EVALUATING THE SOCIAL COSTS OF 

GREENHOUSE GAS EMISSIONS

by 

Samuel Fankhauser 

CSERGE Working Paper GEC 94-01 
EVALUATING THE SOCIAL COSTS OF 

GREENHOUSE GAS EMISSIONS 

by 

Samuel Fankhauser 

Centre for Social and Economic Research 

 on the Global Environment 

University College London 

and 

University of East Anglia 

Acknowledgements:

The Centre for Social and Economic Research on the Global Environment (CSERGE) is a 

designated research centre of the UK Economic and Social Research Council (ESRC). 

I am grateful to Rosemary Clarke, Snorre Kverndokk, David Maddison, David Pearce and David 

Ulph for their comments on an earlier version of the paper. 

ISSN 0967-8875 
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. 
1

1. 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 
2

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. 
3

2. 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. 
4

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). 

 

1

 A conceptually different approach would be to impose an exogenously given carbon 

concentration or emissions constraint. The shadow value of carbon is then determined according 

to Hotelling's rule, see Anderson and Williams (1993). 

2

 This latter feature is of course of less relevance in the present context. 
5

3. A Stochastic Greenhouse Damage Model

3.1 General Description

Greenhouse gases are so-called stock pollutants. That is, global warming damage is not caused 

by the flow of emissions as such, but by their accumulation in the atmosphere. Consequently a 

tonne of emissions has its impact not only in the period of emission, but over several time 

periods - as long as the gas, or fractions of it remain in the atmosphere. The damage costs of a 

tonne of emission of gas i, Si

, are thus a present value figure - the discounted sum of future 

incremental damage, ∂D(t)/∂Ei

(0), 

where δ is the discount rate. The equation can be further disaggregated, as follows. 

A marginal increase in base period emissions will first of all lead to an increase in the 

atmospheric concentration of gas i. The impact on concentration at time s > 0, ∂Qi

(s)/∂Ei(0), 

mainly depends on the removal rate of gas i and on possible interactions with other gases. The 

effect of a higher atmospheric concentration in gas i on global mean temperature (which stands 

as an index for a whole set of climatic changes) is ∂T(t)/∂Qi

(s), t > s. It depends on a variety of 

factors, including the radiative forcing capability of gas i, the atmospheric concentration of other 

greenhouse gases, climatic feedback effects and the inertia of the climate system. If, finally, an 

increase in global mean temperature causes a marginal damage of ∂D(t)/∂T(t), the incremental 

damage at time t from a marginal increase in base period emissions of gas i is, 

see Schmalensee (1993). The marginal costs of an incremental tonne of emissions are then 

The estimation of the social costs of greenhouse gas emissions thus requires several pieces of 

information. First we require a module which represents the world climate system and 

transforms an increase in emissions into incremental atmospheric concentration and then 

warming. The climate system being a highly complex process, models aiming at its simulation, 

such as Global Circulation Models (GCMs) tend to be quite big. Smaller scale representations 

are often able to provide a sufficiently close approximation, though, and our model is based on 

such an approximation. Second, we need to know more about the shape of the damage 

function. Research has almost uniquely concentrated on 2xCO2, and information about the 

damage before and after this benchmark is therefore extremely difficult to obtain. Assumptions 

are often rather ad hoc. Long run damage in particular also heavily depends on the assumed 

e dt

E (0)

D(t) S = - t

0 i

i

δ

τ

∂

∂

∫ (1)

ds

E (0)

Q (s)

Q (s)

T(t)

T(t)

D(t) = E (0)D(t)

i

i

i

t

i 0

















∂

∂ • ∂

∂

∂

∂

∂

∂ ∫ (2)

ds e dt

E (0)

Q (s)

Q (s)

T(t)

T(t)

D(t) S = - t

i

i

i

t

0 0

i

δ

τ

































∂

∂ • ∂

∂

∂

∂ ∫ ∫ (3)
6

discount rate, the choice of which is a highly controversial issue (see section 4.3). Finally, 

because the climate process is non-linear, the shadow value of a tonne of emissions today 

depends on the level of emissions in future periods, and we need predictions about these. 

Contrary to the optimal control problems introduced in the previous section, future emissions 

have to be exogenously determined in the present model. The social costs of emissions in a 

certain period are then achieved by increasing emissions by one tonne in this period and 

comparing the stream of annual damages before and after the increase. 

Future emissions, discount rate, shape of damage function and many of the climatic parameters 

are highly controversial variables about which little is known with certainty. Uncertainty is 

explicitly taken into account in our model by modelling all key parameters as random. In the 

basic case we assumed triangular distributions for all variables. The triangular specification 

appeared to be an obvious choice, given that most scientific predictions take to form of a lower 

bound, upper bound and best guess estimate, values which can directly be used as distribution 

parameters without requiring further alterations. Where no upper and lower bounds are available 

we usually assumed a rather modest range of ±10%. Alternative distributions will later be 

introduced for some parameters to incorporate low probability/high impact events. The full list of 

random parameter and parameter values is given in the Appendix. In the remainder of this 

section the model is introduced in full detail. 

3.2 Future Emissions

The model distinguishes between 10 sources of emission, see Appendix (Table a). Emissions 

follow an exogenous business-as-usual (BAU) path, where the growth rates of each emission 

source were calibrated to mimic the IPCC (1992) scenarios (see Appendix for details). The 

model expands over τ = 230 years, and growth rates may vary over time. For CO2 emissions 

from fossil fuel combustion the procedure is slightly more complex in that the rate of growth of 

emissions at time t, gt, consists of several factors, as follows 

where ct is the percentage change in carbon intensity (carbon emitted per energy unit), ft the 

increase in energy efficiency (energy used per unit of GNP), yt the change in per capita income 

and pt the rate of population growth. The relationship follows from taking time derivatives of the 

following tautological relation (see Proops et al., 1993), 

Note that, while all growth rates are random, they may not be independent of each other. For 

example, a rapid decrease in carbon intensity will not only manifest itself in a significantly 

negative value for ct, but may also lead to a lower growth rate of CH4 emissions from coal mining 

and a higher growth rate of CH4 from gas leakage. The reason for this is that a lower carbon 

intensity is likely to be achieved through switching from carbon intensive coal to cleaner gas, 

which will affect the methane emissions from these sources. In a similar way CH4 from biomass 

burning is correlated to CO2 from deforestation, and growth rates in later periods depend on 

those observed previously. 

As mentioned above the emission rates determined in this way describe a BAU path. That is, 

g =c + f + y + p t t t t t (4)

population population

GNP

GNP

energy

energy

carbon carbon emissions= • • • (5)
7

they do not incorporate measures which might be taken to reduce the emission of greenhouse 

gases, although they cover measures to combat air pollution and ozone layer depletion, which 

will affect emissions indirectly. There is no reason to a priori exclude greenhouse gas 

abatement, and to take this option into account BAU emissions were weighted against an 

abatement path. Emissions follow BAU with probability π, and with probability (1-π) they are 

reduced through an abatement strategy. Emissions of gas i at time t, Et

i

, are therefore 

where STABi

 represents emissions under the abatement policy. For CO2 from fossil fuels this 

means stabilisation at 1990 levels, in the case of emissions from natural sources a complete halt 

of deforestation. No weighting was taken in the case of N2O and for CFCs. For the latter 

stringent abatement regimes are already incorporated in BAU. 

Accelerated abatement will not be costless and weighted future income will therefore be below 

BAU income. The costs of a possible emission stabilisation policy were derived using a back-ofthe-envelope method suggested by Cline (1993). He estimated an elasticity of income with 

respect to energy inputs of about 0.06-0.08, based on the share of energy in total production 

value. He further assumed an elasticity of energy availability with respect to carbon of about 0.5. 

Carbon abatement of x percent would thus reduce GNP by x*0.5*0.07 percent. Efforts aiming at 

halting deforestation were assumed to cost 4 $/tC abated (Cline, 1992a). 

3.3 Atmospheric Concentration

The accumulation of emissions in the atmosphere is modelled through a set of equations of the 

following form 

That is, the atmospheric concentration of a gas, Qt

i

, is assumed to depreciate at a constant rate 

1/Li

, where Li is the lifetime of gas i3. βi is a conversion parameter which transforms emissions 

(measured in tonnes) into concentration (measured in ppm). One gigatonne of emissions 

corresponds to 5.66 ppm, divided by the atomic weight of the gas, thus in the case of CO2 for 

example 1 GtC = 5.66/12 = 0.47 ppm. 

For two gases the concentration equation differs from the generic form given above. In the case 

of methane the equation was extended to contain two decay factors, one representing 

atmospheric depreciation and the other the accumulation of CH4 in the soil (Wigley and Raper, 

1992). In the case of CO2 the notion of a constant depreciation rate would be misleading, 

because CO2 is a very stable compound which does not easily decay. Rather, CO2 is transferred 

from the atmosphere into other reservoirs (e.g. oceans), from where it may return to the 

atmosphere. To represent this carbon cycle, Maier-Reimer and Hasselmann (1987) have 

 

3

 The atmospheric lifetime of a gas is defined as the time it takes to reduce a given increase in 

concentration to 1/e = 36.8% of its initial value (IPCC, 1990a). 

E = BAU +(1- ) STAB i i t i

t π • π • (6)

Q + E

L

1 Q = 1- i

t i

i

t-1

i

i

t • β 





 





 (7)
8

suggested that the carbon stock be represented as a series of five boxes, each with a constant, 

but different atmospheric lifetime. That is, each box is modelled as in equation (7), and 

atmospheric concentration is a weighted sum of all five boxes. Maier-Reimer and Hasselmann 

suggested lifetimes of 1.9 years, 17.3 years, 73.6 years, 362.9 years and infinity, to which they 

attach weights of 0.1, 0.25, 0.32, 0.2 and 0.13, respectively (see also Lashof and Ahuja, 1990). 

The Maier-Reimer and Hasselmann formulation together with their suggested parameter values 

is adopted here4

. Uncertainty is introduced by treating the weights as random variables, while 

lifetimes are assumed to be fixed. 

3.4 Radiative Forcing

As a next step, increases in concentration have to be transformed into an increase in radiative 

forcing, that is into an increased flux of energy re-emitted from the atmosphere back to the earth. 

The relevant representations for this were taken from IPCC (1990a). Because there appears to 

be relatively little controversy about this step, the parameter values in the following equations 

were assumed to be non-random. In the case of CO2 the relationship between concentration and 

radiative forcing, F, is logarithmic 

where Qp

CO2 denotes preindustrial concentration. For CH4 and N2O the relationship is 

where Oi

 is a relatively complicated overlap term between CH4 and N2O, described in IPCC 

(1990a). Finally, for CFCs, the relationship is linear 

The forcing effect of CFCs is diminished through an ozone feedback. Because CFCs react with 

stratospheric ozone, which is itself a greenhouse gas, they have an indirect cooling effect. 

Wigley and Raper (1992) postulate that the ozone depletion potential of a CFC is proportional to 

the number of chlorine atoms it contains and propose the following approximation 

 

4

 The formulation was assumed to hold for all emissions since preindustrial time. Concentration 

in the base period 1990 is therefore already the weighted sum of the 5 boxes, as introduced 

above. Using historic emission rates we derived a CO2 concentration level of 349 ppm in 1990, 

close to IPCC's (1990a) estimate of 353 ppm. 

















Q

Q F = CO2

p

CO2

CO2 t t μ ln (8)

F = ( Q - Q )- Oi i

p

i

t

i i

t φ (9)

F = (Q - Q ) i

p

i

t

i i t ν (10)

FB = a n Qj

t

j

CFC

t •∑ • (11)
9

where a is a factor of proportion (assumed to be random), and nj the number of chlorine atoms in 

CFC j. 

Total radiative forcing in a period is simply the sum of all individual contributions 

It should be noted that this representation neglects the potential cooling effect from sulphur 

emissions. Through an increased backscattering of incoming solar radiation sulphur aerosols 

may cause a noticeable reduction in observed warming (see IPCC, 1992). 

3.5 Temperature Rise 

The characterisation of temperature rise was taken from Nordhaus (1992), whose representation 

itself draws on Schneider and Thompson (1981). The climate system is represented by a multistratum system consisting of three layers, the atmosphere, upper oceans and deep oceans. 

Increased radiative forcing warms up the atmosphere, which in turn heats the upper oceans, 

which then warm up the deep oceans. Both ocean layers impose a certain amount of thermal 

inertia on the system, which therefore only adjusts gradually to an increase in forcing. The 

system is represented by two partial adjustment equations 

Tt

u

 and Tt

l

 are the temperature of the upper and lower layer of oceans, respectively (relative to 

the preindustrial level). Ru

 and Rl denote the thermal capacity of the layers, and θ the transfer 

rate between upper and deep oceans. λ is a climate feedback parameter, related to the climate 

sensitivity of the system. That is, it indicates by how much temperature changes for a given 

increase in radiative forcing. 

3.6 Annual Damage

As mentioned above most research on global warming damage has focused on 2xCO2, and the 

representation of annual damage was consequently centred around this point. Studies 

estimating the monetary damage of 2xCO2 were surveyed in section 2.1. They all perform more 

or less the same hypothetical exercise, and estimate the costs of global warming damage which 

would occur if a society with the economic structure of today was, at some point in the future, 

exposed to a temperature increase of 2.5 to 3°C, the temperature rise usually associated with 

2xCO2. To generalise from this particular set up, we need to expand the representation in three 

directions. First, we have to model how damage changes under temperatures different from that 

associated with 2xCO2. Second, we have to capture the impacts of time and the rate of 

temperature rise, i.e. we want to know how damage alters if 2xCO2 is reached earlier, or later, 

than initially assumed. Third, we need to know how damage develops as the economy changes 

and population grows. The three components are incorporated in a damage function of the form 

F = F - FBt i

t

i

t ∑ (12)





 



 (T -T ) R F - T - R

1

T =T + l

t-1 ut-1

l

u t t-1 u

u

t-1 ut

θ

λ (13)





 



 (T -T ) R

R

1

T =T + l

t-1 ut-1

l

l

l

t-1

l

t

θ (14)
10

where the two parameters Λ and t*

 represent two key assumptions of the 2xCO2 studies of 

section 2.1, viz. the amount of warming associated with concentration doubling and the time at 

which it is assumed to occur. The values are set at Λ=2.5°C and t*

=2050. Note that when Tt

u

=Λ

and t=t*

 annual damage in period t becomes Dt=kt. kt therefore represents the 2xCO2 estimates 

introduced in section 2.1, adjusted for economic and population growth. The two parameters γ

and φ then determine the damage outside the 2xCO2 benchmark. 

Parameter γ defines the relationship between temperature and damage. If temperature rises by 

1%, damage rises by γ%. Little is known about the value of γ, although it can reasonably be 

assumed that γ≥1, i.e. that damage is convex in temperature. The work by Cline (1992a) and a 

poll of experts by Nordhaus (1993c) both suggest a value in the order of 1.3. Simulation studies 

have typically used values between 1 and 3 (Nordhaus, 1991a, b, 1992, 1993a, b; Peck and 

Teisberg, 1992, 1993a, b). 

A temperature rise of 3°C by 2100 is not the same as 3°C obtained in 2025. Damage may be 

considerably reduced if the system is given enough time to adapt. This is particularly the case for 

ecosystems, for which the rate of temperature change may be more crucial than the absolute 

change itself. Under a sufficiently slow change natural systems will be able to acclimatise or 

migrate to more favourable areas. A rapid change on the other hand may lead to the extinction 

of some of the more vulnerable species. In the case of economic damage, a slow rise in 

temperature may allow a gradual adjustment within the normal process of depreciation and 

reinvestment, which will be considerably cheaper than the immediate and premature 

replacement of equipment. While such considerations are not directly modelled, they are on an 

ad hoc basis embodied in the parameter φ, a factor which augments impacts if they occur earlier 

than initially assumed (i.e. before t*

), and diminishes them if they are delayed. φ is assumed to 

be random with a best guess value of 0.006, a figure which was derived from Nordhaus' poll of 

experts (Nordhaus, 1993c). 

This leaves the third question of how damage changes as a consequence of economic 

development and population growth. In Nordhaus (1992, 1993a, b) damage is assumed to grow 

in direct proportion to income, while in the CETA model it is scaled with a labour input index, i.e. 

it grows in proportion to the labour force (expressed in efficiency units, see Peck and Teisberg, 

1992, 1993a, b). In the present model we distinguish between market based damage, apparent 

in the national accounts, and non-market based damage, such as people's valuation of a 

species or a warmer climate. Total greenhouse damage is simply the sum of the two elements. 

The former is assumed to grow in proportion to GNP, 

where pt denotes the rate of growth of population, as introduced earlier. _t is the rate of growth of 

(1+ ) T D = k ( t -t) u

t

t t

*

φ

γ

 •



 





Λ (15)

=(1+ y + p ) k

k

Y t t

t-1

Y

t ˆ (16)
11

per capita income, taking into account the possible costs of carbon abatement (see section 3.2), 

as well as potential warming impacts on growth. 

For non-market impacts the formula is slightly more complex. If people's willingness to pay for 

non-market goods was constant over time, non-market damage would simply grow at the same 

rate as population. However, this will not be the case. As people become richer over time, their 

willingness to pay will also change. Defining εY as the income elasticity of people's willingness to 

pay to avoid non-market damage, the growth factor of non-market damage should therefore be 

written as5

Estimates of εY for environmental goods in general are surveyed by Pearce (1980). Without 

finding any conclusive results, the survey seems to suggest an elasticity value in the order of εY

= 1. The initial values k0

Y

 and k0

P

 were derived from the 2xCO2 studies surveyed in section 2.1. 

Based on the damage classification and estimates of Fankhauser (1992) we assumed that 62% 

of the damage is non-market related and 38% income related. 

3.7 Discounting

Greenhouse damage spans over an extremely long time horizon of several centuries. 

Discounting future impacts is therefore a crucial issue. In our model we follow the consumption 

equivalent technique developed by, among others, Arrow (1966), Arrow and Kurz (1970), 

Bradford (1975), Marglin (1963a and b), and Dasgupta et al. (1972; for a survey see e.g. Lind, 

1982). In the context of global warming this method has been used by e.g. Cline (1992a). 

 

As a first step all expenditures are transformed into consumption equivalents. The relevant 

discount rate is then the social rate of time preference (see Lind, 1982). The social rate of time 

preference, or consumption discount rate, itself consists of two elements. The first one, called 

the pure rate of time preference, deals with the impatience of consumers and reflects their inborn 

preference of immediate over postponed consumption. The second element has to do with 

decreasing marginal utility of income. A decreasing marginal utility of income implies that a dollar 

of additional income will create less additional utility the higher the initial income level. 

Consequently, if income is rising over time, future impacts should be valued less. 

Under the usual assumption of a CRRA (constant relative rate of risk aversion) utility function the 

social rate of time preference, δ, can be written as (see Lind, 1982) 

 

5

 That is, greenhouse damage has both an additive and a multiplicative component. The 

maximand of the optimisation problem corresponding to this specification would be 







 





 • D (T )- D (T )

N

Y( E ) N t P t t Y

t

t

t

t Error! Main Document Only.

where Nt denotes population and Yt GNP, which is a function of emissions. 

=(1+ y + p ) k

k

P Y t t

t-1

P

t ε • ˆ (17)

= + yt t δ ρ ω ˆ (18)
12

ρ is the pure rate of time preference, reflecting impatience, and ω the income elasticity of 

marginal utility or rate of risk aversion. Note that, because the rate of growth of per capita 

income, _t, may vary over time the rate of discount changes over time as well. Growth may also 

be affected by future abatement policies or by greenhouse impacts. The discount rate is 

therefore a function of the corrected growth rate _t, rather than the BAU rate yt. The rate of risk 

aversion, ω, is typically set at 1, which corresponds to a logarithmic utility function, and we follow 

this example here by setting ω=1 for the central case. 

The size of the pure rate of time preference element is highly controversial. Many would argue 

that a positive rate is not acceptable on ethical grounds, as it implicitly attaches less importance 

to future generations. Others point at empirical evidence in favour of a positive rate, and 

Nordhaus (1992, 1993a, b) and Peck and Teisberg (1992, 1993a, b), for example, both use a 

rate of 3%, i.e. ρ=0.03. In the present model, ρ is a random variable with upper and lower 

bounds of 0 and 3%, respectively, and a best guess of 0.5%. We will come back to the 

impatience issue in section 4. 

The appropriate discount rate differs depending on the nature of the occuring damages. The 

social rate of time preference introduced above is only relevant for consumption related 

damages. Impacts affecting investment have to be transformed into consumption equivalents. 

This is done by multiplying them with the shadow price of capital, v. The shadow price of capital 

basically represents the present value of the future consumption stream associated with a 1 $ 

investment, discounted at the social rate of time preference (Lind, 1982). Several ways to 

calculate v have been suggested, see Lind (1982). Here we use a method suggested by Cline 

(1992a), 

Suppose a 1 $ investment project yields an annual payoff of A over a lifetime of N years. The 

present value consumption stream is then (omitting the time subscript on δ) 

If the project has an internal rate of return equal to the rate of return on capital, r, it will further 

satisfy the equation, 

Solving for A, and substituting back yields, after some further rearranging 

which is the formulation used here. See Cline (1992a) for details. Whether or not an expenditure 

has to be transformed primarily depends on its character, as outlined above. Climate impacts 

v= A(1+ )

- N

=1

τ

τ

∑ δ (19)

- 1+ A(1+r ) =0 - N

=1

τ

τ

∑ (20)

δ

δ

t

-N

t

t -N

1-(1+ )

1 -(1+r )

r

v = • (21)
13

affecting investment have to be transformed, while reductions in consumption need not, as they 

are already expressed in the correct units. Following Cline (1992a) we base our estimate on the 

currently observed average savings rate and assume that 20% of market based damage is 

investment related, i.e. has to be multiplied by a factor v. 80% of income related damage and all 

non-market damage is assumed to be consumption based. The 2xCO2 damage variable kt can 

then be rewritten as 

k =( k +0.8 k )+0.2 v k

Y t t Y

t P t t (22)
14

4. The Social Costs of Greenhouse Gas Emissions

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. 

4.2 Other Greenhouse Gases

CO2 is not the only greenhouse gas, albeit by far the most important one, accounting for more 

 

6

 For comparison, the skewedness of a symmetric distribution is zero. Note that a considerable 

part of this is explained by the assumed skewedness in the distribution of parameter ρ. 
15

than half of the total effect. Other gases contributing to the greenhouse effect include CH4, N2O 

and CFCs. The usual way of dealing with greenhouse gases other than CO2 is to transform them 

into CO2-equivalents by using Global Warming Potentials (GWPs). According to this index 

suggested by the IPCC one tonne of CH4 and N2O is equivalent to 11 tonnes of CO2 and 270 

tonnes of CO2, respectively (IPCC, 1992). However, it has repeatedly been pointed out in the 

literature that GWPs are not an adequate index if we are concerned with the damage caused by 

each gas (Reilly, 1992; Schmalensee, 1993; Hoel and Isaksen, 1993). GWPs are a measure of 

the relative radiative forcing capability of gases. Relative forcing, however corresponds to the 

relative damage potential only if the latter is a linear function of the former. As section 3 showed, 

this is clearly not the case. The incremental damage caused by a marginal increase in radiative 

forcing will therefore depend on factors like previous levels of forcing and the degree of warming 

already encountered. The relative damage contribution of a gas will thus vary over time and in 

general be different from its relative forcing capacity. 

To exemplify this point, we have computed the social costs of other greenhouse gases directly 

by calculating the present value marginal damage caused by a marginal increase in other 

greenhouse emissions. Table 2 shows the results for methane and nitrous oxide. Again the 

figures are rising over time, in the case of methane from 108 $/tCH4 in 1991-2000 to 176 $/tCH4

in 2021-2030. The damage from nitrous oxide rises from 2,895 $/tN in 1991-2000 to 4,489 $/tN. 

In terms of CO2 equivalents or "Greenhouse Damage Potentials" this corresponds to values of 

20-23 for CH4 and 333-377 for N2O, depending on the time of emission7

. They are roughly in line 

with the estimates of Hoel and Isaksen (1993), but, for the reasons given above, are 

considerably different from GWPs. The fact that they are higher than GWPs mainly reflects the 

impact of discounting, which lessens the long run impacts of long-lived gases like CO2. The 

figures are restricted to the direct impacts of a gas and neglect indirect effects such as the 

impact of methane on water vapour and tropospheric ozone. Indirect effects would be 

particularly important for CFCs, for which it has been estimated that as much as 80% of the 

initial contribution may be offset through the indirect cooling effect from ozone depletion (IPCC, 

1992; Wigley and Raper, 1992; see also section 3.4). This recent finding has considerably 

downgraded the importance of CFCs as greenhouse gases. For this reason, and because their 

phasing out has by and large already been agreed upon in the Montreal protocol, CFCs are not 

considered here8

. Also note that the figures only refer to the social costs from global warming, 

i.e. they do not include costs from other environmental problems. Again these would be most 

important in the case of CFCs. 

4.3 Sensitivity Analysis I: Discounting

One of the key parameters in the above estimates is the discount rate, not only because of the 

ongoing controversy about its appropriate level, but also because of the high sensitivity of the 

results with respect to it. Our preferred way of discounting has been introduced in section 3.8. It 

involves the transformation of all damage into consumption equivalents by multiplying with the 

shadow value of capital, as appropriate. The relevant discount rate is then the consumption rate, 

δ. 

 

7

 As with Global Warming Potentials the figures compare the impact of one tonne of each gas, i.e. 

they compare a tonne of CH4

 or N2O with of a tonne of CO2. The figures in Table 2 on the other 

hand use the more common measures of tCH4

 for methane, tN for N2O, and tC for CO2. 

8

 Figures for CFCs can be found in Hoel and Isaksen (1993) 
16

Recall from section 3.8 the distinction between the pure rate of time preference (parameter ρ), 

the social rate of time preference, δ, and the rate of return on capital, r. As outlined there, the 

main controversy is about the value of ρ, and in particular whether ρ should be greater than or 

equal to zero (see e.g. Cline, 1992a; Broome, 1992; Markandya and Pearce, 1991). Our 

sensitivity analysis thus concentrates on this parameter. 

As indicated earlier, our results were obtained assuming a probability distribution for the pure 

rate of time preference which is triangular with upper and lower bounds of 0% and 3%, 

respectively, and a best guess value of 0.5%. To illustrate the impacts of different discount rates 

we have re-run the model for ρ held fixed at different values9

. The results are summarised in 

Table 3. If ρ is set at 3% the expected shadow value of 1990 CO2 emissions falls from 20$/tC to 

a mere 5.5 $/tC. By 2030 the figure has risen only slightly to 8.3 $/tC. Interestingly, this is almost 

exactly the Nordhaus (1992; 1993a, b) result. Assuming a pure rate of time preference of 0 on 

the other hand yields an expected value of 48.8 $/tC in 1990, and 62.9 $/tC in 2030, about eight 

times more than under the high rate. Using a higher rate also leads to a considerable reduction 

in the standard deviation, and thus the confidence interval. This is because more uncertain 

future impacts are weighted less under a higher discount rate. The lower skewedness, on the 

other hand, is mainly due to the fact that parameter ρ, which had a skewed distribution in the 

random case, is now fixed. 

The high sensitivity of the results with respect to discounting should come as no surprise. It is a 

direct consequence of the long term character of global warming and the fact that damages will 

only occur several decades into the future. The results clearly underline the importance of the 

discounting question and the crucial role ethical issues ought to play in the future debate on 

global warming. 

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 

 

9

 The rate of risk aversion, ω was also kept fixed in this exercise, at ω=1. 10 An extremely steep damage function can be seen as an approximation of a threshold at T=Λ ̊C. 
17

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. 
18

5. 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. 
19

References

Anderson, D. and R. Williams (1993). Cost Effectiveness and the Investments of the Global 

Environmental Facility. A Background Paper for the Scientific and Technical Advisory 

Pandel of the GEF, Washington DC: The World Bank. 

Arrow, K.J. (1966). Discounting and Public Investment Criteria, in: A.V. Kneese and S.C. Smith 

(eds.), Water Research, Baltimore: Johns Hopkins University Press. 

Arrow, K.J. and M. Kurz (1970). Public Investment, the Rate of Return and Optimal Fiscal Policy, 

Baltimore: Johns Hopkins University Press. 

Ayres, R. and J. Walter (1991). The Greenhouse Effect: Damages, Costs and Abatement, in: 

Environmental and Resource Economics 1: 237-270. 

Bradford, D.F. (1975). Constraints on Government Investment Opportunities and the Choice of 

Discount Rate, in: American Economic Review 65(50): 887-899. 

Broome, J. (1992). Counting the Costs of Global Warming, Cambridge: White Horse Press. 

Cline, W.R. (1992a). The Economics of Global Warming, Washington, DC: Institute for 

International Economics. 

Cline, W.R. (1992b). Optimal Carbon Emissions over Time: Experiments with the Nordhaus 

DICE Model, Mimeo, Institute for International Economics, Washington, DC. 

Cline, W.R. (1993). The Costs and Benefits of Greenhouse Abatement: A Guide to Policy 

Analysis, Paper presented at the OECD/IEA Conference on "The Economics of Global 

Warming", June 1993, Paris. 

Daily, G.C., P.R. Ehrlich, H.A. Mooney, and A.H. Ehrlich (1991). Greenhouse Economics: Learn 

before you Leap, in: Ecological Economics 4: 1-10. 

Dasgupta, P., S.A. Marglin and A.K. Sen (1972). Guidelines for Project Evaluations, New York: 

UNIDO. 

Fankhauser, S. (1992). Global Warming Damage Costs: Some Monetary Estimates, Centre for 

Social and Economic Research on the Global Environment, University College London and 

University of East Anglia, CSERGE GEC Working Paper 92-29. 

Fankhauser, S. (1993). The Economic Costs of Global Warming: Some Monetary Estimates, in: 

Y. Kaya, N. Naki_enovi_, W.D. Nordhaus and F. Toth (eds.), Costs, Impacts and Benefits of 

CO2 Mitigation, IIASA Collaborative Paper Series, CP93-2, Laxenburg, Austria. 

Grubb, M. (1993). The Costs of Climate Change: Critical Elements, in: Y. Kaya, N. Naki_enovi_, 

W.D. Nordhaus and F. Toth (eds.), Costs, Impacts and Benefits of CO2 Mitigation, IIASA 

Collaborative Paper Series, CP93-2, Laxenburg, Austria. 

Hoel, M. and I. Isaksen (1993). Efficient Abatement of Different Greenhouse Gases, 

Memorandum No. 5, Department of Economics, University of Oslo. 

Hohmeyer, O. (1988). Social Costs of Energy Consumption: External Effects of Electricity 

Generation in the Federal Republic of Germany, Berlin: Springer. 

Intergovernmental Panel on Climate Change (1990a). Climate Change: The IPCC Scientific 

Assessment, Cambridge: Cambridge University Press. 
20

Intergovernmental Panel on Climate Change (1990b). Strategies for Adaptation to Sea Level 

Rise. Report of the Coastal Zone Management Subgroup, WMO and UNEP, Geneva. 

Intergovernmental Panel on Climate Change (1990c). The IPCC Impacts Assessment, 

Canberra: Australian Government Publishing Service. 

Intergovernmental Panel on Climate Change (1992). Climate Change 1992. The Supplementary 

Report to the IPCC Scientific Assessment, Cambridge: Cambridge University Press. 

Kane, S., J. Reilly, and J. Tobey (1992). An Empirical Study of the Economic Effects of Climate 

Change on World Agriculture, in: Climatic Change 21: 17-35. 

Lashof, D.A. and D.R. Ahuja (1990). Relative Contributions of Greenhouse Gas Emissions to 

Global Warming, in: Nature 344 (5 April): 529-531. 

Lind, R.C., ed. (1982). Discounting for Time and Risk in Energy Policy, Washington, DC: 

Resources for the Future. 

Lockwood, B. (1992). The Social Costs of Electricity Generation, Centre for Social and 

Economic Research on the Global Environment, University of East Anglia and University 

College London, CSERGE-GEC Working Paper 92-09. 

Maier-Reimer, E. and K. Hasselmann (1987). Transport and Storage of CO2 in the Ocean. An 

Inorganic Ocean-Circulation Carbon Cycle model, in: Climate Dynamics, 11(2): 63-90. 

Manne, A.S. and R.G. Richels (1993). The Costs of Stabilizing CO2 Emissions - A Probabilistic 

Analysis Based on Expert Judgments, Energy Power Research Institute, Draft, Palo Alto, 

CA. 

Marglin, S.A. (1963a). The Opportunity Cost of Public Investment, in: Quarterly Journal of 

Economics 77: 274-289. 

Marglin, S.A. (1963b). The Social Rate of Discount and the Optimal Rate of Investment, in: 

Quarterly Journal of Economics 77: 95-111. 

Markandya, A. and D.W. Pearce (1991). Development, the Environment and the Social Rate of 

Discount, in: The World Bank Observer 6(2): 137-152. 

Nordhaus, W.D. (1991a). To Slow or not to Slow: The Economics of the Greenhouse Effect, in: 

Economic Journal 101(407): 920-937. 

Nordhaus, W.D. (1991b). A Sketch of the Economics of the Greenhouse Effect, in: American 

Economic Review, Papers and Proceedings 81(2): 146-150. 

Nordhaus, W.D. (1992). The DICE Model: Background and Structure of a Dynamic Integrated 

Climate Economy Model of the Economics of Global Warming, Cowles Foundation 

Discussion Paper, No. 1009, New Haven, Connecticut. 

Nordhaus, W.D. (1993a). Optimal Greenhhouse Gas Reductions and Tax Policy in the "DICE" 

Model, in: American Economic Review, Papers and Proceedings 83(2): 313-317. 

Nordhaus, W.D. (1993b). Rolling the "DICE": An Optimal Transition Path for Controlling 

Greenhouse Gases, in: Resources and Energy Economics 15: 27-50. 

Nordhaus, W.D. (1993c). Survey on Uncertainties Associated with Potential Climate Change, 

Mimeo, Yale University, New Haven, Connecticut. 
21

PACE (1990). Environmental Costs of Electricity, Pace University Centre for Environmental and 

Legal Studies, New York: Oceana Publishers. 

Parry, M. (1990). Climate Change and World Agriculture, London: Earthscan. 

Parry, M.L., T.R. Carter, and N.T. Konijn (1988). The Impacts of Climate Variations on 

Agriculture, 2 Volumes, Dordrecht: Kluwer. 

Pearce, D.W. (1980). The Social Incidence of Environmental Costs and Benefits, in: T. O'Riodan 

and R.K. Turner (eds.), Progress in Resource Management and Environmental Planning, 

Vol. 2, Chichester: Wiley. 

Pearce, D.W., C. Bann, and S. Georgiou (1992). The Social Costs of Fuel Cycles, London: 

HMSO. 

Pearce, D.W., T.S. Swanson, A. McGuire, and J. Richardson (1991). Economics, Environment 

and Health. A Report for the European Regional Office on the World Health Organisation, 

CSERGE, University College London and University of East Anglia. 

Peck, S.C. and T.J. Teisberg (1992). CETA: A Model for Carbon Emissions Trajectory 

Assessment, in: Energy Journal 13(1): 55-77. 

Peck, S.C. and T.J. Teisberg (1993a). CO2 Emissions Control: Comparing Policy Instruments, in: 

Energy Policy 21(3): 222-230. 

Peck, S.C. and T.J. Teisberg (1993b). Global Warming Uncertainties and the Value of 

Information: An Analysis Using CETA, in: Resource and Energy Economics 15: 71-97. 

Peters, R.I. and T.E. Lovejoy (1992). Global Warming and Biological Diversity, New Haven: Yale 

University Press. 

Proops, J.L.R., M. Faber, and G. Wagenhals (1993). Reducing CO2 Emissions. A Comparative 

Input-Output Study for Germany and the UK, Berlin: Springer. 

Reilly, J.M. (1992). Climate-Change Damage and the Trace-Gas-Index Issue, in: J.M. Reilly and 

M. Anderson (ed.), Economic Issues in Global Climate Change, Boulder: Westview. 

Rijsberman, F (1991). Potential Costs of Adapting to Sea Level Rise in OECD Countries, in: 

OECD, Responding to Climate Change: Selected Economic Issues, Paris. 

Schneider, S.H. and S.L. Thompson (1981). Atmospheric CO2 and Climate: Importance of the 

Transient Response, in: Journal of Geophysical Research, 86 (20 April): 3135-3147. 

Schmalensee, R. (1993). Comparing Greenhouse Gases for Policy Purposes, in: Energy Journal

14(1): 245-255. 

Smith, J.B. and D.A. Tirpak, ed. (1989). The Potential Effects of Global Climate Change on the 

United States, Washington, DC: US EPA. 

Titus, J. (1992). The Cost of Climate Change to the United States, in: S.K. Majumdar, L.S. 

Kalkstein, B. Yarnal, E.W. Miller, and L.M. Rosenfeld (eds.), Global Climate Change: 

Implications Challenges and Mitigation Measures, Pennsylvania: Pennsylvania Academy of 

Science. 

Titus, J.G., R.A. Park, S.P. Leatherman, J.R. Weggel, M.S. Greene, P.W. Mausel, S. Brown, C. 

Gaunt, M. Trehan, and G. Yohe (1991). Greenhouse Effect and Sea Level Rise: The Cost 
22

of Holding Back the Sea, in: Coastal Zone Management 19: 172-204. 

Waggoner, P.E. (1990). Climate Change and US Water Resources, New York: John Wiley & 

Sons. 

World Health Organisation (1990). Potential Health Effects of Climatic Change, WHO, Geneva. 

Wigley, T.M.L. and S.C.B. Raper (1992). Implications of Climate and Sea Level Rise of Revised 

IPCC Emissions Scenarios, in: Nature 357(28 May): 293-300. 

World Bank (1992). World Development Report, Washington, DC. 
23

TABLE 1: EXISTING ESTIMATES OF CO2 EMISSIONS COSTS ($/tC)

Study 1991-2000 2001-2010 2011-2020 2021-2030 

Nordhaus 

(1991a, b) 

 7.3 

(0.3 - 65.9) 

 

Ayres and Walter 

(1991) 

 30 - 35 

Nordhaus 

(1992) 

 5.3 6.8 8.6a 10.0 

Peck and Teisberg 

(1993b) 

 10 - 12a 12 - 14a 14 - 18a 18 - 22a

(3.4 - 57.6) 

a

 figures measured from graph 

Note: Figures in brackets denote confidence intervals 

Sources: As indicated. 
24

TABLE 2: THE SOCIAL COSTS OF GREENHOUSE GAS EMISSIONS

1991-2000 2001-2010 2011-2020 2021-2030 

CO2

mean ($/tC) 

5th percentile 

95th percentile 

standard dev 

skewedness 

 20.3 

 6.2 

 45.2 

 14.3 

 2.5 

 22.8 

 7.4 

 52.9 

 16.0 

 2.5 

 25.3 

 8.3 

 58.4 

 17.5 

 2.5 

 27.8 

 9.2 

 64.2 

 19.0 

 2.4 

CH4

mean ($/tCH4) 

5th percentile 

95th percentile 

standard dev 

skewedness 

 108 

 48 

 206 

 48 

 1.6 

 129 

 58 

 249 

 54 

 1.6 

 152 

 68 

 249 

 75 

 1.7 

 176 

 79 

 342 

 90 

 1.8 

N2O

mean ($/tN) 

5th percentile 

95th percentile 

standard dev 

skewedness 

 2,895 

 805 

 7,253 

 2,895 

 2.2 

 3,379 

 953 

 8,361 

 2,595 

 2.2 

 3,901 

 1,122 

 9,681 

 2,996 

 2.3 

 4,489 

 1,277 

 11,121 

 3,455 

 2.3 

Source: Own calculations. 
25

TABLE 3: THE SOCIAL COSTS OF CO2 EMISSIONS 

 - THE IMPACT OF DISCOUNTING

 1991-2000 2021-2030 

Random Case

 -> ρ = (0, 0.005, 0.03) 

 -> ω = (0.5, 1, 1.5) 

mean ($/tC) 

5th percentile 

95th percentile 

standard dev. 

skewedness 

 20.3 

 6.2 

 45.2 

 14.3 

 2.5 

 27.8 

 9.2 

 64.2 

 19.0 

 2.4 

Low Discounting

 -> ρ = 0 

 -> ω = 1 

mean ($/tC) 

5th percentile 

95th percentile 

standard dev. 

skewedness 

 48.8 

 27.6 

 80.1 

 15.6 

 0.9 

 62.9 

 34.9 

 104.6 

 22.4 

 1.3 

High Discounting

 -> ρ = 0.03 

 -> ω = 1 

mean ($/tC) 

5th percentile 

95th percentile 

standard dev. 

skewedness 

 5.5 

 3.7 

 7.6 

 1.2 

 0.5 

 8.3 

 5.3 

 12.0 

 2.1 

 0.8 

Source: Own calculations. 
26

FIGURE 1: PRESENT METHODOLOGY VS. OPTIMAL CONTROL

Marginal damage costs depend on the level of emissions. In the usual case of an upwards 

sloping MD curve they are rising with the level of emissions, as shown in the Figure. 

Optimisation models calculate marginal costs at the point where marginal damage equals 

marginal abatement costs - the dashed situation labelled "opt". 

The present model calculates marginal costs at the emissions level actually observed. Since 

emissions are uncertain, and so is the exact shape of the marginal damage curve, calculations 

will result in a range of possible cost figures, each of which is assigned a certain probability of 

occurrence - the probability distribution shown to the left of the Figure. 

Source: Own graph. 

emissions 

emissions range

marg. costs 

marg. 

costs 

opt

damage range MDhigh

MDlow
27

FIGURE 2: THE PROBABILITY DISTRIBUTION OF CO2 DAMAGE

(a) Emissions between 1991 and 2000 ($/tC) 

(b) Emissions between 2001 and 2010 ($/tC) 
28

FIGURE 2, CONT.

(c) Emissions between 2011 and 2020 ($/tC) 

(d) Emissions between 2021 and 2030 ($/tC) 

Source: Own calculations. 
29

FIGURE 3: CO2 DAMAGE DISTRIBUTION AND THE THREAT OF CATASTROPHE 

 ($/tC, 1990-2000 emissions) 

Legend 

Scenarios A to D are associated with the 99th percentiles given below. That is, for each of the 

three parameters considered, there is a 1% probability that the actual parameter value will 

exceed the values given in the table below. Scenario A roughly corresponds to the nocatastrophe case of Figure 2 and Table 2. 

Climate Sensitivity 2xCO2 damage Power of damage 

function 

Scenario A 3.5°C 1.75 % GNP 1.5 

Scenario B 5.5°C 3.00 % GNP 2.5 

Scenario C 6.0°C 3.50 % GNP 3.0 

Scenario D 7.0°C 4.25 % GNP 3.5 

Source: Own calculations. 
30

APPENDIX: OVERVIEW ON PARAMETERS AND PARAMETER VALUES

(a) Initial Values (1990) 

Parameter lower 

bound

best 

guess

upper

bound

Comment / Source 

Emissions 

 CO2 fossil fuels, GtC 

 CO2 deforestation, GtC 

 CH4 from coal mining, MtCH4

 CH4 from gas leakage, MtCH4

 CH4 from biomass burning, MtCH4

 other CH4 emissions, MtCH4

 N2O emissions, MtN 

 CFC-11 emissions, kt 

 CFC-12 emissions, kt 

 HCFCs and HFCs, kt 

Concentrations

 CO2, ppm 

 CH4, ppb 

 N2O, ppb 

 CFC-11, ppb 

 CFC-12, ppb 

 HCFCs, HFCs, ppb 

Other

 GNP/capita, $ 

 population, million 

 1,550 

 279 

 0.250 

 0.436 

 0.110 

 5.6 

 1.3 

 45 

 55 

 40 

 375 

 12.9 

 298 

 363 

 143 

 349 

 1,710 

 310 

 0.280 

 0.484 

 0.122 

 4,200 

 5,252 

 1,890 

 341 

 0.310 

 0.532 

 0.134 

non random, IPCC (1992) 

non random, IPCC (1992) 

non random, IPCC (1992) 

non random, IPCC (1992) 

non random, IPCC (1992) 

non random, IPCC (1992) 

non random, IPCC (1992) 

non random, IPCC (1992) 

non random, IPCC (1992) 

non random, IPCC (1992) 

own calc, see section 3.3 

IPCC (1990a) 

IPCC (1990a) 

IPCC (1990a) 

IPCC (1990a) 

IPCC (1990a) 

World Bank (1992) 

IPCC (1992) 
31

(b) Emission Parameters

Parameter Description lower 

bound

best 

guess 

upper 

bound

Comment / Source 

y1990-2100 

y2101-2220

p1990-2025

p2026-2100

p2101-2220

c1990-2025

c2026-2100

c2101-2220

f1990-2220

g1990-2100

defor

g2101-2220

defor

g1990-2025

CH4

g2026-2100

CH4

g2101-2220

CH4

g1990-2025

N2O

g2026-2100

N2O

g2101-2220

N2O

g1990-2025

CFC11

g2026-2100

CFC11

g2101-2220

CFC11

g1990-2025

CFC12

g2026-2100

CFC12

g2101-2220

CFC12

g1990-2025

OCFC

g2026-2100

OCFC

g2101-2220

OCFC

πfuel

πdeforest

εen

Y

εE

en

Cdefoest

GNP/capita growth, % 

population growth, % 

carbon intensity growth, % 

energy effic improvement, % 

CO2 from deforestation, growth 

rate in % 

CH4 from all sources, growth 

rate in % 

N2O emission growth, % 

CFC-11 emission growth, % 

CFC-12 emission growth, % 

HCFC, HFC emission growth, 

% 

emission weight, fossil fuels 

emission weight, deforestation

elast of output wrt energy 

elast of energy wrt carbon 

costs of halting deforestation 

 1.00 

 0.70 

 1.05 

- 0.20 

- 0.10 

- 0.9 

- 0.7 

- 0.6 

- 1.38 

- 4.3 

- 3.0 

 0.4 

 0.0 

- 0.1 

 0.4 

- 0.1 

- 0.2 

-12.0 

- 5.7 

- 1.1 

-12.0 

- 5.7 

- 1.1 

 5.8 

 0.5 

- 0.3 

 0 

 0 

 0.06 

 0.45 

 0 

 1.60 

 1.60 

 1.35 

 0.40 

 0.10 

- 0.4 

- 0.2 

- 0.1 

- 0.7 

- 1.3 

- 0.8 

 0.7 

 0.4 

 0.3 

 0.6 

 0.1 

 0.1 

-10.0 

- 4.8 

- 0.7 

-10.0 

- 4.8 

- 0.7 

 6.2 

 1.1 

 0.3 

 0.2 

 0.2 

 0.08 

 0.5 

 4 

 2.30 

 2.10 

 1.68 

 0.80 

 0.40 

- 0.20 

- 0.10 

- 0.05 

- 0.2 

- 0.8 

- 0.3 

 0.9 

 0.7 

 0.7 

 0.7 

 0.2 

 0.3 

- 5.0 

- 4.2 

- 0.2 

- 5.0 

- 4.2 

- 0.2 

 6.8 

 1.4 

 0.8 

 0.6 

 0.8 

 0.088 

 0.55 

 6 

after IPCC (1992) 

after IPCC (1992) 

after IPCC (1992) 

Manne/Richels (1993)

after IPCC (1992) 

IPCC (1992), sources 

differ with respect to 

correlation with CO2

after IPCC (1992) 

after IPCC (1992) 

after IPCC (1992) 

after IPCC (1992) 

see section 3.2 

Cline (1993) 

Cline (1993) 

Cline (1992a) 
32

(c) Concentration Parameters

Parameter Description lower 

bound

best 

guess 

upper 

bound

Comment / Source 

LCH4-A

LCH4-S

LN2O

LCFC11

LCFC12

LOCFC

w∞

w363

w74

w17

w2

Atmos. lifetime CH4, yrs 

CH4 deposition in soil 

Atmospheric lifetime N2O 

Atmos. lifetime CFC11 

Atmos. lifetime CFC12 

Lifetime other CFCs etc. 

weight, CO2 with ∞ lifetime 

weight, CO2 363 yrs lifetime 

weight, CO2 74 yrs lifetime 

weight, CO2 17 yrs lifetime 

weight, CO2 22 yrs lifetime 

 10.0 

 135.0 

 119.0 

 50.0 

 104.0 

 14.1 

 0.12 

 0.18 

 - 

 0.22 

 0.09 

 11.0 

 150.0 

 132.0 

 55.0 

 116.0 

 15.7 

 0.13 

 0.20 

 - 

 0.25 

 0.10 

 12.0 

 165.0 

 145.0 

 60.0 

 128.0 

 17.3 

 0.14 

 0.22 

 - 

 0.27 

 0.11 

IPCC (1992) 

Wigley and Raper (1992) 

IPCC (1992) 

IPCC (1992) 

IPCC (1992) 

IPCC (1992), average for 

HCFC22, HFC134a 

Lashof and Ahuja (1990) 

Lashof and Ahuja (1990) 

endog, s.t. Σwi

=1 

Lashof and Ahuja (1990) 

Lashof and Ahuja (1990) 

(d) Radiative Forcing Parameters

Parameter Description lower 

bound

best 

guess 

upper 

bound

Comment / Source 

μ 

φCH4

φN2O

υCFC11

υCFC12

υOCFC

a 

CO2 forcing, Wm-2/ppm 

CH4 forcing, Wm-2/ppb 

N2O forcing, Wm-2/ppb 

CFC11 forcing, Wm-2/ppb 

CFC12 forcing, Wm-2/ppb 

other CFCs, Wm-2/ppb 

ozone feedback param. 0.069 

6.3 

0.036 

0.14 

0.22 

0.28 

0.18 

0.076 0.084 

non random, IPCC (1990a) 

non random, IPCC (1990a) 

non random, IPCC (1990a) 

non random, IPCC (1990a) 

non random, IPCC (1990a) 

IPCC, HCFC22 a. HFC 134a 

Wigley and Raper (1992) 

(e) Temperature Parameters

Parameter Description lower 

bound

best 

guess 

upper 

bound

Comment / Source 

Rl

1/Ru

λ

θ

therm. capacity lower layer 

1/(therm. capacity u. layer) 

climate sensitivity 

rate of thermal transfer 

 201.3 

 0.048 

 0.97 

 450 

 223.7 

 0.065 

 1.46 

 500 

 246.1 

 0.075 

 2.90 

 550 

Nordhaus (1992) 

Nordhaus (1992) 

corresponds to 1.5 ,3 ,4.5°C 

Nordhaus (1992) 
33

(f) Damage Parameters 

Parameter Description lower 

bound 

best 

guess 

upper 

bound 

Comment / Source 

k0

γ

1+φ

ε

Y

2xCO2 damage, % GNP 

power of damage funct 

rate of change param. 

income elast. of WTP 

1.0 

1.0 

1.0045 

0.8 

1.5 

1.3 

1.0060 

1.0 

2.0 

2.0 

1.0075 

1.2 

Fankhauser (1992) 

Cline (1992a) 

Nordhaus (1993c) 

Pearce (1980) 

(g) Discounting Parameters

Parameter Description lower 

bound

best 

guess 

upper 

bound

Comment / Source 

ω

ρ

r 

N 

rate of risk aversion 

pure rate of time pref., % 

rate of return on capital, % 

lifetime of capital, yrs 

 0.5 

 0.0 

 5.0 

 1.0 

 0.5 

 8.0 

15.0 

 1.5 

 3.0 

10.0 

Cline (1992a) 

Cline, Nordhaus (1992) 

Cline (1992a) 

non-random, 

Cline (1992a)