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climate policy^ Climate Policy ISSN: 1469-3062 (Print) 1752-7457 (Online) Journal homepage: http://www.tandfonline.com/loi/tcpo20 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 To cite this article: Alex L. Marten, Elizabeth A. Kopits, Charles W. Griffiths, Stephen C. Newbold & Ann Wolverton (2015) Incremental CH4 and N2O mitigation benefits consistent with the US Government's SC-CO2 estimates, Climate Policy, 15:2, 272-298, DOI: 10.1080/14693062.2014.912981 To link to this article: http://dx.doi.org/10.1080/14693062.2014.912981 El View supplementary material Gf or Submit your article to this journal GF B View related articles G? <a Citing articles: 3 View citing articles Gf fffi| Published online: 20 May 2014. Iilll Article views: 420 (3) View Crossmark data G? CrossMark Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/joumalInformation?journalCode=tcpo20 Download by: [Syracuse University Library] Date: 04 June 2017, At: 13:51 ) Vol. 15, No. 2, 272-298, http://dx.doi.org/10.1080/14693062.2014.912981 research article climate policya 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 esti mates 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 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. This workwas 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. Taylor & Francis Taylor & Francis Croup Social cost of CH4 & N2O consistent w/ US SC-CO2 273 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 weaken ing 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 organiz ations, 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 assess ments of potential regulatory alternatives by the USG and others that rely on the USG SC-CO2 esti mates (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 emis sions 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 incon sistent with USG SC-CO2 modelling assumptions. For example, the recent US Environmental Protec tion 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 rule making' (US EPA, 2012). This article seeks to address that gap by developing a new set of social cost esti mates 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 esti mates consistent with the USG SC-CO2 estimates, any limitations that apply to inputs and modelling CLIMATE POLICY 274 Marten et al. 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 differ ent agencies varied substantially. The USG recently updated their estimates for the SC-CO2 by employ ing 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' CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 275 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 equili brium 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 scen arios 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 radia tive forcing anomalies remain constant at their 2100 levels. Several limitations of the simplifying assumptions underlying the USG approach to scenario devel opment 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 understand ing 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 (econ omic 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 appli cable to the SC-N2O. CLIMATE POLICY 276 Marten et al. 2.1.2. Equilibrium climate sensitivity In reduced-form IAMs, the speed and magnitude of temperature change for a given emissions projec tion 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 sus tained 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 prob ability distribution for the ECS parameter of the form suggested by Roe and Baker (2007). The USG cali brated the parameters of the probability distribution to have a median equal to 3 C, two-thirds probability that the ECS lies between 2 and 4.5 C, which was intended to be consistent with the UN Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) consensus state ment about the ECS (Meehl et al., 2007). The distribution was truncated from above at 10 C. This spe cification 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 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 CO2 emissions occur over many decades, the dis count 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 CLIMATE POLICY 278 Marten et al. 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 Reilly and Richards (1993) Fankhauser (1994) Kandlikar (1995) Kandlikar (1996) Hammitt et al. (1996) Tol (1999) Tol et al. (2003) Hope (2005) N/A N/A N/A N/A N/A FUND 1.6 FUND 1.7 PAGE95 Hope (2006a) PAGE2002 Waldhoff et al. (2011) Marten and Newbold (2012) FUND 3.5 DICE2007 w/ MAGICC Time horizon Discount rate Emissions year 140 years 2, 5, 8% 1990 Scenarioa N/A Climate sensitivity N/A 230 years 100 years 100 years 2200 Ramsey 0, 2, 6% 0, 2, 6% 1,3, 5% 1991-2030 N/A N/A 1995-2015 IS92b IS90a,d IS90a,d IS92a,c,e N/A 3 C 3 C 1.5, 2,5, 4.5 C 2100 2200 2200 2200 3000 2300 0, 1, 3, 5, 10% 0, 1, 3, 5, 10% Ramsey 1995-2014 1995-2014 2000 Ramsey 2001 Ramsey 2010-2019 Ramsey, 2.5, 3, 5% 2010-2050 IS92a IS92a SRES A2 SRES A2 FUND, SRES A1B, A2, B1, B2 EMF-22 MiniCAM Base 2.5 C 2.5 C Probabilistic, mode of 3 C Probabilistic, mean of 3 C 2, 3, 4.5 C Probabilistic, median of 3 C aIS90 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. CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 279 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 emis sions 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 esti mation 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 CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 281 associated with a perturbation of a non-CO2 gas's emissions in a single year, and then adding this radia tive 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 concen tration. 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 deter mined 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 base line 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 esti mates are associated with a one tonne perturbation, to avoid computational rounding error a 1 Mt per turbation 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-mar ginal 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 esti mate. 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 CLIMATE POLICY 282 Marten et al. 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, CTM4 [ppb], such that cCH4 ch4 Ct-1 + ScH4 (cCH4 ch4 ch4 Ct-1 ) + Jch4 e t-1, (1) where SCH4 defines the rate of decay, CTM4 [ppb] is the pre-industrial atmospheric concentration, and gCH4 [ppb/Mt] converts emissions, ETM4 [Mt], from mass to atmospheric volume. The mass to volume conversion factor is gCH4 = 0.3597 ppb/Mt and CTM4 = 700 ppb, following the IPCC TAR. The rate of decay is set to SCH4 = 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 con centration in 2005. The value from the Advanced Global Atmospheric Gases Experiment network as reported in the IPCC AR4 is used so that cC0045 = 1774 ppb. The contribution of atmospheric methane to global radiative forcing, denoted Q^4, is defined using the relationship in Table 6.2 of the IPCC TAR: qCH4 = f 0.036(yCF- yCTM4) - [f(CCH4, CN?) - (CCH4, CNeO)^, (2) where CpNr2eO [ppb] is the pre-industrial atmospheric concentration of nitrous oxide and f(CCH4, CN2?) = 0.47ln[1 + 2.01 x 10"5(CCH4CN20)]0.75 + 5.31 x 10-15cCH4(CCH4CN20)L52]. (3) The function in expression (3) accounts for the overlapping absorption bands of CH4 and N20, 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. Follow ing 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. The pre-industrial concentration of N20 is set consistent with the IPCC TAR, such that CNr2e0 = 270 ppb. CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 283 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 emis sions 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 impli cations of ignoring these interactions by comparing the incremental atmospheric concentration pro jected 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 radia tive 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 there fore 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 concen trations of other gases and increasing atmospheric temperature, which increase the lifetime of atmos pheric CH4. To understand the effect that this difference would have on an estimate of the SC-CH4, an exper iment was conducted using the DICE model in which the additional forcing from a one tonne pertur bation 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 rel evant gases and atmospheric temperature that are accounted for in MAGICC, and the social cost CLIMATE POLICY 284 Marten et al. Figure 2 Effects of perturbation in 2015 CH4 emissions for simple model vs. MAGICC: (a) additional atmospheric concentration; (b) additional radiative forcing 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 CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 285 TABLE 2 Effect of CH4 gas cycle model on SC-CH4 (2007$ per tonne CH4): DICE2010, MiniCAM Perturbation year 2015 2045 Discount rate 2.5% 3.0% 5.0% 2.5% 3.0% 5.0% Simple model 1135 822 349 2490 1933 956 MAGICC 1183 851 354 2707 2084 1006 Percent difference - 4% - 3% - 2% - 8% - 7% - 5% 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, CN2 [ppb], is specified as C^ CN2O Ct-1 + ^jO^re0 CN2O Ct-1 ) + Tn2OEN2O, (4) where SN2O is the rate of decay, and yN2O [ppb N2O/Mt N] converts emissions, ^^2 [Mt N], from mass to atmospheric volume. Following the IPCC AR4, the mass to volume conversion factor is yN2 = 0.2079 ppb N2O/Mt N and the rate of decay is 5N2 = 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 atmos pheric concentration in 2005. The value from the Advanced Global Atmospheric Gases Experiment network as reported in the IPCC AR4 is used, such that C'N205 = 319 ppb. The contribution of atmospheric N2O to global radiative forcing, denoted 0^, is defined using the relationship in Table 6.2 of the IPCC TAR, such that qch4=0.12^yep - yci0) - [f(cch4, cN2) - f^, cno)], (5) where f(CCH4, CN2) 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 dis cussed 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 CLIMATE POLICY 286 Marten et al. 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 per turbation 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 per turbation 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. Sub sequently, 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 projec tion. 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 extra polation 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, con stant. Based on the simple gas cycle models laid out in the earlier sections this implies that, for gas X, X -- dx(CX -- CX100) EX = _ pre 2100 vt > 2100. (6) gx 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 CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 287 Figure 3 Effects of perturbation in 2015 N2O emissions for simple model vs. MAGICC: (a) additional atmospheric concentration; (b) additional radiative forcing CLIMATE POLICY 288 Marten et al. TABLE 3 Effect of climate model on SC-N2O (2007$ per tonne N2O): DICE2010, MiniCAM Perturbation year 2015 2045 Discount rate 2.5% 3.0% 5.0% 2.5% 3.0% 5.0% Simple model 19,689 12,390 3,346 36,968 25,030 8,280 MAGICC 19,819 12,525 3,419 37,358 25,427 8,528 Percent difference - 1% - 1% - 2% -1% - 2% - 3% expression (6), while the dashed lines show two alternative extrapolation approaches, one where emis sions are held constant at their 2100 level and one that assumes emissions intensity (emissions/econ omic 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 emis sions. The two alternatives will not result in the radiative forcing contribution of gas X remaining con stant 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 pro jections 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 cumu lative radiative forcing from the projection over the time horizon differs by less than 0.001%, even for a 450 ** 400 // 350 300 250 ('V- 200 150 100 ------- Constant gradiative forcing 50 ----Constant Emissions *.......Constant Emissions/gross domestic product growth 2000 2050 2100 2150 Year 2200 2250 2300 ------- Constant gradiative forcing ------- Constant Emissions ......... Constant Emissions/gross domestic product growth 2000 2050 2100 2150 Year 2200 2250 2300 Figure 4 EMF-22 MiniCAM extended emissions scenario: (a) CH4 emissions; (b) N2O emissions CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 289 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 pertur bation in 2045 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 resi dence 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 extrapol ation 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 CLIMATE POLICY 290 Marten et al. 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% 3.0% 5.0% N2O 2.5% 3.0% 5.0% 2,490 1,933 956 36,968 25,030 8,280 2,490 1,933 956 36,588 24,837 8,261 2,490 1,933 956 36,662 24,868 8,263 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 emis sions 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 scen arios, the Roe and Baker (2007) distribution for the equilibrium climate sensitivity, and constant dis count 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 percen tile when using the 3.0% discount rate. By using the same assumptions and procedures as the USG, esti mates 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 econ omic systems become more stressed, although the growth rate of the social cost estimate may differ between the gases, as discussed in the following. CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 291 TABLE 5 SC-X (2007$ per tonne) Year Gas 5.0% mean 2020 CO2 CH4 N2O 2050 CO2 CH4 N2O 12 550 4,800 26 1,400 11,000 3.0% mean 43 1,200 15,000 71 2,500 27,000 2.5% mean 64 1,600 22,000 97 3,100 38,000 3% 95th percentile 128 3,200 41,000 220 6,900 74,000 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 disaggre gated 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 rel evant 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 6 Global damage potential Year Gas 5.0% mean 2020 CH4 46 N2O 397 2050 CH4 52 N2O 414 3.0% mean 29 359 36 388 2.5% mean 25 353 32 387 3% 95th percentile 25 317 31 338 CLIMATE POLICY 292 Marten et al. 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 equiva lents that can be valued with the SC-CO2 would probably provide a conservative estimate for the abate ment 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. CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 293 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 pre sented in Table 1 is more difficult as they are based on models and socio-economic and emissions scen arios 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, socio economic 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 scen arios 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 Hope (2006a) Waldhoff et al. (2011 )b Marten and Newbold (2012) Discount Rate Ramsey Ramsey 2.5% 3% 5% Emissions Year 2001 2010-2019 2020 2050 2020 2050 2020 2050 Social cost (2007$/ tonne X)a SC-CH4 SC-N2O 125 265 1,500 3,500 1,100 2,900 550 1,500 7,616 26,000 50,000 17,000 34,000 4,900 12,000 Global damage potential (SC-X/ SC-CO2) CH4 N2O 20 26 8-221 23 32 27 36 42 53 738 383-3,503 403 444 400 439 380 415 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 CO2 fertilization). CLIMATE POLICY 294 Marten et al. 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 maybe 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 differ ence. 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 dis count 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 esti mate 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 approxi mation 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 CLIMATE POLICY Social cost of CH4 & N2O consistent w/ US SC-CO2 295 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 Conser vation 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 (correspon dence 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; Solifio, 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 knowl edge 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 equili brium climate sensitivity of 3 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 ofthe National Academy ofScience ofthe USA, 109, 6435-6440. CLIMATE POLICY 296 Marten et al. Anthoff, D., Hepburn, C., &Tol, R. (2009). Equity weighting and the marginal damage costs of climate change. Eco logical Economics, 68, 836-849. Anthoff, D., & Tol, R. S. J. (2013). The uncertainty about the social cost of carbon: A decomposition analysis using FUND. 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