Climate Policy, Uncertainty, and the Role of Technological Innovation

CLIMATE POLICY, UNCERTAINTY, AND THE ROLE OF

TECHNOLOGICAL INNOVATION

CAROLYN FISCHERResources for the Future

THOMAS STERNERUniversity of Gothenburg

AbstractWe study how uncertainty about climate change severity af-fects the relative benefits of early abatement and a portfo-lio of research and development (R&D) in lowering futureabatement costs. Optimal early abatement depends on thecurvature of the marginal benefit and marginal abatementcost (MAC) functions and how the uncertain parameter af-fects marginal benefits. R&D in a particular technology de-pends on whether uncertainty increases early abatement;whether investment lowers marginal costs for that technol-ogy; whether R&D lowers the slope of that technology’sMAC function; and the shape of that technology’s MACfunction. We illustrate, focusing on the role of backstoptechnologies.

1. Introduction

The ultimate goal of climate policy is to stabilize greenhouse gas (GHG)concentrations at a level that is sustainable both ecologically and

Carolyn Fischer, Senior Fellow, Resources for the Future (RFF), Washington, DC([email protected]). Thomas Sterner, Professor of Environmental Economics, Universityof Gothenburg, P.O. Box 640 40530, Gothenburg, Sweden; University Fellow, RFF([email protected]).

Financial support from the Swedish Research Councils Formas and Mistra (through itsclimate program CLIPORE/INDIGO), as well as the Environmental Economics projectat the Centre for Advanced Study (CAS), Norwegian Academy of Science and Letters, isgratefully acknowledged. We are indebted to Michael Hoel for the invitation to CAS andfor valuable comments and to Miguel Quiroga for research assistance. Thanks also forvaluable comments from Antoine d’Autume, Nicholas Stern, Roger Guesnerie, and BillNordhaus at the College de France Colloque June 2010.

Received September 16, 2010; Accepted November 28, 2011.

C© 2012 Wiley Periodicals, Inc.Journal of Public Economic Theory, 14 (2), 2012, pp. 285–309.

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286 Journal of Public Economic Theory

economically. However, the determination of this level is difficult dueto the uncertainties in geophysical and ecological sciences as well as inthe costs of de-carbonizing economies (e.g., Heal and Kristrom 2002).Furthermore, existing impact assessment models may be ill equipped to dealwith a full range of damage functions—including catastrophic damages—orfat-tailed probability distributions for extreme temperatures (Weitzman2010, 2012; Nordhaus 2012). Thus, the policy problem for planninglong-term reductions in carbon emissions is complicated considerably byuncertainty (see also Dietz and Stern 2008).

Two types of policy tools are important to deal with climate change.First are policies that encourage abatement directly, such as carbon taxesor tradable emissions permits, and possibly instruments to encourage non-fossil energy or conservation. Second, as heavily emphasized in the SternReview (Stern 2007), are technology policies that focus on bringing downthe costs of reducing carbon emissions. Examples include research and de-velopment (R&D) investments in new technologies for energy supply or im-provements in energy efficiency. Importantly, the two types interact becausethe presence of abatement incentives increases the returns to R&D in reduc-ing the cost of technologies, and the costs of the technologies determinehow much abatement can be afforded. Because carbon dioxide (CO2) is es-sentially a stock pollutant, policies to manage long-term concentrations haveflexibility in timing. If more abatement is done early, then less will have tobe done in the future to reach any given target. R&D investment lowers thecosts of reducing emissions in the future. There is currently considerabledisagreement about how much the global community should spend on earlyabatement versus R&D for future technologies. The Kyoto protocol empha-sizes abatement while some other initiatives, such as the U.S.-sponsored Asia-Pacific partnership, put more emphasis on R&D.

When the future target is uncertain, both activities facilitate the adoptionof more ambitious targets and thus help reduce the expected range of costsof future abatement, adaptation, and damages; furthermore, certain kinds ofR&D may also help to reduce the degree of uncertainty in these costs. In thispaper, we explore the effects of climate and emissions target uncertainties onan optimal portfolio of R&D and emissions reduction strategies. We considerR&D trade-offs among different types of technologies, as well as trade-offsbetween the research program and current abatement.

Many studies have addressed the interaction between optimal innova-tion and abatement strategies when policy targets are certain. Some addressthe effect of induced technical change (ITC) on the timing of abatement(Wigley, Richels, and Edmonds 1996; Goulder and Schneider 1999; Goulderand Mathai 2000) or on the costs of attaining a climate target, including theopportunity costs of R&D (e.g., Goulder and Schneider 1999; Popp 2004;Gerlagh 2006). We are concerned with the effect of uncertainty on theseinteractions.

Technological Innovation 287

Several climate modelers conduct sensitivity analysis of abatement effort,timing, and/or costs with respect to atmospheric targets. However differentmodels produce different results. For example, van der Zwaan and Gerlagh(2006) find that the timing of emissions reduction effort in their modelis nearly independent of target uncertainty. Keller, Bolker, and Bradford(2004) find that uncertainty about climate sensitivity and threshold-specificclimate damages can decrease optimal abatement in the near term. On theother hand, Roughgarden and Schneider (1999) deduce that uncertaintyabout climate damages acts to increase optimal carbon taxes.

Several researchers have pointed to the critical role of backstop andalternative energy technologies in influencing different model outcomesand in driving technology policies for climate. Weyant and Olavson (1999)emphasize the need to recognize heterogeneity in technology options,noting that incremental changes in individual technologies do not neces-sarily result in incremental aggregate changes, because innovation in a lesscompetitive technology may allow it to cross a competitive threshold, lead-ing to rapid diffusion—and further incentives for innovation. Chakravorty,Roumasset, and Tse (1997) show that technical change in backstop tech-nologies, not in conventional fossil fuel technologies, is the driver ofchanges in carbon emissions. Popp (2004) finds that adding an alternative(backstop) technology to the model generates larger welfare gains thanthe presence of induced technological change. A recent model comparisonstudy by Edenhofer et al. (2006) reveals that induced technological changein combination with backstop technologies leads to dramatically lower pre-dicted costs of reaching GHG concentration targets. Popp (2006b) identifiesthe incorporation of backstop technologies into climate models, particularlythose of the top-down variety, with R&D-based induced technical changeas a major future research need. Henriet (2012), considers both optimalextraction of nonrenewable fossil resources and investment in a backstoptechnology, finding that climate regulation can raise or lower R&D in thebackstop, depending on the relative size of the resource and the emissionsconstraint.

Another strain of the environmental economics literature has exploredthe effect of uncertainty on climate policy, particularly the role of irreversibil-ity on early abatement effort. For example, Kolstad (1996) recognizes thetwin irreversibilities of investments in abatement capital and additions tothe stock of emissions. He finds that with learning, these irreversibilities canpush the desired amount of early abatement in opposite directions, with thenet effect depending on the relative magnitudes of the rates of pollutiondecay and capital depreciation and on expectations about damages. Ulphand Ulph (1997) also employ a two-period model with learning about cli-mate damages. They find that an irreversibility effect will occur if negativeemissions would be desired but not possible in the second period. Narain,Hanemann, and Fisher (2007) generalize results about irreversibilities


that are generated when first-period actions constrain second-periodoptions.

We use a general, two-period theoretical model to explore the inter-actions among uncertainty, early abatement, and R&D in a portfolio ofdifferent kinds of technologies. Our goal is to complement the diverseclimate modeling literature by developing basic intuition, which will helpus understand how specific choices in representing technologies andtechnological change influence results under uncertainty. While others haveengaged in somewhat similar efforts using stylized forms of individual tech-nologies (see, e.g., Baker, Clarke, and Weyant 2008) or general examplesof single representative technologies (Baker 2009), we explicitly considermultiple technologies and employ general functional forms. We take a socialplanner’s approach and abstract from questions of how to induce innova-tion, which have received much attention in the literature (Carraro, Gerlagh,and van der Zwaan 2003; Fischer, Parry, and Pizer 2003; Jaffe, Newell, andStavins 2003; Fischer and Newell 2008), questions of spillovers (Goulder andSchneider 1999; Jaffe, Newell, and Stavins 2005; Popp 2006a; Fischer 2008),and how to incorporate these aspects into climate policy models (reviewed byGillingham, Newell, and Pizer 2008). We also abstract from uncertainty overthe outcome of research (addressed in Biglaiser and Horowitz 1995 and re-cently reviewed in the context of climate models in Baker and Shittu 2008);we focus instead on how uncertainty over damages or emissions targetsaffects the potential returns to R&D and early abatement. We also specificallyaddress the role of backstop technologies versus conventional technologies.

Our results relate to the literature on prudence as defined by Kimball(1990), in which an agent is “prudent” if and only if the third derivativeof the utility function is positive, carrying the opposite sign of the secondderivative. Weitzman (2012) explores the importance of the shape of the cli-mate damages function. In our framework, prudence is critically related tothe curvature of cumulative marginal abatement costs (MAC), although thatis not the only factor. We find that the effects of benefit (or, similarly, target)uncertainty on early abatement depend in large part on the concavity or con-vexity of MAC, which can depend on the availability and characterization ofa variety of abatement technologies, including backstops. Furthermore, R&Dmay change the shape of the MAC curve, and thereby the need for additionalearly abatement in response to uncertainty. With competing technologies,the impact of uncertainty on the optimal R&D portfolio is more complexthan with a single, stylized technology. Whether investment in a particulartechnology should increase depends on the interaction of multiple factors:whether investment lowers marginal costs for that technology; whether R&Dlowers the slope of that technology’s marginal cost function; and whetherthe marginal cost function for that technology—as well as the cumulativeMAC function—is concave or convex. We illustrate our results with a simpletwo-technology case and relate these results to the array of functional formstypically used in climate policy models.


2. General Model of Abatement Uncertainty

The essence of the problem can be captured by a two-period model that rep-resents actions taken early on and actions performed in the second periodwhen uncertainty has been resolved. Although the cost function is assumedto be certain, the damages due to emissions are uncertain. Consequently, thetarget amount of total abatement T is also uncertain.1

Abatement can be achieved by using various technological options. LetAi

t be abatement with technology i at time t, and let K it be the state of knowl-

edge in that technology at that time. The cost of each type of abatement c i (.)in each period is a function of abatement and of the state of that technol-ogy: c i (Ai

t , K it ), where c i

A > 0, c iAA ≥ 0, c i

K < 0, and c iKK > 0. We will refrain

from assuming a sign for c iAK = c i

KA; it is commonly assumed that innova-tion lowers marginal costs, but it is possible that some improvements canraise costs on the margin, while lowering total costs. Investment I in cost-reducing technical change comes at a current cost of f i (I i

t ) for technologyi, where f i

I > 0 and f iI I ≥ 0. In our two-period model, we normalize K i

1 = 0and K i

2 = I i1 = K i . An implicit assumption in this framework is that the cost

of a certain amount of abatement with a given technology is independentof the abatement conducted with other technologies. Consequently, the rep-resentation corresponds more directly to activities like carbon sequestrationor energy intensity improvements than to actions like energy conservationor renewable energy technologies that displace an energy mix for which theemissions intensity is itself dependent on technology choices. This simpli-fication allows us to abstract from issues like energy demand and focus onabatement costs, which are the larger focus in the climate modeling litera-ture; alternately framing the problem as a more complicated one of energysupply and demand with an uncertain emissions constraint does not alter theessential lessons.2

To distinguish between individual and collective abatement, let Tt ≡∑i Ai

t be total abatement in a given period and Tt be the total abatementtarget, equal to cumulative abatement over both periods. The benefits ofabatement B(.) are a monotonic, nondecreasing, and weakly concave func-tion of total abatement (BT ≥ 0, BTT ≤ 0) and also a function of an uncer-tain parameter, ε. Abatement in the second period can also be thought ofas the difference between the ultimate target and the abatement performed

1 CO2 assimilates slowly from the atmosphere and for simplicity we treat it as a pure stockpollutant.2 For example, with heterogeneous technologies, a cumulative energy cost curve for agiven emissions target could still be defined, including utility costs from changes in en-ergy consumption, and the marginal benefits of emissions would be weighed against theexpected marginal damages of emissions, as here we balance the marginal cost of abate-ment with the expected marginal benefits. Ultimately, the shapes of these curves will de-termine early abatement incentives, and technologies will play a role in shaping those costcurves.


in the first period: T2 = T − T1. Whereas first-period abatement lowers costsin the second period by reducing the required level of effort, investment intechnology lowers the cost of achieving any level of effort. Target abatementis resolved in the second period, balancing marginal costs and benefits afterthey are known; when damages are not perfectly elastic, the target itself willdepend on both first-period emissions and second-period costs.

The planner’s problem is to maximize the benefits of abatement andresearch, net of the costs of these activities, in expectations. Let V2 be thenet benefits in the second period, when the benefit function is known:

V2(K, T1, ε) = maxA2

{B

(T1 +

∑i

Ai2, ε

)−∑

i

c i(Ai2, K i)} . (1)

Let V1 be the expected discounted net benefits of both periods, max-imized with respect to the vectors of abatement and investment for eachtechnology:

V1 = maxA1,K

{δE [V2(K, T1, ε)] −

∑i

c i(Ai1, 0

) −∑

i

f i (K i )

}. (2)

Starting in the second period, after information is revealed, the abate-ment decisions are characterized by the following complementary slacknessconditions for all i:3

Ai2 ≥ 0, c i

A

(Ai

2, K i) ≥ BT (T, ε) (3)

with one of these holding with equality, so Ai2(c i

A(Ai2, K i ) − BT (T, ε)) = 0.

That is, for any abatement technology being used in positive amounts, themarginal abatement costs equal the marginal benefits. If a technology is notbeing used, then c i

A(0, K i ) > BT (T, ε).From this set of conditions, we can define optimal second-period abate-

ment as an implicit function of the first-period variables and the uncertainterm: Ai

2(T1, K, ε), and thereby T2(T1, K, ε).In the first period, the first-order conditions for action are

Ai1 ≥ 0, c i

A

(Ai

1, 0) ≥ δE

[∂V2(K, T1, ε)

∂Ai1

]= δE [BT (T1 + T2(T1, K, ε), ε)]

(4)

3 Note that for now we do not assume an upper bound on the amount of abatement,whereas nonnegativity of emissions was an important factor for irreversibility effects inthat literature (e.g., Baker 2009; Ulph and Ulph 1997). This constraint is unnecessaryin the case of carbon capture and sequestration, for example, and nonbinding in thecase of sufficiently increasing marginal costs. However, this caveat should be noted. In thenumerical results, we consider the effects of such a constraint, in the form of capacitylimits for an abatement technology, which in effect leads to steeply rising MAC.


and

K i ≥ 0, f iK (K i ) ≥ δE

[∂V2(K, T1, ε)

∂K i

]= − δE [c i

K (Ai2(T1, K, ε), K i )]

(5)

with one equation in each pair holding with equality.Equation (4) states that marginal abatement costs in the first period are

equalized with the discounted value of the expected marginal benefits forany abatement technology being used in positive amounts. Note that, be-cause the target will be optimized in the second period, the impact of earlyabatement on changes in the equilibrium target does not affect the choiceof first-period abatement.

Equation (5) states that, if investment in knowledge for technology i oc-curs in positive amounts, then the marginal cost of knowledge investmentwill be equalized with the marginal reduction in expected total costs, dis-counted to the current period. This cost reduction is positive—and there-fore, the investment incentive is also positive—as long as the technology isexpected to be in use with some positive probability.

Let us express the cumulative abatement cost curve (C) in period t asthe minimized costs for achieving a total amount of abatement Tt :

C(Tt , Kt ) ≡ min

[∑i

c i(Ait , K i

t

)], s.t.

∑i

Ait = Tt .

This function increases with total abatement and decreases with invest-ments in a vector of technologies Kt (where we have normalized the costfunction such that K1 = 0, K2 = K). Although individual technologies mightnot be used, one may safely assume that some abatement will occur for posi-tive marginal benefits. Thus, we can re-express the first-order conditions forabatement as a whole in the second period as

CT (T2, K) = BT (T1 + T2, ε) (6)

which defines T 2 as an implicit function of the other variables, and in thefirst period as

CT (T1, 0) = δE [BT (T1 + T2, ε)] = δE [CT (T2, K)] (7)

In other words, the marginal costs of early abatement should be equal-ized with the expected marginal benefits—or equivalently the expectedmarginal costs of achieving the remaining abatement target in the secondperiod.


2.1. Portfolio Response to Uncertainty

2.1.1. Early abatementTo explore the influence of greater uncertainty on optimal policy, one needonly to return to the first-order conditions. It is clear that greater uncertaintywill increase first-period abatement if it increases the right-hand side of Equa-tion (7), the expected marginal damages (and therefore marginal abatementcosts). Otherwise stated, does uncertainty raise the expected shadow price ofcarbon? Of course, an increase in uncertainty can take several forms. Uncer-tainty might stretch out a tail in the distribution of environmental damages,or put more probability weight on a given high-damage outcome; in thesekinds of cases it may affect the expected value of ε, and higher values neces-sarily raise expected marginal damages and early abatement. Greater uncer-tainty in the Rothschild–Stiglitz (1971) sense of a mean-preserving spread inthe probability distribution of ε will also increase expected marginal abate-ment costs4 for all T1 if (and only if)

E [CT (T2(T1, K, ε), K)] > CT (T2(T1, K, E [ε]), K). (8)

In the next section, we will discuss the influence of uncertainty on R&D.For now, consider first the abatement incentives given the set of knowledgethat would occur in the absence of uncertainty.5 Thus, we focus on the di-rect effect of uncertainty, which is to alter optimal second-period abatement,given first-period choices. According to Jensen’s inequality, the relationshipin Equation (8) holds if (and only if) the marginal abatement cost functionis convex with respect to the uncertain parameter. Let � denote this secondderivative, assuming that the function is twice differentiable, so

� ≡ ∂2CT (.)∂ε2

= CTTT(T2,ε

)2 + CTT T2,εε. (9)

The sign of � depends on (i) whether the marginal abatement cost func-tion is concave or convex and (ii) whether second-period abatement is aconcave or convex function of the uncertain parameter, which involves prop-erties of both the cost and benefit functions.

From Equation (6), given K and T 1, T2,ε = BTε

CTT −BTTand T2,εε =

(BTεε + (BTεT + BTTε)T2,ε − (CTTT − BTTT )T 22,ε)/(CTT − BTT ).

From the second-order condition for abatement, CTT − BTT > 0, so thesign of T2,εε depends primarily on the third derivative of the cost func-tion and the second-order derivatives of the marginal benefit function.

4 We choose expected marginal costs rather than expected marginal benefits to allow amore straightforward evaluation of the case of threshold target uncertainty (i.e., perfectlyinelastic marginal benefits). Otherwise, the two formulations are equivalent.5 Otherwise, this expression represents the effect of a small increase in uncertainty at anequilibrium with no uncertainty.


Using these relationships, and noting that BTεT = BTTε, we can rewriteEquation (9):

� = (T2,ε

)2

×

⎛⎜⎜⎜⎜⎜⎝

(i)︷︸︸︷CTTT

( −BTT

CTT − BTT

)︸︷︷︸

T2,T1+

+ CTT︸︷︷︸+

⎛⎜⎜⎜⎝

(i i)︷︸︸︷BTTT

CTT − BTT+

(i i i)︷︸︸︷BTεε(CTT − BTT ) + 2BTTεBTε

B2Tε

⎞⎟⎟⎟⎠

⎞⎟⎟⎟⎟⎟⎠ .

(10)

In essence, the response of early abatement to greater uncertainty de-pends on the relative importance of three factors:

(i) the curvature of the MAC function (sign of CTTT );(ii) the curvature of the marginal benefits function (sign of BTTT and size

of BTT ); and(iii) the effect of the uncertain parameter on the marginal benefits func-

tion.

To explore this relationship, let us consider some commonly used exam-ples for the benefits function.

As a first example, assume constant (but uncertain) marginal benefits, sothat B = (b + ε)T . Then BTT = 0, and all of the third derivatives of the bene-fit function are zero. Reducing (10) reveals � = 0, implying that uncertaintyhas no effect on early abatement.

As a second example, consider linear marginal benefits. An uncertainthreshold target is a case of perfectly inelastic linear marginal benefits (in-finite slope). In this case, rather than focusing on the benefits function, weassume T2 = T + ε − T1. Then T2,ε = 1 and T2,εε = 0, and from Equation(9), � = CTTT .

In a third case, when marginal benefits are linear and decreasing, thecurvature of the MAC function remains a determining factor, since −BTT >

0. Furthermore, since BTTT = 0, part (ii) of Equation (10) is irrelevant. Part(iii) may depend on whether the source of uncertainty lies with the interceptor slope of the marginal benefits function and in the latter case, at what pointthe function pivots. (In the Appendix, we show that slope uncertainty per sedoes not affect early action, if the marginal benefit curve pivots around theexpected target point.)

Thus, when marginal benefits are linear but not constant, the shape ofthe marginal cost curve plays a decisive role in determining the impact ofuncertainty on the optimal policy strategy. If the overall marginal abatementcost curve is convex within the range of potential outcomes, then greater un-certainty increases early abatement because expected MAC are higher thanmarginal costs at the expected mean abatement. In the case of linear MAC,uncertainty has no effect on early abatement. If, however, MAC are concave,


as may be the case with sufficient backstop technologies, then greater uncer-tainty can decrease early abatement.

Of course, if marginal benefits are nonlinear, the relationship in Equa-tion (10) is more complicated, and the additional terms can exacerbate ormitigate the effect of the shape of the marginal cost curve. Convex marginalbenefits tend to raise early abatement, whereas concave marginal benefitstend to lower it. Indeed, if the marginal abatement cost function is linear(CTTT = 0), the nonlinearities in the marginal benefit function are decisive.

Thus, the shapes of the marginal benefits and the cumulative marginalabatement cost curves, representing all technological options, determinewhether the optimal abatement path should become steeper or flatter inresponse to greater uncertainty about future abatement benefits. In general,the less convex the marginal abatement costs, the lower the need to conductadditional early abatement in response to uncertainty.

These results relate to the concept of prudence as used by Kimball (1990).In Kimball’s study, an agent who maximizes expected utility exhibits pru-dence by responding to an increase in future risk by saving more today. Thisbehavior occurs when an increase in risk raises the marginal value of wealth,which equals the expected marginal utility of future consumption. UsingJensen’s inequality, Kimball shows that an agent is “prudent” if and only ifthe third derivative of the utility function is positive, carrying the oppositesign of the second derivative. In an article on risk prevention, Eeckhoudtand Gollier (2005) demonstrate that, by this technical definition based onthe curvature of the objective function, prudence tends to have a negativeimpact on prevention, contrary to popular intuition. Because prudence fa-vors the accumulation of wealth to face future risks, it induces agents not tospend money ex ante on preventive actions.

In our framework, a positive sign on the third derivative of the objec-tive function is in large part (though not solely) related to concavity ofthe marginal abatement cost curve. However, in this case (as in Eeckhoudtand Gollier 2005), greater risk induces less prevention in the form of earlyaction.

An important point to make is that these earlier studies do not considerthe possibility of endogenous prudence, such as the role of R&D in shapingfuture marginal abatement costs. In this case, R&D can then help reducereliance on early action to the extent that it both lowers and flattens marginalabatement costs in future periods. Furthermore, in our model, R&D itselfdepends on the degree of uncertainty. That makes it a fourth element inthe list of factors determining whether uncertainty increases or decreasesearly abatement, as the optimal composition of K on the left-hand side ofEquation (8) will differ from the optimal composition on the right-hand side.Essentially, if the R&D investment portfolio adjusts to greater uncertaintyby bringing down expected marginal abatement costs in the second period,less additional early abatement would be necessary than otherwise. We nextexplore drivers for R&D responses.


2.1.2. Uncertainty and R&DThe cost function shape is also important for determining the optimal R&Dportfolio, but in this case, what matters are the total costs of a given tech-nology rather than the marginal abatement costs of all technologies. In ad-dition, the response of second-period abatement with a given technology tocost changes matters.

Equation (5) demonstrates that, all else equal, the value of additionalknowledge (and thereby the optimal R&D resources spent) for technology iincreases with uncertainty if it raises the expected value of the associated costreductions. In the Rothschild–Stiglitz sense, that means that the expectedvalue of cost reductions must be larger than what would occur at the ex-pected value of the uncertain parameter, given any K i :

− E[c i

K

(Ai

2(T1, K, ε), K i)] > − c iK

(Ai

2(T1, K, E [ε]), K i). (11)

Essentially, this depends on the influence of uncertainty on second-period abatement with the given technology, and on the shape of c i

K . Aswith cumulative early abatement, there will be interactions with changes inother variables in response to uncertainty; however, these all help determineAi

2. The expression in Equation (11) holds if the marginal benefits to knowl-edge investment are convex in the uncertain parameter, or if

ψ i ≡ − c iKAA

(Ai

2,ε

)2 − c iKAAi

2,εε > 0 (12)

Whether this relationship holds in turn depends on the signs of bothc i

KA and c iKAA (whether R&D lowers marginal costs and the slope of the MAC

curve for technology i) and also the sign of Ai2,εε (whether the additional

use of abatement technology i in period 2 is increasing or decreasing undergreater uncertainty).

From Equations (3) and (6), assuming that an interior solution exists,a particular abatement technology will be deployed until its marginal costis equal to overall marginal costs: c i

A(Ai2, K i ) = CT (T2(T1, K, ε), K). Let us

begin by understanding the direct effects of uncertainty, given the levels ofT1 and K. From this relationship, we derive the implicit function for second-period abatement with technology i, where Ai

2,ε = CTT T2,ε/c iAA and

Ai2,εε = 1

c iAA

(CTTT (T2,ε)2 + CTT T2,εε

) − c iAAA

c iAA

(Ai

2,ε

)2.

Consequently, the expression in Equation (12) can be rewritten as

ψ i = −c iKA

c iAA

� −(

c iKAA + − c i

KAc iAAA(

c iAA

)2

) (Ai

2,ε

)2. (13)


Thus, whether greater uncertainty increases optimal investment in a par-ticular technology i depends on four components:

(i) whether investment lowers marginal costs for that technology (the signof c i

KA);(ii) whether uncertainty increases the incentives for early abatement (the

sign of �);(iii) whether R&D lowers the slope of that technology’s marginal cost func-

tion (the sign of c iKAA ); and

(iv) whether the marginal cost function for that technology is concave orconvex (the sign of c i

AAA ).

First, let us consider the common case in which R&D lowers marginal,as well as total, costs of abatement for each technology (c i

KA < 0). In thiscase, whenever uncertainty induces more early abatement (� > 0), it alsoencourages additional investment in all kinds of technologies. Logically, wesee here that R&D and early abatement work in tandem; if we incorporatethe response of early abatement to uncertainty, the need for changes in R&Dis attenuated but not reversed, and vice-versa.6

These results would be reversed if innovation reduced costs to a greaterextent at low levels of abatement, making the marginal abatement cost curvesteeper. Then greater uncertainty would tend to reduce optimal R&D. Mean-while, a parallel shift in costs would mean that the expected gains to inno-vation are invariant to the degree of uncertainty, as with linear supply anddemand for abatement.

In general, uncertainty means a greater emphasis should be placed onthose technologies which have concave marginal costs and for which R&Ddecreases the slope of those marginal costs, especially if those technolo-gies are likely to be used more heavily in the event of higher-than-expectedmarginal damages. In other words, a premium is placed on technologies thatcan help flatten the overall MAC curve. On the other hand, technologieswith more convex marginal costs, because they become increasingly costly,are by nature going to be more limited in their scope for application andshould receive less weight in the R&D portfolio when uncertainty over cli-mate damages looms larger.

This analysis is useful for drawing intuition, but it has certain limita-tions, as we have ignored two kinds of interactions. One is that the extent ofabatement with one technology may affect the marginal costs of abatementwith another; for example, the effectiveness of carbon capture and seques-tration is lower if the power plant has already reduced emissions by changingfrom coal to integrated gasification combined cycle technology. The second

6 That is, if both early abatement and R&D increase in response to uncertainty that raisesexpected marginal abatement costs, the R&D response cannot be strong that those costsare lowered below what would occur in the absence of uncertainty, else the early abate-ment response would not be in equilibrium.


relates to the fact that these results are derived from considering smallchanges around an equilibrium. For a larger range of potential outcomes,however, these relationships may not all hold, partly because of the interac-tion with other technologies. The cost functions for individual technologieswith respect to cumulative target abatement may be discontinuous becauseof the inequality constraints in the first-order conditions. For example, sometargets may not generate sufficient emissions prices to trigger the use of cer-tain technologies, whereas other targets may be so high that some technolo-gies reach their limits of capacity or cost competitiveness. As a result, theeffective cost function over the target range may be rendered more concavethan the underlying cost function for abatement. Greater target uncertaintycan then lower the expected costs of abatement from a particular technologyby decreasing the expected reliance on that technology. Such is the effect ofthe availability of an adjacent technology: for example, a backstop limits themaximum abatement from conventional technologies so, to the extent thatit makes use of the backstop more likely, uncertainty can lower the expectedvalue of investments in conventional methods.

Nor do we directly address all issues important for R&D investments.However, we can learn about their effects from the preceding analysis. First,research success involves its own uncertainty. Our framework clearly indi-cates that the key question is whether uncertainty raises or lowers the ex-pected cost savings from research, given uncertainty about what the re-search expenditures will produce. If uncertainty raises the expected costsavings—such as by allowing for the possibility of some extremely successfuloutcomes—then R&D investment should increase as a response. If uncer-tainty instead increases the expected cost of succeeding, then R&D invest-ment should fall. A balanced R&D portfolio will have to weigh the relativeeffects of research success probabilities and potential gains across differenttechnologies.

Knowledge accumulation may not be driven solely by R&D. Still, intu-ition for the case of learning by doing can be derived from the R&D re-sults. To the extent that abatement is a learning experience, abatement activ-ities carry a dual purpose of reducing emissions and investing in knowledge.Thus, when greater uncertainty would call for increased R&D investment, itsimilarly would call for increased learning by doing, which implies increas-ing abatement in the first period. Thus, in the learning-by-doing case, theinvestment parameter is a proxy for the premium to additional abatementin the first period. Which effect dominates—increasing early abatement toinvest in technological change or decreasing early abatement in anticipationof technological change—may be ambiguous (Goulder and Mathai 2000).

2.2. Numerical Example with a Backstop Technology

We explore some of these issues of the shape of the MAC curve by us-ing a simple combination of two technologies with linear MAC curves: a


conventional technology with upward-sloping marginal costs (superscript“a”), and a backstop technology with constant marginal costs (superscript“b”). To focus on the role of the cost function, we consider simple targetuncertainty, in which � = CTTT .

The intuition of this simple case is useful. Consider what happens inthe absence of a backstop technology: the overall MAC curve is then linear,equal to that of the conventional technology (CTTT = ca

AAA = 0), so � = 0and, given a level of R&D, uncertainty would not directly affect early abate-ment. Furthermore, reducing (13), ψa = −ca

KAA(Aa2,ε)2, meaning R&D only

increases in response to greater uncertainty if it lowers the slope of the MACfunction for the conventional technology (i.e., pivots the curve downward,rather than merely shifting it). We will assume R&D causes a proportionalreduction in costs, which means that greater uncertainty would shift thefirst-period policy toward more investment and thus indirectly toward lessabatement because expected marginal costs then fall.

On the other hand, if the backstop were the only available technology,then the MAC curve would be flat, meaning that a proportional cost reduc-tion would result in a parallel shift in the marginal abatement cost curve(ψ b = 0). Thus, greater uncertainty in the threshold would have no effecton the desired investment.

However, when both technologies are available, the R&D choice is trick-ier because two strategies must be balanced. For the regular technologies,the backstop serves to cap marginal abatement costs so that additional re-ductions do nothing to reduce cost variance in high-abatement states, as longas the backstop is used. Uncertainty can then reduce conventional R&D in-centives if it reduces the likelihood the conventional technology will be themarginal technology. From the perspective of the backstop technology, hav-ing conventional technologies available means the backstop will come intoplay only in high-cost scenarios. In this case, if greater uncertainty increasesthe probability of using the backstop, it raises the expected marginal benefitof R&D to lower the cost of the backstop technology.

Combining these results implies that uncertainty that makes extremeoutcomes more likely (or more extreme) tilts the overall policy portfolio to-ward developing technologies that would come into play in those outcomes.Furthermore, the optimal portfolio tends to call for diverting some resourcesfrom improving existing technologies when greater uncertainty limits theirexpected applicability. Finally, R&D can reduce the need for engaging inearly mitigation to the extent that it reduces the convexity of the cumulativemarginal abatement cost function.

As we discuss later, most numerical climate policy models that do incor-porate backstop technologies assume those technologies are not infinitelyavailable (or substitutable), thus limiting the capacity for their replacementwith conventional technologies. In our framework, when a backstop is avail-able but has limited capacity, the marginal abatement cost curve is piecewiselinear in three pieces: increasing, flat, then increasing again. The marginal


0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000

Target Stringency (GtC)

Ab

atem

ent

(GtC

)

A2a A2b A1a

Figure 1: Abatement by type as a function of target stringency.

Note: A1a is abatement in the first period (using conventional technology). A2a

& A2b are abatement in the second period (using conventional and backstop tech-

nologies, respectively).

cost function is concave at the first of these switch points and convex atthe second. The effect of uncertainty on abatement and R&D in differenttechnologies will depend on the interplay of all these parameters. When thebackstop’s applicability is limited, then there may be a range over which un-certainty increases and then decreases investment in the backstop (with theopposite effect on the conventional technology).

A study of scenarios with a range of cumulative abatement targets cangive a sense of these results. Figures 1–3 show the results from a numericalsimulation of the preceding model, revealing how optimal policy responds toincreasing target stringency. The parameters are described and motivated indetail in the Appendix. The IPCC finds the climate sensitivity to a doublingof carbon dioxide in the atmosphere to range from 2 to 4.5 ◦C; assumingdamages are mostly temperature related, this factor introduces an uncer-tainty of roughly +/− 50% around a stock target. Plausible projections ofemissions lead to a range of cumulative abatement targets between 200 and900 Gigatons of carbon (GtC) for this century. We assume that a backstop isinitially available at US$420/ton of carbon, approximating the cost of pho-tovoltaic power, with a capacity constraint of 300 GtC in the second period.The key point of this exercise is to highlight the role of the changing slopein the marginal abatement cost function as the backstop enters into play andthen reaches its capacity limits.

First, as the target becomes more stringent, conventional abatement inboth periods increases initially and then declines as backstop use in thesecond period increases. This decline occurs because R&D shifts from the


0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000

Target Stringency (GtC)

R&

D (

bn

$)

R&D in Backstop R&D Conventional Technology

Figure 2: Investment mix ($) with different climate target stringency (GtC).

0

100

200

300

400

500

600

700

800

0 50 100 150

Standard Deviation from Expected Target (GtC)

R&

D in

Bac

ksto

p (

bn$

)

Expected Target of 400 GtC Expected Target of 620 GtC

Figure 3: Effect of target uncertainty on backstop R&D.

conventional technology to the backstop, changing the relative marginalabatement costs. However, after the backstop reaches its capacity constraintof 300 GtC, reliance on the conventional technology increases again.

Next, Figure 2 shows that conventional R&D is crowded out as morestringent targets make R&D in the backstop technology more important.After investment in backstop R&D begins, the profitability of conventionalR&D falls—until backstop capacity is reached, at which point R&D in con-ventional technology becomes more attractive again. The patterns for R&Din each technology are similar to those of abatement for each respectivetechnology.


These sensitivity analyses give indications of the effects of uncertainty,which are illustrated in Figure 3. Suppose, first, that the expected target is400 GtC, the cusp at which the backstop would be needed. As uncertaintybroadens the range of potential targets from that point (by increasing thestandard deviation of the target estimate), more scenarios incorporate thebackstop, raising the expected gain from backstop R&D (see the lower, solidline in Figure 3). Meanwhile, the expected returns to conventional R&D de-crease because costs are capped by the backstop and fall as low-target sce-narios become more probable. However, if the simulation starts with an ex-pected target of 620, then uncertainty has the opposite effect: increasing thespread of possible targets means lowering the expected value of the back-stop (because its capacity is maxed out in more situations) and raising theexpected value of lowering conventional technology costs (see the upper,dashed line in Figure 3). For an even larger range of uncertainty, the effectsmay be somewhat ambiguous because each cost curve has convex and con-cave components.

3. Discussion: Marginal Abatement Cost Curves in ClimatePolicy Modeling

In this paper, we have focused on the effects of uncertainty about the sever-ity of climate change on the benefits of early abatement and of R&D invest-ment. We have shown that the effects depend on several factors, includingthe shape of the cumulative marginal abatement cost curve. When that curveis convex, an increase in benefit uncertainty implies the need for more earlyabatement, whereas with a concave MAC curve, uncertainty shifts the focussomewhat away from early action. We find that the MAC curve is shaped bythe characteristics of the technologies and their response to R&D; this aspecthas been ignored in previous studies of prudence and also in many climatemodels, in which the objective function is generally fixed. In the climate pol-icy case, the national or societal marginal abatement cost curve represents asequence of technological options. Backstop technologies can flatten out thecurve and R&D that lowers those costs further changes the shape of the curveover the relevant range of potential abatement requirements. The shape ofthe MAC curve thus interacts with R&D, influencing the optimal portfolio ofinvestments; those investments, in turn, shape the extent of curvature andthe desirability of early action. Thus, given the vast uncertainty in the emis-sions targets needed for climate stability, key empirical questions for climatepolicy aim at revealing the true shape of the future marginal abatement costcurve and the technological options that compose it.

In climate policy modeling, however, little attention seems to have beenpaid to the third derivatives of the cost function. Most economic modelsaddressing the R&D and abatement path question start with a particular


functional form and derive results from it. Few economic models, if any, ac-tually combine R&D with a diversity of technological options.

To interpret climate policy model predictions, one must understandhow they incorporate carbon-free backstop technologies, determine long-run marginal abatement costs, and allow for technological change (seeEdenhofer et al. 2006). The assumption of a true (nonscarce) backstop tech-nology, producing a concave marginal abatement cost curve, is a commonapproach for partial equilibrium models. In contrast, like the vast major-ity of the top-down climate models, general equilibrium models primarilyevaluate a host of energy substitution options, including mix shifting andoutput substitution. However, the typical specifications using nested con-stant elasticity of substitution (CES) functions—even those with a carbon-free technology—necessarily imply convex marginal abatement costs.7 Thatis because the functional form assumes that some fossil energy sources arealways desired, no matter how expensive they become, implying that re-moving carbon from the economy becomes increasingly costly.8 In a meta-analysis of several major climate models, Fischer and Morgenstern (2006)find the marginal abatement costs (as a percentage from baseline) to bebasically linear, which does imply convex marginal costs in terms of levels.However, only one of these models included a backstop technology, andthe range of abatement may not have been stringent enough to evaluatesignificant curvature. Nordhaus (2007) reviews the literature to calibratethe DICE model and concludes that the evidence in favor of convexity isstrong.

Indeed, few energy–economy models allow for the wholesale replace-ment of one technology with another. Those that do allow carbon-free tech-nologies to enter as perfect substitutes for other energy sources employ tech-niques to slow their penetration, such as additional fixed factors of produc-tion or capacity growth constraints, resulting in MAC that are highly convexin the GHG concentration target.9

As a result of these considerations, convexity seems the dominant shapeof the effective marginal abatement cost curves among major climate policymodels. Furthermore, when technology-specific change is incorporated, ittypically manifests itself as a percentage reduction in costs of that technol-ogy, which effectively lowers the slope of that technology’s supply curve.10

7 For example, Popp (2004) uses this technique to incorporate a carbon-free backstoptechnology into a modified DICE model.

8 In other words, if carbon-free technologies are assured a market niche even when theyare more expensive, then coal and other fossil technologies also are assured a niche in thefuture, even when they become more expensive.9 Examples include the EPPA model, MERGE, and most bottom-up models.10 Some climate models assume technology lowers emissions intensity, or that knowledgesubstitutes for polluting factors in production, which can lead marginal abatement coststo rise at some point. See review by Baker and Shittu (2008).


Therefore, we would expect most model results to show that target uncer-tainty should lead to more early action and more R&D in the relevant tech-nologies. The question is, how accurate are the assumptions needed to closethese models and allow for the reasonable computation of solutions?

Unfortunately, the true shape of these curves in the relevant range can-not easily be resolved by empirical studies because that range lies well out-side what has historically been observed. In terms of true backstop technolo-gies, the most-discussed candidates are carbon capture and storage (CCS),nuclear, and solar. Each has the possibility of being utilized at large scales,though location (and risk management) could be constraining factors.11 So-lar energy is particularly large in comparison to societal needs; current worldenergy use of commercial fuel is roughly 450 EJ/year, whereas the solar en-ergy flow to Earth is 5.4 million EJ/year (World Energy Council 2007). Ofcourse, a question that looms large for the more radical technologies is notjust their ultimate capacities, including the availability of their factor inputs,but how rapidly these capacities can be tapped.12 Given the importance ofbackstop technologies, scientists and economists alike should pay greater at-tention to understanding and estimating the future costs and capacities. Cli-mate policy modelers should heed these studies and consider how well theirmodels are able to represent the dramatic shifts in energy technologies thatsome all-too-possible scenarios will require.

Appendix

A.1. Linear Marginal Abatement Costs and SlopeUncertainty

Suppose that B = (b + ε)T − a(T − T)2/2, where T is a pivot point. ThenBT = b + ε − a(T − T), BTT = −a,BTε = 1, and BTTε = BTεT = BTεε = 0.Consequently, part (iii) is zero as well, and Equation (10) reduces to� = (T2,ε)2(a/(CTT + a))CTTT , in which case the sign depends on thatof CTTT . Suppose, instead, that the uncertain component is the slope,not the level, of marginal benefits from abatement; in other words, B =B0 + b(T − T) − (a + ε)(T − T)2/2. Then BT = b − (a + ε)(T − T), BTT =−(a + ε),BTTT = 0, BTTε = BTεT = −1, BTε = T − T , and BTεε = 0. Conse-quently, evaluating at T = T , � = ( T−T

CTT −BTT)2(CTTT ( a+ε

CTT +a+ε) + CTT

2(T−T)

). If

the pivot point occurs at the expected level of total abatement (i.e., T = T),the expression reduces to zero, meaning slope uncertainty per se does not

11 For example, the North Sea aquifer is capable of storing a hundred years’ worth ofEuropean carbon emissions. If carbon could be stored stably in deep sea storage, the ca-pacity would be quite large.12 For example, solar photovoltaics could be constrained by the availability of rare metals,suitable space or skilled labor.


affect early abatement. However, if the pivot point is elsewhere, then there iseffectively a combination of slope and intercept uncertainty, and the sign ofpart (iii) depends on the distance between that pivot point and T .

A.2. Numerical Model Specifications

In this section, we present the model on which the figures and simulations inthe text are based. We consider two technologies, each with linear marginalabatement costs (MAC). The conventional technology has upward slopingMAC, whereas the carbon-free backstop technology has flat MAC, but maybe limited in its ultimate capacity. We consider the case of target (thresh-old) uncertainty, as opposed to uncertainty about some downward-slopingmarginal benefits function.

The simulation model is intended to illustrate the theoretical sectionand is not intended as a “scenario.” The simplifications involved in model-ing the future as two 50-year periods and all technologies collapsed into oneconventional and one backstop make it inappropriate to strive for any preci-sion; nevertheless, we use representative values as far as possible.

Let a denote the conventional technology and b the backstop technol-ogy. Consider the case of linear MAC that are shifted by research and devel-opment (R&D) investment:

ca(Aat , K a

t

) = e −ρaK at

c2

(Aa

t

)2. (A1)

In this case, R&D pivots the MAC curve downward, lowering costs ofachieving any given level of abatement by ρ percent. By this assumption,R&D lowers marginal costs and flattens the conventional MAC curve, whichthe text notes is a determining factor in the results.

For the backstop technology, c b (Abt , K b ) = e −ρb K b

χAbt , with the addi-

tional constraint that the backstop has a maximum capacityAbt ≤ Ab

max. Weconsider cases in which the backstop is uneconomic or infeasible in the firstperiod, so T1 = Aa

1.For R&D investment costs, we assume a simple quadratic function

for technology i, implying linear marginal investment costs f i (K i ) = K i +si (K i )2.

For modeling simplicity, we consider the case of an uncertain target dueto an uncertain catastrophic threshold T resulting in a vertical marginal ben-efit curve. In the second period, uncertainty is resolved, and the total abate-ment target is determined by this threshold. Let p reflect the shadow valueof carbon abatement at that threshold. That price is, in turn, determined bythe equilibrium conditions at the optimum.

Substituting our functional forms into the first-order condition[Equation 940 in the main text], we get

e −ρK acAa

2 = p , Aa2 > 0 (A2)


and

e −ρK bχ = p , Ab

max > Ab2 > 0,

e −ρK bχ > p , Ab

2 = 0,

e −ρK bχ < p , Ab

max = Ab2. (A3)

Let T 2 = e (ρaK a2 −ρb K b

2 )χ/c be the level of cumulative second-period abate-ment at which it is cheaper to switch to the backstop technology for furtherabatement; i.e., T 2 is the kink in the overall marginal abatement cost curve.For T2 < T 2, the conventional technology is the only technology and sup-plies all abatement; for T2 > T 2, the backstop is the marginal technology,and it supplies the amount in excess of T 2. In this case, in the second pe-riod, we can express abatement by each technology as a function of the totaltarget for that period and this kink:

Aa2 = max

[min[T2, T 2], T2 − Ab

max

],

Ab2 = min

[max[0, T2 − T 2], Ab

max

].

(A4)

Furthermore, to meet the cumulative target, T2 = T − T1. Then, thefirst-order conditions for the social planner reduce to

Aa1 = δE

{e −ρaK a

2 Aa2

},

1 + 2saK a2 = E

{ρaδe −ρaK a

2c2

(Aa2)2

},

1 + 2saK b2 = E

{ρbδe −ρb K b

2 χAb2

}.

With these five equations, and a distribution of T , we solve the systemfor Aa

1, Aa2, Ab

2, K a2 , K b

2 .

A.3. Simulation Parameters

Recognizing the limitations of this simplified model, we still attempt to pa-rameterize it with values representative of the greenhouse gas abatementchallenge.

The target value for emissions reductions, T, takes values between 200and 900 gigatons carbon (GtC). Current emissions are around 7 GtC, anda linear interpolation of business-as-usual (BAU) emissions data from Mar-land, Boden, and Andres (2003) would give close to 20 GtC/year, or 1300GtC total emissions by 2100, which also corresponds to the median post SRESscenario of the Intergovernmental Panel on Climate Change (IPCC) fourthassessment report. Stabilization scenarios from Azar (2006) based on Wigley,Richels, and Edmonds (1996) and the IPCC indicate that, to reach targets of550, 450, or 350 parts per million (ppm), emissions would have to stabilize,


falling to 4 or almost 0 GtC/year by 2100. In our simulation, we considertwo 50-year periods that together comprise this century. During this period,the total abatement necessary (compared with the BAU mentioned) is esti-mated by integrating under the emissions curves, which gives a total of 400,630, and 1,000 GtC aggregate emissions reductions for 2000–2100 to meetthe targets of 550, 450, and 350 ppm, respectively. Many authors focus on550 or 450 ppm, thus the range of values analyzed for our target of 200 to900 GtC covers the range generally discussed, such as in the Stern Review(2007).

The discount factor between the two periods was set to 50% (δ = 0.5),corresponding to a discount rate of just under 1.5% per year.13 Several otherparameters were calibrated to give realistic marginal abatement cost figures,in line with those used in Survey of Energy Resources (World Energy Council2007). The cost parameters were set at c = 1.6 × 10−9 $/ton2 in the conven-tional abatement function and χ = $420/ton C for the backstop technology,which is assumed to have a capacity constraint of 300 GtC in the second pe-riod (2050–2100). The cost parameter χ , shows the baseline abatement costfor the backstop technology in the year 2050 before the cost-saving effect ofR&D. This number might appear high but the model is intended to deal withabatement that leads to the equivalent of emission reductions in the order of80%–100% in the year 2100. A backstop abatement cost of 420 $/ton C cor-responds to a 0.06 $/KWh which is a common figure for photovoltaic power,see for instance Chakravorty, Roumasset, and Tse (1997) or UNDP (2004).0.06 $/KWh corresponds to 700 $/ton of C equivalent. The current price ofoil is approximately 380 $/ton C and hence the solar backstop would implya price increase of 420 $/ton C). The parameter c is calibrated so as to givean illustrative mix of backstop and conventional abatement. Depending onthe exact investments in R&D, the backstop becomes profitable after about130 GtC of conventional abatement in the first period and 260 GtC of con-ventional abatement in the second one.

For both types of technologies, costs can be reduced by investments inR&D as described above. The parameters were calibrated to give a cost ofR&D that is roughly equivalent to a range of values corresponding to be-tween one and ten times the annual cost of R&D by member countries tothe International Energy Agency (IEA) in 1980. The parameters were 0.0003for ρa and 0.000306 for ρb ; 0.03 for sa and 0.01 for sb. The cost of R&D in theIEA in 1980 was 15 Billion $ according to OECD (2006). Finally, the prob-ability distribution for the target abatement is a normal distribution with astandard deviation of 125 GtC. The distribution is truncated to preclude neg-ative targets and ensure a symmetric distribution.

13 This is low but can be motivated by the arbitrary 100 year cutoff. It also corresponds wellto the discount rate in the Stern Review where the pure rate of time preference of 0.1%combines with a unitary marginal elasticity of income and per capita growth rates to givea discount rate of 1.4% (Stern 2007).


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Climate Policy, Uncertainty, and the Role of Technological Innovation

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