## Working Paper Series

U.S. Environmental Protection Agency Nation al Center for Environmental Economics 1200 Pennsylvania Avenue, NW (MC 1809) Washington, DC 20460 http://www.epa.gov/economics Estimating the Social Cost of Non

- CO 2 

### GHG Emissions: Methane and Nitrous Oxide

Alex L . Marten and Stephen C. Newbold

Working Paper # 11

- 0 1 Januar y , 20 11

### NCEE Working Paper Series Working Paper # 11

- 01 January , 2011

DISCLAIMER The views expressed in this paper are those of the author(s) and do not necessarily represent those of the U.S. En vironmental Protection Agency. In addition, although the research described in this paper may have been funded entirely or in part by the U.S. Environmental Protection Agency, it has not been subjected to the Agency's required peer and policy review. No official Agency endorsement should be inferred. 

### Estimating the Social Cost of Non

- CO 2 

### GHG Emissions: Methane and Nitrous Oxide Alex L. Marten and Stephen C. Newbold

# Estimating the Social Cost of Non-CO 2 

# GHG Emissions: Methane
and Nitrous Oxide

Alex L. Marten ∗

† 

### Stephen C. Newbold ‡


### February 13, 2012

**Abstract**
Many estimates of the social cost of CO 2 emissions (SCCO 2 ) can be found in the climate economics literature. However, to date far fewer estimates of the social costs of other greenhouse gases have been published, and many of those that are available are not directly comparable to current estimates of the SCCO 2 . In this paper we use a simplified integrated assessment model that combines MAGICC and (elements of) DICE to estimate the social costs of the three most important greenhouse gases—CO 2 , CH 4 , and N 2 O—for the years 2010 through 2050. Insofar as possible, we base our model runs on the assumptions and input parameters of the recent U.S. government inter-agency SCC working group. We compare our estimates of the social costs of CH 4 and N 2 O emissions to those that would be produced by using the SCCO 2 to value the "CO 2 -equivalents" of each of these gases, as calculated using their global warming potentials (GWPs). We examine the estimation error induced by valuing non-CO 2 greenhouse gas emission reductions using GWPs and the SCCO 2 for single- and multi-gas abatement policies. In both cases the error can be large, so estimates of the social costs of these gases, rather than proxies based on GWPs, should be used whenever possible. However, if estimates of the social cost are not available the value of non-CO 2 GHG reductions estimated using GWPs and the SCCO 2 will typically have lower absolute errors than default estimates of zero.
Keywords : social cost of carbon, global warming potential, integrated assessment JEL Classification : Q54, Q58

∗ The views expressed in this paper are those of the authors and do not necessarily represent those of the U.S. EPA. No Agency endorsement should be inferred. † National Center for Environmental Economics, U.S. Environmental Protection Agency, Washington, DC 20460 ‡ National Center for Environmental Economics, U.S. Environmental Protection Agency, Washington, DC 20460

1

## 1 Introduction

The social cost of carbon dioxide (SCCO 2 ) has become a common metric in estimating the benefits associated
with incremental reductions of carbon dioxide emissions. 1 The SCCO 2 has been widely studied (see Pearce (2003) for a review) and researchers have produced a large set of varied estimates (Tol, 2007). Newly developed estimates
of the SCCO 2 are now being used to assess the benefits of CO 2 emission reductions associated with U.S. government regulations. 2 However, recent climate policy analyses have been unable to quantify the benefits of reductions in nonCO 2 greenhouse gas (GHG) emissions due to a lack of comparable social cost estimates for these gases. This paper begins to fill this gap by calculating an internally consistent set of estimates of the social costs of CO 2 , CH 4 , and N 2 O, based on most of the assumptions used by the United States Government Interagency Working Group on the Social Cost of Carbon (USG (2010), hereafter, the “SCC working group”). We also compare the use of direct estimates of the
social costs of non-CO 2 GHGs to alternative estimates suggested by some analysts (e.g., Price et al. (2007)) based on global warming potentials (GWPs), which measure the contribution of non-CO 2 GHG emissions to a long run measure of atmospheric radiative forcing relative to that of CO 2 . The paper is structured as follows. In Section 2 we review the literature on the “social cost of carbon [dioxide],” including a brief recap of the recent SCC working group. We also review the much smaller literature on the social costs of other greenhouse gases, including CH 4 and N 2 O, and discuss the small set of previous studies that have examined the implications of using GWPs to translate non-CO 2 GHGs into “CO 2 -equivalents” for use in economic analysis. Section 3 describes the integrated assessment framework that we use to produce estimates of the social costs of CO 2 , CH 4 , and N 2 O, which combines a climate model (MAGICC, Wigley and Raper (1992), Wigley (2005)) with elements of one of the three integrated assessment models used by the SCC working group (DICE, Nordhaus and Boyer (2000), Nordhaus (2008)). In Section 4 we present our main results, starting with our direct estimates of the social costs of all three GHGs. We then use these estimates to calculate what Samuel Fankhauser denoted as the “global damage potentials” (GDPs) for CH 4 and N 2 O, for comparison to their respective GWPs. The degree to which the GDPs of these gases diverge from their GWPs, combined with the shares of the overall GHG emission reductions attributable to each gas under a particular policy, will determine the error in GWP-based benefit estimates. We calculate the magnitude of this error over a wide range of hypothetical mixed-GHG emission reduction policies, and we compare

1 Much of the previous literature has used the term “SCC” to refer to the social cost of carbon dioxide whether reported in tons of C or CO 2 . In this paper we must be more specific since we are discussing the social cost of other greenhouse gases, including another carbon-based molecule, methane. 2 New rules using the SCCO 2 in analysis include the Department of Energy rule on energy conservation standards for small electric motors and thejoint U.S. Environmental Protection Agency and U.S. National Highway Traffic Safety Administration (NHTSA) rule on light-duty vehicle greenhouse gas emission and corporate average fuel economy standards. The regulatory impact analysis (RIA) for the regulation of efficiency standards for small electrical motors may be found at http://www1.eere.energy.gov/buildings/appliance_standards/commercial/small_electric_motors.html, and the RIA for the light-duty vehicle rule is available at http://www.epa.gov/oms/climate/regulations.htm.

2these results to the error induced by excluding non-CO 2 GHGs from the analysis altogether. We conclude in Section

5 with a brief summary and discussion of the potential policy implications of our results. 

## 2 Background

The social cost of carbon dioxide, SCCO 2 , represents the present value of the future damages that would arise from an
incremental unit of CO 2 (typically one metric ton) being emitted in a given year. In principle, the SCCO 2 summarizes the impacts of climate change on all relevant market and non-market sectors, including agriculture, energy production, water availability, human health, coastal communities, biodiversity, and so on. As such, estimates of the SCCO 2 play an important role in assessing the benefits of policies that result in reductions of CO 2 emissions. SCCO 2 estimates are typically calculated using integrated assessment models (IAMs), which combine simplified models of the climate system and the economy, including the key feedbacks between the two. Small and not-so-small differences in the structural assumptions and the underlying empirical studies used for parameter calibrations among IAMs have led to a wide range of published SCCO 2 estimates, from roughly $0 to $100 per metric ton of CO 2 (NAS, 2009). In 2009 the U.S. government undertook an interagency process to establish consistency across federal agencies when valuing incremental CO 2 emission changes in regulatory impact analyses (RIAs). Towards this end, the SCCworking group used three widely known IAMs and imposed consistency across several key inputs, including the socioeconomic-emission scenarios, discount rate, and climate sensitivity probability distribution. To represent some of the uncertain model inputs, the SCC working group considered five socio-economic-emission scenarios and three discount rates. In the end, the SCC working group selected four estimates of the SCCO 2 for use in upcoming RIAs: $5, $21, $35, and $65. These values are reported in 2007 dollars, apply to emission reductions in 2010, and grow over time at 1-4% per year (USG (2010) Table 4). The first three values are the average estimates across all IAMs and scenarios using discount rates of 5%, 3%, and 2.5% per year, respectively. The last estimate is the 95th percentile across all models and scenarios using a discount rate of 3% per year. These estimates are intended to be used in RIAs for all U.S. federal agency regulations that result in marginal changes in CO 2 emissions. 3 The SCC working group did not provide
estimates of the social costs of non-CO 2 GHGs, though they noted that such values will be important for future policy analyses. The few estimates of the marginal social costs of other GHGs that are available in the climate economics literature rely on outdated modeling assumptions or are otherwise incompatible with recent SCCO 2 estimates. For example, some previous studies primarily focused on marginal emission reductions during the mid 1990s and sometimes the early 2000s (Kandlikar (1995), Tol et al. (2003), and Hope (2005)). With the exception of Fankhauser (1994), no

3 The SCCO 2 may not give an accurate estimate of total benefits if applied to large, or “non-marginal,” emission reductions, so analyzing large policies may require tailored applications of the IAMs to each policy scenario.

3estimates were provided for the years currently of concern to policy makers, and in most cases only a single time

period was considered. Extrapolating these estimates to current and future years is not possible without additional assumptions. Furthermore, many of the previous estimates (Kandlikar (1995), Hammitt et al. (1996), and Tol et al. (2003)) were based on reference scenarios that are nearly 20 years old and have now been superseded by newer studies (Houghton et al. (1992), and Nakicenovic and Swart (2000)). The most recently published estimates of the social
cost of non-CO 2 GHGs are values for CH 4 produced by Hope (2005) using the integrated assessment model PAGE95. However, PAGE95 is substantially different than the current version of the PAGE model (Plambeck and Hope (1996), Plambeck et al. (1997), and Hope (2006)). In recent years much attention has been paid to the social costs of CO 2 , both in terms of updating the integrated assessment models to reflect progress in our understanding of the physical impacts and economic damages from climate change, and exploring the sensitivity of SCCO 2 estimates to important modeling assumptions (Nordhaus (2010), Narita et al. (2010), Hope (2009)). Similar attention to non-CO 2 greenhouse gases would be of great benefit to policy analysts who are currently working to assess the impacts of regulations that affect more than just CO 2 emissions. In the interim it may seem that an easy solution would be to simply convert non-CO 2 GHGs to “CO 2 -equivalents” (CO 2 -e) using their respective global warming potentials (GWPs) and then value these with the SCCO 2 . This approach has been suggested by the U.K. Department for the Environment, Food, and Rural Affairs (Price et al., 2007). While a number of previous studies have shown that this simple solution may be inaccurate (Reilly and Richards (1993), Schmalensee (1993), and Fankhauser (1994)), other studies have shown that in cost-effectiveness analyses, where the aim is to minimize the cost of reaching a concentration or temperature stabilization target in some future year, the increased cost required to reach the target due to using proxy trading ratios based on GWPs might be relatively small (O’Neill (2003), Johansson et al. (2006), and Aaheim et al. (2006)). The goal of developing metrics such as the GWP has been to define a standard relationship between GHGs which represents their relative impact at a particular link along the chain: concentration changes → radiative forcing → climate impacts → socio-economic and environmental impacts → economic damages (e.g., O’Neill (2000), Smith and Wigley (2000), and Shine et al. (2005)). The GWP measure was developed to characterize the relationship between the first two links, concentrations and radiative forcings, in part based on a desire to keep the natural science and economic aspects separate (O’Neill, 2003). However, since its inception the GWP metric has been criticized on both scientific and economic grounds for reasons such as its arbitrary time horizon and use of an unrealistic constant concentration
scenario. 4 However, despite these shortcomings, GWPs still are used in climate change policy studies, probably due to their simple interpretation and transparent definition and the complexity of alternative measures (Shine et al., 2005).

4 We refer the interested reader to O’Neill (2000) and Fuglestvedt et al. (2003) for a more complete review of criticisms against GWPs.

4The continued use of GWPs has lead to a few recent studies that investigate the magnitude of errors that result

from the use of this metric. For example, cost effectiveness studies by O’Neill (2003), Johansson et al. (2006), and Aaheim et al. (2006) have examined the economic implications of using GWPs as the exchange rate within a multi-gas cap-and-trade market as opposed to optimally allocating abatement across GHGs. The GWP approach is known to be suboptimal since holding the trading ratios constant at GWPs will fail to capture the temporal nature of the problem. For example, current emissions of short-lived gases will have a negligible influence on a far-future target, and therefore forcing the trading ratio to be equal in all periods to the GWP will over-value, and in turn lead to over-abatement of, short lived gases in the near term. However, in all cases these authors find that the GWP approach lead to only a modest increase in the overall cost of reaching the target (approximately 4% in Johansson et al. (2006) for a 2 o C stabilization and 2% in O’Neill (2003) for a 550 ppmv CO 2 -e stabilization). This relatively small error can be partly understood by noting that the GWP appears to measure the relative impact of the gases at, or near, the appropriate link in the chain discussed above. That is, for a CO 2 -e concentration target, by definition, GWPs will provide the correct trading ratio at the target date. For a temperature target the relevant end point is only one link further along the chain from radiative forcings, so if the climate model used in the analysis considers the relationship between temperature change and radiative forcing to be approximately linear and temperature adjusts relatively quickly then little additional error will be introduced by using GWPs. Johansson et al. (2006) suggested that the steepness of the marginal abatement cost curves is also important in explaining the relatively small loss in cost-effectiveness. This is because in the future when abatement is high and the majority of costs are borne, large changes in the marginal costs will lead to relatively small changes in the levels of abatement. Therefore at this point, a small change to the trading ratio leading to a small change in the relative marginal costs, will result in only a small change to the distribution of abatement across gases.Unfortunately neither of these factors are relevant when comparing the relative social benefits of emission reductions across GHGs. Not only is there no saving grace analogous to the exponential curvature of marginal abatement costs, but in this case the relevant point in the chain is unequivocally the final endpoint that is associated with economic damages. This is especially problematic given the complexity of the connections along this chain. To see why, we can review the relationship between global warming potential and social costs, following an approach similar to that of Kandlikar (1996). The GWP measures the radiative effect of a given gas relative to a reference gas over a specified time horizon using the ratio of time integrated radiative forcing that results from the instantaneous release of one additional unit of a compound to that of one additional unit of a reference gas (commonly CO 2 ) (Ramaswamy et al., 2001). Specifically,

5the GWP over a time horizon of J years for gas X using CO 2 as the reference gas is

GW P =  ́ t + J

τ = t ∂ R τ ∂ X t d τ  ́ t + J τ = t ∂ R τ ∂ CO 2 , t d τ , (1)

where R t is the total radiative forcing in year t along a pre-defined reference path of emissions of both gases. For comparison, the (consumption-equivalent) social cost of GHG X in year t is

SCX t = ˆ t + H

τ = t ∂ C

τ ∂ X t e − r ( τ

− t ) d τ ,

where H is the time horizon of the benefit-cost analysis, C t is aggregate consumption in year t [$], and r is the discount

rate. 5 Now we can ask, under what conditions would the social cost of gas X be equal to its CO 2 -e counterpart multiplied by the SCCO 2 ? To address this question, we can identify a series of simplifying assumptions that will ultimately lead to an equivalence between these two quantities. Then we can ask whether this set of simplifying assumptions is likely to hold in reality, at least to a close enough approximation for the purpose of policy analysis. The following series of simplifying assumptions is sufficient to make the social cost of gas X equal to its GWP multiplied by the social cost of carbon dioxide: 1.) aggregate consumption in year t is affected only by the temperature anomaly in year t (not the rate of change of temperature or temperature anomalies in previous years), 2.) there is no time lag in the response of the atmospheric temperature to changes in radiative forcing, 3.) the reference emissions scenario for the benefit-cost analysis is the same as that used to calculate the GWP, 4.) the time horizon used for the benefit-cost analysis is the same as that used to calculate the GWP, 5.) the discount rate is zero, 6.) the temperature change is directly proportional to radiative forcing, and 7.) the loss in aggregate consumption is directly proportional to the temperature anomaly. To see why these assumptions are sufficient to make SCX t = GW P × SCCO 2 , note that assumptions 1 and 2 allow us to re-write the social cost of gas X as

SCX t = ˆ t + H

τ = t ∂ C

τ ∂ T τ ∂ T τ ∂ R τ ∂ R τ ∂ X t e − r ( τ

− t ) d τ

. (2)

Assumption 3 means that the ∂ R τ / ∂ X t terms in expressions (1) and (2) will be equivalent, and assumption 4 means
that J = H . Assumption 5 means that r = 0, so the discount factor in expression (2) equals one for all time periods.

5 The SCX t can be interpreted as the amount of money that, if set aside in year t , would be just sufficient to finance compensation payments for the stream of climate damages in all future years from one additional unit of emissions of GHG X in year t . Under this interpretation the discount rate r would be the interest rate that could be earned on such a hypothetical “trust fund”.

6Assumptions 6 and 7 mean that ∂ T t / ∂ R t = b and ∂ C t / ∂ T t = a for all time periods. Putting all of this together, expression (2) simplifies to

SCX t = ˆ t + J

τ = t ab ∂ R τ ∂ X t d τ , (3)
which, when divided by the analogous expression for CO 2 , leads back to expression (1). So here is a route to the desired result, but how realistic are the simplifying assumptions that are required to reach it? Each of the first six assumptions is unrealistic on its own, so this full package of assumptions would seem to be highly unrealistic. Specifically, the loss of consumption in any year t may depend on the temperature change in all years up to year t (as in several common integrated assessment models including FUND (Tol, 2002) and DICE (Nordhaus and Boyer, 2000)); the atmospheric temperature does not adjust immediately to its long run equilibrium level (Wigley and Schlesinger, 1985); the reference emissions scenario and the time horizon for the benefit-cost analysis typically do not match those used to calculate GWPs (Schmalensee, 1993); in a standard Ramsey framework, a discount rate of zero would require both the pure rate of time preference and the per-capita consumption growth rate (or the elasticity of the marginal utility of consumption) to equal zero (Weitzman, 2001); and economic losses generally are not modeled as a simple linear function of temperature (Nordhaus, 1994; Cline, 1992). Of the above simplifying assumptions, only the last is realistic: the equilibrium temperature is typically assumed to be proportional to the radiative forcing (Andronova et al., 2007; Roe and Baker, 2007). The above set of simplifying assumptions is not necessary for the social cost of gas X to be equal to its GWP multiplied by the social cost of carbon dioxide; it is simply the most straightforward set of sufficient conditions. Nevertheless, it would seem to require a highly unlikely convergence of coincidences for GWP to accurately reflect
the differences between SCCO 2 and the social costs of other GHGs given the long list of assumptions that diverge substantially from what is typically assumed when estimating the SCCO 2 . Therefore, it seems that the shortcut offered by the GWP is unlikely to be sufficiently accurate for quantitative policy analysis. Instead, it may be necessary to estimate the social cost of each greenhouse gas directly. The main objective of the remainder this paper is to estimate an internally consistent set of social costs for the three main greenhouse gases, following as closely as possible the approach used by the U.S. government interagency SCC working group, and to examine the errors that could arise from using GWP as a shortcut in estimating the benefits of greenhouse gas emissions reduction policies.


## 3 Integrated Assessment Framework

The integrated assessment framework we use in this paper is based on a modified version of the DICE model,

7as used by the SCC working group. We maintain the key aspects of this setup, changing only those features that

are necessary to facilitate the computation of the social cost of non-CO 2 GHGs. The main issue that arises when using DICE to examine non-CO 2 gases is that the standard version of the model includes an explicit representation of
stocks and flows of CO 2 in the atmosphere, but other GHGs are represented only implicitly in a catch-all “exogenous forcing” variable. To remedy this limitation, we replace the climate sub-model in DICE with the MAGICC climate model, which includes gas-cycle models for CH 4 and N 2 O, and in the case of CH 4 captures important interactions with other gases. The resulting framework uses exogenous socio-economic and emissions projections, the MAGICC climate model, a probability distribution over the equilibrium climate sensitivity parameter, and components of the DICE model. This section provides a brief discussion of these elements in turn. 

### 3.1 EMF Socio-Economic and Emissions Scenarios
Following the SCC working group, we use exogenous socio-economic and emissions projections based on the Stanford Energy Modeling Forum (EMF). During EMF study number 22, ten well known modeling groups produced a series of socio-economic and emissions trajectories through 2100, which span a range of business-as-usual (BAU) and policy scenarios. The SCC working group selected four of the BAU scenarios to represent the reference case: the IMAGE, MERGE Optimistic, MESSAGE, and MiniCAM Base reference scenarios. The SCC working group also
added a fifth lower-than-BAU scenario in which CO 2 -e concentrations stabilize at 550 ppm, to represent the possibility of international action without the U.S. and/or more optimistic abatement technology assumptions. For most scenarios insufficient information is available to model all anthropogenic climate forcings, so in the main body of this paper we examine only the MiniCAM Base reference scenario (Calvin et al., 2009). In the Appendix we examine the other scenarios by using data from the MiniCAM scenario to fill in projections for gases that were not reported as part of
the EMF-22 results. To extend the projections beyond 2100, we follow the strategy of the SCC working group. Specifically, the global population projection is extended by assuming that the growth rate will decline linearly starting in 2100 until it reaches zero in 2200. The growth rate of per capita economic output is assumed to decline linearly from the 2100 level to zero
in 2300. The industrial CO 2 emissions projection is extended by assuming that the carbon intensity (CO 2 /economic output) growth rate will continue to decline after 2100 at the same rate it averaged between 2090 and 2100. The net
CO 2 emissions from land use change is assumed to decline linearly starting in 2100 until it reaches zero in 2200, and the radiative forcings from all other emissions are assumed to remain constant after 2100. 6

6 The SCC working group did not specify how post-2100 radiative forcings from all non-CO 2 sources would remain constant at 2100 levels. We approximate this scenario by assuming that CH 4 and N 2 O emissions drop to their annual decay rate in 2100 in order to keep the stock constant, and we assume that all other non-CO 2 emissions remain constant at their 2100 levels. Under these assumptions, post-2100 non-CO 2 radiative forcing is always within 2% of 2100 levels, which has a negligible effect on the final marginal social cost estimates.

8

### 3.2 MAGICC Climate Module

To estimate the impact of anthropogenic GHG emissions on the climate, we use the Model for the Assessmentof Greenhouse-gas Induced Climate Change (MAGICC). MAGICC is a publicly available set of integrated gas cycle, climate, and ice melt models, which are used to predict changes in climate variables given exogenous emissionsprojections. As a reduced form model designed to emulate more complex global circulation models, MAGICC represents a good approach to incorporating realistic climate dynamics into integrated assessment frameworks (e.g. Calvin et al. (2009)). The model uses historical emissions in conjunction with the supplied scenario of future emissions to compute the global mean temperature from 1765 to the end of the scenario’s time horizon (2300 in this paper). The MAGICC climate model has been extensively used in the Intergovernmental Panel on Climate Change (IPCC) reports (e.g. Houghton et al., 1992, Houghton et al., 2001) and other published research (e.g. Hulme and Viner, 1998, New and Hulme, 2000, Wigley and Raper, 2002, Wigley et al., 2009). In this paper we use the most recent version (5.3) of the model, with all parameters set at their default values except for the equilibrium climate sensitivity. 7 

### 3.3 Climate Sensitivity
The equilibrium climate sensitivity, ∆ T eq 2 × CO 2 , is the change in the equilibrium mean global and annual surface temperature that would result from a sustained radiative forcing, ∆ R 2 × CO 2 , equivalent to that produced by a doubling of atmospheric CO 2 over its pre-industrial level, such that given a constant λ ,

∆ T eq 2 × CO 2 = λ ∆

R 2 × CO 2 . (4)

While there is a great deal of uncertainty regarding this value, estimates based on observations and global climate models have found that it very likely lies between 2 o C and 4.5 o C, though these studies have been unable to eliminate the possibility of higher values (Meehl et al., 2007). Uncertainty surrounding equilibrium climate sensitivity stems in part from uncertainty regarding the magnitude of the climate feedbacks associated with global warming (Bony et al., 2006). Given the inherently non-linear relationship between these feedbacks and the temperature response of the climate, basic theory suggests that the probability density function for the equilibrium climate sensitivity will be heavily skewed towards high values (Roe and Baker, 2007; Roe, 2009), a feature that is commonly found in estimates of the parameter’s density function. To characterize the uncertainty in the equilibrium climate sensitivity, we follow the approach of the SCC working group, which relied mainly on the work of Roe and Baker (2007). The change in equilibrium temperature is assumed to be a function of the reference climate sensitivity parameter, λ 0 , working on the change in radiative forcings along

7 MAGICC version 5.3 as used in this exercise was obtained from http://www.cgd.ucar.edu/cas/wigley/magicc/.

9Figure 1: Probability Density Function for Equilibrium Climate Sensitivity ( o C)

with a series of climate feedbacks whose total effect is assumed to be proportional to the temperature change by a

constant C , such that
∆ T eq 2 × CO 2 = λ

0 ∆ R 2 × CO 2 + C ∆ T eq

2 × CO 2 

. (5)
Combining (4) and (5) and defining the sum of feedbacks as f = λ 0 C , the equilibrium climate sensitivity can be represented as
∆ T eq 2 × CO 2 = λ

0 ∆ R 2 × CO 2 1

− f . The reference climate sensitivity parameter, λ 0 , represents the predicted temperature response in the absence of any
feedback effects and is assumed to be 0.3 o C/(w/m 2 ) , such that λ 0 ∆ R 2 × CO 2 ≈ 1

. 2 o C (Roe and Baker, 2007). To represent the uncertainty in the climate feedbacks, f is assumed to be normally distributed with mean μ f and standard
deviation σ

f . To be consistent with the Fourth Assessment Report of the IPCC (Solomon et al., 2007), these parameters were calibrated to ensure that the median of the resulting probability distribution over ∆ T eq 2 × CO 2 was equal to 3 o C and that two-thirds of the probability mass lies between 2 o C and 4.5 o C, with the distribution truncated at 10 o C. Based on these conditions the calibrated parameters are μ f = 0

. 6198 and σ

f = 0

. 1841. The calibrated probability density

10function of the equilibrium climate sensitivity parameter is shown in Figure 1.



### 3.4 DICE Economic Module
The DICE integrated assessment model combines a Ramsey-style model of global economic growth, based on a Cobb-Douglas production function with capital and labor as inputs, a basic climate module, and a damage function that relates the average global atmospheric temperature to the loss of economic output. DICE was developed as a dynamic optimization model in which carbon dioxide emissions are endogenously determined by global output, the emissions intensity of production, and the optimized time paths of investment and abatement. Carbon dioxide emissions from economic activities enter a three-box representation of the carbon cycle through which they influence radiative forcings and in turn the atmospheric temperature. To complete the loop, an aggregate damage function links the warming climate to net economic output. For more background on DICE, we refer the interested reader to Nordhaus (1993), Nordhaus and Boyer (2000), and Nordhaus (2008). To develop a framework consistent with that of the SCC working group, we incorporate a modified version of the DICE2007 model into our integrated assessment framework. Furthermore, we limit our use of DICE to the economic module since we replace the climate component by MAGICC as discussed above. In the economic model, global output, Y

t , depends on “total factor productivity”, A t , population, N t , physical capital, K t , and the mean global and annual surface temperature, T t , through a Cobb-Douglas production function with a “Hicks-neutral” climate damage
function:
Y t = A t K γ

t N ( 1

− γ ) t [ 1

− D ( T

t )] ,

where γ represents capital’s share of productivity and D ( T t ) is the damage (as a fraction of economic output) from climate change consistent with a change in the average global surface temperature above pre-industrial levels, T t . The rate of saving is assumed to be fixed, so aggregate consumption is C t = ( 1

− s ) Y

t . 8 The dynamics of physical capital are defined by the level of investment as determined by the constant savings rate, s , and the depreciation rate, δ = 0

. 1,
such that
K t = sY t + ( 1

− δ ) K

t

− 1 . (6)
Population is assumed to be exogenous and is taken from the EMF socio-economic-emissions scenarios directly. The path of total factor productivity, A t , is calculated from the EMF scenario’s projections of economic output and population using the dynamics of capital defined by (6). The initial value, A 0 , is set such that the marginal productivity of capital equals 0

. 1.

8 The use of the a constant savings rate represents a departure from the standard DICE model where the savings rate is a control variable that is chosen to maximize the net present value of utility for the representative agent. Here again we follow the SCC working group and use s = 0

. 22, which is close to the average optimal savings rate over the first five or so decades on the optimal path in DICE2007.

11Figure 2: DICE Damage Function

Warming of the climate, as measured by the mean global annual surface temperature above pre-industrial levels,
T t , results in damages expressed as a percentage loss of economic output, Y t . The damage function in DICE2007 has the following form:
D ( T t ) = 1

− 1 1 + aT b t . (7)
The parameters of the damage function were calibrated to account for the impacts of climate change on a variety of market and non-market sectors including agriculture, vulnerable industries, coastal areas, human health, environmental amenities net of adaptation, and the willingness to pay to reduce the risk of low-probability high-impact “catastrophic” events (Nordhaus (1994), Nordhaus and Boyer (2000)). In DICE2007, the calibrated damage function parameters are

a = 0

. 0028388 and b = 2. This gives economic damages equivalent to roughly 2.5% and 9.3% of global economic output if the global average atmospheric temperature is elevated by 3 o C and 6 o C, respectively. Figure 2 shows the calibrated damage function up to 10 o C.
The social cost of GHG X for a specific year, t , is the discounted present value of the loss of consumption due to the release of an extra unit of gas X in year t , i.e.,

SCX t = t + H 

## ∑

τ = t ∆ C τ ∆ X t ( 1 + r )

− ( τ

− t )
,

12where H is the time horizon of the analysis, r is the discount rate, and ∆ C τ is the difference in aggregate consumption in year τ between the baseline scenario and a perturbed scenario with ∆ X t additional units of emissions of gas X in
year t (so SCX t has units of “$/unit of emissions in year t ”). (This is simply the discrete time analog of the expression
for SCX t given in Section 2.) Following the SCC working group, we treat the discount rate r as constant over the time horizon of the analysis. 9 We used the integrated assessment framework described above to calculate the expected value of the social cost of
CO 2 , CH 4 , and N 2 O in the years 2010 to 2050. The integral used to calculate the expected value, given uncertainty surrounding the equilibrium climate sensitivity, was approximated using numerical quadrature. To accommodate the truncation of the climate sensitivity distribution, Simpson’s rule was used with 101 nodal values providing a relatively accurate and efficient approximation of the integral. The number of nodal values was determined based on the level at which the inclusion of additional nodes did not change the social cost when rounded to the nearest dollar. (See Miranda and Fackler (2002) for more information on numerical integration.) 

## 4 Results

Estimates of the expected social cost of marginal CO 2 , CH 4 , and N 2 O emissions in 2010 are presented in Table 1. The average values of the SCCO 2 of $9.4, $33, $52 for the three discount rates, and the 95th percentile value of $74 for the 3% discount rate (2007 U.S. dollars) are comparable to, though somewhat higher than, those produced by the SCC working group using DICE with the MiniCAM base scenario, which were $8.6, $29, $45, and $58 (USG (2010) Table 3). The differences between our estimates and those of the SCC working group are due to the slightly different behavior of MAGICC relative to the carbon cycle model in DICE. Specifically, in MAGICC 5.3 the CO 2 emissions perturbation exhibits a more pronounced and longer lasting impact on radiative forcing than that of the simplified three-box carbon cycle model in DICE2007. The ranges of the social costs for the non-CO 2 GHGs in 2010 are $370 to $2,000 for CH 4 and $3,500 to $29,000 for N 2 O. The significantly higher social cost estimates for an additional ton of CH 4 or N 2 O in 2010 relative to CO 2 are due to the significantly larger radiative forcing generated by these gases. Figure 3a highlights this difference through the expected temperature change due to an additional metric ton of each gas released in 2010. (Note that the y-axis is in a log10 scale to clearly show the three curves in the same figure.) This figure illustrates two of the important characteristics driving the differences among the social cost estimates of these gases: variation in radiative efficiency and lifespan. The difference in radiative efficiency determines the size of the impact each metric ton has on the

9 There are many reasons why the discount rate may not be constant over time (e.g., Weitzman (1998), Newell and Pizer (2003), Dasgupta (2008)), but a full discussion of alternative discounting approaches and their impact on the social cost of greenhouse gas emissions is beyond the scope of this paper.

13Discount Rate 5.0% 3.0% 2.5% 3.0% Gas Avg Avg Avg 95 th

CO 2 9.4 33 52 74 CH 4 370 810 1,100 2,000 N 2 O 3,500 13,000 20,000 29,000

Table 1: Social Cost of CO 2 , CH 4 , and N 2 O for 2010 (2007$/tonne)

equilibrium temperature, while the difference in atmospheric lifespan determines the length of time over which an additional metric ton of each gas exerts an effect on the global mean temperature and in turn economic damages. For example, the relatively short lifespan of CH 4 causes the temperature impact of a perturbation in 2010 to drop from its peak level by nearly an order of magnitude by 2100, while an analogous effect for a CO 2 perturbation does not occur before the end of the 300 year time horizon. The impacts of the marginal emissions initially enter the economic model through the damage function in (7), which determine the percentage of aggregate global economic output lost due to the current level of the global mean temperature change. Beyond this direct impact, changes in the climate have a cumulative effect through their influence on investment and in turn future levels of physical capital, i.e., a “capital offset effect.” However, for small changes in emissions the direct impacts on economic output will have a similar temporal pattern as their impact on temperature.Figure 3b shows the expected economic losses in a given year as a percentage of global economic output. The yaxis is again presented in log10 scale for easy readability. This figure highlights the important interaction between the temporal dynamics of climate impacts and the non-linearity of the damage function. Rather than peaking at the same time as the temperature impact of the perturbation, the additional economic loss peaks years later, even centuries
later as in the case with N 2 O versus CO 2 . This occurs because the global mean temperature in the reference case is expected to rise over time, in turn causing the direct impact of further temperature increases on economic output also to rise. Therefore, even though the impact of the perturbation on the global mean temperature begins to fall shortly after release, its direct effect on economic output continues to rise. This behavior clearly is an important determinant of the social costs of different GHGs, but it s not captured by an index based solely on the physical impacts of these gases, such as the GWP. The total stream of damages is determined by the direct economic losses resulting from the additional emissions plus the indirect impacts caused by the capital offset effect. The discount rate clearly plays an important role in aggregating the stream of future damages to a present value estimate of the marginal social cost of emissions, as may be seen from the results in Table 1. However, the influence of the discount rate also depends on the characteristics of the gases. For gases with shorter lifespans, such as CH 4 , the majority of the damages will occur earlier in time than

14(a) Mean Change in Temperature

(b) Mean Economic Losses Figure 3: Impact of an Additional Tonne in 2010

15those of gases with longer lifespans, such as CO 2 and N 2 O. Therefore the social cost of longer-lived gases will be

more sensitive to the discount rate than the social cost of shorter-lived gases. For example, the social costs of CO 2 and
N 2 O are over 450% higher under a 2.5% discount rate than a 5% discount rate, while the social cost of CH 4 is 200% higher. To further illustrate the importance of the discount rate, along with uncertainty regarding the equilibrium climate sensitivity, Figure 4 shows the probability density functions for the social cost estimates of CH 4 and N 2 O. As expected, the distributions of the social costs are highly skewed due to the skew of the equilibrium climate sensitivity pdf and the convex damage function. The interaction between the discount rate and the characteristics of the various gases plays an important role in determining both the shape and location of these density functions. As explained above, the longer the lifespan of the gas the greater the impacts it will have on future consumption and therefore the more influential the discount rate will be in determining the location of the density function. As a result the overlap of the pdfs across the three discount rates will be smaller for longer lived gases. We also used the model to estimate the expected marginal social costs of each gas through 2050. Because both the atmospheric temperature and economic output are projected to increase over time, and because the damage function is a convex function of the temperature, the marginal social costs also will increase over time. Table 2 presents the social cost of an additional metric ton of emissions in the years up to 2050 for CH 4 and N 2 O. 

### 4.1 Error in Using GWPs for Single-gas Policies

With the direct estimates of the social costs of CH 4 and N 2 O reported above, we can now examine the error associated with using the GWP to convert emissions reductions into CO 2 -e and then valuing these using the SCCO 2 . Table 3 presents the ratio of the average social cost of CH 4 and N 2 O relative to CO 2 for a one metric ton perturbation in the specified year. These values represent the true relationship between the benefits of a marginal reduction in CH 4 or N 2 O emissions relative to the same size reduction in CO 2 emissions, i.e., their “greenhouse damage potentials” (GDPs) (Fankhauser, 1994), conditional on the integrated assessment framework laid out in Section 3. By valuing
reductions in CO 2 -e using the SCCO 2 the analyst is implicitly using GWPs to approximate these GDPs. Given that the 100 year GWPs for CH 4 and N 2 O, as reported by the IPCC in AR4, are 25 and 298 respectively, it is clear that using the GWP to convert gases to CO 2 -e for the purpose of estimating marginal abatement benefits has the potential for significant errors. In 2010 emissions reductions for CH 4 valued using the 100 year GWP could be underestimated by as much as 36% while N 2 O could be underestimated by as much as 24%, depending on the discount rate. As previously noted, the social costs of GHG emissions increase over time because of the higher temperatures and economic output expected in the future and the convexity of the damage function. The estimates of SCCH 4 and
SCN 2 O grow faster than SCCO 2 partially due to their initially higher radiative efficiency of CH 4 and N 2 O relative

16(a) Social Cost of CH 4 for 2010

(b) Social Cost of N 2 O in 2010 Figure 4: Probability Distributions

17CO2CH4N2ODiscount Rate 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0%Avg Avg Avg 95thAvg Avg Avg 95thAvg Avg Avg 95th2010 9.4 33 52 74 370 810 1,100 2,000 3,500 13,000 20,000 29,0002015 11 37 58 83 450 970 1,300 2,300 4,300 15,000 23,000 33,0002020 13 42 64 92 550 1,100 1,500 2,700 4,900 17,000 26,000 37,0002025 15 47 71 100 660 1,300 1,700 3,200 5,800 19,000 29,000 42,0002030 17 52 78 110 800 1,600 2,000 3,700 6,800 22,000 32,000 47,0002035 20 58 86 130 950 1,800 2,300 4,200 7,900 24,000 36,000 53,0002040 23 64 94 140 1,100 2,100 2,700 4,900 9,100 27,000 40,000 59,0002045 26 71 100 150 1,300 2,500 3,100 5,600 11,000 31,000 45,000 66,0002050 29 78 110 170 1,500 2,900 3,500 6,400 12,000 34,000 50,000 73,000Table 2: Social Cost of Marginal CH4and N2O Emissions (2007$/tonne)

18CH 4 N 2 O Discount Rate 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0%

Avg Avg Avg 95 th Avg Avg Avg 95 th

2010 39 25 21 27 372 390 392 392 2015 41 26 22 28 375 395 397 395 2020 42 27 23 30 380 400 403 401 2025 44 29 25 31 384 405 408 410 2030 46 30 26 32 390 411 415 415 2035 47 32 27 34 395 417 422 421 2040 49 33 29 36 402 425 430 431 2045 51 35 30 37 408 431 437 438 2050 53 36 32 39 415 439 444 444

Table 3: Social Cost of CH 4 and N 2 O Relative to CO 2

to CO 2 and the fact that their marginal forcings decrease slower with the increasing atmospheric stock (square root versus log). As a result the ratio of SCCH 4 and SCN 2 O to SCCO 2 increases with the year of the emission reductions, as seen in Table 3. This implies that the error in using a constant such as GWP to scale the benefits will change over time. For example, using the 100 year GWP to evaluate marginal reductions in CH 4 emissions will underestimate the benefits by up to 36% in 2010, growing to as much as 53% by 2050, depending on the discount rate. For N 2 O, using the 100 year GWP underestimates benefits by as much as 24% in 2010 growing to as much as 33% by 2050. The impact of the discount rate on the ratio of SCX to SCCO 2 differs for CH 4 and N 2 O. An increase in the discount rate effectively increases the importance of short-term relative to long-term impacts. Therefore the impact of
the discount rate on the ratio of SCX to SCCO 2 will depend upon the size of the long term impacts for gas X relative
to CO 2 . Due to the relatively short life span of CH 4 compared with CO 2 the effect of an increase in the discount rate is greater for SCCO 2 and in turn the ratio of the two social costs decreases, as seen in Table 3. However, in the case of
N 2 O the decay of a perturbation’s impact on overall radiative forcing is slower than that of a CO 2 perturbation, and in
turn an increase in the discount rate will lower the ratio of SCN 2 O to SCCO 2 .


### 4.2 Error in Using GWPs for Multi-gas Policies
The previous results suggest that using the SCCO 2 to value CO 2 -e reductions will result in large errors when analyzing policies that will reduce emissions of a single gas such as CH 4 or N 2 O. This has significant implications for regulatory analysis of policies where a major source of the benefits are derived from non-CO 2 GHG emission reductions. However, for some policies, such as the recent light duty vehicle rule (EPA, 2010b), reductions of non-CO 2 gases may represent only a minor fraction of the anticipated GHG emission reductions. For such policies, the error

19induced by valuing the social cost of non-CO 2 gases using GWPs may be small. Therefore, in cases where estimates

of the marginal social costs of non-CO 2 GHGs are unavailable, the question becomes whether the error induced bythe use of GWPs will be tolerable to the decision-maker. To examine this question, we consider how small the reduction in non-CO 2 emissions, relative to the CO 2 reduction, needs to be for the GWP approach to provide an adequate approximation, as measured by the error in overall abatement benefits. Consider a policy that will result in emissions reduction for two gases, CO 2 and X. The reduction in CO 2 emissions in period t is denoted as ∆ CO 2 , t and the reduction in X is assumed to be proportional by a factor of α . Therefore the present value of the benefits of these emission reductions are:

PV = H 

## ∑

t = 0 [( α SCX

t + SCCO 2 , t ) × ∆ CO 2 , t ] × ( 1 + r )

− t

.
If instead of using estimates of SCX to value the reduction in emissions of gas X, the GWP was used to convert those reductions to CO2-e, the present value of benefits would be estimated as:

ˆ PV = H 

## ∑

t = 0 [( α GW P + 1 ) × SCCO 2 , t × ∆ CO 2 , t ] × ( 1 + r )

− t

.

As an illustration, we calculated the size of the overall relative error, ˆ PV / PV

− 1, using the 100 year GWP for a generic policy lasting 40 years between 2010 and 2050 in which the level of reductions in CO 2 emissions is constant,
∆ t = ∆ , for all periods. 10 Figure 5a shows the case for a policy in which both CO 2 and CH 4 emissions are reduced. For reference, the dotted vertical line indicates the ratio of global CH 4 to CO 2 emissions, which is roughly 0.011 (Calvin et al., 2009). In the case where r = 3%, the total benefits are underestimated by less than 5% as long as the CH4
reductions are less than 1% of the CO 2 reductions. The error increases rapidly as the ratio of CH 4 to CO 2 reductions,

α , increases. This is particularly evident for the case of higher discount rates for which the GWP provides a much worse approximation, as was explained above. In the case where r = 2.5%, the average ratio of SCCH 4 to SCCO 2 is 26 over the 40 year time horizon. This is very close to the 100 year GWP of 25, so in this case the error remains relatively small regardless of the ratio of emissions reductions between the two gases. Also note that the intersections of the three curves with the vertical dotted line in Figure 5a gives the overall relative error from using GWPs to analyze policies
that would reduce CH 4 and CO 2 emissions by a common fraction. In this case these errors are on the order of -1% to -14% depending on the discount rate. In spite of this potential error the approach of valuing CO 2 -equivalent emissions may be of use to policy makers, when specific SCCH 4 estimates are unavailable, since this approach provides a lower

10 We also examined a case in which the emission reductions grow linearly over time, in the fashion of a “policy ramp.” In this scenario, even with a particularly fast increase in abatement, the requirements for obtaining a given overall error become only slightly stricter.

20bound for the abatement benefits and therefore provides an unambiguously more accurate estimate of the total benefits

over implicitly assuming an SCCH 4 of zero. Figure 5b shows the case for a policy that will reduce both CO 2 and N 2 O emissions. The dotted vertical line indicates the ratio of current global N 2 O to CO 2 emissions, which is around 0.0003 (Calvin et al., 2009). In contrast
to the case of CH 4 , using GWPs to value N 2 O emission reductions results in an error that grows much more rapidly
as the share of N 2 O reductions increases. By the time N 2 O emission reductions are on the order of 0.5% of CO 2 reductions, the GWP approach will underestimate benefits by around 15%-20% compared with an analogous range of
1%-10% for CH 4 . This occurs because the level of N 2 O benefits are larger in level and therefore also as a percent of total benefits. Therefore even though the GDP for CH 4 is closer to the GWP than it is for N 2 O, a markedly smaller proportion of the overall emissions reduction needs to be derived from N 2 O to increase the overall error. The other
noticeable difference between the cases of N 2 O and CH 4 is the relative insensitivity to the discount rate. However, this is not unexpected in light of the discussion in Section 4.1 regarding the impact of the discount rate on these ratios. In Figure 5b all three curves cross the vertical dotted line at nearly the same point. This means that using GWPs to analyze a policy that would reduce N 2 O and CO 2 emissions by a common fraction would underestimate the overall benefits by approximately 2.5% independent of the discount rate. At any value of α the GWP approach will provide a lower bound for the benefits of a policy that reduces N 2 O, and possibly CO 2 , emissions and may therefore provide policy makers with more information than the case in which the SCN 2 O is implicitly assumed to be zero. For policies that affect the emissions of all three gases the magnitude of the bias will depend on not only the overall proportion of CH 4 and N 2 O emissions, but also the discount rate being utilized.

**4.2.1 Abatement Benefits of Light-Duty Vehicle Rule**
One of the first applications of the new interagency SCCO 2 estimates in a RIA was that of the joint rule making between the U.S. Environmental Protection Agency (EPA) and the U.S. National Highway Traffic Safety Administration (NHTSA) on light-duty vehicle greenhouse gas emission and corporate average fuel economy standards (EPA, 2010b). Signed in April of 2010, this rule sets emissions and fuel economy standards for passenger cars, light-duty trucks, and medium-duty passenger vehicles for the model years 2012 through 2016. The rule is expected to reduce the emissions
of CO 2 , CH 4 , and N 2 O where Table 4 presents the EPA’s emission reduction estimates for the years 2020, 2030, 2040,and 2050 (EPA (2010a) Table 5-26). Therefore the social benefits of the rule will be based on the reduction of emissions for multiple GHGs, however, the economic analysis presented in the RIA only quantifies the benefits associated
with CO 2 emission reductions (EPA, 2010a).
The N 2 O emission reductions are consistently around 0.0002% of CO 2 reductions, while CH 4 reductions are

21(a) Error with CH 4 and CO 2 Abatement

(b) Error with N 2 O and CO 2 Abatement Figure 5: Error in Overall Abatement Benefits Estimate

222020 2030 2040 2050

CO 2 139,067,814 273,257,576 360,372,017 458,709,558 CH 4 153,944 302,450 398,851 507,687 N 2 O 302 575 749 953

Table 4: GHG Emission Reductions from Light-Duty Vehicle Rule (tonnes)

consistently around a 0.1% of CO 2 emission reduction by mass. Ignoring the N 2 O reductions for the moment, this policy resembles the illustration above where CH 4 emission reductions were a constant percentage of CO 2 reductions over time. Figure 5a suggests that if GWPs were used to estimate the benefits of CH 4 reductions in this case then the overall benefits would be underestimated by around 1-2%, depending on the discount rate. In fact, comparing the GWP approach and the use of the direct estimates we find that the error associated with valuing CO 2 -e reductions is approximately -1% when using a constant 3% discount rate. 11 Using the estimates of SCCH 4 and SCN 2 O presented in Section 4, the overall error from failing to quantifying the non-CO 2 emission reductions from this rule is approximately 10.6 billion 2007$, which is a relative error of -4%. That is, by using GWPs the relative error could be reduced from -4% to approximately -1%. So this exercise suggests that if direct estimates of the marginal social costs of non-CO 2 GHGs are not available, then the use of GWPs to value non-CO 2 GHG reductions may be preferable to implicitly assuming a value of zero.


## 5 Concluding Remarks

In this paper we used an integrated assessment framework that combined elements of DICE with the simple climate model MAGICC to develop an internally consistent set of estimates of the social costs of CO 2 , CH 4 , and N 2 O. In developing these estimates, we followed as closely as possible the approach of the recent SCC working group. Our results suggest that the possible alternative of using GWPs to convert marginal non-CO 2 GHG emission reductions
into CO 2 -e reductions valued using SCCO 2 can lead to substantial errors for the abatement benefits of individual gases. Based on our estimates for the SCCH 4 and SCN 2 O, this approach can underestimate the benefits of current
CH 4 emission reductions by up to 35% and the benefits of current N 2 O emission reductions by as much as 24%. The above findings apply to single-gas policies, such as improved leak prevention in natural gas systems, improved waste water treatment practices, or the requirement of specific degasification techniques for coal mining, which would

11 Since the annual impacts of the rule on GHG emissions were not reported, we derived the inter-decade values by linear interpolation. We also used linear interpolation to determine the effect prior to 2020 assuming that the effect in 2011 will be zero.

23mainly reduce CH 4 emissions, and changes to the production process for nitric and adipic acids, which would mainly

reduce N 2 O emissions (EPA, 2006). We also examined multi-gas policies, where the reductions in CH 4 and N 2 O emissions represent only a share of the total GHG emission reductions, for example, the recent light duty vehicle rule by EPA and NHTSA. In these cases, the relative error from using the GWP approach will necessarily be smaller than that for single-gas policies and will of course shrink as the proportion of the GHG emission reduction coming
from non-CO 2 gases shrinks. Therefore, depending on the share of non-CO 2 GHG emissions reductions and decisionmakers’ tolerances for under-estimation errors, when direct estimates of marginal social costs of non-CO 2 GHGs are not available the use of GWPs may be preferred to failing to quantify the benefits of non-CO 2 GHGs altogether.



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26

## A Results for Additional Socio-Economic-Emissions Scenarios

To define projections of socio-economic-emissions paths the USG Interagency Working Group selected scenarios from the EMF-22 modeling exercise. The scenarios selected included four BAU scenarios and a fifth lower-than-BAU
scenario in which CO 2 -e concentrations stabilized at 550 ppm. The four BAU scenarios included the IMAGE, MERGE Optimistic, MESSAGE, and MiniCAM Base reference scenarios. The fifth scenario is the average of the stabilization at 550 ppm CO 2 -e without overshoot for the same four models. In the paper we focused on the MiniCAM Base reference scenario due to access to the full suite of emissions projections for this scenario. For the other models EMF only published emissions projections for CO 2 , CH 4 , and
N 2 O, while the climate model used in this paper (MAGICC) requires inputs for tropospheric aerosols and halogenated gases as well. In order to get some insight into the difference in SCX estimates across the scenarios, we combine the model specific projections for economic output, population, and CO 2 , CH 4 , and N 2 O emissions with the MiniCAM trajectories for the remaining input gases. This assumption will affect the SCX estimates in two ways, first due to the non-linearity of the damage function the base line temperature will play an important role and this assumption may over or under represent warming for these additional scenarios. Second the atmospheric lifetime of CH 4 will be dependent upon the concentrations of NO x , CO, and other VOCs.

27CO2CH4N2ODiscount Rate 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0%Avg Avg Avg 95thAvg Avg Avg 95thAvg Avg Avg 95th2010 11 36 57 82 430 910 1,200 2,200 4,000 14,000 21,000 31,0002015 13 41 63 92 530 1,100 1,400 2,600 4,700 16,000 24,000 35,0002020 15 46 69 100 640 1,300 1,600 3,000 5,600 18,000 27,000 40,0002025 17 51 77 110 760 1,500 1,900 3,500 6,500 20,000 30,000 45,0002030 20 57 84 130 900 1,700 2,200 4,000 7,500 23,000 34,000 50,0002035 23 63 92 140 1,100 2,000 2,500 4,600 8,700 25,000 37,000 56,0002040 26 70 100 150 1,200 2,300 2,800 5,200 9,900 28,000 41,000 62,0002045 29 77 110 160 1,400 2,600 3,200 5,900 11,000 32,000 46,000 69,0002050 32 84 120 180 1,600 2,900 3,600 6,600 13,000 35,000 50,000 76,000Table 5: Social Cost of Marginal CH4and N2O Emissions (2007$/tonne) - IMAGE

28CO2CH4N2ODiscount Rate 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0%Avg Avg Avg 95thAvg Avg Avg 95thAvg Avg Avg 95th2010 8 24 35 53 340 700 890 1,600 3,100 9,800 14,000 21,0002015 10 27 38 58 420 820 1,000 1,900 3,600 11,000 16,000 24,0002020 11 30 42 64 510 970 1,200 2,200 4,300 13,000 18,000 27,0002025 13 33 46 71 610 1,100 1,400 2,600 5,000 14,000 20,000 30,0002030 15 36 50 78 730 1,300 1,600 3,000 5,800 16,000 22,000 33,0002035 16 40 54 84 860 1,600 1,900 3,500 6,700 18,000 25,000 37,0002040 18 43 58 90 1,000 1,800 2,200 3,900 7,600 20,000 27,000 41,0002045 20 47 62 95 1,200 2,000 2,500 4,400 8,700 22,000 30,000 45,0002050 22 50 66 100 1,400 2,300 2,800 5,000 9,800 24,000 32,000 49,000Table 6: Social Cost of Marginal CH4and N2O Emissions (2007$/tonne) - MERGE

29CO2CH4N2ODiscount Rate 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0%Avg Avg Avg 95thAvg Avg Avg 95thAvg Avg Avg 95th2010 10 32 47 71 420 850 1,100 2,000 3,700 11,000 17,000 25,0002015 12 36 52 79 510 1,000 1,300 2,400 4,300 13,000 19,000 29,0002020 14 40 58 88 620 1,200 1,500 2,800 5,100 14,000 21,000 32,0002025 16 44 63 98 740 1,400 1,700 3,200 5,900 16,000 23,000 36,0002030 19 49 69 110 880 1,600 2,000 3,600 6,800 18,000 25,000 40,0002035 21 54 76 120 1,000 1,800 2,200 4,100 7,700 20,000 28,000 44,0002040 24 59 82 130 1,200 2,100 2,500 4,700 8,800 22,000 30,000 48,0002045 27 65 89 140 1,400 2,300 2,800 5,200 9,800 24,000 33,000 52,0002050 30 70 96 150 1,500 2,600 3,100 5,800 11,000 26,000 36,000 57,000Table 7: Social Cost of Marginal CH4and N2O Emissions (2007$/tonne) - MESSAGE

30CO2CH4N2ODiscount Rate 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0% 5.0% 3.0% 2.5% 3.0%Avg Avg Avg 95thAvg Avg Avg 95thAvg Avg Avg 95th2010 9 26 40 63 360 720 920 1,700 3,000 9,000 13,000 21,0002015 10 30 44 70 440 840 1,100 2,000 3,500 10,000 15,000 24,0002020 12 33 49 78 530 990 1,200 2,400 4,000 11,000 16,000 27,0002025 13 37 54 87 630 1,100 1,400 2,700 4,600 13,000 18,000 30,0002030 15 41 59 96 740 1,300 1,600 3,100 5,200 14,000 20,000 33,0002035 17 45 65 100 860 1,500 1,900 3,600 5,900 15,000 22,000 36,0002040 19 50 71 120 980 1,700 2,100 4,000 6,600 17,000 24,000 40,0002045 22 55 77 130 1,100 1,900 2,300 4,600 7,300 18,000 26,000 44,0002050 24 60 83 140 1,300 2,200 2,600 5,100 8,100 20,000 28,000 47,000Table 8: Social Cost of Marginal CH4and N2O Emissions (2007$/tonne) - 550 Stabilization

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