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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.

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,
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
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.

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