatwouldaccountcasuallyfortheobservedstatisticalcorrelation,nordoestheexistenceofunexplainedfluctuationsaroundatrendvitiatethepositivestatisticalsignificanceofthetrenditself.Recenttheoreticalefforts,suchasthatbyStockwell(2011),offergeneralphysicalbasisfortheskeptics’contentionthatperiodicradiativeforcingfromastronomicalsources,notaccountedforintheIPCC’sGCMs,couldberesponsibleforthelatter’sfailuresinpredictingrecenthighfrequencyvariationsobservedintheEarth’stemperature.Thetroublewiththislineofspeculativecriticismseemsobviousenough:variationsinsolarradiationarenotthoughttobeaconcurrentlyemergingfeatureinthehistoryofourplanet’sastronomicalenvironment.Consequentlyitishardtounderstandhowthatphenomenoncouldaccountforthe“hockey‐stick”up‐turnobservedinthelasthalf‐millennium’sworthofdataindicatingthelong‐termtrendintheEarth’stemperature.

23HallandBehl(2006)reviewthefindingsfromrecentadvancesinclimatescience,andpointoutthatitsimplicationsthoroughlyunderminethesuppositionlongmaintainedbymainstreamcontributorstotheliteratureonenergyandenvironmentaleconomics,namely,that“climatechange”drivenbyrisingGHGconcentrationlevelscouldbesatisfactorilymodelledasasmoothtransitiontoahigherequilibriumleveloftheglobalmeansurfacetemperature–ashasbeenassumedbytheintegratedassessmentmodels(IAMs)thathavefiguredprominentlyandremainsalientintheenergyandenvironmentaleconomicsfield.SeeHallandBehl(2006:pp.461‐462)foradetaileddiscussionofthisandrelatedfeaturesofthegeophysicalsub‐systeminNordhausandBoyer’s(2000)updatingoftheoriginal(Nordhaus1994)DICEmodel,TheassumptionthatradiativeforcingduetotheaccumulationofatmosphericCO2woulddriveasmoothtransitiontoahigherequilibriumtemperatureoftheEarth’ssurfaceisretainedbyNordhaus(2010)inthelatestupdateofDICE(2010),aswellasintheannualizedversionofthemodelthatCaiJuddandLontzek(2012)createasabasisforDSICE,astochasticversionofthemodel.

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ThepositivefeedbacksthatwoulddriverunawayglobalwarmingdynamicsandthemanifoldentaileddamagestohumanwelfarearethosegeneratedbytheamplificationofthelinkagebetweenelevatedGHGconcentrationlevelsofanthropogenicoriginsandstrongerradiativeforcingthatproducesfasterwarmingofEarth’ssurface.Thewarmingatvariouspointstriggersself‐reinforcingalterationsinthebehaviourofthegeophysicalsystem.ThesefeedbackprocesseswouldoperatetoincreasethestrengthoftheradiativeforcingresultingfromagivenatmosphericGHGconcentrationlevel;boostthesurfaceabsorptionofheat,andhencetherateofwarmingproducedbyagivenlevelofradiativeforcing;supplementdirectanthropogenicemissionsofCO2bytriggeringreleasesofmethane(amuchmorepowerfulGHG)–which,atlowertemperatures,wouldhaveremainednaturallysequesteredinthepermafrostbeneathglacialiceandinthemethanehydrateslyingontheshallowseabedatthenorthernedgeofthearcticocean.

Someoftheinterveningstepsofsuchsequences(depictedschematicallyinFigure1)haveacascade‐likesub‐structurethatservetoextendandfurtheracceleratethepositivefeedbackprocess.Thiscreatesapotentialfortherisingconcentrationof

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“tippingpoint”intheEarth’sclimatesystemthatabruptlytriggerstheonsetofacatastrophicrunawaywarmingprocess.24

24OnabruptclimatechangesseeAlley,Marotzke,Nordhaus,Overpecketal.(2003);Stern(2007),pp.11‐14,forashortoverviewofpositivefeedbacksfromglobalwarming,includingreductionofalbedothroughreducedice‐coverageofthearcticregions,thawingofpermafrostandinducedreleasesofmethane.seeLenton,Held,Kriegleretal.,(2008),forspecificsofidentifiedmajor“tippingelements”intheEarth’sclimatesystem;Barnosky,Hadly,Bascompteetal.(2012)onevidenceindicativeofanapproachingglobalecosystemtippingpoint.O’RiordanandLenton(2011)provideabriefnon‐technicalpresentationoftheconceptsoftippingpointsandtippingelementsandtheirpresentpolicyrelevance.

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Consider,forexample,thatbyloweringalbedo(thefractionofsunlightreflectedbytheearth’ssurface)glacialretreatleadsimmediatelytogreaterlocalheatabsorptionintheaffectedregions.Thispromotesthawingoftheexposedpermafrostandthecreationthaw‐lakesfromwhichmethanegeneratedbytheanaerobicdecayofunderlyingorganicmaterialwillbubbletothesurface,asitdoesfromcontinuallyfloodedricepaddies.Further,warmingofthelargepeatdepositsinthearcticSiberianshelfwouldaugmentthereleaseofmethanefromthatnaturalsource;andevenamoderateriseintheupperocean’stemperature,particularlyintheshallowerArcticwaterscandestabilizethemethaneclathratecompoundsthathadformedontheseabedthereduringanearlierepoch.Methanematters,becauseitisapowerfulgreenhousegaswhoseliberationfromnaturalsequestrationonthelandandundertheoceans’surfaceisanimportantpotentialsourceofself‐reinforcingdynamics.Asthe(red)positivefeedbackloopsinFigure1depict,inprinciplethoseeffectscanbepowerfulenoughtodrivecontinuingawarmingtrendevenwhenanthropogenicCO2emissionshavebeensuppressedtoratesthatcanbematchedbytheEarth’snaturalabatementcapacities. Methane(CH4)isanunstablemoleculethatissubjecttoimmediatedegradationbyexposureintheatmospheretotheOHradical,whichsetsinmotionachemicalchainreactionthatwithinseveraldayswillhavebegunconvertingthenewlyaddedmethanemoleculestomoleculesofwaterandCO2.25Althoughthelifeofamoleculeofmethaneisaverytransientone,thegashasaglobalwarmingpotential(GWP)‐‐themetricexpressingtheratioofitsabsoluteglobalwarmingpotentialrelativetothatofCO2–averaging72overthe20yearhorizonfollowingitsrelease,anddecliningtoanannualaverageGWPof26overthe100yearhorizon.TheGWPvaluesreflectbothverystrongshort‐liveddirecteffectsofonradiativeforcingofa“shot”ofCH4throughoutthe12yearsofitsperturbation(impulsedecay)lifetime,andthepersistingindirecteffectsoftheCO2moleculesthatthedecaying“methaneshot”addstotheatmosphere.26

25SeeArcher(2011:Ch5)foralucidexpositionofthemethanecycle,drawinglargelyonJacob(1999).TheOHradical(denotedOH●)isproducednaturallybytheeffectofsunlightonwater,whichcausesthelatertoloseahydrogenatom,andtoimmediatelystealonefromanavailablemethanemolecule‐‐yieldingH2Oandthemethylradical(CH3●),whichachainofsimplechemicalreactionsendsupproducing2stablemoleculesofwaterandoneofcarbondioxide.

26TheGWPaveragevaluesformethaneof72,4,26.3,and7.6overthe20‐yr.,100‐yr.and500‐yrhorizonsarecalculatedbyBouceret.al.(2009:Table1).TheseagreecloselywiththevaluespresentedbyIPCC(2007:AR4‐WorkingGroupI,Ch.2,p.212).BecausetheyincludetheindirectglobalwarmingeffectsoftheCO2producedbytheoxidationofCH4,thevaluesinthetext(above)arehigherthanthecorrespondingdirecteffectsreportedbythe2001IPCCThirdAssessmentReport,IPCC2001:Sect.6.12.1,Table6.7)gives(direct)GlobalWarmingPotential(GPW)valuesformethaneof62,23and7overthe20‐yr.,100‐yr.and500yr.timehorizons—alsocalculatedasannualaveragesonthebasisofa12yearimpulsedecaylifetimeforCh4,andaCO2responsefunctionthatassumesmixingratiowithothertracegassesthatisconstantovera500yearperiod.TheGPWcalculationforCH4differsfromthatfortheothertracegases,inthatitusesvalueforthemethane’sperturbationlifetimethattakesintoaccountthefeedbackeffectsofitsdegradationontheatmosphericconcentrationmoisture(H2O)andtheavailability

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CloudsofCH4bubblinguptothesurfaceofthearcticocean’sshallowsandrapidlydiffusingintoatmosphericcirculation,wouldthuscausetheCO2‐equivalentconcentrationlevelandthestrengthofradiantforcingtospikeupwards.Consequently,thestrongglobalwarmingeffectasuddenjumpinatmosphericmethaneconcentration(unlikethatofgainsinCO2ppmv)willdissipaterapidlyifthehigherrateofemissionsisnotmaintained,leavingbehindonlythepersistingclimateeffectsoftheelevatedmoisturelevelandtheCO2concentrationproducedbythechemicalreactionsthatdegradeit.Asurgeinwarmingresultingfromaprolongedriseintherateofmethaneflux,however,couldbesufficienttoinducefurtherpositivefeedbackeffectsonmeanglobaltemperatureandhaveapotentialtotriggeraself‐reinforcingtrendriseintheatmosphericconcentrationofCO2.27

MethanegascloudscouldbeabruptlyreleasedbythewarmingofshalloweroceanwatersalongtheArticOcean’sedges,sinceitisestimatedthatariseofonly2∘C.inthewater’stemperaturetherewouldbeenoughtodestabilizethemethaneclathratedepositsthatholdCH4trappedintheircage‐likemolecularstructure.This,theso‐called“ClathrateGun”effectnowisthoughttobeaprimarymechanismofthepre‐historicepisodesofpronouncedhighfrequencytemperatefluctuationsthathaveleftarecordinthedeeparticice‐cores.28 Yetanotherperversefeedbackloopinvolvesforestdie‐back.ThisworriesscientistsstudyingtheborealforeststretchingacrossthenorthernlatitudesofthenorthAmericancontinentandRussia‐‐azonewhosetreesrepresentbetween25and30percentoftheworld’sforestcover,andwhichisreportedtohaveexperiencedthemostpronouncedtemperatureincreasesobservedanywhereontheplanetduringthelastquarteroftwentiethcentury.InthenorthernlatitudeofSiberiathepredominantneedle‐sheddinglarchforestsarebeingreplacedbyevergreenconifersthatgrowmorerapidly

ofOHradicals(theprincipalnaturalsinkforCH4).Seethepreviousfootnoteonthechemistryofthemethanecycle.

27Whileitappearsthatthereislittlelikelihoodofthishappeningspontaneouslythroughnaturalevents‐‐suchasdisruptionsofthedeepoceanseabedbyearthquakesthatopenedunderseaventsformethane‐‐thatwouldoccuronalargeenoughscaletohavecatastrophicclimateconsequences,thesizeandinstabilityoftheEarth’smethanehydratereservesandtheuncertaintiessurroundingthepresentstateofscientificknowledgeleadasoberclimatescientistlikeArcher(2011)tocharacterizethosepotentialitiesas“frightening”.

28Evenquitemoderatewarmingoftheoceanwatersalongthecontinentalshelvesisthoughttobesufficienttodestabilizethemethaneclathratecompoundsthathaveformedontheseabedinnorthernlatitudes.Onthe“ClathrateGun”hypothesisandit’srelevanceasanexplanationofabruptclimatechangeandthephenomenonof“climateflickering”attheendofthelasticeage,seeKennettetal(2003),Maslinetal.(2004),HallandBehl(2006),ReaganandMoridis(2007).Thehighfrequencyofthetemperaturefluctuationsrecordedintheice‐coresareheldtomilitateagainsttheearliertheorythatthisabruptandcatastrophicalterationoftheclimatesystemcouldhavebeenproducedbya“thermohalinecollapse”,whichwouldresultclimatecyclesofmuchlowerfrequencies.

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inthesummerwarmth,buttheevergreentreesabsorbmoresunlightandtheirexpansionisthuscontributingtotheglobalwarmingtrend.29

Thelossofpredictabilityoflocalenvironmentalchangesaccompanyingprofoundecologicaldamageandlossesofhumanlifeandwelfare,andthesocio‐economicrepercussionsthatwouldexacerbatetheprocesstherebysetinmotion,canbelefttotheimaginationatthispoint.Sufficeittosaythatthisprospect,howeveruncertainitstimingandmagnitudeareatpresent,strengthenstheforceofargumentsthattheprecautionaryprincipleshouldbeembracedfirmlyandbecomethetouchstoneofnationalandinternationalclimatestabilizationpolicymeasuresdesignedtoavertthedisasterofcrossingatippingpointintoregimeofrunawaywarmingandthepossibleonsetofcatastropheclimateflickering. 3.2Thewayforward

Obviouslythatismucheasiersaidthandone,onmanycounts.AimingforatimelyattainmentofsomestablelevelofatmosphericCO2‐equiv.concentrationwithanexanteoptimumsetofpolicyinstrumentswouldhavetoallowforthelikelihoodofunforeseeneventsthatcausetheprogramtofallingshortofattainingtheappropriate(moving)CO2emissionsmitigationtargets.Gettingit“backontrack,”however,wouldonlyhavebecometechnicallymoredifficultandentailingstilllargersacrificesofeconomicwelfareandwell‐beingfortheworld’speople(nottomentionotherspecies).Inviewofthepotentiallyinsurmountableadaptationcostsandwelfaredamagesinvolvedinpassingfromaviablequasi‐stableglobalclimatemode(characterizedbytheslowandcontinuouswarmingtrend)tooneofirreversiblyacceleratingandeventuallychaoticregimeofglobalwarmingthemostsensiblecourseofactionistoistofirmlyembracetheimplicationsoftheprecautionaryprinciple.

Thisjudgmentofthepresentsituationcallsforacommitmenttodesignandseek

toimplementclimatestabilizationpoliciesrequiredbyapplicationofthePrecautionaryPrinciplegroundedonregrettheory.Thelatter’saimistominimizethesubjectiveprobabilityoftheworst‐caseoutcomesbeingrealized,i.e.determiningthestepsrequiredtoavertthose(catastrophic)futureoutcomesthatwouldoccasionthemaximumregretweretheyperceivedtobeimmanent.AfeasibleinitialstepinthatdirectionistoinvestigatethenatureandextentofglobalmobilizationandallocationofresourcesrequiredinordertoimplementthetechnicalmeansofmitigatingtheemissionofGHGssoastostabilizeatmosphericconcentrationoftheCO2‐equivppmvatjustbelowaconjecturedlikelylevelofthecatastrophictippingpoint.

29WhetherthisiscompensatedbytheirgreatercapacityforabsorbingCO2isnotclear.Ifsuchisthecase,itisbeingoffsetinthesoutherndrierborealzone,wherewater‐stressedtreesinthesummergrowlessrapidlyandtheforestsarebeingreplacedbygrasslandsandpasture.http://en.wikipedia.org/wiki/Boreal_forest#Climate_change

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Giventheuncertaintiesthatsurroundboththescientificandtechnologicalconditionswhichwillconstrainanysuchanundertaking,thelatterconjecturenecessarilywillbesubjective.Nevertheless,forthepurposesoftheanalysisitcanbetreatedasanexogenousparameterthatimposesakeyconstraintuponthedesignofawelfareoptimizing“technologicalfix”.Bysettingthelevelofthisparameter,giventhepresentlyexistingatmosphericconcentrationlevelofCO2‐equivppmv,willineffectsetahard“carbon‐budgetconstraint”ontheoptimalmitigationprogram;ineffectitfixesthecumulativenetvolumeofCO2emissionsthatcanbeexpendedduringthejust‐in‐timetransitiontoastabilizedclimatethatwouldavertthecatastropheofovershootingthe(conjectured)tippingpoint.

Parametricvariationofthehypothesizedtippingpointcanrevealthesensitivity

ofthetechnicalandeconomicinvestmentrequirementsofthe(constrained)optimaltransitionpath.{Suchexplorationswillnothavemuchpracticalpurposeifthelowerendoftherangeofvariationsisnottruncatedatatippingpointlevelabovethosethatalreadyhavebeensurpassed,becausewhetherornottheactuallyofthatstateisperceived,exhypothesistheconjecturedcatastrophecannotbeaverted.Ifalowaprioriprobabilityweretobeattachedtothatconjecturedlocationofthetippingpoint,thiswouldhavethesameeffect,insufficingtolowertheamountofattentiondevotedtotherequirementsofretrievingsomethingworthwhilewithinthediscouraginglytightconstraintsoftheconjecturedstateofthesystem.Theonethingthisapproachseekstoavoidisinactionintendedtoavoidtheexpenditureofeconomicresourcesonmitigationeffortsbywaitingtoaccumulateinformationthatcouldincreasetheprecisionoftheapriorisubjectiveprobabilitiesassignedtotherangeoftippingpointlocations.Thisfollowsfromtheplausibilityofthepresentscientificconsensusthattheeconomic‐climatesystempresentsituationandlikelyfuturepathwithoutmajormigitationeffortsmakesitunlikelythatacatastrophictippingpointwillnotbereacheduntilfarinthefuture.

Ourmodellingapproachinthispaperbuildsuponthepioneeringworkof

economistsonclimatepolicyanalysisrepresentedinso‐calledintegratedassessmentmodels(IAMs)thatprovideasimplifiedcharacterizationoftheessentialfeaturesofthegeo‐physicalsystem.30ThesequantitythelinkagebetweentheflowofGHGemissionsfromeconomicactivityandtheaugmentedradiativeforcingthatdriveshighermeanglobaltemperaturesattheEarth’ssurface(the“green‐house”effect).ModellingthecarboncycletakesaccountofthenaturalsequestrationofCO2intheforestsandoceans,andtheconsequentlaggedeffectintheadjustmentoftheaccumulatedatmosphericstockofGHG(equivalentCO2ppmv);the“climatesensitivity”parameterdescribestheequilibriummeansurfacetemperature’sresponsetoadoublingoftheCO2‐e

30ForsurveysandreviewsoftheevolvingfieldofresearchonIAMs,afterNordhaus(1993aand1993b),seeDowlatabadi(1995),KellyandKolstad(1999),Parker,Letcher,Jakemanetal(2003),Ackerman,DeCanio,HowarthandSheeran(2009).

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concentrationintheatmosphere.31Withinthatcharacterizationofthephysicalframework,ourmodeladdsspecificationsoftheproductionsectorofanendogenousgrowthmodelinwhichdirectedR&Dexpenditurescanraisetheproductivityofnewlyformedcapitalgoodsembodyingnovel“carbon‐free”technologies,andhenceenhancetheeconomicefficiencyofthoseadditionstoaggregate(sustainable)productioncapacity.32Thisisthenexusthroughwhichpublic“researchpolicy”interventionsthatboostinvestmentsinscienceandR&Dcanpositivelyaffectsocialwelfarebyloweringthecostsofswitchingtoproductionsystemscharacterizedbylow,orinthelimit“GHGemissions‐free”technologies. Nevertheless,theresearchapproachpursuedheregivesprioritytounderstandingtheinter‐temporalresourceallocationrequirementsofaprogramoftechnologicalchangesthatcouldhaltglobalwarmingbycompletingthetransitiontoa“green”(zeronetCO2‐emission)productionregimewithinthepossiblybrieffiniteintervalthatremainsbeforeEarth’sclimateisdrivenbeyondacatastrophictippingpoint.Thispaperformulatesadeterministicmulti‐phasemodelofajust‐in‐timetransitionthatpermitanalysisoftherequirementsofthetransitionpathsthatcanavertthatterribleoutcomeinawelfare‐optimalways,eachbeingconditionalontheconjecturedtippingpointconcentrationlevelofCO2andthearrayoftechnologicaloptionsthatcanbeexercisedtostopshortofthatpoint.

InproceedinginthiswaywearecognizantofthecontroversialpropositionadvancedbyWeitzman(2009b),thatthescientificuncertaintysurroundingthebehaviorofthegeo‐physicalsystem,suchasthedistributionofthe“climatesensitivity”parameter,raisesthepossibilityofcatastrophicallylargeoutcomesthatcannotbeignoredbysupposingtheirmaterializationwouldbegovernedbythevanishinglysmalllikelihoodsfoundattheextremaof‘thin‐tailed”probabilitydistributions.Indeed,itseemsquitesensibletoviewsettinglowtargetsforthepermissibleaccumulationof

31Forpurposesofourmodeldescribedbelow,atmosphericGHG(ppmv)concentrationlevelsaregivenbyaninitialbaselinelevelplusascalarfunctionoftheintegralof(CO2‐e)emissionsfromthebaselinedate,thelatterbeingproportionaltothemeanrateofCO2emittedperunitofoutputproduced(proportionaltoutilizedcapacity)andnotbeingabsorbedbytheforestsandtheupperandlowerocean.ThissimplificationignoresthelageffectsofemissionsonchangesinatmosphericCO2thatresultfromthecarbon‐cyclediffusionofthegasbetweentheatmosphereandtheupperocean,betweentheupperoceanandthelowerocean,andtheupperoceanandtheatmosphere.Inadditionitlinearizestherelationshipbetweentheatmosphericconcentrationofcarbonrelativetoitslevelatabasedate(Et/E0,inournotation)andtheabsolutegaininradiativeforcingfromtheatmosphere,Ft.–F0.WidelyusedIAMs‐‐e.g.,versionsofDICEduetoNordhaus(2002,2007)–typicallyrepresentthechangeinatmosphericradiativeforcingastakingtheformΔFt=η[log(Et/E0)–log(2)]withadjustmentsforthedirectandindirecteffectsofradiativeforcingfromtheupperandloweroceans.Ignoringthelatter,andthelagsintherelationshipbetweenchangesintheradiativeforcingandthoseinEarth’ssurfacetemperature,theparameterηistheapproximate“climatesensitivity”:theexpectedlong‐rungaininTrelativetoitsbaselevelresultingfromdoublingtheatmosphericCO2concentration.Oursimplifieddynamicsofthegeophysicalsubsystemismoreacceptableinmodelingthetransitionpathstoclimatestabilizationthanitwouldbeinsimulatingthecourseofcarbonemissionsandtemperaturechangesoverthe600yearlongtimespanofoptimally”moderated”CO2emissionsenvisagedbyDICE(2007)anditsprecursorIAMs.

32Presently,R&Doutcomesarecompletelydeterministicinourmodel,butweenvisagetheintroductionofstochasticityinseveralrelationships,includingthisone.

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GHGsintheEarth’satmospheretobeaformof“insuranceagainstcatastrophicclimatedamages”especiallywhentheirexpectedmagnitudecannotbereliablygauged,asDeCanio(2003)andWeitzman(2010)havesuggested.33

Atthesametime,however,wearepersuadedthatheedingthefindingsofclimatescientistsmilitatesstronglyagainstcontinuingtoworkwithintheacceptedframeworkoftheIAMresearchliteratureforreasonsthataredistinctfrom,andfarmorecompellingthantroublesomethoughtsthattherobustnessofinter‐temporalcost‐benefitanalysismaybeimperiledbytheexistenceof“fat‐tailed”probabilitydistributions,orthatinconceivablylargedamagestohumanitymightrenderitsapplicationespeciallymisleadinginthecontextofdesigningclimatepolicy.Theparticularfindingsaboutthephenomenonofapotentialclimatecatastrophearethoseconcerningitsform,whichalsohasimplicationsforthemagnitudeoftheentaileddamages.Abruptclimatechangesintheformof“climateflickering”introducemajordiscontinuities,sothattorepresentthedynamicsoftheclimatesystemproperlyinanintegratedpolicyassessmentmodelwouldvitiatehopesofbeingabletoidentifythesocialwelfareefficientprogramofinterventioninresponsetoglobalwarmingbyconsistentapplicationofoptimalcontrolanalysis.Discontinuitiesintroduceinextricablenon‐convexitiesinoptimizationfunction,andconvexityisnecessarytoassurethatandoptimalsolutionexists.34Ignoringthe

33Asdisturbingasthe“dismaltheorem”advancedbyWeitzman(2009a,2009b)atfirstappearedtobe,especiallyforeconomistsreluctanttodiscardcost‐benefitanalysis‐‐awidelyappliedandgenerallyusefultoolforquantitativepolicyanalysis,the“fat‐tailsproblem”groundedinreality,andnotanartifactofremediabletechnicalfeaturesofWeitzman’smodel,SeeMillner(2012)foralucidandinsightfulreviewofthecontroversyignitedbyWeitzman’s“dismaltheorem,”whichpointsoutthattheemergenceofa“fat‐tailed”distributioninWeitzman’smathematicalmodelresultsfromtheintroductionofBayesianstatistics;notfromtheuncertaintiesthatdoubtlessremaininscientificunderstandingaboutthedeterminantsofsuchkeymattersas“theclimatesensitivity”orthewhereaboutsofcatastrophic“tippingpoints”.Furthermore,asMillnerhasshown,theapparentlydismalconclusionsforeconomicpolicyanalysis(duetothenon‐existenceofsolutionstocost‐benefitcalculationsinvolvingpossiblyenormousdamages)areanartifactoftheconstantrelativeriskaversion(CRRA)propertyimplicitinthetraditionalspecificationoftheformofthesocialutilityfunction.This,too,showntobetechnicallyremediable;the“harmonicabsoluteriskaversion”(HARA)utilityfunction‐‐ageneralizationofthetraditional(CRRA)utilityfunctionthatiswidelyusedinthefinanceliterature‐‐notonlyyieldsfinitewelfaremeasureswhenrisksarefat‐tailed;underplausibleparameterconditionsitalsomakespolicyevaluationsrelativelyinsensitivetothetailsoftheconsumptiondistribution.

34ThisisthecriticalpointmadebyHallandBehl(2006:esp.pp.460‐463).Givenitsimportance,theircleararticulationofthedefectsarisingfromthefailureofthefieldofeconomicresearchtopayadequateattentiontothephenomenarevealedbytheadvancesinpaleoclimatologyremainsinadequatelyrecognized,andalthoughitmeritsrepeatinginextenso,thefollowsummaryextractwillhavetosufficehere:“Abruptclimatechange,bothwarmingandcooling,wouldresultinphysicalandeconomicdestructionofthecapitalstock…andtherateofreturnoninvestmentwouldbefurtheralteredinadiscontinuousmannerwitheachclimateflickerandtheexpectationofadditionalclimateflickering….Thedestructionofcapitalfromclimateflickeringshouldchangetheexpectedreturnoncapitalinvestments.Thecostofadaptingtoclimatechangeshouldincreasewithflickeringtakenintoaccount.Thevalueoftechnologicalchangetoadapttosuddendecreasesintemperature,precipitationandambientCO2,forexample,shouldbelostwithsubsequentsuddenincreasesintemperature,precipitation,andambientCO2.ThereisafundamentalproblemwitheconomicoptimizationmodelslikeDICEforeconomicanalysisofclimateinstability:asolutiondoesnotexist.Economicoptimizationrequiresconvexity,andclimateinstabilityresultsinnon‐convexoptimizationfunctions.”(p.460)

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non‐convexitiescansavetheresultingmodel’s“solve‐ability.”ButGalileotaughtusthatto“savethephenomena”wouldbebetter–evenwiththetroubleofhavingtodiscardthemisleadingyetconvenientlyfamiliarmodel.

Thetiming,aswellasthemagnitudeofremedialactionsinresponsetothechallengesposedbyglobalwarmingisprioritytopicofconcern.TheIntergovernmentalPanelonClimateChange(IPCC)hasconcurredintheconclusionthatthereisacriticalthresholdat2degreesC.ofglobalwarmingfromtheearth’spreindustrialmeantemperaturebeyondwhichtheprobabilityofbeingabletoavertcatastrophicrunawayglobalwarmingbeginstodropbelow50‐50.DuetothecumulativevolumeofpersistingGHGemissionsupuntilthispointintime,however,theworldalreadyiscommittedtoafutureriseinmeanglobaltemperature(relativetothepresent)ontheorderof0.5to1degreesKelvin–evenifcarbonemissionswerecompletelystopped.Evenifthe”tipping‐point”weresetatatemperaturegainof3degrees,thisleavesrelativelylittleroomforfurtherwarmingwithoutcatastrophicconsequences,astheSternReportpointedout(Stern,2006:p.15).Theimplicationisthatundera“businessasusual”rateofGHGemissionstheremaynotbeverymuchtimeleftbeforethecriticalthresholdwillbecrossedandtheproblemfacingtheworld’spopulationwillbetransformedtooneoflearningtoadaptasbestwecantothealmostunimaginablemountingdamageandsocietaldisruptionsentailedincopingwithadestabilizedclimatesystem.

Againstthisworrisomebackground,itisaparticularlyharshfactofpresenteconomiclifethattomakemajorchangesinproductionsystemsalsotakesconsiderabletime(andresources).Thisisbecausethetransitionfromcarbon‐basedproductiontocarbon‐freeproductioninvolvesfirstthe(further)developmentofcarbon‐freealternativesandsecondlythesubsequentimplementationofthesealternativesthroughinvestmentintangiblecapitalformationprojects,includinginfrastructuremodificationsthatwillhavelonggestationperiods.Furthermore,thedevelopmentofthenewtechnologiesrequiredwillentailthecommitmentofresourcestoR&Dprojectsofuncertainandpossibleextendeddurations.TheclaimsoftheseprogramsoftangibleandintangibleinvestmentthereforewillpressuponconsumptionlevelsforsomeperiodwithoutyieldingresourcesavingsorsignificantlyloweringtherateofGHGemissions.

Thus,therealityoftransitioningtowardsacarbon‐freeeconomyintimetoavoidcrossingthecriticaltemperaturethresholdintoclimateinstabilitywillbe,atbest,anuncomfortable,unremittingandperilousjourneyforhumanity.TheparticularanalyticalchallengethatistakenupinthispaperishowbesttoscheduleR&Dexpendituresandrelatedtangiblecapitalformationatthemacro‐levelsoastomaximisethesocietalwelfare(ormorerealisticallyminimizethedamagetosocialwelfare)associatedwiththeentiretransitionpathtowardsacarbon‐freeproductionregimeinaGHG‐stabilizedenvironment,takingintoaccountthediversionofresourcesawayfromconsumptionthatthoseinvestmentsentail.Towardsthisendwehaveconstructedamulti‐phase,multi‐technologyendogenousgrowthmodelthatallowsfortheexpenditureofR&Dresourcesonthecreationandimprovementof“carbon‐freetechnology”andacknowledgesthatthisformofinvestmentdivertsrealresourcesfromconsumptionand

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henceadverselyaffectssocietalwelfareintheshortrun(doing‘nothing’wouldhavenegativewelfareeffectsinthelongrun,however).

Takentogether,theeconomicandgeo‐physicalsub‐systemsposeatimingproblem,sinceoldcarbon‐basedtechnologiesgenerateCO2emissions,andpostponingtheimplementationofnew,carbon‐freetechnologiesreducesthetimeavailableforbuildingupnewcapacitywhilecumulativeemissionsofCO2(andotherGHG)remainbelowtheassociatedcriticalthresholdconcentration(andassociatedmeanglobalsurfacetemperature)thatcantriggertheonsetofclimateinstability.StartingsoonenoughtoundertaketheR&D(whichtakesbothtimeandresources)canmakeavailableabetterperformingfamilyoflow‐carbonandcarbon‐freetechnologiesintimetoembodythatknowledgeinnewproductionfacilitiesandavoidcrossingthat“tippingpoint”,buthowsoonissoonenoughwilldependupontherateofR&Dinvestmentsandtheirimpactontheproductivityofcarbon‐freeproductionfacilities,aswellastheeconomy’scapacitytoreplace“dirty”carbon‐usingcapacitywithacarbon‐freecapitalstock.

Thefollowingsectionofthepaperdemonstrateshowthisandrelatedquestionscanbeansweredbyformulatingandsolvingasequenceofoptimalcontrolsub‐problemsforeachdistinctivephaseinthetransitionfroma“business‐as‐usual”carbonbasedeconomytoasustainablecarbonfreeeconomy,andthentyingoptimizedphasestogetherin“stackedHamiltonians”bytheuseoftransversalityconditionsthatguaranteetheoptimalityofthetransitionpathasawhole.Thesub‐sectionsof2applythisapproachindevelopingincreasinglymorecomplicatedmodels,allconstructedonthebasisofthemostelementarygrowthmodel.Section3commentsonanumberofinsightsthatthethreepartialmodelsprovideaboutquestionsoftiminginexercisingvarioustechnology‐fixoptions.Italsoreportspreliminaryresultsfromtheuseofsensitivityanalysistoassesstheeffectsonoptimalinvestmentpathsofvariationsintheassumedlocationofclimate“tippingpoints”.ThepaperconcludesinSection4withabriefreviewofwhathasbeenlearned,whatremainstobestudied,andtheproximatenextstepsinpursuingthislineofresearchintothedesignandimplementationrequirementforasuccessfultechnologyfixforglobalclimateinstability.

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4.Modelingthephasesofatimelytransitiontoanessentially“carbon‐free”productionsystem

4.0Anincrementalmodel‐buildingagenda

Ratherthanundertakingfromtheoutsettospecifythestructureofanequivalentdeterministicdynamicalsystemthatincorporatesnumerousfeaturesofeachofthevariouspossibletechnologicalstrategiescouldbedeployedtostabilizeglobalclimate,weproceedtowardsthatgoalinastep‐by‐stepmanner,takingthreediscretepartialmodel‐buildingsteps,andinvestigatingwhatcanbelearnedaboutthedynamicsofanoptimaltransitionpathfromeachofthem,consideredseparately.

We start from a basic model in which there are two available technologicaloptions, a mature carbon‐intensive technology that is embodied in existing fixedproduction facilities and a carbon‐free technology that has yet to be deployed byappropriate capital formation. The tableau in Figure 1 (below) provides a summaryoverviewofactivitiesthatdistinguishthethreephasesofthetransitionthattransformsthe economyof ourBasicModel froma carbon‐burning “business asusual” regime toone inwhichtheswitch toproducingexclusivelywithcarbon‐freecapital facilitieshasstabilizedtheglobalclimate.Thetableau’shorizontalcolumnsindicatethetwodifferentproductiontechnologiesthatcanbeusedbythegenericeconomy,whereasthedifferentkindoftangible(andintangiblearecompatiblewithefficientresourceallocationineachphase of the transition path investments) that may be undertaken are shown in therows.Theshading(inred, for theBasicModel)showsthecombinationsofconcurrentinvestmentandproductionactivitiesthat.

Figure1:BasicModel(Red)

Investment  Production (Capacity in Operation) 

 Old Carbon High emission rate 

Greened Carbon Lower emission rate

Carbon Free Zero emission rate 

Carbon‐using capital KA 

production business as usual 

   

Carbon‐free capital KB 

joint production    joint production 

   carbon free production 

R&D on carbon‐‐free technologies       

R&D on geo‐engineering 

     

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Next,weintroduceintotheBasicModelset‐upthepossibilityofundertakingR&Dexpendituresduringthe“businessasusualphase”.Theseinvestmentsin“directedtechnologicalchange”areaimedtoreducetheunitcapitalcostsofproductionfacilitiesembodyingthecarbon‐freetechnology,raisingtheaverageproductivityofKBenoughtomatchthatofcapacitybasedonthecarbon‐usingtechnology.Inthiselementarymodelofathree‐phase“endogenousR&D‐driventransition”,onlywhenthattechnologicalgoalisattaineddoesR&Dexpenditures(andfurthertangibleinvestmentincarbon‐intensiveproductioncapacity)cometoahalt,andtangiblecapitalformationbeginsdeployingthecarbon‐freetechnology.ThisisindicatedinFigure2bythetableau’sblueshadedareas.

Figure2:BasicModelwithR&D(Blue)

Thethirdofthepartialmodelstobeexaminedextendsthestructureofthebasicmodelbyallowingfortheexploitationofathirdclassoftechnologicalopportunities.ThesedonotrequiresignificantR&Dinvestments,sincetheymakeuseofknown“core”engineeringtechniquestoprovidean“intermediate”,lesscarbon‐intensivesetofproductiontechnologiesthatineffectserveto“green”existingcarbon‐usingdirectproductionfacilitiesandinfrastructure.BecausetheyarecharacterizedbylowerratesofCO2emissionsperunitofcapitalthantheoldcarbon‐basedtechnologies(evenifahighercapitalcostperunitofoutput),theyprovideareducedemissions‐outputratio.Thustheycan“buytime”tomakethetangibleinvestmentsneededtoswitchtoacarbon‐freeproductionregime.Figures3.1and3.2displayintableauformthepairofalternative5‐phasetrajectoriesthatariseinthecaseofthebuy‐timemodel.Eachversioncanbesolveforanoptimaltransitionpath,buttofindtheoptimumoptimorumitisnecessarytoevaluateandcomparetheimpliedpresentvalueofthesocialwelfareindexassociatedwitheachofthem.35

35Notethattheproductionconstraintsinthemodel,includingthosederivedfromthetechnologicalparametervalues,maydeterminewhich,betweenalternativetrajectoriescansatisfytheoptimality

Investment  Production (Capacity in Operation)

 Old Carbon High emission rate

Greened Carbon Lower emission rate 

Carbon Free Zero emission rate 

Carbon‐using capital KA 

production  business as usual 

   

Carbon‐free capital KB 

joint production   joint production 

   carbon free production 

R&D on carbon‐free technology 

production  business as usual 

   

R&D on geo‐ engineering 

     

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Figure3.1:BuyTimeModelTrajectory1(DarkGreen)

Investment  Production (Capacity in Operation)

 Old Carbon High emission rate 

Greened Carbon Lower emission rate 

Carbon Free Zero emission rate 

Carbon‐using capital KA 

productionbusiness as usual 

   

Carbon‐economizing KD (retrofitted KA)  

joint old & green carbon production 

joint old & green carbon production 

 

 Greened carbon production 

 

Carbon‐free capital KB 

 Joint greened carbon and carbon‐free production 

Joint greened carbon and carbon‐free production 

    Carbon‐free regime 

Figure3.2:BuytimemodelTrajectory2(LightGreen)

Investment  Production (Capacity in Operation)

 Old Carbon High emission rate 

Greened Carbon Lower emission rate 

Carbon Free Zero emission rate 

Carbon‐using capital KA 

production business as usual 

   

Carbon‐economizing KD (retrofitted KA) 

Joint old and green carbon production 

Joint old and green carbon production 

 

 Carbon‐free capital KB 

Joint old and green carbon, carbon‐free production 

Joint old and green carbon, carbon‐free production 

Joint old and green carbon, carbon‐free production 

 Green carbon and carbon‐free production 

Green carbon and carbon‐free production 

   Carbon‐free production 

Intheoptimalcontrolsolutionseachofthethreeforegoing“partial”modelsofaclimatestabilizingtransition,theinternallyoptimizedphasesofthemodelaretiedtogetherbytransversalityconditions.Thatmakesitpossibletoobtainthe“requirements”oftheentireoptimaltransitionpath,intermsoftheoptimumdurationsofitsphases,andtheoptimizedwithin‐phaselevelsofactivityforproduction,consumption,andinvestmentrates(boththeintangibleR&Dandthealternativetangibleformsoftechnology‐embodyingcapitalformation)–aswellastheimpliedflowsofCO2emissionsuptothepointatwhichtheglobaleconomy’sproductionregime

requirements,sothatanswertothequestionofwhichtochoosebecomeanempiricalmatter.Seesection2.3forfurtherdiscussion.

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reachesthegoalofacarbon‐freestatethatavertstheonsetofirreversibleclimateinstability.Eveninthesimplestofpossiblegrowth‐modelsettingthathasbeenspecified,thesolutionsofeachofthesesuccessivelymorecomplicatedmodelstofindtheirrespectiveoveralloptimaltransitionpathsmustbeobtainedbynumericalanalysisoftheresultingsystemsof“stackedHamiltonians”–thedetailsofwhichfollowingsectiondiscussesadseriatim.

ThismodellingframeworkdiffersfromthestandardAKgrowthmodelinitsspecificationofdistinctphasesthatformthetransitionpath,phasesduringwhichproductioncapacityembodyingnew(comparatively“clean”)technologiesisbuiltupcapacityembodyingold(“dirtier’)techniquesisrundownandeventuallydiscarded.Acentraltaskfortheanalysisofeachofthemodels,therefore,mustbetofindtheoptimalconfigurationofspecificinvestmentandproductionactivitiesinconjunctionwiththetheiroptimalsequencingonthetransitionpathtoaviablestabilizedclimate.

Thequestionsaddressedbythismodellingexercisearenotpredictive.Ratherthanventuringtothrowlightonwhatwillhappen,theyaskwhathastobedone,andwhenmustitbedoneinordertogetfromacarbon‐basedproductionsystemtoacarbonfreeproductionsystemthatwouldavertrunawayglobalwarming,whilemaintainingthehighestpresentvalueofsocialwelfarethatisconsistentwithattainingthatgoal.

OurstartingpointintheanalysisistosetupaHamiltoniansystemwithastandardCIESinter‐temporalutilityfunctioninwhichconsumption(percapita)isitsargument,sincepopulationisimplicitlyassumedtobeconstantandthereforecanbesuppressed.36Similarly,laborserviceinputsinproductionactivitiesareassumedconstant,whichisconsistentwithourhavingselectedthesimplestpossibleoveralldynamicsetting,namely,theAK‐modelofendogenouseconomicgrowthduetoRebelo(1991),andBarroandSala‐i‐Martin(2004,ch.4)astheplatformonwhichtodeveloptheBasicModeloftechnologyswitching.WehaveextendedclassicAK‐framework,however,byreplacingitsspecificationofasingle,linearcapital‐usingproductiontechnologybytheassumptionthattherearemultiplediscrete(linear)technologiesthatmaybeusedeithersimultaneouslyorsequentially,includingonethatcanbeenhancedbydirectedinvestmentsinR&Dactivities.

Thereducedunitcostofcapitalembodyingthecarbon‐freetechnologyasaresultofdirectedR&Dexpenditures,however,isonlyrealizedthroughthetechnology’ssubsequentdeploymentingrosstangiblecapitalformation.Toputasomewhatsharperpointonthis,itisnotenoughtothinkaboutR&Dpoliciesandprograms.Mechanismsofdiffusionintouse,asdistinctfromthedisseminationofinformationabouttechnological

36Readersinterestedinthedetailsofthestructuralequationsandsolutionsofthemodelsdiscussedheremayconsultthe“TechnicalAnnex:ModelingOptimalMultiphaseTransitionPathstoSustainableGrowth”(July2011),whichisavailableathttp://siepr.stanford.edu/system/files/shared/OptimalMulti.pdf,orcanbedownloadedasasupplementtoanearlierversionofthispaper(presentedon12/14attheSIEPR‐GEEGSocialScienceandTechnologySeminar)at:http://siepr.stanford.edu/programs/SST_Seminars/index.html.

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innovationsalsomustbefiguredexplicitlyamongtherequirementsofa“technologyfix.”Similarly,inthe“buytimemodel,”theuseofexistingcoreengineeringmethodstoreducetheratioofCO2‐emissionstorealoutputincarbon‐basedproductionfacilitiesentailsincrementaltangibleinvestmentsinretrofittingpartsoftheexisting(KA)capitalstock.

Thisfeatureoftheapproachpursuedhererestsonthepremisethatembodimentinphysicalcapitalgoodsisnecessarytoimplementchangesinthetechnologiesthatwouldlowertheglobalproductionregime’scarbon‐intensity,andinthosethatwouldreducetheCO2emissions‐intensityperunitofoutputfromthecarbon‐fuelledproductionfacilitiesproduction.The“embodiment”assumptionisespeciallyappropriatewhenconsideringtheimpactoftechnicalinnovationsinenergysupplysystems.37Explicitrecognitionofthisconstitutesanotherimportantrespectinwhichthepresentframeworkofanalysis(anditsaccountofthedynamicsoftheoptimalclimate‐stabilizingtransitionpath)departsfromthewaysinwhichtheeffectsofendogenoustechnologicalchangehavebeentreatedinpreviouseconomiccontributionstointegratedmodelingandassessmentofclimatepolicymeasures.38

AlthoughtheAK‐settingisextremelysimple,becauseweallowfordifferentphasesinthetransitionfromcarbonbasedtocarbonfreeproduction,theresultingmodelisabletogenerateasetoftimepathsforthetransitiontoastabilizedclimate(andstationarylevelofatmosphericGHGconcentration)that,inpractice,canbedeterminedonlybytheuseofnumericalmethods.39Afuture,morecomplicated

37Thedevelopmentanduseofenergytechnologiesisviewedasanintegratedsystemcomprisingresearchdiscoveriesandinventions,thecreationofcommercialproductsandprocesses,theirinitialdeploymentandadoptionintocommercialoperations,andsubsequentwiderdiffusion–theviewembracedrecentlybytheReportofthePresident’sCouncilofAdvisorsonScienceandTechnology(PCAST,2012).Accordingly,ErnestMoniz(2012:p.82),formerUndersecretaryoftheU.S.DepartmentofEnergyandaPCASTmember,emphasizestheimportanceoftangiblefixedcapitalformationinconsideringpoliciesdesignedtostimulate“energytechnologyinnovation”:“Adoptionanddiffusionarethestagesatwhichmaterialityof[novel]productsandprocessesarerealized(ornot).Innovation,asIuseithere,referstotheend‐to‐endsystemincludingmarketdiffusion,notfront‐endR&Dalone.”Bycontrast

38Onemaycomparetheimplicitassumption–commontoeachofthefollowingsalientcontributionsonthesubject‐‐thattechnologicalchange(whetherexogenousorendogenous)isdisembodied,andthereforenotaffectedbytherateofinvestmentintangiblecapitalformation:GoulderandSchneider(1999),Nordhaus(2002),Bounanno,CarraroandGaleotti(2003),Edenhofer,CarrirandGaleotti(2004),Popp(2004),Lessman,Kemfertetal.(2006),SueWing(2006).Ratherstrikingly,theusefulsurveyprovidedbyGillingham,NewellandPizer(2008)ofthedifferentapproachesusedinmodelingendogenoustechnologicalchangeinthecontextofclimatepolicyassessmentmodels,doesnotrefertothedistinctionbetweenembodiedanddisembodiedtechnologicalchange,andomitsmentionofadoptionanddiffusionfromitscommentsonthewaysinwhicheconomistsrepresentR&D,andlearning‐by‐doingasdeterminantsofgeneralorenergysector‐specificchangeinproductivityorGHG‐emissionintensity.

39Giventhefactthatwedistinguishexplicitlybetweendifferentsub‐phasesduringthetransition,weendupwitha‘stack’ofHamiltonianproblemsthatarelinkedtogetherthroughasetoftransversalityconditions(TVC’s),SeeLeonardandVanLong(1992:esp.Ch.7).Thefirst‐orderconditions,incombinationwiththeTVC’sandthegiveninitialvaluesofthestatevariables(andthegiventerminalvalueofcumulativeemissions),giverisetoasetofstronglynon‐linearconstraintsontheremaininginitialvaluesofthemodel’simpliedtimepathsforco‐stateandcontrolvariables.Usingtheseinitialvalues,thesimplicityoftheAK‐settingallowsclosedformanalyticalexpressionstobeobtaineddirectintegrationfor

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extensionofthisset‐upisenvisaged,inwhichthecumulativeincreaseinGHGconcentration,orthemeanglobalsurfacetemperaturegainassociatedwithit,enterstheutilityfunctionnegatively.40

Thetransitionphasesmentionedearlierarelinkedtogetherthroughtransversalityconditionsthatimplicitlydefinethephasechangesintermsofrathergeneraloptimalityconditionsthatoftengiverisetoconditionsontheco‐statevariablesthathaveaclear‐cuteconomicinterpretation.Forexample,itcanbeshownthatitisneveroptimaltosimultaneouslyinvestintwoexistingtechnologiesthataredifferentwithrespecttotheircapitalproductivityandtheiremissioncharacteristics.

Thus,inthecurrentmodelsetting,theexistenceofacumulativeemissiontipping‐pointwillgeneratenotionalemissioncostsassociatedwiththeuseofcarbon‐basedcapital.41Investmentinthelattertypeofcapitalwillstopandthatincarbonfreecapitalwillstartthemomenttheshadowpriceofcarbonbasedcapitalfallsbelowthatofcarbonfreecapital.Asthecostofinvestmentisrepresentedbythewelfarelossassociatedwithconsumptionforegone,andasoneunitofinvestmentgeneratesoneunitofconsumptionforegoneinbothcases,thistransversalityconditionimpliestherequirementthatinvestmentwilltakeplaceinthetechnologythatgeneratesthehighestmarginalnetwelfareperunitofinvestment.Likewise,thediscardingofexistingcapacityistypicallyanactivitythatsignalstheendofaparticularphaseandthebeginningofthenextone.

Theoptimumtimingofsuchaphasechange,andhencethephases’durations,willbegovernedbyageneraltransversalitycondition,namelythattheshadowpriceofanincrementalunitofproductioncapacityembodyingtheparticulartypeoftechnologyshouldbezeroattheexactmomentthatitistakenoutofproduction;otherwise,ifithadapositiveproductiveuse,whydiscardit?Thistransversalityconditionturnsouttobe

thetimepathsofallvariables—exceptforthecumulativestockofGHGemissions.Theresultingpathsthemselvesareinparthighlynon‐linearandlargelyintractable(exceptfortheirunderlyingroots/structuralequations)necessitatingrecoursetonumericalexercisesinordertoinvestigatethepropertiesofthemodel,someofwhicharenotintuitivelytransparentapriori.Moreover,thepathforcumulativeemissionscannotbeobtainedbyanalyticalmeansandrequiresnumericalintegrationstartingfromsomeinitialguessofthelengthoftheBAUphase.TheoptimumdurationoftheBAUphasethenisimpliedbytherequirementthattotalcumulativeemissionsovertheentiretransition(allphases)shouldjustmatchapre‐specified“threshold”value.Evidentlyadifferentapproachwillberequiredbyastochasticformulationofthetransitionprocess–ofwhichthemodeldiscussedhererepresentstheequivalentdeterministicsystem.

40SeeArrow(2009)andWeitzman(2009a,b)onthesignificanceofspecifyinganadditivetemperatureeffectthatisnegative,interpretingthisasadirect“environmental”effectuponsocialwelfare.Analternativeformulationisavailable‐‐inwhichthenegativeterminthesocialutilityfunctionistheinverseofthedifferencethecritical“threshold,”or“tippingpoint”temperature(beyondwhichthewarmingprocessisexpectedtobecomeself‐reinforcing)andEarth’sprevailingglobalmeansurfacetemperature.Thisformulationwouldhaveessentiallythesameconsequencesforinter‐temporalresourceallocation,butitwouldadmittheadversepsychiceffectofapproachingtheexpectedpointatwhichhumanitywill,forallintentsandpurposeshavelostitsabilitytostabilizethewarmingtrendandavertthecatastrophiconsetofclimateinstability.

41Weusetheterm“notional”heretodenotetheexistenceofarealcost,thatis,however,generallynot,oratleastnotfully,paidforinpractice.

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equivalenttotherequirementthataunitofexistingcarbon‐basedcapitalshouldbediscardedatthemomentthatthemarginalwelfarebenefitsofusingthatunitofcarbon‐basedcapacitydropbelowthecorrespondingmarginalemissioncosts.42

4.1TheBasicModel–TechnologySwitching

Thefirstandfoundationalversionofoursuiteofmulti‐phasetransitionmodelsiscalled(appropriatelyenough)theBasicModel.Inthistherearetwoalreadyavailableproductiontechnologies,onethatiscarbon‐basedandalreadyinuse,andacarbon‐freetechnologythatattheoutsetisyettobedeployed.43Thisset‐upcreatesthepossibilityoftherebeingthreedistinctphases.ThefeaturesofthisBasic(“technologyswitching”)modelthathavebeenalreadydescribedaresummarizedbythesystemofequationspresentedinTable1(below).

Table1Phase‐SpecificEquationsoftheBasic3‐PhaseTransitionModel

______________________________________________________________________________________________ (carbon‐basedproduction,BAU,JPR)

(netinvestment,BAU)

(netinvestment,JPR)

(NetCO2emissionsflow;,BAU,JPR)

(carbon‐freeproductionJPR,CFR)

. (netinvestment,CFR)

. (netinvestment,JPR)

+ (CumulativenetCO23missions)

. / 1 (intertemp.socialwelfare,ALLphases)

⟺ (TVCdefiningTJPR(equality

Hamiltonians))

⟺ (TVCdefiningTCFR:deactivationofKA)

=0 (TVCvalueofdeactivatedcapital=0)

→ . 0 (TVC,standardAKTVCCFRphase)

42Thisconditioncloselyresemblesthenegativequasi‐rentconditionthatgovernstheeconomiclifetimeofclay‐clayvintagesinaperfectcompetitionsetting(seeMalcomson(1975),forexample).

43Forpurposesofthisanalysisitissupposedthattheperiodunderconsiderationcommenceswhenacarbon‐free(B)technologybecomesavailable,althoughwithaverageproductivitylessthanthatofthecapital(KA)embodyingthecarbon‐usingtechnology;equivalently,thecostoftheproductioncapacity(KB)perunitofoutputinitiallyexceedsthatofKA.

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AsecondphaseopenswiththestartofpositiveinvestmentinfacilitiesembodyingtheCFRtechnology,andthecessationofBAUcapitalformation,thereforemarkstheopeningoftheBasicmodel’ssecondphase.Fromthispointforwardthereisnegativenetinvestmentincarbon‐usingfacilities,sincethephysicaldepreciationoftheexistingstockisnolongerbeingoffsetbypositivegrossinvestmentincapitalofthattype.ThisphaseoftheBasicmodelisreferredtoas‘thejointproduction’(JPR)phase,ascapitalgoodsembodyingbothclassesoftechnologybeingusedtogenerateoutput.Thetransitiontoacarbon‐freeproductionregimeandclimatestabilizationiscompletewiththeshut‐downoftheremainingcarbon‐usingfacilitiesand,hence,stoppageoftheflowofCO2emissionsjustasthecumulativestockofemissions(andthetemperature)approachtheirrespectivecriticalthresholdlevels.Thatmarksthebeginningofthethirdandfinalphaseofsystem’stransitiontosustainable,carbon‐freegrowth.44

Theintensityoftheflowsduringeachphase,aswellasthemomentsintimeatwhichthevariousphasechangesarescheduled,allfollowfromthefirst‐orderconditions(FOCS),thetransversalityconditionsandfromthegiveninitialandterminalvaluesforthestate‐variablesthatarepartoftheoptimumcontrolproblem.Eventsandphase‐changesinthecontextoftheBasicModelaresummarisedinFigure4(below),

44AstheBAUtechnologyhashigherinitialcapitalproductivitythanCFRtechnology,welfarewouldnotbemaximisediftheflowofCO2emissionsceasedbeforethecumulativeemissionlimitwasreached.

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whichshowsthedevelopmentovertimeofthestockofcarbon‐basedcapitalKA,thestockofcarbon‐freecapitalKBandcumulativeemissions,GCO2

Thepointsmarkedonthetime‐axisoftheFigure(TU,TJ,TF)indicatetheoptimalmomentsatwhichtherespectivephases(BAU,JPR,CFR)begin.ItmaybenotedthatalthoughthecumulativestockofemissionscontinuestoriseduringtheJPRphase,isdoessoatadecreasingrateasthestockofcarbon‐basedcapitalKAisrundownandreplacedbyitscarbon‐freesubstitute.Thefinal,carbon‐freeproductionphasestartswhencumulativeemissionsatmosphericconcentration(GCO2)almostreachestheexpectedthrclimate“tipping‐point,andthecurvemarkedCO2becomesflattotherightofTF.

Evidently,thevariousphasesinthemodelarequalitativelydifferent.Thefirstphase,i.e.theBAUphase,usesahighgrowthtechnologywhichunfortunatelyquicklyraisesthestockofcumulativeCO2emissionsthatisboundedfromabovebythecumulativethreshold.Beforethatlevelisreached,investmentincarbonfreetechnologymusthavetakenplaceduringphaseJPRtobringcarbonfreeproductioncapacityuptoalevelwheretheswitchfromusingcarbon‐basedcapacitytousingcarbonfreecapacitywouldnotforcechangesinconsumptionlevelsthataretoodisruptive,sinceconsumersdislikeconsumptionshocks,asisimpliedbyouruseofasocialwelfarefunctionthatdependsuponthepresent(discounted)discountedlevelsofpercapitaconsumption,andisofthe(CIES)formallowingforrelativeriskaversion.

ort>TFtheworldis“green”,and,giventhemoreexpensivecarbon‐freeproductionfacilitiesthatarerequiredtostabilizetheatmosphericCO2‐equivalentconcentrationlevel,theoutput(percapita)willhavetogrowforsomewhileattherelativelyslowpaceatwhichtheKBisaccumulatingwiththegrosscarbon‐freecapitalformationrateconstrainednottocuttooheavilyintoconsumption.Eventually,however,thebuild‐upofthecarbon‐freecapitalstockissufficienttosupportbothrisingconsumptionandahigherrateofinvestmentinKB,whichthereafteraccumulatesataquickenedpace.45

45ThestructureoftheBasicModelhassomecommonalitieswiththeanalysisinValente(2003)ofatwo‐phaseendogenousgrowthmodelinwhichproductionbasedonessential(energy)inputsobtainedfromexhaustibleresourcesswitchestoa“backstoptechnology”thatprovidesaconstantsupplyofsustained(e.g.,solar)energy.R&Dinvestmentspermitgrowththroughproductivityimprovementsthatoccuratthesameratewitheithertechnologies(althoughthelevelsofproductivitycandiffer),andtheoptimaltimingoftechnologyswitchingisdeterminedbywelfaremaximizationinwhichutilitydependsupondiscountedpercapitaconsumption.Valentesimilarlyobtainsoptimalcontrolsolutionsforeachstageandtiesthesepathstogetherwithtransversalityconditions.But,unlikeinthepresentanalysis,thepointatwhichtherenewabletechnologycanbeefficientlyembodiedintangiblecapitalusedinproductionisnotendogenouslydeterminedbydirectedR&Dexpendituresandthediversionofoutputtobuildingthe“renewables‐base”capitalstock.NorisapositiveshadowpriceexplicitlyattachedtousingtheexhaustibleresourceinValente’sanalysis,becauseitabstractsfromthegeophysicalclimate‐systemconstraintsthataffecttheoptimaltransitionpath.Aswillbeseen,theresearchapproachhereexaminesmuchmorecomplicated,multi‐stagetransitions.

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4.2ABasicModelwithEndogenous(R&D‐driven)TechnologicalChange

InadditiontotheBasicModel,wehavespecifiedaversioninwhichR&DcanbeundertakentoimprovetheproductivityoftheCFRtechnologybeforeitsactualimplementationthroughgrossinvestmentintheCFRtechnology.46R&DrequiresresourcestobeinvestednowinreturnforafutureintangibleassetintheformofknowledgeofhowtoembodyCFRproductiontechniquesinproductionfacilitieswhosecapitalcostperunitofoutputwillbelowerthanisthecaseatpresent.Surprisingly,thisviewoftheroletobeplayedbyR&DincontrollingfutureGHGemissionsissomethingofanoveltyinthesmalleconomicliteraturethathasemployedintegratedassessmentmodellingofclimatepolicyoptions,becauseinsofarasthecontributionofinvestmentsinR&Dto“directed”technologychangeandinnovationhasbeenconsideredatall,the“direction”hasbeentakentobetheloweringofCO2emissionsperunittotaloutputintheeconomy.47Tosharpenthecontrastwiththelatterapproach,Section2.3(below)examinestheoptionofachievinggreaterefficienciesintheuseofcarbon‐basedenergycanbeachievedwithoutR&Dexpenditures,butbyinvestmentsintheengineeringimplementationofexistingtechnologicalknowledgethatwouldresultinhigherunit(tangible)capitalcostsofcarbon‐basedproductionfacilities.48

46vanZonandDavid(2013b)presentsthecompleteanalysisofacalibratedversionoftheBasicmodelwithendogenousR&D(asdescribedhere).ThelatterpaperextensivelyrevisesvanZonandDavid(2012)andaddsamodelthatincorporatesendogenouslytimedupwardshiftintheaverageannualrateof(unscheduled)lossesofproductioncapacityduetotheaccumulationofCO2intheatmosphere.ThequalitativeresultsdisplaythemainsubstantivefindingsofthesolutionsandsensitivityanalysisobtainedwiththepreliminarycalibrationoftheBasic+R&Dmodel.

47Tothebestofourknowledge,theearliestpreviousinvestigationoftheeffectsofallowingforendogenoustechnologicalchangeinacomputationalclimatepolicyassessmentmodelappearsintherelatedpapersbyGoulderandMathai(2000),andGoulderandSchneider(1999),whichspecifytheeffectofR&Dexpendituresonchangesinaneconomy‐widetotalfactorproductivitycoefficient.InthesepioneeringinvestigationsoftheimpactofinducedtechnologicalchangeontheattractivenessofCO2abatementpolicies,absolutechangesinproductivity(orrealmarginalcost)levels,ratherthantheproportionaterateofchangeinproductivitywasspecifiedasapositiveincreasing(decreasing)functionofR&Dexpenditures.InGoulderandSchneider(1999:pp.216,223)thisfunctionalrelationshipnotfurtherrestrictedintheirmathematicalanalysisofa2‐periodmodel;whereasthelinearspecification, B R wasusedintheirdynamicmulti‐periodgeneralequilibriumsimulationstudies.Nordhaus(2002)takesadifferentapproach,ineffectassumingthatinducedresearcheffortfocusessolelyonreducingtheCO2emissionsintensityofproduction.Nordhauspositsaseparateproductionfunctionforcarbon‐basedenergyinputswhichareusedinfixedproportiontothenon‐energyinputsinaneconomy‐wideproductionfunction.Hethenspecifiesthattherateofchangeofthecarbon‐intensitycoefficientinenergyproductionisgivenby(dσ/σ)=‐[ψRβ–Ω],whereΨ>0isaconstantandΩ>0isa(constant)rateofobsolenceofthetechnicalknowledgegainedthroughR&Dandreflectedinσ.TheempiricalfindingsofGriliches(1973),Hall(1995)andothersonthelinkbetweencommercialR&DandindustrialproductivitygrowtharecitedbyNordhausinsupportofthisspecification,althoughingeneralthetime‐spanstowhichthedataonindustry‐levelandfirm‐leveldatarelatearefarshorter,andhardlyoftheglobalsembocopetypicallycontemplatedinIAMmodels.

48Ofcourse,thisdistinctionisnotnecessarybecauseonecanmodelthesituationinwhichR&Dexpendituresareallocatedbetweenthetwo“directions”oftechnologicalchange,loweringraisingtheratioofgrossoutputperunitofCO2emissions,andraisingtheproductivityofcarbon‐freetangiblecapitalusedinproduction.Butbecausethepresentinvestigationisconfinedtomodelingthepathstosuccessfulclimatestabilization,andthetimescaleforthatisfarshorterthanthehundredsofyearscontemplatedintheexistingvariantsoftheNordhaus(1993a,1993b,1999,2002,2007)DICEmodel,itisnot

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Furthermore,inspecifyingtheimpactofsuchR&DinvestmentsontheunitcostofCFRcapitalgoods(KB)wedeliberatelydepartfromthe“R&Dproductionfunction”formulationthatisfamiliarinendogenousgrowthmodelsfollowingLucas(1988),Romer(1990)andAghionandHowitt(1991).RatherthantakingtheinstantaneousrateofimprovementintheproductivityofCFB‐embodyingcapital, /B B ,tobeproportionaltothecurrentabsoluteflowofR&Dresourceinputs,R,asin

0 1B R B ,

analternativespecificationisproposedhere:

( ), 0 1B R B B ,

whereςisaconstantproductivityparameter,and representsthemaximumvaluethatBcanattain.49

Thereareseveralfeaturesofthisspecificationthatargueforits’useinthepresentapplicationscontext.Firstly,ithastheadvantageofintroducingdecreasingreturnstoR&Dinasettingthat,unliketheconventionalendogenousgrowthmodels,excludesthepossibilityofaspecifictechnologybeingrenderedinfinitelyproductive(andsoresultingininfinitelyrapidgrowth)merelybytheapplicationofmoreandmoremassiveR&Dexpendituresatanyparticularmomentintime.50AllowingdecreasingmarginalreturnsinR&Drecognizesthatatagivenstageintheadvanceofknowledgethestateoffundamentalscientificunderstandingofthephysicalprocessesinvolvedmaystillbeinadequatetopermittheeffectiveapplicationofmoreandmoreresourcestothesolutionofaparticularpracticalproblem‐‐suchasthefurtherimprovementoftheproductivityofaparticularclassoftechnology‐embodyingcapitalfacilities.

Secondly,thisformulationoftheeffectsofinvestmentinR&DactivitiesmaybethoughttoreflectaPlatonicworldinwhichafinitenumberofsolutionpossibilitiesfortechnicaltransformationsarepresentfromthestartoftime,buttheseasarulewillnot

unreasonabletosupposethatthepresentlyexistingstockofimplementabletechniquesforenhancingtheproductivityofcarbon‐energyinputscouldsufficeforaconsiderablenumberofdecadeswithoutrequiring“refreshment”byfocusedinvestmentofR&Defforts.Seefurtherdiscussionofthe“buytime”optioninsection2.3,below.

49With , , asconstantpositiveparameters,BandRthereforebecomeadditionalstate‐andcontrolvariablesinourdynamicsystem.

50Theequilibrium(steady‐state)growthrateinastandardAK‐modelriseslinearlywiththerategrowthintheproductivityofcapital(cf.BarroandSala‐i‐Martin,2004),andthereforewiththeflowrateofR&Dexpenditures.Theexistenceoftechnology‐specificintrinsicproductivitylimitsset–inthelimit‐‐bythephysicalpropertiesofthematerials,chemicalandelectricalprocessesentailedinproductionmakesthissoimplausiblethatevenitsassertionasametaphorisofdubioususefulness.Popp(2002)presentsevidencetheR&Dinvestmentintheenergysectorissubjecttodiminishingreturns,andtheWITCHmodelofBosettietal.(2006)representsthisbysettingtheelasticityofthe“flowofnewideas”tobeb<1‐c,wherecisthatflow’selasticityw.r.t.thestockofideasand(c+b)<1.

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revealthemselvesspontaneously.Theycanbeuncovered,however,andformulatedforpracticalapplicationthroughcostlyresearchanddevelopmentproceduresbasedupontheexistingstateoffundamentalscientificknowledge,ratherthanbeingcreateddenovoandwithoutlimitbytheexpenditureofresourcesintheperformanceofR&Dactivities.51ThatmorerestrictiveviewofthetransformativepowerofinvestmentinR&Disappropriatenotonlyfortheforegoinggeneralreasons,butalsobecausetheconcerninthiscontextisnotwiththeundirectedglobalexpansionofthetechnologicalopportunitysettypicallyenvisagedintheoreticalgrowthmodels.Rather,theaimofthe“directedR&D”inthepresentmodelistoenhancetheeconomicpropertiesofparticularkindsofprocessinventions,withnewproductinventionsonlyinsofarasalterationsinproductcharacteristicsareconsequentialfortheraisingtheefficiencyofcapitalinputsintocarbon‐freeproductionprocesses.52

Withintheframeworkcreatedbyintroducingthis(oranyother)R&DproductionfunctionintotheBasicmodel,thereareagainthreedistinctphasesofthetransitiontoastabilizedclimate.Table2comparesthephasesintheoriginalbasicmodelwiththeversionintroducingR&D:

Table2.ComparisonoftheBasicandEndogenousR&DModels

Basic model

Phase BAU1 Business as usual 

JPR1 Joint production 

CFR1 

Carbon‐free 

Investment in  Carbon‐based capital Carbon‐free capital Carbon‐free capital

Output using  Carbon‐based capital Both carbon‐based and 

reduced emission capital 

Carbon‐free capital 

only 

Endogenous (R&D‐driven) Technological Change Model 

Phase BAU2 Business as usual 

JPR2 Joint production 

CFR2 

Carbon‐free 

Investment in  Carbon‐based capital Carbon‐free capital Carbon‐free capital

R&D 

investment in Carbon‐free technology  Carbon‐free capital  Carbon‐free capital 

Output using  Carbon‐based capital Both carbon‐based and 

carbon‐free capital 

Carbon‐free capital 

only 

51ItalsohastheadvantageofbeingjointlyconcaveinBandR,whichisanecessaryconditionforthewelfaremaximizationproblemtohaveasolution.

52Followingthisinterpretation,addingendogenoustechnologicalchangetotheBasicModelallowsustocharacterizetheoptimalpathofglobalR&DthatisdirectedtoincreasingtheproductivityofCFRcapital.CorrespondinglytheimpactofR&Dinvestmentoneconomicwelfareismodeledasbeingfeltindirectly,ratherthandirectlyintheformofpureproductqualityenhancements.Inotherwords,thewelfaregainscomethroughreductionofthesacrificeofconsumptionutilityrequiredinthetransition,andforthesubsequentsustainedgrowthof(percapita)consumptionunderstabilizedclimaticconditions.

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FromTable2itmaybeseenthatwhiletheR&DmodelresemblestheBasicModelinhavingthreephasesandtwooptimumswitchingmoments,itdiffersinhavingthreestatevariablesandtwocontrolvariables.ThisisthecasebecauseitturnsouttobeoptimaltoinitiateR&DdirectedtoimprovingaparticulartechnologyfromtheveryfirstmomentthatinformationbecomesavailableabouttheexistenceofapotentiallyworkableCFR‐technology.OntheassumptionthattheCFRtechnologyisdiscoveredattimezerobutislessproductivethanthematurecarbon‐usingtechnologywhenembodiedinequallycostlyproductionfacilities,R&Dactivitythenshouldbeundertaken(only)duringthephaseinwhichtangiblecapitalformationandproductionadheretothecarbon‐dependentfeaturesoftheBasicmodel’sBAUphase.Followingthat,aJPRphasewillcommencewithgrossinvestmentdirectedtodeployingtheimprovedCFRtechnologyinKB‐typeproductionfacilities.

4.3A“Buy‐TimeModel”–GreeningCarbon‐basedCapitalintheBasicModel

Wenowturntothethirdofthepartialmodels,inwhichthestructureofthebasicmodelisenrichedbyintroducingathirdcategoryoftechnologies,namelyaknown“intermediate”classofcarbon‐usingproductiontechniquesthatarecharacterizedbylowerratesofCO2emissionsperunitofcapitalbutcapitalproductivityperunitofoutputthatislowerthanofthematurecarbon‐basedtechnologies,butnotasmuchlowerthanthatoftheinitial(pre‐R&D)versionsofthecarbon‐freetechniquesofproduction.53

Thisconceptualizationcorrespondsbroadlytothevarietyofwell‐groundedengineeringmethodsmaybeusedtoupgradecarbon‐usingproductionfacilities,whetherbyimprovingtheenergyefficiencyofresidential,businessandgovernmentofficebuildingsbybetterinsulation,heatingandcoolingsystems,andreducingthe

53Onthelatter,seetherecentnoticedexampleoftheannualconsumptionofover$3billionworkofelectricpowerintheU.S.byHDTV“set‐top”boxessuppliedbycablecompanies,duetothechoiceoflowcostdesignsthatthatdonotactuallystopdrainingpowerwhentheyareswitchedoff(see,“AtopTVSets,aPowerDrainthatRunsNonstop,”TheNewYorkTimes,June26,2011:p.1.).TheMcKinseyGlobalInstitutedevotedconsiderableattentionintheyearsbeforethefinancialcrisistostudiesofcurrentandnear‐termoptionsforenergyefficiencyroutestoCO2emissions‐reductionsandprivatecostssavingthroughupgradingofproductionanddistributionsystems.See,e.g.,FarrelandRennes(2008);GroveandR.Burgelman(2008).IntheU.S.,numerousproposalsforthiskindof“retrofitting”havehaddifficultygainingpolicy‐tractionduetotheprevailingpolicybiastowardsresearchsubsidizestosupport“innovation”inrenewableenergytechnologies.”Morerecently,thecaseforexpandedexploitationofnaturalgasandgreaterinvestmentinotheropportunitiestoimprovetheproductivityofcarbon‐basedtechnologiesthat(similarly)offerhigheroutputpervolumeofGHGemittedhasbeencogentlyandvigorouslyadvancedbyBurtonRichter(2010).DuringthecrisisandrecessionyearstheattentionoftheEuropeanCommissionshiftedawayfromtheexpensiveandlonger‐termresearchenvisagedbyitsambitiousStrategicEnergyTechnologiesPlan[SET,COM(2007)723];itfocusedinsteadonavarietyofshorter‐termtacticsaimedatstimulatingaggregatedemandinwaysthatwouldimplementalreadyavailabletechnologiesfor“green”purposes,notably:retro‐fittingbuildingsforgreaterenergyefficiency,supportingtheautomotiveindustrytoincreaseproductionoflow‐CO2vehiclesusingelectricbatteriesandsecondgenerationbio‐fuels(seediscussioninDavid,op.cit.(2009).IntheU.S.,numerousproposalsforthiskindof“retrofitting”havehaddifficultygainingpolicy‐tractionduetotheprevailingpolicybiastowardsresearchsubsidizestosupport“innovation”inrenewableenergytechnologies.

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passiveconsumptionelectricitybyelectricalandelectronicappliancesbyconfiguringthemtoswitchoffcompletelywhennotinuse,andsoforth.ButitalsosubsumesproposalsfortheexpandedexploitationofnaturalgasasareducedGHG‐emissionssourceofenergy,includingtheacknowledgementthatincrementalcostsperBTUwouldberequiredtocurtailtheenvironmentaldamagecurrentlyassociatedwith“fracking”methods.

Break‐throughresearchandnovelengineeringprinciples,however,arenotrequiredtoexploitthisclassofcarbon‐basedenergysourcesandproductiontechnologieshere,butspecificapplicationsofcoreengineeringknowledgeadaptationofexistingdesignstolocalcontextswillraisetheaverageunitcapitalcostscarbon‐usingplantequipmentthathasundergonethiskindof“green‐upgrading,”aswellasthatofa“lessdirty”energysourcesuchasnaturalgas,andsafernuclearpower‐plantswithprovisionsforlong‐termsequestrationoftheirtoxicwaste.54Thegaintobehadbyseizingthis“low‐hangingfruit”comesinthereducedrateofCO2,whichmeansundertakingtheentailedincrementalcapitalexpendituresconstitutesawayto“buyingtime”earlyinthetransitioninordertobeabletosubsequentlyproceedmoreslowlyinreplacingthewholecarbon‐basedproductionregimewithonebasedonnew,carbon‐freeproductionfacilities.

Notsurprisingly,therefore,theextenttowhichthe“buytimeoption”willbeattractivetoexploitinthecontextofourBasicmodel,bybuildingupproductioncapacity(KD)inthisintermediate“greened”formratherthancapitalthatembodiesthemature,morecarbon‐intensivetechnology,dependsnotonlyontheassociatedcapitalproductivitybutalsoonthereductiongainedinemissionsperunitofoutput.Itturnsoutthatintroducingthepossibilityofutilizingthisthirdclassoftechnologiesgivesrisetoamodelinwhichthereare5distinctphasesthatcanbearrangedineitheroftwoalternativetransitiontrajectories,asindicatedbyFigures3.1and3.2anddetailedinTable2.55

54Itmaybenotedthattheextractionandprocessingoffossilfuels,includingthecatalyticcrackingofpetroleum,andhydraulicfrackingofnaturalgasalsoresultsinemissionsofmethane,ashort‐livedGHGespeciallyhighGWP(vis‐à‐visCO2)duringthe20yearsfollowingitsreleaseintotheatmosphere(seeabove,sect3.1).Inordertoincludetechnologicalmeasuresformethanemitigationinanintegratedanalysisofclimatestabilization,however,itwillbenecessarytoconstructaconsiderablymorecomplexrepresentationoftheclimatesub‐systemthantheonethatisapproximatedhere.InadditiontomodelingthecarboncycleexchangesofCO2betweentheatmosphereandtheupperandlowerocean,thefastdynamicsofmethane’sinteractionwithOHradicalsandconsequentdegradationintoCO2,anditshighGWPmustbemodeledexplicitly.

55Notethattheactof‘buyingtime’involvesusingatechnologywitharelativelyhighoutput/emissionratio.Hence,logicallyspeaking,buyingtimeisassociatedwithproductionusingthattechnologyratherthanwithinvestmentinthattechnology.Therefore,inthiscase,theBTMphaseissubdividedintothreesub‐phases,inwhichwehavepositiveoutputfromtheBTMtechnology(hereindexed‘D’),andtheCFRphasestartswhentheBTM‐technologyisdeactivated.Typically,thej‐thBTMsub‐phaseoftrajectorykislabeledBTM.

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Moreover,whichtrajectorywillbetheonethatisoptimalforthissimpleeconomytofollowdependsupontheparameterconfigurationthatsetstheBTMtechnology’soutput/emissionratio.Giventhese‘technicaldata’,thechoicebetweenthealternativetrajectoriesthatwillbefollowedinexploitingthe“buytimeoption”isprescribedbycomparingthewelfarevaluationsofthetwosolutionsofthetwooptimalcontrolprograms.56Trajectory1,asdescribedbythefollowingTable,isfoundtobethewelfaredominantmemberofthepairwhenthethatratioishigh,whereaswhentheratioislowitisbettertofollowTrajectory2,whichcallsforashorterperiodofinvestmentinbuildingstocksofKDandanearlierswitch(inthethirdphaseratherthanthefourth)togrosscapitalformationembodyingthecarbon‐freetechnologies.

InTable3(below),theheaderlinescontainthelabelsforthesub‐phasesineachtrajectory.57Theentriesbeloweachphaselabelbelongingtoatrajectorycontaina

Table3.Alternativetrajectoriesinvolvingthebuytime(BTM)technology

Trajectory 1

Phase 

BAU1 Business as 

usual 

BTM11 Buying time 

BTM21 Buying time 

BTM31 Buying time 

CFR1 

Carbon‐free 

Investment in Carbon‐

based capital 

Reduced 

emission 

capital 

Reduced 

emission 

capital 

Carbon‐free 

capital 

Carbon‐free 

capital 

Output using Carbon‐

based capital 

Both carbon‐

based and 

reduced 

emission 

capital 

Reduced 

emission 

capital only 

Carbon‐free 

capital and 

reduced 

emission 

capital 

Carbon‐free 

capital only 

Trajectory 2

Phase 

BAU2 Business as 

usual 

BTM12 Buying time 

BTM22 Buying time 

BTM32 Buying time 

CFR2 

Carbon‐free 

Investment in Carbon‐

based capital 

Low emissions 

capital 

Carbon‐free 

capital 

Carbon‐free 

capital 

Carbon‐free 

capital 

Output using Carbon‐

based capital 

Both carbon‐

based and 

reduced 

emission 

capital 

All three types 

of capital 

Carbon‐free 

capital and 

reduced 

emission 

capital only 

Carbon‐free 

capital only 

56Thatthemodelitselfdirectsattentioninthiswaytotherelevanceofempiricalinformationaboutcertainparametersisworthnotice,becauseitmayhelpinprioritizingareaswarrantingmoreconcreteanddetailedempiricalresearchinengineeringandappliedeconomics.

57Typically,thej‐thBTMsub‐phaseoftrajectorykislabeledBTMj,k.

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shorthanddescriptionoftheactivitiestakingplaceduringoratthebeginningofthesub‐phases.Noticethatthemaindifferencebetweenbothtrajectoriesisthetimeatwhichthecarbon‐usingA‐technologyisde‐activated.Asaconsequence,outputduringsub‐phaseBTM22oftrajectory2comesfromthreedifferentsources,sotheequationdescribingtheaccumulationofBTMcapitalismorecomplicatedthanthatfortrajectory1.58

Bysolvingthestackedoptimumcontrolproblemsassociatedwiththemodelversionsoutlinedabove,wearriveatacompleteandintertemporallyconsistentdescriptionofthenatureandtimingofthevariousphases,aswellastheshapeofthetime‐pathsoftangibleandintangiblecapitalinvestment,levelsofproductionandconsumption,aswellascumulativeemissionsasafunctionofthestructuralparametersofthemodel.Theseparametersincludetheprobablelocationofthecumulativeemissionsthreshold,theproductivityoftheR&Dprocessaswellastheproductivitydifferencesbetweencarbon‐basedandcarbon‐freetechnologies,andthe‘standard’preferenceparametersfortheconsumptioncomponentofthesocialutilityfunction,i.e.therateoftimediscountandtheintertemporalelasticityofsubstitution.

5.Preliminaryresults,experimentswithphysicalsysteminteractions

Tothispointinthepresentresearchprogram,theseveralmodelsdescribedintheforegoingpageshavenotbeenconsistentlycalibratedondatafortheglobaleconomy.NorhavewecompletedthetheintegrationoftheBTMmodelwiththeendogenousR&Dmodel.59ThelatterremainsamatterofparticularinterestbecausebeingabletoextendthelengthoftimeduringwhichR&Dexpendituresaremaintainedis(asfaraswehavebeenabletosee)islikelytobethemostproductiveuseoftheaddedtime“bought”byCO2emission‐ratereductionseffectedbyexercisingtheBTMoption.Usingknowntechniquestoupgradingcarbon‐usinginfrastructuresanddirectlyproductivecapitalfacilitiescertainlywouldbeasociallymoreproductivepurposethanhasteningtheinevitabledescentintoclimateinstabilityjustforthesakeofprolongingcurrentenjoymentofthehigherconsumptionlevelsassociatedwith“businessasusual.”

58Althoughthismakestheentiremodelconsiderablymoredifficulttosolve,itwassolvableforMathematica.

59TheBasicModel,andtheBasic+R&DModelhavebeensocalibratedandtheresultsoftheoptimalsolutionsobtainedarediscussedandcomparedinvanZonandDavid(2013).SolutionshavebeenobtainedforarevisedspecificationfortheBasic+BTMModeldiscussedhere(seeDavidandvanZon(2013,whichtheworkingpaperreferstoasthe“Greeningupgrade”model).Thestructureofthelatteristcomparabletothatoftheothertwomodelsinthesuite,butithasnotbeencomparablyre‐calibrated.Oncethathasbeendoneandsolutionshavebeenobtained,itwouldbeappropriatetoundertakesolutionofanintegratedmodelbyadding“Greeningupgrade”totheBasic+R&DModel,andtrytofindasolutionforthemultistageoptimaltransitionpath.

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Comparisonsoftheresultsobtainedwiththedifferentpartialmodels,however,yieldsanumberofusefulinsightsabouttheroleofdirectedR&Dinvestmentinthetransitiontoclimatestabilization.OnestrikingandintuitivelyunderstandablefindingthatemergesfromtheoptimizedsolutionoftheendogenousR&Dmodelishighlightedbyitsjuxtapositionwiththefeaturesofthetransitionpathfoundforthebasicmodel.Inthelattercase,business‐as‐usualinvestmentincarbon‐usingcapital(KA)comestoahaltwhencarbon‐freetechnologycanbeembodiedinproductionfacilities,regardlessoftheirgreaterunitcapitalcost;whereasintheformermodeltheBAUphaseendsonlywhenR&DsucceedsinrenderingtheunitcostsofproductionfacilitiesembodyingCFRtechniquescompetitivewiththatofKA.60

AllowingforthepossibilityofinvestmentinR&Ddirectedtowardsloweringtheunitcapitalcostsofcarbon‐freeproductionprocesseshastheeffectofraisingthetangibleinvestmentincarbon‐usingproductionfacilities,shorteningtheabsoluteandrelativedurationoftheBAUphase‐‐leavingthelengthofthesubsequentjointproductionphaseessentiallythesame.Inotherwords,beingabletoinvestintheresearchrequiredfora“technicalfix”hastheexpectedresultofspeedingthebeginningofCFRproduction,thecessationofinvestmentincarbon‐usingproductionfacilities,andcorrespondingly,theretirementoftheoldcarbon‐basedcapitalstock.

TheunderlyingeconomiclogichereisthattheanticipationofbeingabletobuildmoreproductiveCFRcapacityinthefuturegeneratesaheightenedderiveddemandforBAUcapacity,andhenceahigherrateoftangiblecapitalformationincarbon‐basedfacilities‐‐sincethedesiredstockofCFRcapitalisaproducedmeansofproduction.TheresultinghighervolumeofKAgeneratesalargeroutputflow,providingagreaterpoolofresourcesthatcanbespentonR&DinvestmentduringtheBAUphase,andsubsequentlyforCFR‐embodyingcapitalformationintheJPRphase.Itshouldbenoted,however,thatthiswouldbeadangerousplantohavepursuedwerethetechnicalimprovementsincarbon‐freeproductionsystemsthathadbeenexpectedtoresultfromR&Dexpendituretofallshortofexpectations.Insuchcircumstances–hardlyunrealisticinviewoftheuncertaintiessurroundingtheperformanceofR&D‐‐itwouldbenecessarytoeventuallymaketherequiredswitchtomuchmorecostlyCFRproductioncapacity,attendedbyconsequentlygreaterlossesofconsumptionandwelfare.

60Strictlyspeaking,thelastpartofthisstatementisnotquitetrueinthemodelonwhichthisdiscussionisbased,becausetheupperlimitonthecapitalproductivityoftheCFRtechnology,B‐barissetbelowthethatforthecarbon‐usingtechnology.R&DremovesasmuchaspossibleoftheproductivitydeficitofKBrelativetoKAbeforeimplementingtheCFRtechnologytangiblecapital.B.Butthisisinnowayessential,andtherearenoapriorireasonsfornotentertainingthepossibilitythatCRFtechnologiescan(eventually)havelowerunitcapitalcoststhancarbon‐basedtechnologies,sothatiftheexponentandconstantintheproductivitychange‐R&Dinputfunctionarequitesmall,themodelisthemodelisnotinconsistentwiththeobservationthattheworldweliveinis(still)adependentuponacarbon‐usingregimeofproduction.

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ThissuggeststhepracticalrelevanceofcombiningtheendogenousR&DmodelandtheBTMmodel,because,byaddingthe“buytimeoption”ofreducingtheCO2emissionsratesonthecarbon‐usingproductioncapacity,therewouldbemoretimelefttobuild‐upthenecessarycarbon‐freecapitalstock.Sincethatcapitalformationprocesswouldweighallthemoreheavilyofconsumptionlevels,exercisingthe“buytimeoption”canserveasapartialinsuranceagainsttheadversewelfareconsequencesofdisappointedexpectationsregardingtheeffectivenessofR&Dinvestmentinenhancingtheproductivityproductionfacilitiesembodyingcarbon‐freetechnologies.Althoughthetwooptionsoftenseemtobediscussedasalternative,substitute“climatepolicies”theyaremoreproperlyseentobecomplementsinanexpanded“technologyfix”portfolio.

Itisafairlystraightforwardmattertoconductsensitivityexperimentswiththesepartialmodels,inordertogetaqualitativeimpressionoftheimpactofparametervariationsthat,giventhedeterministicformthemodelcanbegintosuggesttherangeofdistributionsinthedynamicsthesystemexhibitwerethemodelcomponentreformulatedmorerealisticallyinstochasticterms.Moreover,suchsensitivityexperimentsalsoshedlightonthewayinwhichtherequirementsforasuccessfulclimate‐stabilizingtransitionwillbeaffectedby‐‐andthereforeneedtomakeexanteallowancefor‐‐alterationsintheperceivedandactualdynamicfeedbacksarisingfrominteractionsbetweentheeconomicandthegeo‐physicalsubsystems.61

Sinceatthisstageofourworktheresultsofthesolutionofthemodelconsideringboththebuy‐timeoptionandR&Ddirectedtoinnovationsincarbonfreeproductiontechnologyarestillbeinganalysed,wereporttheresultsofusingsensitivityexperimentswiththe“external”physicalspecificationsofourpartialeconomicmodelsasapreliminarymeansofexploringtheimpactsoftheirinteractions.Amongthevarietyofcomputationalexperimentsthatcanbereadilyexecuted,thefollowingpairhasyieldedresultsthatareofprincipalinterest:(i)loweringthecumulativeGHGemissionstipping‐point,and(ii)increasingtheannualrateofphysicaldepreciationofcarbon‐basedproductioncapacity.

ThefirstoftheseoffersasimplewaytoassessthegrosseffectsofmakingprecautionaryallowancesfortheambiguitysurroundingtheexactleveloftheatmosphericGHGconcentrationlevelthatwillbea“tippingpoint”intothedomainofirreversibleclimateinstability.62Therobustresultwefindforallvariantsoflowering

61Forexample,amorecautionarystancetowardsthedangersofsurpassingthecumulativeemissionsthresholdmayinvolvealoweringofthe‘model’‐thresholdbelowits‘realworld’expectedlevel.

62Theimplicationsofallowingfortheambiguityinthelocationofthe“tippingpoint”beyondwhichwarmingbecomesaself‐reinforcingprocessevenwhereGHGemissionsofimmediateanthropogenicorginshaveceasedcompletelywillneedtobeassessedwithinthecontextofafullyintegratedstochasticversionofourmodel.LemoineandTraeger(2011)introduceprobabilisticfunctionsforcrossingaclimateregimetippingpointintoarecursiveformulationoftheDICEintegratedassessmentmodelforestablishingoptimalclimatepolicies.Thetippingpoint'sprobabilityandtimingthusbecomeendogenouslydeterminedbythechosenemissionpolicy.Recognizingthattheprobabilitydistributionforthe“temperatureThreshold”correspondingtothe“tippingpoint”isnotknownwithconfidence,policy

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thecriticalthresholdfortemperaturegain(orequivalently,thecumulativeemissionstippingpoint)isthattherequiredlengthofthetransitiontoastabilizedclimatewouldbeshortenedbyabridgementoftheBAUphase,leavingthedurationofthejointproductionphaseessentiallyunaltered.Initially,outputisreducedbutconsumptionisraised,sothatinvestmentintangiblecapitalformationispostponed;althoughconsumptionsubsequentlywillbereduced,therealsoislessinvestmentinthenewCFRtechnology,and,indeedandlowerlevelsofactivityacrosstheboard–comparedtothosefoundforthe(basic)referencemodelwhenthetemperature‐gainthresholdissetatahigher,lessconstraininglevel.

Thegeneralfinding,then,isthatwithlessscopeforCO2emissionsbeforetheexpectedcriticalthresholdwillbereached,productionwithcarbon‐usingcapacitymustbecurtailedandthelengthofthetransitionabridged;withlesstimetobuildupcarbon‐freecapitalgoods,theeventualgrowthofoutputandconsumptionhastobedeferreduntilclimatestabilizationwithacarbon‐freeproductionregimehasbeenachieved.Afurther,consistentresultappliesinthespecificcasesoftheendogenousR&DandBMTmodels:becausealowercriticalthresholdleaveslesstimetodoR&Dorto“buytime”.Ininordertocounterthateffecttosomeextent,thedistributionofR&DactivityovertimemustbeshiftedtoinfavourofR&DnowandagainstR&Dlater.

Thus,theplanningmessagestobetakenfromthisisthatsettingalowerGHGppmvtarget‐‐inkeepingwithgreateraversiontoriskambiguityandconsequentadherencetotheminimizeregretstrategydictatedbythe“precautionaryprinciple,”callsforaninitiallyhighandrapidlyrampeduptherateofR&Dexpenditureswhensufficientresearchadvanceshavemadeitattractivetodevotegreaterresourcestodevelopmentandengineeringimplementations.Similarly,itwarrantsboostingattheoutsettherateofcapitalformationinproductionfacilitieswithupgradedoutput/emissionsperformance,soastosmooththeadverseimpactonpercapitalconsumptionofhavingtoquicklydeploylowandzerocarbon‐burningproductioncapacity.Later,oncethebuild‐upofcarbonfreeproductioncapacityiswellunderwaybothtypesofinvestmentwillhavetodecline,firstrelativetooutputandthenabsolutely,.

Oursecondsetofexperimentsprovideasimplifiedwayofemulatingthehigherfrequencyofdamagesthatcanbeexpectedtoresultfromextremeweathereventsassociatedwithchangingclimate(s),andtoassesstheimpactontheoptimizedtransitionplanofanticipatingtheconsequencesofwarmingthatalreadyis“inthepipeline,”duetothepasthistoryofGHGemissions.Anincreasedrateofunscheduledcapitallosses(damagesfromincreasedclimateinstability)hastheeffectofpostponingthearrivaloftheCFRphase,primarilybecauseproductionusingthecarbonbased

decisionscanbemadethatreflect“ambiguityaversion”byselectingstrategiesthatreducethedownsidevariancearoundtheexpected“thresholdtemperature.LemoineandTraeger’ssimulationsshowthatunderreasonableparameterizationoftheDICEmodel,allowancefortippingpointsinthiswaycanraisethenear‐termsocialcostofcarbonemissionsbyasmuchas50%.

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technologyisnegativelyaffected,leadingtoalowerflowofCO2emissionsintheprocess.Thisis“thegoodnews”,but,unfortunatelyitisnotthewholestory.

Sinceitseemsreasonableforpurposesofthisanalysistoassumethatthesenegativeclimateeffectswillimpactoldcarbon‐basedfacilitiesmostseverely,ifnotexclusively,63therateofreturnoninvestmentincarbon‐usingfacilitieswillbelowerthanisthecaseintheabsenceofallowanceforthisfeedbackofclimatedestabilization(i.e.,inthebasemodel).The“badnews”isthatthisresultsinlowerinitialratesofcarbon‐usingcapitalformation(grossinvestmentinKAandKD)andhigherratesofconsumptioninanextendedBAUphase.ConsequentlytheconstraintplacedonthegrowthofproductivecapacityduringthisearlyphaseofthetransitioncurtailstherateofR&Dinvestment,andtheglobaleconomy’ssubsequentabilitytorapidlyaccumulatethenecessarystockofcapitalembodyingcarbon‐freetechnologies.

Oneimplicationoftheforegoingfindingswouldseemtobethatexpendituresaimedataverting“unscheduledlosses”inproductioncapacityduetoclimateinstability‐relateddamages,maybequitea“goodinitialinvestment”.Itshouldbenotedthatundertheassumptionofincreaseddamages,thelevelofR&Dactivityalsoisaffectednegatively;butthatinthecontextofafullyendogenousintegratedmodeltheclimate‐relatedcapitallosseswillbedrivenbystrongnon‐convexityintheeffectsofrisingGHGconcentrationlevelsandconsequentlyhighermeansurfacetemperatures.Theyarethuslikelytotakeaheaviertollonexistingproductioncapacityatdatesfartherinthefuture,ratherthanfromtheoutsetofthetransition,andtheinsurancemotivationwillpushtheshadow‐priceofGHGfartherupwards.Herethedetailsofheatexchangedynamicsbetweenatmosphere,theupperoceansandtheloweroceanwillmatter,andaccordingly,climatescienceresearchprogressspecificallydirectedtoreducethepresentuncertaintiesregardingthosequestions,aswellastheendogenousprocessesaffectingtheclimatesensitivity,couldsignificantlyreshapetheoptimalcourseofpolicyimplementations.

Thesesourcesofnon‐stationarityintheclimatefeedbackfromalterationsinthelevelofCO2emissionscanbeemulated(albeitroughly)byafurthersimulationexperimentinwhichthephysicaldepreciationrateoncarbon‐usingcapitalmovestothehigherlevelonlyafterthetangibleinvestmentinthattypeofcapitalhasstopped.Wemaysupposethattheanticipationofthosefuturecapitallosses,asbefore,willexertadepressingeffect(albeitlessheavily)upontheexpectednetrateofreturntoinvestmentinKAduringtheBAUphase.Consequently,althoughtheinducednear‐termreductionintangible(carbon‐technologyusing)capitalfacilities,andtheriseofconsumptionper

63Theconsiderationunderlyingthisassumptionisthealargeportionofthecarbon‐basedinfrastructureanddirectlyproductivitycapitalstockwillbelegaciesfromtheBAUregimeandthehistoricallyantecedentstate,itwillbelocatedintemperatelatitudesandbuiltinfashionsthatwillleaveitmorevulnerabletotheeffectsofcoastalandriverineflooding,andservewind‐damagefromhurricanesandmonsoons,thantherecentlyconstructedcarbon‐freefacilities.Thelatter,ideally,willhavebeendesignedandsitedwiththoserisksinmind.

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capitawilloccurduringtheBAUphase,thatwouldnothappenfromthephase’soutset.Instead,itwouldbeconcentratedintheperiodjustbeforethecarbon‐usingstockattainsitmaximum,when(undertheassumedtimingoftheincreasedrateofunscheduledcapitallosses)theweather‐createddamagesstarttooccurwithgreaterfrequency.64Theoveralleffectofthesealterationsinthetimingofintangible(R&D)investmentsuponontheterminalvalueoftheproductivityofcapitalembodyingCFRtechnologiesisbounded,however,becausetheBAUphaseduringwhichR&Distakingplacewillhavebeenstretchedout.ThatchangecompensatesforthecumulativeeffectofadecreaseintheflowrateofR&Dinputs,andthesoamelioratethelatter’snegativeimpactupontheextentofproductivityimprovementsinKB.

Amajormessagethatemergesfromtheforegoingmodellingexerciseandparameterizationexercisesisonethatmightwellhavebeenanticipatedatitsoutset.Whatwelearnfromheuristicmodelbuildingofthepresentkindishowtothinkabouttheproblem,andnotnecessarywhattoconcludeaboutthebestcourseofactioninmeetingthechallengeitposes.Eventhehighlysimplifieddynamicalsystemthatwearestudyinghassufficientinterconnectedandmutuallyinterdependent“movingparts”totaxone’sunassistedintuitionsastothewaysthatvariationsintheparametersofthegeophysicalandeconomicsubsystemswillaltertheoptimizedtransitionpathstoastabilizedglobalclimate.

Moreover,whilethesimplicityoftheheuristicgrowthmodelmakesmoretransparentthelogicofchangesinthedirectionsofinvestmentandproductionactivityintheirvariousforms,thesequencedphasestructureofthetransitionisnotsoimmediatelyobvious.Norcantheimpactsofparametricvariationsontheoptimalphases’relativedurationsbeascertainedwithoutundertakingexplicitlyquantitativeanalyses.Thelattercanservetoprioritizeareasforempiricalresearch,byidentifyingtechnicalparameters(andinmodelswithricherspecificationsofagents’behaviors,criticalbehaviouralparameters)‐‐themagnitudesofwhicharefoundtostronglyimpactthewelfarepropertiesandshapetheresourceallocationrequirementsintheearlystagesoftheoptimaltransitionpath.

Buildingsuchmodels,andinvestigatingtheimplicationsofmoresophisticated,integratedsystemsofeconomic‐climateinteractions,shouldnotbeseenasapursuitintendedtoproduceasubstitutefortheexerciseofintuitivejudgementsaboutmattersofeconomicpolicydesign.Intheend,thelatterwillhavetoweighmanyimportantpracticalconsiderationsregardinghumanbehaviors,cultureandpoliticsthatwillresistaccuratecaptureintractablequantitativemodels.Instead,weregardtheexerciseof

64Thisdifferenceintiminghastheeffectofreleasingresourcesthatallowforafasterbuild‐upofcarbon‐freecapital(byassumption,designedsoastobenotsusceptibletotheelevatedseverityoftheweather).Inaddition,duetothespecificationadoptedfortheR&Dproductionfunctioninourmodel,thereleaseofthoseresourcesatalaterpointinthefuture,afterconsiderableR&Dexpenditureshavetakenplace,islesscostly(intermsofCFRproductivitygainsforegone)thanisthecasewhenthevolumeofR&Disloweredfromtheoutset.

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experience‐basedintuitionsandquantitativeanalysestobecomplementaryingredientsinthepolicydesignprocess;andbelievetheywillworkmoreeffectivelyandreliablywheneachisallowedtoinform,sharpenandqualifytheconclusionstowhichoneisledbytheirjointemployment.

6.Whatwillbelearnedfromthenextstagesofthisresearchprogram?

The idealized “optimal planning” framework for endogenous macroeconomicgrowth has been found to be well suited to incorporating representations of thetechnical aspectsof thearrayof existingandpotential technologicaloptionsand theirrespectiveresourcerequirements,aswellasthoserequiredtooperationalizeawelfare‐optimal transition path. Application of multi‐phase optimal control analysis providesDIRAM solutions that describe the optimal flows of tangible and intangible capitalformation, along with the production flows using carbon‐based or alternativetechnologiesineachofthephases,aswellasthesequencingandrespectivedurationsofthelatterwhichcompletelydescribethecompletedtransitionpath.

This very concrete way of setting out what has to be accomplishedtechnologically in each of the phases, in our view, provides useful starting point forthinkingabouthowtodesignandcoordinate themultiplicityofdiverse tasks thatwillneed to be undertaken in order to adequately respond to the daunting existentialchallenges posed by global warming and climate instability. Beyond those alreadynoticed in the preceding pages, other, still more intricate and computationallydemandingmodelingandanalysesoftemporallyextendedmulti‐phasetransitionpathswill be necessary to shed fuller light on the complexities entailed inworking out theproper dynamic sequencing for the integrated development and exploitation of thevarietyofcomplementaryandcompetingtechnologypolicyoptions.Amongthemyriad“additionaloptions”,thefollowinghandfuldeserveprioritypositionsontheagendaforcontinuedfutureDIRAMresearch–byvirtueoftheirvariedfunctionalattributes:

(i)Expandedinvestmentsinbothengineeringresearchandphysicalequipmentrequiredtogreatlyextendandintegrateexistingelectricpowergrids,upgradingthesetocreate interoperable “smart grid” platforms that will combine information‐intensiveload‐smoothing pricingmechanismswith thus use of energy storage techniques (e.g.,batteries, flywheels, pumped water reservoirs) to raise the utilization rates ofintermittent renewable sources of electricity generation, thereby lowering the latter’sunit fixed costs and raising both the private and social rate of return to that form ofcapitalformation;65

65Tabors,ParkerandCaramanis(2013)pointtotheimportance(inadditiontotheattentionfocusedontechnicalengineeringaspectsofsmartgriddevelopment),ofdefiningandimplementingtheuseofstandardmetricsforintermittencyasaquality‐dimensionofelectricitysupply,aswellasa“platformofplatforms”approachtointeroperabilityandefficientmarketperformanceinthepricingofdiversegeographicallydistributedsourcesofelectricpower.

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(ii) R&D expenditures on risky exploratory research programs having longertime horizons than the norm for applied projects because they seek low‐frequency“break‐through”discoveriesand inventionstoenablecommercialexploitationof little‐used alternative renewable energy sources (e.g., thermal pumps), and energy storagetechnologiesbywoulddrasticallyloweringtheirunitcapitalcosts.

(iii)Long‐termresourcesupport forexperimentalgeo‐engineeringprojects thatwork in parallel on the development and field‐testing of safely scalable “back‐stop”technologies for atmospheric carbon capture and sequestration (ACCS), and locallydeployablesolarradiationmanagement(SRM)techniques;66

(iv)Capital formationforreforestationwithfast‐growing leafytrees inordertoefficientlyraisethenaturalcapacityCO2abatementcapacityoftheEarth’spresentforestcover as far as possible. Although it is highly unlikely that this measure couldcompensate for thedegradedabatementcapacityof theoceansthatwouldresult fromcontinuingwarming, pursuing this option should be seen not as “a fix” but as a “buytime”strategyinitseffectsonthenetvolumeofCO2thatisaddedtotheatmospherebyburningcarbon.Policymeasuresaimedatslowingoractuallyhaltingtheclear‐cuttingofforestswouldworkinthesamedirection,andmightalsoinvolvecompensatorycapitalformation to raise agricultural yields and the livestock carrying capacity of alreadycleared lands, thereby tending to reduce the economic pressures that are drivingdeforestationduetohumanagency.

(v) “defensive” expenditures for engineering design research and capitalformationtoimplementphysicalreinforcementsandadditionstoexistinginfrastructurethatwouldreducethelatter’sownvulnerabilitytodamagecausedbyextremeweathereventsandextensiveflooding.Thiswouldservetomitigatedirectandindirectlossesofproductivecapacityaswellasprovidingameasureofprotectionfromlossof livesandlivelihoodsinsomeformsofnaturaldisastersthatarelikelytobecomemoredestructiveduetoregionalclimatechanges.

Quite obviously, it will be no mean task for future research to developinformativeheuristicrepresentationsoftheforegoingdynamicprocesses,andtoexploretheway(s)tosequencetheexerciseoftheenlargedsetofpolicyoptionsinanintegrated

66Undertheassumptionsofourdeterministicoptimalcontrolmodelsoftheclimate‐stablizingtransitionpath, those techniques neverwould need to deployed in a “back‐stop” role, evenwere to some amongthemtobeeconomicallyaswellastechnicallyfeasibleandenvironmentallysafetoimplement.Yet,inthelattercircumstancestheinvestmentinfindingthosemethodcouldneverthelesshaveasubstantialsocialpay‐off,especiallywhenthetransitiontoalowcarbonglobalproductionregimehadtobecompletedinreasonablyshortorder.Inthatcaseitismostlikelythataconsiderablestockofoperationalcarbon‐basedcapital would have to be de‐activated before the start of the sustainable economic growth phase. Bydeploying atmospheric carbon capture (ACC) techniques thatwere (ex hypothesis) technically effectiveand economically practical, the concentration level of CO2 could be gradually lowered far enough toallowingthe“moth‐balled”carbon‐basedproductionfacilitiestobebroughtbackintoproduction,therebyyieldingafiniteflowofsocialquasi‐rents.Afasttransitionalsowouldimplythatthelatter’spresentvaluewouldnothavebeensoseverelyreducedbydiscounting.Ofcourse,inastochasticcontrolsetting,“back‐stop”geo‐engineeringinvestmentwouldhavepositiveinsurancevalueevenweretheresearchresultstoturn out never to be needed, or deemed too risky in their potential environmental side‐effects to bedeployedonlytocapturetheprivatequasi‐rents.

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multiphasemodel.67 But thattaskwillberenderedmore feasibleby tackling itwithinthesimplifying frameworkofa “socialplanningmodel,”as the latter settingdispenseswithalargenumberofcomplicatedassumptions‐‐concerningthemarketbehaviorsofprivate economic agents, and the ability of political authorities to coordinate andimplementcoherentregulatorymeasuresandinstitutionalenforcementmechanismsonaglobalscale‐‐thatotherwisewouldhavetobespecifiedandempiricallyjustified.

Thepresentpaperfocusesonunderstandingthedeterministicsystemofthemodellingframeworkwehaveconstructed,andhasindicatedthedirectionsinwhichwecanproceedtocompletetheintegrationofthepartialmodelswithinacompleteendogenouseconomicandgeo‐physicalsystem.InthenextmajorstageofthisresearchprogramitwillbeimportanttobeginbyreplacingthesimplisticrepresentationofthecarboncyclelagsintheeffectsofcurrentCO2ontheatmosphericconcentrationlevelofthatGHG,andtoexplicitlyspecifytheresultinggaininradiativeforcingandtheresultingriseinthemeanglobalsurfacetemperature.ItwillthenbepossibletofurtherextendtheBasicModelbyintroducingacontinuousendogenous“damageprocess”–whichimpactswelfareindirectly,throughthelossesofproductivecapacitycausedbythepositivetemperature‐dependenteffectsofthefrequency/severityof“extremeweather”eventsthatdisableafractionofproductivecapacity.Usingtheresulting“Basic”platform,thesolutionofacalibratedmodelthatintegratesthepartialmodelsforthetwo“techfix”optionsdiscussedhere,whileallowingcomputationofthewaythatendogenousR&D(directedtoraiseproductivityofcarbonfreetechnologies)andthe“BuyTime”re‐engineeringofexistingandincrementaladditionstocarbon‐usingproductionfacilitiesjointlyaffectthedurationoftheoptimizedtransition’sphases,andthewelfareindicesassociatedwiththeentirepath.Fromthereitwillbestraightforwardtogoontoexaminetherobustnessofthosefindingstovariationsinparameterspecifications.Ofparticularinterest,indeedconcern,willbethealterationsinthephasestructureandallocationofresourcesvaryingthatresultfromvaryingtheconjecturedlocationoftheclimate‐system’stippingpoint.

Furtherbroadeningofthearrayof‘techfix’optionsthataremodelledcanconsiderthequestionofwhetherandwhentobeginconcertedexploratoryR&Donalternativegeo‐engineeringapproachestocreatingeffectiveandenvironmentallymanageably“backstop”technologies–whetherintheformofsolarradiationmanagement(SRM),oraircaptureofcarbonanditssequestration(ACCS).Inthiscaseitwillbeappropriatetoconsiderwhen,ifever,suchresearchshouldbediscontinuedonthegroundthatthedeploymentofcarbonfreetechnologieshadprogressedfarenough

67 The natural starting point for the incremental expansion of the portfolio of tangible and intangibleinvestmentsistoaddtheoptionofmultiplevintages“ofbuytime”retrofittingofcarbon‐basedproductioncapacitytothecalibrated3‐phasegrowthmodelofanoptimaltransitiontoastabilizedglobalclimate,thesolutionofwhich ispresented invanZonandDavid (2013).The lattermodel featuresdirectedR&D inrenewable(carbon‐free)technologiesthatmustbeembodiedinnewphysicalplant,whichisdesignedandsituatedtobefarlessvulnerablethantheexistingCO2‐basedcapitalstocktounscheduledoutputlossesarisingfromsevereweatherdamagedrivenrisingatmosphericCO2concentrationlevels.

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tomakeitstimelycompletionfeasibleatawelfaresacrificethatwouldbenogreaterthanthatofcontinuedresearchonanuntriedapproachtostabilizingtheclimatewouldcallforfieldexperimentationatscalesthatcarriedhard‐to‐assessrisksofcausingseriousenvironmentaldisruption.

Totacklethelatterissueproperly,however,wouldcallforabandoningthedeterministicframeworkinwhichourDIRAMresearchprogramhasbeendeveloped.Thereisagoodbittobesaidforshiftingassoontoastochasticcontrolreformulation,retainingthe“planningmodel”approachinordertominimizerelianceonassumptionsaboutthebehavioursprivatemarketactorsunderuncertainly.Thisshiftwouldentailspecifyingtheprobabilitydistributionsgoverningthe“climatesensitivity”ofthephysicalsystem,68aswellasexplicitlyacknowledgingthestochasticnatureoftheoutputofR&Dexpenditureinputs,andtherealizedpayoffsoftechnologicaladvancespermittinghigherproductivityintheavailablestockofcapitalembodyingcarbon‐freetechnologies.

SimpleintuitionsaboutthealteredqualitativeinsightsthatwouldemergefromtheseandotherreformulationsoftheDIRAMframeworksuggestthatthegreaterimportanceof“buyinginsurance”againstfuturedown‐sideriskswouldforcegreaterearlysacrificesofconsumptioninorderraise(risky)investmentR&Doncarbon‐freetechnologiesandconcurrentlyraisingthevolumeandpaceof“buytime”retrofittingexpendituresthatloweredtheratioofCO2emissionsperunitofoutputproducedwiththeexistingcapitalstock.Butthepointoftheexerciseistogaininsightsregardingthequantitativealterationsthatallowanceforuncertaintieswouldrequireinthemagnitudesofresourcecommitmentsanddurationsoftheoptimaltransitionphases.

OncetheDIRAMapproachiscarriedintothedomainofstochasticoptimizationitwouldbefeasibletousethesemodelstoexplorequestionsaboutthemanywaysinwhichanoptimalmulti‐stageplanmayfailtoberealized,andwhatmightbedone–withattendantwelfarecosts–toamelioratetheresultingdamage.

Inthenearer‐termfuture,however,therestillaremanyinterestingthingstolearn,andquestionstoanswerbyexploringtheequivalentdeterministicversionofourmodel.Fordifferentparameterconstellationsweareabletoshowhowthetimingofthephaseswillchange,andhowtheevolutionovertimeofwelfarepercapitawillbeaffected,butalsohowtherequiredR&Dexpendituresandthevolumeofgrosscapitalformationwillchange,bothintermsoftheirdistributionandintensityovertime.Further,weareabletouseparametersensitivityexperimentstocomputehow

68Thenatureofthedistributionofthefeedbackparameterdescribingthephysicalsystem’sresponse(intermsofglobalmeansurfacetemperaturetoadoublingoftheatmosphericGHGconcentrationlevelissurroundedbyverysubstantialuncertaintiesarisingfromthecomplexitiesoftheinteractionsamongthephysicalandchemicalprocessesthatunderliethefeedbacksequencesdiscussedinsection2.1(above).InthepresentcontextthereisanimportantissueastowhetheritisreasonabletoassumethattheeffectsofchangesinthemeanatmosphericGHGconcentrationonthedistributionaroundthemean“climatesensitivity”arevariance‐preserving.

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uncertaintyregardingthepositionoftheclimatetippingpoint,takenincombinationwithdifferentdegreesofrelativeriskaverse“precautionarybehaviour”–onthepartoftherepresentativeconsumer(orhersocialplanningagent)affectstheoptimumtimingandintensitiesofthevariousactivitiesdistinguishedinthemodel.

Theflipsideofthelattercomputationalanalysisisourabilitytoexplorethewelfaredamageof“policyimplementationfailures”.StartingfromtheoptimalprogramforthetransitiontoaviableandstableGHGconcentrationlevel,itisfeasibletoshowtheeffectsoftimeinconsistenciesintheimplementationofmulti‐periodprivatesectorplans,andofbudgetaryorpoliticalconstraintsthatresultinspecificallytimedpostponementsofpublicinvestmentinR&Dandenergyinfrastructureprograms.Alternatively,thisapproachcouldassesstheimpactsofuncompensatedprivatecutsintheupgradingofcarbon‐basedproductionfacilities,orintheroll‐outofthecarbon‐freetechnologywhen,undernormalbusinessconditionsitwouldbeadvantageoustoundertakeinstallationoftherequiredcapitalinvestments.

Howmuchthetimingofactionmattersinthissystem,andthepenaltiesfordeviationfromtheoptimalpathcanbeinvestigatedundertheassumptionthatnoeffortismadetore‐optimizefromthepositionthathasresultedintheaftermathofsuch“shocks”,andalsoundertheassumptionoftryingto“catchup”afteraparticularrangeofdelaysbymeansofre‐optimizingthetransitionpath.Thus,itispossiblewithinthisheuristicmodellingframeworktocomputationallydescribetherelationshipbetweenthelengthsofimplementationdelaysduringspecificphasesofasuccessfultransitiontoclimatestability,andtheconsequentcostsintermsofnet‐welfareforegone.

7.Centering“TechFix”intheclimatepolicymix:abeginning,nota conclusion: Thisinitialstageinourprojectedexplorationsofthe“requirements”forasociallyoptimaltransitiontosustainableglobaleconomicgrowthinaviablestabilizedclimatehasbeenmotivatedprimarilybytheconvictionthatitisvitallyimportanttogivespecific“technologyfix”optionsacentralplaceinstructuredanalysisofpoliciesthatcanrespondeffectivelytothechallengeofglobalwarming.Environmentalandenergyeconomistshavebeenquicktoemphasizetheallocationalefficiencyofvariousfiscalandregulatorymeansofraisingthemarketpricesofcarbonfuels,andsomehavesuggestedthattheefficacyofthatpolicyapproachwouldbeenhancedbytheireffectsininducing“carbon‐saving”technicalinnovationfromprivatesector.

Ashasbeenpointedout,however,thelatterpropositionpresupposesthatraisingthecostoffossilfuelsourcesofenergywouldnotgeneratenegativeincomeeffectsthatdampenedprivateR&Dexpendituresbyenergy‐intensivesectorsoftheeconomy.Furthermore,theintegratedassessmentmodelsthateconomistshavedevelopedasquantitativetoolstoguidepoliciesaimingtoraisethepriceofcarbon

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typicallyfailtoshowtheconditionsunderwhichtheycouldbeexpectedtoelicitasufficientflowofinnovationsthatweredirectedspecificallytocurtailingandeventuallydisplacingfossilfuelsasadominantglobalsourceofenergy,or,indeed,tohavethedesiredeffectofmitigatingemissionsofCO2.thefirstorddesire.In

Toaddressthis“policyassessmentgap”wouldentailgivinggreaterattentiontospecifyingtherelevantcharacteristicsofthearrayofenergy‐usingtechnologies,andthecorresponding“endogenoustechnologicalprogress”sub‐system,andtoconnectthemwiththeothercomponentsoftheaggregateeconomicgrowthmodelsthatwillgovernthepaceandextentofdeploymentofimprovedproductiontechniques.

Thedynamicintegratedrequirementsanalysismodeling(DIRAM)approachthathasbeenintroducedheremaybeviewedasapreliminarysteptowardsamoreilluminatingrepresentationwithinthecontextoffamiliarIAMsofthepotentialroleoftechnologicalmeasuresinthetransitionfromthepresentdominanceofcarbon‐basedenergytoalowcarbonglobalregimeofproduction.ItsurelywilloccurtosomereaderstoquestionaccordingprioritytoelaboratingthetechnologicalspecificsofexistingIAMs,onthegroundthatmanyotherfeaturesofthesehighlystylizedmodelsalsowarrantfurtherelaboration.Moreover,greaterpolicyrelevancecallsforaspatiallydisaggregatedapproachthatwouldtakeaccountofgeographicalandecologicalvariationsaffectingboththeglobaleconomyandtheclimatesystem.Indeed,therealreadyhavebeenmanyeffortsalongjustsuchlines,impelledbyapolicyinterestinassessingthedifferentialregionalandnationalincidenceofthecostsofcurtailingglobalGHGemissions.69Othersmightarguefortheimportanceofrecognizingtheendogeneityofchangesinthesize,agestructureandspatialdistributionofglobalpopulation,andmoresophisticatedwelfareframeworktoaccountfordemographicaswellaseconomicchangesinthetransitiontoaviablestabilizedclimate.

Evenwerethelatterqualificationtobewavedaway,thereshouldstillberoomtoconsiderthelikelihoodthatarrivingatdomesticandinternationalagreementstoimposefuturetaxesonfossilfuelswouldbepoliticallylessarduouswheretheregoodprospectsoftheavailabilityofaffordabletechnologicalinnovationsthatcouldsignificantlyreducetheadverseimpactsofsuchcommitmentsonfuturerealprofitratesandconsumptionlevels.Justsuchexpectationscouldbecreatedbypriorcommitmentonthepartofthealreadydevelopedandscientificallyandtechnicallyadvancecountriestomajorcoordinatedtechnologicalprograms‐‐suchasthoseaimedatsignificantlyincreasing

69See,Brock,EngstromandXepapadaes(2012),foranintegratedglobalmodelinwhichthespatialvariationsofmeantemperature(inthenorthernhemisphere)areendogenouslygeneratedalongwiththeevolutionofthecorrespondingregionaleconomies.TheRICEmodel(Nordhaus2007,2010)andotherpreviouscontributionstotheliteratureprovidedspatialdistributionsofestimateddamagesduetorisingMGTforzonesaroundtheequator,showingtheregionalincidenceofwelfarelossesalongthedynamicpathoftheglobaleconomythatimposedaglobalcarbontaxthatreflectedonlytheaggregatemagnitudeofthosedamages..

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theefficiencyofenergydistributionanduse,andatloweringtherealunitcostsofnon‐fossilfuelsourcesofenergy.

Risingpricesforcarbon‐basedenergywouldencourageanyformcost‐savinginnovationactivitiesand,bythattoken,itwouldraisetheperceivedmarginalsocialpayofffromexpandingpublicsupportforscienceandtechnologyresearch–ifonlytocreateaknowledgeinfrastructurethatwouldlowerthecostsofdirectedinnovationintheaffectedsectorsandlinesofbusiness.Nevertheless,theaugmentedpublicR&Dfundingwouldhavetobeforthcoming,andadditional,differentialsubsidymeasureswouldneedtobeintroducedtodirectprivateR&D(andsubsequentdeploytheresults)towardloweringtheunitcostsofcarbon‐basedandalternativeenergysources.

Alternatively,awellthoughtoutsupply‐sideclimatepolicythatstartedwiththegoalofexpandingavarietyofapplications‐orientedR&Dprogramswouldtendtocreatecredibleexpectationsofsubstantialfutureresourcesavingswithcarbon‐freeproductionfacilities,andaconcomitantlysmallersacrificeofmaterialwelfareentailedinrestrictingGHGemissions.ThatcouldcontributetoweakeningeconomicallymotivatedresistancetoascheduleofgraduallyrisingcarbontaxesandthereforeimpartwiderandstrongercommitmentstonationalandinternationalagreementsoncoordinatedandverifiableactionsthatwouldcurtailGHGemissions.Bundlingproposedcommitmentsfromlowerincomedevelopingeconomieswithreciprocalloansubsidiesandcostconcessionsinthetransfertonew“greener”andcarbon‐freetechnologieswouldconstituteacrediblepackagefornegotiationsthatwouldgrowinitsattractivenessastheR&Dprogramsmatured.

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AcknowledgementsThepresentpaper isthe latestversionofthethorough‐goingreformulationandelaborationoftheworkthatDavidandvanZonpresentedatthe6‐8July2011conferenceoftheInternationalEnergyWorkshop, held at Stanford University. We take this occasion to repeat the gratefulacknowledgementmadeonthatoccasionofthecontributionsofBronwynHallandLucSoetetoearlier drafts on this approach to climate policy research (David et al., 2010) prepared fordiscussion at the workshop on “Grand Challenges for Science and Technology Research”organized by Dominique Foray and Richard Nelson in Lausanne, on 13‐14 May, 2011. ThepresentpaperhasbenefitedfromthediscussionbyparticipantsintheIEWconferencesessionon“R&DInvestment,ClimateandEnergyPolicy,”andfromcomments(onsubsequentversions)by members of the SIEPR‐CEEG Social Science and Technology Seminar at Stanford on 14December2011;and faculty anddoctoral students attending theCEMI seminarspresentedbyDavidattheÉcolePolytechniqueFédéraledeLausanneon17and30May2012.Weunabletoindividually acknowledge all those who on those occasions asked stimulating questions, anddrew our attention to pertinent research that we should consult, but wish to express ourindebtedness to the perceptivecommentsandsuggestionsofferedbyLawrenceGoulderandThomas Weber and also to Ashish Arora, Dominique Foray, Ward Hanson, and WarrenSanderson.Asonpreviousoccasions,thecommentsofEdwardSteinmuelleronthislatestdraftwereespeciallyhelpful.Davidgratefullyacknowledgesthesupportofa“seedgrant”fromtheStanford Institute for Economic Policy Research, and the hospitality extended to him by theDirector and staff of the United National University‐MERIT on the occasions of his workingsojournsinMaastrichtduring2011‐2013.

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