16-A-i

APPENDIX 16-A. SOCIAL COST OF CARBON FOR REGULATORY IMPACT 

ANALYSIS UNDER EXECUTIVE ORDER 12866

TABLE OF CONTENTS

16-A.1 EXECUTIVE SUMMARY ................................................................................. 16-A-1

16-A.2 MONETIZING CARBON DIOXIDE EMISSIONS ........................................... 16-A-2

16-A.3 SOCIAL COST OF CARBON VALUES USED IN PAST REGULATORY 

ANALYSES ......................................................................................................... 16-A-4

16-A.4 APPROACH AND KEY ASSUMPTIONS ........................................................ 16-A-5

16-A.4.1 Integrated Assessment Models ............................................................................ 16-A-5

16-A.4.2 Global versus Domestic Measures of Social Cost of Carbon ............................ 16-A-11

16-A.4.3 Valuing Non-CO2 Emissions ............................................................................. 16-A-13

16-A.4.4 Equilibrium Climate Sensitivity ........................................................................ 16-A-13

16-A.4.5 Socioeconomic and Emissions Trajectories....................................................... 16-A-16

16-A.4.6 Discount Rate ..................................................................................................... 16-A-19

16-A.5 REVISED SOCIAL COST OF CARBON ESTIMATES ................................. 16-A-26

16-A.6 LIMITATIONS OF THE ANALYSIS .............................................................. 16-A-32

16-A.7 A FURTHER DISCUSSION OF CATASTROPHIC IMPACTS AND

DAMAGE FUNCTIONS .................................................................................. 16-A-34

16-A.8 CONCLUSION .................................................................................................. 16-A-37

16-A.9 ANNEX.............................................................................................................. 16-A-44

16-A.9.1 Other (non-CO2) Gases ...................................................................................... 16-A-45

16-A.9.2 Extrapolating Emissions Projections to 2300 .................................................... 16-A-47

LIST OF TABLES

Table 16-A.1.1 Social Cost of CO2, 2010 – 2050 (in 2007 dollars) ................................. 16-A-2

Table 16-A.4.1 Summary Statistics for Four Calibrated Climate Sensitivity 

Distributions ........................................................................................... 16-A-14

Table 16-A.4.2 Socioeconomic and Emissions Projections from Select EMF-22 

Reference Scenarios ............................................................................... 16-A-18

Table 16-A.5.1 Disaggregated Social Cost of CO2 Values by Model, Socioeconomic 

Trajectory, and Discount Rate for 2010 (in 2007 dollars) ..................... 16-A-29

Table 16-A.5.2 Social Cost of CO2, 2010 – 2050 (in 2007 dollars) ............................... 16-A-31

Table 16-A.5.3 Changes in the Average Annual Growth Rates of SCC Estimates 

between 2010 and 2050 ......................................................................... 16-A-31

Table 16-A.7.1 Probabilities of Various Tipping Points from Expert Elicitation ........... 16-A-35

Table 16-A.9.1 Annual SCC Values: 2010–2050 (in 2007 dollars) ............................... 16-A-44

Table 16-A.9.2 2010 Global SCC Estimates at 2.5 Percent Discount Rate (2007$/ton 

CO2) ....................................................................................................... 16-A-54

Table 16-A.9.3 2010 Global SCC Estimates at 3 Percent Discount Rate (2007$/ton 

CO2) ....................................................................................................... 16-A-55
16-A-ii

Table 16-A.9.4 2010 Global SCC Estimates at 5 Percent Discount Rate (2007$/ton 

CO2) ....................................................................................................... 16-A-56

Table 16-A.9.5 Additional Summary Statistics of 2010 Global SCC Estimates ............ 16-A-57

LIST OF FIGURES 

Figure 16-A.5.1 Annual Consumption Loss as a Fraction of Global GDP in 2100 Due 

to an Increase in Annual Global Temperature in the DICE, FUND, and 

PAGE models......................................................................................... 16-A-10

Figure 16-A.5.2 Annual Consumption Loss for Lower Temperature Changes in DICE, 

FUND, and PAGE ................................................................................. 16-A-11

Figure 16-A.5.3 Estimates of the Probability Density Function for Equilibrium Climate 

Sensitivity (°C) ...................................................................................... 16-A-16

Figure 16-A.6.1 Level of Global GDP across EMF Scenarios ........................................ 16-A-30

Figure 16-A.10.2 Sulfur Dioxide Emission Scenarios ....................................................... 16-A-47

Figure 16-A.10.3 Global Population, 2000-2300 (Post-2100 extrapolations assume the 

population growth rate changes linearly to reach a zero growth rate by 

2200.) ..................................................................................................... 16-A-49

Figure 16-A.10.4 World GDP, 2000-2300 (Post-2100 extrapolations assume GDP per 

capita growth declines linearly, reaching zero in the year 2300) .......... 16-A-50

Figure 16-A.10.5 Global Fossil and Industrial CO2 Emissions, 2000-2300 (Post-2100 

extrapolations assume growth rate of CO2 intensity (CO2/GDP) over 

2090-2100 is maintained through 2300.) ............................................... 16-A-51

Figure 16-A.10.6 Global Net Land Use CO2 Emissions, 2000-2300 (Post-2100 

extrapolations assume emissions decline linearly, reaching zero in the 

year 2200) .............................................................................................. 16-A-51

Figure 16-A.10.7 Global Non-CO2 Radiative Forcing, 2000-2300 (Post-2100 

extrapolations assume constant non-CO2 radiative forcing after 2100) 16-A-52

Figure 16-A.10.8 Global CO2 Intensity (fossil & industrial CO2 emissions/GDP), 2000-

2300 (Post-2100 extrapolations assume decline in CO2/GDP growth 

rate over 2090-2100 is maintained through 2300) ................................. 16-A-53

Figure 16-A.10.9 Histogram of Global SCC Estimates in 2010 (2007$/ton CO2), by 

discount rate ........................................................................................... 16-A-56
16-A-1

APPENDIX 16-A. SOCIAL COST OF CARBON FOR REGULATORY IMPACT 

ANALYSIS UNDER EXECUTIVE ORDER 12866a

16-A.1 EXECUTIVE SUMMARY

Under Executive Order 12866, agencies are required, to the extent permitted by law, “to 

assess both the costs and the benefits of the intended regulation and, recognizing that some costs 

and benefits are difficult to quantify, propose or adopt a regulation only upon a reasoned 

determination that the benefits of the intended regulation justify its costs.” The purpose of the 

“social cost of carbon” (SCC) estimates presented here is to allow agencies to incorporate the 

social benefits of reducing carbon dioxide (CO2) emissions into cost-benefit analyses of 

regulatory actions that have small, or “marginal,” impacts on cumulative global emissions. The 

estimates are presented with an acknowledgement of the many uncertainties involved and with a 

clear understanding that they should be updated over time to reflect increasing knowledge of the 

science and economics of climate impacts.

The SCC is an estimate of the monetized damages associated with an incremental 

increase in carbon emissions in a given year. It is intended to include (but is not limited to) 

changes in net agricultural productivity, human health, property damages from increased flood 

risk, and the value of ecosystem services due to climate change. 

This document presents a summary of the interagency process that developed these SCC 

estimates. Technical experts from numerous agencies met on a regular basis to consider public 

comments, explore the technical literature in relevant fields, and discuss key model inputs and 

assumptions. The main objective of this process was to develop a range of SCC values using a 

defensible set of input assumptions grounded in the existing scientific and economic literatures. 

In this way, key uncertainties and model differences transparently and consistently inform the 

range of SCC estimates used in the rulemaking process. 

 

a Prepared by Interagency Working Group on Social Cost of Carbon, United States Government.

With participation by:

Council of Economic Advisers 

Council on Environmental Quality 

Department of Agriculture

Department of Commerce

Department of Energy

Department of Transportation

Environmental Protection Agency

National Economic Council

Office of Energy and Climate Change

Office of Management and Budget

Office of Science and Technology Policy 

Department of the Treasury
16-A-2

The interagency group selected four SCC values for use in regulatory analyses. Three 

values are based on the average SCC from three integrated assessment models, at discount rates 

of 2.5, 3, and 5 percent. The fourth value, which represents the 95th percentile SCC estimate 

across all three models at a 3 percent discount rate, is included to represent higher-than-expected 

impacts from temperature change further out in the tails of the SCC distribution. 

 

Table 16-A.1.1 Social Cost of CO2, 2010 – 2050 (in 2007 dollars) 

Discount Rate

5% 3% 2.5% 3%

Year Avg Avg Avg 95th

2010 4.7 21.4 35.1 64.9

2015 5.7 23.8 38.4 72.8

2020 6.8 26.3 41.7 80.7

2025 8.2 29.6 45.9 90.4

2030 9.7 32.8 50.0 100.0

2035 11.2 36.0 54.2 109.7

2040 12.7 39.2 58.4 119.3

2045 14.2 42.1 61.7 127.8

2050 15.7 44.9 65.0 136.2

16-A.2 MONETIZING CARBON DIOXIDE EMISSIONS

The SCC is an estimate of the monetized damages associated with an incremental 

increase in carbon emissions in a given year. We report estimates of the SCC in dollars per 

metric ton of carbon dioxide throughout this document.b

 

 

When attempting to assess the incremental economic impacts of carbon dioxide 

emissions, the analyst faces a number of serious challenges. A recent report from the National 

Academies of Science (NRC 2009) points out that any assessment will suffer from uncertainty, 

speculation, and lack of information about (1) future emissions of greenhouse gases, (2) the 

effects of past and future emissions on the climate system, (3) the impact of changes in climate 

on the physical and biological environment, and (4) the translation of these environmental 

impacts into economic damages. As a result, any effort to quantify and monetize the harms 

associated with climate change will raise serious questions of science, economics, and ethics and 

should be viewed as provisional. 

 

b In this document, we present all values of the SCC as the cost per metric ton of CO2 emissions. Alternatively, one 

could report the SCC as the cost per metric ton of carbon emissions. The multiplier for translating between mass of 

CO2 and the mass of carbon is 3.67 (the molecular weight of CO2 divided by the molecular weight of carbon = 44/12 

= 3.67). 
16-A-3

Despite the serious limits of both quantification and monetization, SCC estimates can be 

useful in estimating the social benefits of reducing carbon dioxide emissions. Under Executive 

Order 12866, agencies are required, to the extent permitted by law, “to assess both the costs and 

the benefits of the intended regulation and, recognizing that some costs and benefits are difficult 

to quantify, propose or adopt a regulation only upon a reasoned determination that the benefits of 

the intended regulation justify its costs.” The purpose of the SCC estimates presented here is to 

make it possible for agencies to incorporate the social benefits from reducing carbon dioxide 

emissions into cost-benefit analyses of regulatory actions that have small, or “marginal,” impacts 

on cumulative global emissions. Most federal regulatory actions can be expected to have 

marginal impacts on global emissions. 

For such policies, the benefits from reduced (or costs from increased) emissions in any 

future year can be estimated by multiplying the change in emissions in that year by the SCC 

value appropriate for that year. The net present value of the benefits can then be calculated by 

multiplying each of these future benefits by an appropriate discount factor and summing across 

all affected years. This approach assumes that the marginal damages from increased emissions 

are constant for small departures from the baseline emissions path, an approximation that is 

reasonable for policies that have effects on emissions that are small relative to cumulative global 

carbon dioxide emissions. For policies that have a large (non-marginal) impact on global 

cumulative emissions, there is a separate question of whether the SCC is an appropriate tool for 

calculating the benefits of reduced emissions; we do not attempt to answer that question here. 

An interagency group convened on a regular basis to consider public comments, explore 

the technical literature in relevant fields, and discuss key inputs and assumptions in order to 

generate SCC estimates. Agencies that actively participated in the interagency process include 

the Environmental Protection Agency, and the Departments of Agriculture, Commerce, Energy, 

Transportation, and Treasury. This process was convened by the Council of Economic Advisers 

and the Office of Management and Budget, with active participation and regular input from the 

Council on Environmental Quality, National Economic Council, Office of Energy and Climate 

Change, and Office of Science and Technology Policy. The main objective of this process was 

to develop a range of SCC values using a defensible set of input assumptions that are grounded 

in the existing literature. In this way, key uncertainties and model differences can more 

transparently and consistently inform the range of SCC estimates used in the rulemaking process. 

The interagency group selected four SCC estimates for use in regulatory analyses. For 

2010, these estimates are $5, $21, $35, and $65 (in 2007 dollars). The first three estimates are 

based on the average SCC across models and socioeconomic and emissions scenarios at the 5, 3, 

and 2.5 percent discount rates, respectively. The fourth value is included to represent the higherthan-expected impacts from temperature change further out in the tails of the SCC distribution. 

For this purpose, we use the SCC value for the 95th percentile at a 3 percent discount rate. The 

central value is the average SCC across models at the 3 percent discount rate. For purposes of 

capturing the uncertainties involved in regulatory impact analysis, we emphasize the importance 

and value of considering the full range. These SCC estimates also grow over time. For instance, 

the central value increases to $24 per ton of CO2 in 2015 and $26 per ton of CO2 in 2020. See 

section 16-A.5 for the full range of annual SCC estimates from 2010 to 2050. 
16-A-4

It is important to emphasize that the interagency process is committed to updating these 

estimates as the science and economic understanding of climate change and its impacts on 

society improves over time. Specifically, we have set a preliminary goal of revisiting the SCC 

values within two years or at such time as substantially updated models become available, and to 

continue to support research in this area. In the meantime, we will continue to explore the issues 

raised in this document and consider public comments as part of the ongoing interagency 

process. 

16-A.3 SOCIAL COST OF CARBON VALUES USED IN PAST REGULATORY 

ANALYSES

To date, economic analyses for Federal regulations have used a wide range of values to 

estimate the benefits associated with reducing carbon dioxide emissions. In the final model year 

2011 CAFE rule, the Department of Transportation (DOT) used both a “domestic” SCC value of 

$2 per ton of CO2 and a “global” SCC value of $33 per ton of CO2 for 2007 emission reductions 

(in 2007 dollars), increasing both values at 2.4 percent per year. It also included a sensitivity 

analysis at $80 per ton of CO2. A domestic SCC value is meant to reflect the value of damages 

in the United States resulting from a unit change in carbon dioxide emissions, while a global 

SCC value is meant to reflect the value of damages worldwide. 

A 2008 regulation proposed by DOT assumed a domestic SCC value of $7 per ton CO2

(in 2006 dollars) for 2011 emission reductions (with a range of $0-$14 for sensitivity analysis), 

also increasing at 2.4 percent per year. A regulation finalized by DOE in October of 2008 used a 

domestic SCC range of $0 to $20 per ton CO2 for 2007 emission reductions (in 2007 dollars). In 

addition, EPA’s 2008 Advance Notice of Proposed Rulemaking for Greenhouse Gases identified 

what it described as “very preliminary” SCC estimates subject to revision. EPA’s global mean 

values were $68 and $40 per ton CO2 for discount rates of approximately 2 percent and 3 

percent, respectively (in 2006 dollars for 2007 emissions). 

In 2009, an interagency process was initiated to offer a preliminary assessment of how 

best to quantify the benefits from reducing carbon dioxide emissions. To ensure consistency in 

how benefits are evaluated across agencies, the Administration sought to develop a transparent 

and defensible method, specifically designed for the rulemaking process, to quantify avoided 

climate change damages from reduced CO2 emissions. The interagency group did not undertake 

any original analysis. Instead, it combined SCC estimates from the existing literature to use as 

interim values until a more comprehensive analysis could be conducted. 

The outcome of the preliminary assessment by the interagency group was a set of five 

interim values: global SCC estimates for 2007 (in 2006 dollars) of $55, $33, $19, $10, and $5 per 

ton of CO2. The $33 and $5 values represented model-weighted means of the published 

estimates produced from the most recently available versions of three integrated assessment 

models—DICE, PAGE, and FUND—at approximately 3 and 5 percent discount rates. The $55 

and $10 values were derived by adjusting the published estimates for uncertainty in the discount 

rate (using factors developed by Newell and Pizer (2003)) at 3 and 5 percent discount rates, 

respectively. The $19 value was chosen as a central value between the $5 and $33 per ton 
16-A-5

estimates. All of these values were assumed to increase at 3 percent annually to represent growth 

in incremental damages over time as the magnitude of climate change increases.

 These interim values represent the first sustained interagency effort within the U.S. 

government to develop an SCC for use in regulatory analysis. The results of this preliminary 

effort were presented in several proposed and final rules and were offered for public comment in 

connection with proposed rules, including the joint EPA-DOT fuel economy and CO2 tailpipe 

emission proposed rules. 

16-A.4 APPROACH AND KEY ASSUMPTIONS

 Since the release of the interim values, the interagency group has reconvened on a regular 

basis to generate improved SCC estimates. Specifically, the group has considered public 

comments and further explored the technical literature in relevant fields. This section details the 

several choices and assumptions that underlie the resulting estimates of the SCC. 

It is important to recognize that a number of key uncertainties remain, and that current 

SCC estimates should be treated as provisional and revisable, since they will evolve with 

improved scientific and economic understanding. The interagency group also recognizes that the 

existing models are imperfect and incomplete. The National Academy of Science (2009) points 

out that there is tension between the goal of producing quantified estimates of the economic 

damages from an incremental ton of carbon and the limits of existing efforts to model these 

effects. Throughout this document, we highlight a number of concerns and problems that should 

be addressed by the research community, including research programs housed in many of the 

agencies participating in the interagency process to estimate the SCC. 

The U.S. Government will periodically review and reconsider estimates of the SCC used 

for cost-benefit analyses to reflect increasing knowledge of the science and economics of climate 

impacts, as well as improvements in modeling. In this context, statements recognizing the 

limitations of the analysis and calling for further research take on exceptional significance. The 

interagency group offers the new SCC values with all due humility about the uncertainties 

embedded in them and with a sincere promise to continue work to improve them. 

16-A.4.1 Integrated Assessment Models 

We rely on three integrated assessment models (IAMs) commonly used to estimate the 

SCC: the FUND, DICE, and PAGE models.c

 

c The DICE (Dynamic Integrated Climate and Economy) model by William Nordhaus evolved from a series of 

energy models and was first presented in 1990 (Nordhaus and Boyer 2000, Nordhaus 2008). The PAGE (Policy 

Analysis of the Greenhouse Effect) model was developed by Chris Hope in 1991 for use by European decisionmakers in assessing the marginal impact of carbon emissions (Hope 2006, Hope 2008). The FUND (Climate 

Framework for Uncertainty, Negotiation, and Distribution) model, developed by Richard Tol in the early 1990s, 

originally to study international capital transfers in climate policy. is now widely used to study climate impacts (e.g., 

Tol 2002a, Tol 2002b, Anthoff et al. 2009, Tol 2009).

 These models are frequently cited in the peer-
16-A-6

reviewed literature and used in the IPCC assessment. Each model is given equal weight in the 

SCC values developed through this process, bearing in mind their different limitations (discussed 

below). 

 

These models are useful because they combine climate processes, economic growth, and 

feedbacks between the climate and the global economy into a single modeling framework. At 

the same time, they gain this advantage at the expense of a more detailed representation of the 

underlying climatic and economic systems. DICE, PAGE, and FUND all take stylized, reducedform approaches (see NRC 2009 for a more detailed discussion; see Nordhaus 2008 on the 

possible advantages of this approach). Other IAMs may better reflect the complexity of the 

science in their modeling frameworks but do not link physical impacts to economic damages. 

There is currently a limited amount of research linking climate impacts to economic damages, 

which makes this exercise even more difficult. Underlying the three IAMs selected for this 

exercise are a number of simplifying assumptions and judgments reflecting the various modelers’ 

best attempts to synthesize the available scientific and economic research characterizing these 

relationships. 

The three IAMs translate emissions into changes in atmospheric greenhouse 

concentrations, atmospheric concentrations into changes in temperature, and changes in 

temperature into economic damages. The emissions projections used in the models are based on 

specified socioeconomic (GDP and population) pathways. These emissions are translated into 

concentrations using the carbon cycle built into each model, and concentrations are translated 

into warming based on each model’s simplified representation of the climate and a key 

parameter, climate sensitivity. Each model uses a different approach to translate warming into 

damages. Finally, transforming the stream of economic damages over time into a single value 

requires judgments about how to discount them. 

Each model takes a slightly different approach to model how changes in emissions result 

in changes in economic damages. In PAGE, for example, the consumption-equivalent damages 

in each period are calculated as a fraction of GDP, depending on the temperature in that period 

relative to the pre-industrial average temperature in each region. In FUND, damages in each 

period also depend on the rate of temperature change from the prior period. In DICE, 

temperature affects both consumption and investment. We describe each model in greater detail 

here. In a later section, we discuss key gaps in how the models account for various scientific and 

economic processes (e.g. the probability of catastrophe, and the ability to adapt to climate change 

and the physical changes it causes).

The parameters and assumptions embedded in the three models vary widely. A key 

objective of the interagency process was to enable a consistent exploration of the three models 

while respecting the different approaches to quantifying damages taken by the key modelers in 

the field. An extensive review of the literature was conducted to select three sets of input 

parameters for these models: climate sensitivity, socioeconomic and emissions trajectories, and 

discount rates. A probability distribution for climate sensitivity was specified as an input into all 

three models. In addition, the interagency group used a range of scenarios for the socioeconomic 

parameters and a range of values for the discount rate. All other model features were left 

unchanged, relying on the model developers’ best estimates and judgments. In DICE, these 
16-A-7

parameters are handled deterministically and represented by fixed constants; in PAGE, most 

parameters are represented by probability distributions. FUND was also run in a mode in which 

parameters were treated probabilistically.

The sensitivity of the results to other aspects of the models (e.g. the carbon cycle or 

damage function) is also important to explore in the context of future revisions to the SCC but 

has not been incorporated into these estimates. Areas for future research are highlighted at the 

end of this document.

The DICE Model 

The DICE model is an optimal growth model based on a global production function with 

an extra stock variable (atmospheric carbon dioxide concentrations). Emission reductions are 

treated as analogous to investment in “natural capital.” By investing in natural capital today 

through reductions in emissions—implying reduced consumption—harmful effects of climate 

change can be avoided and future consumption thereby increased. 

For purposes of estimating the SCC, carbon dioxide emissions are a function of global 

GDP and the carbon intensity of economic output, with the latter declining over time due to 

technological progress. The DICE damage function links global average temperature to the 

overall impact on the world economy. It varies quadratically with temperature change to capture 

the more rapid increase in damages expected to occur under more extreme climate change, and is 

calibrated to include the effects of warming on the production of market and nonmarket goods 

and services. It incorporates impacts on agriculture, coastal areas (due to sea level rise), “other 

vulnerable market sectors” (based primarily on changes in energy use), human health (based on 

climate-related diseases, such as malaria and dengue fever, and pollution), non-market amenities 

(based on outdoor recreation), and human settlements and ecosystems. The DICE damage 

function also includes the expected value of damages associated with low probability, high 

impact “catastrophic” climate change. This last component is calibrated based on a survey of 

experts (Nordhaus 1994). The expected value of these impacts is then added to the other market 

and non-market impacts mentioned above.

No structural components of the DICE model represent adaptation explicitly, though it is 

included implicitly through the choice of studies used to calibrate the aggregate damage function. 

For example, its agricultural impact estimates assume that farmers can adjust land use decisions 

in response to changing climate conditions, and its health impact estimates assume 

improvements in healthcare over time. In addition, the small impacts on forestry, water systems, 

construction, fisheries, and outdoor recreation imply optimistic and costless adaptation in these 

sectors (Nordhaus and Boyer, 2000; Warren et al., 2006). Costs of resettlement due to sea level 

rise are incorporated into damage estimates, but their magnitude is not clearly reported. 

Mastrandrea’s (2009) review concludes that “in general, DICE assumes very effective 

adaptation, and largely ignores adaptation costs." 

Note that the damage function in DICE has a somewhat different meaning from the 

damage functions in FUND and PAGE. Because GDP is endogenous in DICE and because 

damages in a given year reduce investment in that year, damages propagate forward in time and 
16-A-8

reduce GDP in future years. In contrast, GDP is exogenous in FUND and PAGE, so damages in 

any given year do not propagate forward.d

 

The PAGE Model

PAGE2002 (version 1.4epm) treats GDP growth as exogenous. It divides impacts into 

economic, non-economic, and catastrophic categories and calculates these impacts separately for 

eight geographic regions. Damages in each region are expressed as a fraction of output, where 

the fraction lost depends on the temperature change in each region. Damages are expressed as 

power functions of temperature change. The exponents of the damage function are the same in 

all regions but are treated as uncertain, with values ranging from 1 to 3 (instead of being fixed at 

2 as in DICE). 

PAGE2002 includes the consequences of catastrophic events in a separate damage subfunction. Unlike DICE, PAGE2002 models these events probabilistically. The probability of a 

“discontinuity” (i.e., a catastrophic event) is assumed to increase with temperature above a 

specified threshold. The threshold temperature, the rate at which the probability of experiencing 

a discontinuity increases above the threshold, and the magnitude of the resulting catastrophe are 

all modeled probabilistically.

 Adaptation is explicitly included in PAGE. Impacts are assumed to occur for temperature 

increases above some tolerable level (2°C for developed countries and 0°C for developing 

countries for economic impacts, and 0°C for all regions for non-economic impacts), but 

adaptation is assumed to reduce these impacts. Default values in PAGE2002 assume that the 

developed countries can ultimately eliminate up to 90 percent of all economic impacts beyond 

the tolerable 2°C increase and that developing countries can eventually eliminate 50 percent of 

their economic impacts. All regions are assumed to be able to mitigate 25 percent of the noneconomic impacts through adaptation (Hope 2006). 

The FUND Model 

Like PAGE, the FUND model treats GDP growth as exogenous. It includes separately 

calibrated damage functions for eight market and nonmarket sectors: agriculture, forestry, water, 

energy (based on heating and cooling demand), sea level rise (based on the value of land lost and 

the cost of protection), ecosystems, human health (diarrhea, vector-borne diseases, and 

cardiovascular and respiratory mortality), and extreme weather. Each impact sector has a 

different functional form, and is calculated separately for sixteen geographic regions. In some 

impact sectors, the fraction of output lost or gained due to climate change depends not only on 

 

d Using the default assumptions in DICE 2007, this effect generates an approximately 25 percent increase in the 

SCC relative to damages calculated by fixing GDP. In DICE2007, the time path of GDP is endogenous. 

Specifically, the path of GDP depends on the rate of saving and level of abatement in each period chosen by the 

optimizing representative agent in the model. We made two modifications to DICE to make it consistent with EMF 

GDP trajectories (see next section): we assumed a fixed rate of savings of 20%, and we re-calibrated the exogenous 

path of total factor productivity so that DICE would produce GDP projections in the absence of warming that 

exactly matched the EMF scenarios.
16-A-9

the absolute temperature change but also on the rate of temperature change and level of regional 

income.e

 In the forestry and agricultural sectors, economic damages also depend on CO2

concentrations. 

 Tol (2009) discusses impacts not included in FUND, noting that many are likely to have a 

relatively small effect on damage estimates (both positive and negative). However, he 

characterizes several omitted impacts as “big unknowns”: for instance, extreme climate 

scenarios, biodiversity loss, and effects on economic development and political violence. With 

regard to potentially catastrophic events, he notes, “Exactly what would cause these sorts of 

changes or what effects they would have are not well-understood, although the chance of any one 

of them happening seems low. But they do have the potential to happen relatively quickly, and if 

they did, the costs could be substantial. Only a few studies of climate change have examined 

these issues.”

Adaptation is included both implicitly and explicitly in FUND. Explicit adaptation is 

seen in the agriculture and sea level rise sectors. Implicit adaptation is included in sectors such 

as energy and human health, where wealthier populations are assumed to be less vulnerable to 

climate impacts. For example, the damages to agriculture are the sum of three effects: (1) those 

due to the rate of temperature change (damages are always positive); (2) those due to the level of 

temperature change (damages can be positive or negative depending on region and temperature); 

and (3) those from CO2 fertilization (damages are generally negative but diminishing to zero). 

Adaptation is incorporated into FUND by allowing damages to be smaller if climate 

change happens more slowly. The combined effect of CO2 fertilization in the agricultural sector, 

positive impacts to some regions from higher temperatures, and sufficiently slow increases in 

temperature across these sectors can result in negative economic damages from climate change.

Damage Functions 

To generate revised SCC values, we rely on the IAM modelers’ current best judgments of 

how to represent the effects of climate change (represented by the increase in global-average 

surface temperature) on the consumption-equivalent value of both market and non-market goods 

(represented as a fraction of global GDP). We recognize that these representations are 

incomplete and highly uncertain. But given the paucity of data linking the physical impacts to 

economic damages, we were not able to identify a better way to translate changes in climate into 

net economic damages, short of launching our own research program. 

 The damage functions for the three IAMs are presented in Figures 16A.4.1 and 16A.4.2, 

using the modeler’s default scenarios and mean input assumptions. There are significant 

differences between the three models both at lower (figure 16A.4.2) and higher (figure 16A.4.1) 

increases in global-average temperature. 

 

e In the deterministic version of FUND, the majority of damages are attributable to increased air conditioning 

demand, while reduced cold stress in Europe, North America, and Central and East Asia results in health benefits in 

those regions at low to moderate levels of warming (Warren et al., 2006).
16-A-10

Figure 16-A.4.1 Annual Consumption Loss as a Fraction of Global 

GDP in 2100 Due to an Increase in Annual Global 

Temperature in the DICE, FUND, and PAGE 

modelsf

The lack of agreement among the models at lower temperature increases is underscored 

by the fact that the damages from FUND are well below the 5th percentile estimated by PAGE, 

while the damages estimated by DICE are roughly equal to the 95th percentile estimated by 

PAGE. This is significant because at higher discount rates we expect that a greater proportion of 

the SCC value is due to damages in years with lower temperature increases. For example, when 

the discount rate is 2.5 percent, about 45 percent of the 2010 SCC value in DICE is due to 

damages that occur in years when the temperature is less than or equal to 3 °C. This increases to 

approximately 55 percent and 80 percent at discount rates of 3 and 5 percent, respectively. 

These differences underscore the need for a thorough review of damage functions—in 

particular, how the models incorporate adaptation, technological change, and catastrophic 

damages. Gaps in the literature make modifying these aspects of the models challenging, which 

highlights the need for additional research. As knowledge improves, the Federal government is 

 

f The x-axis represents increases in annual, rather than equilibrium, temperature, while the y-axis represents the 

annual stream of benefits as a share of global GDP. Each specific combination of climate sensitivity, 

socioeconomic, and emissions parameters will produce a different realization of damages for each IAM. The 

damage functions represented in Figures 1A and 1B are the outcome of default assumptions. For instance, under 

alternate assumptions, the damages from FUND may cross from negative to positive at less than or greater than 3 

°C.
16-A-11

committed to exploring how these (and other) models can be modified to incorporate more 

accurate estimates of damages.

Figure 16-A.4.2 Annual Consumption Loss for Lower Temperature 

Changes in DICE, FUND, and PAGE

16-A.4.2 Global versus Domestic Measures of SCC

Because of the distinctive nature of the climate change problem, we center our current 

attention on a global measure of SCC. This approach is the same as that taken for the interim 

values, but it otherwise represents a departure from past practices, which tended to put greater 

emphasis on a domestic measure of SCC (limited to impacts of climate change experienced 

within U.S. borders). As a matter of law, consideration of both global and domestic values is 

generally permissible; the relevant statutory provisions are usually ambiguous and allow 

selection of either measure.g

 

Global SCC 

Under current OMB guidance contained in Circular A-4, analysis of economically 

significant proposed and final regulations from the domestic perspective is required, while 

analysis from the international perspective is optional. However, the climate change problem is 

highly unusual in at least two respects. First, it involves a global externality: emissions of most 

greenhouse gases contribute to damages around the world even when they are emitted in the 

 

g It is true that federal statutes are presumed not to have extraterritorial effect, in part to ensure that the laws of the 

United States respect the interests of foreign sovereigns. But use of a global measure for the SCC does not give 

extraterritorial effect to federal law and hence does not intrude on such interests.
16-A-12

United States. Consequently, to address the global nature of the problem, the SCC must 

incorporate the full (global) damages caused by GHG emissions. Second, climate change 

presents a problem that the United States alone cannot solve. Even if the United States were to 

reduce its greenhouse gas emissions to zero, that step would be far from enough to avoid 

substantial climate change. Other countries would also need to take action to reduce emissions if 

significant changes in the global climate are to be avoided. Emphasizing the need for a global 

solution to a global problem, the United States has been actively involved in seeking 

international agreements to reduce emissions and in encouraging other nations, including 

emerging major economies, to take significant steps to reduce emissions. When these

considerations are taken as a whole, the interagency group concluded that a global measure of 

the benefits from reducing U.S. emissions is preferable. 

When quantifying the damages associated with a change in emissions, a number of 

analysts (e.g., Anthoff, et al. 2009a) employ “equity weighting” to aggregate changes in 

consumption across regions. This weighting takes into account the relative reductions in wealth 

in different regions of the world. A per-capita loss of $500 in GDP, for instance, is weighted 

more heavily in a country with a per-capita GDP of $2,000 than in one with a per-capita GDP of 

$40,000. The main argument for this approach is that a loss of $500 in a poor country causes a 

greater reduction in utility or welfare than does the same loss in a wealthy nation. 

Notwithstanding the theoretical claims on behalf of equity weighting, the interagency group 

concluded that this approach would not be appropriate for estimating a SCC value used in 

domestic regulatory analysis.h

 For this reason, the group concluded that using the global (rather 

than domestic) value, without equity weighting, is the appropriate approach. 

Domestic SCC

As an empirical matter, the development of a domestic SCC is greatly complicated by the 

relatively few region- or country-specific estimates of the SCC in the literature. One potential 

source of estimates comes from the FUND model. The resulting estimates suggest that the ratio 

of domestic to global benefits of emission reductions varies with key parameter assumptions. 

For example, with a 2.5 or 3 percent discount rate, the U.S. benefit is about 7-10 percent of the 

global benefit, on average, across the scenarios analyzed. Alternatively, if the fraction of GDP 

lost due to climate change is assumed to be similar across countries, the domestic benefit would 

be proportional to the U.S. share of global GDP, which is currently about 23 percent.i

On the basis of this evidence, the interagency workgroup determined that a range of 

values from 7 to 23 percent should be used to adjust the global SCC to calculate domestic 

effects. Reported domestic values should use this range. It is recognized that these values are 

 

h It is plausible that a loss of $X inflicts more serious harm on a poor nation than on a wealthy one, but development 

of the appropriate "equity weight" is challenging. Emissions reductions also impose costs, and hence a full account 

would have to consider that a given cost of emissions reductions imposes a greater utility or welfare loss on a poor 

nation than on a wealthy one. Even if equity weighting—for both the costs and benefits of emissions reductions—is 

appropriate when considering the utility or welfare effects of international action, the interagency group concluded 

that it should not be used in developing an SCC for use in regulatory policy at this time. 

i

Based on 2008 GDP (in current US dollars) from the World Bank Development Indicators Report. 
16-A-13

approximate, provisional, and highly speculative. There is no a priori reason why domestic 

benefits should be a constant fraction of net global damages over time. Further, FUND does not 

account for how damages in other regions could affect the United States (e.g., global migration, 

economic and political destabilization). If more accurate methods for calculating the domestic 

SCC become available, the Federal government will examine these to determine whether to 

update its approach. 

16-A.4.3 Valuing Non-CO2 Emissions

While CO2 is the most prevalent greenhouse gas emitted into the atmosphere, the U.S. 

included five other greenhouse gases in its recent endangerment finding: methane, nitrous oxide, 

hydrofluorocarbons, perfluorocarbons, and sulfur hexafluoride. The climate impact of these 

gases is commonly discussed in terms of their 100-year global warming potential (GWP). GWP 

measures the ability of different gases to trap heat in the atmosphere (i.e., radiative forcing per 

unit of mass) over a particular timeframe relative to CO2. However, because these gases differ in 

both radiative forcing and atmospheric lifetimes, their relative damages are not constant over 

time. For example, because methane has a short lifetime, its impacts occur primarily in the near 

term and thus are not discounted as heavily as those caused by longer-lived gases. Impacts other 

than temperature change also vary across gases in ways that are not captured by GWP. For 

instance, CO2 emissions, unlike methane and other greenhouse gases, contribute to ocean

acidification. Likewise, damages from methane emissions are not offset by the positive effect of 

CO2 fertilization. Thus, transforming gases into CO2-equivalents using GWP, and then 

multiplying the carbon-equivalents by the SCC, would not result in accurate estimates of the 

social costs of non-CO2 gases. 

 

In light of these limitations, and the significant contributions of non-CO2 emissions to 

climate change, further research is required to link non-CO2 emissions to economic impacts. 

Such work would feed into efforts to develop a monetized value of reductions in non-CO2

greenhouse gas emissions. As part of ongoing work to further improve the SCC estimates, the 

interagency group hopes to develop methods to value these other greenhouse gases. The goal is 

to develop these estimates by the time we issue revised SCC estimates for carbon dioxide 

emissions. 

16-A.4.4 Equilibrium Climate Sensitivity

Equilibrium climate sensitivity (ECS) is a key input parameter for the DICE, PAGE, and 

FUND models.j It is defined as the long-term increase in the annual global-average surface 

temperature from a doubling of atmospheric CO2 concentration relative to pre-industrial levels 

(or stabilization at a concentration of approximately 550 parts per million (ppm)). Uncertainties 

in this important parameter have received substantial attention in the peer-reviewed literature.

 

j The equilibrium climate sensitivity includes the response of the climate system to increased greenhouse gas 

concentrations over the short to medium term (up to 100-200 years), but it does not include long-term feedback 

effects due to possible large-scale changes in ice sheets or the biosphere, which occur on a time scale of many 

hundreds to thousands of years (e.g. Hansen et al. 2007).
16-A-14

The most authoritative statement about equilibrium climate sensitivity appears in the 

Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC):

Basing our assessment on a combination of several independent lines of evidence...including 

observed climate change and the strength of known feedbacks simulated in [global climate 

models], we conclude that the global mean equilibrium warming for doubling CO2, or 

‘equilibrium climate sensitivity’, is likely to lie in the range 2 °C to 4.5 °C, with a most likely 

value of about 3 °C. Equilibrium climate sensitivity is very likely larger than 1.5 °C. k

 

For fundamental physical reasons as well as data limitations, values substantially higher 

than 4.5 °C still cannot be excluded, but agreement with observations and proxy data is 

generally worse for those high values than for values in the 2 °C to 4.5 °C range. (Meehl et 

al., 2007, p 799) 

After consulting with several lead authors of this chapter of the IPCC report, the 

interagency workgroup selected four candidate probability distributions and calibrated them to 

be consistent with the above statement: Roe and Baker (2007), log-normal, gamma, and Weibull. 

Table 16A.4.1 included below gives summary statistics for the four calibrated distributions.

Table 16-A.4.1 Summary Statistics for Four Calibrated Climate Sensitivity Distributions

Roe & Baker Log-normal Gamma Weibull

Pr(ECS < 1.5°C) 0.013 0.050 0.070 0.102

Pr(2°C < ECS < 4.5°C) 0.667 0.667 0.667 0.667

5th percentile 1.72 1.49 1.37 1.13

10th percentile 1.91 1.74 1.65 1.48

Mode 2.34 2.52 2.65 2.90

Median (50th percentile) 3.00 3.00 3.00 3.00

Mean 3.50 3.28 3.19 3.07

90th percentile 5.86 5.14 4.93 4.69

95th percentile 7.14 5.97 5.59 5.17

Each distribution was calibrated by applying three constraints from the IPCC: 

 

k This is in accord with the judgment that it “is likely to lie in the range 2 °C to 4.5 °C” and the IPCC definition of 

“likely” as greater than 66 percent probability (Le Treut et al.2007). “Very likely” indicates a greater than 90 percent 

probability.
16-A-15

(1) a median equal to 3°C, to reflect the judgment of “a most likely value of about 3 °C”;l

(2) two-thirds probability that the equilibrium climate sensitivity lies between 2 and 4.5 °C; 

and

(3) zero probability that it is less than 0°C or greater than 10°C (see Hegerl et al. 2006, p. 

721). 

We selected the calibrated Roe and Baker distribution from the four candidates for two 

reasons. First, the Roe and Baker distribution is the only one of the four that is based on a 

theoretical understanding of the response of the climate system to increased greenhouse gas 

concentrations (Roe and Baker 2007, Roe 2008). In contrast, the other three distributions are 

mathematical functions that are arbitrarily chosen based on simplicity, convenience, and general 

shape. The Roe and Baker distribution results from three assumptions about climate response: 

(1) absent feedback effects, the equilibrium climate sensitivity is equal to 1.2 °C; (2) feedback 

factors are proportional to the change in surface temperature; and (3) uncertainties in feedback 

factors are normally distributed. There is widespread agreement on the first point and the second 

and third points are common assumptions. 

Second, the calibrated Roe and Baker distribution better reflects the IPCC judgment that 

“values substantially higher than 4.5°C still cannot be excluded.” Although the IPCC made no 

quantitative judgment, the 95th percentile of the calibrated Roe & Baker distribution (7.1 °C) is 

much closer to the mean and the median (7.2 °C) of the 95th percentiles of 21 previous studies 

summarized by Newbold and Daigneault (2009). It is also closer to the mean (7.5 °C) and 

median (7.9 °C) of the nine truncated distributions examined by the IPCC (Hegerl, et al., 2006) 

than are the 95th percentiles of the three other calibrated distributions (5.2-6.0 °C). 

Finally, we note the IPCC judgment that the equilibrium climate sensitivity “is very 

likely larger than 1.5°C.” Although the calibrated Roe & Baker distribution, for which the 

probability of equilibrium climate sensitivity being greater than 1.5°C is almost 99 percent, is not 

inconsistent with the IPCC definition of “very likely” as “greater than 90 percent probability,” it 

reflects a greater degree of certainty about very low values of ECS than was expressed by the 

IPCC. 

 

l Strictly speaking, “most likely” refers to the mode of a distribution rather than the median, but common usage 

would allow the mode, median, or mean to serve as candidates for the central or “most likely” value and the IPCC 

report is not specific on this point. For the distributions we considered, the median was between the mode and the 

mean. For the Roe and Baker distribution, setting the median equal to 3°C, rather than the mode or mean, gave a 95th

percentile that is more consistent with IPCC judgments and the literature. For example, setting the mean and mode 

equal to 3°C produced 95th percentiles of 5.6 and 8.6 °C, respectively, which are in the lower and upper end of the 

range in the literature. Finally, the median is closer to 3°C than is the mode for the truncated distributions selected 

by the IPCC (Hegerl, et al., 2006); the average median is 3.1 °C and the average mode is 2.3 °C, which is most 

consistent with a Roe and Baker distribution with the median set equal to 3 °C.
16-A-16

Figure 16-A.4.3 Estimates of the Probability Density Function for 

Equilibrium Climate Sensitivity (°C)

To show how the calibrated Roe and Baker distribution compares to different estimates 

of the probability distribution function of equilibrium climate sensitivity in the empirical 

literature, Figure 16A.4.3 (above) overlays it on Figure 9.20 from the IPCC Fourth Assessment 

Report. These functions are scaled to integrate to unity between 0 °C and 10 °C. The horizontal 

bars show the respective 5 percent to 95 percent ranges; dots indicate the median estimate.m

16-A.4.5 Socioeconomic and Emissions Trajectories

 

Another key issue considered by the interagency group is how to select the set of 

socioeconomic and emissions parameters for use in PAGE, DICE, and FUND. Socioeconomic 

pathways are closely tied to climate damages because, all else equal, more and wealthier people 

tend to emit more greenhouse gases and also have a higher (absolute) willingness to pay to avoid 

climate disruptions. For this reason, we consider how to model several input parameters in 

tandem: GDP, population, CO2 emissions, and non-CO2 radiative forcing. A wide variety of 

scenarios have been developed and used for climate change policy simulations (e.g., SRES 2000, 

CCSP 2007, EMF 2009). In determining which scenarios are appropriate for inclusion, we 

aimed to select scenarios that span most of the plausible ranges of outcomes for these variables. 

 

m The estimates based on instrumental data are from Andronova and Schlesinger (2001), Forest et al. (2002; dashed 

line, anthropogenic forcings only), Forest et al. (2006; solid line, anthropogenic and natural forcings), Gregory et al. 

(2002a), Knutti et al. (2002), Frame et al. (2005), and Forster and Gregory (2006). Hegerl et al. (2006) are based on 

multiple palaeoclimatic reconstructions of north hemisphere mean temperatures over the last 700 years. Also shown 

are the 5-95 percent approximate ranges for two estimates from the last glacial maximum (dashed, Annan et al. 

2005; solid, Schneider von Deimling et al. 2006), which are based on models with different structural properties.
16-A-17

To accomplish this task in a transparent way, we decided to rely on the recent Stanford 

Energy Modeling Forum exercise, EMF-22. EMF-22 uses ten well-recognized models to 

evaluate substantial, coordinated global action to meet specific stabilization targets. A key 

advantage of relying on these data is that GDP, population, and emission trajectories are 

internally consistent for each model and scenario evaluated. The EMF-22 modeling effort also is 

preferable to the IPCC SRES due to their age (SRES were developed in 1997) and the fact that 3 

of 4 of the SRES scenarios are now extreme outliers in one or more variables. Although the 

EMF-22 scenarios have not undergone the same level of scrutiny as the SRES scenarios, they are 

recent, peer-reviewed, published, and publicly available. 

To estimate the SCC for use in evaluating domestic policies that will have a small effect 

on global cumulative emissions, we use socioeconomic and emission trajectories that span a 

range of plausible scenarios. Five trajectories were selected from EMF-22 (see Table 16A.4.2 

below). Four of these represent potential business-as-usual (BAU) growth in population, 

wealth, and emissions and are associated with CO2 (only) concentrations ranging from 612 to 

889 ppm in 2100. One represents an emissions pathway that achieves stabilization at 550 ppm 

CO2e (i.e., CO2-only concentrations of 425 – 484 ppm or a radiative forcing of 3.7 W/m2) in 

2100, a lower-than-BAU trajectory.n

 Out of the 10 models included in the EMF-22 exercise, we 

selected the trajectories used by MiniCAM, MESSAGE, IMAGE, and the optimistic scenario 

from MERGE. For the BAU pathways, we used the GDP, population, and emission trajectories 

from each of these four models. For the 550 ppm CO2e scenario, we averaged the GDP, 

population, and emission trajectories implied by these same four models. 

 

n Such an emissions path would be consistent with widespread action by countries to mitigate GHG emissions, 

though it could also result from technological advances. It was chosen because it represents the most stringent case 

analyzed by the EMF-22 where all the models converge: a 550 ppm, not to exceed, full participation scenario.
16-A-18

Table 16-A.4.2 Socioeconomic and Emissions Projections from Select EMF-22 Reference 

Scenarios

Reference Fossil and Industrial CO2 Emissions (GtCO2/yr)

EMF – 22 Based Scenarios 2000 2010 2020 2030 2050 2100

IMAGE 26.6 31.9 36.9 40.0 45.3 60.1

MERGE Optimistic 24.6 31.5 37.6 45.1 66.5 117.9

MESSAGE 26.8 29.2 37.6 42.1 43.5 42.7

MiniCAM 26.5 31.8 38.0 45.1 57.8 80.5

550 ppm average 26.2 31.1 33.2 32.4 20.0 12.8

Reference GDP (using market exchange rates in trillion 2005$)o

EMF – 22 Based Scenarios 2000 2010 2020 2030 2050 2100

IMAGE 38.6 53.0 73.5 97.2 156.3 396.6

MERGE Optimistic 36.3 45.9 59.7 76.8 122.7 268.0

MESSAGE 38.1 52.3 69.4 91.4 153.7 334.9

MiniCAM 36.1 47.4 60.8 78.9 125.7 369.5

550 ppm average 37.1 49.6 65.6 85.5 137.4 337.9

Global Population (billions)

EMF – 22 Based Scenarios 2000 2010 2020 2030 2050 2100

IMAGE 6.1 6.9 7.6 8.2 9.0 9.1

MERGE Optimistic 6.0 6.8 7.5 8.2 9.0 9.7

MESSAGE 6.1 6.9 7.7 8.4 9.4 10.4

MiniCAM 6.0 6.8 7.5 8.1 8.8 8.7

550 ppm average 6.1 6.8 7.6 8.2 8.7 9.1

We explore how sensitive the SCC is to various assumptions about how the future will 

evolve without prejudging what is likely to occur. The interagency group considered formally 

assigning probability weights to different states of the world, but this proved challenging to do in 

an analytically rigorous way given the dearth of information on the likelihood of a full range of 

future socioeconomic pathways. 

 

o While the EMF-22 models used market exchange rates (MER) to calculate global GDP, it is also possible to use 

purchasing power parity (PPP). PPP takes into account the different price levels across countries, so it more 

accurately describes relative standards of living across countries. MERs tend to make low-income countries appear 

poorer than they actually are. Because many models assume convergence in per capita income over time, use of 

MER-adjusted GDP gives rise to projections of higher economic growth in low income countries. There is an 

ongoing debate about how much this will affect estimated climate impacts. Critics of the use of MER argue that it 

leads to overstated economic growth and hence a significant upward bias in projections of greenhouse gas 

emissions, and unrealistically high future temperatures (e.g., Castles and Henderson 2003). Others argue that 

convergence of the emissions-intensity gap across countries at least partially offset the overstated income gap so that 

differences in exchange rates have less of an effect on emissions (Holtsmark and Alfsen, 2005; Tol, 2006). 

Nordhaus (2007b) argues that the ideal approach is to use superlative PPP accounts (i.e., using cross-sectional PPP 

measures for relative incomes and outputs and national accounts price and quantity indexes for time-series 

extrapolations). However, he notes that it important to keep this debate in perspective; it is by no means clear that 

exchange-rate-conversion issues are as important as uncertainties about population, technological change, or the 

many geophysical uncertainties.
16-A-19

 There are a number of caveats. First, EMF BAU scenarios represent the modelers’ 

judgment of the most likely pathway absent mitigation policies to reduce greenhouse gas 

emissions, rather than the wider range of possible outcomes. Nevertheless, these views of the 

most likely outcome span a wide range, from the more optimistic (e.g. abundant low-cost, lowcarbon energy) to more pessimistic (e.g. constraints on the availability of nuclear and 

renewables).p Second, the socioeconomic trajectories associated with a 550 ppm CO2e 

concentration scenario are not derived from an assessment of what policy is optimal from a 

benefit-cost standpoint. Rather, it is indicative of one possible future outcome. The emission 

trajectories underlying some BAU scenarios (e.g. MESSAGE’s 612 ppm) also are consistent 

with some modest policy action to address climate change.

q

 We chose not to include 

socioeconomic trajectories that achieve even lower GHG concentrations at this time, given the 

difficulty many models had in converging to meet these targets.

For comparison purposes, the Energy Information Agency in its 2009 Annual Energy 

Outlook projected that global carbon dioxide emissions will grow to 30.8, 35.6, and 40.4 

gigatons in 2010, 2020, and 2030, respectively, while world GDP is projected to be $51.8, $71.0 

and $93.9 trillion (in 2005 dollars using market exchange rates) in 2010, 2020, and 2030, 

respectively. These projections are consistent with one or more EMF-22 scenarios. Likewise, 

the United Nations’ 2008 Population Prospect projects population will grow from 6.1 billion 

people in 2000 to 9.1 billion people in 2050, which is close to the population trajectories for the 

IMAGE, MiniCAM, and MERGE models. 

In addition to fossil and industrial CO2 emissions, each EMF scenario provides 

projections of methane, nitrous oxide, fluorinated greenhouse gases, and net land use CO2

emissions out to 2100. These assumptions also are used in the three models while retaining the 

default radiative forcings due to other factors (e.g. aerosols and other gases). See the Annex for 

greater detail.

16-A.4.6 Discount Rate

The choice of a discount rate, especially over long periods of time, raises highly 

contested and exceedingly difficult questions of science, economics, philosophy, and law. 

Although it is well understood that the discount rate has a large influence on the current value of 

future damages, there is no consensus about what rates to use in this context. Because carbon 

dioxide emissions are long-lived, subsequent damages occur over many years. In calculating the 

SCC, we first estimate the future damages to agriculture, human health, and other market and 

non-market sectors from an additional unit of carbon dioxide emitted in a particular year in terms 

of reduced consumption (or consumption equivalents) due to the impacts of elevated 

 

p For instance, in the MESSAGE model’s reference case total primary energy production from nuclear, biomass, and 

non-biomass renewables is projected to increase from about 15 percent of total primary energy in 2000 to 54 percent 

in 2100. In comparison, the MiniCAM reference case shows 10 percent in 2000 and 21 percent in 2100. 

q For example, MiniCAM projects if all non-US OECD countries reduce CO2 emissions to 83 percent below 2005 

levels by 2050 (per the G-8 agreement) but all other countries continue along a BAU path CO2 concentrations in 

2100 would drop from 794 ppmv in its reference case to 762 ppmv.
16-A-20

temperatures, as represented in each of the three IAMs. Then we discount the stream of future 

damages to its present value in the year when the additional unit of emissions was released using 

the selected discount rate, which is intended to reflect society's marginal rate of substitution 

between consumption in different time periods. 

For rules with both intra- and intergenerational effects, agencies traditionally employ 

constant discount rates of both 3 percent and 7 percent in accordance with OMB Circular A-4. 

As Circular A-4 acknowledges, however, the choice of discount rate for intergenerational 

problems raises distinctive problems and presents considerable challenges. After reviewing 

those challenges, Circular A-4 states, “If your rule will have important intergenerational benefits 

or costs you might consider a further sensitivity analysis using a lower but positive discount rate 

in addition to calculating net benefits using discount rates of 3 and 7 percent.” For the specific 

purpose of developing the SCC, we adapt and revise that approach here.

Arrow et al. (1996) outlined two main approaches to determine the discount rate for 

climate change analysis, which they labeled “descriptive” and “prescriptive.” The descriptive 

approach reflects a positive (non-normative) perspective based on observations of people’s 

actual choices—e.g., savings versus consumption decisions over time, and allocations of savings 

among more and less risky investments. Advocates of this approach generally call for inferring 

the discount rate from market rates of return “because of a lack of justification for choosing a 

social welfare function that is any different than what decision makers [individuals] actually use” 

(Arrow et al. 1996). 

One theoretical foundation for the cost-benefit analyses in which the social cost of carbon 

will be used—the Kaldor-Hicks potential-compensation test—also suggests that market rates 

should be used to discount future benefits and costs, because it is the market interest rate that 

would govern the returns potentially set aside today to compensate future individuals for climate 

damages that they bear (e.g., Just et al. 2004). As some have noted, the word “potentially” is an 

important qualification; there is no assurance that such returns will actually be set aside to 

provide compensation, and the very idea of compensation is difficult to define in the 

intergenerational context. On the other hand, societies provide compensation to future 

generations through investments in human capital and the resulting increase in knowledge, as 

well as infrastructure and other physical capital.

The prescriptive approach specifies a social welfare function that formalizes the 

normative judgments that the decision-maker wants explicitly to incorporate into the policy 

evaluation—e.g., how inter-personal comparisons of utility should be made, and how the welfare 

of future generations should be weighed against that of the present generation. Ramsey (1928), 

for example, has argued that it is “ethically indefensible” to apply a positive pure rate of time 

preference to discount values across generations, and many agree with this view. 

Other concerns also motivate making adjustments to descriptive discount rates. In 

particular, it has been noted that the preferences of future generations with regard to 

consumption versus environmental amenities may not be the same as those today, making the 

current market rate on consumption an inappropriate metric by which to discount future climaterelated damages. Others argue that the discount rate should be below market rates to correct for 
16-A-21

market distortions and uncertainties or inefficiencies in intergenerational transfers of wealth, 

which in the Kaldor-Hicks logic are presumed to compensate future generations for damage (a 

potentially controversial assumption, as noted above) (Arrow et al. 1996, Weitzman 1999). 

Further, a legitimate concern about both descriptive and prescriptive approaches is that 

they tend to obscure important heterogeneity in the population. The utility function that 

underlies the prescriptive approach assumes a representative agent with perfect foresight and no 

credit constraints. This is an artificial rendering of the real world that misses many of the 

frictions that characterize individuals’ lives and indeed the available descriptive evidence 

supports this. For instance, many individuals smooth consumption by borrowing with credit 

cards that have relatively high rates. Some are unable to access traditional credit markets and 

rely on payday lending operations or other high-cost forms of smoothing consumption. Whether 

one puts greater weight on the prescriptive or descriptive approach, the high interest rates that 

credit-constrained individuals accept suggest that some account should be given to the discount 

rates revealed by their behavior. 

We draw on both approaches but rely primarily on the descriptive approach to inform the 

choice of discount rate. With recognition of its limitations, we find this approach to be the most 

defensible and transparent given its consistency with the standard contemporary theoretical 

foundations of benefit-cost analysis and with the approach required by OMB’s existing guidance. 

The logic of this framework also suggests that market rates should be used for discounting future 

consumption-equivalent damages. Regardless of the theoretical approach used to derive the 

appropriate discount rate(s), we note the inherent conceptual and practical difficulties of 

adequately capturing consumption trade-offs over many decades or even centuries. While 

relying primarily on the descriptive approach in selecting specific discount rates, the interagency 

group has been keenly aware of the deeply normative dimensions of both the debate over 

discounting in the intergenerational context and the consequences of selecting one discount rate 

over another. 

Historically Observed Interest Rates

In a market with no distortions, the return to savings would equal the private return on 

investment, and the market rate of interest would be the appropriate choice for the social 

discount rate. In the real world risk, taxes, and other market imperfections drive a wedge 

between the risk-free rate of return on capital and the consumption rate of interest. Thus, the 

literature recognizes two conceptual discount concepts—the consumption rate of interest and the 

opportunity cost of capital. 

According to OMB’s Circular A-4, it is appropriate to use the rate of return on capital 

when a regulation is expected to displace or alter the use of capital in the private sector. In this 

case, OMB recommends Agencies use a discount rate of 7 percent. When regulation is expected 

to primarily affect private consumption—for instance, via higher prices for goods and services—

a lower discount rate of 3 percent is appropriate to reflect how private individuals trade-off 

current and future consumption. 
16-A-22

The interagency group examined the economics literature and concluded that the 

consumption rate of interest is the correct concept to use in evaluating the benefits and costs of a 

marginal change in carbon emissions (see Lind 1990, Arrow et al 1996, and Arrow 2000). The 

consumption rate of interest also is appropriate when the impacts of a regulation are measured in 

consumption (-equivalent) units, as is done in the three integrated assessment models used for 

estimating the SCC. 

Individuals use a variety of savings instruments that vary with risk level, time horizon, 

and tax characteristics. The standard analytic framework used to develop intuition about the 

discount rate typically assumes a representative agent with perfect foresight and no credit 

constraints. The risk-free rate is appropriate for discounting certain future benefits or costs, but 

the benefits calculated by IAMs are uncertain. To use the risk-free rate to discount uncertain 

benefits, these benefits first must be transformed into "certainty equivalents," that is the 

maximum certain amount that we would exchange for the uncertain amount. However, the 

calculation of the certainty-equivalent requires first estimating the correlation between the 

benefits of the policy and baseline consumption. 

If the IAM projections of future impacts represent expected values (not certaintyequivalent values), then the appropriate discount rate generally does not equal the risk-free rate. 

If the benefits of the policy tend to be high in those states of the world in which consumption is 

low, then the certainty-equivalent benefits will be higher than the expected benefits (and vice 

versa). Since many (though not necessarily all) of the important impacts of climate change will 

flow through market sectors such as agriculture and energy, and since willingness to pay for 

environmental protections typically increases with income, we might expect a positive (though 

not necessarily perfect) correlation between the net benefits from climate policies and market 

returns. This line of reasoning suggests that the proper discount rate would exceed the riskless 

rate. Alternatively, a negative correlation between the returns to climate policies and market 

returns would imply that a discount rate below the riskless rate is appropriate. 

This discussion suggests that both the post-tax riskless and risky rates can be used to 

capture individuals’ consumption-equivalent interest rate. As a measure of the post-tax riskless 

rate, we calculate the average real return from Treasury notes over the longest time period 

available (those from Newell and Pizer 2003) and adjust for Federal taxes (the average marginal 

rate from tax years 2003 through 2006 is around 27 percent).r

 This calculation produces a real 

interest rate of about 2.7 percent, which is roughly consistent with Circular A-4’s 

recommendation to use 3 percent to represent the consumption rate of interest.s

 

r The literature argues for a risk-free rate on government bonds as an appropriate measure of the consumption rate of 

interest. Arrow (2000) suggests that it is roughly 3-4 percent. OMB cites evidence of a 3.1 percent pre-tax rate for 

10-year Treasury notes in the A-4 guidance. Newell and Pizer (2003) find real interest rates between 3.5 and 4 

percent for 30-year Treasury securities. 

 A measure of 

the post-tax risky rate for investments whose returns are positively correlated with overall equity 

s The positive approach reflects how individuals make allocation choices across time, but it is important to keep in 

mind that we wish to reflect preferences for society as a whole, which generally has a longer planning horizon.
16-A-23

market returns can be obtained by adjusting pre-tax rates of household returns to risky 

investments (approximately 7 percent) for taxes, which yields a real rate of roughly 5 percent.t

 

The Ramsey Equation

Ramsey discounting also provides a useful framework to inform the choice of a discount 

rate. Under this approach, the analyst applies either positive or normative judgments in selecting 

values for the key parameters of the Ramsey equation: η (coefficient of relative risk aversion or 

elasticity of the marginal utility of consumption) and ρ (pure rate of time preference).u These are 

then combined with g (growth rate of per-capita consumption) to equal the interest rate at which 

future monetized damages are discounted: ρ + η∙g.v In the simplest version of the Ramsey 

model, with an optimizing representative agent with perfect foresight, what we are calling the 

“Ramsey discount rate,” ρ + η∙g, will be equal to the rate of return to capital, i.e., the market 

interest rate.

A review of the literature provides some guidance on reasonable parameter values for the 

Ramsey discounting equation, based on both prescriptive and descriptive approaches. 

• η. Most papers in the climate change literature adopt values for η in the range of 0.5 to 3 

(Weitzman cites plausible values as those ranging from 1 to 4), although not all authors 

articulate whether their choice is based on prescriptive or descriptive reasoning.w

 

t Cambell et al (2001) estimates that the annual real return from stocks for 1900-1995 was about 7 percent. The 

annual real rate of return for the S&P 500 from 1950 – 2008 was about 6.8 percent. In the absence of a better way to 

population-weight the tax rates, we use the middle of the 20 – 40 percent range to derive a post-tax interest rate 

(Kotlikoff and Rapson 2006).

 

Dasgupta (2008) argues that η should be greater than 1 and may be as high as 3, since η

equal to 1 suggests savings rates that do not conform to observed behavior. 

u The parameter ρ measures the pure rate of time preference: people’s behavior reveals a preference for an 

increase in utility today versus the future. Consequently, it is standard to place a lower weight on utility in the 

future. The parameter η captures diminishing marginal utility: consumption in the future is likely to be higher than 

consumption today, so diminishing marginal utility of consumption implies that the same monetary damage will 

cause a smaller reduction of utility for wealthier individuals, either in the future or in current generations. If η = 0, 

then a one dollar increase in income is equally valuable regardless of level of income; if η = 1, then a one percent 

increase in income is equally valuable no matter the level of income; and if η > 1, then a one percent increase in 

income is less valuable to wealthier individuals. 

v In this case, g could be taken from the selected EMF socioeconomic scenarios or alternative assumptions about the 

rate of consumption growth.

w Empirical estimates of η span a wide range of values. A benchmark value of 2 is near the middle of the range of 

values estimated or used by Szpiro (1986), Hall and Jones (2007), Arrow (2007), Dasgupta (2006, 2008), Weitzman 

(2007, 2009), and Nordhaus (2008). However, Chetty (2006) developed a method of estimating η using data on 

labor supply behavior. He shows that existing evidence of the effects of wage changes on labor supply imposes a 

tight upper bound on the curvature of utility over wealth (CRRA < 2) with the mean implied value of 0.71 and 

concludes that the standard expected utility model cannot generate high levels of risk aversion without contradicting 

established facts about labor supply. Recent work has jointly estimated the components of the Ramsey equation. 

Evans and Sezer (2005) estimate η = 1.49 for 22 OECD countries. They also estimate ρ = 1.08 percent per year 

using data on mortality rates. Anthoff, et al. (2009b) estimate η = 1.18, and ρ = 1.4 percent. When they multiply the 

bivariate probability distributions from their work and Evans and Sezer (2005) together, they find η = 1.47, and ρ = 

1.07. 
16-A-24

• ρ. With respect to the pure rate of time preference, most papers in the climate change 

literature adopt values for ρ in the range of 0 to 3 percent per year. The very low rates 

tend to follow from moral judgments involving intergenerational neutrality. Some have 

argued that to use any value other than ρ = 0 would unjustly discriminate against future 

generations (e.g., Arrow et al. 1996, Stern et al. 2006). However, even in an intergenerational setting, it may make sense to use a small positive pure rate of time 

preference because of the small probability of unforeseen cataclysmic events (Stern et al. 

2006). 

• g. A commonly accepted approximation is around 2 percent per year. For the 

socioeconomic scenarios used for this exercise, the EMF models assume that g is about 

1.5-2 percent to 2100. 

Some economists and non-economists have argued for constant discount rates below 2 

percent based on the prescriptive approach. When grounded in the Ramsey framework, 

proponents of this approach have argued that a ρ of zero avoids giving preferential treatment to 

one generation over another. The choice of η has also been posed as an ethical choice linked to 

the value of an additional dollar in poorer countries compared to wealthier ones. Stern et al. 

(2006) applies this perspective through his choice of ρ = 0.1 percent per year, η = 1 and g = 1.3 

percent per year, which yields an annual discount rate of 1.4 percent. In the context of 

permanent income savings behavior, however, Stern’s assumptions suggest that individuals 

would save 93 percent of their income.x

Recently, Stern (2008) revisited the values used in Stern et al. (2006), stating that there is 

a case to be made for raising η due to the amount of weight lower values place on damages far in 

the future (over 90 percent of expected damages occur after 2200 with η = 1). Using Stern’s 

assumption that ρ = 0.1 percent, combined with a η of 1.5 to 2 and his original growth rate, 

yields a discount rate of greater than 2 percent. 

We conclude that arguments made under the prescriptive approach can be used to justify 

discount rates between roughly 1.4 and 3.1 percent. In light of concerns about the most 

appropriate value for η, we find it difficult to justify rates at the lower end of this range under the 

Ramsey framework. 

Accounting for Uncertainty in the Discount Rate 

While the consumption rate of interest is an important driver of the benefits estimate, it is 

uncertain over time. Ideally, we would formally model this uncertainty, just as we do for climate 

sensitivity. Weitzman (1998, 2001) showed theoretically and Newell and Pizer (2003) and 

Groom et al. (2006) confirm empirically that discount rate uncertainty can have a large effect on 

net present values. A main result from these studies is that if there is a persistent element to the 

 

x Stern (2008) argues that building in a positive rate of exogenous technical change over time reduces the implied 

savings rate and that η at or above 2 are inconsistent with observed behavior with regard to equity. (At the same 

time, adding exogenous technical change—all else equal—would increase g as well.)
16-A-25

uncertainty in the discount rate (e.g., the rate follows a random walk), then it will result in an 

effective (or certainty-equivalent) discount rate that declines over time. Consequently, lower 

discount rates tend to dominate over the very long term (see Weitzman 1998, 1999, 2001; 

Newell and Pizer 2003; Groom et al. 2006; Gollier 2008; Summers and Zeckhauser 2008; and 

Gollier and Weitzman 2009). 

The proper way to model discount rate uncertainty remains an active area of research. 

Newell and Pizer (2003) employ a model of how long-term interest rates change over time to 

forecast future discount rates. Their model incorporates some of the basic features of how 

interest rates move over time, and its parameters are estimated based on historical observations 

of long-term rates. Subsequent work on this topic, most notably Groom et al. (2006), uses more 

general models of interest rate dynamics to allow for better forecasts. Specifically, the volatility 

of interest rates depends on whether rates are currently low or high and the variation in the level 

of persistence over time. 

While Newell and Pizer (2003) and Groom et al (2006) attempt formally to model 

uncertainty in the discount rate, others argue for a declining scale of discount rates applied over 

time (e.g., Weitzman 2001, and the UK’s “Green Book” for regulatory analysis). This approach 

uses a higher discount rate initially, but applies a graduated scale of lower discount rates further

out in time.y

 A key question that has emerged with regard to both of these approaches is the 

trade-off between potential time inconsistency and giving greater weight to far future outcomes 

(see the EPA Science Advisory Board’s recent comments on this topic as part of its review of 

their Guidelines for Economic Analysis).z

The Discount Rates Selected for Estimating SCC

In light of disagreement in the literature on the appropriate market interest rate to use in 

this context and uncertainty about how interest rates may change over time, we use three 

discount rates to span a plausible range of certainty-equivalent constant discount rates: 2.5, 3, 

and 5 percent per year. Based on the review in the previous sections, the interagency workgroup 

determined that these three rates reflect reasonable judgments under both descriptive and 

prescriptive approaches.

The central value, 3 percent, is consistent with estimates provided in the economics 

literature and OMB’s Circular A-4 guidance for the consumption rate of interest. As previously 

 

y For instance, the UK applies a discount rate of 3.5 percent to the first 30 years; 3 percent for years 31 - 75; 2.5 

percent for years 76 - 125; 2 percent for years 126 - 200; 1.5 percent for years 201 - 300; and 1 percent after 300 

years. As a sensitivity, it recommends a discount rate of 3 percent for the first 30 years, also decreasing over time. 

z Uncertainty in future damages is distinct from uncertainty in the discount rate. Weitzman (2008) argues that 

Stern’s choice of a low discount rate was “right for the wrong reasons.” He demonstrates how the damages from a 

low probability, catastrophic event far in the future dominate the effect of the discount rate in a present value 

calculation and result in an infinite willingness-to-pay for mitigation today. Newbold and Daigneault, (2009) and 

Nordhaus (2009) find that Weitzman’s result is sensitive to the functional forms chosen for climate sensitivity, 

utility, and consumption. Summers and Zeckhauser (2008) argue that uncertainty in future damages can also work in 

the other direction by increasing the benefits of waiting to learn the appropriate level of mitigation required. 
16-A-26

mentioned, the consumption rate of interest is the correct discounting concept to use when future 

damages from elevated temperatures are estimated in consumption-equivalent units. Further, 3 

percent roughly corresponds to the after-tax riskless interest rate. The upper value of 5 percent is 

included to represent the possibility that climate damages are positively correlated with market 

returns. Additionally, this discount rate may be justified by the high interest rates that many 

consumers use to smooth consumption across periods. 

The low value, 2.5 percent, is included to incorporate the concern that interest rates are 

highly uncertain over time. It represents the average certainty-equivalent rate using the meanreverting and random walk approaches from Newell and Pizer (2003) starting at a discount rate 

of 3 percent. Using this approach, the certainty equivalent is about 2.2 percent using the random 

walk model and 2.8 percent using the mean reverting approach.aa

16-A.5 REVISED SCC ESTIMATES 

 Without giving preference to a 

particular model, the average of the two rates is 2.5 percent. Further, a rate below the riskless 

rate would be justified if climate investments are negatively correlated with the overall market 

rate of return. Use of this lower value also responds to certain judgments using the prescriptive 

or normative approach and to ethical objections that have been raised about rates of 3 percent or 

higher. 

Our general approach to estimating SCC values is to run the three integrated assessment 

models (FUND, DICE, and PAGE) using the following inputs agreed upon by the interagency 

group: 

• A Roe and Baker distribution for the climate sensitivity parameter bounded between 0 

and 10 with a median of 3 °C and a cumulative probability between 2 and 4.5 °C of twothirds. 

• Five sets of GDP, population, and carbon emissions trajectories based on EMF-22. 

• Constant annual discount rates of 2.5, 3, and 5 percent. 

Because the climate sensitivity parameter is modeled probabilistically, and because PAGE and 

FUND incorporate uncertainty in other model parameters, the final output from each model run 

is a distribution over the SCC in year t. 

For each of the IAMs, the basic computational steps for calculating the SCC in a particular year t

are:

1. Input the path of emissions, GDP, and population from the selected EMF-22 

scenarios, and the extrapolations based on these scenarios for post-2100 years.

2. Calculate the temperature effects and (consumption-equivalent) damages in each 

year resulting from the baseline path of emissions. 

 

aa Calculations done by Pizer et al. using the original simulation program from Newell and Pizer (2003).
16-A-27

a. In PAGE, the consumption-equivalent damages in each period are 

calculated as a fraction of the EMF GDP forecast, depending on the 

temperature in that period relative to the pre-industrial average 

temperature in each region. 

b. In FUND, damages in each period depend on both the level and the rate of 

temperature change in that period. 

c. In DICE, temperature affects both consumption and investment, so we 

first adjust the EMF GDP paths as follows: Using the Cobb-Douglas 

production function with the DICE2007 parameters, we extract the path of 

exogenous technical change implied by the EMF GDP and population 

paths, then we recalculate the baseline GDP path taking into account 

climate damages resulting from the baseline emissions path. 

3. Add an additional unit of carbon emissions in year t. (The exact unit varies by 

model.) 

4. Recalculate the temperature effects and damages expected in all years beyond t

resulting from this adjusted path of emissions, as in step 2. 

5. Subtract the damages computed in step 2 from those in step 4 in each year. 

(DICE is run in 10-year time steps, FUND in annual time steps, while the time 

steps in PAGE vary.) 

6. Discount the resulting path of marginal damages back to the year of emissions 

using the agreed upon fixed discount rates. 

7. Calculate the SCC as the net present value of the discounted path of damages 

computed in step 6, divided by the unit of carbon emissions used to shock the 

models in step 3. 

8. Multiply by 12/44 to convert from dollars per ton of carbon to dollars per ton of 

CO2 (2007 dollars) in DICE and FUND. (All calculations are done in tons of CO2 

in PAGE).

The steps above were repeated in each model for multiple future years to cover the time horizons 

anticipated for upcoming rulemaking analysis. To maintain consistency across the three IAMs, 

climate damages are calculated as lost consumption in each future year. 

It is important to note that each of the three models has a different default end year. The 

default time horizon is 2200 for PAGE, 2595 for DICE, and 3000 for the latest version of FUND. 

This is an issue for the multi-model approach because differences in SCC estimates may arise 

simply due to the model time horizon. Many consider 2200 too short a time horizon because it 

could miss a significant fraction of damages under certain assumptions about the growth of 

marginal damages and discounting, so each model is run here through 2300. This step required a 

small adjustment in the PAGE model only. This step also required assumptions about GDP, 
16-A-28

population, and greenhouse gas emission trajectories after 2100, the last year for which these 

data are available from the EMF-22 models. (A more detailed discussion of these assumptions is 

included in the Annex.) 

This exercise produces 45 separate distributions of the SCC for a given year, the product 

of 3 models, 3 discount rates, and 5 socioeconomic scenarios. This is clearly too many separate 

distributions for consideration in a regulatory impact analysis. 

To produce a range of plausible estimates that still reflects the uncertainty in the 

estimation exercise, the distributions from each of the models and scenarios are equally weighed 

and combined to produce three separate probability distributions for SCC in a given year, one for 

each assumed discount rate. These distributions are then used to define a range of point estimates 

for the global SCC. In this way, no IAM or socioeconomic scenario is given greater weight than 

another. Because the literature shows that the SCC is quite sensitive to assumptions about the 

discount rate, and because no consensus exists on the appropriate rate to use in an 

intergenerational context, we present SCCs based on the average values across models and 

socioeconomic scenarios for each discount rate. 

The interagency group selected four SCC values for use in regulatory analyses. Three 

values are based on the average SCC across models and socioeconomic and emissions scenarios 

at the 2.5, 3, and 5 percent discount rates. The fourth value is included to represent the higherthan-expected economic impacts from climate change further out in the tails of the SCC 

distribution. For this purpose, we use the SCC value for the 95th percentile at a 3 percent discount 

rate. (The full set of distributions by model and scenario combination is included in the Annex.) 

As noted above, the 3 percent discount rate is the central value, and so the central value that 

emerges is the average SCC across models at the 3 percent discount rate. For purposes of 

capturing the uncertainties involved in regulatory impact analysis, we emphasize the importance 

and value of considering the full range. 

As previously discussed, low probability, high impact events are incorporated into the 

SCC values through explicit consideration of their effects in two of the three models as well as 

the use of a probability density function for equilibrium climate sensitivity. Treating climate 

sensitivity probabilistically results in more high-temperature outcomes, which in turn lead to 

higher projections of damages. Although FUND does not include catastrophic damages (in 

contrast to the other two models), its probabilistic treatment of the equilibrium climate sensitivity 

parameter will directly affect the non-catastrophic damages that are a function of the rate of 

temperature change.

In Table 16A.5.1, we begin by presenting SCC estimates for 2010 by model, scenario, 

and discount rate to illustrate the variability in the SCC across each of these input parameters. 

As expected, higher discount rates consistently result in lower SCC values, while lower discount 

rates result in higher SCC values for each socioeconomic trajectory. It is also evident that there 

are differences in the SCC estimated across the three main models. For these estimates, FUND 

produces the lowest estimates, while PAGE generally produces the highest estimates. 
16-A-29

Table 16-A.5.1 Disaggregated Social Cost of CO2 Values by Model, Socioeconomic 

Trajectory, and Discount Rate for 2010 (in 2007 dollars) 

Discount rate: 5% 3% 2.5% 3% 

Model Scenario Avg Avg Avg 95th DICE

IMAGE 10.8 35.8 54.2 70.8 

MERGE 7.5 22.0 31.6 42.1 

Message 9.8 29.8 43.5 58.6 

MiniCAM 8.6 28.8 44.4 57.9 

550 Average 8.2 24.9 37.4 50.8 

PAGE

IMAGE 8.3 39.5 65.5 142.4 

MERGE 5.2 22.3 34.6 82.4 

Message 7.2 30.3 49.2 115.6 

MiniCAM 6.4 31.8 54.7 115.4 

550 Average 5.5 25.4 42.9 104.7 

FUND

IMAGE -1.3 8.2 19.3 39.7 

MERGE -0.3 8.0 14.8 41.3 

Message -1.9 3.6 8.8 32.1 

MiniCAM -0.6 10.2 22.2 42.6 

550 Average -2.7 -0.2 3.0 19.4 

These results are not surprising when compared to the estimates in the literature for the 

latest versions of each model. For example, adjusting the values from the literature that were 

used to develop interim SCC values to 2007 dollars for the year 2010 (assuming, as we did for 

the interim process, that SCC grows at 3 percent per year), FUND yields SCC estimates at or 

near zero for a 5 percent discount rate and around $9 per ton for a 3 percent discount rate. There 

are far fewer estimates using the latest versions of DICE and PAGE in the literature: Using 

similar adjustments to generate 2010 estimates, we calculate a SCC from DICE (based on 

Nordhaus 2008) of around $9 per ton for a 5 percent discount rate, and a SCC from PAGE 

(based on Hope 2006, 2008) close to $8 per ton for a 4 percent discount rate. Note that these 

comparisons are only approximate since the literature generally relies on Ramsey discounting, 

while we have assumed constant discount rates.bb

 

bb Nordhaus (2008) runs DICE2007 with ρ = 1.5 and η = 2. The default approach in PAGE2002 (version 1.4epm) 

treats ρ and η as random parameters, specified using a triangular distribution such that the min, mode, and max = 

0.1, 1, and 2 for ρ, and 0.5, 1, and 2 for η, respectively. The FUND default value for η is 1, and Tol generates SCC 

estimates for values of ρ = 0, 1, and 3 in many recent papers (e.g. Anthoff et al. 2009). The path of per-capita 

consumption growth, g, varies over time but is treated deterministically in two of the three models. In DICE, g is 
16-A-30

The SCC estimates from FUND are sensitive to differences in emissions paths but 

relatively insensitive to differences in GDP paths across scenarios, while the reverse is true for 

DICE and PAGE. This likely occurs because of several structural differences among the models. 

Specifically in DICE and PAGE, the fraction of economic output lost due to climate damages 

increases with the level of temperature alone, whereas in FUND the fractional loss also increases 

with the rate of temperature change. Furthermore, in FUND increases in income over time 

decrease vulnerability to climate change (a form of adaptation), whereas this does not occur in 

DICE and PAGE. These structural differences among the models make FUND more sensitive to 

the path of emissions and less sensitive to GDP compared to DICE and PAGE. 

Figure 16A.5.1 shows that IMAGE has the highest GDP in 2100 while MERGE 

Optimistic has the lowest. The ordering of global GDP levels in 2100 directly corresponds to the 

rank ordering of SCC for PAGE and DICE. For FUND, the correspondence is less clear, a result 

that is to be expected given its less direct relationship between its damage function and GDP.

Figure 16-A.5.1 Level of Global GDP across EMF Scenarios 

Table 16A.5.2 shows the four selected SCC values in five-year increments from 2010 to 

2050. Values for 2010, 2020, 2040, and 2050 are calculated by first combining all outputs 

(10,000 estimates per model run) from all scenarios and models for a given discount rate. Values 

for the years in between are calculated using a simple linear interpolation.

 

endogenous. Under Ramsey discounting, as economic growth slows in the future, the large damages from climate 

change that occur far out in the future are discounted at a lower rate than impacts that occur in the nearer term.

0

50

100

150

200

250

300

350

400

450

2000 2010 2020 2030 2050 2100

Global 

GDP

(trillions

of U.S. 

dollars)

IMAGE

MERGE Optimistic

MESSAGE

MiniCAM

3.7 W/m2 radiative forcing
16-A-31

Table 16-A.5.2 Social Cost of CO2, 2010 – 2050 (in 2007 dollars) 

Discount 5% 3% 2.5% 3%

Year Avg Avg Avg 95th

2010 4.7 21.4 35.1 64.9

2015 5.7 23.8 38.4 72.8 

2020 6.8 26.3 41.7 80.7

2025 8.2 29.6 45.9 90.4 

2030 9.7 32.8 50.0 100.0

2035 11.2 36.0 54.2 109.7 

2040 12.7 39.2 58.4 119.3

2045 14.2 42.1 61.7 127.8 

2050 15.7 44.9 65.0 136.2

The SCC increases over time because future emissions are expected to produce larger 

incremental damages as physical and economic systems become more stressed in response to 

greater climatic change. Note that this approach allows us to estimate the growth rate of the SCC 

directly using DICE, PAGE, and FUND rather than assuming a constant annual growth rate as 

was done for the interim estimates (using 3 percent). This helps to ensure that the estimates are 

internally consistent with other modeling assumptions. Table 16A.5.3 illustrates how the growth 

rate for these four SCC estimates varies over time. The full set of annual SCC estimates between 

2010 and 2050 is reported in the Annex. 

Table 16-A.5.3 Changes in the Average Annual Growth Rates of SCC Estimates between 

2010 and 2050 

Average Annual 

Growth Rate (%)

5% 3% 2.5% 3.0% 

Avg Avg Avg 95th

2010-2020 3.6% 2.1% 1.7% 2.2% 

2020-2030 3.7% 2.2% 1.8% 2.2%

2030-2040 2.7% 1.8% 1.6% 1.8% 

2040-2050 2.1% 1.4% 1.1% 1.3%

While the SCC estimate grows over time, the future monetized value of emissions 

reductions in each year (the SCC in year t multiplied by the change in emissions in year t) must 

be discounted to the present to determine its total net present value for use in regulatory analysis. 

Damages from future emissions should be discounted at the same rate as that used to calculate 

the SCC estimates themselves to ensure internal consistency—i.e., future damages from climate 

change, whether they result from emissions today or emissions in a later year, should be 

discounted using the same rate. For example, climate damages in the year 2020 that are 
16-A-32

calculated using a SCC based on a 5 percent discount rate also should be discounted back to the 

analysis year using a 5 percent discount rate.cc

16-A.6 LIMITATIONS OF THE ANALYSIS

 

As noted, any estimate of the SCC must be taken as provisional and subject to further 

refinement (and possibly significant change) in accordance with evolving scientific, economic, 

and ethical understandings. During the course of our modeling, it became apparent that there are 

several areas in particular need of additional exploration and research. These caveats, and 

additional observations in the following section, are necessary to consider when interpreting and 

applying the SCC estimates.

Incomplete treatment of non-catastrophic damages. The impacts of climate change are 

expected to be widespread, diverse, and heterogeneous. In addition, the exact magnitude of these 

impacts is uncertain because of the inherent complexity of climate processes, the economic 

behavior of current and future populations, and our inability to accurately forecast technological 

change and adaptation. Current IAMs do not assign value to all of the important physical, 

ecological, and economic impacts of climate change recognized in the climate change literature 

(some of which are discussed above) because of lack of precise information on the nature of 

damages and because the science incorporated into these models understandably lags behind the 

most recent research. Our ability to quantify and monetize impacts will undoubtedly improve 

with time. But it is also likely that even in future applications, a number of potentially significant 

damage categories will remain non-monetized. (Ocean acidification is one example of a 

potentially large damage from CO2 emissions not quantified by any of the three models. Species 

and wildlife loss is another example that is exceedingly difficult to monetize.) 

Incomplete treatment of potential catastrophic damages. There has been considerable 

recent discussion of the risk of catastrophic impacts and how best to account for extreme 

scenarios, such as the collapse of the Atlantic Meridional Overturning Circulation or the West 

Antarctic Ice Sheet, or large releases of methane from melting permafrost and warming oceans. 

Weitzman (2009) suggests that catastrophic damages are extremely large—so large, in fact, that 

the damages from a low probability, catastrophic event far in the future dominate the effect of 

the discount rate in a present value calculation and result in an infinite willingness-to-pay for 

mitigation today. However, Nordhaus (2009) concluded that the conditions under which 

Weitzman's results hold “are limited and do not apply to a wide range of potential uncertain 

scenarios." 

Using a simplified IAM, Newbold and Daigneault (2009) confirmed the potential for 

large catastrophe risk premiums but also showed that the aggregate benefit estimates can be 

highly sensitive to the shapes of both the climate sensitivity distribution and the damage function 

at high temperature changes. Pindyck (2009) also used a simplified IAM to examine high-

 

cc However, it is possible that other benefits or costs of proposed regulations unrelated to CO2 emissions will be 

discounted at rates that differ from those used to develop the SCC estimates. 
16-A-33

impact, low-probability risks, using a right-skewed gamma distribution for climate sensitivity as 

well as an uncertain damage coefficient, but in most cases found only a modest risk premium. 

Given this difference in opinion, further research in this area is needed before its practical 

significance can be fully understood and a reasonable approach developed to account for such 

risks in regulatory analysis. (The next section discusses the scientific evidence on catastrophic 

impacts in greater detail.)

Uncertainty in extrapolation of damages to high temperatures: The damage functions in 

these IAMs are typically calibrated by estimating damages at moderate temperature increases 

(e.g., DICE was calibrated at 2.5 °C) and extrapolated to far higher temperatures by assuming 

that damages increase as some power of the temperature change. Hence, estimated damages are 

far more uncertain under more extreme climate change scenarios. 

Incomplete treatment of adaptation and technological change: Each of the three 

integrated assessment models used here assumes a certain degree of low- or no-cost adaptation. 

For instance, Tol assumes a great deal of adaptation in FUND, including widespread reliance on 

air conditioning; so much so, that the largest single benefit category in FUND is the reduced 

electricity costs from not having to run air conditioning as intensively (NRC 2009). 

Climate change also will increase returns on investment to develop technologies that 

allow individuals to cope with adverse climate conditions, and IAMs to do not adequately 

account for this directed technological change.dd For example, scientists may develop crops that 

are better able to withstand higher and more variable temperatures. Although DICE and FUND 

have both calibrated their agricultural sectors under the assumption that farmers will change land 

use practices in response to climate change (Mastrandrea, 2009), they do not take into account 

technological changes that lower the cost of this adaptation over time. On the other hand, the 

calibrations do not account for increases in climate variability, pests, or diseases, which could 

make adaptation more difficult than assumed by the IAMs for a given temperature change. 

Hence, models do not adequately account for potential adaptation or technical change that might 

alter the emissions pathway and resulting damages. In this respect, it is difficult to determine 

whether the incomplete treatment of adaptation and technological change in these IAMs 

understate or overstate the likely damages.

Risk aversion: A key question unanswered during this interagency process is what to 

assume about relative risk aversion with regard to high-impact outcomes. These calculations do 

not take into account the possibility that individuals may have a higher willingness to pay to 

reduce the likelihood of low-probability, high-impact damages than they do to reduce the 

likelihood of higher-probability, but lower-impact, damages with the same expected cost. (The 

inclusion of the 95th percentile estimate in the final set of SCC values was largely motivated by 

this concern.) If individuals do show such a higher willingness to pay, a further question is 

whether that fact should be taken into account for regulatory policy. Even if individuals are not 

risk-averse for such scenarios, it is possible that regulatory policy should include a degree of 

risk-aversion. 

 

dd However these research dollars will be diverted from whatever their next best use would have been in the absence 

of climate change (so productivity/GDP would have been still higher).
16-A-34

Assuming a risk-neutral representative agent is consistent with OMB’s Circular A-4, 

which advises that the estimates of benefits and costs used in regulatory analysis are usually 

based on the average or the expected value and that “emphasis on these expected values is 

appropriate as long as society is ‘risk neutral’ with respect to the regulatory alternatives. While 

this may not always be the case, [analysts] should in general assume ‘risk neutrality’ in [their] 

analysis.” 

Nordhaus (2008) points to the need to explore the relationship between risk and income 

in the context of climate change across models and to explore the role of uncertainty regarding 

various parameters in the results. Using FUND, Anthoff et al (2009) explored the sensitivity of 

the SCC to Ramsey equation parameter assumptions based on observed behavior. They conclude

that “the assumed rate of risk aversion is at least as important as the assumed rate of time 

preference in determining the social cost of carbon.” Since Circular A-4 allows for a different 

assumption on risk preference in regulatory analysis if it is adequately justified, we plan to 

continue investigating this issue.

16-A.7 A FURTHER DISCUSSION OF CATASTROPHIC IMPACTS AND 

DAMAGE FUNCTIONS

As noted above, the damage functions underlying the three IAMs used to estimate the 

SCC may not capture the economic effects of all possible adverse consequences of climate 

change and may therefore lead to underestimates of the SCC (Mastrandrea 2009). In particular, 

the models’ functional forms may not adequately capture: (1) potentially discontinuous “tipping 

point” behavior in Earth systems, (2) inter-sectoral and inter-regional interactions, including 

global security impacts of high-end warming, and (3) limited near-term substitutability between 

damage to natural systems and increased consumption. 

It is the hope of the interagency group that over time researchers and modelers will work 

to fill these gaps and that the SCC estimates used for regulatory analysis by the Federal 

government will continue to evolve with improvements in modeling. In the meantime, we 

discuss some of the available evidence.

Extrapolation of climate damages to high levels of warming

The damage functions in the models are calibrated at moderate levels of warming and 

should therefore be viewed cautiously when extrapolated to the high temperatures found in the 

upper end of the distribution. Recent science suggests that there are a number of potential 

climatic “tipping points” at which the Earth system may exhibit discontinuous behavior with 

potentially severe social and economic consequences (e.g., Lenton et al, 2008, Kriegler et al., 

2009). These tipping points include the disruption of the Indian Summer Monsoon, dieback of 

the Amazon Rainforest and boreal forests, collapse of the Greenland Ice Sheet and the West 

Antarctic Ice Sheet, reorganization of the Atlantic Meridional Overturning Circulation, 

strengthening of El Niño-Southern Oscillation, and the release of methane from melting 
16-A-35

permafrost. Many of these tipping points are estimated to have thresholds between about 3 °C 

and 5 °C (Lenton et al., 2008). Probabilities of several of these tipping points were assessed 

through expert elicitation in 2005–2006 by Kriegler et al. (2009); results from this study are 

highlighted in Table 16A.7.1. Ranges of probability are averaged across core experts on each 

topic. 

As previously mentioned, FUND does not include potentially catastrophic effects. DICE 

assumes a small probability of catastrophic damages that increases with increased warming, but 

the damages from these risks are incorporated as expected values (i.e., ignoring potential risk 

aversion). PAGE models catastrophic impacts in a probabilistic framework (see Figure 16A.4.1), 

so the high-end output from PAGE potentially offers the best insight into the SCC if the world 

were to experience catastrophic climate change. For instance, at the 95th percentile and a 3 

percent discount rate, the SCC estimated by PAGE across the five socioeconomic and emission 

trajectories of $113 per ton of CO2 is almost double the value estimated by DICE, $58 per ton in 

2010. We cannot evaluate how well the three models account for catastrophic or noncatastrophic impacts, but this estimate highlights the sensitivity of SCC values in the tails of the 

distribution to the assumptions made about catastrophic impacts. 

Table 16-A.7.1 Probabilities of Various Tipping Points from Expert Elicitation 

Possible Tipping Points

Duration before

effect is fully

realized (in years)

Additional Warming by 2100 

0.5-1.5 C 1.5-3.0 C 3-5 C 

Reorganization of Atlantic Meridional 

Overturning Circulation about 100 0-18% 6-39% 18-67% 

Greenland Ice Sheet collapse at least 300 8-39% 33-73% 67-96% 

West Antarctic Ice Sheet collapse at least 300 5-41% 10-63% 33-88% 

Dieback of Amazon rainforest about 50 2-46% 14-84% 41-94% 

Strengthening of El Niño-Southern Oscillation about 100 1-13% 6-32% 19-49% 

Dieback of boreal forests about 50 13-43% 20-81% 34-91% 

Shift in Indian Summer Monsoon about 1 Not formally assessed

Release of methane from melting permafrost Less than 100 Not formally assessed.

PAGE treats the possibility of a catastrophic event probabilistically, while DICE treats it 

deterministically (that is, by adding the expected value of the damage from a catastrophe to the 

aggregate damage function). In part, this results in different probabilities being assigned to a 

catastrophic event across the two models. For instance, PAGE places a probability near zero on a 

catastrophe at 2.5 °C warming, while DICE assumes a 4 percent probability of a catastrophe at 

2.5 °C. By comparison, Kriegler et al. (2009) estimate a probability of at least 16-36 percent of 
16-A-36

crossing at least one of their primary climatic tipping points in a scenario with temperatures 

about 2-4 °C warmer than pre-Industrial levels in 2100. 

It is important to note that crossing a climatic tipping point will not necessarily lead to an 

economic catastrophe in the sense used in the IAMs. A tipping point is a critical threshold across 

which some aspect of the Earth system starts to shifts into a qualitatively different state (for 

instance, one with dramatically reduced ice sheet volumes and higher sea levels). In the IAMs, a 

catastrophe is a low-probability environmental change with high economic impact. 

Failure to incorporate inter-sectoral and inter-regional interactions

The damage functions do not fully incorporate either inter-sectoral or inter-regional 

interactions. For instance, while damages to the agricultural sector are incorporated, the effects 

of changes in food supply on human health are not fully captured and depend on the modeler’s 

choice of studies used to calibrate the IAM. Likewise, the effects of climate damages in one 

region of the world on another region are not included in some of the models (FUND includes 

the effects of migration from sea level rise). These inter-regional interactions, though difficult to 

quantify, are the basis for climate-induced national and economic security concerns (e.g., 

Campbell et al., 2007; U.S. Department of Defense 2010) and are particularly worrisome at 

higher levels of warming. High-end warming scenarios, for instance, project water scarcity 

affecting 4.3-6.9 billion people by 2050, food scarcity affecting about 120 million additional 

people by 2080, and the creation of millions of climate refugees (Easterling et al., 2007; 

Campbell et al., 2007). 

Imperfect substitutability of environmental amenities

Data from the geological record of past climate changes suggests that 6 °C of warming 

may have severe consequences for natural systems. For instance, during the Paleocene-Eocene 

Thermal Maximum about 55.5 million years ago, when the Earth experienced a geologically 

rapid release of carbon associated with an approximately 5 °C increase in global mean 

temperatures, the effects included shifts of about 400-900 miles in the range of plants (Wing et 

al., 2005), and dwarfing of both land mammals (Gingerich, 2006) and soil fauna (Smith et al., 

2009). 

The three IAMs used here assume that it is possible to compensate for the economic 

consequences of damages to natural systems through increased consumption of non-climate 

goods, a common assumption in many economic models. In the context of climate change, 

however, it is possible that the damages to natural systems could become so great that no 

increase in consumption of non-climate goods would provide complete compensation (Levy et 

al., 2005). For instance, as water supplies become scarcer or ecosystems become more fragile 

and less bio-diverse, the services they provide may become increasingly more costly to replace. 

Uncalibrated attempts to incorporate the imperfect substitutability of such amenities into IAMs 

(Sterner and Persson, 2008) indicate that the optimal degree of emissions abatement can be 

considerably greater than is commonly recognized. 
16-A-37

16-A.8 CONCLUSION

The interagency group selected four SCC estimates for use in regulatory analyses. For 

2010, these estimates are $5, $21, $35, and $65 (in 2007 dollars). The first three estimates are 

based on the average SCC across models and socioeconomic and emissions scenarios at the 5, 3, 

and 2.5 percent discount rates, respectively. The fourth value is included to represent the higherthan-expected impacts from temperature change further out in the tails of the SCC distribution. 

For this purpose, we use the SCC value for the 95th percentile at a 3 percent discount rate. The 

central value is the average SCC across models at the 3 percent discount rate. For purposes of 

capturing the uncertainties involved in regulatory impact analysis, we emphasize the importance 

and value of considering the full range. These SCC estimates also grow over time. For instance, 

the central value increases to $24 per ton of CO2 in 2015 and $26 per ton of CO2 in 2020. 

We noted a number of limitations to this analysis, including the incomplete way in which 

the integrated assessment models capture catastrophic and non-catastrophic impacts, their 

incomplete treatment of adaptation and technological change, uncertainty in the extrapolation of 

damages to high temperatures, and assumptions regarding risk aversion. The limited amount of 

research linking climate impacts to economic damages makes this modeling exercise even more 

difficult. It is the hope of the interagency group that over time researchers and modelers will 

work to fill these gaps and that the SCC estimates used for regulatory analysis by the Federal 

government will continue to evolve with improvements in modeling. 

 
16-A-38

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16-A-44

16-A.9 ANNEX

Table 16-A.9.1 Annual SCC Values: 2010–2050 (in 2007 dollars) 

Discount Rate 5% 3% 2.5% 3%

Year Avg Avg Avg 95th

2010 4.7 21.4 35.1 64.9

2011 4.9 21.9 35.7 66.5

2012 5.1 22.4 36.4 68.1

2013 5.3 22.8 37.0 69.6

2014 5.5 23.3 37.7 71.2

2015 5.7 23.8 38.4 72.8

2016 5.9 24.3 39.0 74.4

2017 6.1 24.8 39.7 76.0

2018 6.3 25.3 40.4 77.5

2019 6.5 25.8 41.0 79.1

2020 6.8 26.3 41.7 80.7

2021 7.1 27.0 42.5 82.6

2022 7.4 27.6 43.4 84.6

2023 7.7 28.3 44.2 86.5

2024 7.9 28.9 45.0 88.4

2025 8.2 29.6 45.9 90.4

2026 8.5 30.2 46.7 92.3

2027 8.8 30.9 47.5 94.2

2028 9.1 31.5 48.4 96.2

2029 9.4 32.1 49.2 98.1

2030 9.7 32.8 50.0 100.0

2031 10.0 33.4 50.9 102.0

2032 10.3 34.1 51.7 103.9

2033 10.6 34.7 52.5 105.8

2034 10.9 35.4 53.4 107.8

2035 11.2 36.0 54.2 109.7

2036 11.5 36.7 55.0 111.6

2037 11.8 37.3 55.9 113.6

2038 12.1 37.9 56.7 115.5

2039 12.4 38.6 57.5 117.4

2040 12.7 39.2 58.4 119.3

2041 13.0 39.8 59.0 121.0

2042 13.3 40.4 59.7 122.7

2043 13.6 40.9 60.4 124.4

2044 13.9 41.5 61.0 126.1

2045 14.2 42.1 61.7 127.8

2046 14.5 42.6 62.4 129.4

2047 14.8 43.2 63.0 131.1

2048 15.1 43.8 63.7 132.8

2049 15.4 44.4 64.4 134.5

2050 15.7 44.9 65.0 136.2

This Annex provides additional technical information about the non-CO2 emission 

projections used in the modeling and the method for extrapolating emissions forecasts through 

2300 and shows the full distribution of 2010 SCC estimates by model and scenario combination. 
16-A-45

16-A.9.1 Other (non-CO2) gases 

In addition to fossil and industrial CO2 emissions, each EMF scenario provides 

projections of methane (CH4), nitrous oxide (N2O), fluorinated gases, and net land use CO2

emissions to 2100. These assumptions are used in all three IAMs while retaining each model’s 

default radiative forcings (RF) due to other factors (e.g., aerosols and other gases). Specifically, 

to obtain the RF associated with the non-CO2 EMF emissions only, we calculated the RF 

associated with the EMF atmospheric CO2 concentrations and subtracted them from the EMF 

total RF.ee This approach respects the EMF scenarios as much as possible and at the same time 

takes account of those components not included in the EMF projections. Since each model treats 

non-CO2 gases differently (e.g., DICE lumps all other gases into one composite exogenous 

input), this approach was applied slightly differently in each of the models. 

FUND: Rather than relying on RF for these gases, the actual emissions from each 

scenario were used in FUND. The model default trajectories for CH4, N20, SF6, and the CO2

emissions from land were replaced with the EMF values. 

PAGE: PAGE models CO2, CH4, sulfur hexafluoride (SF6), and aerosols and contains an 

"excess forcing" vector that includes the RF for everything else. To include the EMF values, we 

removed the default CH4 and SF6 factorsff, decomposed the excess forcing vector, and 

constructed a new excess forcing vector that includes the EMF RF for CH4, N20, and fluorinated 

gases, as well as the model default values for aerosols and other factors. Net land use CO2

emissions were added to the fossil and industrial CO2 emissions pathway. 

DICE: DICE presents the greatest challenge because all forcing due to factors other than 

industrial CO2 emissions is embedded in an exogenous non-CO2 RF vector. To decompose this 

exogenous forcing path into EMF non-CO2 gases and other gases, we relied on the references in 

DICE2007 to the Intergovernmental Panel on Climate Change’s (IPCC) Fourth Assessment 

Report (AR4) and the discussion of aerosol forecasts in the IPCC’s Third Assessment Report 

(TAR) and in AR4, as explained below. In DICE2007, Nordhaus assumes that exogenous 

forcing from all non-CO2 sources is -0.06 W/m2 in 2005, as reported in AR4, and increases 

linearly to 0.3 W/m2 in 2105, based on GISS projections, and then stays constant after that time. 

According to AR4, the RF in 2005 from CH4, N20, and halocarbons (approximately 

similar to the F-gases in the EMF-22 scenarios) was 0.48 + 0.16 + 0.34 = 0.98 W/m2 and RF 

from total aerosols was -1.2 W/m2. Thus, the -.06 W/m2 non-CO2 forcing in DICE can be 

 

ee Note EMF did not provide CO2 concentrations for the IMAGE reference scenario. Thus, for this scenario, we fed 

the fossil, industrial, and land CO2 emissions into MAGICC (considered a "neutral arbiter" model, which is tuned to 

emulate the major global climate models) and the resulting CO2 concentrations were used. Note also that MERGE 

assumes a neutral biosphere so net land CO2 emissions are set to zero for all years for the MERGE Optimistic 

reference scenario, and for the MERGE component of the average 550 scenario (i.e., we add up the land use 

emissions from the other three models and divide by 4).

ff Both the model default CH4 emissions and the initial atmospheric CH4 is set to zero to avoid double counting the 

effect of past CH4 emissions.
16-A-46

decomposed into: 0.98 W/m2 due to the EMF non-CO2 gases, -1.2 W/m2 due to aerosols, and the 

remainder, 0.16 W/m2, due to other residual forcing. 

For subsequent years, we calculated the DICE default RF from aerosols and other nonCO2 gases based on the following two assumptions: 

(1) RF from aerosols declines linearly from 2005 to 2100 at the rate projected by the TAR 

and then stays constant thereafter; and 

(2) With respect to RF from non-CO2 gases not included in the EMF-22 scenarios, the share 

of non-aerosol RF matches the share implicit in the AR4 summary statistics cited above and 

remains constant over time. 

Assumption (1) means that the RF from aerosols in 2100 equals 66 percent of that in 2000, 

which is the fraction of the TAR projection of total RF from aerosols (including sulfates, black 

carbon, and organic carbon) in 2100 vs. 2000 under the A1B SRES emissions scenario. Since

the SRES marker scenarios were not updated for the AR4, the TAR provides the most recent 

IPCC projection of aerosol forcing. We rely on the A1B projection from the TAR because it 

provides one of the lower aerosol forecasts among the SRES marker scenarios and is more 

consistent with the AR4 discussion of the post-SRES literature on aerosols: 

Aerosols have a net cooling effect and the representation of aerosol and aerosol precursor 

emissions, including sulfur dioxide, black carbon and organic carbon, has improved in the 

post-SRES scenarios. Generally, these emissions are projected to be lower than reported in 

SRES. {WGIII 3.2, TS.3, SPM}.gg

Assuming a simple linear decline in aerosols from 2000 to 2100 also is more consistent 

with the recent literature on these emissions. For example, the figure below shows that the sulfur 

dioxide emissions peak over the short term of some SRES scenarios above the upper bound 

estimates of the more recent scenarios.hh Recent scenarios project sulfur emissions to peak earlier 

and at lower levels compared to the SRES in part because of new information about present and 

planned sulfur legislation in some developing countries, such as India and China.ii

 The lowerbound projections of the recent literature have also shifted downward slightly compared to the 

SRES scenario (IPCC 2007). 

 

gg AR4 Synthesis Report, p. 44, http://www.ipcc.ch/pdf/assessment-report/ar4/syr/ar4_syr.pdf

hh See Smith, S.J., R. Andres, E. Conception, and J. Lurz, 2004: Historical sulfur dioxide emissions, 1850-2000: 

methods and results. Joint Global Research Institute, College Park, 14 pp.

ii See Carmichael, G., D. Streets, G. Calori, M. Amann, M. Jacobson, J. Hansen, and H. Ueda, 2002: Changing 

trends in sulphur emissions in Asia: implications for acid deposition, air pollution, and climate. Environmental 

Science and Technology, 36(22):4707- 4713; Streets, D., K. Jiang, X. Hu, J. Sinton, X.-Q. Zhang, D. Xu, M. 

Jacobson, and J. Hansen, 2001: Recent reductions in China’s greenhouse gas emissions. Science, 294(5548): 1835-

1837.
16-A-47

With these assumptions, the DICE aerosol forcing changes from -1.2 in 2005 to -0.792 in 

2105 W/m2; forcing due to other non-CO2 gases not included in the EMF scenarios declines from 

0.160 to 0.153 W/m2

. 

. 

Figure 16-A.9.2 Sulfur Dioxide Emission Scenarios 

Notes: Thick colored lines depict the four SRES marker scenarios and black dashed lines 

show the median, 5th, and 95th percentile of the frequency distribution for the full 

ensemble of 40 SRES scenarios. The blue area (and the thin dashed lines in blue) 

illustrates individual scenarios and the range of Smith et al. (2004). Dotted lines indicate 

the minimum and maximum of SO2 emissions scenarios developed pre-SRES.

Source: IPCC (2007), AR4 WGIII 3.2, 

http://www.ipcc.ch/publications_and_data/ar4/wg3/en/ch3-ens3-2-2-4.html. 

Although other approaches to decomposing the DICE exogenous forcing vector are 

possible, initial sensitivity analysis suggests that the differences among reasonable alternative 

approaches are likely to be minor. For example, adjusting the TAR aerosol projection above to

assume that aerosols will be maintained at 2000 levels through 2100 reduces average SCC values 

(for 2010) by approximately 3 percent (or less than $2); assuming all aerosols are phased out by 

2100 increases average 2010 SCC values by 6-7 percent (or $0.50-$3)–depending on the 

discount rate. These differences increase slightly for SCC values in later years but are still well 

within 10 percent of each other as far out as 2050. 

Finally, as in PAGE, the EMF net land use CO2 emissions are added to the fossil and 

industrial CO2 emissions pathway. 

16-A.9.2 Extrapolating Emissions Projections to 2300 

To run each model through 2300 requires assumptions about GDP, population, 

greenhouse gas emissions, and radiative forcing trajectories after 2100, the last year for which 
16-A-48

these projections are available from the EMF-22 models. These inputs were extrapolated from 

2100 to 2300 as follows: 

1. Population growth rate declines linearly, reaching zero in the year 2200. 

2. GDP/per capita growth rate declines linearly, reaching zero in the year 2300. 

3. The decline in the fossil and industrial carbon intensity (CO2/GDP) growth rate over 

2090-2100 is maintained from 2100 through 2300. 

4. Net land use CO2 emissions decline linearly, reaching zero in the year 2200. 

5. Non-CO2 radiative forcing remains constant after 2100. 

Long run stabilization of GDP per capita was viewed as a more realistic simplifying 

assumption than a linear or exponential extrapolation of the pre-2100 economic growth rate of 

each EMF scenario. This is based on the idea that increasing scarcity of natural resources and 

the degradation of environmental sinks available for assimilating pollution from economic 

production activities may eventually overtake the rate of technological progress. Thus, the 

overall rate of economic growth may slow over the very long run. The interagency group also 

considered allowing an exponential decline in the growth rate of GDP per capita. However, 

since this would require an additional assumption about how close to zero the growth rate would 

get by 2300, the group opted for the simpler and more transparent linear extrapolation to zero by 

2300. 

The population growth rate is also assumed to decline linearly, reaching zero by 2200. 

This assumption is reasonably consistent with the United Nations long run population forecast, 

which estimates global population to be fairly stable after 2150 in the medium scenario (UN 

2004).jj The resulting range of EMF population trajectories (figure below) also encompass the 

UN medium scenario forecasts through 2300—global population of 8.5 billion by 2200, and 9 

billion by 2300. 

Maintaining the decline in the 2090-2100 carbon intensity growth rate (i.e., CO2 per 

dollar of GDP) through 2300 assumes that technological improvements and innovations in the 

areas of energy efficiency and other carbon reducing technologies (possibly including currently 

unavailable methods) will continue to proceed at roughly the same pace that is projected to occur 

towards the end of the forecast period for each EMF scenario. This assumption implies that total 

cumulative emissions in 2300 will be between 5,000 and 12,000 GtC, which is within the range 

of the total potential global carbon stock estimated in the literature.

 

Net land use CO2 emissions are expected to stabilize in the long run, so in the absence of 

any post 2100 projections, the group assumed a linear decline to zero by 2200. Given no a priori 

reasons for assuming a long run increase or decline in non-CO2 radiative forcing, it is assumed to 

remain at the 2100 levels for each EMF scenario through 2300. 

 

jj United Nations. 2004. World Population to 2300. 

http://www.un.org/esa/population/publications/longrange2/worldpop2300final.pdf
16-A-49

Figures below show the paths of global population, GDP, fossil and industrial CO2

emissions, net land CO2 emissions, non-CO2 radiative forcing, and CO2 intensity (fossil and 

industrial CO2 emissions/GDP) resulting from these assumptions. 

Figure 16-A.9.3 Global Population, 2000-2300 (Post-2100 

extrapolations assume the population growth rate 

changes linearly to reach a zero growth rate by 

2200.) 

Note: In the fifth scenario, 2000-2100 population is equal to the average of the population under 

the 550 ppm CO2e, full-participation, not-to-exceed scenarios considered by each of the four 

models. 

5.5

6.5

7.5

8.5

9.5

10.5

11.5

2000 2050 2100 2150 2200 2250 2300

IMAGE

MERGE

MESSAGE

MiniCAM

5th scenario

Extrapolations

Global Population [billion]

Year
16-A-50

Figure 16-A.9.4 World GDP, 2000-2300 (Post-2100 extrapolations 

assume GDP per capita growth declines linearly, 

reaching zero in the year 2300)

Note: In the fifth scenario, 2000-2100 GDP is equal to the average of the GDP under the 550 

ppm CO2e, full-participation, not-to-exceed scenarios considered by each of the four models. 

0

500

1000

1500

2000

2000 2050 2100 2150 2200 2250 2300

IMAGE

MERGE

MESSAGE

MiniCAM

5th scenario

Extrapolations

Year

World GDP [$trillion]

0

50

100

150

200

2000 2050 2100 2150 2200 2250 2300

IMAGE

MERGE

MESSAGE

MiniCAM

5th scenario

Extrapolations

Fossil&Industrial CO2 Emissions [GtCO2/decade]

Year
16-A-51

Figure 16-A.9.5 Global Fossil and Industrial CO2 Emissions, 2000-

2300 (Post-2100 extrapolations assume growth rate 

of CO2 intensity (CO2/GDP) over 2090-2100 is 

maintained through 2300) 

Note: In the fifth scenario, 2000-2100 emissions are equal to the average of the emissions under 

the 550 ppm CO2e, full-participation, not-to-exceed scenarios considered by each of the four 

models. 

Figure 16-A.9.6 Global Net Land Use CO2 Emissions, 2000-2300 

(Post-2100 extrapolations assume emissions decline 

linearly, reaching zero in the year 2200)

kk

Note: In the fifth scenario, 2000-2100 emissions are equal to the average of the emissions under 

the 550 ppm CO2e, full-participation, not-to-exceed scenarios considered by each of the four 

models. 

 

kk MERGE assumes a neutral biosphere so net land CO2 emissions are set to zero for all years for the MERGE 

Optimistic reference scenario, and for the MERGE component of the average 550 scenario (i.e., we add up the land 

use emissions from the other three models and divide by 4).

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

2000 2050 2100 2150 2200 2250 2300

IMAGE

MERGE

MESSAGE

MiniCAM

5th scneario

Extrapolations

Net land CO2 emissions [GtCO2/yr]

Year

z
16-A-52

Figure 16-A.9.7 Global Non-CO2 Radiative Forcing, 2000-2300 

(Post-2100 extrapolations assume constant non-CO2

radiative forcing after 2100) 

Note: In the fifth scenario, 2000-2100 emissions are equal to the average of the emissions under 

the 550 ppm CO2e, full-participation, not-to-exceed scenarios considered by each of the four 

models. 

0.00

0.75

1.50

2.25

3.00

3.75

2000 2050 2100 2150 2200 2250 2300

IMAGE

MERGE

MESSAGE

MiniCAM

5th scenario

Extrapolations

nonCO2 RF [W/m^2]

Year
16-A-53

Figure 16-A.9.8 Global CO2 Intensity (fossil & industrial CO2

emissions/GDP), 2000-2300 (Post-2100 

extrapolations assume decline in CO2/GDP growth 

rate over 2090-2100 is maintained through 2300) 

Note: In the fifth scenario, 2000-2100 emissions are equal to the average of the emissions under 

the 550 ppm CO2e, full-participation, not-to-exceed scenarios considered by each of the four 

models. 

0

0

0

0

0

1

1

1

1

2000 2050 2100 2150 2200 2250 2300

IMAGE

MERGE

MESSAGE

MiniCAM

5th scenario

Extrapolations

Fossil & Industrial CO2 intensity [GtCO2/trillion $]

Year
16-A-54

Table 16-A.9.2 2010 Global SCC Estimates at 2.5 Percent Discount Rate (2007$/ton CO2) 

Percentile 1st 5th 10th 25th 50th Avg 75th 90th 95th 99th

Scenario PAGE

IMAGE 3.3 5.9 8.1 13.9 28.8 65.5 68.2 147.9 239.6 563.8

MERGE optimistic 1.9 3.2 4.3 7.2 14.6 34.6 36.2 79.8 124.8 288.3

Message 2.4 4.3 5.8 9.8 20.3 49.2 50.7 114.9 181.7 428.4

MiniCAM base 2.7 4.6 6.4 11.2 22.8 54.7 55.7 120.5 195.3 482.3

5th scenario 2.0 3.5 4.7 8.1 16.3 42.9 41.5 103.9 176.3 371.9

Scenario DICE

IMAGE 16.4 21.4 25 33.3 46.8 54.2 69.7 96.3 111.1 130.0

MERGE optimistic 9.7 12.6 14.9 19.7 27.9 31.6 40.7 54.5 63.5 73.3

Message 13.5 17.2 20.1 27 38.5 43.5 55.1 75.8 87.9 103.0

MiniCAM base 13.1 16.7 19.8 26.7 38.6 44.4 56.8 79.5 92.8 109.3

5th scenario 10.8 14 16.7 22.2 32 37.4 47.7 67.8 80.2 96.8

Scenario FUND

IMAGE -33.1 -18.9 -13.3 -5.5 4.1 19.3 18.7 43.5 67.1 150.7

MERGE optimistic -33.1 -14.8 -10 -3 5.9 14.8 20.4 43.9 65.4 132.9

Message -32.5 -19.8 -14.6 -7.2 1.5 8.8 13.8 33.7 52.3 119.2

MiniCAM base -31.0 -15.9 -10.7 -3.4 6 22.2 21 46.4 70.4 152.9

5th scenario -32.2 -21.6 -16.7 -9.7 -2.3 3 6.7 20.5 34.2 96.8
16-A-55

Table 16-A.9.3 2010 Global SCC Estimates at 3 Percent Discount Rate (2007$/ton CO2) 

Percentile 1st 5th 10th 25th 50th Avg 75th 90th 95th 99th

Scenario PAGE

IMAGE 2.0 3.5 4.8 8.1 16.5 39.5 41.6 90.3 142.4 327.4

MERGE optimistic 1.2 2.1 2.8 4.6 9.3 22.3 22.8 51.3 82.4 190.0

Message 1.6 2.7 3.6 6.2 12.5 30.3 31 71.4 115.6 263.0

MiniCAM base 1.7 2.8 3.8 6.5 13.2 31.8 32.4 72.6 115.4 287.0

5th scenario 1.3 2.3 3.1 5 9.6 25.4 23.6 62.1 104.7 222.5

Scenario DICE

IMAGE 11.0 14.5 17.2 22.8 31.6 35.8 45.4 61.9 70.8 82.1

MERGE optimistic 7.1 9.2 10.8 14.3 19.9 22 27.9 36.9 42.1 48.8

Message 9.7 12.5 14.7 19 26.6 29.8 37.8 51.1 58.6 67.4

MiniCAM base 8.8 11.5 13.6 18 25.2 28.8 36.9 50.4 57.9 67.8

5th scenario 7.9 10.1 11.8 15.6 21.6 24.9 31.8 43.7 50.8 60.6

Scenario FUND

IMAGE -25.2 -15.3 -11.2 -5.6 0.9 8.2 10.4 25.4 39.7 90.3

MERGE optimistic -24.0 -12.4 -8.7 -3.6 2.6 8 12.2 27 41.3 85.3

Message -25.3 -16.2 -12.2 -6.8 -0.5 3.6 7.7 20.1 32.1 72.5

MiniCAM base -23.1 -12.9 -9.3 -4 2.4 10.2 12.2 27.7 42.6 93.0

5th scenario -24.1 -16.6 -13.2 -8.3 -3 -0.2 2.9 11.2 19.4 53.6
16-A-56

Table 16-A.9.4 2010 Global SCC Estimates at 5 Percent Discount Rate (2007$/ton CO2) 

Percentile 1st 5th 10th 25th 50th Avg 75th 90th 95th 99th

Scenario PAGE

IMAGE 0.5 0.8 1.1 1.8 3.5 8.3 8.5 19.5 31.4 67.2

MERGE optimistic 0.3 0.5 0.7 1.2 2.3 5.2 5.4 12.3 19.5 42.4

Message 0.4 0.7 0.9 1.6 3 7.2 7.2 17 28.2 60.8

MiniCAM base 0.3 0.6 0.8 1.4 2.7 6.4 6.6 15.9 24.9 52.6

5th scenario 0.3 0.6 0.8 1.3 2.3 5.5 5 12.9 22 48.7

Scenario DICE

IMAGE 4.2 5.4 6.2 7.6 10 10.8 13.4 16.8 18.7 21.1

MERGE optimistic 2.9 3.7 4.2 5.3 7 7.5 9.3 11.7 12.9 14.4

Message 3.9 4.9 5.5 7 9.2 9.8 12.2 15.4 17.1 18.8

MiniCAM base 3.4 4.2 4.7 6 7.9 8.6 10.7 13.5 15.1 16.9

5th scenario 3.2 4 4.6 5.7 7.6 8.2 10.2 12.8 14.3 16.0

Scenario FUND

IMAGE -11.7 -8.4 -6.9 -4.6 -2.2 -1.3 0.7 4.1 7.4 17.4

MERGE optimistic -10.6 -7.1 -5.6 -3.6 -1.3 -0.3 1.6 5.4 9.1 19.0

Message -12.2 -8.9 -7.3 -4.9 -2.5 -1.9 0.3 3.5 6.5 15.6

MiniCAM base -10.4 -7.2 -5.8 -3.8 -1.5 -0.6 1.3 4.8 8.2 18.0

5th scenario -10.9 -8.3 -7 -5 -2.9 -2.7 -0.8 1.4 3.2 9.2

Figure 16-A.9.9 Histogram of Global SCC Estimates in 2010 

(2007$/ton CO2), by discount rate 

* The distribution of SCC values ranges from -$5,192 to $66,116, but the X-axis has been 

truncated at approximately the 1st and 99th percentiles to better show the data.

0

2000

4000

6000

8000

10000

12000

14000

16000

-25-12

1

14274053667992

105118131144157170183196209222235248261274

All 2010, 5.0% All 2010, 3.0% All 2010, 2.5%
16-A-57

Table 16-A.9.5 Additional Summary Statistics of 2010 Global SCC Estimates 

Discount 

Rate Scenario

DICE PAGE FUND

5% 

Mean 9 6.5 -1.3 

Variance 13.1 136 70.1 

Skewness 0.8 6.3 28.2 

Kurtosis 0.2 72.4 1,479.00 

3% 

Mean 28.3 29.8 6 

Variance 209.8 3,383.70 16,382.50 

Skewness 1.1 8.6 128 

Kurtosis 0.9 151 18,976.50 

2.50% 

Mean 42.2 49.3 13.6 

Variance 534.9 9,546.00 ####### 

Skewness 1.2 8.7 149 

Kurtosis 1.1 143.8 23,558.30