1
Technical Support Document: -
Technical Update of the Social Cost of Carbon for Regulatory Impact Analysis -
Under Executive Order 12866 -
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
Domestic Policy Council
Environmental Protection Agency
National Economic Council
Office of Management and Budget
Office of Science and Technology Policy
Department of the Treasury
May 2013
Revised November 2013
See Appendix B for Details on Revision
2
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 (CO
2
) emissions into cost-benefit analyses of regulatory actions that impact cumulative global
emissions. 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.
The interagency process that developed the original U.S. government’s SCC estimates is described in the
2010 interagency technical support document (TSD) (Interagency Working Group on Social Cost of
Carbon 2010). Through that process 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 (IAMs), 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.
While acknowledging the continued limitations of the approach taken by the interagency group in 2010,
this document provides an update of the SCC estimates based on new versions of each IAM (DICE, PAGE,
and FUND). It does not revisit other interagency modeling decisions (e.g., 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 SCC estimates using the updated versions of the models are higher than those reported in the 2010
TSD. By way of comparison, the four 2020 SCC estimates reported in the 2010 TSD were $7, $26, $42
and $81 (2007$). The corresponding four updated SCC estimates for 2020 are $12, $43, $64, and $128
(2007$). The model updates that are relevant to the SCC estimates include: an explicit representation of
sea level rise damages in the DICE and PAGE models; updated adaptation assumptions, revisions to
ensure damages are constrained by GDP, updated regional scaling of damages, and a revised treatment
of potentially abrupt shifts in climate damages in the PAGE model; an updated carbon cycle in the DICE
model; and updated damage functions for sea level rise impacts, the agricultural sector, and reduced
space heating requirements, as well as changes to the transient response of temperature to the buildup
of GHG concentrations and the inclusion of indirect effects of methane emissions in the FUND model.
The SCC estimates vary by year, and the following table summarizes the revised SCC estimates from
2010 through 2050.
3
Revised Social Cost of CO
2
, 2010 – 2050 (in 2007 dollars per metric ton of CO
2
)
Discount Rate
5.0%
3.0%
2.5%
3.0%
Year
Avg
Avg
Avg
95th
2010
11
32
51
89
2015
11
37
57
109
2020
12
43
64
128
2025
14
47
69
143
2030
16
52
75
159
2035
19
56
80
175
2040
21
61
86
191
2045
24
66
92
206
2050
26
71
97
220
4
I. Purpose
The purpose of this document is to update the schedule of social cost of carbon (SCC) 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.”
2
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.
3
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 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 agencies participating in the interagency working group
continue to investigate potential improvements to the way in which economic damages associated with
changes in CO
2
emissions are quantified.
Section II 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 III
presents the updated schedule of SCC estimates for 2010 – 2050 based on these versions of the models.
Section IV provides a discussion of other model limitations and research gaps.
II. Summary of Model Updates
This section briefly summarizes changes to 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, as summarized in Table 1. 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 by GDP,
updated regional scaling of damages, and a revised treatment of potentially abrupt shifts in climate
damages. The DICE model’s simple carbon cycle has been updated to be more consistent with a 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 transient
response of temperature to the buildup of GHG concentrations and the inclusion of indirect effects of
1
In this document, we present all values of the SCC as the cost per metric ton of CO
2
emissions. Alternatively, one
could report the SCC as the cost per metric ton of carbon emissions. The multiplier for translating between mass of
CO
2
and the mass of carbon is 3.67 (the molecular weight of CO
2
divided by the molecular weight of carbon =
44/12 = 3.67).
2
http://www.whitehouse.gov/sites/default/files/omb/inforeg/eo12866/eo13563_01182011.pdf
3
See p. 1, 3, 4, 29, and 33 (Interagency Working Group on Social Cost of Carbon 2010).
5
methane emissions. Changes made to parts of the models that are superseded by the interagency
working group’s modeling assumptions – regarding equilibrium climate sensitivity, discounting, and
socioeconomic variables – are not discussed here but can be found in the references provided in each
section below.
Table 1: Summary of Key Model Revisions Relevant to the Interagency SCC
IAM
Version used in
2010 Interagency
Analysis
New
Version
Key changes relevant to interagency SCC
DICE
2007
2010
Updated calibration of the carbon cycle model and
explicit representation of sea level rise (SLR) and
associated damages.
FUND
3.5
(2009)
3.8
(2012)
Updated damage functions for space heating, SLR,
agricultural impacts, changes to transient response of
temperature to buildup of GHG concentrations, and
inclusion of indirect climate effects of methane.
PAGE
2002
2009
Explicit representation of SLR damages, revisions to
damage function to ensure damages do not exceed
100% of GDP, change in regional scaling of damages,
revised treatment of potential abrupt damages, and
updated adaptation assumptions.
A. DICE
DICE 2010 includes a number of changes over the previous 2007 version used in the 2010 interagency
report. The model changes that are 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) and on DICE2010 in Nordhaus (2010). The
DICE2010 model and documentation is also available for download from the homepage of William
Nordhaus.
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
6
Gas Induced Climate Change (MAGICC)” (Nordhaus 2008 p 44).
4
Carbon cycle transfer coefficient values
in DICE2010 are based on re-calibration of the model to match the newer 2009 version of MAGICC
(Nordhaus 2010 p 2). 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 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.
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.
5
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 (AR4).
6
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 for temperature anomalies between 1
o
C and 3.5 °C.
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.
4
MAGICC is a simple climate model initially developed by 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 more
sophisticated state of the art earth system simulation models (Randall et al. 2007).
5
Documentation on the new sea level rise module of DICE is available on William Nordhaus’ website at:
http://nordhaus.econ.yale.edu/documents/SLR_021910.pdf.
6
For a review of post-IPCC AR4 research on sea level rise, see Nicholls et al. (2011) and NAS (2011).
7
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 between 3 °C and 6 °C to a maximum rate
of 0.025 meters per decade at a temperature anomaly of 6
°C.
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 economic 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.
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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), 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
o
C in DICE2007. However, in DICE2010, annual damages are lower in
most of the early periods of the modeling horizon but higher in later periods 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 given that
relative increases in damages in later periods are discounted more heavily, all else equal.
B. FUND
FUND version 3.8 includes a number of changes over the previous version 3.5 (Narita et al. 2010) used in
the 2010 interagency report. Documentation supporting FUND and the model’s source code for all
versions of the model is available from the model authors.
8
Notable changes, due to their impact on the
7
The model and documentation, including formulas, are available on the author’s
webpage at http://www.econ.yale.edu/~nordhaus/homepage/RICEmodels.htm.
8
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, 2013a). For the
purpose of computing the SCC, the relevant changes (between 3.7 to 3.8) are associated with improving
8
SCC estimates, 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.
9
We discuss each of these in turn.
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 and that 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
of large temperature anomalies, 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.
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 convex function of sea level rise, thereby assuming that the slope of the
shore line increases moving inland. The effect of this change is to typically reduce the vulnerability of
some regions to sea level rise based land loss, thereby lowering the expected SCC estimate.
10
Agriculture
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.
9
The other damage sectors (water resources, space cooling, land loss, migration, ecosystems, human health, and
extreme weather) were not significantly updated.
10
For stability purposes this report also uses an update to the model which assumes that regional coastal
protection measures will be built to protect the most valuable land first, such that the marginal benefits of coastal
protection is decreasing in the level of protection following Fankhauser (1995).
9
In FUND, the damages associated with the agricultural sector are measured as proportional to the
sector’s value. The fraction is bounded from above by one and is made up of three additive 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 coefficients of this loss function are modeled as the ratio of two random normal variables. This
specification had the potential for unintended extreme behavior as draws from the parameter in the
denominator approached zero or went negative. In FUND 3.8, the coefficients are drawn directly from
truncated normal distributions so that they remain in the range
[0, )
and
( ,0]
, respectively,
ensuring the correct sign and eliminating the potential for divide by zero errors. 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 decrease the range of the distribution while
spreading out the distributions’ mass over the remaining range relative to the previous version. The net
effect of this change on the SCC estimates is difficult to predict.
Transient Temperature Response
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 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, a relationship first
noted by Hansen et al. (1985) based on the heat uptake of the deep ocean. 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.
Methane
The IPCC AR4 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).
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 methane emissions on its own lifetime. The radiative forcing associated with atmospheric
methane has also been increased by 40% to account for its net impact on ozone production and
stratospheric water vapor. All else equal, the effect of this increased radiative forcing will be to increase
the estimated SCC values, due to greater projected temperature anomaly.
10
C. PAGE
PAGE09 (Hope 2013) includes a number of changes from PAGE2002, the version used in the 2010 SCC
interagency report. The changes that most directly affect the SCC estimates 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.
11
More
details on PAGE09 can be found in Hope (2011a, 2011b, 2011c). A description of PAGE2002 can be found
in Hope (2006).
Sea Level Rise
While PAGE2002 aggregates all damages into two categories – economic and non-economic impacts -,
PAGE09 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. In PAGE09 sea level
damages increase less than linearly with sea level under the assumption that land, people, and GDP are
more concentrated in low-lying shoreline areas. Damages from the economic and non-economic sector
were adjusted to account for the introduction of this new category.
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 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.
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). 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 developed
countries, and higher damages in developing countries.
11
Because several changes in the PAGE model are structural (e.g., the addition of sea level rise and treatment of
discontinuity), it is not possible to assess the direct impact of each change on the SCC in isolation as done for the
other two models above.
11
Probability of a Discontinuity
In PAGE2002, the damages associated with a “discontinuity” (nonlinear extreme event) were modeled
as an expected value. Specifically, a stochastic probability of a discontinuity was multiplied by the
damages associated with a discontinuity to obtain an expected value, and this was added to the
economic and non-economic impacts. That is, additional damages from an extreme event, such as
extreme melting of 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 either 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.
Adaptation
As in PAGE2002, adaptation is available to help mitigate any climate change impacts that 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 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 2°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 2°C by 50-90 percent after 20 years. Beyond 2°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)
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.
Other Noteworthy Changes
12
Two other changes in the model are worth noting. There is a change in the way the model accounts for
decreased CO
2
absorption on land and in the ocean as temperature rises. PAGE09 introduces a linear
feedback from global mean temperature to the percentage gain in the excess concentration of CO
2
,
capped at a maximum level. In PAGE2002, an additional amount was added to the CO
2
emissions each
period to account for a decrease in ocean absorption and a loss 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
PAGE2002, 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, to capture relatively greater changes in temperature forecast to be
experienced at higher latitudes.
III. Revised SCC Estimates
The updated versions of the three integrated assessment models were run using the same methodology
detailed in the 2010 TSD (Interagency Working Group on Social Cost of Carbon 2010). 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 IPCC AR4, 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 global SCC. The approach laid out in the 2010 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 and additional summary statistics for the 2020 values is available in the
Appendix.) As noted in the 2010 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”
(Interagency Working Group on Social Cost of Carbon 2010, 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 2 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
13
model run) from all scenarios and models for a given discount rate. Values for the years in between are
calculated using linear interpolation. The full set of revised annual SCC estimates between 2010 and
2050 is reported in the Appendix.
Table 2: Revised Social Cost of CO
2
, 2010 – 2050 (in 2007 dollars per metric ton of CO
2
)
Discount Rate
5.0%
3.0%
2.5%
3.0%
Year
Avg
Avg
Avg
95th
2010
11
32
51
89
2015
11
37
57
109
2020
12
43
64
128
2025
14
47
69
143
2030
16
52
75
159
2035
19
56
80
175
2040
21
61
86
191
2045
24
66
92
206
2050
26
71
97
220
The SCC estimates using the updated versions of the models are higher than those reported in the 2010
TSD due to the changes to the models outlined in the previous section. By way of comparison, the 2020
SCC estimates reported in the original TSD were $7, $26, $42 and $81 (2007$) (Interagency Working
Group on Social Cost of Carbon 2010). Figure 1 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 1: Distribution of SCC Estimates for 2020 (in 2007$ per metric ton CO
2
)
14
As was the case in the 2010 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 compute the
cost of a marginal ton emitted in the future by running the models for a set of perturbation years out to
2050. Table 3 illustrates how the growth rate for these four SCC estimates varies over time.
Table 3: Average Annual Growth Rates of SCC Estimates between 2010 and 2050
Average Annual Growth
5.0%
3.0%
2.5%
3.0%
Rate (%)
Avg
Avg
Avg
95th
2010-2020
1.2%
3.3%
2.4%
4.4%
2020-2030
3.4%
2.1%
1.7%
2.4%
2030-2040
3.0%
1.9%
1.5%
2.1%
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 2010 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.
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
15
the world even when they are emitted in the 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. For
additional discussion, see the 2010 TSD.
IV. Other Model Limitations and Research Gaps
The 2010 interagency SCC TSD 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 inter-sectoral linkages are modeled. While the new version of the
models discussed above offer some improvements in these areas, further work remains warranted. The
2010 TSD 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 research on modeling and valuation of climate impacts that can
potentially improve SCC estimation in the future.
References
Anthoff, D. and Tol, R.S.J. 2013a. The uncertainty about the social cost of carbon: a decomposition
analysis using FUND. Climatic Change 117: 515–530.
Anthoff, D. and Tol, R.S.J. 2013b. Erratum to: The uncertainty about the social cost of carbon: A
decomposition analysis using FUND. Climatic Change. Advance online publication. doi: 10.1007/s10584-
013-0959-1.
Fankhauser, S. 1995. Valuing climate change: The economics of the greenhouse. London, England:
Earthscan.
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. 2007. 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
[Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M.Tignor and H.L. Miller (eds.)].
Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.
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Hope, Chris. 2006. “The Marginal Impact of CO
2
from PAGE2002: An Integrated Assessment Model
Incorporating the IPCC’s Five Reasons for Concern.” The Integrated Assessment Journal. 6(1): 19–56.
Hope, Chris. 2011a “The PAGE09 Integrated Assessment Model: A Technical Description” Cambridge
Judge Business School Working Paper No. 4/2011 (April). Accessed November 23, 2011:
http://www.jbs.cam.ac.uk/research/working_papers/2011/wp1104.pdf.
Hope, Chris. 2011b “The Social Cost of CO
2
from the PAGE09 Model” Cambridge Judge Business School
Working Paper No. 5/2011 (June). Accessed November 23, 2011:
http://www.jbs.cam.ac.uk/research/working_papers/2011/wp1105.pdf.
Hope, Chris. 2011c “New Insights from the PAGE09 Model: The Social Cost of CO
2
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Business School Working Paper No. 8/2011 (July). Accessed November 23, 2011:
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Hope, C. 2013. Critical issues for the calculation of the social cost of CO
2
: why the estimates from
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Analysis under Executive Order 12866. February. United States Government.
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RIA.pdf.
Meehl, G.A., T.F. Stocker, W.D. Collins, P. Friedlingstein, A.T. Gaye, J.M. Gregory, A. Kitoh, R. Knutti, J.M.
Murphy, A. Noda, S.C.B. Raper, I.G. Watterson, A.J. Weaver and Z.-C. Zhao. 2007. Global Climate
Projections. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the
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Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L. Miller (eds.)]. Cambridge University Press,
Cambridge, United Kingdom and New York, NY, USA.
Narita, D., R. S. J. Tol and D. Anthoff. 2010. Economic costs of extratropical storms under climate change:
an application of FUND. Journal of Environmental Planning and Management 53(3): 371-384.
National Academy of Sciences. 2011. Climate Stabilization Targets: Emissions, Concentrations, and
Impacts over Decades to Millennia. Washington, DC: National Academies Press, Inc.
Nicholls, R.J., N. Marinova, J.A. Lowe, S. Brown, P. Vellinga, D. de Gusmão, J. Hinkel and R.S.J. Tol. 2011.
Sea-level rise and its possible impacts given a ‘beyond 4°C world’ in the twenty-first century. Phil. Trans.
R. Soc. A 369(1934): 161-181.
Nordhaus, W. 2010. Economic aspects of global warming in a post-Copenhagen environment.
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Nordhaus, W. 2008. A Question of Balance: Weighing the Options on Global Warming Policies. New
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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. 2007. Climate Models and Their Evaluation. In: Climate
Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment
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Kingdom and New York, NY, USA.
18
Appendix A
Table A1: Annual SCC Values: 2010-2050 (2007$/metric ton CO
2
)
Discount Rate
5.0%
3.0%
2.5%
3.0%
Year
Avg
Avg
Avg
95th
2010
11
32
51
89
2011
11
33
52
93
2012
11
34
54
97
2013
11
35
55
101
2014
11
36
56
105
2015
11
37
57
109
2016
12
38
59
112
2017
12
39
60
116
2018
12
40
61
120
2019
12
42
62
124
2020
12
43
64
128
2021
12
43
65
131
2022
13
44
66
134
2023
13
45
67
137
2024
14
46
68
140
2025
14
47
69
143
2026
15
48
70
146
2027
15
49
71
149
2028
15
50
72
152
2029
16
51
73
155
2030
16
52
75
159
2031
17
52
76
162
2032
17
53
77
165
2033
18
54
78
168
2034
18
55
79
172
2035
19
56
80
175
2036
19
57
81
178
2037
20
58
83
181
2038
20
59
84
185
2039
21
60
85
188
2040
21
61
86
191
2041
22
62
87
194
2042
22
63
88
197
2043
23
64
89
200
2044
23
65
90
203
2045
24
66
92
206
2046
24
67
93
209
2047
25
68
94
211
2048
25
69
95
214
2049
26
70
96
217
2050
26
71
97
220
19
Table A2: 2020 Global SCC Estimates at 2.5 Percent Discount Rate (2007$/metric ton CO
2
)
Percentile
1st
5th
10th
25th
50th
Avg
75th
90th
95
th
99th
Scenario
12
PAGE
IMAGE
6
11
15
27
58
129
139
327
515
991
MERGE
Optimistic
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
Optimistic
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
-14
-2
4
15
31
39
55
86
107
157
MERGE
Optimistic
-6
1
6
14
27
35
46
70
87
141
MESSAGE
-16
-5
1
11
24
31
43
67
83
126
MiniCAM Base
-7
2
7
16
32
39
55
83
103
158
5th Scenario
-29
-13
-6
4
16
21
32
53
69
103
Table A3: 2020 Global SCC Estimates at 3 Percent Discount Rate (2007$/metric ton CO
2
)
Percentile
1st
5th
10th
25th
50th
Avg
75th
90th
95th
99th
Scenario
PAGE
IMAGE
4
7
10
18
38
91
95
238
385
727
MERGE
Optimistic
2
4
6
11
23
56
58
142
232
481
MESSAGE
3
5
7
13
29
75
74
197
330
641
MiniCAM Base
3
5
8
14
30
73
75
184
300
623
5th Scenario
1
3
4
7
17
58
48
136
264
660
Scenario
DICE
IMAGE
16
21
24
32
43
48
60
79
90
102
MERGE
Optimistic
10
13
15
19
25
28
35
44
50
58
MESSAGE
14
18
20
26
35
40
49
64
73
83
MiniCAM Base
13
17
20
26
35
39
49
65
73
85
5th Scenario
12
15
17
22
30
34
43
58
67
79
Scenario
FUND
IMAGE
-13
-4
0
8
18
23
33
51
65
99
MERGE
Optimistic
-7
-1
2
8
17
21
29
45
57
95
MESSAGE
-14
-6
-2
5
14
18
26
41
52
82
MiniCAM Base
-7
-1
3
9
19
23
33
50
63
101
5th Scenario
-22
-11
-6
1
8
11
18
31
40
62
12
See 2010 TSD for a description of these scenarios.
20
Table A4: 2020 Global SCC Estimates at 5 Percent Discount Rate (2007$/metric ton CO
2
)
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
Optimistic
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
Optimistic
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
-4
-1
2
3
6
10
14
24
MERGE
Optimistic
-6
-4
-2
0
3
4
6
11
15
26
MESSAGE
-10
-6
-4
-1
1
2
5
9
12
21
MiniCAM Base
-7
-4
-2
0
3
4
6
11
14
25
5th Scenario
-11
-7
-5
-3
0
0
3
5
7
13
21
Table A5: Additional Summary Statistics of 2020 Global SCC Estimates
Discount rate:
5.0%
3.0%
2.5%
Statistic:
Mean
Variance
Skewness
Kurtosis
Mean
Variance
Skewness
Kurtosis
Mean
Variance
Skewness
Kurtosis
DICE
12
26
2
15
38
409
3
24
57
1097
3
30
PAGE
22
1616
5
32
71
14953
4
22
101
29312
4
23
FUND
3
41
5
179
19
1452
-42
8727
33
6154
-73
14931
22
Appendix B
The November 2013 revision of this technical support document is based on two corrections to the runs
based on the FUND model. First, the potential dry land loss in the algorithm that estimates regional
coastal protections was misspecified in the model’s computer code. This correction is covered in an
erratum to Anthoff and Tol (2013a) published in the same journal (Climatic Change) in October 2013
(Anthoff and Tol (2013b)). Second, the equilibrium climate sensitivity distribution was inadvertently
specified as a truncated Gamma distribution (the default in FUND) as opposed to the truncated Roe and
Baker distribution as was intended. The truncated Gamma distribution used in the FUND runs had
approximately the same mean and upper truncation point, but lower variance and faster decay of the
upper tail, as compared to the intended specification based on the Roe and Baker distribution. The
difference between the original estimates reported in the May 2013 version of this technical support
document and this revision are generally one dollar or less.
