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Abstract

The paper provides an assessment of the order of magnitude of the marginal social costs of

greenhouse gas emissions. The calculations are based on a stochastic greenhouse damage

model in which all key parameters are random. This, on the one hand, allows a closer

representation of current scientific understanding, on the other hand it also enables to calculate

a damage probability distribution, and thus to account explicitly for the uncertain nature of the

global warming phenomenon. As a benchmark we estimate that CO2 emissions impose social

costs in the order of 20 $/tC for emissions between 1991 and 2000, a value which rises over

time to reach about 28 $/tC by 2021-2030. Similar figures for CH4 and N2O are also provided. As

a consequence of the prevailing uncertainty on greenhouse impacts, the standard deviation of

the estimates is rather high. The distribution is positively skewed, i.e. an extremely disastrous

outcome is more likely to occur than a modest result with a similar deviation from the mean. This

implies that the currently predominant method of using best guess values will lead to an

underestimation of the expected costs of emissions.

Introduction

There is now a wide and growing body of literature on the potential impacts of global warming.

Most notably this includes the work by the US Environmental Protection Agency (Smith and

Tirpak, 1989) and by the Intergovernmental Panel on Climate Change (IPCC), whose Working

Group Two is entirely devoted to the impacts of climate change (IPCC, 1990c). In addition there

are numerous studies on particular aspects of the problem, including for example Parry et al.

(1988) and Parry (1990) on agriculture, Titus et al. (1991) on sea level rise, Peters and Lovejoy

(1992) on biological diversity, Waggoner (1990) on water, and World Health Organisation (1990)

on health effects, to name only a few. In most parts this work is on a descriptive level, though, or

limited to a quantification in physical terms. Few attempts exist to a monetary quantification of

global warming damage (Nordhaus, 1991a, b; and Cline, 1992a; Titus, 1992; Fankhauser, 1993,

1992).

On a policy level, a monetary assessment of greenhouse damage is crucial. A comparison

between the costs of greenhouse prevention and the benefits from avoided warming is only

feasible if damage can be expressed in monetary terms. Similarly, a monetary estimate is

required to assess individual abatement projects such as those financed by the Global

Environment Facility (GEF). Considerable effort has recently been put into analysing the social

costs of the fuel cycle, with the aim of deriving externality adders which are to be put onto the

price of fossil fuels to internalise the social costs of fuel consumption (see e.g. Hohmeyer, 1988;

PACE, 1990; Pearce et al., 1992; Lockwood, 1992). The studies typically concentrate on classic

air pollutants like NOx and SOx. To complete the picture an additional adder would be required

reflecting the social costs of global warming.

The aim of the present paper is to fill this gap and provide an order of magnitude assessment of

the social costs, or the shadow value, of greenhouse gas emissions. Assessing greenhouse

damage is not possible without accounting, in one way or another, for the huge uncertainty

prevailing in the global warming debate. Although scientists have achieved a remarkable

consensus with respect to many aspects, our ignorance of global warming impacts is still vast,

particularly with respect to regional and long term impacts. Most studies allow for uncertainty by

working with different climate scenarios. In the present paper we chose a different approach and

incorporated uncertainty directly by describing uncertain parameters as random. Using a

stochastic model of this type has several advantages. First of all it allows a better representation

of current scientific understanding. Scientific predictions usually take the form of a best guess

value supplemented by a range of possible outcomes. Concentrating on the best guess value

therefore neglects a large part of the information provided, while, on the other hand, a stochastic

model can make full use of it. Secondly, and probably more importantly, a stochastic model

allows the calculation of an entire damage probability distribution, thereby providing important

additional information on the likelihood of the estimates and the possibility of extremely adverse

events.

Care should nevertheless be exercised when interpreting the figures presented below. Although,

as we believe, based on the best available scientific information, they cannot provide anything

better than a rough order of magnitude assessment. A distinction should also be drawn between

the actual marginal costs of greenhouse gas emissions and the shadow value along the optimal

emissions path. This paper concerns the former, as explained in Figure 1. Our results give

therefore little indication about the socially optimal carbon tax on an international level, the

calculation of which would require an optimal control model (see Nordhaus, 1992, 1993a, b;

Peck and Teisberg, 1992, 1993a, b). Arguably, a figure on the actual costs may be more relevant for individual abatement projects, however. As will become clear later, the shadow value

of greenhouse gas emissions depends on the amount of emissions discharged in the future.

Optimal shadow values would therefore only be relevant for actual projects if the world was to

follow the optimal emissions trajectory calculated in the model. There is no guarantee that this

will be the case. The current approach, which treats future emissions as uncertain, seems

therefore more realistic. Arguably, the resulting range will encompass the optimal path.

Also note that, for the same reason, the figures are only relevant for small scale abatement

projects, which do not significantly affect the trajectory of future emissions. The appraisal of large

scale abatement policies such as an international carbon agreement, which affect future

emission levels, is somewhat more complex, and would require an adjustment of the future

emission trajectory. Given that with the exception of the top four emitters no country accounts for

more than 4% of total greenhouse gas emissions, large scale abatement in the above sense will

however be the exception, and is arguably confined to internationally concerted efforts.

The structure of the paper is as follows. Section 2 reviews existing estimates of both the costs of

CO2 concentration doubling and of estimates of the shadow value of carbon. Section 3 then

introduces the stochastic model utilised in this paper, and section 4 presents the resulting

estimates. Section 5 outlines policy implications and concludes.

Existing Damage Estimates

2.1 The Damage from a Concentration Doubling

Scientific research on greenhouse impacts so far has almost entirely concentrated on the

benchmark case of warming under an atmospheric CO2 concentration of twice the preindustrial

level (2xCO2). As a consequence studies on the economic costs of global warming have tended

to concentrate on the same benchmark. By far the best studied aspects of 2xCO2 damage are

the impacts on agriculture (e.g. Kane et al., 1992; Parry, 1990; Parry et al., 1988) and the costs

of sea level rise (e.g. IPCC, 1990b; Titus et al., 1991; Rijsberman, 1991). There are nonetheless

some studies which try to provide a more comprehensive picture of global warming damage by

including all damage aspects. The pioneering paper in this area is Nordhaus (1991a, b). Still

mainly concentrating on the costs of agriculture and sea level rise, he estimated an overall

damage of global warming in the order of a quarter percent of GNP. To allow for the many nonmarket

impacts neglected in the study this value is raised to 1%, with a range of error of 0.25-

2%. The figures are based on US-data, but Nordhaus claims that they may hold worldwide.

Improvements on Nordhaus' back-of-the-envelope estimate have been provided by Cline

(1992a) and Titus (1992), two papers again focusing on the US, and by Fankhauser (1993;

1992), who distinguishes between several geopolitical regions. Despite considerable differences

in individual damage categories, the three studies roughly agree on the overall result, all

predicting a 2xCO2 damage in the order of 1% to 2% of world GNP. Despite the attention the

2xCO2 case enjoys in the literature, it is not directly relevant for practical purposes, though. For

the appraisal of abatement projects it is more important to know the costs per tonne of emission.

We turn to this aspect next.

2.2 The Damage per Tonne of Emission

Most studies estimating the social costs of greenhouse gas emissions do so in an optimal

control framework, and primarily aim at calculating the socially optimal greenhouse emissions

trajectory over time. In such a setup the shadow price of emissions is equivalent to the pollution

tax required to keep emissions on the optimal path.

The pioneering paper on the social costs of CO2 emissions is again Nordhaus (1991a, b). Using

a simplified approach which does not constitute a fully fledged optimal control model, he

calculates social costs of 7.3 $ per tonne of carbon emitted. Imposing different assumptions on

the rate of discount and the 2xCO2 damage leads to a range of 0.3 $/tC to 65.9 $/tC. Implying

that abatement should only be undertaken as long as costs do not exceed $ 7.3 per tonne of

carbon abated, the estimates formed the backbone of Nordhaus' claim that global warming may

not, after all, be such a big problem, and may justify only a modest policy response.

This view has been fiercely criticised by many authors (see for example Ayres and Walter, 1991;

Daily et al., 1991; Grubb, 1993). The main objection concerned Nordhaus' 2xCO2 estimate which

has repeatedly been attacked as being too low. Only few of the criticisms appear to be based on

sound analysis, though, and more important than the problems with 2xCO2 damage are probably

the shortcomings of the model itself (see Cline, 1992a). Particularly questionable is the

assumption of a resource steady state, which inter alia implies a constant level of CO2 emissions

over time. Obviously this is unrealistic. The IPCC for example predicts an increase in annual

CO2 emissions from about 7 GtC in 1990 to about 9-14 GtC by 2025 (IPCC, 1992). The simple

(linear) structure of the climate and damage sectors also implies that costs will remain constant

at 7.3 $/tC throughout. Climate processes are clearly non-linear, and the costs of CO2 emissions

will thus depend on future concentration and warming levels, i.e. they will vary over time.

Subsequent estimates suggest that they may in fact rise over time. That is, a tonne of CO2

added to an already large stock of atmospheric CO2 is likely to cause a higher damage than a

tonne emitted under a low concentration level.

These objections are also relevant to the study by Ayres and Walter (1991), whose calculations

are based on the Nordhaus model. The paper has additional shortcomings. In particular their

analysis is based on figures of an earlier draft version of the Nordhaus (1991a, b) papers, which

differ from those in the published version. Further, by considering both the costs of sea level rise

protection and the costs of climate refugees from coastal regions they appear to double count at

least some of the sea level rise impacts. On a whole, their cost estimate of 30-35 $/tC must

therefore be regarded as suspect.

The shortcomings of the earlier model were recognised and corrected in Nordhaus' subsequent

approach, the DICE (Dynamic Integrated Climate Economy) model (Nordhaus, 1992, 1993a, b).

DICE is an optimal growth model in the Ramsey tradition, extended to include a climate module

and a damage sector which feeds climate changes back to the economy1

. The shadow values of

carbon following from DICE are in the same order as Nordhaus' previous results, starting at 5.3

$/tC in 1995 and gradually rising to 6.8 $/tC in 2005 and 10 $/tC in 2025 (see Table 1). Note that

figures for future periods are current value estimates, i.e. they denote the social costs valued at

the time of emission. The DICE model was also used by Cline (1992b), who concludes that

Nordhaus' choice of parameter values may have lead to an underestimation of the true costs.

Unfortunately, Cline's paper only reports alternative emission trajectories, but not the

corresponding shadow values.

Figures slightly higher than those by Nordhaus were suggested by Peck and Teisberg (1992,

1993a, b), who came up with a shadow value of carbon of about 10$/tC in 1990, rising to about

22 $/tC by 2030 (see Table 1). The CETA (Carbon Emission Trajectory Assessment) model, on

which their calculations are based, possesses a similar climate and damage sector as DICE, but

is more detailed on the economy side by incorporating a carefully modelled energy sector2

.

Differences between the estimates appear to be mainly due to different assumptions about the

size of 2xCO2 damage. Common to both papers is the assumption of a 3% utility discount rate, a

figure which may be rather high, according to many authors (Cline, 1992a; Hoel and Isaksen,

1993; see also section 4).

4.1 The Social Costs of CO2

We have used the model of section 3 for Monte Carlo simulations of the social costs of CO2

emissions over four decades, from 1991 to 2030. The results are shown in Table 2. As

expected, damage per tonne of emission is rising over time, from about 20 $/tC between 1991

and 2000 to about 28 $/tC in the decade 2021-2030. The rise is mainly due to income and

population growth, i.e. the fact that kt is rising over time. The impact of higher future

concentration levels on the other hand is ambiguous. In some constellations with a low

parameter γ the logarithmic relationship between forcing and concentration may dominate over

the concavity of the damage relationship, and a higher concentration may actually lead to a

decrease in marginal damage. If it was not for economic and population growth, the shadow

value would fall over time in these cases. The figures for future periods are again current value

estimates and denote the social costs valued at the time of emission.

The expected value figures alone do not of course tell a complete story. The optimal policy

response is likely to differ depending on the confidence in the results, the distribution of possible

outcomes and the probability of high impact events. What is lacking is thus some information

about the probability distribution of greenhouse damage. A probability distribution of greenhouse

damage is obtained directly from our stochastic model, and the relevant statistics are also shown

in Table 2. The distributions for CO2 emissions are depicted in Figure 2. The Figure shows rather

wide distributions with standard errors around 14 to 19, reflecting the generally low level of

confidence in these figures. Not surprisingly the standard error is increasing over time as the

estimates for more distant periods are more widely spread than that for the decade 1991-2000.

The shape is clearly asymmetric and skewed to the right, with coefficients of skewedness in the

order of 2.5 (see Table 2 6

. Loosely, this means that the probability of an extremely disastrous

outcome is higher than that of an extremely modest result.

Our damage estimates are somewhat higher than those of existing studies like Nordhaus (1992,

1993a, b) and Peck and Teisberg (1992, 1993a, b). Partly this is due to different assumptions on

the value of some key parameters. The pure rate of time preference, for example, is set at 3% in

DICE and CETA, a value which constitutes the upper bound for this parameter in our study. On

the other hand we used more moderate assumptions about the slope of the damage function.

Conceptually more important is a second source of discrepancy, which arises from the fact that

our figures represent expected values, while the other estimates are best guesses. As shown in

Figure 2 global warming damage is not distributed symmetrically but skewed to the right. Under

these circumstances the mean will be greater than the mode, and expected value figures are

therefore bound to be higher than a best guess estimate which ignores this asymmetry. The

higher value of our figures is thus also a consequence of the incorporation of high impact events.

In our model the difference between the expected value and a non-random best guess is about

25%. Encompassing extreme events thus appears to be crucial, and expected value estimates

should be favoured over best guess assessments.

4.4 Sensitivity Analysis II: Greenhouse Angst

Although the parameter values underlying the above results broadly reflect the current

understanding of global warming, there is still an element of subjectivity inherent in them. In

particular, by assuming a triangular distribution for random parameters they neglect the

possibility of a climate catastrophe. It has often been noted that, given the complexity of the

climatic system and the unprecedented stress imposed on it, surprises cannot be fully excluded,

particularly in the long run (beyond 2xCO2). Catastrophic scenarios implied in the literature

include the melting of the antarctic ice-sheet, a redirection of the gulf stream and the release of

methane from previously frozen materials through the melting of permafrost soils. The probability

of a catastrophic outcome is clearly greater than zero.

The easiest way to incorporate such instances of greenhouse angst is by using probability

distributions with a domain greater than zero, i.e. to assume that parameter values are bounded

below but unbounded upwards. Even extremely high parameter values then still occur with a

positive probability. A distribution with this property is the lognormal, and as a sensitivity test we

have run the model assuming a lognormal distribution for three key parameters: Climate

sensitivity, 2xCO2 damage and the slope of the damage function, thus allowing for catastrophic

outcomes with respect to climate, with respect to impacts and with respect to the existence of

thresholds10. The distributions were calibrated such that the lower bound remains

unchanged and the most likely value equals the scientific best guess, as before, while the

probability of extremely high outcomes was gradually increased. The results of this exercise are

summarised in Figure 3. The Figure shows the mean and 90% confidence interval of the social costs of 1990s CO2 emissions under the different scenarios considered. With respect to the

mean the difference between the lowest scenario A, which roughly corresponds to the triangular

case used before and the most extreme scenario considered is about 60%. If, for example, we

allow a 1% chance (in each case) that 2xCO2 rises temperature by more than 7°C, that a 2.5 °C

rise causes damage of more than 4.25% of GNP, and that the damage function rises steeper

than to the power 3.5, the social costs of CO2 emissions will rise to about 33 $/tC. As expected

the 95th percentile rises stronger than the mean, by about 80%, thus further increasing the

skewedness of the distribution. Although illustrative, the analysis therefore clearly underlines the

importance of low probability/high impact events.

Policy Implications and Conclusions

The paper estimates the monetary costs of greenhouse gas emissions. As a rough benchmark

figure we suggest a value of 20 $/tC for emissions between 1991 and 2000. In subsequent

decades the value rises to 23 $/tC, 25 $/tC and finally 28 $/tC for emissions in the third decade

of the next century. Like all greenhouse damage estimates these results are highly uncertain

and the confidence intervals attached to them are correspondingly wide. The stochastic

character of our model allowed the explicit calculation of a damage probability distribution. It was

shown that the distribution is skewed to the right, even for the runs neglecting the possibility of a

climate catastrophe. That is, even when abstracting from actual extremes, an extremely

disastrous outcome is still more likely to occur than a correspondingly modest result.

Incorporating the possibility of a future climate catastrophe considerably increases both the

mean and the skewedness of the distribution. In the most extreme case considered expected

damage rose to about 33 $/tC. It was also confirmed that the results crucially depend on the

choice of the discount rate, and ethical considerations will therefore have to stage prominently in

the future debate.

The main application for the estimates is probably project appraisal. For small projects the

interpretation of the figures is straightforward. For a reforestation project sequestering 1 mtC per

year over 30 years, for example, we can expect benefits of 20 m$/yr in the first decade, 23 m$/yr

in the second and 25 m$/yr in the third. Total (undiscounted) benefits are therefore

200+230+250=680 m$. Investment decisions can then be made in the usual way by comparing

the relative net benefits of rival projects. The analysis is more complicated with respect to large

scale abatement policies big enough to affect the future emissions trajectory. Because the

shadow value of carbon depends on future emissions the social costs of CO2 emissions will

change with the implementation of the policy and would have to be recalculated for the new

emissions trajectory. In this way Cline (1992a) has found favourable benefit cost ratios for a

suggested freeze of carbon emissions at 4 GtC/year. For policies affecting the trajectory only

slightly the above estimates may suffice as a rough assessment, though. The procedure is then

the same as above.

The appraisal of individual abatement projects has to be distinguished from the task of designing

an optimal policy response to global warming. Our model does not deal with this latter question,

and the figures provided give therefore only little, if any indication of the socially optimal carbon

tax. Calculating a socially optimal emissions trajectory would require the use of an optimal

control model like CETA or DICE, and both models provide a first assessment as to what the

optimal emissions trajectory might be (see Peck and Teisberg, 1992, 1993a, b; Nordhaus, 1992,

1993a, b; Cline, 1992b). However, not least because they are based on non-random

parameters, neither model offers a fully satisfactory approach to the uncertainty issue,

particularly with respect to low risk/high impact outcomes. This is underlined by the fact that

optimal trajectories differ considerably between scenarios. What is needed is a model which

directly incorporates uncertainty, rather than working with scenarios. To our knowledge no such

model exists at present. Further research efforts should thus be made in two directions: Firstly

into projects aiming at reducing existing greenhouse uncertainties, and secondly into projects

evaluating the optimal policy in the light of them.