APPENDIX 14-B. TECHNICAL UPDATE OF SOCIAL COST OF CARBON FOR 

REGULATORY IMPACT ANALYSIS UNDER EXECUTIVE ORDER 12866

TABLE OF CONTENTS

14-B.1 PREFACE............................................................................................................ 14-B-2

14-B.2 PURPOSE............................................................................................................ 14-B-2

14-B.3 SUMMARY OF MODEL UPDATES................................................................. 14-B-3

14-B.3.1 DICE .................................................................................................................... 14-B-3

14-B.3.1.1 Carbon Cycle Parameters.............................................................. 14-B-3

14-B.3.1.2 Sea Level Dynamics...................................................................... 14-B-4

14-B.3.1.3 Re-calibrated Damage Function.................................................... 14-B-5

14-B.3.2 FUND................................................................................................................... 14-B-5

14-B.3.2.1 Space Heating................................................................................ 14-B-6

14-B.3.2.2 Sea Level Rise and Land Loss ...................................................... 14-B-6

14-B.3.2.3 Agriculture..................................................................................... 14-B-6

14-B.3.2.4 Temperature Response Model....................................................... 14-B-7

14-B.3.2.5 Methane ......................................................................................... 14-B-7

14-B.3.3 PAGE................................................................................................................... 14-B-7

14-B.3.3.1 Sea Level Rise ............................................................................... 14-B-8

14-B.3.3.2 Revised Damage Function to Account for Saturation................... 14-B-8

14-B.3.3.3 Regional Scaling Factors............................................................... 14-B-8

14-B.3.3.4 Probability of a Discontinuity ....................................................... 14-B-8

14-B.3.3.5 Adaptation ..................................................................................... 14-B-9

14-B.3.3.6 Other Noteworthy Changes........................................................... 14-B-9

14-B.4 REVISED SCC ESTIMATES ........................................................................... 14-B-10

14-B.5 OTHER MODEL LIMITATIONS OR RESEARCH GAPS ............................ 14-B-12

LIST OF TABLES

Table 14-B.4.1 Revised Social Cost of CO2, 2010 – 2050 (in 2007 dollars per ton of 

CO2) ....................................................................................................... 14-B-11

Table 14-B.4.2 Average Annual Growth Rates of SCC Estimates between 2010 and 

2050........................................................................................................ 14-B-12

Table 14-B.5.1 Annual SCC Values: 2010-2050 (2007$/ton CO2)................................ 14-B-15

Table 14-B.5.2 202 Global SCC Estimates at 2.5 Percent Discount Rate (2007$/ton 

CO2) ....................................................................................................... 14-B-16

Table 14-B.5.3 SCC Estimates at 3 Percent Discount Rate (2007$/ton CO2) ............... 14-B-16

Table 14-B.5.4 2020 Global SCC Estimates at 5 Percent Discount Rate (2007$/ton 

CO2) ....................................................................................................... 14-B-17

LIST OF FIGURES

Figure 14-B.4.2 Distribution of SCC Estimates for 2020 (in 2007$ per ton CO2) .......... 14-B-11

14-B-i
APPENDIX 14-B. TECHNICAL UPDATE OF SOCIAL COST OF CARBON FOR 

REGULATORY IMPACT ANALYSIS UNDER EXECUTIVE ORDER 12866

14-B.1 PREFACE

The following text is reproduced almost verbatim from the May 2013 report of the 

Interagency Working Group on the Social Cost of Carbon of the United States Government. 

Minor changes were made to the working group's report to make it more consistent with the rest 

of this technical support document.

14-B.2 PURPOSE

The purpose of this document is to update the schedule of social cost of carbon (SCC) a

estimates from the 2010 interagency technical support document (TSD) (Interagency Working 

Group on Social Cost of Carbon 2010).1 E.O. 13563 commits the Administration to regulatory 

decision making “based on the best available science.”b Additionally, the interagency group 

recommended in 2010 that the SCC estimates be revisited on a regular basis or as model updates 

that reflect the growing body of scientific and economic knowledge become available.c

 New 

versions of the three integrated assessment models used by the U.S. government to estimate the 

SCC (DICE, FUND, and PAGE), are now available and have been published in the peer 

reviewed literature. While acknowledging the continued limitations of the approach taken by the 

interagency group in 2010 (documented in the original 2010 TSD), this document provides an 

update of the SCC estimates based solely on the latest peer-reviewed version of the models, 

replacing model versions that were developed up to ten years ago in a rapidly evolving field. It 

does not revisit other assumptions with regard to the discount rate, reference case socioeconomic 

and emission scenarios, or equilibrium climate sensitivity. Improvements in the way damages are 

modeled are confined to those that have been incorporated into the latest versions of the models 

by the developers themselves in the peer-reviewed literature. The Environmental Protection 

Agency (EPA), in collaboration with other Federal agencies such as the Department of Energy 

(DOE), continues to investigate potential improvements to the way in which economic damages 

associated with changes in CO2 emissions are quantified. 

Section 14-B.3 summarizes the major updates relevant to SCC estimation that are 

contained in the new versions of the integrated assessment models released since the 2010 

interagency report. Section 14-B.4 presents the updated schedule of SCC estimates for 2010 –

2050 based on these versions of the models.

a

 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. b http://www.whitehouse.gov/sites/default/files/omb/inforeg/eo12866/eo13563_01182011.pdf

c See p. 1, 3, 4, 29, and 33 (Interagency Working Group on Social Cost of Carbon 2010).1

14-B-2

 
14-B.3 SUMMARY OF MODEL UPDATES

This section briefly summarizes changes integrated into the most recent versions of the 

three integrated assessment models (IAMs) used by the interagency group in 2010. We focus on 

describing those model updates that are relevant to estimating the social cost of carbon. For 

example, both the DICE and PAGE models now include an explicit representation of sea level 

rise damages. Other revisions to PAGE include: updated adaptation assumptions, revisions to 

ensure damages are constrained GDP, updated regional scaling of damages, and a revised 

treatment of potentially abrupt shifts in climate damages. In the most recent version of DICE, 

the model’s simple carbon cycle has been updated to be more consistent with a relatively more 

complex climate model. The FUND model includes updated damage functions for sea level rise 

impacts, the agricultural sector, and reduced space heating requirements, as well as changes to 

the response of temperature to the buildup of GHG concentrations and the inclusion of indirect 

effects of methane emissions. Changes made to parts of the models that are superseded by the 

interagency working group’s modeling assumptions – regarding climate sensitivity, discounting, 

and socioeconomic variables – are not discussed.

14-B.3.1 DICE

Changes in the DICE model relevant for the SCC estimates developed by the interagency 

working group include: 1) updated parameter values for the carbon cycle model, 2) an explicit 

representation of sea level dynamics, and 3) a re-calibrated damage function that includes an 

explicit representation of economic damages from sea level rise. Changes were also made to 

other parts of the DICE model—including the equilibrium climate sensitivity parameter, the rate 

of change of total factor productivity, and the elasticity of the marginal utility of consumption—

but these components of DICE are superseded by the interagency working group’s assumptions 

and so will not be discussed here. More details on DICE2007 can be found in Nordhaus (2008)2

and on DICE2010 in Nordhaus (2010)3 and the associated on-line appendix containing 

supplemental information.

14-B.3.1.1 Carbon Cycle Parameters

DICE uses a three-box model of carbon stocks and flows to represent the accumulation 

and transfer of carbon among the atmosphere, the shallow ocean and terrestrial biosphere, and 

the deep ocean. These parameters are “calibrated to match the carbon cycle in the Model for the 

Assessment of Greenhouse Gas Induced Climate Change (MAGICC)” (Nordhaus 2008 p 44).2d

Carbon cycle transfer coefficient values in DICE2010 are based on re-calibration of the model to 

match the newer version of MAGICC (Nordhaus 2010 p 2).3 For example, in DICE2010 in each 

decade, 12 percent of the carbon in the atmosphere is transferred to the shallow ocean, 4.7 

percent of the carbon in the shallow ocean is transferred to the atmosphere, 94.8 percent remains 

in the shallow ocean, and 0.5 percent is transferred to the deep ocean. For comparison, in DICE 

2007, 18.9 percent of the carbon in the atmosphere is transferred to the shallow ocean each 

d MAGICC is a simple climate model initially developed within the U.S. National Center for Atmospheric Research 

that has been used heavily by the Intergovernmental Panel on Climate Change (IPCC) to emulate projections from 

much more sophisticated state of the art earth system simulation models (Randall et al. 2007).

4

14-B-3

 
decade, 9.7 percent of the carbon in the shallow ocean is transferred to the atmosphere, 85.3 

percent remains in the shallow ocean, and 5 percent is transferred to the deep ocean.

The implication of these changes for DICE2010 is in general a weakening of the ocean as 

a carbon sink and therefore a higher concentration of carbon in the atmosphere than in 

DICE2007, for a given path of emissions. All else equal, these changes will generally increase 

the level of warming and therefore the SCC estimates in DICE2010 relative to those from 

DICE2007.

14-B.3.1.2 Sea Level Dynamics

A new feature of DICE2010 is an explicit representation of the dynamics of the global 

average sea level anomaly to be used in the updated damage function (discussed below). This 

section contains a brief description of the sea level rise (SLR) module; a more detailed 

description can be found on the model developer’s website.e The average global sea level 

anomaly is modeled as the sum of four terms that represent contributions from: 1) thermal 

expansion of the oceans, 2) melting of glaciers and small ice caps, 3) melting of the Greenland 

ice sheet, and 4) melting of the Antarctic ice sheet. 

The parameters of the four components of the SLR module are calibrated to match 

consensus results from the IPCC’s Fourth Assessment Report.4,f The rise in sea level from 

thermal expansion in each time period (decade) is 2 percent of the difference between the sea 

level in the previous period and the long run equilibrium sea level, which is 0.5 meters per 

degree Celsius (°C) above the average global temperature in 1900. The rise in sea level from the 

melting of glaciers and small ice caps occurs at a rate of 0.008 meters per decade per °C above 

the average global temperature in 1900.

The contribution to sea level rise from melting of the Greenland ice sheet is more 

complex. The equilibrium contribution to SLR is 0 meters for temperature anomalies less than 1

o

C and increases linearly from 0 meters to a maximum of 7.3 meters. The contribution to SLR in 

each period is proportional to the difference between the previous period’s sea level anomaly and 

the equilibrium sea level anomaly, where the constant of proportionality increases with the 

temperature anomaly in the current period.

The contribution to SLR from the melting of the Antarctic ice sheet is -0.001 meters per 

decade when the temperature anomaly is below 3 °C and increases linearly to a maximum rate of 

0.025 meters per decade at a temperature anomaly of 6 °C.

e Documentation on the new sea level rise module of DICE is available on William Nordhaus’ website at: 

http://www.econ.yale.edu/~nordhaus/homepage/documents/SLR_021910.pdf. f For a review of post-IPCC AR4 research on sea level rise, see Nicholls et al. (2011)

5 and NAS (2011).6

14-B-4

 
14-B.3.1.3 Re-calibrated Damage Function

Economic damages from climate change in the DICE model are represented by a 

fractional loss of gross economic output in each period. A portion of the remaining economic

output in each period (net of climate change damages) is consumed and the remainder is invested 

in the physical capital stock to support future production, so each period’s climate damages will 

reduce consumption in that period and in all future periods due to the lost investment. The 

fraction of output in each period that is lost due to climate change impacts is represented as one 

minus a fraction, which is one divided by a quadratic function of the temperature anomaly, 

producing a sigmoid (“S”-shaped) function. The loss function in DICE2010 has been expanded 

by adding a quadratic function of SLR to the quadratic function of temperature. In DICE2010 the 

temperature anomaly coefficients have been recalibrated to avoid double-counting damages from 

sea level rise that were implicitly included in these parameters in DICE2007. 

The aggregate damages in DICE2010 are illustrated by Nordhaus (2010 p 3),3 who notes 

that “...damages in the uncontrolled (baseline) (i.e., reference) case ... in 2095 are $12 trillion, 

or 2.8 percent of global output, for a global temperature increase of 3.4 o

C above 1900 levels.” 

This compares to a loss of 3.2 percent of global output at 3.4 oC in DICE2007. However, in 

DICE2010 (as downloaded from the homepage of William Nordhaus), annual damages are lower 

in most of the early periods but higher in later periods of the time horizon than would be 

calculated using the DICE2007 damage function. Specifically, the percent difference between 

damages in the base run of DICE2010 and those that would be calculated using the DICE2007 

damage function starts at +7 percent in 2005, decreases to a low of -14 percent in 2065, then 

continuously increases to +20 percent by 2300 (the end of the interagency analysis time horizon), 

and to +160 percent by the end of the model time horizon in 2595. The large increases in the far 

future years of the time horizon are due to the permanence associated with damages from sea 

level rise, along with the assumption that the sea level is projected to continue to rise long after 

the global average temperature begins to decrease. The changes to the loss function generally 

decrease the interagency working group SCC estimates slightly, all else equal.

14-B.3.2 FUND

FUND version 3.8 includes a number of changes over the previous version 3.5 used in 

the interagency report. Documentation supporting FUND and the model’s source code for all 

versions of the model is available from the model authors.g Notable changes, due to their impact 

on the estimates of expected SCC, are adjustments to the space heating, agriculture, and sea level 

rise damage functions in addition to changes to the temperature response function and the 

inclusion of indirect effects from methane emissions.h We discuss each of these in turn.

g http://www.fund-model.org/. This report uses version 3.8 of the FUND model, which represents a modest update 

to the most recent version of the model to appear in the literature (version 3.7) (Anthoff and Tol, 2013).7 For the 

purpose of computing the SCC, the relevant changes are associated with improving consistency with IPCC AR4 by 

adjusting the atmospheric lifetimes of CH4 and N2O and incorporating the indirect forcing effects of CH4, along 

with making minor stability improvements in the sea wall construction algorithm.

h The other damage sectors (water resources, space cooling, land loss, migration, ecosystems, human health, and 

extreme weather) were not the subject of significant updates.

14-B-5

 
14-B.3.2.1 Space Heating

In FUND, the damages associated with the change in energy needs for space heating are 

based on the estimated impact due to one degree of warming. These baseline damages are scaled 

based on the forecasted temperature anomaly’s deviation from the one degree benchmark and 

adjusted for changes in vulnerability due to economic and energy efficiency growth. In FUND 

3.5, the function that scales the base year damages adjusted for vulnerability allows for the 

possibility that in some simulations the benefits associated with reduced heating needs may be an 

unbounded convex function of the temperature anomaly. In FUND 3.8, the form of the scaling 

has been modified to ensure that the function is everywhere concave, meaning that for every 

simulation there will exist an upper bound on the benefits a region may receive from reduced 

space heating needs. The new formulation approaches a value of two in the limit as the 

temperature anomaly increases, or in other words, assuming no decrease in vulnerability, the 

reduced expenditures on space heating at any level of warming will not exceed two times the 

reductions experienced at one degree of warming. Since the reduced need for space heating 

represents a benefit of climate change in the model, or a negative damage, this change will 

increase the estimated SCC. This update accounts for a significant portion of the difference in the 

expected SCC estimates reported by the two versions of the model when run probabilistically.

14-B.3.2.2 Sea Level Rise and Land Loss

The FUND model explicitly includes damages associated with the inundation of dry land 

due to sea level rise. The amount of land lost within a region is dependent upon the proportion of 

the coastline being protected by adequate sea walls and the amount of sea level rise. In FUND 

3.5 the function defining the potential land lost in a given year due to sea level rise is linear in 

the rate of sea level rise for that year. This assumption implicitly assumes that all regions are 

well represented by a homogeneous coastline in length and a constant uniform slope moving 

inland. In FUND 3.8 the function defining the potential land lost has been changed to be a nonlinear function of sea level rise, thereby assuming that the slope of the shore line is not constant 

moving inland, with a positive first derivative. The effect of this change is to typically reduce the 

vulnerability of some regions to sea level rise based land loss, therefore having an effect of 

lowering the expected SCC estimate. The model has also been updated to assume that the value 

of dry land at risk of inundation is not uniform across a region but will be a decreasing function 

of protection measure, thereby implicitly assuming that the most valuable land will be protected 

first.

14-B.3.2.3 Agriculture

In FUND, the damages associated with the agricultural sector are measured as 

proportional to the sector’s value. The fraction is made up of three additively separable 

components that represent the effects from carbon fertilization, the rate of temperature change, 

and the level of the temperature anomaly. In both FUND 3.5 and FUND 3.8, the fraction of the 

sector’s value lost due to the level of the temperature anomaly is modeled as a quadratic function 

with an intercept of zero. In FUND 3.5, the linear and quadratic coefficients are modeled as the 

ratio of two normal distributions. Within this specification, as draws from the distribution in the 

14-B-6
denominator approached zero the share of the sector’s value “lost” approaches (+/-) infinity 

independent of the temperature anomaly itself. In FUND 3.8, the linear and quadratic 

coefficients are drawn directly from truncated normal distributions so that they remain in the 

range [0,∞) and (−∞,0], respectively, where the means for the new distributions are set equal to 

the ratio of the means from the normal distributions used in the previous version. In general the 

impact of this change has been to increase the likelihood that increases in the temperature level 

will have either larger positive or negative effects on the agricultural sector relative to the 

previous version (through eliminating simulations in which the “lost” value approached (+/-) 

infinity). The net effect of this change on the SCC estimates is difficult to predict. 

14-B.3.2.4 Temperature Response Model

The temperature response model translates changes in global levels of radiative forcing 

into the current expected temperature anomaly. In FUND, a given year’s increase in the 

cumulative temperature anomaly is based on a mean reverting function where the mean equals 

the equilibrium temperature anomaly that would eventually be reached if that year’s level of 

radiative forcing were sustained. The rate of mean reversion defines the rate at which the 

transient temperature approaches the equilibrium. In FUND 3.5, the rate of temperature response 

is defined as a decreasing linear function of equilibrium climate sensitivity to capture the fact 

that the progressive heat uptake of the deep ocean causes the rate to slow at higher values of the 

equilibrium climate sensitivity. In FUND 3.8, the rate of temperature response has been updated 

to a quadratic function of the equilibrium climate sensitivity. This change reduces the sensitivity 

of the rate of temperature response to the level of the equilibrium climate sensitivity. Therefore 

in FUND 3.8, the temperature response will typically be faster than in the previous version. The 

overall effect of this change is likely to increase estimates of the SCC as higher temperatures are 

reached during the timeframe analyzed and as the same damages experienced in the previous 

version of the model are now experienced earlier and therefore discounted less.

14-B.3.2.5 Methane

The IPCC notes a series of indirect effects of methane emissions, and has developed 

methods for proxying such effects when computing the global warming potential of methane 

(Forster et al. 2007).8 FUND 3.8 now includes the same methods for incorporating the indirect 

effects of methane emissions. Specifically, the average atmospheric lifetime of methane has been 

set to 12 years to account for the feedback of CH4 emissions on its own lifetime. The radiative 

forcing associated with atmospheric methane has also been increase by 40% to account for its net 

impact on ozone production and increase in stratospheric water vapor. The general effect of this 

increased radiative forcing will be to increase the estimated SCC values, where the degree to 

which this occurs will be dependent upon the relative curvature of the damage functions with 

respect to the temperature anomaly.

14-B.3.3 PAGE

PAGE09 (Hope 2012)9 includes a number of changes from PAGE2002, the version used 

in the 2009 SCC interagency report. The changes that most directly affect the SCC estimates 

14-B-7
include: explicitly modeling the impacts from sea level rise, revisions to the damage function to 

ensure damages are constrained by GDP, a change in the regional scaling of damages, a revised 

treatment for the probability of a discontinuity within the damage function, and revised 

assumptions on adaptation. The model also includes revisions to the carbon cycle feedback and 

the calculation of regional temperatures. More details on PAGE2009 can be found in three 

working papers (Hope 2011a, 2011b, 2011c).10, 11, 12 A description of PAGE2002 can be found 

in Hope (2006).13

14-B.3.3.1 Sea Level Rise

While PAGE2002 aggregates all damages into two categories – economic and noneconomic impacts - PAGE2009 adds a third explicit category: damages from sea level rise. In the 

previous version of the model, damages from sea level rise were subsumed by the other damage 

categories. PAGE09 models damages from sea level rise as increasing less than linearly with sea 

level based on the assumption that low-lying shoreline areas will be associated with higher 

damages than current inland areas. Damages from the economic and non-economic sector were 

adjusted to account for the introduction of this new category. 

14-B.3.3.2 Revised Damage Function to Account for Saturation

In PAGE09, small initial economic and non-economic benefits (negative damages) are 

modeled for small temperature increases, but all regions eventually experience positive economic 

damages from climate change, where damages are the sum of additively separable polynomial 

functions of temperature and sea level rise. Damages transition from this polynomial function to 

a logistic path once they exceed a certain proportion of remaining Gross Domestic Product 

(GDP) to ensure that damages do not exceed 100 percent of GDP. This differs from PAGE2002, 

which allowed Eastern Europe to potentially experience large benefits from temperature 

increases, and which also did not bound the possible damages that could be experienced.

14-B.3.3.3 Regional Scaling Factors

As in the previous version of PAGE, the PAGE09 model calculates the damages for the 

European Union (EU) and then, assumes that damages for other regions are proportional based 

on a given scaling factor. The scaling factor in PAGE09 is based on the length of a region’s 

coastline relative to the EU (Hope 2011b).11 Because of the long coastline in the EU, other 

regions are, on average, less vulnerable than the EU for the same sea level and temperature 

increase, but all regions have a positive scaling factor. PAGE2002 based its scaling factors on 

four studies reported in the IPCC’s third assessment report, and allowed for benefits from 

temperature increase in Eastern Europe, smaller impacts in developing countries, and higher 

damages in developing countries. 

14-B.3.3.4 Probability of a Discontinuity

In PAGE2002, the damages associated with a “discontinuity” were modeled as an 

expected value. That is, additional damages from an extreme event, such as extreme melting of 

14-B-8
the Greenland ice sheet, were multiplied by the probability of the event occurring and added to 

the damage estimate. In PAGE09, the probability of “discontinuity” is treated as a discrete event 

for each year in the model. The damages for each model run are estimated with or without a 

discontinuity occurring, rather than as an expected value. A large‐scale discontinuity becomes 

possible when the temperature rises beyond some threshold value between 2 and 4°C. The 

probability that a discontinuity will occur beyond this threshold then increases by between 10 

and 30 percent for every 1°C rise in temperature beyond the threshold. If a discontinuity occurs, 

the EU loses an additional 5 to 25 percent of its GDP (drawn from a triangular distribution with a 

mean of 15 percent) in addition to other damages, and other regions lose an amount determined 

by the regional scaling factor. The threshold value for a possible discontinuity is lower than in 

PAGE2002, while the rate at which the probability of a discontinuity increases with the 

temperature anomaly and the damages that result from a discontinuity are both higher than in 

PAGE2002. The model assumes that only one discontinuity can occur and that the impact is 

phased in over a period of time, but once it occurs, its effect is permanent.

14-B.3.3.5 Adaptation

As in PAGE2002, adaptation is available to increase the tolerable level of temperature 

change and can help mitigate any climate change impacts that still occur. In PAGE this 

adaptation is the same regardless of the temperature change or sea level rise and is therefore akin 

to what is more commonly considered a reduction in vulnerability. It is modeled by modifying 

the temperature change and sea level rise used in the damage function or by reducing the 

damages by some percentage. PAGE09 assumes a smaller decrease in vulnerability than the 

previous version of the model and assumes that it will take longer for this change in vulnerability 

to be realized. In the aggregated economic sector, at the time of full implementation, this 

adaptation will mitigate all damages up to a temperature increase of 1°C, and for temperature 

anomalies between 1°C and 3°C, it will reduce damages by 15-30 percent (depending on the 

region). However, it takes 20 years to fully implement this adaptation. In PAGE2002, adaptation 

was assumed to reduce economic sector damages up to 3°C by 50-90 percent after 20 years. 

Beyond 3°C, no adaptation is assumed to be available to mitigate the impacts of climate change. 

For the non-economic sector, in PAGE09 adaptation is available to reduce 15 percent of the 

damages due to a temperature increase between 0°C and 2°C and is assumed to take 40 years to 

fully implement, instead of 25 percent of the damages over 20 years assumed in PAGE2002. 

Similarly, adaptation is assumed to alleviate 25-50 percent of the damages from the first 0.20 to 

0.25 meters of sea level rise but is assumed to be ineffective thereafter. Hope (2011c)12 estimates 

that the less optimistic assumptions regarding the ability to offset impacts of temperature and sea 

level rise via adaptation increase the SCC by approximately 30 percent.

14-B.3.3.6 Other Noteworthy Changes

Two other changes in the model are worth noting. A revised carbon cycle feedback is 

introduced to simulate decreased CO2 absorption by the terrestrial biosphere and ocean as the 

temperature rises. This feedback is linear in the average global and annual temperature anomaly 

but is capped at a maximum value. In the previous version of PAGE, an additional amount was 

added to the CO2 emissions each period to account for a decrease in ocean absorption and a loss 

14-B-9
of soil carbon. Also updated is the method by which the average global and annual temperature 

anomaly is downscaled to determine annual average regional temperature anomalies to be used 

in the regional damage functions. In the previous version of PAGE, the scaling was determined 

solely based on regional difference in emissions of sulfate aerosols. In PAGE09, this regional 

temperature anomaly is further adjusted using an additive factor that is based on the average 

absolute latitude of a region relative to the area weighted average absolute latitude of the Earth’s 

landmass.

14-B.4 REVISED SCC ESTIMATES

The updated versions of the three integrated assessment models were run using the same 

methodology detailed in the 2010 TSD.1 The approach along with the inputs for the 

socioeconomic emissions scenarios, equilibrium climate sensitivity distribution, and discount 

rate remains the same. This includes the five reference scenarios based on the EMF-22 modeling 

exercise, the Roe and Baker equilibrium climate sensitivity distribution calibrated to the Fourth 

Assessment Report of the IPCC, and three constant discount rates of 2.5, 3, and 5 percent.

As was previously the case, the use of three models, three discount rates, and five 

scenarios produces 45 separate distributions for the SCC. The approach laid out in the TSD 

applied equal weight to each model and socioeconomic scenario in order to reduce the 

dimensionality down to three separate distributions representative of the three discount rates. The 

interagency group selected four values from these distributions for use in regulatory analysis. 

Three values are based on the average SCC across models and socio-economic-emissions 

scenarios at the 2.5, 3, and 5 percent discount rates, respectively. The fourth value was chosen to 

represent the higher-than-expected economic impacts from climate change further out in the tails 

of the SCC distribution. For this purpose, the 95th percentile of the SCC estimates at a 3 percent 

discount rate was chosen. (A detailed set of percentiles by model and scenario combination is 

available in the Annex.) As noted in the original TSD, “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” (TSD, p. 25). However, for purposes of capturing the uncertainties involved in 

regulatory impact analysis, the interagency group emphasizes the importance and value of 

including all four SCC values.

Table 14-B.4.1 shows the four selected SCC estimates in five year increments from 2010 

to 2050. Values for 2010, 2020, 2030, 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 basic linear interpolation. The full set of 

annual SCC estimates between 2010 and 2050 is reported in the Annex.

14-B-10
Table 14-B.4.1 Revised Social Cost of CO2, 2010 – 2050 (in 2007 dollars per ton of CO2)

Discount Rate 5.0% 3.0% 2.5% 3.0%

Year Avg Avg Avg 95th

2010 11 33 52 90

2015 12 38 58 109

2020 12 43 65 129

2025 14 48 70 144

2030 16 52 76 159

2035 19 57 81 176

2040 21 62 87 192

2045 24 66 92 206

2050 27 71 98 221

The SCC estimates using the updated versions of the models are higher than those 

reported in the TSD due to the changes to the models outlined in the previous section. Figure 14-

B.4.2 illustrates where the four SCC values for 2020 fall within the full distribution for each 

discount rate based on the combined set of runs for each model and scenario (150,000 estimates 

in total for each discount rate). In general, the distributions are skewed to the right and have long 

tails. The Figure also shows that the lower the discount rate, the longer the right tail of the 

distribution.

Figure 14-B.4.2 Distribution of SCC Estimates for 2020 (in 2007$ per ton CO2)

As was the case in the original TSD, 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. The approach taken by the 

interagency group is to allow the growth rate to be determined endogenously by the models 

14-B-11
through running them for a set of perturbation years out to 2050. Table 14-B.4.2 illustrates how

the growth rate for these four SCC estimates varies over time.

Table 14-B.4.2 Average Annual Growth Rates of SCC Estimates between 2010 and 2050

Average Annual 5.0% 3.0% 2.5% 3.0%

Rate (%) Avg Avg Avg 95th

2010-2020 1.2% 3.2% 2.4% 4.3%

2020-2030 3.4% 2.1% 1.7% 2.4%

2030-2040 3.0% 1.8% 1.5% 2.0%

2040-2050 2.6% 1.6% 1.3% 1.5%

The future monetized value of emission 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. As previously discussed in the original 

TSD, 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.

14-B.5 OTHER MODEL LIMITATIONS OR RESEARCH GAPS

The 2010 interagency SCC technical support report discusses a number of important 

limitations for which additional research is needed. In particular, the document highlights the 

need to improve the quantification of both non-catastrophic and catastrophic damages, the 

treatment of adaptation and technological change, and the way in which inter-regional and intersectoral linkages are modeled. It also discusses the need to more carefully assess the implications 

of risk aversion for SCC estimation as well as the inability to perfectly substitute between 

climate and non-climate goods at higher temperature increases, both of which have implications 

for the discount rate used. EPA, DOE, and other agencies continue to engage in long-term 

research work on modeling and valuation of climate impacts that we expect will inform 

improvements in SCC estimation in the future.

14-B-12
REFERENCES

1. Interagency Working Group on Social Cost of Carbon, Social Cost of Carbon for 

Regulatory Impact Analysis under Executive Order 12866, February, 2010. United States 

Government. <http://www.whitehouse.gov/sites/default/files/omb/inforeg/foragencies/Social-Cost-of-Carbon-for-RIA.pdf>

2. Nordhaus, W., A Question of Balance. 2008. Yale University Press: New Haver.

3. Nordhaus, W., Economic aspects of global warming in a post-Copenhagen environment.

Proceedings of the National Academy of Sciences, 2010. 107(26): pp. 11721-11726 

4. Randall, D. A., R.A. Wood, S. Bony, R. Colman, T. Fichefet, J. Fyfe, V. Kattsov, A. 

Pitman, J. Shukla, J. Srinivasan, R.J. Stouffer, A. Sumi and K.E. Taylor, Climate Models 

and Their Evaluation. In Climate Change 2007: The Physical Science Basis. 

Contribution of Working Group I to the Fourth Assessment Report of the 

Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, 

M. Marquis, K.B. Averyt, M.Tignor and H.L. Miller, Editor. 2007. Cambridge University 

Press: Cambridge, United Kingdom and New York, NY, USA

5. Nicholls, R. J., N. Marinova, J.A. Lowe, S. Brown, P. Vellinga, D. de Gusmão, J. Hinkel 

and R.S.J. Tol, Sea-level rise and its possible impacts given a ‘beyond 4°C world’ in the 

twenty-first century. Phil. Trans. R. Soc. A 2011. 369(1934): pp. 161-181 

6. National Academy of Sciences, Climate Stabilization Targets: Emissions, 

Concentrations, and Impacts over Decades to Millennia. 2011. National Academies 

Press, Inc: Washington, DC.

7. Anthoff, D. and R. S. J. Tol, The uncertainty about the social cost of carbon: a 

decomposition analysis using FUND. Climatic Change, 2013(Forthcoming)

8. Forster, P., V. Ramaswamy, P. Artaxo, T. Berntsen, R. Betts, D.W. Fahey, J. Haywood, 

J. Lean, D.C. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz and R. Van 

Dorland, Changes in Atmospheric Constituents and in Radiative Forcing. In Climate 

Change 2007: The Physical Science Basis. Contribution of Working Group I to the 

Fourth Assessment Report of the Intergovernmental Panel on Climate Change S. 

Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M.Tignor and H.L. 

Miller Editor. 2007. Cambridge University Press: Cambridge, United Kingdom and New 

York, NY, USA

9. Hope, C., Critical issues for the calculation of the social cost of CO2: why the estimates 

from PAGE09 are higher than those from PAGE2002. Climatic Change, 

2012(Forthcoming)

14-B-13
10. Hope, C., The PAGE09 Integrated Assessment Model: A Technical Description. 2011, 

Cambridge Judge Business School 

http://www.jbs.cam.ac.uk/research/working_papers/2011/wp1104.pdf

11. Hope, C., The Social Cost of CO2 from the PAGE09 Model. 2011, Cambridge Judge 

Business School http://www.jbs.cam.ac.uk/research/working_papers/2011/wp1105.pdf

12. Hope, C., New Insights from the PAGE09 Model: The Social Cost of CO2. 2011, 

Cambridge Judge Business School 

http://www.jbs.cam.ac.uk/research/working_papers/2011/wp1108.pdf

13. Hope, C., The Marginal Impact of CO2 from PAGE2002: An Integrated Assessment 

Model Incorporating the IPCC’s Five Reasons for Concern. The Integrated Assessment 

Journal, 2006. 6(1): pp. 19-56 

14-B-14
ANNEX

Table 14-B.5.1 Annual SCC Values: 2010-2050 (2007$/ton CO2)

Discount Rate 5.0% 3.0% 2.5% 3.0%

Year Avg Avg Avg 95th

2010 11 33 52 90

2011 11 34 54 94

2012 11 35 55 98

2013 11 36 56 102

2014 11 37 57 106

2015 12 38 58 109

2016 12 39 60 113

2017 12 40 61 117

2018 12 41 62 121

2019 12 42 63 125

2020 12 43 65 129

2021 13 44 66 132

2022 13 45 67 135

2023 13 46 68 138

2024 14 47 69 141

2025 14 48 70 144

2026 15 49 71 147

2027 15 49 72 150

2028 15 50 73 153

2029 16 51 74 156

2030 16 52 76 159

2031 17 53 77 163

2032 17 54 78 166

2033 18 55 79 169

2034 18 56 80 172

2035 19 57 81 176

2036 19 58 82 179

2037 20 59 84 182

2038 20 60 85 185

2039 21 61 86 188

2040 21 62 87 192

2041 22 63 88 195

2042 22 64 89 198

2043 23 65 90 200

2044 23 65 91 203

2045 24 66 92 206

2046 24 67 94 209

2047 25 68 95 212

2048 25 69 96 215

2049 26 70 97 218

2050 27 71 98 221

14-B-15
Table 14-B.5.2 202 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 6 11 15 27 58 129 139 327 515 991

MERGE 4 6 9 16 34 78 82 196 317 649

MESSAGE 4 8 11 20 42 108 107 278 483 918

MiniCAM Base 5 9 12 22 47 107 113 266 431 872

5th Scenario 2 4 6 11 25 85 68 200 387 955

Scenario DICE

IMAGE 25 31 37 47 64 72 92 123 139 161

MERGE 14 18 20 26 36 40 50 65 74 85

MESSAGE 20 24 28 37 51 58 71 95 109 221

MiniCAM Base 20 25 29 38 53 61 76 102 117 135

5th Scenario 17 22 25 33 45 52 65 91 106 126

Scenario FUND

IMAGE -17 -1 5 17 34 44 59 90 113 176

MERGE -7 2 7 16 30 35 49 72 91 146

MESSAGE -19 -4 2 12 27 32 46 70 87 135

MiniCAM Base -9 1 8 18 35 45 59 87 108 172

5th Scenario -30 -12 -5 6 19 24 35 57 72 108

Table 14-B.5.3 SCC Estimates at 3 Percent Discount Rate (2007$/ton CO2)

Percentile 1st 5th 10th 25th 50th Avg 75th 90th 95th 99th

Scenario PAGE

IMAGE 4 7 10 18 38 91 95 238 385 727

MERGE 2 4 6 11 23 56 58 142 232 481

MESSAGE 3 5 7 13 29 75 74 197 330 641

MiniCAM Base 3 5 8 14 30 73 75 184 300 623

5th Scenario 1 3 4 7 17 58 48 136 264 660

Scenario DICE

IMAGE 16 21 24 32 43 48 60 79 90 102

MERGE 10 13 15 19 25 28 35 44 50 58

MESSAGE 14 18 20 26 35 40 49 64 73 83

MiniCAM Base 13 17 20 26 35 39 49 65 73 85

5th Scenario 12 15 17 22 30 34 43 58 67 79

Scenario FUND

IMAGE -14 -3 1 9 20 25 35 54 69 111

MERGE -8 -1 3 9 18 22 31 47 60 97

MESSAGE -16 -5 -1 6 16 18 28 43 55 88

MiniCAM Base -9 -1 3 10 21 27 35 53 67 107

5th Scenario -22 -10 -5 2 10 13 20 33 42 63

14-B-16
Table 14-B.5.4 2020 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 1 2 2 5 10 28 27 71 123 244

MERGE 1 1 2 3 7 17 17 45 75 153

MESSAGE 1 1 2 4 9 24 22 60 106 216

MiniCAM Base 1 1 2 3 8 21 21 54 94 190

5th Scenario 0 1 1 2 5 18 14 41 78 208

Scenario DICE

IMAGE 6 8 9 11 14 15 18 22 25 27

MERGE 4 5 6 7 9 10 12 15 16 18

MESSAGE 6 7 8 10 12 13 16 20 22 25

MiniCAM Base 5 6 7 8 11 12 14 18 20 22

5th Scenario 5 6 6 8 10 11 14 17 19 21

Scenario FUND

IMAGE -9 -5 -3 -1 2 3 6 11 15 25

MERGE -6 -3 -2 0 3 4 7 12 16 27

MESSAGE -10 -6 -4 -1 2 2 5 9 13 23

MiniCAM Base -7 -3 -2 0 3 4 7 11 15 26

5th Scenario -11 -7 -5 -2 0 0 3 6 8 14

14-B-17