management of energy technology for sustainability: how...

Management of Energy Technology for Sustainability:How to Fund Energy Technology Research and

Development

Erin BakerDepartment of Mechanical and Industrial Engineering, College of Engineering, University of Massachusetts, Amherst, Massachusetts

01003, USA, [email protected]

Senay SolakDepartment of Operations and Information Management, Isenberg School of Management, University of Massachusetts, Amherst,

Massachusetts 01003, USA, [email protected]

O perations management methods have been applied profitably to a wide range of technology portfolio managementproblems, but have been slow to be adopted by governments and policy makers. We develop a framework that

allows us to apply such techniques to a large and important public policy problem: energy technology R&D portfoliomanagement under climate change. We apply a multi-model approach, implementing probabilistic data derived fromexpert elicitations into a novel stochastic programming version of a dynamic integrated assessment model. We note thatwhile the unifying framework we present can be applied to a range of models and data sets, the specific results dependon the data and assumptions used and therefore may not be generalizable. Nevertheless, the results are suggestive, andwe find that the optimal technology portfolio for the set of projects considered is fairly robust to different specifications ofclimate uncertainty, to different policy environments, and to assumptions about the opportunity cost of investing. We alsoconclude that policy makers would do better to over-invest in R&D rather than under-invest. Finally, we show that R&Dcan play different roles in different types of policy environments, sometimes leading primarily to cost reduction, othertimes leading to better environmental outcomes.

Key words: energy technology; R&D portfolio; climate change; public policy; stochastic progammingHistory: Received: September 2012; Accepted: January 2103 by Daniel Guide, after 2 revisions.

1. Introduction

Climate change is one of the biggest public policyproblems currently facing the world. It is a very diffi-cult problem for a number of reasons, including thelong time frames, the global nature of the problem,and the deep uncertainty surrounding it. It is becomingclear that rapid technological change will be necessaryin order to limit climate change in a way that is consis-tent with sustainable economic growth and currentpolicies (Nordhaus 2011). One way of supporting suchrapid technological change is through government-supported research and development (R&D) invest-ment. While governments around the world have sup-ported R&D for a very long time, there has been recentinterest in applying a scientific basis to their resourceallocation (National Research Council 2007).In this study, we develop a framework that uses

empirical data for the assessment of possible R&D pol-icy choices for sustainability. More specifically, weaddress the following important public policy ques-tions: given the uncertainty defined by currently avail-able data in future technological success and climate

change, what energy technology investment policieswill maximize expected social welfare? And how dooptimal investment policies differ under alternativestrategies proposed for dealing with climate change,such as those suggested by Al Gore (Gore 2007), theStern report (Stern 2007), and the Kyoto Protocol?In order to address these questions and provide

policy insights, we develop a multi-step multi-modelapproach involving a dynamic and stochastic R&Dportfolio decision process. While doing so, we com-bine methods from multiple strands of research inoperations management, including elicitation baseddecision analysis, stochastic programming, microeco-nomics, and computational economic analysis. In theremainder of this section we present the generalframework for our problem, describe the research inthe area, and discuss how our analysis and findingscontribute to the existing literature.

1.1. General Decision FrameworkThere are two key near-term societal responses to cli-mate change. The first and most direct is abatement,that is to reduce emissions of the greenhouse gases

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Vol. 23, No. 3, March 2014, pp. 348–365 DOI 10.1111/poms.12068ISSN 1059-1478|EISSN 1937-5956|14|2303|0348 © 2013 Production and Operations Management Society

that are causing climate change to a level below whatthey would otherwise be. Examples of questionsrelated to this response would be the determinationof the optimal path of emissions in future years, emis-sions allocations, or the level of a carbon tax. A secondresponse to climate change is to invest in energy tech-nology R&D so that emissions abatement will be lesscostly in the future. A given emissions path influencesthe set of technologies society would like to have inthe economy, and the set of technologies actuallyavailable influences the optimal level of emissionsreductions. We explicitly recognize and model thisinterdependency as part of our analysis in this study.Specifically, we simultaneously determine the opti-mal investment in a portfolio of technology R&D pro-jects and the optimal emissions path so that theexpected societal costs of climate change are mini-mized. Our analysis is a global one in that climatechange is a global problem, with worldwide emis-sions affecting all parts of the globe. On the otherhand, the R&D project data is based on US govern-ment investment options.The decision process we consider for our R&D

investment optimization framework consists of twodistinct but interlinked decision stages. These corre-spond to near-term decisions to be made over the next50 years under climate change and technologicaluncertainty and long-term decisions to be made aftermore information on uncertainties becomes availableafter the 50-year period. The near-term decisions arehow much to invest in which technologies and thelevel of short-term abatement. These decisions aremade under the uncertainty of technical success,which is dependent on the projects that are funded ineach technology category, where success for a projectmeans that a particular goal has been met. Hence, theuncertainty over technological success is endogenous:it depends on the decisions that will be made. Eachtechnological success realization has a specific impli-cation for future abatement costs, meaning that tech-nological success will impact the costs of reducingemissions. The second stochastic characterization inour framework is an exogenous one and correspondsto the damages due to climate change. The uncertaintyin these damages is represented through the parame-ters of a damage function, where the damage functiondepends on the stock of emissions in the atmosphere.The second stage decisions, which involve long-termabatement decisions, will be determined after infor-mation about future abatement costs and the damagesbecomes available. The objective for the overalldecision problem is to maximize expected total socialutility over the entire planning horizon involving thenext four centuries. Surrounding all these decisions isthe policy framework that defines the boundaries andlimits for the decision making process.

1.2. Relevant LiteraturePrevious approaches to addressing climate changepolicy have included a great deal of theoretical worklooking at how the optimal near-term policy changeswith different characterizations of uncertainty (seeBaker 2009 for a review). These studies, however, donot involve R&D decisions and use purely illustrativeprobability distributions to represent uncertainty.While Baker and Shittu (2008) review a set of papersthat study R&D decisions in the face of climate and/or technology uncertainty, these papers are againbased on illustrative distributions, and, moreover,they consider only one technology at a time.There are few papers that study the impact of

uncertainty on a portfolio of energy technologies (seeBaker and Solak 2011 for a review, including thosethat consider learning-by-doing rather than R&D).The one study we know of, Blanford (2009), usesillustrative probability distributions and simplyassumes there are decreasing returns to scale in R&Dinvestment. Our study differs in that we use empiri-cal probability distributions obtained through expertelicitations within a comprehensive stochastic port-folio model we develop.While Baker and Solak (2011) also describe a sto-

chastic R&D optimization model based on elicitednumerical data, it is a simplified model that repre-sents the economy and the impacts of climate changewith a single equation and two planning periods. Dueto this simple structure it is unable to consider multi-ple policy frameworks. On the other hand, theinsights from this model serve as input to the compre-hensive analysis performed in this study.On the other end of the spectrum from the theoreti-

cal analysis is a body of work based on technologi-cally detailed Integrated Assessment Models (IAMs),1

which integrate economic models with climate mod-els in order to provide policy relevant insights(Clarke et al. 2008, 2009). While these analyses pro-vide important insights into the value of technologyin society’s response to climate change, they do notexplicitly incorporate uncertainty or address thequestion of the optimal R&D policy. One exception isa recent analysis by Anadon et al. (2011), where theauthors combine empirical data with an IAM-basedanalysis to perform portfolio optimization. Unlikeour study, however, their data do not differentiatebetween different projects within technology catego-ries, and the optimization itself is not stochastic—they consider only the most likely outcome for anygiven R&D investment. Yet, a recent study by theNational Academy suggests that uncertainty beexplicitly included in the US Department of Energydecisions about investments into R&D (NationalResearch Council 2007). Thus, our study is unique inexplicitly incorporating uncertainty and stochastic

Baker and Solak: Management of Energy Technology for SustainabilityProduction and Operations Management 23(3), pp. 348–365, © 2013 Production and Operations Management Society 349

R&D optimization within a detailed IAM-based anal-ysis while maintaining tractability in the resultingmodel.The remainder of this study is structured as fol-

lows. In section 2, we describe the general structurefor our modeling approach. The components of themodel are developed in section 3, and stochastic opti-mization procedures are described in section 4. Theexperimental setup for policy analysis is discussed insection 5, while the numerical results and their impli-cations are described in section 6. Finally, in section 7we provide a summary of our conclusions.

2. Integrated R&D and AbatementPolicy Optimization Model

The stochastic optimization problem representing thedecision process described in section 1.1 involves thedetermination of an optimal portfolio of technologyinvestments and an abatement policy such that theexpected total social utility over the planning horizonis maximized. For a general mathematical representa-tion of this problem, we first let the investment deci-sions be denoted by a vector γ, and the near-term andlong-term emissions abatement decisions by vectorslN and lL, respectively.2 Note that abatement isdefined as the fraction of emissions reduced belowthe business-as-usual level. Similar to the notationused for abatement, the vectors yN and yL representthe total output of goods and services in near-termand long-term, while sN and sL are the atmospherictemperatures. In addition, the vectors xN and xL areused to denote the set of other decision variables ineach stage that define the relationships between cli-mate change, the economy, and social utility. We rep-resent the two critical functions in our framework,namely, the abatement cost function and the damagefunction, as cðlsÞ and DðssÞ, s = N,L, indicating theirdependence on abatement decisions and atmospherictemperatures, respectively. Moreover, we representuncertainty about technology and climate changeinformation through the set Ω of all possible scenar-ios, with x 2 Ω representing a single scenario. Theprobability of the occurrence for each scenario isdenoted by px. Given this representation, the inte-grated R&D and abatement policy optimizationmodel is stated in general form as follows:

max!;lN ;yN ;sN ;xN ;l

XL;yX

L;sXL;xX

L

UNð!; lN; yN; sN; xNÞ

þXx2X

pxULðlxL ; yxL ; sxL ; xxL ;xÞ ð1Þ

s.t. yN ¼ gðcðlNÞ;DðsNÞ; xNÞ ð2Þ

yxL ¼ gðcðlxL Þ;DðsxL Þ; xN; xxL ;xÞ 8x ð3Þ

GNð!; lN; yN; sN; xNÞ�bN ð4Þ

GLð!; lN; yN; sN; xN; lxL ; yxL ; sxL ; xxL ;xÞ�bxL 8x; ð5Þ

where the superscript in lxL ; yxL ; s

xL , and xxL denotes

the dependence of these decision variables on therealized values of the stochastic parameters for each

scenario, while the superscript in lXL ; yXL ; s

XL , and xXL

implies that the optimization is performed over thecorresponding variables in all scenarios, as we let

lXL ¼ hl1L; . . .;ljXjL i, yXL ¼ hy1L; . . .;yjXjL i, sXL ¼ hs1L; . . .;sjXjL i,and xXL ¼ hx1L; . . .;xjXjL i. The function g(�) in constraints(2) and (3) represents the relationship between out-put, climate changes damages, and abatement ofemissions.The functions Usð�Þ, s = N,L represent total social

utility over the near- and long-term stages, each ofwhich consists of multiple time periods. Hence, objec-tive (1) involves maximization of the summation ofthe near-term and the expected long-term social utili-ties, where the expectation is defined over all possiblescenarios. Equations (2) and (3) represent the relation-ship between output of goods and services, climatechange damages, and abatement costs for the near-term and long-term decision problems, respectively.Similarly, the constraint sets (4) and (5) correspondto the relationships defining the interplay betweenclimate change, the economy, and social utility. Notethat the second stage constraints (3) and (5), and thusthe optimal long-term abatement policy, is dependenton the technology investments !, near-term abate-ment lN , the output levels yN , the atmospheric tem-peratures sN , and other related decisions xN made inthe initial decision stage.There are several challenges, however, that need to

be overcome to fully implement this model as a validenergy technology R&D policy analysis. Theseinvolve the development of functional representa-tions and inputs for this general problem structure, aswell as methodological integration and implementa-tion within a tractable stochastic optimization frame-work. We address these challenges by seekinganswers to the following questions through a multi-step multi-model process: (1) step 1: modeling of theinvestment options for decision vector !: what tech-nology projects should be considered? What are thereturn characteristics for these technology projects?(2) Step 2: modeling of the social utility functionsUsð�Þ, constraint sets Gsð�Þ, s = N,L, and the outputfunction g(�): how should the interplay between socialutility, climate change, and the economy be modeled?How does R&D investment impact these relation-ships? (3) Step 3: modeling of uncertainty for scenarioset Ω: how should the uncertainty in climate changedamages and the uncertainty in R&D-induced technical

Baker and Solak: Management of Energy Technology for Sustainability350 Production and Operations Management 23(3), pp. 348–365, © 2013 Production and Operations Management Society

change be modeled? (4) Step 4: implementation andsolution of the stochastic optimization problem (1)–(5): how should different modeling components beintegrated and implemented under a tractable sto-chastic optimization framework?In the next two sections, we describe how we

address these issues to identify policy results forenergy technology R&D under climate change. Thefirst two steps listed above correspond to generalmodel component development and are discussed in sec-tion 3. The last two steps, which involve uncertaintymodeling and stochastic optimization, are described insection 4.

3. Model Component Development

We discuss model component development sepa-rately for each of the first two steps listed in section 2above. For some parts of these steps, we utilize resultsfrom relevant modeling and analysis efforts that aredescribed in detail in other studies. In the descriptionsbelow, we provide references to these studies and alsodiscuss how we relate the results from these modelsto our integrated R&D and abatement policy optimi-zation framework.

3.1. Step 1: Modeling of the Investment Options3.1.1. Identification of Technologies and Projects.

Our analysis considers investment options in threekey technology areas: carbon capture and storage(CCS), nuclear fission, and solar photovoltaics. Whilethis does not cover the full portfolio of energy tech-nologies, or even electricity technologies, it provides agood representation of the problem. Lewis andNocera (2006) have pointed out in their analysis thatthese three technologies are the only ones with suffi-cient resources to provide the carbon-neutral energyneeded to address the climate change problem. Thus,our work can provide specific insights into how tobalance among three key technologies as well as aframework that can be expanded into more technolo-gies in the future as necessary. Each of the three keytechnology categories contains multiple researchareas, or “projects,” in which R&D investments can bemade. The research areas considered for each technol-ogy are listed in Appendix S3. These projects werechosen jointly with experts, with the aim of consider-ing the projects in each technology that have the pos-sibility of resulting in a breakthrough. Hence, theyrepresent the most relevant investment options ineach technology from a policy perspective.

3.1.2. Characterization of Success Probabilitiesfor Individual Technology Projects. The probabilityof success in each project is defined through expertelicitations. Expert elicitation is a formal process for

quantifying an expert’s judgment about uncertainquantities and capturing those judgments in terms ofprobabilities that can be used in further analyses(Hora 2004). While expert elicitations are subject to anumber of known biases (Tversky and Kahneman1974), no other method exists that can be used to gaininformation about potential future breakthroughs intechnologies. In fact, in a review of the climate changeassessment of the Intergovernmental Panel on Cli-mate Change, Inter Academy Council (2010) specifi-cally suggests that “to inform policy decisionsproperly, it is important for uncertainties to be charac-terized and communicated clearly and coherently ...[w]here practical, formal expert elicitation proceduresshould be used to obtain subjective probabilities forkey results.”We base our model on the expert elicitations sum-

marized in Appendix S3, and described in detail byBaker et al. (2008, 2009a, 2009b). The elicitationsassume that each project can be invested in at one ofmultiple potential levels, where investments includeonly US government funding are measured based onnet present value. Each project is also associated withspecific endpoints or targets to be assessed, such as agiven cost and efficiency level, which define successfor that project. The specific probabilities of successdefined through the elicitations for different invest-ment levels of each project reflect an aggregation ofthe individual experts’ judgments. Expert input wasalso used to define both the funding levels and theendpoints to be assessed.3

3.2. Step 2: Modeling of the Social UtilityFunctions and the Constraint SetsThe modeling of the social utility functions Usð�Þ, theconstraint sets Gsð�Þ for s = N,L, and the output func-tion g(�) involves multiple phases. First, the complexrelationships between climate change, emissionsabatement, the economy, and social utility are repre-sented in basic form through a well-known IAM,namely, the Dynamic Integrated Model of Climateand the Economy (DICE) (Nordhaus 1993). Then,these relationships are expanded to include R&Dinvestments and the impact of resulting technicalchange. This requires the quantification of the impactof R&D on abatement cost functions and the integra-tion of this quantitative measure into the modelingframework as part of the constraint sets.

3.2.1. Basic Representation through the DICEModel. DICE is a deterministic global optimalgrowth model that includes interactions between eco-nomic activities and the climate. The model covers along planning horizon, typically around 400–600years, in 10-year periods. In each period, economicoutput (measured as the gross domestic product


(GDP)) is divided between consumption and invest-ment in new capital, consistent with the standardoptimal growth framework in economic analysis.DICE adds to this framework by modeling the emis-sions of greenhouse gases into the atmosphere as partof the production process. The general formulation ofthe DICE model is given in Nordhaus (2008), and isalso summarized through Equations (6)–(13) below.We will later extend constraints (8) and (11) in thisformulation through inclusion of uncertainty andinvestment decisions. The summary formulation uti-lizes the parameters and variables shown in Table 1.

maxl;y;s;x

Xt

Rtut ð6Þ

s.t. ut ¼ LtðotLtÞ

1�b � 1

1� b8t ð7Þ

yt ¼ ot þ lt 8t ð8Þkt ¼ lt�1 þ ð1� rÞkt�1 8t ð9Þ

st ¼ Hðst�1; etÞ 8t ð10Þ

yt ¼ 1� cDðltÞDDðstÞ y

gt 8t ð11Þ

ygt ¼ AtL

1�ct kct 8t ð12Þ

et ¼ Stð1� ltÞygt þ Et 8t ð13ÞSimilar to the notation used in the general descrip-

tion in section 2, the vector x ¼ ho;yg;k; l; e;ui in

objective (6) is used to refer to all other variables inthe formulation, except for the abatement vector l,output vector y, and temperature vector τ. Key inde-pendent decision variables in the formulation are l

and o, while the others are dependent variables deter-mined by the values of l and o. Note that elements ofl, y, τ, and x consist of both near-term and long-termdecision variables, as they include all periods, so nosuch distinction is made in the notation used. More-over, the formulation does not involve R&D invest-ment, which we later include through extensions ofthe given relationships.In the formulation above, objective (6) ensures that

policies are chosen to maximize the discounted sumof social utility ut over time. Utility is based on percapita consumption ot, as defined through the rela-tionship in Equation (7). This constraint defines utilityin each period as an isoelastic function of consump-tion, where b is the calibrated elasticity parameter.Consumption is defined by Equation (8) as the differ-ence between output of goods/services yt and thecapital investment lt. Capital balance relationship isrepresented through constraint (9). Constraint (10)represents a set of constraints that link greenhousegas emissions et to the global temperatures st. Notethat the accumulation of greenhouse gases, especiallycarbon dioxide, affects welfare by increasing globaltemperatures. Thus, the representative functionHðst�1; etÞ is increasing in et. A key equation in themodel is Equation (11), which represents the relation-ship between output of goods/services yt and theimpacts of climate change. This representationinvolves the unadjusted output y

gt in each period,

which is determined by inputs of labor Lt and capitalkt as defined by Equation (12). Note that the climatechange damage function in DICE, that is, DDðstÞ inthe denominator of the right-hand side of Equation(11), is an increasing function of st. This implies that ahigher temperature negatively impacts the output yt.In order to mitigate this effect, an abatement level ltcan be chosen each period, which reduces emissionset below what would otherwise occur for a given pro-duction level. This relationship between abatement ltand emissions et is represented through constraint(13). While abatement has benefits, it is costly, as theabatement cost function cDðltÞ in the numerator ofEqution (11) is increasing in lt. Hence, higher abate-ment reduces the output available for consumption orinvestment in every period. In other words, lowerabatement positively impacts the output yt. Thistrade-off needs to be managed by choosing the bestabatement effort lt in each period, as the optimalabatement path reflects a balance between benefitsand costs.Here we highlight two equations that we will use to

incorporate R&D investments and stochasticity into

Table 1 List of Parameters, Variables, and Functions Used in theSummary Formulation of the DICE Model

ParametersRt : Utility discount factor for period tAt : Level of total factor productivity in period tSt : Ratio of uncontrolled emissions to output in period tEt : Emissions from deforestation in period tLt : Population and labor input in period tb: Elasticity of marginal utility of consumptionc: Elasticity of output with respect to capitalr: Rate of depreciation of capitalFunctionsH(�): Function linking emissions to atmospheric temperaturecDð�Þ: Abatement cost function in the DICE modelDDð�Þ: Climate change damage function in the DICE modelVariablesot : Consumption of goods/services in period tyt : Net output of goods/services in period tygt : Unadjusted output in period tkt : Capital stock in period tlt : Investment in period tet : Total carbon emissions in period tlt : Emissions abatement in period tst : Atmospheric temperature in period tut : Social utility in period t


our modeling framework. The first is Equation (8),which shows how economic output yt in each periodis used. We will include R&D investments into themodel through the modification of this constraint,which we describe in section 3.2.3. The second equa-tion we highlight is Equation (11), which shows howthe cost of abatement and the damages from climatechange impact economic output yt in each period t.The abatement cost function cDðltÞ, for which adetailed description is provided in Appendix S5, willbe revised to include the impact of technical changedue to R&D investments. This procedure is alsodescribed in section 3.2.3. On the other hand,DDðstÞ ¼ 1 þ ps2t in Equation (11) represents thedamages from climate change resulting from atmo-spheric temperature st, where p is the damageparameter. We will take p to be a stochastic parame-ter in our model, representing the uncertainty in cli-mate change damages, which we describe further insection 4.1.1.The DICE model formulation links to our general

model (1)–(5) as follows: the utility function in Equa-tion (1) is represented by objective (6) and Equation(7), Equations (2)–(3) correspond to Equation (11),and the general constraints (4)–(5) involve Equations(8)–(10) and Equations (12)–(13).

3.2.2. Quantifying the Impact of R&D onAbatement Costs. The basic relationships repre-sented through the DICE model need to be expandedto include R&D investment decisions and theirimpacts on other problem components. To achievethis, we first need to define measures that model howtechnical change resulting from R&D impacts abate-ment costs. We will then develop a procedure to inte-grate these quantified impacts into the modelingframework.Recall that the second stage decision of “long-term

abatement,” involves choosing an emissions abate-ment level for each period such that expected totalsocial utility is maximized. Social utility is related tothe cost of abatement, as higher costs would implylower net economic output. On the other hand, thecost of abatement is dependent on the realized tech-nological success in the invested R&D projects.Hence, we need to derive abatement cost functionsunder different technological success outcomes toimplement in the model. We achieve this through thetwo phase process described below, which is also dis-cussed by Baker and Solak (2011).

3.2.2.1. Deriving Marginal Abatement Cost Curves:Rather than deriving abatement cost functionsdirectly for each technological success outcome, wefirst derive Marginal Abatement Cost Curves (MACs),which reflect the cost of reducing emissions byan additional tonne. We then use these curves to

parameterize the impact of technical change on abate-ment cost functions.We utilize the definitions of success described in

section 3.1 to derive MACs using a technologicallydetailed integrated assessment model, namely, theGlobal Change Assessment Model (GCAM) (Brenkertet al. 2003, Edmonds et al. 2004). We use MACsrather than abatement cost curves for two reasons.First, the MAC is a key unit of analysis in our decisionproblem: as long as there is an interior solution to thesecond stage decision for a given realization of uncer-tain parameters, abatement will be optimized wherethe marginal cost of abatement is just equal to themarginal damages avoided by abatement. Second, theMAC is easy to generate from IAMs and is morelikely to be consistent across IAMs than the abatementcost curve.To derive the MACs, curves were generated in

GCAM that relate levels of emissions reduction tocarbon prices, thus approximating the marginal costof abatement. This was done for each possible combi-nation of projects assuming success in each project. Aselection of the MACs that were derived usingGCAM are shown in Appendix S6, where the base-line MAC used to measure the impact of technicalchange refers to the case with no R&D-induced tech-nical change as defined by Clarke et al. (2008). Wedemonstrate in Appendix S6 the impact of three pro-jects (one from each technology, i.e., CCS, nuclear,and solar), if each of them were successful indepen-dently as well as the MAC that is generated byGCAM if all three of the projects were successfulsimultaneously. The changes with respect to the base-line MAC are a combination of pivoting the curveclockwise around zero and shifting the entire curvedown. CCS has more of a pivot, as it results in anearly proportional reduction in the MAC. Nuclear,on the other hand, has more of a constant downwardshift, with a much smaller pivot effect. Solar has avery similar qualitative impact as nuclear, althoughits overall impact is small.

3.2.2.2. Parameterizing the Impact of R&D-InducedTechnical Change on Abatement Cost Functions: Theprocess described above resulted in numerical MACcurves for each combination of successful technologyprojects. In order to make this tractable and portableto our framework, the next step was to estimateparameters that quantify how each technology combi-nation impacts the baseline MAC. To this end, foreach combination of successful projects, we usedEquation (14) below to estimate a pivot vectora ¼ haCCS; anuclear; asolari, with each component repre-senting the pivoting effect of the correspondingtechnology based on the successful projects in thattechnology, as well as a shift parameter h(a). The shiftparameter was represented as a function of a, because


a unique shift effect was observed for every combina-tion of values of ai, i = CCS,nuclear,solar:

gMACðl; aÞ ¼Yi

ð1� aiÞMACðlÞ � hðaÞMACð0:5Þ;

ð14Þwhere MAC(l) is the numerical baseline MAC fromGCAM, with l 2 [0,1] denoting the level of abate-ment, and gMACðl; aÞ is the estimated MAC aftertechnical change, where technical change is repre-sented through the vector a. The product termQi

ð1 � aiÞ models the pivoting of the function

MAC(l) due to technical success, while h(a) modelsthe corresponding shift. Notice that the shift h(a) isanchored on 50% abatement to make this represen-tation portable from GCAM, in which the parame-ters were derived, to other modeling frameworks.Let S ¼ [iSi refer to some given combination of

successful technology projects, where Si denotes theset of successful projects in technology i, i = CCS,nuclear,solar. The process for deriving the values of aiand h(a) for any given set S was as follows. First, aproject pivot parameter, denoted by aij was estimatedusing the generated MACs for each individual projectj 2 Si in technology i. The values of these parameters,which vary depending on the level of success in a pro-ject, are listed in Appendix S7. Second, we makethe assumption that, within any technology i, only thebest project (the one with the greatest impact onthe MAC) will impact the economy. Therefore, wedefine ai as ai ¼ maxjfaij : j 2 Sig. Finally, for everycombination of possible technological outcomes rep-resented by the three ais for the three technologies, ashift parameter h(a) was estimated numerically.The relationship in Equation (14), which is

defined over the MACs, needs to be transformedinto a relationship over abatement costs for imple-mentation in our model. We do this by integrationand define a functional Φ(c(l),a) that translates anygeneric baseline cost function (without technicalchange), denoted by c(l), to a new abatement costfunction with technical change. Specifically wedefine a functional U : F � Rn ! F , where F is aset of functions and Rn is a set of real vectors, asfollows:

UðcðlÞ; aÞ ¼Yi

ð1� aiÞcðlÞ � hðaÞcð0:5Þl: ð15Þ

This can be used to model the impact of technicalchange on any abatement cost function.

3.2.3. Integrating R&D Investment andR&D-Induced Technical Change into the ModelThe investment decisions for each technology and theparametric representation of the resulting impacts

need to be integrated into the modeling frameworkthrough the introduction of new variables and con-straints. We discuss this procedure here.We noted in section 3.2.2 that nuclear and solar

have similar impacts, in that they both havestrong shifts as well as pivots, as opposed to CCS,which mainly has pivoting effects. Given thisstructure, we combine nuclear and solar into onecategory, calculating the resulting pivot values asa2 ¼ 1 � ð1 � anuclearÞð1 � asolarÞ. Thus, we repre-sent R&D investments by using only two technol-ogy categories in the model (i = 1 for CCS andi = 2 for solar/nuclear).

3.2.3.1. Integrating R&D Investment Decisions intothe Model: Modification of Constraint (8): We assumethat R&D investment will take place over the next50 years at a constant rate. In the basic representa-tion in section 3.2.1, output in each period isdivided between consumption and investment intraditional capital as noted in Equation (8). Weextend this relationship to include R&D investmentfor periods t � 5 as follows. Note that each plan-ning period corresponds to 10 years, that is, t = 5implies 50 years:

yt ¼ ot þ lt þ jð!1 þ !2Þ=5 8t� 5; ð16Þ

where j is an opportunity cost multiplier, and !i isthe investment in each technology area i, with theindex i corresponding to CCS and solar–nuclear asdefined above. Hence, the total output in each periodis either consumed, as represented by the variable ot,or invested in traditional capital, as represented bythe variable lt, or invested in R&D, as represented byjð!1 þ !2Þ=5. While !i is a decision variable, theopportunity cost j is a parameter for which we per-form sensitivity analysis as part of the numericalexperiments described in section 5.1.

3.2.3.2. Integrating R&D-Induced Technical Changeinto the Model: Modification of Constraint (11): Follow-ing the cost function structure described by Equation(15) in section 3.2.2, we model the impact of technicalchange by altering constraint (11) as follows:

yt ¼ 1�UðcDðltÞ;aÞDDðstÞ y

gt

¼ 1�Qið1� aiÞ½cDðltÞ � hðaÞcDð0:5Þl�

DDðstÞ ygt 8t:

ð17Þ

The model of technical change in Equation (17),however, results in a non-convex model, involvingmultilinear terms due to multiplication of ai, whichdepend on the investment decision variables !i. Todeal with this, we estimate tight linear approxima-tions to the actual functions. More specifically, weuse our data on the ai and h(a) to estimate the two


quantities of ð1 � a1Þð1 � a2Þ � 1 � 0:8a1 � 0:92a2and ð1 � a1Þð1 � a2ÞhðaÞ � 0:02 � 0:06a1 þ 0:14a2.Thus, we express the revised production function inour model for t > 5 as follows.

We show in Appendix S8 that modeling the pivotand shift effects through these linear approximationsensures that convexity of the optimization model ismaintained in the extended stochastic model for thegiven practical bounds for variables.

4. Uncertainty Modeling and StochasticOptimization

In this section, we describe how we model the sto-chastic structure in the energy technology R&D port-folio problem through a scenario set, and how wesolve the resulting optimization model using stochas-tic programming.

4.1. Step 3: Modeling of UncertaintyAs noted in section 1.1, our model involves two typesof uncertainty: the exogenous uncertainty in climatechange damages and the endogenous uncertainty intechnical change that is a function of the R&D invest-ment decisions.

4.1.1. Modeling the Uncertainty in ClimateChange Damages. We model the uncertainty inclimate change damages through a probabilisticcharacterization of the parameter p in the damageequation DDðstÞ ¼ 1 þ pst2. This is done by defininga three-point discrete probability distribution for pbased on previous elicitations (Nordhaus 1994). Aspart of our analysis, we consider several risk cases forclimate change, which are represented by differentdistributions of the parameter p. These risk cases anddistributions are discussed in section 5.3.

4.1.2. Modeling the Uncertainty in TechnicalChange. In section 3.1, we identified individual suc-cess probabilities for technology projects, and in sec-tion 3.2.2, we modeled how different technologicalsuccess outcomes, defined through the pivot parame-ters a, impact emission abatement costs. For a givenportfolio of projects, it is possible to calculate theprobability of each success outcome from the elicita-tion data in Appendix S3 through multiplication ofindividual project success probabilities. These proba-bilities, however, are dependent on technology invest-ment decisions, as they will change based on theproject portfolio selected. This is the endogenous

uncertainty described in section 1.1, where the proba-bility of a specific outcome is not fixed but ratherchanges with different decisions. However, such deci-sion dependent probability distributions are typically

not amenable for direct use in stochastic optimization,specifically in stochastic programming. To overcomethis, we develop a procedure to derive returns func-tions with fixed probabilities, where each functionrepresents how the values of a, that is, returns fromtechnology investments, change as a function of theinvestment amounts γ.

4.1.2.1. A Reduced-Form Portfolio Model: The proce-dure we develop to derive returns functions withfixed probabilities is built upon some insightsobtained from the reduced form portfolio model inBaker and Solak (2011), summarized in Appendix S9.Two key conclusions from this work are directlyrelated to our analysis in this study. First, the authorsnote that for a given budget level the composition ofthe optimal portfolio of projects is robust to risk in cli-mate damages. This conclusion implies that we donot have to explicitly model the individual technologyprojects in our analysis. Instead, we consider a dis-crete set of potential R&D investment levels and iden-tify the optimal set of technology projects for eachof these investment levels. Recall that for a givenportfolio of projects, it is possible to calculate theprobability of each possible a value using the elicita-tion data in Appendix S3. Hence, this process resultsin a probability distribution for the pivot (and shift)parameters for each investment level. As describedlater in this section, we use these distributions toderive “returns functions,” in which probabilities arefixed, and pivot and shift parameters change as afunction of R&D investment.Additionally, Baker and Solak (2011) conclude that

the optimal amount of R&D funding does changewith increases in the riskiness of climate damages in anon-monotonic way. Specifically, when an increase inrisk is modeled as a mean-preserving spread thatstretches out the tail, it is found that the optimalamount of R&D funding first increases and thendecreases in risk. The reason has to do with the com-plex interplay between technology investment andlong-term emissions abatement. This result supportsthe motivation for our current model in which we usea stochastic dynamic optimization model in order tocapture the interactions between climate change dam-ages, abatement, and the impact of R&D under multi-ple policy frameworks. Through inclusion of severalfactors such as capital accumulation in the economy,

yt ¼ ½1� ðð1� 0:8a1 � 0:92a2ÞcDðltÞ � ð0:02� 0:06a1 þ 0:14a2ÞcDð0:5ÞltÞ�DDðstÞ y

gt : ð18Þ


carbon concentration in the atmosphere, and thewarming of the deep oceans, our current work is ableto represent these complex dynamics in order to pro-vide a convincing policy analysis.

4.1.2.2. Derivation of Stochastic Characterizations ofReturns to R&D: For stochastic characterizations ofreturns to R&D, we develop a probabilistic mappingfrom investment decisions !i to the technical changevariables ai, which represent the returns to R&D intechnology category i, i = 1,2. As discussed above,this is done by initially considering a discrete set ofpossible investment levels or budgets. Given a budgetlevel, the reduced-form R&D model identifies an opti-mal portfolio of projects for that budget level. Eachportfolio is associated with a probability distributionover the possible outcomes of ai for each technologycategory i. Since there is only one optimal portfolioper budget level, this allows us to associate a proba-bility distribution over the ai values to each givenbudget level.In the right half of Table 2, we show these values

for CCS, with a probability distribution in each bud-get column and the a1 values in the last column. Animportant issue is the selection of the budget levelsfor this discrete representation of R&D investment.We considered a wide range of possible R&D bud-gets, and chose those that were optimal investmentsin some instance of the reduced-form model orresulted in a significant welfare improvement overother R&D budgets that we considered.As noted previously, however, endogenous proba-

bilities given in the lower half of Table 2 are not ame-nable to stochastic optimization; rather we need amapping where the probabilities are fixed and the aivalues change with the investment decisions. Weachieve this by deriving a set of random piecewiselinear returns functions, which we denote by Ai, forthe two technology categories i = 1,2. Each realizationof Ai maps R&D investment levels !i to technologyparameters ai, that is, Ai : !i ! ai. The functions Ai

are piecewise linear, as they are defined based on adiscrete set of investment levels.To derive the functions Ai, we started by enumerat-

ing all possible functions. As an example, one possi-ble combination for CCS corresponds to the case

when a1 is realized as 0 at all budget levels. Thisenumeration, however, results in a large number offunctions, which is intractable for optimization pur-poses. Thus, we perform a scenario reduction processand identify a subset of the possible returns functionsthat provides a good approximation of the actualdata-based distributions. First, we eliminated allreturns functions that did not exhibit a dependencebetween funding levels—that is, we assume that if aproject is successful at a lower budget level, it will besuccessful at a higher budget level. Then, we followeda process based on the minimization of the standarddeviation of the differences between the actual proba-bility distributions and the probability distributionsderived from the subset of the functions. Finally, inorder to improve the overall match for solar nuclear,we added in two returns functions that did not exhi-bit dependence.Table 3 shows the estimated returns functions for

CCS, while the corresponding functions for the solar–nuclear technology category are included inAppendix S10. For example, in Table 3, the third rowrepresents a returns function that has a1 ¼ A1ð!1Þ ¼ 0if !1 \ $319 million and a1 ¼ A1ð!1Þ ¼ 0:319 if!1 � $319 million. The probability that this particularfunction is realized is 0.07. As noted above, thesefunctions together with their probabilities provide avery good estimate of the actual probability distribu-tions, with an average standard deviation of the errorsof 0.02. Table 2 compares the estimated data with theactual data for CCS, showing the estimated probabili-ties and the actual probabilities of possible a1 valuesat each investment level. They are very close, with thedifferences being less than 1 percentage point in eachcase. Similar results hold for the approximations ofthe solar–nuclear returns functions as well, with dif-ferences being less than 4 percentage points in eachcase. Note that the set of ai values shown in Table 3and Appendix S10 are based on the values of theparameters aij for each project j, which are listed inAppendix S7, and are derived as described in section3.2.2. While a1 is directly based on CCS projects, thecombined solar/nuclear parameter a2 is calculated byfirst identifying anuclear and asolar, and then settinga2 ¼ 1 � ð1 � anuclearÞð1 � asolarÞ.

Table 2 Comparison of the Estimated and Actual Probability Distribution Data over Each Possible Outcome of a1 for Different Levels of Investmentin CCS

Budget ($million) 52 108 319 729 961 a1 52 108 319 729 961 a1

Estimates Actual data

Probabilities 0.41 0.24 0.17 0.11 0.11 0 0.41 0.24 0.17 0.11 0.10 00.59 0.34 0.40 0.41 0.35 0.319 0.59 0.34 0.40 0.41 0.35 0.3190 0 0.01 0.06 0.12 0.346 0 0 0.02 0.06 0.13 0.3460 0.42 0.42 0.42 0.42 0.38 0 0.42 0.42 0.42 0.42 0.38


The resulting stochastic returns functions Ai areused in conjunction with Equation (18). The integra-tion of these piecewise linear functions into the modelrequires the addition of new variables and con-straints. The details of this implementation aredescribed in Appendix S11.

4.1.3. Characterization of a Scenario SetThe probabilistic characterizations for the two typesof model inputs, that is, the climate change damagesand technical change due to R&D, result in three dis-tinct stochastic entities, which we denote through therandom vector ðp;A1;A2Þ. Given that possible valuesfor the three parameters are discrete and finite, thisrandom vector can take on a finite number of values.Each of these distinct realizations corresponds to ascenario x 2 Ω as described in section 2. The proba-bility of occurrence for each scenario px is calculatedbased on the probabilities of individual parametervalue realizations. For example, a sample scenario x0

could correspond to realizations involving the firstrows in Table 3 and Appendix S10, and a p value of 1.Assuming that the latter can occur with a probabilityof 1 and using the probabilities shown in Tables 3 andAppendix S10, the probability of scenario x0 can becalculated as px

0 ¼ ð1Þð0:11Þð0:087Þ ¼ 0:00957.

4.2. Step 4: Stochastic ProgrammingImplementation

Stochastic programming is a natural approach for ourproblem, as the interactions represented through theDICE model form a complex structure that preventsthe problem from being amenable to other methodssuch as dynamic programming. This is especially thecase as the formulation has many decision variablesbut relatively few stages.The optimization problem (1)–(5) can be expressed

as one single non-linear programming problem.

However, in order to utilize special algorithmic solu-tion procedures, we further represent this formula-tion by replacing the first stage decision vectors!; lN; yN; sN; xN by possibly different vectors!x; lxN; y

xN; s

xN; x

xN , similar to the notation used for

second stage decisions. Using this, we can define aproblem formulation for each scenario, but at thesame time, require that the values of these first stagevariables do not depend on the realization ofrandom data. This can be achieved by linking theindividual scenario problems through a set of con-straints, which are referred to as the non-anticipativi-ty constraints. The non-anticipativity constraintsensure that the decisions in all scenarios are thesame for the first 50 years, and are defined explicitlyby setting the variables to be equal for each scenariofor the first 50 years. In our model, these constraintsinvolve the R&D investment, capital stock and per-iod utility decisions for the first 50 years, that is, !i,kt, and ut, respectively. It must be noted here that theset of decision variables at each period in the modelinvolves a large number of other variables asdepicted in the base formulation (6)–(13). However,we show in Appendix S8 that non-anticipativity inthe three decisions above is sufficient for the overallmodel. As a fewer number of constraints needs to beused, this result allows for a less complex represen-tation of the stochastic programming model. More-over, this also enables a tractable implementation ofthe Lagrangian decomposition procedure that weuse as our solution methodology.Given this structure, the overall stochastic pro-

gramming model can be defined as follows:

max!X;lX;yX;sX;xX

Xx2X

pxXt

Rtuxt ð19Þ

s.t. Jxw ð!x; lx; yx; sx; xxÞ� bxw 8w;x ð20Þ

!xi �

Xx02X

px0!x0

i ¼ 0 8i;x ð21Þ

kxt �Xx02X

px0kx

0t ¼ 0 uxt �

Xx02X

px0ux

0t ¼ 0 8t� 5;x;

ð22Þwhere the superscripts in !X, lX, yX, sX, and xX

denote that the optimization is performed over allscenarios in the scenario set Ω. As in the DICEmodel description in section 3.2.1, xx refers to allother variables in each scenario, and the indepen-dent decision variables are !x; lx and ox. In thisformulation, objective (19) corresponds to the objec-tive function (1) in the general formulation and rep-resents the maximization of expected total socialutility over all scenarios. Constraints (20) define thecorresponding set of constraints for any given scenario

Table 3 Piecewise Linear Returns Functions for CCS, Where theCentral Columns Show Values of a1 for Discrete Levels ofInvestment.

Budget($million) 52 108 319 729 961 Probability

a1 0 0 0 0 0 0.110 0 0 0.319 0.319 0.060 0 0.319 0.319 0.319 0.070 0.319 0.319 0.319 0.319 0.170.319 0.319 0.319 0.319 0.319 0.050.319 0.319 0.319 0.319 0.346 0.060.319 0.319 0.319 0.346 0.346 0.040.319 0.319 0.346 0.346 0.346 0.010.319 0.38 0.38 0.38 0.38 0.42

Note: Each row, which corresponds to a realization of the function A1, isassociated with a probability given in the far right column.


x. These constraints, each of which is indicated byw = 1,…,Ψ, involve the standard economic relation-ships as given by Equations (7) and (9), (10), (12),(13) as well as the extended relationships modeledby Equations (16) and (18) and the required con-straints for the piecewise linear mappings describedin Appendix S11. The variables in each of these con-straints are indexed by a superscript x, and the con-straints are defined separately for each x 2 Ω.Constraints (21)–(22) are the non-anticipativity con-straints ensuring that decisions in the first 50 yearsare the same for all scenarios. The structure used inthe formulation of the non-anticipativity constraintsaccounts for the scenario probabilities and preventthe ill conditioning in the Lagrangian dual as dis-cussed by Louveaux and Schultz (2003). Note thatconstraints (20)–(22) together define a reformulationof constraints (2)–(5) in the general formulationdescribed in section 2.Model (19)–(22) is a stochastic non-linear program-

ming problem that can be solved through decompo-sition methods, as the size of the scenario set doesnot allow for a direct solution. As a solutionapproach, we use a Lagrangian decomposition basedprocedure, which is similar to the method describedby Caroe and Schultz (1999). The details of thisimplementation, as well as some additional compu-tational improvement procedures, are described inAppendix S12.

5. Experimental Setup for R&D PolicyAnalysis

In this section, we discuss the policy experiments weran with our framework. We start by briefly discuss-ing some assumptions about the opportunity cost ofinvestment. We then describe a number of alternativepolicy environments and the different risk cases weconsider.

5.1. Opportunity CostThe R&D funding levels used in the elicitations andreported in the tables in Appendix S3 represent theamount of money going into the hands of high qual-ity researchers in the appropriate areas; this does notaccount for additional costs to society. In order toaddress this issue, our baseline assumption is thatthe opportunity cost of investing in R&D is fourtimes the out-of-pocket cost (i.e., j = 4 in Equation(16) for the base case). This assumption reflects thecurrent state of the literature (Nordhaus 2002, Pizerand Popp 2008), but in fact there is very littleresearch directed at determining what this opportu-nity cost actually is. Thus, we perform sensitivityanalysis over the parameter j and discuss it in ouranalysis in section 6.

5.2. Alternative Policy EnvironmentsFollowing Nordhaus (2008), we consider a number ofdifferent policy environments that prescribe differentalternative strategies in dealing with climate change.Specifically, we consider six policy environmentswhich we refer to as DICE Optimal, Stern, SternFixed, Gore, Kyoto Strong, and Lim 2, as well as abaseline no-controls case. We choose these policiesbecause they are representative of the range of policyrecommendations being debated around the world.Here we describe these policies, which are also sum-marized in Table 4. For each policy environment weassume there is no knowledge of technological suc-cess and damages until year 2055, and we run themodel out for 400 years.In the “DICE Optimal” policy the model chooses

the optimal R&D investment and abatement path.The “baseline” case models the levels of major eco-nomic and environmental variables as they wouldoccur without any climate-change policies, that is,abatement is forced to be 0 in all periods after the first.The “Stern” policy is intended to reflect the policysuggestions laid out in the Stern Report (Stern 2007).Nordhaus (2008) identified the key differencebetween Stern and DICE as being the very low dis-count rate in the former. Thus, this policy is imple-mented by first running the DICE model at a very lowdiscount rate. We then take the resulting abatementlevels and fix those in the model with the default dis-count rate. This is so the results of all the policies canbe evaluated at one common interest rate. For ourimplementation, we have run two versions of this pol-icy. In one case (referred to as “Stern Fixed”), R&Dinvestment is fixed as calculated from the run withthe very low discount rate. In the other case (referredto as “Stern”), R&D investment is chosen in the sec-ond run based on the DICE discount rate.4

The “Gore” policy is intended to reflect the policysuggestions laid out by Al Gore (Gore 2007). This pol-icy fixes a lower bound for abatement of 0.25, 0.45,0.65, 0.85 for the periods beginning 2015, 2025, 2035,and 2045, respectively. Thereafter the lower bound

Table 4 Attributes of Policies Considered

Policy Abatement Key characteristics

Baseline No controls –DICE Optimal Optimal –Stern Optimal Abatement chosen under low

interest rateStern Fixed Optimal Abatement and R&D chosen

under low interest rateGore Lower bound between

0.25–0.95Limited participation

Kyoto Strong Fixed for150 years

Limited participation

Lim 2 Optimal Upper bound on temperature


for abatement is fixed at 0.95. However, for ourmodel, we assumed that when climate change uncer-tainty is realized with a no damage outcome, abate-ment is chosen optimally. The Gore policy alsoreflects limited participation in the early periods, inwhich not all countries and regions will participate inthe abatement. Specifically, it is assumed that the par-ticipation rate will increase gradually from 0.6 to 1over the next 50 years.“Kyoto Strong” represents a very aggressive but

potentially achievable international agreement on cli-mate change. This is intended to follow the spirit ofthe Kyoto Protocol but to continue on indefinitely andhave more and more nations join on through time. Inthis policy, abatement is fixed for the first 150 years.To be able to model the learning about climate dam-ages and R&D, we altered this aspect, as in the Gorepolicy, by allowing abatement to be chosen optimallyin the case where damages are zero. Thus, abatementdoes not respond to the outcome of R&D for the first150 years or to higher than expected damages. Also,similar to Gore, the cost of abatement is increased atearlier stages when fewer countries have joined in.After 150 years, future abatement is chosen optimallyand responds to the particular scenario.Finally, the “Lim 2” policy adds a single constraint

that limits the average global temperature increase to2C. In our modeling framework this constraint isonly minimally binding.

5.3. Risk CasesOne of our central questions is how uncertainty aboutclimate change damages impacts near-term invest-ments. In order to address this question, we considermultiple cases for uncertainty over climate damages.Table 5 shows the five cases we consider. Each proba-bility distribution is given a name in the columnheads. The first row shows the percent GDP lossgiven a 2C increase in global mean temperature ascalculated using Equation (11). We choose this valueas our anchor because it is used to calibrate the DICEmodel and is the value used in the elicitations inNordhaus (1994). We use mean-preserving spreadsaround this value. That is, each probability distribu-tion has a mean GDP loss of 1.1% given a 2C warm-ing. The second row shows the probabilities of eachoutcome in that distribution. The last row shows the

value of the parameter p for each respective outcome.While previous work uses mean-preserving spreadsaround p, the damages in the DICE model are con-cave in p, therefore we hold the mean of the expectedGDP loss constant in the mean-preserving spreadsused in this study.

6. Results and R&D Policy Analysis

In this section, we discuss the results from the optimi-zation model, focusing on the impact of R&D on soci-etal costs and on the range of scenarios considered inthe analysis. While we describe several conclusionsderived from our model and data, we emphasize thatthe analysis boundaries are tight, and therefore theresults may not be generalizable.

6.1. Optimal Investment in R&DWe find that the optimal investment in the R&D pro-jects considered is quite robust, both across different pol-icy environments and across different risk cases. Figure1 illustrates the optimal investment across risk andpolicy environments. The horizontal axis representsrisk cases 1–3 from Table 5. As the optimal invest-ment is the same in each case for DICE Optimal,Gore, and Kyoto Strong, we have graphed thesetogether; the same goes for Stern and Lim 2. We seethat in 12 out of the 15 cases we are showing, thetotal optimal investment is equal to $5303 million.5

In the three other cases, the optimal investmentsdrop by less than $300 million, a relatively smallamount. This robustness can be partly explained byreferring to the reduced-form R&D model wherethe portfolio of technology projects was alsoobserved to be robust to climate damages for anygiven R&D budget. This is because the elicitationdata revealed the technologies to be quite diverse,with some projects clearly superior to others. Here,however, our robustness result is even stronger. Wefind that the same level of funding is optimal overa wide range of very different abatement paths anddifferent risk levels.Not shown in Figure 1 is the DICE Optimal

investment under very high risk, which falls to$2696 million. In general, we see a somewhat mono-tonic response to risk in our results, with the opti-mal investment in R&D decreasing in risk under at

Table 5 Probability Distributions Defining Climate Change Damage Uncertainty

No risk Medium risk High risk Very high risk Intermediate(1) (2) (3) (4) (5)

GDP loss 1.1% 0.0% 3.3% 0.0% 20.0% 0.0% 40.0% 0.0% 1.1% 20.0%Probability 1.000 0.667 0.333 0.945 0.055 0.973 0.028 0.309 0.673 0.018p 0.003 0.000 0.009 0.000 0.063 0.000 0.167 0.000 0.003 0.063


least some of the policies. This is because whendamages are very high, abatement is at 100% withor without technical change. A mean-preservingspread that increases the magnitude of the damageswill simultaneously reduce the probability of thosedamages. Thus, an increase in risk of this kindleads to a lower probability of full abatement andtherefore a lower expected value for technicalchange.The optimal investment is also fairly robust to

assumptions about the opportunity cost of R&Dinvestments. If the opportunity cost multiplier j isbetween 1 and 4, then the optimal investment is stableas above at $5303 million. If it is between 5 and 6, thenthe optimal investment is slightly lower at $5071 mil-lion. If the opportunity cost is between 7 and 10, theoptimal investment drops to $2696 million. Thus, theinvestment in the R&D projects considered is not verysensitive to assumptions about opportunity cost untilthe opportunity cost gets very high.

The optimal investment is much higher in SternFixed, in which the investment is chosen with a verylow discount rate. The optimal action in this policyenvironment is to invest $21,132 million, the maxi-mum amount we have available in our model. This isnot surprising, and it underlines the importance ofcoming to an agreement on discount rates.

6.2. Impact of R&D on Expected Policy CostsIn Figure 2, we illustrate the impact of R&D on thedifferent policy environments. Figure 2(a) shows theexpected total cost of each policy with and withoutR&D, while Figure 2(b) shows the expected relativeutility of each policy intervention with respect to thebaseline.The vertical axis in Figure 2(a) represents the

expected net present value of the cost of abatementplus the cost of climate damages in trillions of 2005dollars. The vertical axis in Figure 2(b) representsexpected utility in the same units. Each bar represents

Figure 1 Optimal Investment Across Risk and Policy Scenarios, Where the Horizontal Axis Values Correspond to the GDP Loss for the High DamageOutcome of Risk Cases 1–3 from Table 5

Expe

cted

Tota

lCos

t($

tri)

Lim 2GoreKyotoStern FixedOptimal

50

40

30

20

10

0

No R&DOptimal R&D

(a)

Expe

cted

Rel

ativ

e U

tilit

y ($

tri)

Lim 2GoreKyoto StrongStern FixedOptimal

5

0

-5

-10

-15

No R&DOptimal R&D

(b)

Figure 2 Expected Costs and Utilities of Policy Interventions: (a) Effect of R&D on Total Costs; (b) Expected Relative Utility of Policy Interventions


the extra utility gained (or lost) from the baseline byimplementing the policy intervention. The darkerbars are in the absence of R&D and are very similar tothe results in Nordhaus (2008). The lighter bars arewhen R&D is available and chosen optimally. Notethat some of the policy environments are improve-ments over doing nothing, whereas some are worsethan doing nothing, at least as evaluated within ourframework. The Stern Fixed policy is too stringent inthe DICE model, as it is chosen in response to a verylow interest rate, but evaluated under a higher inter-est rate.The first result here is that the availability of R&D is

more valuable in the second best policy environments. Thevalue of having R&D is greater in the non-optimalenvironments and is greatest in the Gore environ-ment. Of particular interest are the Kyoto Strong andLim 2 results. Kyoto Strong is a possibly implement-able policy. In the absence of R&D, it is barely betterthan doing nothing. However, with R&D it becomesclearly positive, almost equivalent to the optimalwithout R&D. The Lim 2 goes from being a net loss toa net benefit with R&D.Figure 3(a) shows the expected utility of policy

intervention for the DICE Optimal policy, comparingno R&D, optimal R&D (of between 5.0 and 5.3billion), and full R&D investment in all of the tech-nologies (of $21 billion) for three risk cases. What isstriking here is the asymmetrical effect of over-investment relative to under-investment: over-invest-ment has a smaller downside. To further analyzethis, we look at the expected utility of policy inter-vention for the DICE-optimal policy for R&D invest-ments that are marginally higher and lower than theoptimal. Specifically, we considered the four follow-ing budgets (in millions): $5689, $5303, $5071, and

$4743. The middle two values are the two budgetsthat are optimal in Figure 1. The higher and lowernumbers increase and decrease these central valuesby $386 million and $328 million, respectively. Fig-ure 3(b) shows that while the two central budgetlevels lead to very similar expected utility, there is anasymmetric effect of increasing or decreasing the budgetfurther, with under-investment being more costly thanover-investment.

6.3. Impact of R&D on the Range of ScenariosFigure 4(a) shows the range of abatement paths overtime in the Risk 1 case for DICE Optimal when R&Dis invested optimally. There are a total of 36 scenar-ios, each depending on the success outcomes of thetechnologies. On the right edge of the graph, weshow the probability of being in a group of scenarios.The first cluster, with probability of 45%, is associ-ated with scenarios in which there is success in bothnuclear and CCS. The next cluster, with a probabilityof 52%, includes scenarios in which either nuclear orCCS fails. The lowest line is the case where all tech-nology fails. In Figures 4(b) and 5, we just show therange of paths without associated probabilities, asthey follow a similar pattern. Figure 4(b) comparesthe range of emissions paths from the DICE Optimal,Stern, and Kyoto Strong policies. Note that in theabsence of technical change the Kyoto Strong path ishigher than the optimal abatement path. With tech-nology, however, it falls about in the middle of theoptimal paths. Thus, the presence of R&D greatlyenhances the value of the fixed emissions path prescribedby Kyoto Strong.Figure 5(a) shows the range of temperature paths,

that is, the change in the average global temperatureover time, in the Risk 1 case for DICE Optimal and

Expe

cted

Rel

ativ

e U

tilit

y ($

tri)

Risk 3Risk 2Risk 1sksk

6

5

4

3

2

1

0

No R&DOptimal R&DFull R&D

R&D Investment ($mil)

Nor

mal

ized

Exp

ecte

d R

elat

ive

Uti

lity

($tr

i)

580056005400520050004800

2.69

2.68

2.67

2.66

2.65Risk 3

Risk 1Risk 2

(a) (b)

Figure 3 Expected Utility of Policy Intervention: (a) Expected Utility of Policy Intervention for the DICE Optimal Policy for No and Full R&D Budgets;(b) Expected Utility for the Dice Optimal Policy for R&D Budgets Marginally Different from Optimal


for Stern. We can make three observations from thisfigure. First, all the DICE Optimal paths are above2C between 2075 and 2200, while all Stern paths arealways below. What we can conclude is that Stern withno advances in technology will lead to lower temperaturesthan DICE Optimal with great advances in technology.Second, the impact of R&D on the temperature ismuch stronger in the DICE Optimal policy than in theStern policy. As the third observation, we note that allStern paths and the DICE Optimal paths with themost successful R&D peak in temperature between2100 and 2200. Temperature will peak in any scenarioafter abatement hits 100%. All paths hit full abate-ment eventually, but R&D can significantly affect thetiming.Figure 5(b) shows the abatement costs for all sce-

narios for the Risk 1 case of DICE Optimal and Stern.We see that until 2105 R&D has a much larger impacton Stern than on DICE Optimal. In fact, Figure 5(b) is

almost the opposite of Figure 5(a) showing the tem-perature paths. If we are in a policy environment in whichabatement is relatively high, then R&D will have a largeeffect on abatement costs and a smaller effect on emissions,temperature, and other physical variables. If, on the otherhand, we are in a policy environment that leanstoward lower abatement, then R&D will have a largeeffect on emissions and temperatures and a smallereffect on costs. The robustness of R&D investment todifferent policy environments and risk cases can bepartially explained by this phenomenon. Even thoughthe policy environments are radically different intheir abatement paths, technological change has a roleto play in both: cost reduction when abatement is highand improved environmental impacts resulting fromhigher abatement when abatement is generally lower.As an additional analysis, we also present in

Appendix S14 how investment into R&D impactsthe riskiness of the policy outcomes, where we

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Figure 4 Ranges of Abatement Paths for Different Realizations of Technical Uncertainties: (a) Range of Abatement Paths in the Risk 1 Case for DiceOptimal; (b) Comparision of the Range of Abatement Paths from Dice, Optimal, Stern, and Kyoto Strong

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Figure 5 Ranges of Temperature and Abatement Cost Paths: (a) Range of Temperature Paths in the Risk 1 case for DICE Optimal and Stern; (b)Range of Abatement Cost Paths in the Risk 1 Case for DICE Optimal and Stern


conclude that in general R&D provides risk reduc-tion.

7. Conclusions and Further PolicyInsights

Finding an optimal R&D portfolio in the face ofclimate change is a challenging problem, and theavailable data are sparse and not as airtight as wewould like. It is, however, a real and pressing prob-lem faced by the United States and other govern-ments around the world. Thus, our approach is touse the best data available and explicitly includeuncertainty in our analysis in order to arrive atrobust insights conditional on the current state of knowl-edge. With this aim in mind, we have developed mul-tiple models and implemented data-baseduncertainty on the returns from R&D into a newlydeveloped stochastic version of an IAM in order toget insights about the optimal technology R&D port-folio in the face of climate change. Overall, we devel-oped a general framework to determine optimalR&D portfolios through a dynamic stochastic model.Thus, this work provides a framework that can beupdated as new information becomes available, suchas more detailed elicitations about these technologiesor data on other technologies.First, we have found that, given our data based on

expert elicitations, focused investments in NuclearLWR and HTR as well as in CCS and solar technolo-gies are very robust. The optimal investment in theseprojects was robust to the policy environment, to theriskiness of climate damages, and to opportunitycost. Conversely, not investing in the Nuclear FRand Solar 3rd G projects was also robust. We do seea lower investment when there is a very small proba-bility of very high damages and a larger investmentwhen the interest rate is very low, but otherwise theoptimal investment falls within a very small range.This robustness is interesting, as, for example, theGore and the DICE Optimal policies are different inmost other ways. It is also a very useful result,implying that near-term decisions to invest in theprojects considered in this analysis may not dependheavily on the outcomes of long-term climate policydecisions.This robustness is driven by two effects. The first is

a result of using data (rather than theoretical explora-tions): we found that individual projects were quitedifferentiated, with some projects having relativelylower costs, large impacts if successful, and highprobabilities of success, while other projects did notperform well on all or some of these aspects. Clearly,our conclusions are conditional on the boundaries ofthe elicitation data, as robust results can not be guar-anteed for any set of data. However, we believe that

robustness is more likely than not when using realdata, as there will always be a relatively narrow bandof benefits to costs that will put a project on the knife’sedge.The second driver relates to the role of R&D in the

different scenarios. This role varies considerably,both with the policy environment and with theuncertainty over damages. In policy environments inwhich abatement is fixed or tends to be very high(near 1), R&D primarily has a “cost-side benefit”: theenvironmental variables are less affected while thecost of abatement is significantly affected. This groupof policies and risk cases include the Stern and Gorepolicies and also high risk cases. On the other hand,in instances in which abatement is relatively lowin the absence of R&D, R&D primarily has an “envi-ronmental-side benefit”: the environmental variablesare significantly affected, while the cost of abatementhas only small effects and in fact sometimes is highergiven a much higher level of abatement. These twovery different roles mean that technological changeends up having an important role to play whetherabatement is high or low. This insight would be unli-kely to arise outside of our framework that combinesa dynamic optimization model with data-based prob-ability distributions.Second, we have shown that a larger-than-optimal

investment in technology is less costly than a smaller-than-optimal investment. Thus, it appears that policymakers should prefer to err on the high side ratherthan the low side of R&D investment. Given thisresult, the level of robustness, and the deep uncer-tainty about climate damages, our observations sup-port a conclusion that investing roughly $5 billion inthese technologies probably makes sense.Our research is plagued by the same difficulties

that plague all climate change research—the optimalinvestment depends on the interest rate used to valuethe far future. We see that the optimal investment inR&D is considerably higher—in fact full funding inall the projects we considered—when evaluated at thelow Stern interest rate. If policy makers believe thatthe “appropriate” interest rate is no higher than thatin Nordhaus (2008) (as very few economists are mak-ing that argument), this again suggests that policymakers err on the side of higher investments ratherthan lower. Assumptions about the opportunity costof R&D investments have little impact on the resultsin this study.There are some important caveats to these conclu-

sions that need to be considered in a final investmentdecision. First, this is a “lumpy” problem, with theprojects defined by discrete investment levels, someof which are much higher than others. Moreover, theanalysis is based on a specific set of projects deemedrelevant for R&D portfolio optimization by a set of


experts. Hence, biases inherent in any expert elicita-tion process may exist in the set of projects consid-ered. This is not atypical of R&D portfolio problemsand is driven by the difficulty of assessing potentialR&D projects. Nevertheless, some of the robustnessmay be driven by this characteristic. Future work maybe aimed at minimizing this problem. More generally,data gathered from expert elicitations are typicallysubject to a number of biases and may vary greatlydepending on the structure of the elicitation process.Certainly, given the scale of the climate change prob-lem, more and better information on the potential ofenergy technology R&D is likely of great value (Bakerand Peng 2012).In addition, the models we worked with (and we

believe this is true for all models) could not accountfor the socio-political aspects of nuclear energy. Inparticular, concerns about proliferation are not ade-quately reflected in this analysis. Thus, nuclear maybe a riskier investment than we show. Also, there isonly a weak understanding of how intermittent re-newables, such as solar photovoltaics, will be able tobe integrated into the grid on a large scale. Thus,while the models we used consider this problem in areasonable way, it is quite possible that the impact ofimprovements in solar photovoltaics will be largerthan the current models show, especially if simulta-neous investments are made in the grid and grid inte-gration. Thus, these two technology-specific aspectsshould be considered in a final portfolio allocation.More generally, we made a number of assumptionsalong the way in order to integrate the data and themany components of the framework. Hence, as is typ-ical in approaches to such complex problems, theresults should be interpreted with caution and maynot be generalizable.Beyond the specific contributions to climate change

energy R&D policy, this study provides an exampleof a framework for combining elicitation-based proba-bilistic data on future uncertain systems and multipleeconomic models into a tractable stochastic decisionframework. We introduced the idea of randomreturn-to-R&D functions, which were then effectivelyintegrated into a novel representation of a highly non-linear stochastic problem. Overall, we were able tointegrate probabilistic data into a fully dynamicmodel in order to derive robust policy insights. Thisframework may be applied not only to the broad andimportant field of energy technology portfolio selec-tion, but also to other public policy areas such as R&Dinto space exploration, health, and military as well asagencies such as the Environmental ProtectionAgency, who face choices of a portfolio of policies thathave uncertain uptake and response on firm side anduncertain benefits (in the sense of poorly understoodpollutants).

Acknowledgments

This research was partially supported by the NSF underaward number SES-0745161 and the Precourt Energy Effi-ciency Center at Stanford University.

Notes

1Acronyms used throughout the study are summarized inAppendix S1 for reference purposes.2The notation used throughout the study is summarizedin Appendix S2 for reference purposes.3We note here that while other elicitation data exist on thethree technologies, they are not applicable to the type ofR&D portfolio analysis studied in this study. See Appen-dix S4 for more details.4The reader can refer to Nordhaus (2008) for more infor-mation on how the interest rates are modeled.5We show the allocation of the total investment inresearch areas for the optimal levels of investment inAppendix S13.

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Supporting InformationAdditional Supporting Information may be found in theonline version of this article:

Appendix S1. Definitions of Acronyms.

Appendix S2. Definitions of Variables and Parameters.

Appendix S3. Summary of Expert Elicitation Results.

Appendix S4. Description of Inapplicability of Other Elic-itation Data.

Appendix S5. Description of Cost of Abatement in DICE.

Appendix S6. Representative Marginal Abatement CostCurves.

Appendix S7. Pivot Parameter Values for IndividualTechnology Projects.

Appendix S8. Proofs of Analytical Results.

Appendix S9. Reduced Form R&DModel.

Appendix S10. Returns Functions for the Solar-NuclearTechnology Category.

Appendix S11. Representation of Stochastic ReturnsFunctions.

Appendix S12. Description of the Solution Procedure.

Appendix S13. Allocation of Total Investment under Dif-ferent Optimal Investment Values.

Appendix S14. R&D and Riskiness of Outcomes.


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