## 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

Environmental Protection Agency

National Economic Council

Office of Management and Budget

Office of Science and Technology Policy

Department of the Treasury

May 2013

Revised Ju ly 2015

See Appendix B for Details on Revision

1Executive Summary

Under Executive Order 12866, agencies are θ͊ηϡΉθ͊͆΁ φΩ φΆ͊ ͊ςφ͊΢φ ε͊θΡΉφφ͊͆ ̻ϳ Λ̮ϭ΁ ͡φΩ ̮μμ͊μμ ̻ΩφΆ

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

̻͊΢͔͊Ήφμ Ω͔ φΆ͊ Ή΢φ͊΢͆͊͆ θ͊ͼϡΛ̮φΉΩ΢ ΕϡμφΉ͔ϳ Ήφμ ̼Ωμφμ ́͢ ΐΆ͊ εϡθεΩμ͊ Ω͔ φΆ͊ ͡μΩ̼Ή̮Λ ̼Ωμφ Ω͔ ̼̮θ̻Ω΢͢ (ΊCC)

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.

ΐΆ͊ Ή΢φ͊θ̮ͼ͊΢̼ϳ εθΩ̼͊μμ φΆ̮φ ͆͊Ϭ͊ΛΩε͊͆ φΆ͊ ΩθΉͼΉ΢̮Λ Δ ́Ί ́ ͼΩϬ͊θ΢Ρ͊΢φ͞μ ΊCC ͊μφΉΡ̮φ͊μ Ήμ ͆͊μ̼θΉ̻͊͆ Ή΢ φΆ͊

2010 interagency technical support document (TSD) (Interagency Working Group on Social Cost of Carbon

2010). Th rough 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 o f

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.

2Revised 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 10 31 50 86

2015 1 1 36 56 105

2020 12 42 62 123

2025 14 46 68 138

2030 16 50 73 152

2035 18 55 78 168

2040 21 60 84 183

2045 23 64 89 197

2050 2 6 69 95 212

3I. 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 ́ͷ ́ 13563 ̼ΩΡΡΉφμ φΆ͊ !͆ΡΉ΢Ήμφθ̮φΉΩ΢ φΩ θ͊ͼϡΛ̮φΩθϳ ̼͆͊ΉμΉΩ΢ Ρ̮ΘΉ΢ͼ ̻̮͡μ͊͆ Ω΢ φΆ͊ ̻͊μφ ̮Ϭ̮ΉΛ̮̻Λ͊

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 di scount 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 ΡΩ͆͊Λ͞μ μΉΡεΛ͊ ̼̮θ̻Ω΢ ̼ϳ̼Λ͊ Ά̮μ ̻͊͊΢ ϡε̮͆φ͊͆ φΩ ̻͊ 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).

4methane emissions. Changes made to parts of the models that are superseded by the interagency working

ͼθΩϡε͞μ ΡΩ͆͊ΛΉ΢ͼ ̮μμϡΡεφΉΩ΢ s – 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 E xplicit representation of SLR damages, revisions to

damage function to ensure damages do not exceed

100% of GDP

, change in regional scaling of damages,

r evised 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 ͞μ 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

ε̮θ̮Ρ͊φ͊θμ ̮θ͊ ̼̮͡ΛΉ̻θ̮φ͊͆ φΩ Ρ̮φ̼Ά φΆ͊ ̼̮θ̻Ω΢ ̼ϳ̼Λ͊ Ή΢ φΆ͊ Ͱ odel for the Assessment of Greenhouse

G̮μ ͛΢͆ϡ̼͊͆ CΛΉΡ̮φ͊ CΆ̮΢ͼ͊ (Ͱ!G͛CC)͢ (ͱΩθ͆Ά̮ϡμ 2008 ε 44)

. 4 Carbon cycle transfer coefficient values

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).

5in 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

͆͊Ϭ͊ΛΩε͊θ͞μ ϭ̻͊μΉφ͊ ́ 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

φΆ͊ ͛΃CC͞μ FΩϡθφΆ !μμ͊μμΡ͊΢φ Ά͊εΩθφ (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 previ Ωϡμ ε͊θΉΩ͆͞μ μ̮͊

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

the temperature anomaly in the current period.

5 Documentation on the new sea level rise module of DICE is available on William Nord Ά̮ϡμ͞ ϭ̻͊μΉφ͊ ̮φ΃

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).

6The 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 εθΩ͆ϡ̼φΉΩ΢΁ μΩ ̮̼͊Ά ε͊θΉΩ͆͞μ ̼ΛΉΡ̮φ͊ ̮͆Ρ̮ͼ͊μ ϭΉΛΛ θ͊͆ϡ̼͊ ̼Ω΢μϡΡεφΉΩ΢ Ή΢ φΆ̮φ

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

ηϡ̮͆θ̮φΉ̼ ͔ϡ΢̼φΉΩ΢ Ω͔ φΆ͊ φ͊Ρε͊θ̮φϡθ͊ ̮΢ΩΡ̮Λϳ΁ εθΩ͆ϡ̼Ή΢ͼ ̮ μΉͼΡΩΉ͆ (͡Ί͢ -shaped) function. 7 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

.

ΐΆ͊ ̮ͼͼθ͊ͼ̮φ͊ ̮͆Ρ̮ͼ͊μ Ή΢ D͛CE2010 ̮θ͊ ΉΛΛϡμφθ̮φ͊͆ ̻ϳ ͱΩθ͆Ά̮ϡμ (2010 ε 3)΁ ϭΆΩ ΢Ωφ͊μ φΆ̮φ ͡ ̮̈́͆Ρ̮ͼ͊μ

in the uncontrolled (baseline) [i .e., reference] case  ̈́ Ή΢ 2095 ̮θ͊ $12 φθΉΛΛΉΩ΢΁ Ωθ 2 ́8 ε͊θ̼͊΢φ Ω͔ ͼΛΩ̻̮Λ

output, for a global temperature increase of 3.4 o C ̮̻ΩϬ͊ 1900 Λ͊Ϭ͊Λμ ́͢ ΐΆΉμ ̼ΩΡε̮θ͊μ φΩ ̮ ΛΩμμ Ω͔ 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 +1 60 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 ̮΢͆ φΆ͊ ΡΩ͆͊Λ͞μ μΩϡθ̼͊ ̼Ω͆͊ 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 ͞μ

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, 2013 ). For the

purpose of computing the SCC, the relevant changes (between 3.7 to 3.8) are associated with improving

7SCC 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

͔Ωθ̼̮͊μφ͊͆ φ͊Ρε͊θ̮φϡθ͊ ̮΢ΩΡ̮Λϳ͞μ ͆͊ϬΉ̮φΉΩ΢ ͔θΩΡ φΆ͊ Ω΢͊ ͆͊ͼθ͊͊ ̻͊΢̼ΆΡ̮θΘ 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

le ngth 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

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).

8Agriculture

In FUND, φΆ͊ ̮͆Ρ̮ͼ͊μ ̮μμΩ̼Ή̮φ͊͆ ϭΉφΆ φΆ͊ ̮ͼθΉ̼ϡΛφϡθ̮Λ μ̼͊φΩθ ̮θ͊ Ρ̮͊μϡθ͊͆ ̮μ εθΩεΩθφΉΩ΢̮Λ φΩ φΆ͊ μ̼͊φΩθ͞μ

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 ͔θ̮̼φΉΩ΢ Ω͔ φΆ͊ μ̼͊φΩθ͞μ Ϭ̮Λϡ͊ ΛΩμφ ͆ϡ͊ φΩ φΆ͊

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 and , 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 d ΉμφθΉ̻ϡφΉΩ΢μ͞ Ρ̮μμ ΩϬ͊θ φΆ͊ θ͊Ρ̮Ή΢Ή΢ͼ θ̮΢ͼ͊ 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 i ͔ φΆ̮φ ϳ̮͊θ͞μ Λ͊Ϭ͊Λ Ω͔ θ̮͆Ή̮φΉϬ͊ ͔Ωθ̼Ή΢ͼ were sustained

. The rate of mean reversion

defin es 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 fo r

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

9stratospheric 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.

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 Λ͊΢ͼφΆ Ω͔ ̮ θ͊ͼΉΩ΢͞μ ̼Ω̮μφΛΉ΢͊ θ͊Λ̮φΉϬ͊ φΩ φΆ͊ EΔ (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

Ήφμ μ̼̮ΛΉ΢ͼ ͔̮̼φΩθμ Ω΢ ͔Ωϡθ μφϡ͆Ή͊μ θ͊εΩθφ͊͆ Ή΢ φΆ͊ ͛΃CC͞μ φΆΉθ͆ ̮μμ͊μμΡ͊΢φ report, and allowed for benefits

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.

10from temperature increase in Eastern Europe, smaller impacts in develop ed countries, and higher

damages in developing countries.

Probability of a Discontinuity

͛΢ ΃!GE2002΁ φΆ͊ ̮͆Ρ̮ͼ͊μ ̮μμΩ̼Ή̮φ͊͆ ϭΉφΆ ̮ ͆͡Ήμ̼Ω΢φΉ΢ϡΉφϳ͢ (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 adapt at ion 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.

11Other Noteworthy Changes

Two other changes in the model are worth noting. The re 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 la φΉφϡ͆͊ Ω͔ φΆ͊ E̮θφΆ͞μ

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 wa s 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

an d 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 model run)

from all scenarios and models for a given discount rate

. Values for the years in between are calculated

12using 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 10 31 50 86

2015 1 1 36 56 105

2020 12 42 62 123

2025 14 46 68 138

2030 16 50 73 152

2035 18 55 78 168

2040 21 60 84 183

2045 23 64 89 197

2050 2 6 69 95 212

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 )

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

13response 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

Rate (%) 5.0%

Avg 3.0%

Avg 2.5%

Avg 3.0%

95th

2010

- 2020

2020

- 2030

2030

- 2040

2040

- 2050 1.2%

3.4%

3.0%

2.6 % 3.2 %

2.1%

1. 9 %

1 .6% 2.4%

1.7%

1.5%

1.3% 4. 4 %

2.3 %

2.0 %

1.6 %

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

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 noncatastrophic 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

14well 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

.

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analysis using FUND. Climatic Change 117: 515

– 530

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Anthoff, D. and Tol, R.S.J. 2013. 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

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HΩε͊΁ CΆθΉμ ́ 2006 ́ ͡ΐΆ͊ Ͱ̮θͼΉ΢̮Λ ͛Ρε̮̼φ Ω͔ Cͷ 2 from PAGE2002: An Integrated Assessment Model

͛΢̼ΩθεΩθ̮φΉ΢ͼ φΆ͊ ͛΃CC͞μ FΉϬ͊ Ά̮͊μΩ΢μ ͔Ωθ CΩ΢̼͊θ΢ ́͢ The Integrated Assessment Journal

. 6(1): 19

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Judg e Business School Working Paper No. 4/2011 (April). Accessed November 23, 2011:

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

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16Appendix 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 10 31 50 86

2011 11 32 51 90

2012 11 33 53 93

2013 11 34 54 97

2014 11 35 55 101

2015 11 36 56 105

2016 11 38 57 108

2017 11 39 59 112

2018 12 40 60 116

2019 12 41 61 120

2020 12 42 62 123

2021 12 42 63 126

2022 13 43 64 129

2023 13 44 65 132

2024 13 45 66 135

2025 14 46 68 138

2026 14 47 69 141

2027 15 48 70 143

2028 15 49 71 146

2029 15 49 72 149

2030 16 50 73 152

2031 16 51 74 155

2032 17 52 75 158

2033 17 53 76 161

2034 18 54 77 164

2035 18 55 78 168

2036 19 56 79 171

2037 19 57 81 174

2038 20 58 82 177

2039 20 59 83 180

2040 21 60 84 183

2041 21 61 85 186

2042 22 61 86 189

2043 22 62 87 192

2044 23 63 88 194

2045 23 64 89 197

2046 24 65 90 200

2047 24 66 92 203

2048 25 67 93 206

2049 25 68 94 209

2050 26 69 95 212

17Table A2 : 20 20 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 10 15 26 55 123 133 313 493 949

MERGE Optimistic 4 6 8 15 32 75 79 188 304 621

MESSAGE 4 7 10 19 41 104 103 266 463 879

MiniCAM Base 5 8 12 21 45 102 108 255 412 835

5th Scenario 2 4 6 11 24 81 66 192 371 915

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 : 20 20 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 9 17 36 87 91 228 369 696

MERGE Optimistic 2 4 6 10 22 54 55 136 222 461

MESSAGE 3 5 7 13 28 72 71 188 316 614

MiniCAM Base 3 5 7 13 29 70 72 177 288 597

5th Scenario 1 3 4 7 16 55 46 130 252 632

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.

18Table A4 : 20 20 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 4 10 27 26 68 118 234

MERGE Optimistic 1 1 2 3 6 17 17 43 72 146

MESSAGE 1 1 2 4 8 23 22 58 102 207

MiniCAM Base 1 1 2 3 8 20 20 52 90 182

5th Scenario 0 1 1 2 5 17 14 39 75 199

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

19Table 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 21 1481 5 32 68 13712 4 22 97 26878 4 23

FUND 3 41 5 179 19 1452

- 42 8727 33 6154

- 73 14931

20Appendix 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 mis με̼͊Ή͔Ή͊͆ Ή΢ φΆ͊ ΡΩ͆͊Λ͞μ ̼ΩΡεϡφ͊θ ̼Ω͆͊ ́ This correction is covered in an erratum to

Anthoff and Tol (2013) 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 general ly one dollar or less.

The Ju ly 2015 revision of this technical support document is based on two corrections. First, the DICE

model had been run up to 2300 rather than through 2300, as was intended, thereby leaving out the

marginal damages in the last year of the time horizon. Second, due to an indexing error, the results from

the PAGE model were in 2008 U.S. dollars rather than 2007 U.S. dollars, as was intended. In the current

revision, all models have been run through 2300, and all estimates are in 2007 U.S. dollars. On average

the revised SCC estimates are one dollar less than the mean SCC estimates reported in the November

2013 version of this technical support document. The difference between the 95 th percentile estimates

with a 3% discount rate is slightly larger, as those estimates are heavily influenced by results from the

PAGE model.

21