The Marginal Damage Costs of Different 

Greenhouse Gases: An Application of FUND 

Stephanie Waldhoff 

U.S. Environmental Protection Agency, Washington, D.C. 

David Anthoff 

University of California, Berkeley 

Steven Rose 

Electric Power Research Institute, Washington, D.C. 

Richard S.J. Tol 

Economic and Social Research Institute, Dublin, Vrije Universiteit, Amsterdam, 

Trinity College, Dublin 

Abstract We use FUND 3.5 to estimate the social cost of carbon dioxide, methane, nitrous 

oxide, and sulphur hexafluoride emissions. We show the results of a range of sensitivity 

analyses, focusing on the impact of carbon dioxide fertilization. Ignored in previous studies of 

the social cost of greenhouse gas emissions, carbon dioxide fertilization has a positive effect at 

the margin, but only for carbon dioxide. Because of this, the ratio of the social cost of a 

greenhouse gas to that of carbon dioxide (the global damage potential) is higher – that is, 

previous papers underestimated the importance of reducing non-carbon dioxide greenhouse gas 

emissions. When leaving out carbon dioxide fertilization, our estimate of the social cost of 

methane is comparable to previous estimates. Our estimate of the global damage potential of 

methane is close to the estimates of the global warming potential because discounting roughly 

cancels carbon dioxide fertilization. Our estimate of the social cost of nitrous oxide is higher 

than previous estimates, also when omitting carbon dioxide fertilization. This is because, in 

FUND, vulnerability to climate change falls over time (with development) while in the long run 

carbon dioxide is a more potent greenhouse gas than nitrous oxide. Our estimate of the global 

damage potential of nitrous oxide is larger than the global warming potential because of carbon 

dioxide fertilization, discounting, and rising atmospheric concentrations of both gases. Our 

estimate of the social cost of sulphur hexafluoride is similar to the one previous estimate. Its 

global damage potential is higher than the global warming potential because of carbon dioxide 

fertilization, discounting, and rising concentrations.

Paper submitted to the special issue 

The Social Cost of Carbon

JEL Q54 

Keywords Climate change; social cost; carbon dioxide; methane; nitrous oxide; sulphur 

hexafluoride

Correspondence Richard S.J. Tol, Economic and Social Research Institute, Whitaker Square, 

Sir John Rogerson's Quay, Dublin 2, Ireland; e-mail: richard.tol@esri.ie

Discussion Paper

No. 2011-43 | October 14, 2011 | http://www.economics-ejournal.org/economics/discussionpapers/2011-43

© Author(s) 2011. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany
3

1. Introduction

Carbon dioxide is the main anthropogenic greenhouse gas, but certainly not the only one. 

In order to be effective and least cost, climate policy requires the reduction of the 

emissions of all greenhouse gases (Weyant et al. 2006). This in turn requires a 

mechanism to understand the potential trade-offs between the various greenhouse gases. 

There are three ways to compare different greenhouse gases. A physical measure, such as 

the IPCC‘s Global Warming Potential (Forster et al. 2007), is often used, however this is 

essentially random from a decision analytic perspective because it does not weigh the 

potential welfare changes from emission (reduction) across gases. The ratio of the 

shadow prices (Manne and Richels 2001) is appropriate when seeking to meet a specific

temperature, concentrations, or emissions target at the lowest possible cost. Finally, as is 

done in this paper, the ratio of marginal impacts should be used if one seeks to maximize 

welfare.

The appropriate trade-off between greenhouse gases in a cost-benefit framework was 

recognized in the early 1990s (Eckaus 1992;Michaelis 1992;Schmalensee 1993) and 

shortly thereafter a number of papers sought to quantify these ratios of the relative global 

marginal damage potential of greenhouse gas i with respect to the marginal damage of 

carbon dioxide (Fankhauser 1995;Hammitt et al. 1996;Kandlikar 1995;Kandlikar 

1996;Reilly and Richards 1993;Wallis and Lucas 1994), then dubbed the ―global damage 

potential.‖ . Since then, there has been little research (Hope 2006;Tol 1999) even though 

our understanding of the impacts of climate change has changed dramatically. We 

therefore revisit the empirical estimates of the global damage potential of methane, 

nitrous oxide, and sulphur hexafluoride emissions using the FUND model.
4

An additional motivation for this paper is that policy-makers have begun to value 

changes in greenhouse gas emissions in regulatory decisions (Rose, 2010). However, 

with the legal focus on CO2 emissions and a dearth of non-CO2 GHG emission reduction 

cost estimates, decision-makers have opted to use CO2 equivalents based on global 

warming potentials (US EPA, 2008a, 2008b) or, more recently, not value changes in nonCO2 GHG emissions at all (USDoE 2010) due to the recognition that the GWP ratios may 

not be the correct transformation to use for the global damage potentials. This paper will 

help inform this issue by providing direct estimates of these potentials.

The paper continues as follows: Section 2 presents the model, Section 3 discusses the 

results, and Section 4 concludes.

2. The model

The results in this paper are generated with version 3.5 of the Climate Framework for 

Uncertainty, Negotiation and Distribution (FUND). Version 3.5 of FUND corresponds to 

version 1.6 (Tol et al. 1999;Tol 2001;Tol 2002c) except for the impact module which 

now includes diarrhoea and tropical and extratropical storms (Link and Tol 2004;Narita 

et al. 2009;Narita et al. 2010;Tol 2002a;Tol 2002b). A full list of papers, the source code, 

and the technical documentation for the model can be found on line at http://www.fundmodel.org/.

The model distinguishes 16 major regions of the world, viz. the United States of 

America, Canada, Western Europe, Japan and South Korea, Australia and New Zealand, 

Central and Eastern Europe, the former Soviet Union, the Middle East, Central America, 

South America, South Asia, Southeast Asia, China, North Africa, Sub-Saharan Africa, 

and Small Island States. The model runs from 1950 to 3000 in time steps of one year. The 
5

prime reason for starting in 1950 is to initialize the climate change impact module. In 

FUND, the impacts of climate change are assumed to depend on the impact of the 

previous year, this way reflecting the process of adjustment to climate change. Because 

the initial values to be used for the year 1950 cannot be approximated very well, both 

physical and monetized impacts of climate change tend to be misrepresented in the first 

few decades of the model runs.1 The centuries after the 21st are included to assess the 

long-term implications of climate change. Previous versions of the model stopped at 

2300.

The scenarios are defined by exogenous assumptions on the rates of population growth, 

economic growth, autonomous energy efficiency improvements as well as the rate of 

decarbonization of the energy use (autonomous carbon efficiency improvements), and 

emissions of carbon dioxide from fossil fuel and land use change, and emissions of 

methane, nitrous oxide, sulphur hexafluoride and aerosols. The scenarios of economic 

and population growth are perturbed by the impact of climatic change. Population 

decreases with increasing climate change related deaths that result from changes in heat 

stress, cold stress, malaria, and storms. Heat and cold stress are assumed to have an effect 

only on the elderly, non-reproductive population. In contrast, the other sources of 

mortality also affect the number of births. Heat stress only affects the urban population. 

The share of the urban population among the total population is based on the World 

Resources Databases (http://earthtrends.wri.org). It is extrapolated based on the statistical 

 

1 The period of 1950–2000 is used for the calibration of the model, which is based on the IMAGE 100-year 

database (Batjes and Goldewijk 1994). The scenario for the period 2010–2100 is based on the EMF14 

Standardized Scenario, which lies somewhere in between IS92a and IS92f (Leggett et al. 1992). The 2000–

2010 period is interpolated from the immediate past (http://earthtrends.wri.org), and the period 2100–3000

extrapolated.
6

relationship between urbanization and per capita income, which are estimated from a 

cross-section of countries in 1995. Climate-induced migration between the regions of the 

world also causes the population sizes to change. Immigrants are assumed to assimilate 

immediately and completely with the respective host population.

FUND derives atmospheric concentrations of carbon dioxide, methane, nitrous oxide and 

sulphur hexafluoride, the global mean temperature, the impact of carbon dioxide 

emission reductions on the economy and on emissions, and the impact of the damages to 

the economy and the population caused by climate change. Methane and nitrous oxide are 

taken up in the atmosphere, and then geometrically depleted. The atmospheric 

concentration of carbon dioxide, measured in parts per million by volume, is represented 

by the five-box model (Hammitt et al. 1992;Maier-Reimer and Hasselmann 1987). The 

model also contains sulphur emissions (Tol 2006).

The radiative forcing of carbon dioxide, methane, nitrous oxide, sulphur hexafluoride and 

sulphur aerosols is as in the IPCC (Ramaswamy et al. 2001). The global mean 

temperature T is governed by a geometric build-up to its equilibrium (determined by the 

radiative forcing RF), with an e-folding time of 66 years. In the base case, the global 

mean temperature rises in equilibrium by 3.0°C for a doubling of carbon dioxide 

equivalents. Regional temperatures follow from multiplying the global mean temperature 

by a fixed factor, which corresponds to the spatial climate change pattern averaged over 

14 GCMs (Mendelsohn et al. 2000). The dynamics of the global mean sea level are also 

geometric, with its equilibrium level determined by the temperature and an e-folding time 

of 500 years. Both temperature and sea level are calibrated to correspond to the best 

guess temperature and sea level for the IS92a scenario (Kattenberg et al. 1996).
7

The climate impact module includes the following categories: agriculture, forestry, sea 

level rise, cardiovascular and respiratory disorders related to cold and heat stress, malaria, 

dengue fever, schistosomiasis, energy consumption, water resources, unmanaged 

ecosystems (Tol 2002a;Tol 2002b), diarrhoea (Link and Tol 2004), and tropical and extra 

tropical storms (Narita et al. 2009;Narita et al. 2010). Climate change related damages 

can be attributed to either the rate of change (benchmarked at 0.04°C/yr) or the level of 

change (benchmarked at 1.0°C). Damages from the rate of temperature change slowly 

fade, reflecting adaptation (Tol 2002b).

Climate change affects population growth through premature deaths or migration due to

sea level rise. Like all the impacts of climate change in FUND, these effects are 

monetized. The value of a statistical life is set to be 200 times the annual per capita 

income. The resulting value of a statistical life lies in the middle of the observed range of 

values in the literature (Cline 1992). The value of emigration is set to be 3 times the per 

capita income (Tol 1995), the value of immigration is 40 per cent of the per capita 

income in the host region (Cline 1992). Losses of dryland and wetlands due to sea level 

rise are modeled explicitly. The monetary value of a loss of one square kilometre of 

dryland was on average $4 million in OECD countries in 1990 (Fankhauser 1994a). 

Dryland value is assumed to be proportional to GDP per square kilometre. Wetland losses 

are valued at $2 million per square kilometre on average in the OECD in 1990 

(Fankhauser 1994a). The wetland value is assumed to have logistic relation to per capita 

income. Coastal protection is based on cost-benefit analysis, including the value of 

additional wetland lost due to the construction of dikes and subsequent coastal squeeze.
8

Other impact categories, such as agriculture, forestry, energy, water, storm damage, and 

ecosystems, are directly expressed in monetary values without an intermediate layer of 

impacts measured in their  ̳natural‘ units (Tol 2002a). Impacts of climate change on 

energy consumption, agriculture, and cardiovascular and respiratory diseases explicitly 

recognize that there is a climatic optimum, which is determined by a variety of factors, 

including plant physiology and the behaviour of farmers. Impacts are positive or negative 

depending on whether the actual climate conditions are moving closer to or away from 

that optimum climate. Impacts are larger if the initial climate conditions are further away 

from the optimum climate. The optimum climate is of importance with regard to the 

potential impacts. The actual impacts lag behind the potential impacts, depending on the 

speed of adaptation. The impacts of not being fully adapted to new climate conditions are 

always negative (Tol 2002b).

The impacts of climate change on coastal zones, forestry, tropical and extratropical 

storms, unmanaged ecosystems, water resources, diarrhoea, malaria, dengue fever, and 

schistosomiasis are modelled as simple power functions. Impacts are either negative or 

positive, and they do not change sign (Tol 2002b).

Vulnerability to climate change changes with population growth, economic growth, and 

technological progress. Some systems are expected to become more vulnerable over time 

with increasing climate change, such as water resources (with population growth), heatrelated disorders (with urbanization), and ecosystems and health (with higher per capita 

incomes). Other systems such as energy consumption (with technological progress), 

agriculture (with economic growth) and vector- and water-borne diseases (with improved 

health care) are projected to become less vulnerable at least over the long term (Tol 
9

2002b). The income elasticities (Tol 2002b) are estimated from cross-sectional data or 

taken from the literature.

We estimated the SCC cost of carbon by computing the total, monetised impact of 

climate change along a business as usual path and along a path with slightly higher 

emissions between 2010 and 2019.2 Differences in monetized damages from climate 

change impacts were calculated, discounted back to the current year, and normalised by 

the difference in emissions.3 The SCC is thereby expressed in 1995 dollars per tonne of 

carbon at a point in time (2010)—the standard measure of the additional impacts globally 

and over time of an additional global tonne of emissions. It is also used as a measure of 

how much future damage would be avoided if today‘s emissions were reduced by one 

tonne. The social cost of any greenhouse gas is computed as follows:

   

3000 3000

, 1950 1950 , 1950

,

2010 1950

,

2010

,..., ,...,

1

for 2010 220

0 for allother cases

t r t t t r t

r i t t

t

s r

s

t

D E E D E E

SCC

g

t

 



 









  



 

  

 



 



(1)

where,

 SCCr,i is the regional social cost of greenhouse gas i (in 1995 US dollars per tonne 

of i);

 r denotes region;

 i denotes greenhouse gas;

 t and s denote time (in years);

 D are monetised impacts (in US dollars per year);

 E are emissions of greenhouse gas i (in metric tonnes of i per year);

 

2 The social cost of emissions in future or past periods is beyond the scope of this paper.

3 We abstained from levelizing the incremental impacts within the period 2010–2019 because the 

numerical effect of this correction is minimal while it is hard to explain.
10

 δ are incremental emissions (in metric tonnes of i per year);

 ω are increment emissions (in metric tonnes of i per year);

 ρ is the pure rate of time preference (in fraction per year);

 η is the elasticity of marginal utility with respect to consumption; and

 g is the growth rate of per capita consumption (in fraction per year).

We first compute the SCCi per region, and then aggregate, as follows

16

2010,

,

1 2010,

ref

i r i

r r

Y

SCC SCC

Y





 

       

(2)

where

 SCCi is the global social cost of greenhouse gas i (in 1995 US dollars per tonne of 

i);

 SCCr,i is the regional social cost of greenhouse gas i (in 1995 US dollars per tonne 

of i);

 r denotes region; 

 i denotes greenhouse gas;

 Yref is the average per capita consumption in the reference region (in US dollars

per person per year); the reference region may be the world (Fankhauser et al. 

1997) or one of the regions (Anthoff et al. 2009);

 Yr is the regional average per capita consumption (in US dollars per person per 

year); and

 ε is the rate of inequity aversion; ε = 0 in the case without equity weighing; ε = η

in the case with equity weighing.

The global damage potential, i.e., the relative marginal damage of greenhouse gas i with 

respect to the social cost of carbon dioxide, is defined as

2

i

i

CO

SCC GDP

SCC



(3)

where

 GDPi is the global damage potential of greenhouse gas i (unitless);

 SCCi is the global social cost of greenhouse gas i (in US dollars per tonne of i); 

and

 i denotes greenhouse gas.
11

Because the impact of non-CO2 GHGs differs from CO2 with respect to carbon dioxide 

fertilization, it is useful to split the social cost of carbon dioxide into the social cost of 

carbon dioxide through its effect on climate change and its fertilization effect.

2 2 2 2 2

( , )

: :

( , ) ( , )

i i i

i cc fert

CO CO CO CO CO

SCC SCC f GDP

SCC SCC SCC f g

 

   

  

 

(4)

Equation (4) is an expansion of Equation (3), highlighting that the social cost of carbon 

dioxide through climate change and the social cost of other greenhouse gases are similar 

functions of the same vector of parameters. The social cost of carbon dioxide through 

fertilization is a different function with partly overlapping parameters. This implies that, 

without carbon dioxide fertilization, one would expect the global damage of greenhouse 

gas i with respect to the social cost of carbon dioxide potential to be largely robust to 

parameter variations. With carbon dioxide fertilization, one would not expect that to be 

the case.

3. Results and sensitivities

3.1. Social Cost of Carbon Dioxide

Figure 1 shows the social costs of carbon dioxide. The base case estimate is $8/tCO2. 

This number depends on a large number of assumptions. Here we examine the sensitivity 

of this estimate with respect to carbon dioxide fertilization, tropical forest dieback, 

climate sensitivity, pure rate of time preference, equity weights, and socio-economic and 

emissions scenarios.

The SCC is reasonably low because of the positive effects of carbon dioxide fertilization 

on agriculture. If we turn that off, the social cost rises to $14/tCO2. The carbon dioxide 
12

fertilization effect is comparatively large because it occurs in the near future, thus having 

a relatively larger effect on the net present value than the negative impacts that occur in 

later time periods. 

On the other hand, the social cost estimate is pushed up because the base case assumes 

that, because of climate change, tropical forests will die back and release substantial 

amounts of carbon dioxide. If we turn that off, the social cost falls to $7/tCO2. Compared

to the carbon dioxide fertilization effect, this effect is relatively small because it occurs in 

the distant future, thus discounted more heavily. 

The climate sensitivity, or the equilibrium warming due to a doubling of carbon dioxide 

concentrations, has a larger effect on the SCC estimates. In the base case, we assume a 

climate sensitivity of 3.0°C equilibrium warming due to a doubling of ambient carbon 

dioxide. If we use climate sensitivities of 2.0°C or 4.5°C instead, the social cost falls to 

$3/tCO2 and rises to $18/tCO2, respectively. 

Assumptions about the discount rate have an even larger effect on the estimates. In the 

base case, the pure rate of time preference is 1% per year. If instead we use a pure rate of 

time preference of 0.1% or 3% per year, the social cost rises to $51/tCO2 or falls to only 

$0.3/tCO2, respectively. Additionally, the base case does not use equity weights. If 

world-average equity weights are used instead, the social cost rises to $25/tCO2. If, 

instead, US or sub-Saharan African equity weights are used, the social cost estimates are

$154/tCO2 and $2/tCO2, respectively. 

Finally, the base case scenario uses population, income, and emissions according to the 

FUND scenario. If the SRES scenarios (Nakicenovic and Swart 2001) are used instead, 

the social cost is $2/tCO2 for the B1 scenario which is a low emissions/low growth 
13

scenario, $3/tCO2 for A1B which represents a high emissions/low growth world, $8/tCO2

for B2 which has low emissions and high growth, or $12/tCO2 for A2, the high 

emissions/high growth world. The alternate scenarios make clear that the social cost of 

carbon dioxide depends not only on the level of emissions and climate change, but also 

the level of economic growth, because the valuation of impacts is measured as a function 

of income.

3.2. Social Cost of Methane

The social costs of methane emissions are shown in Figure 2. As for SC-CO2, the 

sensitivity of SC-CH4 is estimated with respect to a number of assumptions. In the base 

case, the estimate is $205/tCH4. As one would expect, the qualitative pattern is the same 

as in Figure 1. The impacts of climate change respond in the same way to parameter 

variations regardless of whether climate change is caused by methane or carbon dioxide. 

One difference is that the social cost of methane is only slightly higher without carbon 

dioxide fertilization than with. The reason is that the methane does not have the positive 

effects of carbon fertilization, so economic growth is slightly slower and people are a bit 

more vulnerable to climate change.

Figure 3 shows the global damage potential, that is, the ratio of the social cost of methane 

to the social cost of carbon dioxide. In the base case, the estimated damage from emitting 

an additional tonne of methane is 25 times more than the damage from emitting an 

additional tonne of carbon dioxide. As seen in Figure 3, the global damage potential for 

methane varies with the assumptions described above. Without carbon dioxide 

fertilization, carbon dioxide is a lot more damaging and methane only slightly more, so 

that the global damage potential falls to 16. Because carbon dioxide fertilization is such a 
14

large part of the social cost of carbon dioxide (cf. Figure 1), Figure 3 shows the global 

damage potential with and without carbon dioxide fertilization for changes in each of 

these assumptions. 

The feedback of climate change on the terrestrial carbon cycle has the same proportional 

effect on the social costs of methane and carbon dioxide; the global damage potential

hardly changes. The climate sensitivity is more important for a long-lived gas such as 

carbon dioxide than for a short-lived gas such as methane so the global damage potential

falls to 19 when the climate sensitivity is 4.5°C and rises to 40 with a climate sensitivity 

of 2.0°C. This effect is largely due to carbon dioxide fertilization. 

The same effect, but stronger, is observed for variations in the pure rate of time 

preference. The global damage potential falls to 9 for a pure rate of time preference of 

0.1% and rises to 221 as the pure rate of time preference is increased to 3.0%/yr. Again, 

this is amplified by carbon dioxide fertilization.

Equity weighting is therefore more important for carbon dioxide, and the global damage 

potential falls to 22 using global equity weights. This is because poor countries contribute 

less to the marginal impact during the short life-time of methane than during the long 

life-time of carbon dioxide. The same, but weaker effect is observed without carbon 

dioxide fertilization.

Similarly, the differences between scenarios are more pronounced in the long term and 

hence have a greater effect on longer lived gases and the social cost of carbon dioxide.

The global damage potential therefore varies considerably between scenarios, ranging 

between 20 and 55 for the A2 and B1 scenarios, respectively. Again, carbon fertilization 

strengthens the differences. Note that methane is relatively more potent on the margin in 
15

the A1B and B1 scenarios, where emissions are relatively lower and society richer and 

more equal than the other scenarios. In these contexts, society is more sensitive to 

changes in methane emissions.

Figure 4 shows our estimates of the global damage potential of methane in comparison to 

earlier estimates (Fankhauser 1994b;Hammitt et al. 1996;Hope 2006;Kandlikar 

1995;Kandlikar 1996;Reilly and Richards 1993;Tol 1999). The 61 previous estimates are 

shown as the empirical cumulative density function in blue. Without carbon dioxide 

fertilization, our base estimate of the global damage potential for methane is 16, with a 

range of 7 to 25. The base estimate is the 57th percentile of previous estimates, falling in 

the middle of the range of earlier work which did not include the effects of carbon 

dioxide fertilization. However, the primary estimate which includes carbon dioxide 

fertilization, is 25, with a range of 8 to 221. Therefore the primary estimate in this work is 

at the 82nd percentile – on the high side due to the explicit modeling of the CO2

fertilization processes for the different gases.

The latest IPCC 100-year global warming potential (GWP) estimate is 25 (Forster et al. 

2007) and the official UNFCCC estimate is 21 (Schimel et al. 1996). The GWP estimates 

are comparable to our base estimate of the global damage potential with CO2 fertilization.

However, the GWP estimates appear high relative to the scenarios with less favorable 

circumstances in the future (e.g., high climate sensitivity, higher emissions, and more 

vulnerable populations) and low relative to scenarios with more favorable circumstances.

In our estimates without carbon dioxide fertilization, the global damage potential is lower 

than the global warming potential estimates because the benefits in the near term from 
16

CO2 fertilization are not reaped for the SC-CO2 and the these losses are not proportional

in the SC-CH4, which has a much smaller benefit from CO2 fertilization in the base case.

3.3. Social Cost of Nitrous Oxide

Figure 5 shows the social cost of nitrous oxide emissions. The estimate is $5,900/tN2O 

using the base case assumptions. Qualitatively, the pattern is the same as for carbon 

dioxide and methane (Figures 1 and 2). However, because of the longer atmospheric 

lifetime for nitrous oxide, its social cost is more sensitive than the social cost of methane 

to the pure rate of time preference, the climate sensitivity, and the socioeconomic 

scenario, all of which have stronger impacts in the long term.

Figure 6 shows the global damage potential of nitrous oxide. In the base case the net 

present value of the damage from nitrous oxide is 713 times more than for carbon 

dioxide. Without the effect of carbon dioxide fertilization, the estimate falls to 437.

Eliminating the climate change feedback on the terrestrial carbon cycle causes the global 

damage potential to rise slightly to 748. 

As with the pattern for methane, the global damage potential falls to 572 and rises to 

1162 as the climate sensitivity is changed to 4.5°C or 2.0°C, respectively. Without carbon 

dioxide fertilization, the marginal impacts of nitrous oxide and carbon dioxide respond in 

the same way to the climate sensitivity because they both have comparatively long 

atmospheric lifetimes. 

As the pure rate of time preference is changed to 0.1%/yr and 3.0%/yr, while maintaining 

the other base case assumptions, the global damage potential falls to 449 and rises to

3503, respectively. Without carbon dioxide fertilization, however, the global damage 
17

potential is highest for the middle pure rate of time preference, as there is more carbon 

dioxide (relative to the initial pulse) than nitrous oxide in both the short run and the very 

long run – this follows from the pattern of atmospheric decomposition of the two gases.

However, with carbon dioxide fertilization the global damage potential is highest for the 

highest pure rate of time preference because the initial benefits of carbon dioxide 

fertilization are more pronounced compared to the longer term damages of both gases 

which are discounted more heavily. As with methane, the global damage potential falls

with equity weighting, from 713 to 645, because the positive impact of carbon dioxide 

fertilization weighs more heavily.

As would be expected, the global damage potential varies between scenarios, ranging 

from 648 (A2) to 1281 (B1) with CO2 fertilization. It is lowest in scenarios with higher

economic growth and carbon dioxide emissions because the absolute value of agriculture 

(and hence CO2 fertilization) is higher in richer scenarios and because radiative forcing is 

proportional to the logarithm of carbon dioxide but to the square root of nitrous oxide.

Without the fertilization effect, though, the nitrous oxide damage potentials are very 

similar across scenarios, between 383 and 437, because the changes in damages due to 

varying levels of economic development and carbon emissions are essentially cancelled 

out.

Figure 7 shows our estimates of the global damage potential of nitrous oxide in 

comparison to earlier estimates (Fankhauser 1994b;Hammitt et al. 1996;Kandlikar 

1995;Reilly and Richards 1993;Tol 1999). The 33 previous estimates are shown as the 

empirical cumulative density function. Without carbon dioxide fertilization, our base 

estimate is 437, with a range of 367 to 438. Our base estimate is higher than any previous 
18

estimate. It is also much higher than the most recent IPCC 100-year global warming 

potential of 298 (Forster et al. 2007), and the official UNFCCC value of 310 (Schimel et 

al. 1996). Figure 6 shows that the global damage potential of nitrous oxide decreases as 

carbon dioxide emissions are higher – this is because radiative forcing is proportional to 

the logarithm of carbon dioxide but to the square root of nitrous oxide. An additional 

difference between global warming potentials and global damage potentials is that the 

former assumes constant concentrations while the latter assumes rising concentrations.

Under a scenario with rising concentrations, the damages from nitrous oxide become 

relatively more important. Finally, discounting reduces the importance of impacts in the 

long run when the damages from carbon dioxide dominate those of nitrous oxide.

The higher global damage potential for nitrous oxide in this work compared to earlier 

estimates is due to the temporal pattern of radiative forcing between N2O and CO2 and 

the pattern of adaptation in FUND. The incremental radiative forcing of nitrous oxide 

relative to carbon dioxide starts high and rises for some 30 years, after which it 

continuously falls. Additionally, as FUND assumes a greater degree of adaptation and 

falling vulnerability to climate change with development, impacts in the more remote 

future are less pronounced than in other models. These effects together imply that the 

medium-term damages from nitrous oxide emissions are more important than the longer 

term carbon dioxide damages.

3.4. Social Cost of Sulphur Hexafloride

Sulphur hexafluoride is one of the more prominent of the high-GWP gases. Figure 8 

shows the social cost of SF6 under varying assumptions. In the base case, the estimate is 

$519,000/tSF6. Qualitatively, the pattern is similar to that in Figures 1, 2 and 4.
19

Responsiveness of the SC-SF6 is similar to the social cost of nitrous oxide to most of the 

assumptions modeled here. One important exception is that the social cost of sulphur 

hexafluoride is more responsive to the pure rate of time preference due to its much long 

atmospheric lifetime of 3,200 years, as opposed to 114 years for nitrous oxide and 12 

years for methane. 

Figure 9 shows the global damage potential of sulphur hexafluoride. It is 62,700 in the 

base case. Without carbon dioxide fertilization, it falls to 38,300 because a lack of carbon 

dioxide fertilization only slightly increases the social cost of SF6 but almost doubles the 

social cost of CO2. Without the climate change feedback on the terrestrial carbon cycle, 

the global damage potential rises slightly to 65,200. As with methane and nitrous oxide, 

the global damage potential with CO2 fertilization falls to 55,900 and rises to 99,400 with

climate sensitivities of 4.5°C and 2.0°C, respectively.

With a pure rate of time preference of 0.1% the global damage potential is 84,700 and 

208,700 when the pure rate of time preference is 3.0%/yr. This reflects the long life time 

of sulphur hexafluoride where damages from emissions today continue to have a strong 

impact for centuries and are therefore relatively more sensitive than CO2 to lower pure 

rates of time preference. The global damage potential falls (to 56,900) with all forms of 

equity weighting, implying that equity weighting reduces the relative value of SF6

emissions in the nearer term, most likely because impacts in developing regions that tend 

to occur over shorter time horizons are more heavily valued. The global damage potential

varies between scenarios, ranging from a low of 62,700 using the FUND scenario, to 

102,000 with the SRES B1 scenario (which is poorer and therefore more vulnerable).

Carbon dioxide fertilization again enhances the differences between the scenarios.
20

The only other estimate of the global damage potential (Hope 2006) is 38,600, which is 

very close to our estimate without carbon dioxide fertilization. The latest IPCC 100-year 

global warming potential is 22,800 (Forster et al. 2007) and the UNFCCC official value 

is 23,900 (Schimel et al. 1996). These differences are due to the socioeconomic and 

emissions assumptions under which the values are estimated. Figure 8 shows that the 

global damage potential is negatively correlated with socioeconomic and emissions 

scenarios, because the global warming potential is evaluated with constant concentrations

– or rather because radiative forcing is proportional to the logarithm of the atmospheric 

concentration carbon dioxide but proportional to the concentration of sulphur 

hexafluoride.

4. Discussion and conclusion

We estimate the marginal damage cost of emissions of carbon dioxide, methane, nitrous 

oxide, and sulphur hexafluoride. We also report the global damage potentials, that is, the 

ratios of the marginal damage costs to that of carbon dioxide. We do this because it is the 

global damage potentials, rather than carbon dioxide equivalent values based on global 

warming potentials, that represent the appropriate trade-off between greenhouse gases in 

a cost-benefit analysis. These values are estimated for a range of scenarios and parameter 

specifications in order to explore the drivers of variation in global damage potentials 

across these gases.

Under our base case assumptions, the social cost of carbon dioxide is $8/tCO2 in 2010 for 

a pure rate of time preference of 1%, well in line with previous estimates (Tol 2009). The 

inclusion of the positive effects of carbon dioxide fertilization on agriculture and forestry

in the FUND model substantially reduces the social cost of carbon dioxide, while having 
21

very little effect on the social costs of the other greenhouse gases. As a result, our 

estimates of the global damage potentials are substantially higher than previous estimates

under our base case assumptions. If we exclude carbon dioxide fertilization, our estimates 

for methane and sulphur hexafluoride are more comparable with previous estimates of the 

global damage potential. Our base estimate for methane‘s global damage potential is low 

compared to its global warming potential because the incremental impacts are smaller in 

the short run when temperature changes are lower. However, our sensitivity results reveal 

that changes in methane become more important in terms of marginal impacts under 

lower emissions and less vulnerable conditions. This is because the social cost of CO2 is 

lower under these scenarios, which causes the ratio of methane to carbon dioxide to 

increase.

Our estimate of the global damage potential of nitrous oxide is higher than previous 

estimates because the model assumes substantial acclimatization and falling vulnerability 

so that medium-term incremental impacts are dominant. The temporal pattern of radiative 

forcing of N2O relative to CO2 causes the impacts from N2O to be most potent in the 

nearer term, and hence discounted less heavily than the longer term impacts from CO2

emissions.

The global damage potential of sulphur hexafluoride is especially high compared to its 

global warming potential because the former is evaluated against rising concentrations 

and the latter against constant concentrations – while this is true for all greenhouse gases, 

it matters particularly for SF6 because radiative forcing is linear in its concentration. This 

is combined with SF6‘s extremely long lifetime of 3,200 years which causes the estimates 
22

of the social cost of sulphur hexafluoride to increase faster than the social cost of carbon 

dioxide.

The results presented here suggest that, based on the higher marginal benefits of non-CO2

emissions reductions compared with the marginal benefit of CO2 reductions, climate 

policy would benefit from placing more emphasis on abatement of the three non-carbon 

dioxide greenhouse gases examined here than using a simple CO2 equivalent conversion

would suggest.

There are, however, a number of caveats to these results. These conclusions are based on 

a single model and a limited set of sensitivity analyses and are applicable to only the 

three non-CO2 greenhouse gases discussed in this paper. More importantly, we omit 

uncertainty from the analysis. Because part of carbon dioxide stays in the atmosphere 

essentially forever, irreversibility and the potential to cross dangerous thresholds may 

well put a premium on carbon dioxide emission reduction. Additionally, the model omits 

the damages due to ocean acidification from CO2. Inclusion of these damages would 

likely increase the social cost of carbon dioxide, providing another reason to favour 

carbon dioxide abatement over non-CO2 greenhouse gases, essentially lowering their 

global damage potentials. However, these matters are deferred to future research.

Acknowledgements

We are grateful to Joel Smith for excellent discussions. David Anthoff and Richard Tol

thank the US EPA and the EU FP7 project ClimateCost for financial support. David 

Anthoff thanks the Ciriacy Wantrup Fellowship program for support. The views in this 
23

paper are those of the authors and do not necessarily reflect those of the U.S. 

Environmental Protection Agency.
24

Figures

Figure 1. The social cost of carbon dioxide emissions. Red denotes the estimate with our 

base assumptions for each parameter. The darker colours are with carbon dioxide 

fertilization; the total columns are without carbon dioxide fertilization; the lighter colours 

are the difference.

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

5 0

Yes

No

Yes

No

2.03.04.5

0.1%1.0%3.0%

No

World

SSA

USA

FUND

A1B

A 2

B1B2

$/tC

CO2

fertilization

Terrestrial

feedback

Climate

sensitivity

Pure rate of

time preference

Equity

weighting

Emissions

scenario

50+21 154+87
25

Figure 2. The social costs of methane emissions. Red denotes the base assumptions. 
26

Figure 3. The global damage potential of methane; for comparison, the global warming 

potential is shown as well (green line); top panel: carbon dioxide fertilization; bottom 

panel: no carbon dioxide fertilization.
27

Figure 4. Our base estimates of the global damage potential of methane (red dots) 

compared to previous estimates (cumulative density function).
28

Figure 5. The social cost of nitrous oxide emissions. Red denotes the estimate with our 

base assumptions.
29

Figure 6. The global damage potential of nitrous oxide; for comparison, the global 

warming potential is shown as well (green line); top panel: with carbon dioxide 

fertilization; bottom panel: with no carbon dioxide fertilization.
30

Figure 7. Our estimate of the global damage potential of nitrous oxide (red dot) compared 

to previous estimates (cumulative density function).
31

Figure 8. The social costs of sulphurhexafluoride emissions. Red denotes the estimate 

with our base assumptions. 
32

Figure 9. The global damage potential of sulphurhexafluoride; for comparison the global 

warming potential is shown as well (green line); top panel: carbon dioxide fertilization; 

bottom panel: no carbon dioxide fertilization.
33

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