## 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 0967-8875Abstract

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 CO 2 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 CH 4 and N 2 O 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 P anel 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 co sts 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 NO

x and SO

x . 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 i gnorance 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 describ ing 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 scientif ic 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

CO 2 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 CO 2 concentration of twice the preindustrial level (2xCO 2 ). 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 2xCO 2 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 overalldamage 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-envel ope 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 2xCO 2 damage in the order of 1% to 2% of world GNP. Despite the attention the

2xCO 2 case enjoys in the literature, it is not directly relevant for practical purposes, though. For the appraisal of abatement projects it is more im portant 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 calcul ating 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 CO 2 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 2xCO 2 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' 2xCO 2 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 2xCO 2 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 CO 2 emissions over time. Obviously this is unrealistic. The IPCC for example predicts an increase in annual

CO 2 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 CO 2 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 CO 2 added to an already large stock of atmospheric CO 2 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 C limate Economy) model (Nordhaus, 1992, 1993a, b). DICE is an optimal growth model in the Rams ey tradition, extended to include a climate module and a damage sector which feeds climate changes back to the economy 1 . 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 inco rporating a carefully modelled energy sector 2

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

size of 2xCO 2 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 woul d be to impose an exogenously given carbon

concentration or emissions constraint. The sha dow 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 t heir 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, S i , are thus a present value figure - the discounted sum of future incremental damage, ∂ D(t)/ ∂ E i (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, ∂ Q i (s)/ ∂ E i (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)/ ∂ Q i (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 i nertia 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 clos e 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 2xCO 2 , 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 

### dt e (0) E D(t)

= S t

-

i 0 i δ τ



### ∂ ∂ 

# ∫ (1)



### ds (0) E (s) Q
(s) Q T(t)
T(t) D(t)

= (0) E D(t)

i i

i t

0 i 

###        

∂ ∂

• ∂

∂

∂ ∂

∂ ∂ 

# ∫ (2)



### dt e ds (0) E (s) Q
(s) Q 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 introduc ed 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 f unction and many of the climatic parameters are highly controversial variables about which littl e 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 CO 2 emissions from fossil fuel combustion the procedure is slightly more complex in that the rate of growth of emissions at time t, g t , consists of several factors, as follows

where c t is the percentage change in carbon intensity (carbon emitted per energy unit), f t the increase in energy efficiency (energy used per unit of GNP), y t the change in per capita income and p t 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 c t , but may also lead to a lower growth rate of CH 4 emissions from coal mining and a higher growth rate of CH 4 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 CH 4 from biomass burning is correlated to CO 2 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, 

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



### population population GNP

GNP energy

energy carbon

= emissions carbon • • • (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, E t i , are therefore

where STAB i represents emissions under the abatement policy. For CO 2 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 N 2 O 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 belowBAU 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, Q t i , is assumed to depreciate at a constant rate
1/L i , where L i is the lifetime of gas i 3

. β i 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 CO 2 for example 1 GtC = 5.66/12 = 0.47 ppm.

For two gases the concentration equation differs fr om 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 CH 4 in the soil (Wigley and Raper, 1992). In the case of CO 2 the notion of a constant depreciation rate would be misleading,

because CO 2 is a very stable compound which does not easily decay. Rather, CO 2 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). STAB )

- (1 + BAU = E i i

t i

t 

### • • π π (6)



### E + Q L 1

- 1 = Q i

t i i

1

- t

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 here 4 . 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 CO 2 the relationship between concentration and radiative forcing, F, is logarithmic

where Q p CO2 denotes preindustrial concentration. For CH 4 and N 2 O the relationship is

where O i is a relatively complicated overlap term between CH 4 and N 2 O, 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 em issions since preindustrial time. Concentration in the base period 1990 is therefore already th e weighted sum of the 5 boxes, as introduced above. Using historic emission rates we derived a CO

2 

### concentration level of 349 ppm in 1990, close to IPCC's (1990a) estimate of 353 ppm.  
 
 
 

Q

Q

= F CO2

p CO2

t CO2

t 

### ln μ (8)



### O

- ) Q

- Q ( = F i i

p i

t i i

t 

### φ (9)



### ) Q

- Q ( = F i

p i

t i i

t 

### ν (10)



### Q n a = FB j

t j

CFC t 

### • • 

# ∑ (11)

## 9 where a is a factor of proportion (assumed to be random), and n j 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 c limate 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

T t u and T t l are the temperature of the upper and lower layer of oceans, respectively (relative to the preindustrial level). R u and R l 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 indicate s 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 2xCO 2 , and the representation of annual damage was consequently centred around this point. Studies estimating the monetary damage of 2xCO 2 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

2xCO 2 . To generalise from this particular set up, we need to expand the representation in three directions. First, we have to model how damage c hanges under temperatures different from that

associated with 2xCO 2 . 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 2xCO 2 is reached earlier, or later, than initially assumed. Third, we need to k now how damage develops as the economy changes and population grows. The three components are incorporated in a damage function of the form 

### FB

- F = F t i

t

i t 

# ∑ (12)



###       ) T

- T ( R

- T

- F R 1 + T = T l
1

- t u 1

- t l

u 1

- t t u u 1

- t u
t 

### θ λ (13)



###       ) T

- T ( R

R 1 + T = T l
1

- t u 1

- t l

l l
1

- t l

t 

### θ (14)

## 10 where the two parameters Λ and t * represent two key assumptions of the 2xCO 2 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 T t u = Λ

and t=t * annual damage in period t becomes D t =k t . k t therefore represents the 2xCO 2 estimates introduced in section 2.1, adjusted for economic and population growth. The two parameters γ and φ then determine the damage outside the 2xCO 2 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 tem perature. 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 nat ural 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 considerati ons 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 dam age is simply the sum of the two elements. The former is assumed to grow in proportion to GNP,

where p t denotes the rate of growth of population, as introduced earlier. _ t is the rate of growth of 

### ) + (1 T k = D t)

- t ( u
t

t t * 

### φ γ



### •      

Λ (15)



### ) p + y + (1 = k k

t t Y
1

- t 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 ε Y 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 as 5

Estimates of ε Y 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 ε Y = 1. The initial values k 0 Y and k 0 P were derived from the 2xCO 2 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



###        

• ) T ( D

- ) T ( D N ) E Y( N t P

t t Y

t

t t

t 

## Error! Main Document Only.

where N

t 

### denotes population and Y

t 

### GNP, which is a function of emissions. ) p + y + (1 = k k

t t Y P
1

- t P

t 

### ˆ • ε (17)



### y + = t t 

### ˆ ω ρ δ (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 y t . 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 c haracter, as outlined above. Climate impacts 

### ) + (1 A = v - N

=1 τ

τ 

### δ 

# ∑ (19)



### 0 = ) r + (1 A + 1

- - N

=1 τ

τ 

# ∑ (20)



### δ δ

t -N

t

N

- t 

### ) + (1

- 1

) r + (1

- 1 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 2xCO 2 damage variable k t can then be rewritten as



### k v 0.2 + ) k 0.8 + k ( = 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 CO 2 We have used the model of section 3 for Monte Carlo simulations of the social costs of CO 2 emissions over four decades, from 1991 to 2030. The results are shown in Table 2. As expected, damage per tonne of emission is risi ng 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 k t 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 m odel, and the relevant statistics are also shown
in Table 2. The distributions for CO 2 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
CO 2 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 CH 4 , N 2 O and CFCs. The usual way of dealing with greenhouse gases other than CO 2 is to transform them

into CO 2 -equivalents by using Global Warming Potentials (GWPs). According to this index suggested by the IPCC one tonne of CH 4 and N 2 O is equivalent to 11 tonnes of CO 2 and 270
tonnes of CO 2 , 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 dam age 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 so cial 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 $/tCH 4 in 1991-2000 to 176 $/tCH 4 in 2021-2030. The damage from nitrous oxide rise s from 2,895 $/tN in 1991-2000 to 4,489 $/tN.

In terms of CO 2 equivalents or "Greenhouse Damage Potentials" this corresponds to values of

20-23 for CH 4 and 333-377 for N 2 O, depending on the time of emission 7 . 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 CO 2 . 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 here 8 . Also note that the figures only refer to the social costs from global warming, i.e. they do not include costs from other envir onmental 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 c onsumption 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 co mpare the impact of one tonne of each gas, i.e. they compare a tonne of CH

4 

### or N

2 

### O with of a tonne of CO

2 

### . The figures in Table 2 on the other

hand use the more common measures of tCH

4 

### for methane, tN for N

2 

### O, and tC for CO

2 

### .

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 values 9 . The results are summarised in
Table 3. If ρ is set at 3% the expected shadow value of 1990 CO 2 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 impos ed on it, surprises cannot be fully excluded, particularly in the long run (beyond 2xCO 2 ). 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, 2xCO 2 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

thresholds 10 . 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 CO 2 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 2xCO 2 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 CO 2 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 abstrac ting 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 expec t 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 CO 2 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 sati sfactory 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 gr eenhouse uncertainties, and secondly into projects evaluating the optimal policy in the light of them.

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## 23 TABLE 1: EXISTING ESTIMATES OF CO 2 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 8.6 a 10.0

Peck and Teisberg

(1993b) 10 - 12 a 12 - 14 a 14 - 18 a 18 - 22 a (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

CO 2

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

CH 4

mean ($/tCH 4 )

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

N 2 O

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 CO 2 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 ran g emarg. costs marg.
costs

o p tdamage range MD hi g h

MD low

## 27 FIGURE 2: THE PROBABILITY DISTRIBUTION OF CO 2 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: CO 2 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 willexceed the values given in the table below. Scenario A roughly corresponds to the nocatastrophe case of Figure 2 and Table 2.

Climate Sensitivity 2xCO 2 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

CO 2 fossil fuels, GtC

CO 2 deforestation, GtC

CH 4 from coal mining, MtCH 4 CH 4 from gas leakage, MtCH 4 CH 4 from biomass burning, MtCH 4 other CH 4 emissions, MtCH 4

N 2 O emissions, MtN

CFC-11 emissions, kt CFC-12 emissions, kt HCFCs and HFCs, kt

Concentrations

CO 2 , ppm CH 4 , ppb

N 2 O, 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

y 1990-2100 y 2101-2220

p 1990-2025 p 2026-2100 p 2101-2220

c 1990-2025

c 2026-2100

c 2101-2220

f 1990-2220

g 1990-2100 defor

g 2101-2220 defor

g 1990-2025 CH4

g 2026-2100 CH4

g 2101-2220 CH4

g 1990-2025 N2O

g 2026-2100 N2O

g 2101-2220 N2O

g 1990-2025 CFC11

g 2026-2100 CFC11

g 2101-2220 CFC11

g 1990-2025 CFC12

g 2026-2100 CFC12

g 2101-2220 CFC12

g 1990-2025 OCFC

g 2026-2100 OCFC

g 2101-2220 OCFC

π fuel

π deforest

ε en Y

ε E en

C defoest GNP/capita growth, %

population growth, %

carbon intensity growth, %

energy effic improvement, %

CO 2 from deforestation, growth

rate in %

CH 4 from all sources, growth

rate in %

N 2 O 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 CO 2

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

L CH4-A L CH4-S L N2O L CFC11 L CFC12 L OCFC

w ∞

w 363

w 74

w 17

w 2 Atmos. lifetime CH 4 , yrs CH 4 deposition in soil Atmospheric lifetime N 2 O

Atmos. lifetime CFC11

Atmos. lifetime CFC12

Lifetime other CFCs etc.

weight, CO 2 with ∞ lifetime weight, CO 2 363 yrs lifetime weight, CO 2 74 yrs lifetime weight, CO 2 17 yrs lifetime weight, CO 2 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. Σ w i =1 Lashof and Ahuja (1990) Lashof and Ahuja (1990)

(d) Radiative Forcing Parameters

Parameter Description lower

bound best

guess upper bound Comment / Source

μ

φ CH4

φ N2O

υ CFC11

υ CFC12

υ OCFC

a CO 2 forcing, Wm -2 /ppm

CH 4 forcing, Wm -2 /ppb

N 2 O 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

R l

1/R u

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

k 0 γ 1+ φ

ε Y 2xCO 2 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)