Investment in risky R&D programs in the face of climate uncertainty

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Energy Economics 30 (2008) 465–486
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Investment in risky R&D programs in the faceof climate uncertainty

Erin Baker ⁎, Kwame Adu-Bonnah

220 Elab, Universtiy of Massachusetts, Amherst, MA 01003, United States

Received 6 March 2006; received in revised form 29 September 2006; accepted 7 October 2006Available online 27 November 2006

Abstract

We analyze how the socially optimal technology R&D investment changes with the risk-profile of theR&D program and with uncertainty about climate damages. We show that how technology is represented inthe model is crucial to the results; and that uncertainty in damages interacts with uncertainty in the returnsto R&D. We consider R&D that reduces the cost of abatement multiplicatively, and argue that this is a goodrepresentation of R&D into non-carbon technologies; and R&D that reduces the emissions-to-output ratio,and argue that this is a good representation of R&D into fossil fuel technologies. For R&D programs intonon-carbon technologies, optimal investment is higher in riskier programs. Our empirical model indicatesthat the optimal investment in a risky program is about 3 1/2 times larger than in a program with certainreturns. For R&D programs aimed at reducing emissions in fossil fuel based technologies, our results showthat, qualitatively, investment is higher in less risky programs under most uncertain damage scenarios. Ourempirical model shows, however, that the risk-profile of fossil fuel based R&D programs generally has littlequantitative impact on optimal investment. The exception is that when the probability of a catastropheinducing full abatement is very high, investment is about twice as high in risky programs compared toprograms with certain returns.© 2006 Published by Elsevier B.V.

Keywords: Climate change; Technology R&D; Uncertainty; Environmental policy

1. Introduction

Policy makers are concerned with limiting the future cost of climate change. The economicsliterature has focussed on the optimal abatement path (e.g. Baker, 2005; Gollier et al., 2000;

⁎ Corresponding author. Tel.: +1 413 545 0670.E-mail address: [email protected] (E. Baker).

0140-9883/$ - see front matter © 2006 Published by Elsevier B.V.doi:10.1016/j.eneco.2006.10.003

mailto:[email protected]

http://dx.doi.org/10.1016/j.eneco.2006.10.003

466 E. Baker, K. Adu-Bonnah / Energy Economics 30 (2008) 465–486

Keller et al., 2004; Kolstad, 1996; Nordhaus and Boyer, 2000; Manne, 1996; Pizer, 1999; Ulphand Ulph, 1997; Webster, 2002) and the relative merits of different abatement-related policyinstruments for climate change or related environmental issues.1 Policy makers in the U.S.,however, have shied away from any emissions policy, and instead have focussed on technologypolicy.2 In the face of uncertainty – about both eventual climate-related damages and technicalsuccess – it is unclear how much R&D is desirable and which categories of technologies shouldbe targeted. Baker et al. (2006) analyzed how socially optimal investment in broad classes oftechnology R&D was impacted by uncertainty in the damages from climate change. In this paper,we extend their model, considering two categories of technologies, and analyze how the optimaltechnology R&D investment changes with the risk-profile of the R&D program as well as withuncertainty about climate damages.

This paper is related to the literature on investment under uncertainty and stochasticdominance, as well as R&D portfolio problems. The classic investment under uncertaintyproblem considers how optimal investment is impacted by uncertainty in the environment, suchas prices or demand (see Dixit and Pyndyck (1994); Caballero (1991). This literature has alsoconsidered R&D programs with uncertain returns and has shown that there may be an optionvalue to investing even when the program has an overall negative expected value, and that thisoption value may increase in the riskiness of the project (Huchzermeier and Loch, 2001; Robertsand Weitzman, 1981). Much of the stochastic dominance literature is focused on determiningwhat kinds of stochastic shifts in the environment induce more investment (Athey, 2002). Anotherstrand of the literature considers how the choice between risky prospects is related to the level ofrisk aversion (Gollier, 1995; Jewitt, 1989).

In this paper we combine exogenous uncertainty in climate damages with uncertainty in R&D,for multiple technologies, to determine how the riskiness of the R&D program impacts theoptimal level of investment in that program; and how this is impacted by uncertainty in thedamages from climate change. We recognize that different R&D programs can have differentlevels of risk. Some programs are primarily aimed at incremental improvements, and tend to below-risk: a larger investment leads to larger incremental returns with a great deal of certainty.Other programs are aimed at achieving breakthroughs, and tend to be high risk: an increase ininvestment increases the probability of success. We define a breakthrough as technologicalchange that will reduce the cost of abatement to near zero, for example a reduction in the cost ofvery low-carbon energy that makes it widely economically competitive with fossil fueltechnologies, or a combination of efficiency gains and sequestration that would allow for nearzero-emissions fossil fuel based energy.3 We model an investment in a risky R&D program asinducing a first order shift in the probability distribution over the possible outcomes of thatprogram. We consider how an increase in the riskiness of a program impacts the optimalinvestment in a first order shift in the program.

This problem differs from classic R&D portfolio problems (See Keefer et al., 2004 for areview) because the effect of technological change is not inherent in the technology alone, but

1 See Aidt and Dutta (2004); Baldursson and Von der Fehr (2004); Bansal and Gangopadhyay (2003) for recent workcomparing instruments for generic environmental regulation and Hahn and Stavins (1995); Stavins (1997) for anoverview of instrument choice for climate change. See Downing and White (1986); Fischer et al. (2003); Goulder andMathai (2000); Jung et al. (1996); Milliman and Prince (1989); Montero (2002); Parry (1998) for discussions of theimpact of policy instruments on environmental technical change.2 See http://www.doe.gov for information on the Climate Change Technology Program.3 The main greenhouse gasses (GHG) are Carbon Dioxide (CO2), Nitrous Oxide, Methane, and CFCs. We will often

refer to carbon, as it is the most economically important of the GHGs and the largest contributor to climate change.

http://www.doe.gov

467E. Baker, K. Adu-Bonnah / Energy Economics 30 (2008) 465–486

must be understood through the technology's effect on the marginal abatement cost curve (MAC)as it interacts with the eventual damage curve. For example, incremental improvements (asopposed to a breakthrough) in solar energy will only have widespread impacts on the economy ifclimate damages turn out to be severe, thus inducing a high level of abatement.

We present two alternative ways of modeling technical change – both common in the literature –and show that our results differ significantly for the two representations. For the first rep-resentation, technical change reduces the cost of abatement by a fixed percentage — it pivotsthe abatement cost curve down. We argue that this most closely represents investments into verylow emissions technologies. For the second representation, technical change reduces theemissions-to-output ratio, pivoting the abatement cost curve to the right. We argue that this mostclosely represents investments into reducing emissions in conventional, fossil fuel basedtechnologies. While the validity of these interpretations is an open empirical question, it is clearthat the representation of technical change has serious impacts for the conclusions drawn.

When R&D pivots the cost curve down by improving alternative, zero-emissions technologies,optimal investment is significantly higher in riskier programs. Our empirical model indicates thatthe optimal goal in a risky program is about 3 1

2 times more ambitious than in a program withcertain returns, and that optimal investment is more than 12 times higher. For R&D programs thatreduce the emissions-output ratio, our results show that, qualitatively, investment is higher in lessrisky programs under most uncertain damage scenarios. Our empirical model shows, however,that the risk-profile of these R&D programs generally has very little quantitative impact onoptimal investment. The only exception is that when the probability of full abatement is very high,investment is about twice as high in risky programs compared to programs with certain returns.

Optimal investment in alternative R&D programs increases as the program gets riskier for thefollowing reasons. Alternative energy is not widely competitive and is not likely to be afterincremental improvements, unless climate damages are very high. Therefore, incrementalimprovements in alternative energy are likely to have very little impact on the cost of abatement,unless climate damages are high. Therefore, the downside of investing in a risky program asopposed to a certain program – that the program might fail, and society would lose out on theincremental improvements that could have been achieved by a less risky program – is limited. Onthe other hand, a breakthrough in alternative energy technologies would have a large impact onthe economy, reducing abatement costs while leading to very high levels of abatement. Therefore,the upside of a risky program outweighs the downside, unless climate damages are very high. Ifdamages are very high, the logic is reversed. High damages mean that alternative energy will bewidely competitive, therefore incremental improvements will have a large impact and thereforethe downside of a risky program is larger.

The logic is again reversed for conventional technologies, which are competitive whendamages are mild or moderate, but not when damages are high. Thus, when the probability of acatastrophe is low alternative energy investments increase and conventional energy investmentsdecrease in the riskiness of the program. When, however, the probability of a catastrophe is veryhigh, the results may be reversed.

The rest of the paper is organized as follows: in the next section we present two representationsof R&D programs with their interpretations. In Section 3 we present a diagrammatic analysis ofhow the different R&D programs impact the MAC, and thus, optimal abatement. In Section 4 weperform a simple analysis indicating when investment will tend to increase in risk. In Section 5 wepresent our computational model, based on the well-known DICE model, and our results. Weperform sensitivity analysis over various damage scenarios, and then we perform sensitivityanalysis over probability distributions over damages scenarios. We conclude in Section 6.


2. Technical change and R&D

We represent technical change as an impact on the abatement cost function, and give aninterpretation about what different assumptions mean. We define abatement as a reduction inemissions below business-as-usual (BAU). In the next two subsections, we present the descriptionand interpretation of technical change found in Baker et al. (2006). In Subsection 2.3 we presentour model of uncertainty in the outcome of R&D.

2.1. Alternative R&D

Fig. 1 illustrates technical change that pivots the abatement cost function downward by a fixedpercentage, denoted by α. This representation is found in a number of papers, including Goulderand Mathai (2000), Montero (2002), Fischer et al. (2003), and Parry (1998). The original cost ofabatement is c (μ) where μmeasures abatement in terms of the fractional emissions reduction. Letthe quantities associated with the new technology be marked with a ∼. The new cost function,which allows for proportionally lower costs of abatement for all abatement levels, is given by

cðl; aÞ ¼ ½1−a�cðlÞ: ð1ÞNote that a shift of α has a small absolute impact on the lower part of the cost curve, and a large

impact as abatement nears 1. We argue that this program should be interpreted as primarilyreducing the cost of low-carbon, alternative energy sources, such as wind, solar, or nuclear. Forexample, a reduction in the cost of photovoltaic cells combined with the development of low-costhydrogen or battery technologies (to carry electricity to applications such as transportation) wouldreduce the cost of reaching zero-emissions, but would also reduce the costs of achieving smalldecreases in emissions because these technologies could be cost-effectively deployed in smaller,niche markets. We will call this program ARD (for Alternative technology R&D).

2.2. Conventional technology

In this section we consider technical change that decreases the emissions-output ratio by aproportional amount α. This is another common representation of R&D, found in Farzin and Kort(2000) as an alteration to the production function, and in Buonanno et al. (2003), Nordhaus(2002), and Gerlagh and Van der Zwaan (2006) as a reduction in the emission-output parameter.

Fig. 2 shows how this assumption maps onto the abatement cost function. A reduction in theemissions-output ratio means that for a given set of inputs and output, the emissions after

Fig. 1. The impact on the cost of abatement of alternative R&D.

Fig. 2. The impact of conventional R&D on the cost (left-hand panel) and the marginal cost (right hand panel) ofabatement.


technical change are a fraction α of the emissions before technical change. First, note that the costof abatement for any amount μ≤α will be zero. The pre-technical change BAU level ofemissions are reduced by α by employing the new technology; thus abatement equal to α isachieved at no cost by implementing the new technology. Second, note that the cost of fullabatement, μ=1, will be unchanged by this technical change. At full abatement, there are noemissions, so a fractional reduction in emissions has no impact. Finally, consider actions thatbefore the R&D result in abatement of μ at a cost of c . Remaining emissions are proportional to(1− μ). After technical change, the remaining emissions are reduced by α. Thus, the same actions(at a cost of c ) that resulted in abatement of μ before technical change, will result in abatement ofμ= μ+α(1− μ) after technical change. As illustrated in Fig. 2, this pivots the abatement cost curveto the right. This implies that the cost of abating μ (after technical change) is equal to the pre-technical change cost of abating l ¼ l−a

1−a. Thus, the new cost function is related to the originalcost function through the following relationship:

cðl; aÞ ¼ c maxl−a1−a

; 0h i� �

: ð2Þ

Note that technical change has the largest effect on the higher-emitting portions of theabatement cost function and no effect on zero-carbon technologies. This technology is bestinterpreted as representing carbon capture and sequestration; we have shown in other work,however, that the qualitative results tend to be similar for increases in efficiency of fossil fueltechnologies such as the Natural Gas Combined Cycle (NGCC) electricity generation (Baker andShittu, 2005). We term this program CRD (for Conventional technology R&D).

The right hand panel shows that CRD increases the MAC over some regions. We see in theleft-hand panel that the cost of abatement is everywhere (weakly) lower after R&D; however, thecost of full abatement remains unchanged. This is because in order to achieve full abatementsociety will substitute away from conventional, fossil fuel burning technology. Thus, the slope ofthe cost curve is steeper after R&D over the higher range of abatement. Since conventionaltechnology has improved, the jump from conventional to alternative energy is now greater. Thusthe marginal cost of abatement is greater after R&D for higher abatement (above 75% in thiscase). This phenomenon will exist whenever there is a ladder approach to abatement, withprogressively cleaner technologies substituting for dirtier ones as abatement gets higher.4 An

4 See Fullerton et al. (1997) for an example of sulphur dioxide abatement.


investment into one technology on the ladder will increase the marginal cost of abatement forhigher levels of abatement, since higher levels of abatement will require society to substitute awayfrom the improved technology.

2.3. Representing risky R&D

We represent the investment in R&D through a target amount of technical change, α. Thisrepresents the amount of technical change that would be achieved in a deterministic program; andthe expected value of technical change achieved in a risky program. For example, investmentmight be aimed at reducing the cost differential between solar PVs and NGCC by 10%, onaverage. In a risky program, the actual cost reduction achieved may be higher or lower than 10%.We assume that there is a one-to-one relationship between the amount of the investment and thetarget amount of technical change; and that the target amount increases as the investmentincreases.

We assume that an investment in R&D will result in one of three outcomes: the target amountof technical change, total failure, or a breakthrough. For purposes of exposition, we define abreakthrough as technical change which will allow for full abatement at no ongoing cost (α=1).In fact, all but one of the analytical results remain the same for a less radical breakthrough,α=αHb1.5 We do assume, however, that this breakthrough cannot be achieved in a deterministicprogram: 0≤ αbαH.

In the ARD program, a radical breakthrough α=1 would represent major improvements inwind and solar along with batteries and electricity distribution that would allow non-carbonenergy to be widely economically competitive with carbon energy. In that case, emissions willdrop to zero with virtually no further investment. In the CRD program, a radical breakthroughwould represent establishing carbon capture and sequestration which would allow for zero-cost6

sequestration of 100% of emissions. A less radical breakthrough would allow for zero-costsequestration of a portion of the emissions equal to αH.

The probability distribution over these three outcomes depends on the target amount oftechnical change, which in turn depends on investment in R&D. Given an investment of g(α) theprobability distribution over the three possible outcomes is as follows:

a ¼value probability0 p½1− a�a 1−p1 p a

8>><>>:

9>>=>>;: ð3Þ

The parameter p determines the riskiness of the R&D program, with p=0 representing a no-risk program, and p=1 representing a high risk program. Increasing p results in a mean-preserving-spread (Rothschild and Stiglitz, 1970) for any given α. The expected value of α equalsα for any p. Increasing α results in a first order stochastic shift for any given p. Note that p can bethought of as representing the proportion of a risky program in a portfolio containing both a safeand a risky program (Jewitt, 1989). We will investigate how the riskiness of the program,

5 See Section 4.2 for the exception. See author for analysis.6 In fact, the results are identical if we assume that there is a fixed cost for implementing the carbon capture and

sequestration system.


represented by p, impacts the optimal level of investment in the program, represented by theoptimal targeted amount of R&D α⁎.

3. Optimal abatement and technical change

Our basic framework is a two-stage, social planning model, in order to explore the sociallyoptimal level of R&D. In the first stage, the decision maker chooses a level of investment in anR&D project in order to improve the abatement cost curve. The resulting future abatement costcurve is uncertain, depending on the success of the project. The climate damage curve is alsouncertain. The second stage is at some future point in time after learning takes place, when societychooses a level of abatement that minimizes societal costs. The costs at that point are the sum ofthe abatement costs and the damage costs. The objective is to minimize R&D costs together withsecond stage expected societal costs. Formally, the R&D decision problem can be represented asfollows:

min0VaV1

gð aÞ þ EZ;aðaÞ min0VlV1

cðl; aÞ þ DðS−l; ZÞ� ��

ð4Þ

where α is the target amount of technical change; g(α) is the cost (including the opportunity cost)of implementing a program with target α; μ is second period abatement, measured as the fractionof emissions reduced below the business-as-usual level of emissions; α is a random variablerepresenting the realized level of technical change. Technical change impacts the abatement costfunction c(·,·). We assume that a breakthrough reduces the cost of abatement to zero: c(μ; 1)=0.The probability distribution over α depends on the initial investment in R&D, α. S is the stock ofemissions in the absence of abatement; Z is the random variable that impacts damages; and D (·;·)is the damage from global climate change. We make the standard assumptions that g(·) and c(·)are increasing and convex; and that D(s;·) is increasing and convex in the stock s=S−μ.Furthermore, we assume that both damages and marginal damages increase in Z: this assures thatsecond stage optimal abatement is increasing in Z.

Abatement in the second stage is assumed to be optimal, and to depend on both technicalsuccess and climate damages. Formally, the optimal interior value of μ⁎(α, Z) satisfies the firstorder condition

AcAl

¼ ADAs

: ð5Þ

We may, however, have a corner point solution, where μ⁎(α, Z)=1 andAcAμ

bADAs

. In particular,μ⁎(1, Z)=1 for all Z.

We are interested in comparative statics on the optimal level of targeted R&D, α⁎. Inparticular, when does α⁎ increase in the riskiness of the R&D program? How is this relationshipimpacted by the riskiness in climate damages, Z?

In the next section we present a simple diagrammatic illustration of how R&D impacts optimalabatement under each of the programs.

3.1. Comparison of programs

Fig. 3 shows the marginal abatement cost curve (MAC) before and after technical change andresulting optimal abatement: the left-hand panel shows a 50% reduction in costs (ARD); and the

Fig. 3. Marginal cost of abatement, before and after R&D, with associated optimal abatement levels for different marginaldamages. The left-hand panel is ARD, the right hand panel is CRD.


right hand panel shows a 50% reduction in the emissions-output ratio (CRD). The upward slopinglines represent the MAC before and after R&D. The horizontal lines in each panel representmarginal damages in different scenarios. Optimal abatement is chosen by equating marginal coststo marginal damages. When the marginal damages are greater than the marginal costs everywhereon the curve then optimal abatement is 1. Thus, if a breakthrough is achieved in either program(α=1), then abatement will be equal to 1 regardless of the damages.

First consider low damages. This is representative of the base case damages for climatechange.7 In each panel, we show two points related to low damages: μL, optimal abatement in theabsence of technical change and μLα, optimal abatement after technical change equal to α=0.5. Inthe left-hand panel notice that the impact on optimal abatement of certain ARD (α= .5) is smallcompared to the potential payoff of risky R&D (α=1). On the other hand, in the right hand panel,the impact on optimal abatement of certain CRD (α=.5) is about half of the potential payoff ofrisky R&D (α=1). A breakthrough has a disproportionately large effect on ARD, but not on CRD,when damages are low. Said another way, incremental improvements in ARD have a small impacton optimal abatement; incremental improvements in CRD have a large impact. This means that abreakthrough in ARD (leading to full abatement) has a disproportionately large effect on optimalabatement when damages are low.

Now consider “medium” damages in the left-hand panel, that is, a level of damage that doesnot induce full abatement under the original abatement cost curve, but does induce full abatementunder the new cost curve (notice this case doesn't exist in the right hand panel). In this case,incremental R&D has the same impact on optimal abatement as a breakthrough resulting fromrisky R&D — they both lead to full abatement. A breakthrough would impact costs, but notactions in this case, and thus has a less dramatic effect.

Finally, consider “high” damages in both panels. In this case, full abatement, μ=1, is optimalbefore technical change. In the left-hand panel, we see that ARD has no impact on the optimalabatement. In the right hand panel, however, we see that optimal abatement decreases inincremental R&D: μHαbμH. This is a direct result of the marginal abatement costs being higher

7 For example, Nordhaus' survey of expert opinion on climate change reports “best-guess” damages resulting from a2.5C increase as between 1.9 and 3.6% loss of GDP (Nordhaus, 1994). A selection of integrated assessment modelsestimate damages between 1 and 2.5% of GDP (Nordhaus and Boyer, 2000) p. 70.


after technical change. Thus, there is a significant payoff to risky R&D compared to certain R&D,in terms of the amount abated.

The key point of this section is that under certain conditions a technological breakthrough has amuch larger effect on optimal abatement than an incremental improvement. This is true for ARDwhen damages are low, and for CRD when damages are high. This effect holds even if we relaxthe simple probability structure from Section 2.3, in which a breakthrough leads to no-cost fullabatement and failure is total. As long as “risky” R&D is defined by having a great deal of weighton the tails – a high probability of a little or no improvement and a high probability of a very largeimprovement – the patterns described in this section will exist.

4. Analysis

In this section, we analytically investigate when optimal investment into R&D increases in theriskiness of the program. Recall that an investment into R&D induces a first order stochastic shift,while an increase in riskiness implies a mean-preserving-spread. We start by discussing the resultsfor given climate damages, and then briefly discuss how uncertainty in the damages impacts theresults.

4.1. Alternative R&D

We re-write decision problem (4), suppressing the initial stock of emissions, S, and climateuncertainty Z, applying the probability distribution for α described in Subsection 2.3, and usingthe representation of ARD from Subsection 2.1.

mina

gð aÞ þ p½1− a�½cðl⁎Þ þ Dðl⁎Þ� þ p aDð1Þ þ ½1−p�½ð1− aÞcðl⁎ð aÞÞ þ Dðl⁎ð aÞÞ� ð6Þ

where μ⁎ represents optimal abatement in the absence of R&D and μ⁎(α) represents optimalabatement given technical change equal to α. Note that the second term is the probability offailure p[1− α] multiplied by the payoff given failure; the third term is the probability of abreakthrough pα multiplied by the payoff given a breakthrough; and the fourth term is theprobability of achieving the mean technical change [1−p] multiplied by the payoff given meantechnical change. The expected payoff from an investment of g(α) is a weighted average of theexpected returns from risky R&D and the return from no-risk R&D. Applying the envelopetheorem, the first order condition for optimality of α is

gVð aÞ ¼ p½cðl⁎Þ þ Dðl⁎Þ−Dð1Þ� þ ½1−p�cðl⁎ð aÞÞ: ð7Þ

The marginal benefits from investing in R&D are a weighted average of the marginal benefitsto risky R&D (the quantity multiplied by p) and the marginal benefits of no-risk R&D (thequantity multiplied by [1−p]). Since the marginal benefits from investing in R&D (the right handside of (7)) are linear in p, they will increase in risk (as represented by p) when

cðl⁎Þ þ Dðl⁎Þ−Dð1Þzcðl⁎ð aÞÞ: ð8Þ

Thus, the optimal investment in R&D will increase in risk when the marginal benefits to riskyR&D (the left-hand side of (8)) are greater than the marginal benefits to no-risk R&D (the righthand side). So, the central question of this section is, when does the inequality in (8) hold?


Note that the marginal returns to risky R&D are constant in the targeted amount α. This isbecause an increase in the targeted amount simply moves probability from a failure to abreakthrough, thus the marginal returns are simply the difference in payoff between a failure and abreakthrough. The marginal benefits to no-risk R&D are equal to the marginal cost savings due totechnical change. These are increasing in α: the more R&D, the more abatement is optimal, andthus the more cost savings.

Whether (8) holds depends directly on μ⁎ and α, which depend on Z, and g, the cost ofproducing R&D. First, when damages are very high, abatement will be full regardless of theoutcome of R&D: μ⁎=μ⁎(α)=1. This implies that the right hand side of (8) is equal to the left-hand side: the marginal benefits to R&D are independent of risk. In this case risk should have noimpact on optimal investment in R&D. The benefits to the no-risk program are a certain reductionin the cost of full abatement equal to [1− α]; the benefits to the risky program are a full reductionin the cost of full abatement with probability [1− α], thus the expected reduction in cost is equal to[1− α]. Now, assume that damages are not so high. Specifically assume that μ⁎b1,that abatement in the absence of technical change is less than full. In this case, when α≈0then c(μ⁎(α))≈c(μ⁎), and the left-hand side is greater than the right hand side. When α is high, sothat μ⁎(α)≈1, then c(μ⁎(α))≈c(1). By optimality of μ⁎ we know that

cðl⁎Þ þ Dðl⁎ÞV cð1Þ þ Dð1Þ: ð9Þ

Therefore the left-hand side of (8) is less than the right hand side.This implies that when damages are low and the cost of producing R&D are high (inducing

small amounts of R&D), then the marginal benefits to riskier R&D are greater than the marginalbenefits to no-risk R&D. On the other hand, when damages are high and/or the cost of producingR&D is low, (inducing a relatively large amount of R&D), then marginal benefits are lower underrisk than certainty. When full abatement is optimal given α, there is no environmental-side benefitto a breakthrough; there is, however, an environmental-side loss to a failure. This implies thatoptimal R&D investment is higher when returns are certain.

Thus we predict that when damages are very high, risk will have little impact on optimalinvestment; when the cost of R&D and the magnitude of the damages are such that optimalinvestment in the no-risk program is very high, then investment will decrease in risk; when thecost of R&D and the magnitude of damages are such that optimal investment is low, theninvestment will increase in risk. In particular, when damages are low and the cost of R&D is high,optimal investment will increase in risk.

4.2. Conventional R&D

We follow the logic above to analyze CRD. First, we note that the marginal returns to riskyR&D (the left-hand side of (8)) are independent of the representation of R&D. This is because wehave modeled a breakthrough in either program as reducing the cost of abatement to zero. Themarginal benefits to no-risk R&D – the right hand side of (8) – are equal to the marginal costsavings due to technical change, and thus they do depend on the representation of R&D. Themarginal benefits of no-risk CRD are as follows:

−A

Aac

l⁎−a1−a

� � �l⁎¼l⁎ðaÞ

¼ cVl⁎ðaÞ−a1−a

� 1−l⁎ðaÞ½1−a�2

" #: ð10Þ


Clearly the marginal benefits from incremental CRD are quite different from the marginalbenefits from ARD. Here we re-write (8) for CRD. The optimal value of α will increase in riskwhen:

cðl⁎Þ þ Dðl⁎Þ−Dð1ÞzcVl⁎ðaÞ−a1−a

� 1−l⁎ðaÞ½1−a�2

" #: ð11Þ

Again, start by considering the case when damages are very high and μ⁎(α) approaches 1.When this happens the marginal benefits to no-risk R&D (the right hand side of (11)) will be veryclose to zero. This is driven by the fact that CRD has very little impact on the cost of abatement athigh levels of abatement. The left-hand side, on the other hand, approaches c(1)N0 as damagesget large. Thus, for large enough damages, condition (11) will hold, and investment will increasein risk. This result holds for a less radical breakthrough, α=αHb1, under the condition thatoptimal abatement given the breakthrough is less than 1: μ⁎ (αH)b1.8

We can also consider the impact of α. In the Appendix we show that the marginal benefits tono-risk R&D increase in α. This indicates that the lower α is when the program is certain, themore likely it is to increase with risk; and vice versa. Thus, we expect investment to increase inrisk as the cost of R&D increases.

The intuition is that CRD has very little impact when abatement is high, because at very highlevels of abatement, fossil fuel technology will not be widely employed (unless there is abreakthrough). Thus, the payoff from an incremental improvement is limited when damages arehigh. This is especially true when the cost of R&D is high, leading to lower levels of α. Anincremental investment in the risky program, however, has a significant payoff, since it increasesthe probability of a breakthrough. A breakthrough in CRD has the same impact as a breakthroughin ARD — it reduces the cost of abatement to zero, thus allowing for full abatement. So, asdamages get higher, we expect that it is more likely for optimal investment to increase in risk, andfor this to be exacerbated when the cost of R&D is high. Furthermore, we expect the optimalinvestment in the no-risk CRD program to decrease in the risk of climate damages, since CRD haslittle benefit when damages are very low, and little benefit when damages are very high.

4.3. Impact of uncertainty in climate change damages

In the Appendix we illustrate the difficulty in analyzing the interaction between uncertainty indamages and uncertainty in R&D. We show that even under the simplest of assumptions, wecannot provide unambiguous results. The conclusions we draw from this are that 1) com-putational work is essential in determining these interactions, but that 2) it is crucial to performsensitivity analysis over multiple representations of increasing risk.

5. An empirical implementation

In this section, we investigate whether the qualitative predictions from the analytical modelhold up by performing sensitivity analysis over different damage scenarios, and we investigatehow uncertainty in the damages impacts the choice of a risky R&D program. Subsections 5.1, 5.2

8 If damages are extremely high however, so that even given a (less radical) breakthrough it is optimal to abate fully(and therefore not use the new technology), then the marginal benefits to R&D, whether risky or not, are zero, and therewill be no investment in CRD in either case.


and 5.3 describe a modified version of the well-known DICE model in which we incorporateR&D and climate uncertainty.9 Subsections 5.4 and 5.5 present the results of the model.

The application here is meant to augment more detailed, but deterministic studies. Along theselines, the approach includes a number of simplifications. R&D only occurs in the near-term (thereis not a continuous R&D path) and climate uncertainty resolves at precisely the same time that thebenefits from R&D accrue. And, at a more fundamental level, DICE itself is a very compactmodel of an enormously complex system.

5.1. The DICE model

DICE is a global optimal growth model extended to include interactions between economicactivities and the climate. The model covers the period from 1995 to 2335 in ten-year periods. Ineach period, output is divided between consumption and investment in new capital, consistentwith the standard optimal growth framework. DICE adds to this framework by allowing foremissions of greenhouse gases (GHGs) into the atmosphere as part of the production process. Theaccumulation of these GHGs affects welfare by increasing global temperatures, which, in turn,reduce production. In order to mitigate this effect, an abatement level can be chosen in eachperiod, which reduces emissions below what would otherwise occur for a given production level.While abatement has obvious benefits, it is costly, reducing the amount of output available forconsumption or investment in every period. The objective of the model is to maximize thediscounted sum of utility over time, where utility is based on consumption. The optimalabatement path reflects a balance between benefits and costs.10

Below are two equations from the model that are pertinent to the changes that will be made toincorporate R&D and uncertainty. (We do not present the full DICE model here. Readersunfamiliar with the DICE framework are encouraged to consult Nordhaus and Boyer (2000) for amore thorough treatment.)

Qt ¼ 1

1þ h1Tt þ h2T2t

1−b1lb2t �

AtKgt L

ð1−gÞt ð12Þ

Et ¼ ½1−lt�rtAtKgt L

ð1−gÞt : ð13Þ

Eq. (12) shows the output relationship in the model. Output each period, Qt, is based on inputsof labor, L, and capital, K, modified by a general technological change parameter A. Abatement,

μ, reduces available output through the term [1−b1μb2], where b1= .03 and b2=2.15 areparameters of the model. Hence, the cost of abatement is c(μ)=b1μ

b2 and the MAC is very closeto a straight line (since b2 is close to 2). The accumulation of GHGs impacts production throughthe temperature effects in the term 1

1þh1Tþh2T2, where θ1 and θ2 are parameters of the model. Eq.(13) shows the emissions relationship of the model. Absent abatement, emissions each period, Et

are based linearly on unadjusted production, AKtγLt

(1−γ), through the emissions-output ratioparameter σ. This parameter changes over time exogenously. Abatement reduces emissions by afraction μ.
9 These subsections draw heavily from the description of the model in Baker et al. (2006) with kind permission of
Springer Science and Business Media.10 Note that DICE uses a standard exponential approach to discounting with a discount rate of 5%. The use of differentdiscount rates or different functional forms for discounting the far future changes the optimal level of R&D, but does notchange the qualitative characteristics of our results.


5.2. Incorporating R&D

The R&D decision is made at the beginning of the first period, in 1995, before all other actionstake place. The cost of R&D is given by g(α), where α represents the mean level of technologicaladvance, as in the above sections. These costs are subtracted from the initial capital stock asfollows

K1 ¼ K−gðaÞ: ð14ÞThis is a simplification of the R&D investment process and represents a diversion of the capital

base into R&D; rather than an ongoing investment over the R&D period. The qualitative resultspresented below are not impacted by this simplification. The costs of R&D are given bygðaÞ ¼ ja2

1− a.11 Along with simplicity, this functional form has two desirable qualities. First, it

exhibits decreasing returns to scale in R&D. Second, it ensures that a deterministic investment inR&Dwill not bring about zero-cost full abatement: a breakthrough can only be achieved in a riskyprogram. The constant κ determines the capital intensity of the R&D investment. For example, ifwe consider the alternative technologies program with κ=1, in order to reduce the gap betweenthe cost of non-carbon technologies and currently economic technologies by 10%, an investmentof $1.1 billion will be needed. On the other hand, if κ=15, achieving a 10% decrease in the gapwould cost $15.15 billion.

The benefits of R&D, technological advance, accrue starting in 2045. Hence, ct(μ)=ct(α, μ)for t≥2045, and remain unchanged for tb2045, where α represents realized technical change.(Recall that DICE includes exogenously specified general technological change affecting theparameter At in Eq. (12). This remains in the model for all t.) As we discuss below uncertainty inclimate damages is also resolved after 50 years. The time lag between effort and results isintended to capture the idea that it takes time to transition from the results of R&D to the point ofwidespread technology deployment.

The lack of an opportunity for additional R&D after uncertainty is resolved is an importantconceptual simplification of the model. It represents the idea that by the time uncertainty isresolved, it will take too long for additional R&D to bear fruit if quick action is needed. Thissimplification should be kept in mind when interpreting the model results. In particular, if asecond decision were available, it would most likely put downward pressure on all of the types ofnear-term R&D.

We explore the programs discussed in Subsections 2.1 and 2.2 individually. In DICE, theabatement cost function is c(μ)=b1μ

b2 and is the proportion of output that is reduced to pay forabatement μ. To be consistent with Subsection 2.1 we implement ARD by modifying theabatement cost function to c(μ, α)= [1−α]b1μb2. Specifically, Eq. (12) is modified after 2045 to be

Qt ¼ 1

1þ h1Tt þ h2T2t

1−ð1−aÞb1lb2t �

AtKgt L

ð1−gÞt : ð15Þ

In order to implement CRD, we take the approach of Buonanno et al. (2003), Nordhaus (2002),and Gerlagh and Van der Zwaan (2006), and have technical change decrease the emission-output

11 A reviewer pointed out that the implied marginal cost function for R&D has a zero intercept, which may beinconsistent with the general characteristics of labor supply curves, particularly those that use specialized labor as doesR&D. Sensitivity analysis indicates that the qualitative results hold when marginal costs have a non-zero intercept.

Table 1Parameters for the increasing probability scenarios

Probability of θ2=0 0% 19.8% 55% 91.7%Probability of θ2= .0035 100% 78.4% 45% 0%Probability of θ2= .042 0% 1.8% 5% 8.3%


parameter σ. Emissions from Eq. (13) are multiplied by [1−α], thus reducing the emissions-to-output ratio, σ:

Et ¼ ½1−lt�ð1−aÞrtAtKgt L

ð1−gÞt : ð16Þ

As we have shown in Subsection 2.2, this is equivalent to our analytical representation ofpivoting the abatement cost curve to the right.

The probability distribution for α depends on α as described in Subsection 2.3.

5.3. Incorporating uncertainty in climate damages

The impact of a changed climate on human welfare is a fundamental uncertainty for climatechange planning, whether for R&D or emissions policy. The less deleterious the implications ofincreased atmospheric GHG concentrations, the lower the appropriate near-term response. Butthis uncertainty has not been resolved to date, and, in fact, remains a matter of debate.

In the DICE model, the impact on human welfare is captured as a translation of temperatureincreases into reduced production (see Eq. (12) above), with the parameters θ1 and θ2 deter-mining the degree of negative impact.

Uncertainty in climate damages is captured here by considering θ2 to be a random variable withthree possible outcomes, θL, θM, and θH, representing low, mean, and high damages. We take astochastic programming approach, setting θ2 equal to the standard value in DICE, θM=0.0035,until 2045.12 At this point, learning takes place, and the world splits off into three paths. θ2 maytake on either low damage, mean-damage, or high damage values, θL, θM, and θH, where theprobability distribution maintains θM as the mean. The model is solved using GAMS/CONOPT.

The use of discrete distributions to represent uncertainty presents fundamental conceptualchallenges. The method chosen to approximate a continuous distribution with a discrete distri-bution may have serious ramifications for results.13 Of particular importance, different discretedistributions derived from the same underlying continuous distribution may have fundamentallydifferent uncertainty characteristics — one distribution may be a mean-preserving-spread of theother, therefore exhibiting more uncertainty. Additionally, some discretization methods willinvolve extreme values, while others will be more centered.

Additionally, in climate change, there seems to be most concern about high damage, lowprobability scenarios. We use discrete distributions aimed at underlining these issues, and modelincreasing uncertainty using two distinct cases, inspired by Nordhaus (1994): (1) an “increasingprobability” case and (2) an “increasing damages” case. Tables 1 and 2 give the key parametervalues for each case. For the “increasing probability” case, the magnitude of the high damage

12 See Manne (1996) for another example of this approach. We did sensitivity analysis over the initial value of θ2, andfound no significant differences in the results.13 See Smith (1993) for a discussion of the performance of four discretization methods.

Table 2Parameters for the increasing damage scenarios

Value of high damage θH – .042 (20%) .057 (26%) 0.1 (38%)Probability of θ2=0 0% 19.8% 20.27% 20.84%Probability of θ2= .0035 100% 78.4% 78.4% 78.4%Probability of θ2=θ

H 0% 1.8% 1.33% 0.76%

The values in parentheses in the first row indicate the percentage GDP loss given a 2.5 °C increase in temperature.


scenario, θH, is held constant, but probability is moved from the mean to the extremes: theprobability of a given catastrophe is higher in each successive distribution. This corresponds todifferent beliefs about the chance of a pre-defined “catastrophe”.14 Four scenarios are considered:one deterministic and three uncertain scenarios. In each of the uncertain scenarios, θH is set to.042, which implies a great depression sized loss of GDP (a 20% loss) for a 2.5 °C increase intemperature. The probability of high damages for the first uncertain scenario, pH= .018, iscalibrated from the estimates from Nordhaus and Boyer (2000), which in turn are based on anexpert survey from Nordhaus (1994).15 The third uncertain scenario assigns a probability of 8.3%to θH. To put this in perspective, the average probability assigned by the scientists in the surveyby Nordhaus (as opposed to the economists) was 12%.

For the “increasing damage” case, the magnitude of the high damage scenario θH is increasedto capture increasing uncertainty. This reflects differing beliefs about how bad a catastrophe mightbe.16 In the three uncertain scenarios, we hold pHθH constant— the expected catastrophe doesn'tchange. The probability of low damages is adjusted to retain the mean. The four scenarios, labeledby the value of θH, were chosen to illustrate the non-monotonic response of optimal R&D toincreasing uncertainty. The highest damage scenario here, with θH= .1, implies about a 38% lossof GDP for a 2.5 °C increase in temperature.

5.4. Results: risky R&D and deterministic damages

Fig. 4 shows the results from the empirical model. On the left-hand side is the alternativeprogram; on the right hand side is the conventional program. The horizontal axis represents the %GDP loss given a 2.5 °C warming. The vertical axis shows the optimal target amount of R&D, α⁎.We see that for alternative technologies investment is much higher in the risky program whendamages are low. Qualitatively, this is reversed for higher damages, but quantitatively the impactof risk is insignificant when damages are higher. For conventional technologies, the overallinvestment decreases in very large damages when the program is certain. This is because whendamages are very high it is optimal for the economy to move to a no-emissions world. Unlessthere is a breakthrough, conventional technologies will always produce some emissions. Thus, ina certain world – a world without a breakthrough – there is no benefit to investing in conventionalR&D if damages are very high. However, the level of damages at which the no-risk investment ismaximized increases sharply as the cost of R&D decreases. Quantitatively, the difference betweenthe no-risk and risky program is small, until the damages are very high, at which point investmentin the risky program is significantly higher than in the no-risk program.

14 See the discussion in Nordhaus (1994) regarding different assessments of the probability of a catastrophe.15 A group of expertswere asked to assess the probability of a great depression sized catastrophe (damages equal to about 20%of GDP) given a 2.5 °C rise in temperature. Nordhaus combined the survey responses, then updated it with new informationavailable since 1994, to get a probability of 1.8%. In our framework this implies that θ2=.042 with probability 1.8%.16 See the discussion in Nordhaus (1994) regarding different assessments of the 90th percentile damages.

Fig. 4. Optimal investment in R&D when damages are deterministic. We represent the results for two values of the costconstant K. The two higher lines in each figure represent low-cost R&D; the lower lines represent high-cost R&D.


5.5. Results: risky R&D and uncertain damages

In this section we investigate the optimal investment in R&D under different probabilitydistributions over the damages. As Lempert et al. (2004) note, there is “deep” uncertainty aboutclimate change, characterized by wide disagreement about appropriate models and the priorprobability distributions of those models. One way to address this uncertainty is to determine howactions are impacted by various probability distributions. Thus, we do sensitivity analysis over theprobability distributions discussed in Subsection 5.3 above. In each of the figures, a move to theright represents a mean-preserving-spread.

Fig. 5 presents the results. The graphs on the left are for alternative R&D, on the right areconventional R&D; the graphs on the top represent increasing risk in term of increasing damages,on the bottom, in terms of increasing probability. The figures show the optimal target amount ofR&D, α⁎.

For ARD, investment is significantly higher in risky programs than in programs with certainreturns, under all risk scenarios.17 This is not surprising, given the results in Fig. 4, where we seethat there is a big gap in between the two when damages are low, and very little gap whendamages are high. Investments in the no-risk program begin to approach investment in the riskyprogram only when the probability of a catastrophe gets large.

For conventional technologies, we get an almost opposite result. The risk-profile of the R&Dprogram is unimportant, except when there is a very high probability of a catastrophe. Because,on average, damages are expected to be low, investment in the no-risk program tends to be fairlylow. When α is low in the no-risk program, it has virtually no impact when damages are high; sothe risky program has a higher payoff when α is low, and damages are high. When the probabilityof high damages gets high enough, investment in the risky program is higher than in the no-riskprogram.

The patterns for optimal investment as climate damage risk increases are complex. Baker et al.(2006), under the assumption of certain returns to R&D, showed that optimal investment inconventional technologies tends to decrease in climate risk; and optimal investment in alternativetechnologies increases in the probability of full abatement; while all R&D programs tend todecrease under the increasing damages scenario. These results hold for the no-risk programs, but

17 When translated into dollar amounts, investment in the risky R&D program ranges from 12 to 115 times higher forK=1; and 30 to 2000 times higher for K=15.

Fig. 5. Optimal R&D under uncertainty about climate damages. The black lines represent R&D investment when theprogram is risky; the grey lines represent investment when the program is certain. The two higher lines in each graphrepresent investment when K=1; the lower lines when K=15.


not for the risky programs. From these figures we can conclude that 1) increasing risk in climatedamages has a smaller impact on riskier programs than on less risky programs and 2) thequalitative impact of increasing risk in climate damages can be different for risky and no-riskprograms.

Finally, we note that for both ARD and CRD, the quantitative difference between the riskyprogram and the no-risk program is large only when investment is higher in the riskier program.This combined with the fact that increasing risk in climate damages has a small impact on theoptimal investment in a risky program, indicates that investing in riskier programs may be a morerobust response to the deep uncertainty surrounding climate change than investing in less riskyprograms (IPCC, 2001).

6. Conclusions

In this paper we set up a simple model with two contrasting assumptions about technicalchange. In the first case, we assume that investments in R&D will lead to a proportionatereduction in abatement costs, and we argue that these represent investments into alternative, non-carbon energy programs. We find that optimal investment is higher in risky R&D than in non-risky, except when there is a large chance of a catastrophe occurring. This is because theseinvestments only have a significant payoff if something dramatic happens: either if technicalchange is large OR climate damages are severe. Alternative technologies are only found in nichemarkets right now: incremental improvements will incrementally increase the niches, but not have


a huge impact on the economy. This means that, if damages are moderate, the only thing that willhave a big impact is a breakthrough in the technology which will allow it to be widelycompetitive. Therefore, pursuing risky R&D (with a chance of a breakthrough as well as a chanceof failure) makes sense. However, if damages are severe, society will use a much larger proportionof alternative, non-carbon technologies. In that case any improvements in these technologies willreverberate through society. When incremental improvements have a big impact risks are lessworth taking.

In the second case, we assume that investment in R&D will reduce the emissions-to-outputratio, and we argue this represents investments into reducing the emissions from fossil fueltechnologies. Here, we get opposite results from those above: optimal investment is, quan-titatively, largely independent of risk, and, qualitatively, higher in non-risky R&D than risky,except when the probability of a catastrophe is high. This case is different because R&D intofossil fuel technologies have a significant impact when damages are moderate, but little impactwhen damages are high. Since fossil fuel use is widespread, incremental improvements will havea widespread effect on the economy and a significant payoff, which make risk less worth taking.But, in the event of really serious damages, society will reduce the use of fossil fuel technologies,making incremental improvements in fossil fuel technologies much less important. In this case,the only thing that will help is a breakthrough (reducing emissions from fossil fuels to near zero),therefore risky R&D is worth pursuing.

The bottom line is that the optimal investment in R&D depends crucially on the type oftechnology considered and the uncertainty in both damages and the R&D process.

The policy implications of these results depend on beliefs about the chance of a catastrophe. Ingeneral, one justification for technology policy is the assumption that private actors tend to avoidhigh risk projects with far-future payoff dates (Clarke and Weyant, 2002). If the probability of acatastrophe is low (i.e. closer to the economists' view of the world in Nordhaus (1994)), an R&Dportfolio aimed at reducing the costs of alternative technologies should optimally be tilted towardriskier projects. This means there may be a role for government involvement in R&D into lowprobability, game-changing alternative technologies — technologies that will be widely com-petitive with fossil technologies, if successful. On the other hand, if the probability of catastropheis high, the government may have a role in supporting research aimed at developing a radical,emission-free fossil fuel based technology.

This model is a considerable simplification from real-world technology decisions. We haveconsidered two broad categories of technical change, represented by different shifts to theabatement cost curve. We argue that they are broadly related to classes of technologies, but workneeds to be done connecting the impacts of specific technical change on the marginal cost ofabatement. In fact, the key conclusion of this paper is that it matters how technology is modeled,and so research must start connecting potential real-life R&D projects with their representations inmodels. We have not considered the history of any particular technology, nor are we commentingon the likelihood of a breakthrough in any particular technology. Rather, we suggest that workneeds to be done on assessing the future potential of technologies, whether fossil or non-fossilbased. Additionally, we use a simple, two-period model. Thus, this work is not commenting onthe option value that is created by considering sequential investments in R&D programs. On theone hand, there is a value to waiting to learn more about climate change damages (which wouldput a downward pressure on all R&D investments); on the other hand, there is a value to investinga small amount in a risky project in order to learn more about the probability of success (whichwould put upward pressure on risky technologies). This work is primarily considering the impactof the interaction between uncertainty in damages and uncertainty in R&D.


We are looking at the overall optimal level of R&D investment in the economy in response toclimate change. We are not considering ancillary benefits or costs from the technical change. TheDICE model includes autonomous technical change, both in growth in production, and in adecrease in the emissions-output ratio. Thus, the R&D considered here is additional to the assumedautonomous technical change. Furthermore, the rationale for government technology policy is thegap between the overall optimal investment and what is provided by the private sector. We havebegun to address the question of the overall optimal investment; an investigation of private sectorinvestment is an important area of future research. Finally, this work assumes that future decisionswill be optimal, implying that a carbon policy is implemented eventually, after more information isrevealed. If this is not true and future abatement is inoptimally low, that will tend to favor riskierARD and less risky CRD; if future abatement is inoptimally high, the result is reversed.

Acknowledgment

Baker acknowledges partial funding from a Faculty Research Grant, University ofMassachusetts, Amherst.

Appendix A

We show that the marginal benefits to no-risk CRD increase in α. From Subsection 4.2 themarginal benefits are:

MBucVl⁎ðaÞ−a1−a

� 1−l⁎ðaÞ½1−a�2

" #: ð17Þ

The derivative of (17) with respect to α is

AMBAl

AlAa

þ AMBAa

ð18Þ

AMBAl

¼ cWl−a1−a

� 1−l½1−a�3 −cV

l−a1−a

� 1

½1−a�2 ð19Þ

AlAa

¼cW l− a

1− a

� �1−l

½1−a�3 −cVl−a1−a

� �1

½1− a�2

SOC: ð20Þ

Where SOC is the second order condition for μ to be optimal. Thus the first term in (18) is

cW l−a1−a

� �1−l

½1−a�3 −cVl− a1−a

� �1

½1−a�2h i2

SOCz0 ð21Þ

AMBAa

¼ cWl−a1−a

� 1−l2

½1−a�4 þ cVl−a1−a

� 1−l½1−a�3 z0: ð22Þ

(21) and (22) imply that (17) is increasing in α.


A.1. Impact of uncertainty in climate change damages

What we would like to know is how increasing risk (in the Rothschild and Stiglitz (1970)sense) in climate damages impacts the difference between the marginal benefits of risky and no-risk R&D. We will focus on ARD since it is simpler and more likely to give unambiguous results.The following quantity is the expected difference between the marginal benefits to risky and no-risk R&D, when Z is uncertain:

EZ½cðl⁎ðZÞÞ þ Dðl⁎ðZÞ; ZÞ−Dð1; ZÞ−cðl⁎ða; ZÞÞ�: ð23ÞIf increasing risk increases this difference, then risky R&D becomes relatively more attractive

as damage risk increases; if risk decreases this difference then no-risk R&D becomes relativelymore attractive as damage risk increases. Recall that the expected value of a function increases inrisk if it is convex and decreases in risk if it is concave. Therefore, we investigate the convexity/concavity of the quantity inside the brackets in (23) with respect to Z. In order to illustrate thedifficulties, we make extreme simplifying assumptions: damages are linear in Z; costs anddamages are quadratic in μ; and abatement is not constrained — it is possible to abate more than100% of emissions, and in particular, it is possible to abate the entire stock of emissions.Specifically, the second period optimization problem given α is

minlð1−aÞl2 þ ZðS−lÞ2: ð24Þ

The first order conditions tell us that

l⁎ a; Zð Þ ¼ ZS1−aþ Z

: ð25Þ

If α=0, then l⁎ ¼ ZS1þ Z

. If α=1 then μ⁎=S. The quantity inside the brackets in (23) is equalto

ZS1þ Z

� 2

þZ S−ZS

1þ Z

� 2

−0−ZS

1−a þ Z

� 2

: ð26Þ

This quantity is neither concave nor convex in Z for any value of αb1, implying that (23) isambiguous in risk. If we constrain μ≤1, the expression simply gets more complicated. Thus,under even the simplest assumptions the effect of risk is ambiguous: some increases in risk favorrisky R&D, while other increases favor no-risk R&D. Thus, we turn to a computational analysis.

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Investment in risky R&D programs in the face of climate uncertainty

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