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# Climate Policy Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tcpo20 

# Incremental CH 4



# and N 2

# O mitigation benefits consistent with the US Government's SC-CO 2 

# estimates

Alex L. Marten a 

### , Elizabeth A. Kopits a 

### , Charles W. Griffiths a 

### , Stephen C. Newbold a

### & Ann Wolverton a

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 CH 4 

### and N 2

### O mitigation benefits consistent with the US Government's SC-CO 2 

### estimates, Climate Policy, DOI: 10.1080/14693062.2014.912981

To link to this article: http://dx.doi.org/10.1080/14693062.2014.912981

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## B research article



# Incremental CH 4 

# and N 2 

# O mitigation benefits consistent with the US Government’s SC-CO 2 

# 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 CO 2 (SC-CO 2) to develop analyses that more fully capture the climate change impacts of GHG abatement. The SCCO 2 represents the aggregate willingness to pay to avoid the damages associated with an additional tonne of CO 2 emissions. In comparison, the social costs of non-CO 2 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-CO 2 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-CO 2 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-CO 2 estimates to value the impact of CO 2 emissions changes. However, the value of changes in non-CO 2 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-CO 2 GHGs, methane and nitrous oxide. These new estimates are designed to be compatible with the USG SC-CO 2 estimates currently in use and may therefore be directly applied to value emissions changes for these non-CO 2 gases within the benefit–cost analyses used to evaluate future policies. Keywords : integrated assessment; non-CO 2 GHGs; social cost of carbon



### 1. Introduction

The social cost of CO 2 (SC-CO 2) 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 CO 2 emissions. Specifically, it represents society’s aggregate willingness to pay to prevent future impacts that occur when one additional unit of CO 2 is emitted into the atmosphere in a particular year. Estimates of SC-CO 2

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.therefore provide a way to value changes in CO 2 emissions in benefit –cost analyses (BCAs) of policy alternatives. Without an estimate of the SC-CO 2, the benefits of mitigating the climate change impacts from CO 2 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-CO 2 estimates in the BCAs used to evaluate major regulations that impact CO 2 emissions (USG, 2010), including over 30 regulatory actions to date. The USG SC-CO 2 estimates are alsoincreasingly 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 CO 2 is the primary anthropogenic GHG, other GHGs such as methane (CH 4), nitrous oxide (N 2 O), hydrofluorocarbons (HFCs), perfluorocarbons (PFCs), and sulfur hexafluoride (SF 6) 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 CO 2 concentration contributed 64% of overall radiative forcing, while CH 4 and N 2 O accounted for approximately 23% (Myhre et al., 2013 ). Non-CO 2 GHGs, notably CH 4 and N 2 O, therefore contribute significantly to the negative impacts on human well-being from climate change. Furthermore, several recent studies have shown that consideration of non-CO 2 GHGs, particularly CH 4 and N 2 O, 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-CO 2 GHGs has not been included in USG policyanalysis 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-CO 2 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 CO 2 emissions are considered while ignoring changes in CH 4 and other GHG emissions (Alvarez, Pacala, Winebrake, Chameides, & Hamburg, 2011 ). A key reason for the value of non-CO 2 GHG emissions impacts not being included in USG analyses so far is that existing estimates of the social cost of non-CO 2 GHGs presented in the literature are inconsistent with USG SC-CO 2 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-CO 2, ‘the methane climate benefit estimates availablein 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 CH 4 and N 2 O (SC-CH 4 and SC-N 2 O, respectively) that are fully consistent with the modelling assumptions underlying the current USG SC-CO 2 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-CO 2 .It is important to note at the outset that by restricting attention to the derivation of social cost estimates consistent with the USG SC-CO 2 estimates, any limitations that apply to inputs and modelling 2 Marten et al.

CLIMATE POLICYassumptions underlying the USG SC-CO 2 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-CH 4 and SC-N 2 O 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-CO 2, 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 SCCO 2 estimation approach and how it compares to the existing literature on the social cost of non-CO 2 GHGs, including a discussion of some of the critiques of the approach. Section 3 presents the approach for estimating the SC-CH 4 and SC-N 2 O in a manner consistent with the USG SC-CO 2 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-CO 2 estimates for use by all Executive Branch agencies to value marginal changes in CO 2 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 CO 2 emissions. Before the release of these estimates, CO 2 emissions changes were valued in some but not all regulatory analyses, and the SC-CO 2 estimates used by different agencies varied substantially. The USG recently updated their estimates for the SC-CO 2 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-CO 2, describes some critiques of the approach by other researchers, and discusses the existing literature on the social cost of non-CO 2 GHGs.



### 2.1. USG SC-CO 2 

### estimation approach To estimate the SC-CO 2 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 CH 4 & N 2 O consistent w/ US SC-CO 2 3

CLIMATE POLICYclimate system submodels and the functions that map climate change into economic damages asimplemented 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-CO 2 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 usingresults 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 CO 2 e 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 CO 2 concentrations in 2100 ranged from approximately 450 to 890 ppm (550 –1130 ppm in CO 2 e). 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 (CO 2 emissions/economic output) remains constant at its 2090 –2100 average; starting in 2100 net land-use CO 2 emissions decline linearly to zero in 2200; and for all years beyond 2100 non-CO 2 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 CH 4 , it is important for understanding the impacts of long lived GHGs such as CO 2 and N 2 O 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 onlyone 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 CO 2 and N 2 O are relatively similar in shape and therefore the general findings of studies that explore the sensitivity of the SC-CO 2 to these assumptions should also be applicable to the SC-N 2 O. 4 Marten et al.

CLIMATE POLICY

### 2.1.2. Equilibrium climate sensitivityIn 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 representsthe long-term global average temperature response to a level of radiative forcing associated with a sustained doubling of atmospheric CO 2 concentration (around 550 ppm). To represent the uncertainty inthe 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 8 C, two-thirds probability that the ECS lies between 2 and 4.5 8 C, which was intended to be consistent with the UNIntergovernmental 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 8 C. This specification of the ECS distribution is retained to maintain consistency with the USG estimates of the SCCO 2, 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 8 C 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 CO 2 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-CO 2 . 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-CO 2 The process to estimate the SC-CO 2 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 CO 2 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 Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 5

CLIMATE POLICYthe 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-CO 2 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-CO 2 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-CO 2 in a given year, one for each assumed discount rate. Four SC-CO 2 estimates were selected from these three probability distributions to reflect the global damages caused by one tonne of CO 2 emissions. Three estimates are based on the average SC-CO 2 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-CO 2 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-CO 2 

### GHG emissionsA significant limitation of the aforementioned USG interagency process is that the social costs of nonCO 2 GHG emissions were not estimated. Therefore, as an alternative to applying direct estimates for the social costs of non-CO 2 GHG emissions in the primary BCA, several recent USG regulatory analyses have approximated the benefits of non-CO 2 GHG emissions reductions in sensitivity analyses by transforming the non-CO 2 GHG emissions to ‘CO 2 -equivalents’ using estimates of the GWP for the GHG in question and then using the USG SC-CO 2 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 CO 2, 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 tomeasure 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 CO 2 over a specifictime horizon (e.g. 100 years). The GWP and other gas-comparison metrics are problematic as an SCCO 2 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-CO 2 estimates to capture the impact of non-CO 2 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 6 Marten et al.

CLIMATE POLICYcausation (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-CO 2 GHG emissions using IAMs, although the number of such estimates is small compared to the large number of SC-CO 2 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-CO 2 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-CO 2 . Normalizing the SC-CH 4 or

TABLE 1 Previous estimates of the social cost of CH 4 and N 2 O emissions

Study Model Time horizon Discount rate Emissions year Scenario a 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 IS92 b N/A Kandlikar ( 1995) N/A 100 years 0, 2, 6% N/A IS90a,d 3 8 C Kandlikar ( 1996) N/A 100 years 0, 2, 6% N/A IS90a,d 3 8 C Hammitt et al. ( 1996) N/A 2200 1, 3, 5% 1995–2015 IS92a,c,e 1.5, 2,5, 4.5 8 C

Tol ( 1999) FUND 1.6 2100 0, 1, 3, 5, 10% 1995–2014 IS92a 2.5 8 C Tol et al. (2003) FUND 1.7 2200 0, 1, 3, 5, 10% 1995–2014 IS92a 2.5 8 C Hope (2005) PAGE95 2200 Ramsey 2000 SRES A2 Probabilistic, mode of 3 8 C Hope (2006a) PAGE2002 2200 Ramsey 2001 SRES A2 Probabilistic, mean of 3 8 C Waldhoff et al. (2011 ) FUND 3.5 3000 Ramsey 2010–2019 FUND, SRES A1B, A2, B1, B2 2, 3, 4.5 8 C

Marten and Newbold (2012) DICE2007 w/ MAGICC 2300 Ramsey, 2.5, 3, 5% 2010–2050 EMF-22 MiniCAM Base Probabilistic, median of 3 8 C

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). bThe particular IS92 scenario used was not specified. Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 7

CLIMATE POLICYSC-N 2 O estimate using the SC-CO 2, 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-CH 4 and SC-N 2 O 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 SCCH 4 and SC-N 2 O 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-CH 4 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 CO 2, CH 4 , N 2 O, and SF 6 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 CO 2, CH 4 , and N 2 O 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-CO 2, 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-CO 2 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-CO 2 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-CH 4 and SC-N 2 O.



### 3. Estimating the social cost of non-CO 2 

### GHGs consistent with USG SC-CO 2 The primary obstacle in estimating the social cost of non-CO 2 GHG emissions in a manner consistent with the USG SC-CO 2 estimates is that not all of the IAMs used include explicit representations of the non-CO 2 gases of interest. This section describes the degree to which non-CO 2 GHGs are currently 8 Marten et al.

CLIMATE POLICYrepresented 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-CO 2 

### GHGs in DICE, PAGE, and FUND The FUND model explicitly considers CH 4 , N 2 O, and SF 6 in addition to CO 2 . The model uses one-box atmospheric gas cycle models for these gases, with geometric decay towards pre-industrial levels. For CH 4 and N 2 O, 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 CH 4 to account for the influences of stratospheric water vapour and tropospheric ozone changes. Because FUND uses CH 4 and N 2 O 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 CO 2; 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-CO 2, the USG decomposed the default DICE exogenous radiative forcing vector into CH 4 , N 2 O, F-gases, aerosols, and other residual forcing components. The USG then replaced the radiative forcing attributed to CH 4 , N 2 O, and F-gases with estimates associated with the EMF-22 scenarios. As non-CO 2 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 CH 4 and SF 6 , but represents the effects of other non-CO 2 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 CH 4 component. Instead, the same exogenous radiative forcing projection was used for the effect of CH 4 , N 2 O, and Fgas emissions as was used for DICE. Since then, a N 2 O component has been added to the PAGE model, although in the recent 2013 SC-CO 2 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-CO 2 emissions that are consistent with the USG SC-CO 2 estimates. For these reasons, computing estimates for the social cost of non-CO 2 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-CO 2 estimates, making this work inconsistent with the USG SCCO 2 estimates currently used in regulatory analysis.



### 3.2. Estimating the social cost of non-CO 2 

### GHGs in DICE and PAGE The process used in this article to estimate the social cost of non-CO 2 GHGs in DICE and PAGE as implemented by the USG requires first generating a forecast of the additional radiative forcing Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 9

CLIMATE POLICYassociated with a perturbation of a non-CO 2 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 thechange in atmospheric concentration and the radiative forcing associated with the additional concentration. For both CH 4 and N 2 O, 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 CH 4 and N 2 O 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 baselineand 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-CO 2 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-CO 2 to non-marginal emission changes show that the average per tonne SC-CO 2 estimate is relatively constant over large differences in perturbation size. Additional experiments in the context of this article foundthat 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 CH 4 and N 2 O, and explores the sensitivity of these projections to 10 Marten et al.

CLIMATE POLICYtwo 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 CH 4 and N 2 O concentrations based on a more sophisticated climate model. Second, it explores the sensitivity of the results to the method used for extrapolating non-CO 2 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-CO 2 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 , C CH 4 t [ppb], such that

CCH 4 t = C CH 4 t

− 1 + d CH 4 ( C CH 4 pre − C CH 4 t

− 1 ) + g CH 4 ECH 4 t

− 1 , (1)

where d CH 4 defines the rate of decay, C CH 4 pre [ppb] is the pre-industrial atmospheric concentration, and
g

CH 4 [ppb/Mt] converts emissions, ECH 4 t

− 1 [Mt], from mass to atmospheric volume. The mass to volume conversion factor is g CH 4 1⁄4 0.3597 ppb/Mt and C CH 4 pre 1⁄4 700 ppb, following the IPCC TAR. The rate of decay is set to d CH 4 1⁄4 1/12 following the IPCC AR4 stated CH 4 lifetime of 12 years. The iteration begins in the year 2006 using the emissions from the EMF-22 scenario (linearly interpolatedbetween 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 C CH 4 2005 1⁄4 1774 ppb. The contribution of atmospheric methane to global radiative forcing, denoted QCH 4 t , is defined using the relationship in Table 6 .2 of the IPCC TAR:

Q CH 4

t = f 0

. 036 C CH 4

t 

− C CH 4

pre   

− [f ( C CH 4 t , CN 2 O pre )

− ( C CH 4 pre , CN 2 O pre )]   , (2)

where CN 2 O pre [ppb] is the pre-industrial atmospheric concentration of nitrous oxide and

f ( C CH 4 , CN 2 O ) = 0

. 47 ln 1 + 2

. 01 × 10 − 5 ( C CH 4 CN 2 O )] 0

. 75 + 5

. 31 × 10 − 15 C CH 4 ( C CH 4 CN 2 O ) 1

. 52 

. (3)

The function in expression (3) accounts for the overlapping absorption bands of CH 4 and N 2 O, thereby reducing their effective absorption. Parameter f is used to proxy for indirect effects of CH 4that 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 N 2 O is set consistent with the IPCC TAR, such that CN 2 O pre 1⁄4 270 ppb. Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 11

CLIMATE POLICYA key simplification in this approach is the constant decay rate used in the atmospheric gas cyclemodel. 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 CH 4 in the atmosphere and the other gases and climate variables. This exercise uses CH 4 emissions from the EMF-22 MiniCAM reference scenario and considers a one tonne perturbation of CH 4 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 modeland MAGICC is also of importance. Although MAGICC relies on similar equations to derive the radiative forcing of atmospheric CH 4 concentrations, it differs in the way it handles indirect effects of CH 4on 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 CH 4 perturbation in both models. The average increase in radiative forcing over thedecade 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 constantdecay 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 CH 4 . To understand the effect that this difference would have on an estimate of the SC-CH 4 , an experiment was conducted using the DICE model in which the additional forcing from a one tonne perturbation of CH 4 , 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 greaterfurther 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 12 Marten et al.

CLIMATE POLICYestimates 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 CH 4 emissions for simple model vs. MAGICC: (a) additional atmospheric concentration; (b) additional radiative forcing Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 13

CLIMATE POLICYsocial 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 N 2 O takes a similar form to the model used for CH 4 , such that the concentration of nitrous oxide in year t , CN 2 O t [ppb], is specified as

CN 2 O

t = CN 2 O t

− 1 + d N 2 O ( CN 2 O pre − CN 2 O t

− 1 ) + g N 2 O EN 2 O t

− 1 , (4)

where d N 2 O is the rate of decay, and g N 2 O [ppb N 2 O/Mt N] converts emissions, EN 2 O t

− 1 [Mt N], from mass to atmospheric volume. Following the IPCC AR4, the mass to volume conversion factor is g N 2 O 1⁄4 0.2079 ppb N 2 O/Mt N and the rate of decay is d N 2 O 1⁄4 1/114 based on a 114-year lifetime. As with CH 4 , the iteration begins in the year 2006 using the emissions from the EMF-22 scenarios (linearlyinterpolated 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 CN 2 O 2005 1⁄4 319 ppb. The contribution of atmospheric N 2 O to global radiative forcing, denoted QN 2 O t , is defined using the relationship in Table 6 .2 of the IPCC TAR, such that

QCH 4

t = 0

. 12 CN 2 O

t 

− CN 2 O

pre   

− [f ( CCH 4 pre , CN 2 O t )

− f ( C CH 4 pre , CN 2 O pre )], (5)

where f ( C CH 4 , CN 2 O ) is defined in expression (3).

As with CH 4 , a key simplifying assumption is the constant decay rate used in the simple gas cyclemodel (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 N 2 O will depend on the atmospheric concentration of N 2 O 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 CH 4 were performed. Given future TABLE 2 Effect of CH 4 gas cycle model on SC-CH 4 (2007$ per tonne CH 4): 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% 14 Marten et al.

CLIMATE POLICYN 2 O emissions based on the EMF-22 MiniCAM reference scenario, a one tonne N 2 O 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 projectionsdo 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 CH 4 . Figure 3 (b) presents the estimates of average additional radiative forcing per decade as a result of the N 2 O perturbation using both models. The additional radiative forcing from the N 2 O perturbation inthe 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 CH 4 , to assess the effect that this difference would have on the SC-N 2 O, an experiment was conducted using the DICE model in which the additional forcing from a one tonne perturbation of N 2 O 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 CH 4 , 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-CO 2 

### 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-CO 2 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-CO 2 . However, estimating the social cost of non-CO 2 GHGs requires explicit projections of baseline emissions of non-CO 2 gases in orderto correctly determine the effect of the perturbation. The USG’s broad assumption regarding the extrapolation of non-CO 2 gases is therefore problematic as constant non-CO 2 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-CO 2 gas falls to a level equal to its respective rate of decay in2100. 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,

E

X t = − d X ( C X pre − C X 2100 )

g

X ∀t . 2100

. (6)

To put this assumption into context, the solid lines in Figure 4 (a) and (b) present the emissions paths for CH 4 and N 2 O, respectively, under the MiniCAM EMF-22 reference scenario extrapolated using Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 15

CLIMATE POLICYFigure 3 Effects of perturbation in 2015 N 2 O emissions for simple model vs. MAGICC: (a) additional atmospheric concentration; (b) additional radiative forcing 16 Marten et al.

CLIMATE POLICYexpression (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 CO 2 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-CO 2 radiative forcing remains constant. Noteworthy is the fact that the assumption in (6) is almost analogous to keeping CH 4 emissions constant at their 2100 levels, whereas for N 2 O 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 CH 4 , 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) CH 4 emissions; (b) N 2 O emissions TABLE 3 Effect of climate model on SC-N 2 O (2007$ per tonne N 2 O): 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% Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 17

CLIMATE POLICYperturbation 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 CH 4 emissions after 2100 unimportant for near-term perturbations. Post2100 emissions will have a larger effect in the case of N 2 O, 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-CH 4 and SC-N 2 O, 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 CH 4 leads to a situation in which post-2100 assumptions do not affect SC-CH 4 estimates, even in 2045. For the longer-lived gas N 2 O, 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) CH 4 perturbation in 2015; (b) N 2 O perturbation in 2015; (c) CH 4 perturbation in 2045; (d) N 2 O perturbation in 2045 18 Marten et al.

CLIMATE POLICYassumptions is less than 1% and the projections are equivalent to two significant digits. Therefore, in the remainder of this article, non-CO 2 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 CH 4 and N 2 O 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-CO 2 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 additionalassumptions 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. Estimatesare 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-CO 2 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-CO 2, which revised the original 2010 USG upwards based on new versions of the IAMs used. The non-CO 2 results, as well as the USG SC-CO 2 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 CH 4 and N 2 O emissions are substantially higher than for CO 2 . The values are higher at lower discount rates, although the impact of the discount rate is lower for CH 4 given its relatively short lifetime. Similar to CO 2, the social cost estimates for CH 4 and N 2 O 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

CH 4 2.5% 2,490 2,490 2,490 3.0% 1,933 1,933 1,933 5.0% 956 956 956 N 2 O 2.5% 36,968 36,588 36,662 3.0% 25,030 24,837 24,868 5.0% 8,280 8,261 8,263 Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 19

CLIMATE POLICYTo better understand how the social costs of CH 4 and N 2 O compare to CO 2, 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-CO 2, 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 CO 2 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 CH 4 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-CO 2 than the SC-CH 4 . This finding is robust across the models. The estimates in Table 6 also present the same result for N 2 O in the aggregate case, althoughthis 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 N 2 O increases with lower discount rates due to a lower effective decay rate over the relevant time horizon for N 2 O than CO 2 . 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 CO 2 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 CO 2 12 43 64 128 CH 4 550 1,200 1,600 3,200 N 2 O 4,800 15,000 22,000 41,000 2050 CO 2 26 71 97 220 CH 4 1,400 2,500 3,100 6,900 N 2 O 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 CH 4 46 29 25 25 N 2 O 397 359 353 317 2050 CH 4 52 36 32 31 N 2 O 414 388 387 338 20 Marten et al.

CLIMATE POLICYimpact on the SC-CO 2, thereby lowering the global damage potential. If one were to remove those impacts from the FUND model the global damage potential for N2 O 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 N 2 O 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 CO 2, which causes the global damage potential for N 2 O 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 CO 2 fertilization impacts on the global damage potential. CO 2 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-CO 2 that is not present for the SC-CH 4 and SC-N 2 O, 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 CO 2 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 CH 4 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 CO 2 fertilization benefits, they are included by using the temperature anomaly as a proxy for the increasing atmospheric CO 2 concentration. Fertilization benefits would therefore be allowed to falsely accrue to perturbations of other GHG emissions besides CO 2 . It is not clear the degree to which these models try to incorporate CO 2 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 CH 4 and 298 for N 2 O; 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 CH 4 , the global damage potential in Table 6 is 0 –84% higher than the GWP in 2020, increasing to 24 –108% in 2050. For N 2 O, 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 CO 2 equivalents that can be valued with the SC-CO 2 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 CH 4 and N 2 O concentrations within the modelling. The recent AR5 by the IPCC (Myhre et al., 2013 ) has increased the estimate of the indirect effects of CH 4 , which gives a higher 100-year GWP for CH 4 of 28. A reduction in their estimate of the radiative efficacy of N 2 O 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. Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 21

CLIMATE POLICY

### 4.1. Comparison with previous estimates For comparison, Table 7 presents the social cost estimates, when available, and the global damage potential estimates for CH 4 and N 2 O 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 CH 4 , and in the range of Waldhoff et al. ( 2011 ) for N 2 O. 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-CH 4 estimates is that the earlier studies rely on older model versions (PAGE2002 and FUND3.5), neither of which include the indirect effects of CH 4 emissions on radiative forcing, but are included within this analysis. As noted in Section 3.3 the indirect effects of CH 4 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-CH 4 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 significantlyhigher 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 CH 4 and N 2 O emissions

Study Discount Rate Emissions Year Social cost (2007$/ tonne X) a Global damage potential (SC-X/ SC-CO 2)

SC-CH 4 SC-N 2 O CH 4 N 2 O
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

aAll values are discounted to the year of the emissions perturbation. bThe 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 CO 2 fertilization). 22 Marten et al.

CLIMATE POLICYand model. This result is in part based on the fact that both sets of results include the indirect effects of CH 4 , 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-CH 4 and slightly lower for the SCN 2 O 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-CH 4 and SC-N 2 O (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-CO 2 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 CH 4 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 CH 4 perturbation explains the majority of the difference. In comparison to Marten and Newbold ( 2012), the results presented in Table 6 are relatively similar for CH 4 in both the aggregate and disaggregated results. For N2 O, similar results are found inthe 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 CH 4 (SC-CH 4) and N2 O (SC-N 2 O) in a manner that is consistent with estimates of the social cost of CO 2 (SC-CO 2)already in use in benefit –cost analysis (BCA) for US Federal regulations. This approach is used to estimate the SC-CH 4 and SC-N 2 O 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-CO 2 . 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-CO 2 GHGs. The social costs associated with emissions of non-CO 2 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 CH 4 and N 2 O 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 CH 4 and $1.5 –12 million (2007$) for N 2 O 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-CO 2 estimates, the myriad issues related to Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 23

CLIMATE POLICYwhether those estimates can themselves be improved are set aside. 6 Any limitations that apply to the USG SC-CO 2 estimates therefore also apply to the SC-CH 4 and SC-N 2 O 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 8 C. 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.



### References

Alvarez, R., Pacala, S., Winebrake, J., Chameides, W., & Hamburg, S. (2011). Greater focus needed on methane leakage from natural gas infrastructure. Proceedings of the National Academy of Science of the USA , 109, 6435 –6440. 24 Marten et al.

CLIMATE POLICYAnthoff, D., Hepburn, C., & Tol, R. (2009). Equity weighting and the marginal damage costs of climate change. Ecological Economics , 68 , 836 –849. Anthoff, D., & Tol, R. S. J. (2013). The uncertainty about the social cost of carbon: A decomposition analysis using FUND. Climatic Change, 117, 515 –530. Arrow, K., Cropper, M., Gollier, C., Groom, B., Heal, G., Newell, R.,

... Weitzman, M. (2013). Determining benefits and costs for future generations. Science, 341 , 349 –350. Calvin, K., Edmonds, J., Bond-Lamberty, B., Clarke, L., Kim, S., Kyle, P.,

... Wise, M. (2009). Limiting climate change to 450 ppm CO 2 equivalent in the 21st century. Energy Economics , 31 , S107 –S120. Carson, R. T. (2012). Contingent valuation: A practical alternative when prices aren’t available. Journal of Economic Perspectives , 26, 27 –42.Clarke, L., Edmonds, J., Krey, V., Richels, R., Rose, S., & Tavoni, M. (2009). International climate policy architectures: Overview of the EMF 22 international scenarios. Energy Economics , 31 , 564–581. Collins, M., Knutti, R., Arblaster, J., Dufresne, J., Fichefet, T., Friedlingstein, P., & Wehner, M. Long-term climate change: Projections, commitments, and irreversibility. In T. F. Stocker, D. Qin, G.-K. Plattner, M. Tignor, S. K. Allen, J. Boschung,

... P. M. Midgley (Eds.), Climate change 2013: The physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (pp. 1110 –1112). Cambridge: Cambridge University Press. Dasgupta, P. (2008). Discounting climate change. Journal of Risk and Uncertainty, 37, 141 –169. Ehhalt, D. M., Prather, F., Dentener, R., Derwent, E., Dlugokencky, E., Holland, I.,

... Wang, Y. (2001). Atmospheric chemistry and greenhouse gases. In J. T. Houghton, Y. Ding, D. J. Griggs, M. Noguer, P. J. van der Linden, X. Dai,

... C. A. Johnson (Eds.), Climate change 2001: The scientific basis. contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change (pp. 248–251). Cambridge: Cambridge University Press. Fankhauser, S. (1994). The social costs of greenhouse gas emissions: An expected value approach. The Energy Journal, 15, 157 –184. Forster, P., Ramaswamy, V., Artaxo, P., Berntsen, T., Betts, R., Fahey, D. W.,

... Van Dorland, R. (2007). Changes in atmospheric constituents and in radiative forcing. In S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt,

... H. L. Miller (Eds.), Climate change 2007: The physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (pp. 210–216). Cambridge: Cambridge University Press. Griffiths, C., Kopits, E., Marten, A., Moore, C., Newbold, S., & Wolverton, A. (2012). The social cost of carbon: Valuing carbon reductions in policy analysis. In I. P. R de Mooij & M. Keen (Eds.), Fiscal policy to mitigate climate change (pp. 69–87). Washington, DC: International Monetary Fund. Hammitt, J., Jain, A., Adams, J., & Wuebbles, D. (1996). A welfare-based index for assessing environmental effects of greenhouse-gas emissions. Nature, 381 , 301 –303. Hausman, J. (2012). Contingent valuation: From dubious to hopeless. Journal of Economic Perspectives , 26 (4), 43 –56. Hope, C. (2005). The climate change benefits of reducing methane emissions. Climatic Change, 68 , 21 –39. Hope, C. (2006a). The marginal impacts of CO 2 , CH 4 and SF 6 emissions. Climate Policy, 6, 537–544. Hope, C. (2006b). The marginal impact of CO 2 from PAGE2002: An integrated assessment model incorporating the IPCC’s five reasons for concern. Integrated Assessment Journal, 6 (1), 19 –56. Hope, C. (2008). Optimal carbon emissions and the social cost of carbon under uncertainty. Integrated Assessment Journal, 8 , 107–122. IPCC (1990). Climate change: The IPCC scientific assessment. J. Houghton, G. Jenkins, & J. Ephraums (Eds.). Cambridge: Cambridge University Press. IPCC (1992). Climate change 1992: The supplementary report to the IPCC scientific assessment. J. Houghton, B. Callander, & S. Varney (Eds.). Cambridge: Cambridge University Press. IPCC (2000). Special report on emissions scenarios: A special report of Working Group III of the Intergovernmental Panel on Climate Change . N. Nakic  ́ enovic  ́ & R. Swart (Eds.). Cambridge: Cambridge University Press. Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 25

CLIMATE POLICYKandlikar, M. (1995). The relative role of trace gas emissions in greenhouse abatement policies. Energy Policy, 23 , 879 –883. Kandlikar, M. (1996). Indices for comparing greenhouse gas emissions: Integrating science and economics. Energy Economics , 18 , 265 –281. Keohane, N. (2010a). Answer testimony of Nathaniel Keohane, in the matter of commission consideration of public service company of Colorado Plan in compliance with House Bill 10-1365, Clean Air –Clean Jobs Act (Docket no. 10M-245E, 17 September). Retrieved from https://www.dora.state.co.us/pls/efi/efi_p2_v2_demo.show_ document?p_dms_document_id=75566 Keohane, N. (2010b). Declaration to United States Court of Appeals for the District of Columbia Circuit, 31 October. Retrieved from http://docs.nrdc.org/legislation/files/leg_10110401k.pdf Kling, C. L., Phaneuf, D. J., & Zhao, J. (2012). From Exxon to BP: Has some number become better than no number? Journal of Economic Perspectives , 26 (4), 3 –26. Kopp, R. E., & Mignone, B. K. (2012). The U.S. government’s social cost of carbon estimates after their first two years: Pathways for improvement. Economics , 6 (15), 1 –41. Longo, A., Markandya, A., & Petrucci, M. (2008). The internalization of externalities in the production of electricity: Willingness to pay for the attributes of a policy for renewable energy. Ecological Economics , 67, 140 –152. Marten, A. L. (2011). Transient temperature response modeling in IAMs: The effects of over simplification on the SCC. Economics , 5, 2011 –2018. Marten, A. L., & Newbold, S. C. (2012). Estimating the social cost of non-CO 2 GHG emissions: Methane and nitrous oxide. Energy Policy, 51 , 957–972. Marten, A. L., Kopp, R., Shouse, K., Griffiths, C., Hodson, E., Kopits, E.,

... Wolverton, A. (2013). Improving the assessment and valuation of climate change impacts for policy and regulatory analysis. Climatic Change, 117, 433 –438. Meehl, G. A., Stocker, T. F., Collins, W. D., Friedlingstein, P., Gaye, A. T., Gregory, J. M.,

... Zhao, Z.-C. (2007). Global climate projections. In S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt,

... H. L. Miller (Eds.), Climate change 2007: The physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (pp. 748 –845). Cambridge: Cambridge University Press. Myhre, G., Shindell, D., Bre  ́ on, F.-M., Collins, W., Fuglestvedt, J., Huang, J.,

... Zhang, H. (2013). Anthropogenic and natural radiative forcing. In T. F. Stocker, D. Qin, G.-K. Plattner, M. Tignor, S. K. Allen, J. Boschung,

... P. M. Midgley (Eds.), Climate change 2013: The physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (pp. 659 –740). Cambridge: Cambridge University Press. Nordhaus, W. (2008). A question of balance: Weighing the options on global warming policies . New Haven, CT: Yale University Press. Nordhaus, W., & Boyer, J. (2000). Warming the world: Economic models of global warming. Cambridge, MA: MIT Press. O’Neill, B. (2010). Multi-century scenario development and socioeconomic uncertainty. In Improving the assessmentand valuation of climate change impacts for policy and regulatory analysis: Modeling climate change impacts and associated economic damages . US Environmental Protection Agency/US Department of Energy. Retrieved from http:// yosemite.epa.gov/ee/epa/eerm.nsf/vwAN/EE-0564-115.pdf/$file/EE-0564-115.pdf Oppenheimer, M. (2013). Climate change impacts: Accounting for the human response. Climatic Change, 117, 439– 449. Parry, I., & Strand, J. (2012). International fuel tax assessment: An application to Chile. Environment and Development Economics , 17(2), 127–144. Ramaswamy, V., Boucher, O., Haigh, J., Hauglustaine, D., Haywood, J., Myhre, G.,

... Betts, R. (2001). Radiative forcing of climate change. In J. T. Houghton, Y. Ding, D. J. Griggs, M. Noguer, P. J. van der Linden, X. Dai,

... C. A. Johnson (Eds.), Climate change 2001: The scientific basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change (pp. 351–416). Cambridge: Cambridge University Press. 26 Marten et al.

CLIMATE POLICYReilly, J., & Richards, K. (1993). Climate change damage and the trace gas index issue. Environmental and Resource Economics , 3 , 41 –61. Reilly, J., Prinn, R., Harnisch, J., Fitzmaurice, J., Jacoby, H., Kicklighter, D.W.,

... Ng, C. (1999). Multi-gas assessment of the Kyoto protocol. Nature, 401 , 549 –555. Roe, G., & Baker, M. (2007). Why is climate sensitivity so unpredictable? Science, 318 , 629–632. Shine, K., Fuglestvedt, J., Hailemariam, K., & Stuber, N. (2005). Alternatives to the global warming potential for comparing climate impacts of emissions of greenhouse gases. Climatic Change, 68 , 281 –302. Smith, S., Lowe, J., Bowerman, N., Gohar, L., Huntingford, C., & Allen, M. (2012). Equivalence of greenhouse gas emissions for peak temperature limits. Nature Climate Change, 2, 535 –538. Solin  ̃ o, M. (2010). External benefits of biomass-e in Spain: An economic valuation. Bioresource Technology, 101 , 1992 –1997. Tanaka, K., O’Neill, B., Rokityanskiy, D., Obersteiner, M., & Tol, R. (2009). Evaluating global warming potentials with historical temperature. Climatic Change, 96, 443 –466. Tol, R. (1999). The marginal costs of greenhouse gas emissions. The Energy Journal, 20 (1), 61 –81. Tol, R. (2002a). Estimates of the damage costs of climate change. Part I: Benchmark estimates. Environmental and Resource Economics , 21 , 47 –73. Tol, R. (2002b). Estimates of the damage costs of climate change. Part II: Dynamic estimates. Environmental and Resource Economics , 21 , 135 –160. Tol, R. (2009). An analysis of mitigation as a response to climate change (Discussion Paper). Frederiksberg, Denmark: Copenhagen Consensus Center. Tol, R., Heintz, R., & Lammers, P. (2003). Methane emission reduction: An application of FUND. Climatic Change, 57, 71 –98. US EPA. (2010). Final rulemaking to establish light-duty vehicle greenhouse gas emission standards and corporate average fuel economy standards: Regulatory impact analysis . Retrieved from http://www.epa.gov/otaq/climate/regulations/ 420r10009.pdf US EPA. (2012). Regulatory impact analysis supporting the 2012 U.S. environmental protection agency final new source performance standards and amendments to the national emissions standards for hazardous air pollutants for the oil and natural gas industry. Retrieved from http://www.epa.gov/ttn/ecas/regdata/RIAs/oil_natural_gas_final_neshap_ nsps_ria.pdf US EPA. (2013). Regulatory impact analysis: Final rulemaking for 2017–2025 light-duty vehicle greenhouse gas emission standards and corporate average fuel economy standards . Retrieved from http://www.epa.gov/otaq/climate/ documents/420r12016.pdf USG. (2010, February). Technical support document: Social cost of carbon for regulatory impact analysis under executive order 12866 . Retrieved from http://www.epa.gov/oms/climate/regulations/scc-tsd.pdf USG. (2013, May). Technical support document: Technical update of the social cost of carbon for regulatory impact analysis under executive order 12866 . Retrieved from http://www.whitehouse.gov/sites/default/files/omb/assets/inforeg/ technical-update-social-cost-of-carbon-for-regulator-impact-analysis.pdf Waldhoff, S., Anthoff, D., Rose, S., & Tol, R. S. J. (2011). The marginal damage costs of different greenhouse gases: An application of FUND (Economics Discussion Paper No. 2011–43). Kiel: Kiel Institute for the World Economy. Warren, R., Mastrandrea, M. D., Hope, C., & Hof, A. F. (2010). Variation in the climatic response to SRES emissions scenarios in integrated assessment models. Climatic Change, 102, 671 –785. Weyant, J. P., De La Chesnaye, C. F., & Blenford, J. (2006). Overview of EMF21: Multi-greenhouse gas mitigation and climate policy. Energy Journal, 27 (Special Issue), 1 –33. Social cost of CH 4 & N 2 O consistent w/ US SC-CO 2 27

CLIMATE POLICY