APPENDIX 14

- B. TECHNICAL UPDATE OF SOCIAL COST OF CARBO N FOR

REGULATORY IMPACT AN ALYSIS UNDER EXECUTI VE ORDER 12866

TABLE OF CONTENTS

14

- B.1 PREFACE

................................ ................................ ................................ ............ 14

- B

- 1

14

- B.2 PURPOSE

................................ ................................ ................................ ............ 14

- B

- 1

14

- B.3 SUMMARY OF MODEL UPD ATES

................................ ................................ . 14

- B

- 2

14

- B.3.1 DICE

................................ ................................ ................................ .................... 14

- B

- 2

14

- B.3.1.1 Carbon Cycle Parameters

................................ .............................. 14

- B

- 2

14

- B.3.1.2 Sea Level Dynamics

................................ ................................ ...... 14

- B

- 3

14

- B.3.1.3 Re

- calibrated Damage Function

................................ .................... 14

- B

- 4

14

- B.3.2 FUND

................................ ................................ ................................ ................... 14

- B

- 4

14

- B.3.2.1 Space Heating

................................ ................................ ................ 14

- B

- 5

14

- B.3.2.2 Sea Level Rise and Land Loss

................................ ....................... 14

- B

- 5

14

- B.3.2.3 Agriculture

................................ ................................ ..................... 14

- B

- 5

14

- B.3.2.4 Temperature Response Model

................................ ....................... 14

- B

- 6

14

- B.3.2.5 Methane

................................ ................................ ......................... 14

- B

- 6

14

- B.3.3 PAGE

................................ ................................ ................................ ................... 14

- B

- 6

14

- B.3.3.1 Sea Level Rise

................................ ................................ ............... 14

- B

- 7

14

- B.3.3.2 Revised Damage Function to Account for Saturation

................... 14

- B

- 7

14

- B.3.3.3 Regional Scaling F actors

................................ ............................... 14

- B

- 7

14

- B.3.3.4 Probability of a Discontinuity

................................ ....................... 14

- B

- 7

14

- B.3. 3.5 Adaptation

................................ ................................ ..................... 14

- B

- 8

14

- B.3.3.6 Other Noteworthy Changes

................................ ........................... 14

- B

- 8

14

- B.4 REVISED SCC ESTIMATE S

................................ ................................ ............. 14

- B

- 9

14

- B.5 OTHER MODEL LIMITATI ONS OR RESEARCH GAPS

............................. 14

- B

- 11

LIST OF TABLES

Table 14

- B.4.1 Revised Social Cost of CO 2 , 2010

– 2050 (in 2007 dollars per ton of

CO 2 )

................................ ................................ ................................ ....... 14

- B

- 10

Table 14

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

2050

................................ ................................ ................................ ........ 14

- B

- 11

Table A1. Annual SCC Values: 2010

- 2050 (2007$/ton CO 2 )

................................ ............. 14

- B

- 14 Table A2. 2020 Global SCC Estimates at 2.5 Percent Discount Rate (2007$/ton CO 2 )

..... 14

- B

- 15 Table A3. 2020 Global SCC Estimates at 3 Percent Discount Rate (2007$/ton CO2)

....... 14

- B

- 15

Table A4. 2020 Global SCC Estimates at 5 Percent Discount Rate (2007$/ton CO 2 )

........ 14

- B

- 16

LIST OF FIGURES

Figure 14

- B.4.2 Distribution of SCC Estimates for 2020 (in 2007$ per ton CO 2 )

.......... 14

- B

- 10

14

- B

- iAPPENDIX 14

- B. TECHNICAL UPDATE OF SOCIAL COST OF CARBO N FOR

REGULATORY IMPACT AN ALYSIS UNDER EXECUTI VE ORDER 12866

14

- B.1 PREFACE

The following text is reproduced almost verbatim from the May 2013 report of the Interagency Working Group on the Social Cost of Carbon of the United States Government

. Minor changes were made to the working group's report to make it more consistent with t he rest of this technical support document.

14

- B.2 PURPOSE

The purpose of this document is to update the schedule of social cost of carbon (SCC) a estimates from the 2010 interagency technical support document (TSD) (Interagency Working Group on Social Cost of Carbon 2010). 1 E.O. 13563 commits the Administration to regulatory decision making “based on the best available science.” b Additionally, the interagency group recommended in 2010 that the SCC estimates be revisited on a regular basis or as model updates that reflect the growing body of scientific and economic knowledge become available. c New versions of the three integrated assessment models used by the U .S. government to estimate the SCC (DICE, FUND, and PAGE), are now available and have been published in the peer reviewed literature. While acknowledging the continued limitations of the approach taken by the interagency group in 2010 (documented in the or iginal 2010 TSD), this document provides an update of the SCC estimates based solely on the latest peer

- reviewed version of the models, replacing model versions that were developed up to ten years ago in a rapidly evolving field. It

does not revisit other assumptions with regard to the discount rate, reference case socioeconomic and emission scenarios, or equilibrium climate sensitivity. Improvements in the way damages are modeled are confined to those that have been incorporated into the latest versions of the models by the developers themselves in the peer

- reviewed literature. The Environmental Protection Agency (EPA), in collaboration with other Federal agencies such as the Department of Energy (DOE), continues to investigate potential improvements to the way in which economic damages associated with changes in CO 2 emissions are quantified.

Section 3 summarizes the major updates relevant to SCC estimation that are contained in the new versions of the integrated assessment models released since the 2010 interagency report.

Section 4 presents the updated schedule of SCC estimates for 2010

– 2050 based on these

versions of the models. Section 5 provides a discussion of recent workshops to support improvements in SCC estimation.

a 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

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

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

14

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- 114

- B.3 SUMMARY OF MODEL UPD ATES

Thi s section briefly summarizes changes integrated into the most recent versions of the three integrated assessment models (IAMs) used by the interagency group in 2010. We focus on describing those model updates that are relevant to estimating the social cost of carbon. For example, both the DICE and PAGE models now include an explicit representation of sea level rise damages. Other revisions to PAGE include: updated adaptation assumptions, revisions to ensure damages are constrained GDP, updated regional scal ing of damages, and a revised treatment of potentially abrupt shifts in climate damages. In the most recent version of DICE, the model’s simple carbon cycle has been updated to be more consistent with a relatively more complex climate model. The FUND mode l includes updated damage functions for sea level rise impacts, the agricultural sector, and reduced space heating requirements, as well as changes to the response of temperature to the buildup of GHG concentrations and the inclusion of indirect

effects of methane emissions. Changes made to parts of the models that are superseded by the interagency working group’s modeling assumptions

– regarding climate sensitivity, discounting,

and socioeconomic variables

– are not discussed.

14

- B.3.1 DICE

Changes in the DICE mod el 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 expli cit representation of economic damages from sea level rise. Changes were also made to other parts of the DICE model

— including the equilibrium climate sensitivity parameter, the rate of change of total factor productivity, and the elasticity of the marginal utility of consumption

— but these components of DICE are superseded by the interagency working group’s assumptions
and so will not be discussed here. More details on DICE2007 can be found in Nordhaus (2008) 2

and on DICE2010 in Nordhaus (2010) 3 and the associated on

- line appendix containing supplemental information.

14

- B.3.1.1 Carbon Cycle Parameters

DICE uses a three

- box model of carbon stock s and flows to represent the accumulation and transfer of carbon among the atmosphere, the shallow ocean and terrestrial biosphere, and the deep ocean. These parameters are “calibrated to match the carbon cycle in the Model for the

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

Carbon cycle transfer coefficient values in DICE2010 are based on re

- calibration of the model to
match the newer version of MAGICC (Nordhaus 2010 p 2). 3 For example, in DICE2010 in each decade, 12 percent of the carbon in the atmosphere is transferred to the shallow ocean, 4.7 percent of the carbon in the shallow ocean is transferred to the atmosphere, 94.8 percent remains in the shallow ocean, and 0.5 percent is transferred to the deep ocean. For comparison, in DICE 2007, 18.9 percent of the carbon in the atmosphere is transferred to the shallow ocean each

d MAGICC is a simple climate model initially developed within the U.S. National Center for Atmospheric Research that has been used heavily by the Intergovernmental Panel on Climate Change (IPCC) to emulate projections from much more sophisticated state of the art earth system simulation models (Randall et al. 2007). 4

14

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- 2decade, 9.7 per cent 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 t o those from

DICE2007.

14

- B.3.1.2 Sea Level Dynamics

A new feature of DICE2010 is an explicit representation of the dynamics of the global average sea level anomaly to be used in the updated damage function (discussed below). This section contains a brief descriptio n of the sea level rise (SLR) module; a more detailed description can be found on the model developer’s website. e The average global sea level anomaly is modeled as the sum of four terms that represent contributions from: 1) thermal expansion of the oceans, 2) melting of glaciers and small ice caps, 3) melting of the Greenland ice sheet, and 4) melting of the Antarc tic ice sheet.

The parameters of the four components of the SLR module are calibrated to match consensus results from the IPCC’s Fourth Assessment Report. 4 f The rise in sea level from thermal expansion in each time period (decade) is 2 percent of the difference between the sea level in the previous period an d 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

t he 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 me ters to a maximum of 7.3 meters. The contribution to SLR in each period is proportional to the difference between the previous period’s sea level anomaly and the equilibrium sea level anomaly, where the constant of proportionality increases with the

temper ature anomaly in the current period.

The contribution to SLR from the melting of the Antarctic ice sheet is

- 0.001 meters per decade when the temperature anomaly is below 3 °C and increases linearly to a maximum rate of 0.025 meters per decade at a tempe rature anomaly of 6 °C.

e Documentation on the new sea level rise module of DICE is avai lable on William Nordhaus’ website at: http://nordhaus.econ.yale.edu/documents/SLR_021910.pdf.

f For a review of post

- IPCC AR4 research on sea level rise, see Nicholls et al. (2011) 5 and NAS (2011). 6

14

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- 314

- B.3.1.3 Re

- calibrated Damage Function

Economic damages from climate change in the DICE model are represented by a fractional loss of gross economic output in each period. A portion of the remaining economic output in each period (net of cl imate change damages) is consumed and the remainder is invested in the physical capital stock to support future production, so each period’s climate damages will reduce consumption in that period and in all future periods due to the lost investment. The

fr action of output in each period that is lost due to climate change impacts is represented as one minus a fraction, which is one divided by a quadratic function of the temperature anomaly, producing a sigmoid (“S”

- shaped) function. The loss function in DICE 2010 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 include d in these parameters in DICE2007.

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

that “...d amages 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 (as downloaded from the homepage of William Nordhaus), annual damages are lower in most of the early periods but higher in later periods of the time horizon than would be calculated using the DICE2007 damage function. Specifi cally, 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 perc ent 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

lev el rise, along with the assumption that the sea level is projected to continue to rise long after the global average temperature begins to decrease. The changes to the loss function generally decrease the interagency working group SCC estimates slightly, all else equal.

14

- B.3.2 F UND

FUND version 3.8 includes a number of changes over the previous version 3.5 used in the interagency report. Documentation supporting FUND and the model’s source code for all

versions of the model is available from the model authors. g Notable changes, due to their impact on the estimates of expected SCC, are adjustments to the space heating, agriculture, and sea level rise damage functions in addition to changes to the temperature response function and the

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

g http://www.fund

- model.org / . This report uses version 3.8 of the FUND model, which represents a modest update

to the most recent version of the model to appear in the literature (version 3.7) (Anthoff and Tol, 2013). 7 For the
purpose of computing the SCC, the relevant changes are associated with improving consistency with IPCC AR4 by adjusting the atmospheric lifetimes of CH4 and N2O and incorporating the indirect forcing effects of CH4, along with making minor stabi lity improvements in the sea wall construction algorithm.

h The other damage sectors (water resources, space cooling, land loss, migration, ecosystems, human health, and extreme weather) were not the subject of significant updates.

14

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- 414

- B.3.2.1 Space Heating

In FUND, the damages associated with the change in energy needs for space heating are based on the estimated impact due to one degree of warming. These baseline damages are scaled

ba sed 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 vulnerabili ty allows for the possibility that in some simulations the benefits associated with reduced heating needs may be an unbounded convex function of the temperature anomaly. In FUND 3.8, the form of the scaling

has been modified to ensure that the function is everywhere concave, meaning that for every simulation there will exist an upper bound on the benefits a region may receive from reduced space heating needs. The new formulation approaches a value of two in the limit as the temperature anomaly increases, or in other words, assuming no decrease in vulnerability, the reduced expenditures on space heating at any level of warming will not exceed two times the reductions experienced at one degree of warming. Since the reduced need for space heating represents a b enefit 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 prob abilistically.

14

- B.3.2.2 Sea Level Rise and Land Loss

The FUND model explicitly includes damages associated with the inundation of dry land due to sea level rise. The amount of land lost within a region is dependent upon the proportion of the coastline being protec ted 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 r egions 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 non

linear function of sea level rise, thereby assuming that the slope of the shore line is not constant moving inland, with a positive first derivative. The effect of this change is to typically reduce the vulnerability of some regions to sea level rise based land loss, therefore having an effect of lowering the expec ted SCC estimate. The model has also been updated to assume that the value of dry land at risk of inundation is not uniform across a region but will be a decreasing function of protection measure, thereby implicitly assuming that the most valuable land wi ll be protected

first.

14

- B.3.2.3 Agriculture

In FUND, the damages associated with the agricultural sector are measured as proportional to the sector’s value. The fraction is made up of three additively separable components that represent the effects from carbon fer tilization, the rate of temperature change, and the level of the temperature anomaly. In both FUND 3.5 and FUND 3.8, the fraction of the sector’s value lost due to the level of the temperature anomaly is modeled as a quadratic function with an intercept of zero. In FUND 3.5, the linear and quadratic coefficients are modeled as the ratio of two normal distributions. Within this specification, as draws from the distribution in the

14

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- 5denominator approached zero the share of the sector’s value “lost” approaches ( +/

- ) infinity independent of the temperature anomaly itself. In FUND 3.8, the linear and quadratic coefficients are drawn directly from truncated normal distributions so that they remain in the

range [0, ) ∞ and ( ,0]

− ∞ , respectively, where the means for the new distributions are set equal to the ratio of the means from the normal distributions used in the previous version. In general the impact of this change has been to increase the likelihood that increases in the tem perature level will have either larger positive or negative effects on the agricultural sector relative to the previous version (through eliminating simulations in which the “lost” value approached (+/

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

14

- B.3.2.4 Temperature Response Model

The temperature response model translates changes in global levels of radiative forcing into the current expected temperature anomaly. In FUND, a given year’s increase in the cumulative temper ature 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 th e 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 th e 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 temper ature response to the level of the equilibrium climate sensitivity. Therefore in FUND 3.8, the temperature response will typically be faster than in the previous version. The overall effect of this change is likely to increase estimates of the SCC as highe r temperatures are reached during the timeframe analyzed and as the same damages experienced in the previous version of the model are now experienced earlier and therefore discounted less.

14

- B.3.2.5 Methane

The IPCC notes a series of indirect effects of methane emi ssions, and has developed methods for proxying such effects when computing the global warming potential of methane
(Forster et al. 2007). 8 FUND 3.8 now includes the same methods for incorporating the indirect effects of methane emissions. Specifically, the average atm ospheric lifetime of methane has been set to 12 years to account for the feedback of CH4 emissions on its own lifetime. The radiative forcing associated with atmospheric methane has also been increase by 40% to account for its net impact on ozone productio n and increase in stratospheric water vapor. The general effect of this increased radiative forcing will be to increase the estimated SCC values, where the degree to which this occurs will be dependent upon the relative curvature of the damage functions wi th respect to the temperature anomaly.

14

- B.3.3 PAGE

PAGE09 (Hope 2012) 9 includes a number of changes from PAGE2002, the version used in the 2009 SCC interagency report. The changes that m ost directly affect the SCC estimates

14

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- 6include: 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 probabil ity of a discontinuity within the damage function, and revised assumptions on adaptation. The model also includes revisions to the carbon cycle feedback and the calculation of regional temperatures. More details on PAGE2009 can be found in three working pa pers (Hope 2011a, 2011b, 2011c). 10

, 11

, 12 A description of PAGE2002 can be found
in Hope (2006). 13

14

- B.3.3.1 Sea Level Rise

While PAGE2002 aggregates all damages into two categories

– economic and non

economic impacts

- PAGE2009 adds a third explicit category: damages from sea level rise. In the previous vers ion of the model, damages from sea level rise were subsumed by the other damage categories. PAGE09 models damages from sea level rise as increasing less than linearly with sea level based on the assumption that low

- lying shoreline areas will be associated with higher damages than current inland areas. Damages from the economic and non

- economic sector were adjusted to account for the introduction of this new category.

14

- B.3.3.2 Revised Damage Function to Account for Saturation

In PAGE09, small initial economic and n on

- economic benefits (negative damages) are modeled for small temperature increases, but all regions eventually experience positive economic damages from climate change, where damages are the sum of additively separable polynomial functions of temperature and sea level rise. Damages transition from this polynomial function to a logistic path once they exceed a certain proportion of remaining Gross Domestic Product (GDP) to ensure that damages do not exceed 100 percent of GDP. This differs from PAGE2002,

whi ch allowed Eastern Europe to potentially experience large benefits from temperature increases, and which also did not bound the possible damages that could be experienced.

14

- B.3.3.3 Regional Scaling Factors

As in the previous version of PAGE, the PAGE09 model calculates the damages for the European Union (EU) and then, assumes that damages for other regions are proportional based on a given scaling factor. The scaling factor in PAGE09 is based on the length of a region’s coastline relative to the EU (Hope 2011b ). 11 Because of the long coastline in the EU, other regions are, on average, less vulnerable than the EU for the same sea level and temperature increase, but all regions have a positive scaling factor. PAGE2002 based its scaling factors on four studies reported in the IPCC’s third assessment report, and allowed for benefits from temperature increase in Eastern Europe, sma ller impacts in developing countries, and higher damages in developing countries.

14

- B.3.3.4 Probability of a Discontinuity

In PAGE2002, the damages associated with a “discontinuity” were modeled as an expected value. That is, additional damages from an extreme ev ent, such as extreme melting of

14

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- 7the 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. Th e 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 probab ility 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 t riangular 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 per iod of time, but once it occurs, its effect is permanent.

14

- B.3.3.5 Adaptation

As in PAGE2002, adaptation is available to increase the tolerable level of temperature change and can help mitigate any climate change impacts that still occur. In PAGE this adaptation i s the same regardless of the temperature change or sea level rise and is therefore akin to what is more commonly considered a reduction in vulnerability. It is modeled by modifying the temperature change and sea level rise used in the damage function or by reducing the damages by some percentage. PAGE09 assumes a smaller decrease in vulnerability than the previous version of the model and assumes that it will take longer for this change in vulnerability to be realized. In the aggregated economic sector, at the time of full implementation, this adaptation will mitigate all damages up to a temperature increase of 1°C, and for temperature anomalies between 1°C and 3°C, it will reduce damages by 15

- 30 percent (depending on the region). However, it takes 20 year s to fully implement this adaptation. In PAGE2002, adaptation was assumed to reduce economic sector damages up to 3°C by 50

- 90 percent after 20 years. Beyond 3°C, no adaptation is assumed to be available to mitigate the impacts of climate change.

For the n on

- 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 PA GE2002. Similarly, adaptation is assumed to alleviate 25

- 50 percent of the damages from the first 0.20 to 0.25 meters of sea level rise but is assumed to be ineffective thereafter. Hope (2011c) 12 estimates that the less optimistic assumptions regarding the ability to offset impacts of temperature and sea level rise via adaptation increase the SCC by approxi mately 30 percent.

14

- B.3.3.6 Other Noteworthy Changes

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

introduced to simulate decreased CO 2 absorption by the terrestrial biosphere and ocean as the temperature rises. This feedback is linear in the average global and annual temperature anomaly but is capped at a maximum value. In the previous version of PAGE, an additional amount was

added to t he CO 2 emissions each period to account for a decrease in ocean absorption and a loss

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- 8of soil carbon. Also updated is the method by which the average global and annual temperature anomaly is downscaled to determine annual average regional temperature anoma lies to be used in the regional damage functions. In the previous version of PAGE, the scaling was determined solely based on regional difference in emissions of sulfate aerosols. In PAGE09, this regional temperature anomaly is further adjusted using an ad ditive factor that is based on the average absolute latitude of a region relative to the area weighted average absolute latitude of the Earth’s

landmass.

14

- B.4 REVISED SCC ESTIMATE S

The updated versions of the three integrated assessment models were run using t he same
methodology detailed in the 2010 TSD. 1 The approach along with the inputs for the socioeconomic emissions scenarios, equilibrium climate sensitivity distribution, and discount

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

- 2 2 modeling exercise, the Roe and Baker equilibrium climate sensitivity distribution calibrated to the Fourth Assessment Report of the IPCC, and three constant discount rates of 2.5, 3, and 5 percent.

As was previously the case, the use of three models, th ree discount rates, and five scenarios produces 45 separate distributions for the SCC. The approach laid out in the TSD applied equal weight to each model and socioeconomic scenario in order to reduce the dimensionality down to three separate distributions representative of the three discount rates. The interagency group selected four values from these distributions for use in regulatory analysis. Three values are based on the average SCC across models and socio

- economic

- emissions
scenarios at the 2.5, 3, a nd 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 a t a 3 percent discount rate was chosen. (A detailed set of percentiles by model and scenario combination is available in the Annex.) As noted in the original TSD, “the 3 percent discount rate is the central value, and so the central value that emerges is the average SCC across models at the 3 percent discount rate” (TSD, p. 25). However, for purposes of capturing the uncertainties involved in regulatory impact analysis, the interagency group emphasizes the importance and value of including all four SCC val ues.

Table 14

- B.4.1 shows the four selected SCC estimates in five year increments from 2010 to 2050. Values for 2010, 2020, 2030, 2040, and 2050 are calculated by first combining all outputs (10,000 estimates per model run) from all scenarios and models for a given discount rate. Values for the years in between are calculated using basic linear interpolation. The full set of

annual SCC estimates between 2010 and 205 0 is reported in the Annex.

14

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- 9Table 14

- B.4.1 Revised Social Cost of CO 2 , 2010

– 2050 (in 2007 dollars per ton of CO 2 )

Discount Rate 5.0% 3.0% 2.5% 3.0%

Year Avg Avg Avg 95th

2010 11 33 52 90

2015 12 38 58 109

2020 12 43 65 129

2025 14 48 70 144

2030 16 52 76 159

2035 19 57 81 176

2040 21 62 87 192

2045 24 66 92 206

2050 27 71 98 221

The SCC estimates using the updated versions of the models are higher than those reported in the TSD due to the changes to the models outlined in the previous section. Figure 14

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

discount rate based on the combined set of runs for each model and scenario (150,000 estimates in total for each discount rate). In general, the distributions are skewed to the right and have long tails. The Figure also shows that the lower the discount rate, the longer the right tail of the

distribution.

Figure 14

- B.4.2 Dis tribution of SCC Estimates for 2020 (in 2007$ per ton CO 2 )

As was the case in the original TSD, the SCC increases over time because future emissions are expected to produce larger incremental damages as physical and economic systems

become more stressed in response to greater climatic change. The approach taken by the interagency group is to allow the growth rate to be determined endogenously by the models

14

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- 10through running them for a set of perturbation years out to 2050. Table 14

- B.4.2 illustrates how the growth rate for these four SCC estimates varies over time.

Table 14

- B.4.2 Average Annual Growth Rates of SCC Estimates between 2010 and 2050
Average Annual 5.0% 3.0% 2.5% 3.0% Rate (%) Avg Avg Avg 95th

2010

- 2020 1.2% 3.2% 2.4% 4.3%

2020

- 2030 3.4% 2.1% 1.7% 2.4%

2030

- 2040 3.0% 1.8% 1.5% 2.0%

2040

- 2050 2.6% 1.6% 1.3% 1.5%

The future monetized value of emission reductions in each year (the SCC in year t multiplied by the change in emissions in year t) must be discounted to the present to determine its total net present value for use in regulatory analysis. As previously discussed in the original TSD, damages from future emissions should be discounted at the same rate a s that used to calculate the SCC estimates themselves to ensure internal consistency

– i.e., future damages from climate change, whether they result from emissions today or emissions in a later year, should be discounted using the same rate.

14

- B.5 OTHER MODEL LI MITATIONS OR RESEARC H GAPS

The 2010 interagency SCC technical support report discusses a number of important limitations for which additional research is needed. In particular, the document highlights the need to improve the quantification of both non

- catastrophic and catastrophic damages, the treatment of adaptation and technological change, and the way in which inter

- regional and inter

sectoral linkages are modeled. It also discusses the need to more carefully assess the implications

of risk avers ion 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 lo ng

- term research work on modeling and valuation of climate impacts that we expect will inform improvements in SCC estimation in the future.

14

- B

- 11REFERENCES

1. Interagency Working Group on Social Cost of Carbon, Social Cost of Carbon for Regulatory Impact Analysis under Executive Order 12866, February, 2010. United States

Government. < http://www.whitehouse.gov/sites/defa ult/files/omb/inforeg/for

agencies/Social

- Cost

- of

- Carbon

- for

- RIA.pdf >

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

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

- Copenhagen environment

. Proceedings of th e National Academy of Sciences , 2010. 107(26): pp. 11721

- 11726

4. Randall, D. A., R.A. Wood, S. Bony, R. Colman, T. Fichefet, J. Fyfe, V. Kattsov, A. Pitman, J. Shukla, J. Srinivasan, R.J. Stouffer, A. Sumi and K.E. Taylor, Climate Models

and Their Evalu ation . In Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change , S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M.Tignor and H.L. Miller, Editor. 2007. Cambridge University Press: Cambridge, United Kingdom and New York, NY, USA

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

- level rise and its possible impacts given a ‘ beyond 4°C world’ in the

twenty

- first century

. Phil. Trans. R. Soc. A 2011. 369(1934): pp. 161

- 181

6. National Academy of Sciences, Climate Stabilization Targets: Emissions, Concentrations, and Impacts over Decades to Millennia . 2011. National Academies Press, Inc: Washington, DC.

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

. Climatic Change , 2013(Forthcoming)

8. Forster, P., V. Ramaswamy, P. Artaxo, T. Berntsen, R. Betts, D.W. Fa hey, J. Haywood, J. Lean, D.C. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz and R. Van Dorland, Changes in Atmospheric Constituents and in Radiative Forcing . In Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M.Tignor and H.L. Miller Editor. 2007. Cambridge University Press: Cambridge, United Kingdom and New York, NY, U SA

9. Hope, C., Critical issues for the calculation of the social cost of CO2: why the estimates from PAGE09 are higher than those from PAGE2002

. Climatic Change

, 2012(Forthcoming)

14

- B

- 1210. Hope, C., The PAGE09 Integrated Assessment Model: A Technical Descrip tion . 2011, Cambridge Judge Business School http://www.jbs.cam.ac.uk/research/working_papers/2011/wp1104.pdf

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

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

12. Hope, C., New Insights from the PAGE09 Model: The Social Cost of CO2 . 2011, Cambridge Judge Business School http://www.jbs.cam.ac.uk/research/working_papers/2011/wp1108.pdf

13. Hope, C., The Marginal Impact of CO2 from PAGE2002: An Integra ted Assessment Model Incorporating the IPCC’s Five Reasons for Concern

. The Integrated Assessment

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

- 56

14

- B

- 13ANNEX

Table A1. Annual SCC Values: 2010

- 2050 (2007$/ton CO 2 )

Discount Rate 5.0% 3.0% 2.5% 3.0%
Year Avg Avg Avg 95th

2010 11 33 52 90

2011 11 34 54 94

2012 11 35 55 98

2013 11 36 56 102

2014 11 37 57 106

2015 12 38 58 109

2016 12 39 60 113

2017 12 40 61 117

2018 12 41 62 121

2019 12 42 63 125

2020 12 43 65 129

2021 13 44 66 132

2022 13 45 67 135

2023 13 46 68 138

2024 14 47 69 141

2025 14 48 70 144

2026 15 49 71 147

2027 15 49 72 150

2028 15 50 73 153

2029 16 51 74 156

2030 16 52 76 159

2031 17 53 77 163

2032 17 54 78 166

2033 18 55 79 169

2034 18 56 80 172

2035 19 57 81 176

2036 19 58 82 179

2037 20 59 84 182

2038 20 60 85 185

2039 21 61 86 188

2040 21 62 87 192

2041 22 63 88 195

2042 22 64 89 198

2043 23 65 90 200

2044 23 65 91 203

2045 24 66 92 206

2046 24 67 94 209

2047 25 68 95 212

2048 25 69 96 215

2049 26 70 97 218

2050 27 71 98 221

14

- B

- 14Table A2. 2020 Global SCC Estimates at 2.5 Percent Discount Rate (2007$/ton CO 2 )

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

IMAGE 6 11 15 27 58 129 139 327 515 991

MERGE 4 6 9 16 34 78 82 196 317 649

MESSAGE 4 8 11 20 42 108 107 278 483 918

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

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

Scenario DICE
IMAGE 25 31 37 47 64 72 92 123 139 161

MERGE 14 18 20 26 36 40 50 65 74 85

MESSAGE 20 24 28 37 51 58 71 95 109 221

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

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

Scenario FUND
IMAGE

- 17

- 1 5 17 34 44 59 90 113 176

MERGE

- 7 2 7 16 30 35 49 72 91 146

MESSAGE

- 19

- 4 2 12 27 32 46 70 87 135

MiniCAM Base

- 9 1 8 18 35 45 59 87 108 172

5th Scenario

- 30

- 12

- 5 6 19 24 35 57 72 108

Table A3. 2020 Global SCC Estimates at 3 Percent Discount Rate (2007$/ton CO2)

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

Scenario PAGE

IMAGE 4 7 10 18 38 91 95 238 385 727

MERGE 2 4 6 11 23 56 58 142 232 481

MESSAGE 3 5 7 13 29 75 74 197 330 641

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

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

Scenario DICE
IMAGE 16 21 24 32 43 48 60 79 90 102

MERGE 10 13 15 19 25 28 35 44 50 58

MESSAGE 14 18 20 26 35 40 49 64 73 83

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

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

Scenario FUND
IMAGE

- 14

- 3 1 9 20 25 35 54 69 111

MERGE

- 8

- 1 3 9 18 22 31 47 60 97

MESSAGE

- 16

- 5

- 1 6 16 18 28 43 55 88

MiniCAM Base

- 9

- 1 3 10 21 27 35 53 67 107

5th Scenario

- 22

- 10

- 5 2 10 13 20 33 42 63

14

- B

- 15Table A4. 20 2 0 Global SCC Estimates at 5 Percent Discount Rate (2007$/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 1 1 2 3 7 17 17 45 75 153

MESSAGE 1 1 2 4 9 24 22 60 106 216

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

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

Scenario DICE
IMAGE 6 8 9 11 14 15 18 22 25 27

MERGE 4 5 6 7 9 10 12 15 16 18

MESSAGE 6 7 8 10 12 13 16 20 22 25

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

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

Scenario FUND
IMAGE

- 9

- 5

- 3

- 1 2 3 6 11 15 25

MERGE

- 6

- 3

- 2 0 3 4 7 12 16 27

MESSAGE

- 10

- 6

- 4

- 1 2 2 5 9 13 23

MiniCAM Base

- 7

- 3

- 2 0 3 4 7 11 15 26

5th Scenario

- 11

- 7

- 5

- 2 0 0 3 6 8 14

14

- B

- 16