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Incremental CH4 and N2O mitigation benefits

consistent with the US Government's SC-CO2

estimates

Alex L. Martena, Elizabeth A. Kopitsa, Charles W. Griffithsa, Stephen C.

Newbolda & Ann Wolvertona

a

 National Center for Environmental Economics, US Environmental

Protection Agency, 1200 Pennsylvania Avenue, Washington, DC 20460, USA

Published online: 20 May 2014.

To cite this article: Alex L. Marten, Elizabeth A. Kopits, Charles W. Griffiths, Stephen C. Newbold & Ann

Wolverton (2014): Incremental CH4 and N2O mitigation benefits consistent with the US Government's SC-CO2

estimates, Climate Policy, DOI: 10.1080/14693062.2014.912981

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B research article

Incremental CH4 and N2O mitigation benefits

consistent with the US Government’s SC-CO2

estimates

ALEX L. MARTEN*, ELIZABETH A. KOPITS, CHARLES W. GRIFFITHS, STEPHEN C. NEWBOLD,

ANN WOLVERTON†

National Center for Environmental Economics, US Environmental Protection Agency, 1200 Pennsylvania Avenue, Washington, DC

20460, USA

Benefit–cost analysis can serve as an informative input into the policy-making process, but only to the degree it characterizes the

major impacts of the regulation under consideration. Recently, the US, amongst other nations, has begun to use estimates of the

social cost of CO2 (SC-CO2) to develop analyses that more fully capture the climate change impacts of GHG abatement. The SCCO2 represents the aggregate willingness to pay to avoid the damages associated with an additional tonne of CO2 emissions. In

comparison, the social costs of non-CO2 GHGs have received little attention from researchers and policy analysts, despite their

non-negligible climate impact. This article addresses this issue by developing a set of social cost estimates for two highly

prevalent non-CO2 GHGs, methane and nitrous oxide. By extending existing integrated assessment models, it is possible to

develop a set of social cost estimates for these gases that are consistent with the SC-CO2 estimates currently in use by the US

federal government.

Policy relevance

Within the benefit–cost analyses that inform the design of major regulations, all Federal agencies within the US Government

(USG) use a set of agreed upon SC-CO2 estimates to value the impact of CO2 emissions changes. However, the value of changes

in non-CO2 GHG emissions has not been included in USG policy analysis to date. This article addresses that omission by

developing a set of social cost estimates for two highly prevalent non-CO2 GHGs, methane and nitrous oxide. These new estimates are designed to be compatible with the USG SC-CO2 estimates currently in use and may therefore be directly applied to

value emissions changes for these non-CO2 gases within the benefit–cost analyses used to evaluate future policies.

Keywords: integrated assessment; non-CO2 GHGs; social cost of carbon

1. Introduction

The social cost of CO2 (SC-CO2) is a measure of the monetary value of the damages occurring both

within and outside economic markets as the result of an additional unit of CO2 emissions. Specifically,

it represents society’s aggregate willingness to pay to prevent future impacts that occur when one

additional unit of CO2 is emitted into the atmosphere in a particular year. Estimates of SC-CO2

B *Corresponding author. E-mail: marten.alex@epa.gov †

The views expressed in this article are those of the authors and do not necessarily reflect the views or policies of the US

Environmental Protection Agency.

http://dx.doi.org/10.1080/14693062.2014.912981

This work was authored as part of the Contributor’s official duties as an Employee of the United States Government and is

therefore a work of the United States Government. In accordance with 17 USC. 105, no copyright protection is available

for such works under US Law.

Downloaded by [US EPA Library] at 06:29 22 May 2014 
therefore provide a way to value changes in CO2 emissions in benefit –cost analyses (BCAs) of policy

alternatives. Without an estimate of the SC-CO2, the benefits of mitigating the climate change

impacts from CO2 emissions would implicitly be valued at zero in BCAs, thereby significantly weakening the information provided by such analyses. Since 2009, the US Federal Government (USG) has used

a set of agreed-upon SC-CO2 estimates in the BCAs used to evaluate major regulations that impact CO2

emissions (USG, 2010), including over 30 regulatory actions to date. The USG SC-CO2 estimates are also

increasingly being used in analysis and discussions outside the USG (e.g. by states, regional organizations, other nations, international organizations, NGOs, and academic researchers)1 and have even

figured in several recent public hearings and court cases (e.g. Keohane, 2010a, 2010b).

Although CO2 is the primary anthropogenic GHG, other GHGs such as methane (CH4), nitrous

oxide (N2O), hydrofluorocarbons (HFCs), perfluorocarbons (PFCs), and sulfur hexafluoride (SF6) are

also important contributors to climate change. The combined effect of all GHGs accumulated in the

atmosphere is to increase the Earth’s radiative forcing, which is the amount of energy from the Sun

that is trapped in the Earth’s atmosphere and therefore acts to warm the planet and change the

climate. In 2011, the atmospheric CO2 concentration contributed 64% of overall radiative forcing,

while CH4 and N2O accounted for approximately 23% (Myhre et al., 2013). Non-CO2 GHGs, notably

CH4 and N2O, therefore contribute significantly to the negative impacts on human well-being from

climate change. Furthermore, several recent studies have shown that consideration of non-CO2

GHGs, particularly CH4 and N2O, is important for the design of cost-effective climate policy (Reilly

et al., 1999; Tol, Heintz, & Lammers, 2003; Weyant, De La Chesnaye, & Blenford, 2006).

The monetary value of changes in emissions of non-CO2 GHGs has not been included in USG policy

analysis to date. This shortcoming prevents the development of accurate and comprehensive assessments of potential regulatory alternatives by the USG and others that rely on the USG SC-CO2 estimates (Kopp & Mignone 2012; Marten & Newbold, 2012). For example, fossil fuels (e.g. coal and

natural gas) have different compositions of GHG emissions across gases when considering the entire

process of extraction, production, transmission, and combustion. Thus, if a regulation is anticipated

to cause an industry to substitute between fuels, analysts may be providing inadequate information

to decision makers and the public about its benefits if only the welfare implications of direct CO2 emissions are considered while ignoring changes in CH4 and other GHG emissions (Alvarez, Pacala, Winebrake, Chameides, & Hamburg, 2011).

A key reason for the value of non-CO2 GHG emissions impacts not being included in USG analyses so

far is that existing estimates of the social cost of non-CO2 GHGs presented in the literature are inconsistent with USG SC-CO2 modelling assumptions. For example, the recent US Environmental Protection Agency BCA of new pollution standards for the oil and natural gas industry concluded that,

because they are not consistent with the USG SC-CO2, ‘the methane climate benefit estimates available

in the current literature are not acceptable to use to value the methane reductions finalized in this rulemaking’ (US EPA, 2012). This article seeks to address that gap by developing a new set of social cost estimates for CH4 and N2O (SC-CH4 and SC-N2O, respectively) that are fully consistent with the modelling

assumptions underlying the current USG SC-CO2 estimates. This article also develops an approach to

extending the models used by the USG to generate estimates of the social cost of additional GHGs that

are consistent with the latest USG estimates of the SC-CO2.

It is important to note at the outset that by restricting attention to the derivation of social cost estimates consistent with the USG SC-CO2 estimates, any limitations that apply to inputs and modelling

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assumptions underlying the USG SC-CO2 estimates (e.g. Arrow et al., 2013; Kopp & Mignone 2012;

Marten, 2011; O’Neil, 2010; Warren, Mastrandrea, Hope, & Hof, 2010) also apply to the SC-CH4 and

SC-N2O estimates derived here. Thus, while it is anticipated that the USG will continue to improve

the models and data it uses to estimate the SC-CO2, this article focuses on the more immediate task

of developing a set of consistent estimates for the social cost of other GHG emissions so that they

need not be implicitly assigned a value of zero in USG policy analyses.

The remainder of the article is organized as follows. Section 2 presents an overview of the USG SCCO2 estimation approach and how it compares to the existing literature on the social cost of non-CO2

GHGs, including a discussion of some of the critiques of the approach. Section 3 presents the approach

for estimating the SC-CH4 and SC-N2O in a manner consistent with the USG SC-CO2 estimates. Section

4 presents the results and a comparison of the relative social costs to the previous literature and the

global warming potential (GWP)-based metric that is often used as an approximation in the absence

of direct estimates, and Section 5 provides concluding remarks.

2. Background

In 2009 –2010 the USG formed an interagency working group to develop a set of SC-CO2 estimates for

use by all Executive Branch agencies to value marginal changes in CO2 emissions in regulatory impact

analyses (USG, 2010). The goal of this exercise was to improve the accuracy and consistency with which

agencies value marginal changes in CO2 emissions. Before the release of these estimates, CO2 emissions

changes were valued in some but not all regulatory analyses, and the SC-CO2 estimates used by different agencies varied substantially. The USG recently updated their estimates for the SC-CO2 by employing new versions of the three underlying integrated assessment models (IAMs), but leaving the original

estimation approach and underlying assumptions unchanged (USG, 2013). This section provides a

brief overview of the estimation approach and assumptions used by the USG for estimating SC-CO2,

describes some critiques of the approach by other researchers, and discusses the existing literature

on the social cost of non-CO2 GHGs.

2.1. USG SC-CO2 estimation approach

To estimate the SC-CO2 the USG used three IAMs that couple simplified models of atmospheric gas

cycles and climate systems with highly aggregate models of the global economy and human behaviour

to capture the effects that GHG emissions, through their effect on the climate, have on human welfare.

Within IAMs, the modelling that guides the transition from emissions into climate impacts is based on

scientific assessments, while the mapping of climate impacts into changes in human welfare is based

on economic research that has studied the effect of climate on various market and non-market sectors.

Nordhaus and Boyer (2000) provide a very informative and detailed description of how such models are

developed.2

The three models used by the USG are those that feature most prominently in the published social

cost of carbon literature: the Dynamic Integrated Climate and Economy (DICE) (Nordhaus, 2008;

Nordhaus & Boyer, 2000), the Policy Analysis of the Greenhouse Effect (PAGE) (Hope, 2006b,

2008), and the Climate Framework for Uncertainty, Negotiation, and Distribution (FUND)

(Anthoff, Hepburn, & Tol, 2009; Tol, 2002a, 2002b, 2009) models. The USG chose to use the IAMs’

Social cost of CH4 & N2O consistent w/ US SC-CO2 3

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climate system submodels and the functions that map climate change into economic damages as

implemented by the model developers, but adopted a common set of input assumptions for equilibrium climate sensitivity, discount rates, global population, economic output, and GHG emissions

projections. The remainder of this section provides a brief description of these common assumptions

and the steps used to calculate the SC-CO2 estimates. Interested readers can find more details in the

USG’s 2010 technical support document (USG, 2010).

2.1.1. Reference socio-economic-emissions scenarios

The USG selected five scenarios of economic output, population, and GHG emissions projections using

results from the 2009 Stanford Energy Modeling Forum exercise number 22 (EMF-22). Four of the scenarios are based on baseline runs from global economic models (MERGE, MESSAGE, MiniCAM, and

IMAGE) and span a range of emissions projections and plausible outcomes for future population

and economic output absent significant global action to address climate change. These scenarios

allowed for internally consistent forecasts of economic output, population, and emissions for the

years 2000 –2100. The fifth scenario used by the USG is based on the average of the 550 ppm CO2e

stabilization runs for each of the four models from which baseline scenarios were selected to represent

potential action by the rest of the world absent US action. Across the five scenarios, atmospheric CO2

concentrations in 2100 ranged from approximately 450 to 890 ppm (550 –1130 ppm in CO2e). Over

the time horizon, the forecasts of the average growth rate for global per capita economic output

ranged from 1.5% to 2.0% per year, and the average global population growth rate ranged from

0.4% to 0.5% per year. To run the IAMs through the year 2300, the USG extrapolated the selected

EMF scenarios using the following assumptions: starting in 2100 the population growth rate declines

linearly to zero in 2200; starting in 2100 the growth rate of economic output per capita declines linearly

to zero in 2300; for all years after 2100 the growth rate of the carbon intensity of the global economy

(CO2 emissions/economic output) remains constant at its 2090 –2100 average; starting in 2100 net

land-use CO2 emissions decline linearly to zero in 2200; and for all years beyond 2100 non-CO2 radiative forcing anomalies remain constant at their 2100 levels.

Several limitations of the simplifying assumptions underlying the USG approach to scenario development have been discussed by other researchers. O’Neil (2010) pointed out that the selected EMF

scenarios do not reflect the full range of outcomes that appear in other studies in the literature, and

Kopp and Mignone (2012) suggested that the selected scenarios may effectively over-sample the

peaks of the distributions. As for the extrapolations, while running the models out for multi-century

time horizons is not necessary for relatively short-lived GHGs like CH4, it is important for understanding the impacts of long lived GHGs such as CO2 and N2O that will affect human welfare well beyond

2100. As emphasized by O’Neil (2010) and Kopp and Mignone (2012), the state of the world beyond

2100 is highly uncertain and the scenario extrapolation approach taken by the USG represents only

one of many possibilities. Furthermore, the extrapolations for each component of the scenarios (economic output, population, emissions) are separate and nothing ensures internal consistency within the

scenarios past 2100. As shown by Marten and Newbold (2012), the temporal decomposition of

damages for a perturbation of CO2 and N2O are relatively similar in shape and therefore the general

findings of studies that explore the sensitivity of the SC-CO2 to these assumptions should also be applicable to the SC-N2O.

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2.1.2. Equilibrium climate sensitivity

In reduced-form IAMs, the speed and magnitude of temperature change for a given emissions projection are influenced largely by the ‘equilibrium climate sensitivity’ (ECS) parameter. The ECS represents

the long-term global average temperature response to a level of radiative forcing associated with a sustained doubling of atmospheric CO2 concentration (around 550 ppm). To represent the uncertainty in

the responsiveness of the climate system to changing atmospheric conditions, the USG used a probability distribution for the ECS parameter of the form suggested by Roe and Baker (2007). The USG calibrated the parameters of the probability distribution to have a median equal to 3 8C, two-thirds

probability that the ECS lies between 2 and 4.5 8C, which was intended to be consistent with the UN

Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) consensus statement about the ECS (Meehl et al., 2007). The distribution was truncated from above at 10 8C. This specification of the ECS distribution is retained to maintain consistency with the USG estimates of the SCCO2, but it is noted that the recently released AR5 by the IPCC has revisited the equilibrium climate

sensitivity and revised the range downwards to 1.5 –4.5 8C and no longer provides a most likely

value (Collins et al., 2013). The ultimate effect of updating the ECS distribution to be consistent

with the IPCC AR5 findings will depend heavily on the central tendency selected for the distribution.

2.1.3. Discount rates

Because the damages from an additional tonne of CO2 emissions occur over many decades, the discount rate, which reflects the tradeoff between present and future consumption, plays a critical role

in estimating the SC-CO2. In light of disagreement in the literature regarding the appropriate discount

rate to use in this context and uncertainty about future conditions that impact the discount rate, the

USG used three constant discount rates intended to span a plausible range: 2.5%, 3%, and 5% per year.

It is worth noting that the debate regarding not only the appropriate discount rate but also its time path

is ongoing (Arrow et al., 2013; Dasgupta, 2008). While the appropriate value for the discount rate will

presumably remain an area of active debate for some time to come, there appears to be agreement that

the use of a constant discount rate over long time horizons with uncertain changes in the consumption

per capita growth is not theoretically consistent. This article uses the same three constant discount

rates as the USG estimation process, but in Appendix C results are reported from a series of sensitivity

analyses using a Ramsey discounting approach. Similar to Marten and Newbold (2012), it is found that

applying Ramsey discounting using plausible values for the components of the consumption discount

rate gives a range of social cost estimates that is broadly consistent with the range of results obtained

using the constant discount rates.

2.1.4. Calculating the SC-CO2

The process to estimate the SC-CO2 for emissions in year t has four steps. First, each model is used to

forecast monetized impacts associated with the baseline path of emissions, economic output, and

population. Second, each model is re-run with an additional unit of CO2 emissions in year t to forecast

monetized impacts for all years beyond t along this perturbed path of emissions. Third, the marginal

damages in each year are calculated as the difference between the monetized impacts forecast in

steps 1 and 2. Finally, the resulting path of marginal damages is discounted and summed to calculate

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the present value of the marginal damages in the year when the additional unit of emissions used to

perturb the model is emitted.

The USG repeated this process with each model, discount rate, and socio-economic-emissions scenario for each decade between 2010 and 2050. Because the ECS parameter is modelled probabilistically,

and because PAGE and FUND incorporate uncertainty in other model parameters, the final output from

each model run represents a distribution over the SC-CO2 in each year. These distributions were estimated using 10,000 simulations in each model run. Therefore, the exercise produced 45 separate distributions of the SC-CO2 for a given emissions year, based on the three models, three discount rates,

and five socio-economic-emissions scenarios considered. To provide a range of estimates that reflects

this uncertainty but still emphasizes the central tendency, the distributions from each of the models

and scenarios were equally weighted and combined to produce three separate probability distributions

for the SC-CO2 in a given year, one for each assumed discount rate. Four SC-CO2 estimates were selected

from these three probability distributions to reflect the global damages caused by one tonne of CO2

emissions. Three estimates are based on the average SC-CO2 across the three models and five socioeconomic-emissions scenarios for the 5%, 3%, and 2.5% discount rates, respectively. The fourth

value is the 95th percentile of the SC-CO2 distribution at the 3% discount rate, and was chosen to represent potential higher-than-expected impacts from anthropogenic GHG emissions.

2.2. Existing estimates of the social cost of non-CO2 GHG emissions

A significant limitation of the aforementioned USG interagency process is that the social costs of nonCO2 GHG emissions were not estimated. Therefore, as an alternative to applying direct estimates for

the social costs of non-CO2 GHG emissions in the primary BCA, several recent USG regulatory analyses

have approximated the benefits of non-CO2 GHG emissions reductions in sensitivity analyses by transforming the non-CO2 GHG emissions to ‘CO2-equivalents’ using estimates of the GWP for the GHG in

question and then using the USG SC-CO2 for valuation (e.g. US EPA, 2012, 2013).

Gas comparison metrics, such as the GWP, have been designed to measure the impact of different

GHGs relative to CO2, where the point of comparison along the pathway from emissions to monetized

damages (depicted in Figure 1) may differ across measures. The GWP, in particular, is designed to

measure the additional radiative forcing (i.e. the amount of energy absorbed by atmospheric concentrations of GHGs) from a perturbation of a given GHG relative to a perturbation of CO2 over a specific

time horizon (e.g. 100 years). The GWP and other gas-comparison metrics are problematic as an SCCO2 scalar in BCA, as the remaining linkages in the pathway depicted in Figure 1 are complex and nonlinear. Marten and Newbold (2012) demonstrate that using the GWP to adjust SC-CO2 estimates to

capture the impact of non-CO2 gases provides a significant improvement over the implicit assumption

that they are zero when such benefits are left unquantified, but may still underestimate mitigation

benefits. Alternative gas comparison metrics that compare GHGs at different points in the chain of

Figure 1 Path from GHG emissions to monetized damages

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causation (e.g. global temperature change potential (Shine, Fuglestvedt, Hailemariam, & Stuber, 2005),

peak commitment temperature (Smith et al., 2012), temperature proxy index (Tanaka, O’Neill, Rokityanskiy, Obersteiner, & Tol, 2009)) have also been shown to be imperfect substitutes for direct

estimates.

Several researchers have directly estimated the social cost of non-CO2 GHG emissions using IAMs,

although the number of such estimates is small compared to the large number of SC-CO2 estimates

available in the literature. Among these previous direct estimates there is considerable variation in

the model versions and input assumptions used. See Table 1 for a summary of the 11 non-CO2

studies published to date.

As shown in Table 1, the estimates cover emissions years from 1990 to 2050, although the specific

perturbation year is not stated in all studies. The studies also cover a wide range of constant and variable

discount rate specifications and consider a range of baseline socio-economic and emissions scenarios

that have been developed over the last 20 years. Finally, some studies in the literature have chosen

not to report the social cost estimates directly. Instead, they opt to report only the ‘global damage

potential’, which is a ratio of the social cost of gas X to the SC-CO2. Normalizing the SC-CH4 or

TABLE 1 Previous estimates of the social cost of CH4 and N2O emissions

Study Model

Time

horizon Discount rate

Emissions

year Scenarioa Climate sensitivity

Reilly and Richards

(1993)

N/A 140 years 2, 5, 8% 1990 N/A N/A

Fankhauser (1994) N/A 230 years Ramsey 1991–2030 IS92b N/A

Kandlikar (1995) N/A 100 years 0, 2, 6% N/A IS90a,d 3 8C

Kandlikar (1996) N/A 100 years 0, 2, 6% N/A IS90a,d 3 8C

Hammitt et al.

(1996)

N/A 2200 1, 3, 5% 1995–2015 IS92a,c,e 1.5, 2,5, 4.5 8C

Tol (1999) FUND 1.6 2100 0, 1, 3, 5, 10% 1995–2014 IS92a 2.5 8C

Tol et al. (2003) FUND 1.7 2200 0, 1, 3, 5, 10% 1995–2014 IS92a 2.5 8C

Hope (2005) PAGE95 2200 Ramsey 2000 SRES A2 Probabilistic, mode

of 3 8C

Hope (2006a) PAGE2002 2200 Ramsey 2001 SRES A2 Probabilistic, mean

of 3 8C

Waldhoff et al.

(2011)

FUND 3.5 3000 Ramsey 2010–2019 FUND, SRES A1B,

A2, B1, B2

2, 3, 4.5 8C

Marten and

Newbold (2012)

DICE2007 w/

MAGICC

2300 Ramsey, 2.5,

3, 5%

2010–2050 EMF-22 MiniCAM

Base

Probabilistic, median

of 3 8C

a

IS90 scenarios are based on the IPCC First Assessment Report (IPCC, 1990); IS92 scenarios are based on the IPCC Supplementary Report (IPCC,

1992); SRES scenarios are based on the IPCC Special Report on Emissions (IPCC, 2000); the FUND scenario is the default scenario in the FUND

model; EMF-22 scenarios are based on results from Stanford’s Energy Modeling Forum’s 22nd exercise (Clarke et al., 2009).b

The particular IS92

scenario used was not specified.

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SC-N2O estimate using the SC-CO2, in part, controls for differences in the modelling to allow for a

better comparison with other estimates in the literature.

Fankhauser (1994) was one of the first to develop estimates of the average SC-CH4 and SC-N2O for

emissions in the 2010 and 2020 decades given a 100-year time horizon for climate change damages.

Kandlikar (1995) and Hammitt, Jain, Adams, and Wuebbles (1996) also developed estimates of SCCH4 and SC-N2O for a single socio-economic-emissions scenario and using constant discount rates.

Tol et al. (2003) and Hope (2005, 2006a) developed estimates for the SC-CH4 in 2000 using the

FUND and PAGE models, respectively. Waldhoff, Anthoff, Rose, and Tol (2011) used a newer version

of the FUND model to develop estimates of the social cost of marginal CO2, CH4, N2O, and SF6 emissions for the average year in the 2010 decade. While they considered only a single emissions period,

they conducted a wide range of sensitivity analyses including four socio-economic-emissions scenarios

from the IPCC special report on emissions (IPCC, 2000) in addition to the default FUND scenario. In

Section 4, the specific results of these previous studies are discussed with a comparison to the estimates

obtained in the present study.

The above-mentioned previous studies provide a basic understanding of the relative social costs of

different GHGs but do not provide sufficient information about how this relationship changes over

time. Marten and Newbold (2012) used an IAM that couples the climate model MAGICC (Model for

the Assessment of Greenhouse-gas Induced Climate Change) with economic components of the

2007 version of William Nordhaus’ DICE model to directly estimate the social cost of marginal CO2,

CH4, and N2O emissions. They estimated the annual social costs for the years 2010 –2050 along a

single socio-economic-emissions pathway given uncertainty about the equilibrium climate sensitivity

parameter. An advantage of their approach is that through the use of a more detailed, yet still relatively

simple, climate model their results are not affected by over-simplification of temperature response or

atmospheric chemistry, which have been shown to have non-negligible effects on the estimates of

social costs (Marten, 2011; Warren et al., 2010).

The work of Marten and Newbold (2012) uses many of the assumptions used by the USG in its estimation of SC-CO2, including discount rates, the equilibrium climate sensitivity distribution, and post2100 socio-economic and emissions extrapolations. However, they focus on only one of the three

models and one of the five socio-economic-emissions scenarios used by the USG. Furthermore, they

use a different climate sub-model, which leads their estimate of the SC-CO2 to be different from the

USG estimate, even for the same IAM and scenario combination. Therefore, although these studies,

including Marten and Newbold (2012), have increased our understanding about the relative social

costs of GHG emissions, they have not provided a set of estimates that are entirely consistent with

the USG SC-CO2 estimates. In Section 4, the estimates derived in this article are compared with

those of Marten and Newbold (2012) to more clearly demonstrate the similarities and differences in

the two sets of estimates for SC-CH4 and SC-N2O.

3. Estimating the social cost of non-CO2 GHGs consistent with USG SC-CO2

The primary obstacle in estimating the social cost of non-CO2 GHG emissions in a manner consistent

with the USG SC-CO2 estimates is that not all of the IAMs used include explicit representations of the

non-CO2 gases of interest. This section describes the degree to which non-CO2 GHGs are currently

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represented in the default versions of DICE, PAGE, and FUND, and then discusses how they are

amended to estimate the social cost of these gases.

3.1. Representation of non-CO2 GHGs in DICE, PAGE, and FUND

The FUND model explicitly considers CH4, N2O, and SF6 in addition to CO2. The model uses one-box

atmospheric gas cycle models for these gases, with geometric decay towards pre-industrial levels. For

CH4 and N2O, FUND estimates the additional radiative forcing imposed by the atmospheric buildup

of these gases using the simplified expressions presented in Chapter 6 of the IPCC’s Third Assessment

Report (TAR) (Ramaswamy et al., 2001). FUND also augments the TAR expression for the additional

radiative forcing from CH4 to account for the influences of stratospheric water vapour and tropospheric

ozone changes. Because FUND uses CH4 and N2O emissions as inputs and internally computes their

impact on the climate system, it is possible to directly estimate the social cost of those gases without

modifying the model.

In the DICE model, the only GHG that is explicitly represented is CO2; an exogenous radiative

forcing projection is used to account for the impact of all other gases on the climate. To develop an

exogenous radiative forcing pathway consistent with the emissions scenarios used to estimate the

SC-CO2, the USG decomposed the default DICE exogenous radiative forcing vector into CH4, N2O,

F-gases, aerosols, and other residual forcing components. The USG then replaced the radiative

forcing attributed to CH4, N2O, and F-gases with estimates associated with the EMF-22 scenarios. As

non-CO2 emissions are not a direct input into DICE, it is not possible to simply perturb the emissions

projection and re-run the model to obtain a forecast of additional damages.

The 2002 version of the PAGE model, which was used by the USG in developing its first set of estimates (USG, 2010), includes an atmospheric model for CH4 and SF6, but represents the effects of

other non-CO2 GHGs in an exogenous radiative forcing projection. Presumably to simplify the

process and maintain consistency with DICE, the USG did not use PAGE’s internal CH4 component.

Instead, the same exogenous radiative forcing projection was used for the effect of CH4, N2O, and Fgas emissions as was used for DICE. Since then, a N2O component has been added to the PAGE

model, although in the recent 2013 SC-CO2 update the USG maintained the approach of using the

same single exogenous forcing projection as was applied to DICE (USG, 2013). Therefore PAGE, as

implemented by the USG, faces the same limitations as DICE with respect to estimating the social

costs of marginal non-CO2 emissions that are consistent with the USG SC-CO2 estimates. For these

reasons, computing estimates for the social cost of non-CO2 gases in DICE and PAGE requires either

replacing the climate component of these models with a more complete representation, as was done

with DICE by Marten and Newbold (2012), or deriving an estimate of the path of additional radiative

forcing that would result from a perturbation of the gas in question. This article uses the latter approach

for DICE and PAGE, as the former would represent a substantial change to the underlying IAMs and

would have implications for the SC-CO2 estimates, making this work inconsistent with the USG SCCO2 estimates currently used in regulatory analysis.

3.2. Estimating the social cost of non-CO2 GHGs in DICE and PAGE

The process used in this article to estimate the social cost of non-CO2 GHGs in DICE and PAGE as

implemented by the USG requires first generating a forecast of the additional radiative forcing

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associated with a perturbation of a non-CO2 gas’s emissions in a single year, and then adding this radiative forcing perturbation to each model’s exogenous radiative forcing projection. To determine the

additional radiative forcing associated with the emission perturbation, there is a need to model the

change in atmospheric concentration and the radiative forcing associated with the additional concentration. For both CH4 and N2O, a simple one-box atmospheric gas cycle model with a constant decay

rate is used to estimate the atmospheric concentration of each gas based on its assumed emissions. The

use of a one-box gas cycle for CH4 and N2O with constant decay follows the approach used by the IPCC

to compute GWPs (Forster et al., 2007) and the FUND model (Anthoff & Tol, 2013). In both the baseline

and the perturbed case, the contribution of the gas to the global radiative forcing anomaly is determined by the forcing relationships presented in the IPCC TAR (Ramaswamy et al., 2001), which

were not updated by the IPCC in AR4. The incremental radiative forcing is defined by the difference

between the baseline forcing path and the emissions path that includes a one tonne perturbation in

a given year. Next, the path of additional radiative forcing is added to the stream of exogenous radiative

forcing in each IAM to estimate the climate damages in the perturbed scenario. These damages are then

compared to the baseline damages to determine the social cost of gas X (SC-X). Specifically, the process

is as follows:

1. Run the IAM as described in the SC-CO2 technical support document (USG, 2010) to estimate baseline damages.

2. Estimate the baseline atmospheric concentration for gas X.

3. Estimate the baseline radiative forcing contribution of gas X.

4. Perturb the stream of gas X emissions by one tonne in year t.

5. Estimate atmospheric concentration for gas X in the perturbed scenario.

6. Estimate the radiative forcing contribution of gas X in the perturbed scenario.

7. Compute the incremental radiative forcing as the difference between the results of steps 3 and 6.

8. Add the additional radiative forcing from step 7 to the exogenous radiative forcing path used in the

IAM in step 1.

9. Re-run the IAM to compute the damages along the perturbed emissions path.

10. Compute the social cost of gas X for emission year t as the present value of the difference in

damages estimated in steps 1 and 9.

Two practical issues associated with implementation are worth noting. First, while the SC-X estimates are associated with a one tonne perturbation, to avoid computational rounding error a 1 Mt perturbation is used and then the resulting change in damages is scaled to get the average effect per tonne.

Experiments conducted by Griffiths et al. (2012) to assess the applicability of the SC-CO2 to non-marginal emission changes show that the average per tonne SC-CO2 estimate is relatively constant over

large differences in perturbation size. Additional experiments in the context of this article found

that alternative perturbation sizes do not significantly change the average one tonne social cost estimate. Second, the additional radiative forcing due to the emissions perturbation is computed based

on an annual time step, but because DICE and PAGE use longer time steps the average radiative

forcing over the time step is added to the model’s exogenous radiative forcing vectors.

The remainder of this section describes the procedure for modelling the incremental radiative

forcing of a perturbation for CH4 and N2O, and explores the sensitivity of these projections to

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two issues. First, it evaluates whether the simple one-box gas cycle model with a constant decay rate

produces a close approximation to the forecasts of future atmospheric CH4 and N2O concentrations

based on a more sophisticated climate model. Second, it explores the sensitivity of the results to the

method used for extrapolating non-CO2 emissions from 2100 to 2300. This is important, because

the USG did not specify a particular set of emissions pathways for each constituent gas, instead

assuming only that non-CO2 radiative forcing remains constant past 2100. Such a situation could

arise from a myriad of possible individual gas projections and the USG did not specify which it

was assuming.

3.3. Methane

A simple one-box atmospheric gas cycle model for methane specifies the concentration in year t, CCH4

t

[ppb], such that

CCH4

t = CCH4

t−1 + dCH4 (CCH4

pre − CCH4

t−1 ) + gCH4 ECH4t−1 , (1)

where dCH4 defines the rate of decay, CCH4

pre [ppb] is the pre-industrial atmospheric concentration, and

gCH4 [ppb/Mt] converts emissions, ECH4

t−1 [Mt], from mass to atmospheric volume. The mass to volume

conversion factor is gCH4 1⁄4 0.3597 ppb/Mt and CCH4

pre 1⁄4 700 ppb, following the IPCC TAR. The rate of

decay is set to dCH4 1⁄4 1/12 following the IPCC AR4 stated CH4 lifetime of 12 years. The iteration

begins in the year 2006 using the emissions from the EMF-22 scenario (linearly interpolated

between the decadal values reported), therefore requiring an assumption about the atmospheric concentration in 2005. The value from the Advanced Global Atmospheric Gases Experiment network as

reported in the IPCC AR4 is used so that CCH4

2005 1⁄4 1774 ppb.

The contribution of atmospheric methane to global radiative forcing, denoted QCH4

t , is defined using

the relationship in Table 6.2 of the IPCC TAR:

QCH4

t = f 0.036



CCH4

t



−



CCH4

pre   

− [f (CCH4

t , CN2O

pre ) − (CCH4

pre , CN2O

pre )]  , (2)

where CN2O

pre [ppb] is the pre-industrial atmospheric concentration of nitrous oxide and

f (CCH4 , CN2O) = 0.47 ln 1 + 2.01 × 10−5(CCH4CN2O)]0.75 + 5.31 × 10−15CCH4 (CCH4CN2O)

1.52  	. (3)

The function in expression (3) accounts for the overlapping absorption bands of CH4 and N2O,

thereby reducing their effective absorption. Parameter f is used to proxy for indirect effects of CH4

that include the enhancement of stratospheric water vapour and tropospheric ozone changes. Following the IPCC AR4, an enhancement effect of 40% (25% from tropospheric ozone change and 15% for

stratospheric water vapour enhancement) is used, such that f 1⁄4 1.4. The pre-industrial concentration

of N2O is set consistent with the IPCC TAR, such that CN2O

pre 1⁄4 270 ppb.

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A key simplification in this approach is the constant decay rate used in the atmospheric gas cycle

model. As discussed by IPCC Working Group I in Chapter 4 of the TAR, the lifetime of methane emissions in the atmosphere depends on temperature and the concentrations of CO, NOx, and other VOCs

in the atmosphere (Ehhalt et al., 2001). Sensitivity analysis is used to understand the potential implications of ignoring these interactions by comparing the incremental atmospheric concentration projected by the simple model described above to the analogous projection from the climate model

MAGICC,3 which, while still relatively simple, incorporates these interactions between the lifetime

of CH4 in the atmosphere and the other gases and climate variables. This exercise uses CH4 emissions

from the EMF-22 MiniCAM reference scenario and considers a one tonne perturbation of CH4 in 2015.

It is noted that these results are robust across alternative emissions levels.4

Figure 2(a) presents the projected average decadal increment to atmospheric concentrations using

both the simple one-box model with a constant decay rate and the MAGICC model with a variable

decay rate. At the time of the perturbation (2015), the inter-annual time step of MAGICC allows for

an uptake of the additional emissions into the atmosphere, whereas the strict annual time step of

the simple model causes a year to pass before the change is registered. After the initial year, the

models originally differ by around 15%. This difference falls to under 10% within the first decade,

with the faster effective growth in the simple model causing its additional concentration to eventually

fall below that of MAGICC.

The difference in the incremental radiative forcing from the perturbation between the simple model

and MAGICC is also of importance. Although MAGICC relies on similar equations to derive the radiative forcing of atmospheric CH4 concentrations, it differs in the way it handles indirect effects of CH4

on tropospheric ozone and stratospheric water vapour, in addition to including other temperaturerelated feedbacks. Figure 2(b) presents the average additional radiative forcing per decade attributed

to the 2015 CH4 perturbation in both models. The average increase in radiative forcing over the

decade is considered because this is the input required by DICE due to its ten-year time step and therefore a more relevant comparison (PAGE requires a similar multi-year average). When considering the

average additional radiative forcing over the decade, the initial difference in concentration between

MAGICC and the simple model has a minimal effect and the difference in radiative forcing between

the two models is less than 2% over the first two decades. However, this difference grows to –18%

over the subsequent two decades. This escalation in the difference is in part due to the use of a constant

decay rate in the simple model, whereas MAGICC takes into account the growing atmospheric concentrations of other gases and increasing atmospheric temperature, which increase the lifetime of atmospheric CH4.

To understand the effect that this difference would have on an estimate of the SC-CH4, an experiment was conducted using the DICE model in which the additional forcing from a one tonne perturbation of CH4, as computed using both the simple model and MAGICC, is added to the exogenous

forcing projection. As above, the MiniCAM scenario is used and the sensitivity of the results to both

perturbation year and discount rate is examined. Table 2 presents the results of this experiment. In

line with the results comparing the radiative forcing perturbations above, the two approaches

produce similar social cost estimates for emissions in 2015, where additional analysis has shown

these results to hold with PAGE as well. The impact of assuming a constant decay rate is greater

further out into the future, due to the projected increase in the atmospheric concentration of other relevant gases and atmospheric temperature that are accounted for in MAGICC, and the social cost

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estimates begin to diverge for later emissions years. For the same reason, the two approaches will show

greater differences for lower discount rates that give increased weight to future time periods. While

over-simplification of the climate system can, in some circumstances, have significant effects on

Figure 2 Effects of perturbation in 2015 CH4 emissions for simple model vs. MAGICC: (a) additional

atmospheric concentration; (b) additional radiative forcing

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social cost estimates (e.g. Marten 2011), the near-term differences based on this simplification seem

relatively small considering the precision of such social cost estimates.

3.4. Nitrous oxide

The simple one-box atmospheric gas cycle model for N2O takes a similar form to the model used for

CH4, such that the concentration of nitrous oxide in year t, CN2O

t [ppb], is specified as

CN2O

t = CN2O

t−1 + dN2O(CN2O

pre − CN2O

t−1 ) + gN2OEN2Ot−1 , (4)

where dN2O is the rate of decay, and gN2O [ppb N2O/Mt N] converts emissions, EN2O

t−1 [Mt N], from mass to

atmospheric volume. Following the IPCC AR4, the mass to volume conversion factor is gN2O 1⁄4

0.2079 ppb N2O/Mt N and the rate of decay is dN2O 1⁄4 1/114 based on a 114-year lifetime. As with

CH4, the iteration begins in the year 2006 using the emissions from the EMF-22 scenarios (linearly

interpolated between the decadal values reported), therefore requiring an assumption about the atmospheric concentration in 2005. The value from the Advanced Global Atmospheric Gases Experiment

network as reported in the IPCC AR4 is used, such that CN2O

2005 1⁄4 319 ppb.

The contribution of atmospheric N2O to global radiative forcing, denoted QN2O

t , is defined using the

relationship in Table 6.2 of the IPCC TAR, such that

QCH4

t = 0.12



CN2O

t



−



CN2O

pre   

− [f (CCH4

pre , CN2O

t ) − f (CCH4

pre , CN2O

pre )], (5)

where f (CCH4 , CN2O) is defined in expression (3).

As with CH4, a key simplifying assumption is the constant decay rate used in the simple gas cycle

model (and potentially the time it takes the gas to become well mixed within the atmosphere). As discussed in the IPCC TAR, the decay rate of N2O will depend on the atmospheric concentration of N2O

and so will not be constant in reality. To examine the extent to which this impacts the results of the

simple model, an analogous set of experiments as conducted for CH4 were performed. Given future

TABLE 2 Effect of CH4 gas cycle model on SC-CH4 (2007$ per tonne CH4): DICE2010, MiniCAM

Perturbation year Discount rate Simple model MAGICC Percent difference

2015 2.5% 1135 1183 2 4%

3.0% 822 851 2 3%

5.0% 349 354 2 2%

2045 2.5% 2490 2707 2 8%

3.0% 1933 2084 2 7%

5.0% 956 1006 2 5%

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N2O emissions based on the EMF-22 MiniCAM reference scenario, a one tonne N2O perturbation in

2015 is considered. Figure 3(a) shows the projected atmospheric concentration increase from the perturbation using the simple one-box model with a constant decay rate and the MAGICC model with a

variable decay rate. This comparison illustrates that the simple model tracks the output of MAGICC

well for the entire 300-year time horizon. Outside the initial perturbation year, the two projections

do not differ by more than 2% within the first century, with the largest difference occurring in the perturbation year, for the same reasons as with CH4.

Figure 3(b) presents the estimates of average additional radiative forcing per decade as a result of the

N2O perturbation using both models. The additional radiative forcing from the N2O perturbation in

the one-box model is forecast to be slightly lower (7%) in the first decade compared to MAGICC. Subsequently, the difference is within 2% through to 2300.

As with CH4, to assess the effect that this difference would have on the SC-N2O, an experiment was

conducted using the DICE model in which the additional forcing from a one tonne perturbation of

N2O computed using both the simple model and MAGICC is added to the exogenous forcing projection. As before, the MiniCAM scenario is used and the sensitivity of the results to both perturbation

year and discount rate is examined. Table 3 presents the results of this experiment. As the comparisons

of the projected radiative forcing perturbations would suggest, the difference between the social cost

estimates for the two approaches is relatively small. In contrast to the case of CH4, here an increase

in the discount rate increases rather than decreases the divergence between the estimates due to the

greater weight being placed on the earlier years when the radiative forcing perturbations have a slightly

higher degree of divergence.

3.5. Effect of post-2100 non-CO2 radiative forcing assumptions

The EMF-22 socio-economic-emissions scenarios used by the USG include years only up to 2100, while

the USG ran the IAMs out to 2300. Therefore, additional assumptions were required to extrapolate the

scenarios beyond 2100. For the purposes of this study, the most important of these assumptions is that

non-CO2 radiative forcing will remain constant at its 2100 level until 2300. Such a broad assumption

was sufficient for the purposes of the USG in estimating the SC-CO2. However, estimating the social

cost of non-CO2 GHGs requires explicit projections of baseline emissions of non-CO2 gases in order

to correctly determine the effect of the perturbation. The USG’s broad assumption regarding the extrapolation of non-CO2 gases is therefore problematic as constant non-CO2 radiative forcing post 2100

may occur in an infinite number of ways. For instance, one way to achieve this outcome is to

assume that emissions of each non-CO2 gas falls to a level equal to its respective rate of decay in

2100. This assumption would keep atmospheric concentrations, and in turn radiative forcing, constant. Based on the simple gas cycle models laid out in the earlier sections this implies that, for gas X,

EX

t = −dX(CX

pre − CX

2100)

gX

∀t . 2100. (6)

To put this assumption into context, the solid lines in Figure 4(a) and (b) present the emissions paths

for CH4 and N2O, respectively, under the MiniCAM EMF-22 reference scenario extrapolated using

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Figure 3 Effects of perturbation in 2015 N2O emissions for simple model vs. MAGICC: (a) additional

atmospheric concentration; (b) additional radiative forcing

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expression (6), while the dashed lines show two alternative extrapolation approaches, one where emissions are held constant at their 2100 level and one that assumes emissions intensity (emissions/economic output) continues to decline at the same rate forecast by the EMF-22 scenario in 2090 –2100

(dotted line). This latter alternative is analogous to the USG assumption regarding industrial CO2 emissions. The two alternatives will not result in the radiative forcing contribution of gas X remaining constant post-2100, but do not in themselves violate the assumption that overall non-CO2 radiative

forcing remains constant. Noteworthy is the fact that the assumption in (6) is almost analogous to

keeping CH4 emissions constant at their 2100 levels, whereas for N2O the assumption requires a

sudden decrease in emissions of over 35%.

While Figure 4 illustrates that these three extrapolation approaches can lead to vastly different projections for emissions after 2100, the relevant comparison is how these assumptions affect the

additional radiative forcing from a perturbation of the gas and in turn the SC-X estimates. Figure

5(a –d) present the additional radiative forcing resulting from a one tonne perturbation based on the

simple model presented in Sections 3.1 and 3.2. Figure 5(a) and (b) demonstrates the difference for a

perturbation in 2015, whereas Figure 5(c) and (d) represents perturbations in 2045. For CH4, the cumulative radiative forcing from the projection over the time horizon differs by less than 0.001%, even for a

Figure 4 EMF-22 MiniCAM extended emissions scenario: (a) CH4 emissions; (b) N2O emissions

TABLE 3 Effect of climate model on SC-N2O (2007$ per tonne N2O): DICE2010, MiniCAM

Perturbation year Discount rate Simple model MAGICC Percent difference

2015 2.5% 19,689 19,819 2 1%

3.0% 12,390 12,525 2 1%

5.0% 3,346 3,419 2 2%

2045 2.5% 36,968 37,358 2 1%

3.0% 25,030 25,427 2 2%

5.0% 8,280 8,528 2 3%

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perturbation in 2045. Accordingly, the relevant annual difference is smaller even than one-thousandth

of a percent. This result occurs because of the short atmospheric lifetime of the gas, which renders

assumptions regarding CH4 emissions after 2100 unimportant for near-term perturbations. Post2100 emissions will have a larger effect in the case of N2O, which has a much longer atmospheric residence time. However, even for a perturbation in 2045, the difference in cumulative additional radiative

forcing is less than 2.5% across the extrapolation assumptions.

To examine the impact of these assumptions on SC-CH4 and SC-N2O, an experiment was conducted

using the DICE model based on the EMF-22 MiniCAM socio-economic-emissions scenario. The results

of this experiment are presented in Table 4 for the perturbation year 2045 (noting that the extrapolation method will have greater impact on future emissions years). As may be seen, the relatively

short atmospheric lifetime of CH4 leads to a situation in which post-2100 assumptions do not affect

SC-CH4 estimates, even in 2045. For the longer-lived gas N2O, in emission year 2045, where the

effect of the post-2100 extrapolation approach would be largest, the difference across the three

Figure 5 Effect of extrapolation approach on radiative forcing perturbation from simple model: (a)

CH4 perturbation in 2015; (b) N2O perturbation in 2015; (c) CH4 perturbation in 2045; (d) N2O perturbation in 2045

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assumptions is less than 1% and the projections are equivalent to two significant digits. Therefore, in

the remainder of this article, non-CO2 emissions are extrapolated past 2100 using expression (6) to

ensure that the gas-specific contribution to overall radiative forcing remains constant in the simple

model. While additional study may lead to improvements of long-term forecasts of CH4 and N2O emissions and possible correlations, compared to the paths in Figure 5(a), the very minimal effect of such

assumptions on the social cost estimates suggests the impact of such efforts would be minimal in this

context.

4. Results

For FUND, the social cost of non-CO2 GHGs is estimated by perturbing the paths of emissions directly,

while for DICE and PAGE the approach presented in Section 3 is used. In both cases, all additional

assumptions made by the USG are applied, including the five EMF-22 socio-economic-emissions scenarios, the Roe and Baker (2007) distribution for the equilibrium climate sensitivity, and constant discount rates of 2.5%, 3.0%, and 5.0%. Following the USG, the estimates for the expected social cost

are averaged across scenarios and models, with each model and scenario given equal weight. Estimates

are not combined across discount rates, and a fourth estimate is included representing the 95th percentile when using the 3.0% discount rate. By using the same assumptions and procedures as the USG, estimates of the SC-CO2 derived in this article are identical to the values used in US Federal rule making.

Specifically, these estimates are equivalent to the recent 2013 update of the USG SC-CO2, which revised

the original 2010 USG upwards based on new versions of the IAMs used. The non-CO2 results, as well as

the USG SC-CO2 estimates, are presented in Table 5 for emissions years 2020 and 2050.5 Results for

additional years, and the results of sensitivity analyses using Ramsey discounting, may be found in

Appendix B and C, respectively.

As expected, considering their higher radiative efficacy, the social costs associated with a tonne of

CH4 and N2O emissions are substantially higher than for CO2. The values are higher at lower discount

rates, although the impact of the discount rate is lower for CH4 given its relatively short lifetime.

Similar to CO2, the social cost estimates for CH4 and N2O increase over time as the climate and economic systems become more stressed, although the growth rate of the social cost estimate may differ

between the gases, as discussed in the following.

TABLE 4 Effect of post-2100 extrapolation on the 2045 SC-X (2007$ per tonne): DICE2010, MiniCAM

Gas Discount rate Constant RF Constant emissions Constant emissions intensity growth

CH4 2.5% 2,490 2,490 2,490

3.0% 1,933 1,933 1,933

5.0% 956 956 956

N2O 2.5% 36,968 36,588 36,662

3.0% 25,030 24,837 24,868

5.0% 8,280 8,261 8,263

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To better understand how the social costs of CH4 and N2O compare to CO2, Table 6 presents the

global damage potentials corresponding to the social cost estimates from Table 5. (The disaggregated

results, by model and scenario, for 2020 are provided in Appendix B.) As explained in Section 2, the

global damage potential for gas X is the ratio of SC-X to SC-CO2, and therefore by construction captures

all the important linkages between emissions and monetized climate change damages (to the degree

they are captured by the IAMs) directly within the gas comparison metric. As noted by Frankhauser

(1994), this is preferred to the commonly used GWP gas comparison metric, which only measures

the additional radiative forcing from a perturbation of a given GHG relative to a perturbation of

CO2 over a specific time horizon (e.g. 100 years) and ignores important nonlinear relationships

beyond radiative forcing in the chain between emissions and damages.

The global damage potential of CH4 decreases with the discount rate due to the relatively shorter

atmospheric lifetime. This difference in atmospheric lifetime leads to a situation where lowering the

discount rate has a greater impact on the SC-CO2 than the SC-CH4. This finding is robust across the

models. The estimates in Table 6 also present the same result for N2O in the aggregate case, although

this characteristic is not consistent across the models or the previous literature. Based on the disaggregated results (presented in Appendix B), the results from the DICE model suggests the global damage

potential for N2O increases with lower discount rates due to a lower effective decay rate over the relevant time horizon for N2O than CO2. This result is consistent with previous findings by Marten

and Newbold (2012). However, for FUND the opposite is seen to hold. Waldhoff et al. (2011) show

that this result is primarily due to the inclusion of increased production in the agriculture and forestry

sectors from CO2 fertilization effects. At lower discount rates these benefits place a greater downward

TABLE 5 SC-X (2007$ per tonne)

Year Gas 5.0% mean 3.0% mean 2.5% mean 3% 95th percentile

2020 CO2 12 43 64 128

CH4 550 1,200 1,600 3,200

N2O 4,800 15,000 22,000 41,000

2050 CO2 26 71 97 220

CH4 1,400 2,500 3,100 6,900

N2O 11,000 27,000 38,000 74,000

TABLE 6 Global damage potential

Year Gas 5.0% mean 3.0% mean 2.5% mean 3% 95th percentile

2020 CH4 46 29 25 25

N2O 397 359 353 317

2050 CH4 52 36 32 31

N2O 414 388 387 338

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impact on the SC-CO2, thereby lowering the global damage potential. If one were to remove those

impacts from the FUND model the global damage potential for N2O becomes relatively insensitive

to the discount rate. One would expect the role of the discount rate in determining the global

damage potential in PAGE to be the same as in DICE, but the results suggest that this is not the case.

It seems most likely that this is because the PAGE model has only ten time steps to cover the entire

time horizon, which results in very large, up to 100-year, time steps further out in time. As noted in

Section 3, the additional radiative forcing from the N2O perturbation is implemented as the average

across the model’s time steps. It seems that PAGE does not average radiative forcing over the time

step for CO2, which causes the global damage potential for N2O to decrease with the discount rate.

It is not clear if this result would hold if the size of the time steps in the model were reduced.

A comparison across models further highlights the importance of CO2 fertilization impacts on the

global damage potential. CO2 emissions, and the resulting increase in atmospheric concentration,

have the potential to increase yields in the agriculture and forestry sector. This characteristic is not

shared by other GHG emissions. Accordingly, the FUND model, which explicitly captures this effect,

exerts downward pressure on the SC-CO2 that is not present for the SC-CH4 and SC-N2O, allowing

for the possibility of substantially higher global damage potential estimates. The results based on

the FUND model presented in this article exhibit this effect; however, the CO2 fertilization effect is

not explicitly modelled in DICE and PAGE and therefore they are found to produce lower estimates

of the global damage potential. For example, using the 3% discount rate, the global damage potential

for CH4 as estimated by FUND ranges between 58 and 88 depending on the scenario, whereas it ranges

from 19 to 28 for DICE and PAGE. As the DICE and PAGE models only consider two natural system

impacts, temperature and sea level, if they do implicitly include potential CO2 fertilization benefits,

they are included by using the temperature anomaly as a proxy for the increasing atmospheric CO2

concentration. Fertilization benefits would therefore be allowed to falsely accrue to perturbations of

other GHG emissions besides CO2. It is not clear the degree to which these models try to incorporate

CO2 fertilization effects and therefore the degree to which this issue is of concern.

Finally, the results in this article show that the 100-year GWP (25 for CH4 and 298 for N2O; Forster

et al., 2007) probably provides an underestimate of the global damage potential of each gas, a finding

consistent with previous studies by Marten and Newbold (2012) and Waldhoff et al. (2011). Unlike the

GWP as calculated by the IPCC, the global damage potential will be dependent upon the year of the

emissions perturbations, so the degree of underestimation varies by year. For CH4, the global

damage potential in Table 6 is 0 –84% higher than the GWP in 2020, increasing to 24 –108% in

2050. For N2O, the global damage potential is 6 –33% higher than the GWP in 2020, increasing to

13 –39% in 2050. While inaccurate, using the GWP to convert emissions reductions into CO2 equivalents that can be valued with the SC-CO2 would probably provide a conservative estimate for the abatement benefits.

For the comparison above, the GWP estimates presented in the AR4 by the IPCC (Forster et al., 2007)

were used to maintain consistency with the assumptions regarding the direct and indirect effect of CH4

and N2O concentrations within the modelling. The recent AR5 by the IPCC (Myhre et al., 2013) has

increased the estimate of the indirect effects of CH4, which gives a higher 100-year GWP for CH4 of

28. A reduction in their estimate of the radiative efficacy of N2O has decreased its 100-year GWP to

265. It is likely that updated modelling of the social cost estimates based on similar assumptions

would maintain the finding that the GWP is an underestimate of the global damage potential.

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4.1. Comparison with previous estimates

For comparison, Table 7 presents the social cost estimates, when available, and the global damage

potential estimates for CH4 and N2O from three recent studies in the literature whose features are

more up to date and therefore more directly comparable with this study: Hope (2006a), Waldhoff

et al. (2011), and Marten and Newbold (2012). A direct comparison to the longer list of studies presented in Table 1 is more difficult as they are based on models and socio-economic and emissions scenarios that were developed up to 20 years ago in a rapidly evolving field.

The social cost estimates presented in Table 5 are higher than the estimates in Hope (2006a) and

Waldhoff et al. (2011) for CH4, and in the range of Waldhoff et al. (2011) for N2O. This result holds

whether the comparison is made with the aggregate results in Table 5 or the disaggregated modelspecific results. One reason for the significant difference in the SC-CH4 estimates is that the earlier

studies rely on older model versions (PAGE2002 and FUND3.5), neither of which include the indirect

effects of CH4 emissions on radiative forcing, but are included within this analysis. As noted in Section

3.3 the indirect effects of CH4 are modelled as a 40% increase in its effective radiative forcing. The result

of this change alone would likely be a greater than 40% increase in the SC-CH4 due to the nonlinear

damage functions. Furthermore, the assumptions regarding preference parameters in the main cases

of Hope (2006a) and Waldhoff et al. (2011) lead to effective discount rates that are significantly

higher than 3%. Other differences in input assumptions (e.g. equilibrium climate sensitivity, socioeconomic emissions scenario) will also lead to differences, although these are likely to be of secondorder importance given the relative similarity in the assumptions.

However, the results in Table 5 averaged across the combinations of the three models and five scenarios are relatively similar to those of Marten and Newbold (2012), which focused on a single scenario

TABLE 7 Previous estimates of the social cost of CH4 and N2O emissions

Study Discount Rate Emissions Year

Social cost (2007$/

tonne X)a

Global damage

potential (SC-X/

SC-CO2)

SC-CH4 SC-N2O CH4 N2O

Hope (2006a) Ramsey 2001 125 – 20 –

Waldhoff et al. (2011)

b Ramsey 2010–2019 265 7,616 26 738

– – 8–221 383–3,503

Marten and Newbold (2012) 2.5% 2020 1,500 26,000 23 403

2050 3,500 50,000 32 444

3% 2020 1,100 17,000 27 400

2050 2,900 34,000 36 439

5% 2020 550 4,900 42 380

2050 1,500 12,000 53 415

a

All values are discounted to the year of the emissions perturbation.

b

The first row presents the base case and the second row presents the range found from sensitivity analysis (over socio-economic scenario, climate

sensitivity, pure rate of time preference, climate sensitivity and CO2 fertilization).

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and model. This result is in part based on the fact that both sets of results include the indirect effects of

CH4, use the same discount rates and equilibrium climate sensitivity distribution, and relatively similar

scenarios. The estimates in this study are slightly higher for the SC-CH4 and slightly lower for the SCN2O compared to Marten and Newbold (2012). Of particular interest is the specific comparison of this

article’s estimates based on DICE 2010 and the MiniCAM scenario to those of Marten and Newbold

(2012) using the same scenario, discount rates, and equilibrium climate sensitivity but an the older

2007 version of the DICE model and a more complete climate sub-model. In this case, estimates for

both the SC-CH4 and SC-N2O (presented in Appendix B) are notably lower. The myriad of differences

between the model vintages and climate sub-models make it difficult to assess which differences are

most important for explaining this relationship.

As previously noted, the global damage potential may provide a better value with which to compare

across studies that estimate the social cost of non-CO2 GHG emissions, as it helps to control for some of

the underlying differences in assumptions across studies. For example, the global damage potential is

far less sensitive to the discount rate used than the SC-X values themselves. However, the global

damage potential does not address the lack of indirect CH4 effects, as may be seen in the lower estimates

of Hope (2006a) and Waldhoff et al. (2011). In these cases the exclusion of the 40% additional increase

in radiative forcing from the indirect effects of the CH4 perturbation explains the majority of the difference. In comparison to Marten and Newbold (2012), the results presented in Table 6 are relatively

similar for CH4 in both the aggregate and disaggregated results. For N2O, similar results are found in

the DICE estimates, but notable differences are found in how the aggregate results respond to the discount rate, due to the differences in this relationship between the models as noted above.

5. Concluding remarks

This article presents a simple and transparent approach to estimating the social cost of CH4 (SC-CH4)

and N2O (SC-N2O) in a manner that is consistent with estimates of the social cost of CO2 (SC-CO2)

already in use in benefit –cost analysis (BCA) for US Federal regulations. This approach is used to estimate the SC-CH4 and SC-N2O for the period 2010 –2050. These directly modelled estimates are found

to be larger than approximations of the social costs of these gases based on the application of common

physical gas comparison metrics, such as global warming potentials (GWPs), to the SC-CO2. This result

generalizes the empirical findings of Marten and Newbold (2012) that using a GWP-based approximation approach will likely offer a conservative estimate of the social cost of non-CO2 GHGs.

The social costs associated with emissions of non-CO2 GHGs are substantial and should be included

within the BCAs used to assess the overall welfare implications of policy alternatives. For example, by

not including monetized values of the benefits from reducing CH4 and N2O emissions, the BCA for

recent standards regulating the fuel efficiency and GHG emissions of light duty vehicles implicitly

assigned them a value of zero (US EPA, 2010). However, the results of this article suggest that those

reductions have benefits of US$85 –493 million (2007$) for CH4 and $1.5 –12 million (2007$) for

N2O in the year 2020 alone. Failing to account for such impacts could limit the ability of the analysis

to serve as a transparent and informative input into the decision-making process about the relative

benefits and costs of regulatory alternatives. That said, by restricting the article to a derivation of

social cost estimates consistent with the USG SC-CO2 estimates, the myriad issues related to

Social cost of CH4 & N2O consistent w/ US SC-CO2 23

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whether those estimates can themselves be improved are set aside.6 Any limitations that apply to the

USG SC-CO2 estimates therefore also apply to the SC-CH4 and SC-N2O estimates derived here.

Supplemental data

Supplemental data for this article can be accessed 10.1080/14693062.2014.912981.

Notes

1. Examples include Minnesota’s draft methodology for setting the value of a tariff to compensate solar panel

owners for the surplus power they deliver to utilities (http://www.eenews.net/stories/1059992297, http://mn.

gov/commerce/energy/images/DRAFT-MN-VOS-Methodology-111913.pdf), the Northwest Power and Conservation Council’s symposium supporting the development of the 7th Power Plan (http://www.nwcouncil.org/

energy/powerplan/7/symposiums/greenhouse/agenda), BCA of Canada’s Heavy-duty Vehicle and Engine

Greenhouse Gas Emission Regulations (http://canadagazette.gc.ca/rp-pr/p2/2013/2013-03-13/html/sordors24-eng.html), analysis of climate change projects at the Inter-American Development Bank (correspondence with Patrick Doyle, Senior Climate and Energy Officer, Structured and Corporate Finance Department),

the International Monetary Fund’s recent Energy Subsidy Reform report (http://www.imf.org/external/np/pp/

eng/2013/012813.pdf), and Parry and Strand (2012).

2. An alternative approach for estimating the social cost of GHG emissions could be based on stated preference (SP)

surveys designed to elicit respondents’ maximum willingness-to-pay for various levels of GHG emission

reductions (e.g. Longo, Markandya, & Petrucci, 2008; Solin ̃o, 2010). This approach would not suffer from the

difficulties associated with creating and parameterizing a numerical integrated assessment model. However, it

would suffer from its own set of difficulties, including well-known general limitations that affect all SP

studies including the potential for ‘hypothetical bias’ (e.g. Carson, 2012; Hausman, 2012; Kling, Phaneuf, &

Zhao, 2012), plus difficulties that may be specific to this application stemming from the generally limited knowledge base regarding the potential climatic, biophysical, and especially economic impacts of GHG emissions on

current and far future generations that most respondents will bring to the survey.

3. The fork of MAGICC version 5.3 included in Pacific Northwest National Laboratory’s open source model GCAM

version 2 (Calvin et al., 2009) is used without carbon cycle feedbacks and, unless otherwise specified, an equilibrium climate sensitivity of 3 8C. We note that sensitivity analysis found the general results of this side analysis

to be robust to other values of the equilibrium climate sensitivity.

4. The EMF-22 scenario is extended past 2100 assuming that emissions stay constant at the 2100 level. This

assumption is revisited later in this article.

5. The PAGE 2009 model restricts the user to representing the entire time horizon, in this case out to 2300, with

only ten time steps. This leads to the unrealistic situation in a small number of simulations where the marginal

unit of emissions can cause ‘catastrophic’ climate impacts to occur one period earlier, which could be 100 years

earlier in some cases. We consider these occurrences to be a limitation of the model and drop them from the

overall distribution of estimates. Appendix A contains further details about this issue.

6. In addition to the critiques previously cited, we point the interested reader to the work of Marten et al. (2013)

and Oppenheimer (2013) for a review of literature that considers potential improvements in the assessment and

valuation of climate change impacts.

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