# Technical Support Document:

Social Cost of Carbon for Regulatory Impact Analysi s

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 Energy and Climate Change Office of Management and Budget Office of Science and Technology Policy Department of the Treasury



## February 20101

Executive Summary

Under Executive Order 12866, agencies are required, to the extent permitted by law, “to assess both th e costs and the benefits of the intended regulation a nd, recognizing that some costs and benefits are difficult to quantify, propose or adopt a regulatio n only upon a reasoned determination that the benefits of the intended regulation justify its cos ts.” The purpose of the “social cost of carbon” (S CC) estimates presented here is to allow agencies to in corporate the social benefits of reducing carbon dioxide (CO 2 ) emissions into cost-benefit analyses of regulator y actions that have small, or “marginal,” impacts on cumulative global emissions. The estima tes are presented with an acknowledgement of the many uncertainties involved and with a clear unders tanding that they should be updated over time to reflect increasing knowledge of the science and eco nomics of climate impacts.

The SCC is an estimate of the monetized damages ass ociated with an incremental increase in carbon emissions in a given year. It is intended to inclu de (but is not limited to) changes in net agricultu ral productivity, human health, property damages from i ncreased flood risk, and the value of ecosystem services due to climate change.

This document presents a summary of the interagency process that developed these SCC estimates. Technical experts from numerous agencies met on a r egular basis to consider public comments, explore the technical literature in relevant fields, and di scuss key model inputs and assumptions. The main objective of this process was to develop a range of SCC values using a defensible set of input assumptions grounded in the existing scientific and economic literatures. In this way, key uncertainti es and model differences transparently and consistentl y inform the range of SCC estimates used in the rulemaking 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, at discount rates of 2.5, 3, and 5 percent

. The fourth value, which represents the 95 th percentile SCC estimate across all three models at a 3 percent discount rate, is included to represent hig her-than-expected impacts from temperature change
further out in the tails of the SCC distribution.

Social Cost of CO 2 , 2010 – 2050 (in 2007 dollars)

Discount Rate 5% 3% 2.5% 3%
Year Avg Avg Avg 95th

2010 4.7 21.4 35.1 64.9
2015 5.7 23.8 38.4 72.8

2020 6.8 26.3 41.7 80.7

2025 8.2 29.6 45.9 90.4

2030 9.7 32.8 50.0 100.0

2035 11.2 36.0 54.2 109.7

2040 12.7 39.2 58.4 119.3

2045 14.2 42.1 61.7 127.8

2050 15.7 44.9 65.0 136.22

I. Monetizing Carbon Dioxide Emissions

The “social cost of carbon” (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 limit ed to) changes in net agricultural productivity, human hea lth, property damages from increased flood risk, an d the value of ecosystem services. We report estimat es of the social cost of carbon in dollars per metr ic ton of carbon dioxide throughout this document. 1

When attempting to assess the incremental economic impacts of carbon dioxide emissions, the analyst faces a number of serious challenges. A recent rep ort from the National Academies of Science (NRC 2009) points out that any assessment will suffer fr om uncertainty, speculation, and lack of informatio n about (1) future emissions of greenhouse gases, (2) the effects of past and future emissions on the climate system, (3) the impact of changes in climat e on the physical and biological environment, and ( 4) the translation of these environmental impacts into economic damages. As a result, any effort to quantify and monetize the harms associated with cli mate change will raise serious questions of science

, economics, and ethics and should be viewed as provi sional.

Despite the serious limits of both quantification a nd monetization, SCC estimates can be useful in estimating the social benefits of reducing carbon d ioxide emissions. Under Executive Order 12866, agencies are required, to the extent permitted by l aw, “to assess both the costs and the benefits of t he intended regulation and, recognizing that some cost s and benefits are difficult to quantify, propose o r adopt a regulation only upon a reasoned determinati on that the benefits of the intended regulation justify its costs.” The purpose of the SCC estimat es presented here is to make it possible for agenci es to incorporate the social benefits from reducing carbo n dioxide emissions into cost-benefit analyses of regulatory actions that have small, or “marginal,” impacts on cumulative global emissions. Most federa l regulatory actions can be expected to have marginal impacts on global emissions.

For such policies, the benefits from reduced (or co sts from increased) emissions in any future year ca n be estimated by multiplying the change in emissions in that year by the SCC value appropriate for that year. The net present value of the benefits can th en be calculated by multiplying each of these futur e benefits by an appropriate discount factor and summ ing across all affected years. This approach assumes that the marginal damages from increased em issions are constant for small departures from the baseline emissions path, an approximation that is reasonable for policies that have effects on emissions that are small relative to cumulative glo bal carbon dioxide emissions. For policies that ha ve a large (non-marginal) impact on global cumulative em issions, there is a separate question of whether th e SCC is an appropriate tool for calculating the bene fits of reduced emissions; we do not attempt to answer that question here.

An interagency group convened on a regular basis to consider public comments, explore the technical literature in relevant fields, and discuss key inpu ts and assumptions in order to generate SCC estimat es. Agencies that actively participated in the interage ncy process include the Environmental Protection

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 be tween mass of
CO 2 and the mass of carbon is 3.67 (the molecular weig ht of CO 2 divided by the molecular weight of carbon = 44/12 = 3.67).3

Agency, and the Departments of Agriculture, Commerc e, Energy, Transportation, and Treasury. This process was convened by the Council of Economic Adv isers and the Office of Management and Budget, with active participation and regular input from th e Council on Environmental Quality, National Economic Council, Office of Energy and Climate Chan ge, and Office of Science and Technology Policy. The main objective of this process was to develop a range of SCC values using a defensible set of inpu t assumptions that are grounded in the existing liter ature. In this way, key uncertainties and model differences can more transparently and consistently inform the range of SCC estimates used in the rulemaking process.

The interagency group selected four SCC estimates f or use in regulatory analyses. For 2010, these estimates are $5, $21, $35, and $65 (in 2007 dollar s). The first three estimates are based on the aver age SCC across models and socio-economic and emissions scenarios at the 5, 3, and 2.5 percent discount rates, respectively. The fourth value is included to represent the higher-than-expected impacts from temperature change further out in the tails of the SCC distribution. For this purpose, we use the SCC
value for the 95 th percentile at a 3 percent discount rate. The cent ral value is the average SCC across models at the 3 percent discount rate. For purpose s of capturing the uncertainties involved in regulatory impact analysis, we emphasize the import ance and value of considering the full range. These SCC estimates also grow over time. For instance, t he central value increases to $24 per ton of CO 2 in 2015 and $26 per ton of CO 2 in 2020. See Appendix A for the full range of ann ual SCC estimates from
2010 to 2050.

It is important to emphasize that the interagency p rocess is committed to updating these estimates as the science and economic understanding of climate c hange and its impacts on society improves over time. Specifically, we have set a preliminary goal of revisiting the SCC values within two years or a t such time as substantially updated models become availab le, and to continue to support research in this area. In the meantime, we will continue to explore the issues raised in this document and consider public comments as part of the ongoing interagency process.

II. Social Cost of Carbon Values Used in Past Regulator y Analyses

To date, economic analyses for Federal regulations have used a wide range of values to estimate the benefits associated with reducing carbon dioxide em issions. In the final model year 2011 CAFE rule, t he Department of Transportation (DOT) used both a “dom estic” SCC value of $2 per ton of CO 2 and a “global” SCC value of $33 per ton of CO 2 for 2007 emission reductions (in 2007 dollars), in creasing both values at 2.4 percent per year. It also included a sensitivity analysis at $80 per ton of CO 2 . A domestic SCC value is meant to reflect the value of damages in the United States resulting from a unit change i n carbon dioxide emissions, while a global SCC value is meant to reflect the value of damages worldwide.

A 2008 regulation proposed by DOT assumed a domesti c SCC value of $7 per ton CO 2 (in 2006 dollars) for 2011 emission reductions (with a range of $0-$1 4 for sensitivity analysis), also increasing at 2.4 percent per year. A regulation finalized by DOE in October of 2008 used a domestic SCC range of $0 to $20 per ton CO 2 for 2007 emission reductions (in 2007 dollars). I n addition, EPA’s 2008 Advance Notice of Proposed Rulemaking for Greenhouse Gases identif ied what it described as “very preliminary” SCC estimates subject to revision. EPA’s global mean va lues were $68 and $40 per ton CO 2 for discount rates of approximately 2 percent and 3 percent, respectiv ely (in 2006 dollars for 2007 emissions).4

In 2009, an interagency process was initiated to of fer a preliminary assessment of how best to quantif y the benefits from reducing carbon dioxide emissions . To ensure consistency in how benefits are evaluated across agencies, the Administration sough t to develop a transparent and defensible method, specifically designed for the rulemaking process, t o quantify avoided climate change damages from
reduced CO 2 emissions. The interagency group did not undertak e any original analysis. Instead, it combined SCC estimates from the existing literature to use as interim values until a more comprehensive analysis could be conducted.

The outcome of the preliminary assessment by the i nteragency group was a set of five interim values: global SCC estimates for 2007 (in 2006 dollars) of $55, $33, $19, $10, and $5 per ton of CO 2. The $33 and $5 values represented model-weighted means of the p ublished estimates produced from the most recently available versions of three integrated ass essment models—DICE, PAGE, and FUND—at approximately 3 and 5 percent discount rates. The $ 55 and $10 values were derived by adjusting the published estimates for uncertainty in the discount rate (using factors developed by Newell and Pizer (2003)) at 3 and 5 percent discount rates, respecti vely. The $19 value was chosen as a central value between the $5 and $33 per ton estimates. All of t hese values were assumed to increase at 3 percent annually to represent growth in incremental damages over time as the magnitude of climate change
increases.

These interim values represent the first sustained interagency effort within the U.S. government to develop an SCC for use in regulatory analysis. The results of this preliminary effort were presented in several proposed and final rules and were offered f or public comment in connection with proposed rules, including the joint EPA-DOT fuel economy and CO 2 tailpipe emission proposed rules.

III. Approach and Key Assumptions

Since the release of the interim values, interagenc y group has reconvened on a regular basis to genera te improved SCC estimates. Specifically, the group ha s considered public comments and further explored
the technical literature in relevant fields. This section details the several choices and assumptions that underlie the resulting estimates of the SCC.

It is important to recognize that a number of key u ncertainties remain, and that current SCC estimates should be treated as provisional and revisable sinc e they will evolve with improved scientific and economic understanding. The interagency group also recognizes that the existing models are imperfect and incomplete. The National Academy of Science (2 009) points out that there is tension between the goal of producing quantified estimates of the econo mic damages from an incremental ton of carbon and the limits of existing efforts to model these effec ts. Throughout this document, we highlight a numbe r of concerns and problems that should be addressed b y the research community, including research programs housed in many of the agencies participati ng in the interagency process to estimate the SCC.

The U.S. Government will periodically review and re consider estimates of the SCC used for cost-benefit analyses to reflect increasing knowledge of the sci ence and economics of climate impacts, as well as improvements in modeling. In this context, stateme nts recognizing the limitations of the analysis and calling for further research take on exceptional si gnificance. The interagency group offers the new S CC values with all due humility about the uncertaintie s embedded in them and with a sincere promise to continue work to improve them.5

A. Integrated Assessment Models

We rely on three integrated assessment models (IAMs ) commonly used to estimate the SCC: the FUND, DICE, and PAGE models. 2 These models are frequently cited in the peer-rev iewed literature and used in the IPCC assessment. Each model is given equal wei ght in the SCC values developed through this process, bearing in mind their different limitation s (discussed below).

These models are useful because they combine climat e processes, economic growth, and feedbacks between the climate and the global economy into a s ingle modeling framework. At the same time, they gain this advantage at the expense of a more detail ed representation of the underlying climatic and economic systems. DICE, PAGE, and FUND all take st ylized, reduced-form approaches (see NRC 2009 for a more detailed discussion; see Nordhaus 2008 on th e possible advantages of this approach). Other IAMs may better reflect the complexity of the scien ce in their modeling frameworks but do not link physical impacts to economic damages. There is cur rently a limited amount of research linking climate impacts to economic damages, which makes this exerc ise even more difficult. Underlying the three
IAMs selected for this exercise are a number of sim plifying assumptions and judgments reflecting the various modelers’ best attempts to synthesize the a vailable scientific and economic research characterizing these relationships.

The three IAMs translate emissions into changes in atmospheric greenhouse concentrations, atmospheric concentrations into changes in temperat ure, and changes in temperature into economic damages. The emissions projections used in the mod els are based on specified socio-economic (GDP and population) pathways. These emissions are trans lated into concentrations using the carbon cycle built into each model, and concentrations are trans lated into warming based on each model’s simplified representation of the climate and a key parameter, climate sensitivity. Each model uses a different approach to translate warming into damages. Finally , transforming the stream of economic damages over time into a single value requires judgments ab out how to discount them.

Each model takes a slightly different approach to m odel how changes in emissions result in changes in economic damages. In PAGE, for example, the consump tion-equivalent damages in each period are calculated as a fraction of GDP, depending on the t emperature in that period relative to the preindustrial average temperature in each region. In FUND, damages in each period also depend on the rate of temperature change from the prior period. In DICE, temperature affects both consumption and investment. We describe each model in greater deta il here. In a later section, we discuss key gaps i n how the models account for various scientific and e conomic processes (e.g. the probability of catastrophe, and the ability to adapt to climate ch ange and the physical changes it causes).

2 The DICE (Dynamic Integrated Climate and Economy) m odel by William Nordhaus evolved from a series of e nergy models and was first presented in 1990 (Nordhaus an d Boyer 2000, Nordhaus 2008). The PAGE (Policy Anal ysis of the Greenhouse Effect) model was developed by Chris Hope in 1991 for use by European decision-makers i n assessing the marginal impact of carbon emissions ( Hope 2006, Hope 2008). The FUND (Climate Framework for Uncertainty, Negotiation, and Distribution) model, developed by Richard Tol in the early 1990s, origin ally to study international capital transfers in climate policy. is now widely used to study climate impacts (e.g., Tol 2002a, Tol 2002b, Anthoff et al. 2009, Tol 2009).6

The parameters and assumptions embedded in the thre e models vary widely. A key objective of the interagency process was to enable a consistent expl oration of the three models while respecting the different approaches to quantifying damages taken b y the key modelers in the field. An extensive
review of the literature was conducted to select th ree sets of input parameters for these models: climate sensitivity, socio-economic and emissions t rajectories, and discount rates. A probability distribution for climate sensitivity was specified as an input into all three models. In addition, th e interagency group used a range of scenarios for the socio-economic parameters and a range of values
for the discount rate. All other model features we re left unchanged, relying on the model developers’ best estimates and judgments. In DICE, these param eters are handled deterministically and represented by fixed constants; in PAGE, most parameters are re presented by probability distributions. FUND was also run in a mode in which parameters were treated probabilistically.

The sensitivity of the results to other aspects of the models (e.g. the carbon cycle or damage functio n) is also important to explore in the context of future revisions to the SCC but has not been incorporated
into these estimates. Areas for future research ar e highlighted at the end of this document.

**The DICE Model**

The DICE model is an optimal growth model based on a global production function with an extra stock variable (atmospheric carbon dioxide concentrations ). Emission reductions are treated as analogous to investment in “natural capital.” By investing in n atural capital today through reductions in emission s— implying reduced consumption—harmful effects of cli mate change can be avoided and future consumption thereby increased.

For purposes of estimating the SCC, carbon dioxide emissions are a function of global GDP and the carbon intensity of economic output, with the latte r declining over time due to technological progress

. The DICE damage function links global average tempe rature to the overall impact on the world economy. It varies quadratically with temperature change to capture the more rapid increase in damages expected to occur under more extreme climat e change, and is calibrated to include the effects of warming on the production of market and nonmarke t goods and services. It incorporates impacts on agriculture, coastal areas (due to sea level rise), “other vulnerable market sectors” (based primarily on changes in energy use), human health (based on clim ate-related diseases, such as malaria and dengue fever, and pollution), non-market amenities (based on outdoor recreation), and human settlements and ecosystems. The DICE damage function also include s the expected value of damages associated with low probability, high impact “catastrophic” climate change. This last component is calibrated based o n a survey of experts (Nordhaus 1994). The expected value of these impacts is then added t o the other market and non-market impacts mentioned above.

No structural components of the DICE model represen t adaptation explicitly, though it is included implicitly through the choice of studies used to ca librate the aggregate damage function. For exampl e, its agricultural impact estimates assume that farme rs can adjust land use decisions in response to changing climate conditions, and its health impact estimates assume improvements in healthcare over time. In addition, the small impacts on forestry, w ater systems, construction, fisheries, and outdoor recreation imply optimistic and costless adaptation in these sectors (Nordhaus and Boyer, 2000; Warren7

et al., 2006). Costs of resettlement due to sea le vel rise are incorporated into damage estimates, bu t their magnitude is not clearly reported. Mastrandr ea’s (2009) review concludes that “in general, DICE assumes very effective adaptation, and largely igno res adaptation costs."

Note that the damage function in DICE has a somewha t different meaning from the damage functions in FUND and PAGE. Because GDP is endogenous in DICE an d because damages in a given year reduce investment in that year, damages propagate forward in time and reduce GDP in future years. In contrast, GDP is exogenous in FUND and PAGE, so dam ages in any given year do not propagate forward. 3

**The PAGE Model**

PAGE2002 (version 1.4epm) treats GDP growth as exog enous. It divides impacts into economic, noneconomic, and catastrophic categories and calculate s these impacts separately for eight geographic regions. Damages in each region are expressed as a fraction of output, where the fraction lost depend s on the temperature change in each region. Damages are expressed as power functions of temperature change. The exponents of the damage function are t he same in all regions but are treated as uncertain

, with values ranging from 1 to 3 (instead of being f ixed at 2 as in DICE).

PAGE2002 includes the consequences of catastrophic events in a separate damage sub-function. Unlike DICE, PAGE2002 models these events probabilisticall y. The probability of a “discontinuity” (i.e., a catastrophic event) is assumed to increase with tem perature above a specified threshold. The threshol d temperature, the rate at which the probability of e xperiencing a discontinuity increases above the threshold, and the magnitude of the resulting catas trophe are all modeled probabilistically.

Adaptation is explicitly included in PAGE. Impacts are assumed to occur for temperature increases above some tolerable level (2°C for developed count ries and 0°C for developing countries for economic impacts, and 0°C for all regions for non-economic i mpacts), but adaptation is assumed to reduce these impacts. Default values in PAGE2002 assume that th e developed countries can ultimately eliminate up to 90 percent of all economic impacts beyond the to lerable 2°C increase and that developing countries can eventually eliminate 50 percent of their econom ic impacts. All regions are assumed to be able to mitigate 25 percent of the non-economic impacts thr ough adaptation (Hope 2006).

**The FUND Model**

Like PAGE, the FUND model treats GDP growth as exog enous. It includes separately calibrated damage functions for eight market and nonmarket sectors: a griculture, forestry, water, energy (based on heati ng and cooling demand), sea level rise (based on the v alue of land lost and the cost of protection),

3 Using the default assumptions in DICE 2007, this e ffect generates an approximately 25 percent increas e in the SCC relative to damages calculated by fixing GDP. I n DICE2007, the time path of GDP is endogenous. Sp ecifically, the path of GDP depends on the rate of saving and l evel of abatement in each period chosen by the opti mizing representative agent in the model. We made two mod ifications to DICE to make it consistent with EMF G DP trajectories (see next section): we assumed a fixed rate of savings of 20%, and we re-calibrated the e xogenous path of total factor productivity so that DICE woul d produce GDP projections in the absence of warming that exactly matched the EMF scenarios.8

ecosystems, human health (diarrhea, vector-borne di seases, and cardiovascular and respiratory mortality), and extreme weather. Each impact secto r has a different functional form, and is calculate d separately for sixteen geographic regions. In some impact sectors, the fraction of output lost or gai ned due to climate change depends not only on the absol ute temperature change but also on the rate of temperature change and level of regional income. 4 In the forestry and agricultural sectors, economi c damages also depend on CO 2 concentrations.

Tol (2009) discusses impacts not included in FUND, noting that many are likely to have a relatively sm all effect on damage estimates (both positive and negat ive). However, he characterizes several omitted impacts as “big unknowns”: for instance, extreme cl imate scenarios, biodiversity loss, and effects on economic development and political violence. With regard to potentially catastrophic events, he notes

, “Exactly what would cause these sorts of changes or what effects they would have are not wellunderstood, although the chance of any one of them happening seems low. But they do have the potential to happen relatively quickly, and if they did, the costs could be substantial. Only a few s tudies of climate change have examined these issues.”

Adaptation is included both implicitly and explicit ly in FUND. Explicit adaptation is seen in the agriculture and sea level rise sectors. Implicit a daptation is included in sectors such as energy and human health, where wealthier populations are assum ed to be less vulnerable to climate impacts. For example, the damages to agriculture are the sum of three effects: (1) those due to the rate of temperature change (damages are always positive); ( 2) those due to the level of temperature change (damages can be positive or negative depending on r egion and temperature); and (3) those from CO 2 fertilization (damages are generally negative but d iminishing to zero).

Adaptation is incorporated into FUND by allowing da mages to be smaller if climate change happens more slowly. The combined effect of CO 2 fertilization in the agricultural sector, positive impacts to some regions from higher temperatures, and sufficiently slow increases in temperature across these sectors can result in negative economic damages from climat e change.

**Damage Functions**

To generate revised SCC values, we rely on the IAM modelers’ current best judgments of how to represent the effects of climate change (represente d by the increase in global-average surface temperature) on the consumption-equivalent value of both market and non-market goods (represented as a fraction of global GDP). We recognize that th ese representations are incomplete and highly uncertain. But given the paucity of data linking t he physical impacts to economic damages, we were no t able to identify a better way to translate changes in climate into net economic damages, short of launching our own research program.

4 In the deterministic version of FUND, the majority of damages are attributable to increased air condit ioning demand, while reduced cold stress in Europe, North America, and Central and East Asia results in healt h benefits in those regions at low to moderate levels of warming (Warren et al., 2006).9

Figure 1A: Annual Consumption Loss as a Fraction of Global GDP in 2100 Due to an Increase in Annual Global Temperature in the DICE, FUND, and PAGE mode ls 5

The damage functions for the three IAMs are present ed in Figures 1A and 1B, using the modeler’s default scenarios and mean input assumptions. Ther e are significant differences between the three models both at lower (figure 1B) and higher (figure 1A) increases in global-average temperature.

The lack of agreement among the models at lower tem perature increases is underscored by the fact that the damages from FUND are well below the 5 th percentile estimated by PAGE, while the damages estimated by DICE are roughly equal to the 95 th percentile estimated by PAGE. This is significant because at higher discount rates we expect that a g reater proportion of the SCC value is due to damage s in years with lower temperature increases. For exa mple, when the discount rate is 2.5 percent, about 45 percent of the 2010 SCC value in DICE is due to damages that occur in years when the temperature is less than or equal to 3 °C. This increases to appro ximately 55 percent and 80 percent at discount rate s of 3 and 5 percent, respectively.

These differences underscore the need for a thoroug h review of damage functions—in particular, how the models incorporate adaptation, technological ch ange, and catastrophic damages. Gaps in the literature make modifying these aspects of the mode ls challenging, which highlights the need for additional research. As knowledge improves, the Fe deral government is committed to exploring how these (and other) models can be modified to incorpo rate more accurate estimates of damages.

5 The x-axis represents increases in annual, rather t han equilibrium, temperature, while the y-axis repr esents the annual stream of benefits as a share of global GDP. Each specific combination of climate sensitivity, socioeconomic, and emissions parameters will produce a d ifferent realization of damages for each IAM. The damage functions represented in Figures 1A and 1B are the outcome of default assumptions. For instance, unde r alternate assumptions, the damages from FUND may cross from n egative to positive at less than or greater than 3 °C.10

Figure 1B: Annual Consumption Loss for Lower Temper ature Changes in DICE, FUND, and PAGE

B. Global versus Domestic Measures of SCC

Because of the distinctive nature of the climate ch ange problem, we center our current attention on a global measure of SCC. This approach is the same a s that taken for the interim values, but it otherwi se represents a departure from past practices, which t ended to put greater emphasis on a domestic measure of SCC (limited to impacts of climate chang e experienced within U.S. borders). As a matter of law, consideration of both global and domestic valu es is generally permissible; the relevant statutory provisions are usually ambiguous and allow selectio n of either measure. 6

**Global SCC**

Under current OMB guidance contained in Circular A- 4, analysis of economically significant proposed and final regulations from the domestic perspective is required, while analysis from the international perspective is optional. However, the climate chan ge problem is highly unusual in at least two respec ts. First, it involves a global externality: emissions of most greenhouse gases contribute to damages arou nd 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 S tates alone cannot solve. Even if the United State s 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

6 It is true that federal statutes are presumed not to have extraterritorial effect, in part to ensure that the laws of the United States respect the interests of foreign sovereigns. But use of a global measure for the SCC does not give extraterritorial effect to federal law and hence do es not intrude on such interests.11

significant changes in the global climate are to be avoided. Emphasizing the need for a global soluti on to a global problem, the United States has been active ly 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 c onsiderations are taken as a whole, the interagency group concluded that a global measure of the benefi ts from reducing U.S. emissions is preferable.

When quantifying the damages associated with a chan ge in emissions, a number of analysts (e.g., Anthoff, et al. 2009a) employ “equity weighting” to aggregate changes in consumption across regions. This weighting takes into account the relative redu ctions in wealth in different regions of the world. A per-capita loss of $500 in GDP, for instance, is we ighted more heavily in a country with a per-capita GDP of $2,000 than in one with a per-capita GDP of $40, 000. The main argument for this approach is that a loss of $500 in a poor country causes a greater red uction in utility or welfare than does the same los s in a wealthy nation. Notwithstanding the theoretical claims on behalf of equity weighting, the interagen cy group concluded that this approach would not be app ropriate for estimating a SCC value used in domestic regulatory analysis. 7 For this reason, the group concluded that using t he global (rather than domestic) value, without equity weighting, is the a ppropriate approach.

**Domestic SCC**

As an empirical matter, the development of a domest ic SCC is greatly complicated by the relatively few region- or country-specific estimates of the SCC in the literature. One potential source of estimates comes from the FUND model. The resulting estimates suggest that the ratio of domestic to global benefits of emission reductions varies with key par ameter assumptions. For example, with a 2.5 or 3 percent discount rate, the U.S. benefit is about 7- 10 percent of the global benefit, on average, acros s the scenarios analyzed. Alternatively, if the fractio n of GDP lost due to climate change is assumed to b e similar across countries, the domestic benefit woul d be proportional to the U.S. share of global GDP, which is currently about 23 percent. 8

On the basis of this evidence, the interagency work group determined that a range of values from 7 to 2 3 percent should be used to adjust the global SCC to calculate domestic effects. Reported domestic value s should use this range. It is recognized that these values are approximate, provisional, and highly speculative. There is no a priori reason why domest ic benefits should be a constant fraction of net gl obal damages over time. Further, FUND does not account for how damages in other regions could affect the United States (e.g., global migration, economic and political destabilization). If more accurate meth ods for calculating the domestic SCC become available, the Federal government will examine these to determine whether to update its approach.

7 It is plausible that a loss of $X inflicts more ser ious harm on a poor nation than on a wealthy one, b ut development of the appropriate "equity weight" is c hallenging. Emissions reductions also impose costs , and hence a full account would have to consider that a given cost of emissions reductions imposes a greater util ity or welfare loss on a poor nation than on a wealthy one. Even i f equity weighting—for both the costs and benefits of emissions reductions—is appropriate when considering the util ity or welfare effects of international action, the interagency group concluded that it should not be used in devel oping an SCC for use in regulatory policy at this t ime.
8 Based on 2008 GDP (in current US dollars) from the **World Bank Development Indicators Report**

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C. Valuing Non-CO 2 Emissions

While CO 2 is the most prevalent greenhouse gas emitted into the atmosphere, the U.S. included five other greenhouse gases in its recent endangerment f inding: methane, nitrous oxide, hydrofluorocarbons, perfluorocarbons, and sulfur he xafluoride. The climate impact of these gases is commonly discussed in terms of their 100-year globa l warming potential (GWP). GWP measures the ability of different gases to trap heat in the atmo sphere (i.e., radiative forcing per unit of mass) o ver a particular timeframe relative to CO 2 . However, because these gases differ in both radi ative forcing and atmospheric lifetimes, their relative damages are n ot constant over time. For example, because methane has a short lifetime, its impacts occur pri marily in the near term and thus are not discounted as heavily as those caused by longer-lived gases. Imp acts other than temperature change also vary across gases in ways that are not captured by GWP. For in stance, CO 2 emissions, unlike methane and other greenhouse gases, contribute to ocean acidification . Likewise, damages from methane emissions are not offset by the positive effect of CO 2 fertilization. Thus, transforming gases into CO 2 -equivalents using GWP, and then multiplying the carbon-equivalents by the SCC, would not result in accurate estimates of
the social costs of non-CO 2 gases.

In light of these limitations, and the significant contributions of non-CO 2 emissions to climate change, further research is required to link non-CO 2 emissions to economic impacts. Such work would fe ed into efforts to develop a monetized value of reductions in non-CO 2 greenhouse gas emissions. As part of ongoing work to further improve the SCC estimates, the interagency group hopes to develop methods to value these other greenhouse gases. The goal is to develop these estimates by the time we issue
revised SCC estimates for carbon dioxide emissions.

D. Equilibrium Climate Sensitivity

Equilibrium climate sensitivity (ECS) is a key inpu t parameter for the DICE, PAGE, and FUND models. 9 It is defined as the long-term increase in the annual global-average surface temperature from a doubling of atmospheric CO 2 concentration relative to pre-industrial levels (o r stabilization at a concentration of approximately 550 parts per million (ppm)). Uncerta inties in this important parameter have received substantial attention in the peer-reviewed literatu re.

The most authoritative statement about equilibrium climate sensitivity appears in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC):

**Basing our assessment on a combination of several i ndependent lines of evidence...including**  **observed climate change and the strength of known f eedbacks simulated in [global climate models],**  **we conclude that the global mean equilibrium warmin g for doubling CO**  **2 , or ‘equilibrium climate** 

9 The equilibrium climate sensitivity includes the r esponse of the climate system to increased greenhou se gas concentrations over the short to medium term (up to 100-200 years), but it does not include long-term feedback effects due to possible large-scale changes in ice sheets or the biosphere, which occur on a time scal e of many hundreds to thousands of years (e.g. Hansen et al. 2007).13

**sensitivity’, is likely to lie in the range 2 °C to 4.5 °C, with a most likely value of about 3 °C.**  **Equilibrium climate sensitivity is very likely larg er than 1.5 °C.**  10

**For fundamental physical reasons as well as data li mitations, values substantially higher than 4.5 °C**  **still cannot be excluded, but agreement with observ ations and proxy data is generally worse for**  **those high values than for values in the 2 °C to 4. 5 °C range.**  (Meehl et al., 2007, p 799)

After consulting with several lead authors of this chapter of the IPCC report, the interagency workgro up selected four candidate probability distributions a nd calibrated them to be consistent with the above statement: Roe and Baker (2007), log-normal, gamma, and Weibull. Table 1 included below gives summary statistics for the four calibrated distribu tions.

Table 1: Summary Statistics for Four Calibrated Cli mate Sensitivity Distributions Roe & Baker Log-normal Gamma Weibull Pr(ECS < 1.5°C) 0.013 0.050 0.070 0.102 Pr(2°C < ECS < 4.5°C) 0.667 0.667 0.667 0.667
5 th percentile 1.72 1.49 1.37 1.13

10 th percentile 1.91 1.74 1.65 1.48
Mode 2.34 2.52 2.65 2.90 Median (50 th percentile) 3.00 3.00 3.00 3.00
Mean 3.50 3.28 3.19 3.07
90 th percentile 5.86 5.14 4.93 4.69

95 th percentile 7.14 5.97 5.59 5.17

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

(1) a median equal to 3°C, to reflect the judgment of “ a most likely value of about 3 °C”; 11 (2) two-thirds probability that the equilibrium climate sensitivity lies between 2 and 4.5 °C; and (3) zero probability that it is less than 0°C or greate r than 10°C (see Hegerl et al. 2006, p. 721).

We selected the calibrated Roe and Baker distributi on from the four candidates for two reasons. First

, the Roe and Baker distribution is the only one of t he four that is based on a theoretical understandin g of the response of the climate system to increased gre enhouse gas concentrations (Roe and Baker 2007,

10 This is in accord with the judgment that it “is likely to l ie in the range 2 °C to 4.5 °C” and the IPCC defini tion of “likely” as greater than 66 percent probability (Le Treut et al.2007). “Very likely” indicates a greate r than 90 percent probability.

11 Strictly speaking, “most likely” refers to the mod e of a distribution rather than the median, but com mon usage would allow the mode, median, or mean to serve as c andidates for the central or “most likely” value an d the IPCC report is not specific on this point. For the dist ributions we considered, the median was between the mode and the mean. For the Roe and Baker distribution, setti ng the median equal to 3°C, rather than the mode or mean, gave a 95 th percentile that is more consistent with IPCC judgm ents and the literature. For example, setting the mean and mode equal to 3°C produced 95 th percentiles of 5.6 and 8.6 °C, respectively, which are in the lower and upper end of the range in the literature. Finally, the median is closer to 3°C than is the mode for t he truncated distributions selected by the IPCC (Hegerl, et al., 2006); the average median is 3.1 °C and the averag e mode is 2.3 °C, which is most consistent with a Roe and Baker d istribution with the median set equal to 3 °C.14

Roe 2008). In contrast, the other three distributi ons are mathematical functions that are arbitrarily chosen based on simplicity, convenience, and genera l shape. The Roe and Baker distribution results from three assumptions about climate response: (1) absent feedback effects, the equilibrium climate sensitivity is equal to 1.2 °C; (2) feedback factor s are proportional to the change in surface tempera ture; and (3) uncertainties in feedback factors are norma lly distributed. There is widespread agreement on the first point and the second and third points are common assumptions.

Second, the calibrated Roe and Baker distribution b etter reflects the IPCC judgment that “values substantially higher than 4.5°C still cannot be exc luded.” Although the IPCC made no quantitative judgment, the 95 th percentile of the calibrated Roe & Baker distribut ion (7.1 °C) is much closer to the mean and the median (7.2 °C) of the 95 th percentiles of 21 previous studies summarized by N ewbold and Daigneault (2009). It is also closer to the mean ( 7.5 °C) and median (7.9 °C) of the nine truncated distributions examined by the IPCC (Hegerl, et al., 2006) than are the 95 th percentiles of the three other calibrated distributions (5.2-6.0 °C).

Finally, we note the IPCC judgment that the equilib rium climate sensitivity “is very likely larger tha n 1.5°C.” Although the calibrated Roe & Baker distrib ution, for which the probability of equilibrium cli mate sensitivity being greater than 1.5°C is almost 99 p ercent, is not inconsistent with the IPCC definitio n of “very likely” as “greater than 90 percent probabili ty,” it reflects a greater degree of certainty abou t very low values of ECS than was expressed by the IPCC.

Figure 2: Estimates of the Probability Density Func tion for Equilibrium Climate Sensitivity (°C)

Calibrated Roe & Baker

To show how the calibrated Roe and Baker distributi on compares to different estimates of the probability distribution function of equilibrium cl imate sensitivity in the empirical literature, Figu re 2 (below) overlays it on Figure 9.20 from the IPCC Fo urth Assessment Report. These functions are scaled15

to integrate to unity between 0 °C and 10 °C. The h orizontal bars show the respective 5 percent to 95 percent ranges; dots indicate the median estimate. 12

E. Socio-Economic and Emissions Trajectories

Another key issue considered by the interagency gro up is how to select the set of socio-economic and emissions parameters for use in PAGE, DICE, and FUN D. Socio-economic pathways are closely tied to climate damages because, all else equal, more and w ealthier people tend to emit more greenhouse gases and also have a higher (absolute) willingness to pay to avoid climate disruptions. For this rea son, we consider how to model several input parameters i n tandem: GDP, population, CO 2 emissions, and
non-CO 2 radiative forcing. A wide variety of scenarios ha ve been developed and used for climate change policy simulations (e.g., SRES 2000, CCSP 2007, EMF 2009). In determining which scenarios are appropriate for inclusion, we aimed to select scena rios that span most of the plausible ranges of
outcomes for these variables.

To accomplish this task in a transparent way, we de cided to rely on the recent Stanford Energy Modelin g Forum exercise, EMF-22. EMF-22 uses ten well-recog nized models to evaluate substantial, coordinated global action to meet specific stabilization target s. A key advantage of relying on these data is tha t GDP, population, and emission trajectories are internall y consistent for each model and scenario evaluated. The EMF-22 modeling effort also is preferable to th e IPCC SRES due to their age (SRES were developed i n 1997) and the fact that 3 of 4 of the SRES scenario s are now extreme outliers in one or more variables

. Although the EMF-22 scenarios have not undergone th e same level of scrutiny as the SRES scenarios, they are recent, peer-reviewed, published, and publ icly available.

To estimate the SCC for use in evaluating domestic policies that will have a small effect on global cumulative emissions, we use socio-economic and emi ssion trajectories that span a range of plausible scenarios. Five trajectories were selected from EM F-22 (see Table 2 below). Four of these represent potential business-as-usual (BAU) growth in populat ion, wealth, and emissions and are associated with
CO 2 (only) concentrations ranging from 612 to 889 ppm in 2100. One represents an emissions pathway that achieves stabilization at 550 ppm CO 2 e (i.e., CO 2 -only concentrations of 425 – 484 ppm or a radiative forcing of 3.7 W/m 2 ) in 2100, a lower-than-BAU trajectory. 13 Out of the 10 models included in the EMF-22 exercise, we selected the trajectories u sed by MiniCAM, MESSAGE, IMAGE, and the optimistic scenario from MERGE. For the BAU pathwa ys, we used the GDP, population, and emission trajectories from each of these four models. For th e 550 ppm CO 2 e scenario, we averaged the GDP, population, and emission trajectories implied by th ese same four models.

12 The estimates based on instrumental data are from A ndronova and Schlesinger (2001), Forest et al. (200 2; dashed line, anthropogenic forcings only), Forest e t al. (2006; solid line, anthropogenic and natural forcings), Gregory et al. (2002a), Knutti et al. (2002), Frame et al. (2005), and Forster and Gregory (2006). Heg erl et al. (2006) are based on multiple palaeoclimatic reconstruction s of north hemisphere mean temperatures over the la st 700 years. Also shown are the 5-95 percent approximate ranges for two estimates from the last glacial max imum (dashed, Annan et al. 2005; solid, Schneider von De imling et al. 2006), which are based on models with different structural properties.

13 Such an emissions path would be consistent with wi despread action by countries to mitigate GHG emissi ons, though it could also result from technological adva nces. It was chosen because it represents the most stringent case analyzed by the EMF-22 where all the models co nverge: a 550 ppm, not to exceed, full participatio n scenario.16

Table 2: Socioeconomic and Emissions Projections fr om Select EMF-22 Reference Scenarios

Reference Fossil and Industrial CO 2 Emissions (GtCO 2 /yr)
EMF

– 22 Based Scenarios 2000 2010 2020 2030 2050 2100 IMAGE 26.6 31.9 36.9 40.0 45.3 60.1 MERGE Optimistic 24.6 31.5 37.6 45.1 66.5 117.9 MESSAGE 26.8 29.2 37.6 42.1 43.5 42.7 MiniCAM 26.5 31.8 38.0 45.1 57.8 80.5 550 ppm average 26.2 31.1 33.2 32.4 20.0 12.8

Reference GDP (using market exchange rates in trill ion 2005$) 14

EMF

– 22 Based Scenarios 2000 2010 2020 2030 2050 2100 IMAGE 38.6 53.0 73.5 97.2 156.3 396.6 MERGE Optimistic 36.3 45.9 59.7 76.8 122.7 268.0 MESSAGE 38.1 52.3 69.4 91.4 153.7 334.9 MiniCAM 36.1 47.4 60.8 78.9 125.7 369.5 550 ppm average 37.1 49.6 65.6 85.5 137.4 337.9

Global Population (billions)

EMF

– 22 Based Scenarios 2000 2010 2020 2030 2050 2100 IMAGE 6.1 6.9 7.6 8.2 9.0 9.1 MERGE Optimistic 6.0 6.8 7.5 8.2 9.0 9.7 MESSAGE 6.1 6.9 7.7 8.4 9.4 10.4 MiniCAM 6.0 6.8 7.5 8.1 8.8 8.7 550 ppm average 6.1 6.8 7.6 8.2 8.7 9.1

We explore how sensitive the SCC is to various assu mptions about how the future will evolve without prejudging what is likely to occur. The interagenc y group considered formally assigning probability weights to different states of the world, but this proved challenging to do in an analytically rigorou s way given the dearth of information on the likelihood o f a full range of future socio-economic pathways.

There are a number of caveats. First, EMF BAU sce narios represent the modelers’ judgment of the most likely pathway absent mitigation policies to reduce greenhouse gas emissions, rather than the wider range of possible outcomes. Nevertheless, these vi ews of the most likely outcome span a wide range,

14 While the EMF-22 models used market exchange rates (MER) to calculate global GDP, it is also possible to use purchasing power parity (PPP). PPP takes into acco unt the different price levels across countries, so it more accurately describes relative standards of living a cross countries. MERs tend to make low-income coun tries appear poorer than they actually are. Because many models assume convergence in per capita income over time, use of MER-adjusted GDP gives rise to projections of highe r economic growth in low income countries. There i s an ongoing debate about how much this will affect esti mated climate impacts. Critics of the use of MER a rgue that it leads to overstated economic growth and hence a sig nificant upward bias in projections of greenhouse g as emissions, and unrealistically high future temperat ures (e.g., Castles and Henderson 2003). Others ar gue that convergence of the emissions-intensity gap across c ountries at least partially offset the overstated i ncome gap so that differences in exchange rates have less of an effect on emissions (Holtsmark and Alfsen, 2005; To l, 2006). Nordhaus (2007b) argues that the ideal approach is to use superlative PPP accounts (i.e., using cross- sectional PPP measures for relative incomes and outputs and natio nal accounts price and quantity indexes for time-se ries extrapolations). However, he notes that it importan t to keep this debate in perspective; it is by no m eans clear that exchange-rate-conversion issues are as important as uncertainties about population, technological chan ge, or the many geophysical uncertainties.17

from the more optimistic (e.g. abundant low-cost, l ow-carbon energy) to more pessimistic (e.g. constraints on the availability of nuclear and rene wables). 15 Second, the socio-economic trajectories associated with a 550 ppm CO 2 e concentration scenario are not derived from an as sessment of what policy is optimal from a benefit-cost standpoint. Rather, it is indicative of one possible future out come. The emission trajectories underlying some BAU scena rios (e.g. MESSAGE’s 612 ppm) also are consistent with some modest policy action to address climate c hange. 16 We chose not to include socio-economic trajectories that achieve even lower GHG concentrat ions at this time, given the difficulty many models had in converging to meet these targets.

For comparison purposes, the Energy Information Age ncy in its 2009 Annual Energy Outlook projected that global carbon dioxide emissions will grow to 3 0.8, 35.6, and 40.4 gigatons in 2010, 2020, and 203 0, respectively, while world GDP is projected to be $5 1.8, $71.0 and $93.9 trillion (in 2005 dollars usin g market exchange rates) in 2010, 2020, and 2030, res pectively. These projections are consistent with one or more EMF-22 scenarios. Likewise, the United Nations’ 2008 Population Prospect projects population will grow from 6.1 billion people in 200 0 to 9.1 billion people in 2050, which is close to the population trajectories for the IMAGE, MiniCAM, and MERGE models.

In addition to fossil and industrial CO 2 emissions, each EMF scenario provides projections of methane, nitrous oxide, fluorinated greenhouse gases, and ne t land use CO 2 emissions out to 2100. These assumptions also are used in the three models while retaining the default radiative forcings due to ot her factors (e.g. aerosols and other gases). See the A ppendix for greater detail.

F. Discount Rate

The choice of a discount rate, especially over long periods of time, raises highly contested and exceedingly difficult questions of science, economi cs, philosophy, and law. Although it is well understood that the discount rate has a large influ ence on the current value of future damages, there is
no consensus about what rates to use in this contex t. Because carbon dioxide emissions are long-lived

, subsequent damages occur over many years. In calcu lating the SCC, we first estimate the future damages to agriculture, human health, and other mar ket and non-market sectors from an additional unit of carbon dioxide emitted in a particular year in terms of reduced consumption (or consumption equivalents) due to the impacts of elevated tempera tures, as represented in each of the three IAMs. Then we discount the stream of future damages to it s present value in the year when the additional uni t of emissions was released using the selected discou nt rate, which is intended to reflect society's marginal rate of substitution between consumption i n different time periods.

For rules with both intra- and intergenerational ef fects, agencies traditionally employ constant disco unt rates of both 3 percent and 7 percent in accordance with OMB Circular A-4. As Circular A-4 acknowledges, however, the choice of discount rate for intergenerational problems raises distinctive

15 For instance, in the MESSAGE model’s reference cas e total primary energy production from nuclear, bio mass, and non-biomass renewables is projected to increase from about 15 percent of total primary energy in 2 000 to 54 percent in 2100. In comparison, the MiniCAM refere nce case shows 10 percent in 2000 and 21 percent in 2100.
16 For example, MiniCAM projects if all non-US OECD co untries reduce CO 2 emissions to 83 percent below 2005 levels by 2050 (per the G-8 agreement) but all othe r countries continue along a BAU path CO 2 concentrations in 2100 would drop from 794 ppmv in its reference case to 762 ppmv.18

problems and presents considerable challenges. Aft er reviewing those challenges, Circular A-4 states, “If your rule will have important intergenerational ben efits or costs you might consider a further sensiti vity analysis using a lower but positive discount rate i n addition to calculating net benefits using discou nt rates of 3 and 7 percent.” For the specific purpos e of developing the SCC, we adapt and revise that approach here.

Arrow et al. (1996) outlined two main approaches to determine the discount rate for climate change analysis, which they labeled “descriptive” and “pre scriptive.” The descriptive approach reflects a positive (non-normative) perspective based on obser vations of people’s actual choices—e.g., savings versus consumption decisions over time, and allocat ions of savings among more and less risky investments. Advocates of this approach generally call for inferring the discount rate from market ra tes of return “because of a lack of justification for c hoosing a social welfare function that is any diffe rent than what decision makers [individuals] actually us e” (Arrow et al. 1996).

One theoretical foundation for the cost-benefit ana lyses in which the social cost of carbon will be us ed— the Kaldor-Hicks potential-compensation test—also s uggests that market rates should be used to discount future benefits and costs, because it is t he market interest rate that would govern the retur ns potentially set aside today to compensate future in dividuals for climate damages that they bear (e.g., Just et al. 2004). As some have noted, the word “potentially” is an i mportant qualification; there is no assurance that such returns will actually be set as ide to provide compensation, and the very idea of compensation is difficult to define in the intergen erational context. On the other hand, societies provide compensation to future generations through investments in human capital and the resulting increase in knowledge, as well as infrastructure an d other physical capital.

The prescriptive approach specifies a social welfar e function that formalizes the normative judgments that the decision-maker wants explicitly to incorpo rate into the policy evaluation—e.g., how interpersonal comparisons of utility should be made, and how the welfare of future generations should be weighed against that of the present generation. Ra msey (1928), for example, has argued that it is “ethically indefensible” to apply a positive pure r ate of time preference to discount values across generations, and many agree with this view.

Other concerns also motivate making adjustments to descriptive discount rates. In particular, it has been noted that the preferences of future generatio ns with regard to consumption versus environmental amenities may not be the same as thos e today, making the current market rate on consumption an inappropriate metric by which to dis count future climate-related damages. Others argue that the discount rate should be below market rates to correct for market distortions and uncertainties or inefficiencies in intergenerationa l transfers of wealth, which in the Kaldor-Hicks lo gic are presumed to compensate future generations for d amage (a potentially controversial assumption, as noted above) (Arrow et al. 1996, Weitzman 1999).

Further, a legitimate concern about both descriptiv e and prescriptive approaches is that they tend to obscure important heterogeneity in the population. The utility function that underlies the prescripti ve approach assumes a representative agent with perfec t foresight and no credit constraints. This is an artificial rendering of the real world that misses many of the frictions that characterize individuals ’ lives19

and indeed the available descriptive evidence suppo rts this. For instance, many individuals smooth consumption by borrowing with credit cards that hav e relatively high rates. Some are unable to access traditional credit markets and rely on payday lendi ng operations or other high cost forms of smoothing consumption. Whether one puts greater weight on th e prescriptive or descriptive approach, the high
interest rates that credit-constrained individuals accept suggest that some account should be given to the discount rates revealed by their behavior.

We draw on both approaches but rely primarily on th e descriptive approach to inform the choice of discount rate. With recognition of its limitations , we find this approach to be the most defensible a nd transparent given its consistency with the standard contemporary theoretical foundations of benefitcost analysis and with the approach required by OMB ’s existing guidance. The logic of this framework also suggests that market rates should be used for discounting future consumption-equivalent damages. Regardless of the theoretical approach used to deri ve the appropriate discount rate(s), we note the inherent conceptual and practical difficulties of a dequately capturing consumption trade-offs over man y decades or even centuries. While relying primarily on the descriptive approach in selecting specific discount rates, the interagency group has been keen ly aware of the deeply normative dimensions of both the debate over discounting in the intergenera tional context and the consequences of selecting
one discount rate over another.

**Historically Observed Interest Rates**

In a market with no distortions, the return to savi ngs would equal the private return on investment, a nd the market rate of interest would be the appropriat e choice for the social discount rate. In the real world risk, taxes, and other market imperfections d rive a wedge between the risk-free rate of return o n capital and the consumption rate of interest. Thus , the literature recognizes two conceptual discount concepts—the consumption rate of interest and the o pportunity cost of capital.

According to OMB’s Circular A-4, it is appropriate to use the rate of return on capital when a regulat ion is expected to displace or alter the use of capital in the private sector. In this case, OMB recommen ds Agencies use a discount rate of 7 percent. When reg ulation is expected to primarily affect private consumption—for instance, via higher prices for goo ds and services—a lower discount rate of 3 percent is appropriate to reflect how private individuals t rade-off current and future consumption.

The interagency group examined the economics litera ture and concluded that the consumption rate of interest is the correct concept to use in evaluatin g the benefits and costs of a marginal change in ca rbon emissions (see Lind 1990, Arrow et al 1996, and Arr ow 2000). The consumption rate of interest also is appropriate when the impacts of a regulation are me asured in consumption (-equivalent) units, as is done in the three integrated assessment models used for estimating the SCC.

Individuals use a variety of savings instruments th at vary with risk level, time horizon, and tax characteristics. The standard analytic framework u sed to develop intuition about the discount rate typically assumes a representative agent with perfe ct foresight and no credit constraints. The risk-f ree rate is appropriate for discounting certain future benefits or costs, but the benefits calculated by I AMs are uncertain. To use the risk-free rate to discou nt uncertain benefits, these benefits first must be20

transformed into "certainty equivalents," that is t he maximum certain amount that we would exchange for the uncertain amount. However, the calculation of the certainty-equivalent requires first estimat ing the correlation between the benefits of the policy and baseline consumption.

If the IAM projections of future impacts represent expected values (not certainty-equivalent values), then the appropriate discount rate generally does n ot equal the risk-free rate. If the benefits of th e policy tend to be high in those states of the world in which consumption is low, then the certaintyequivalent benefits will be higher than the expecte d benefits (and vice versa). Since many (though not necessarily all) of the important impacts of climat e change will flow through market sectors such as agriculture and energy, and since willingness to pa y for environmental protections typically increases with income, we might expect a positive (though not necessarily perfect) correlation between the net benefits from climate policies and market returns. This line of reasoning suggests that the proper
discount rate would exceed the riskless rate. Alte rnatively, a negative correlation between the retur ns to climate policies and market returns would imply that a discount rate below the riskless rate is appropriate.

This discussion suggests that both the post-tax ris kless and risky rates can be used to capture indivi duals’ consumption-equivalent interest rate. As a measure of the post-tax riskless rate, we calculate the average real return from Treasury notes over the lo ngest time period available (those from Newell and Pizer 2003) and adjust for Federal taxes (the avera ge marginal rate from tax years 2003 through 2006 i s around 27 percent). 17 This calculation produces a real interest rate of about 2.7 percent, which is roughly consistent with Circular A-4’s recommendati on to use 3 percent to represent the consumption
rate of interest. 18 A measure of the post-tax risky rate for investm ents whose returns are positively correlated with overall equity market returns can b e obtained by adjusting pre-tax rates of household returns to risky investments (approximately 7 perce nt) for taxes yields a real rate of roughly 5 perce nt. 19

**The Ramsey Equation**

Ramsey discounting also provides a useful framework to inform the choice of a discount rate. Under this approach, the analyst applies either positive or normative judgments in selecting values for the key parameters of the Ramsey equation: η (coefficient of relative risk aversion or elastici ty of the marginal utility of consumption) and ρ (pure rate of time preference). 20 These are then combined with g (growth

17 The literature argues for a risk-free rate on gove rnment bonds as an appropriate measure of the consu mption rate of interest. Arrow (2000) suggests that it is roughly 3-4 percent. OMB cites evidence of a 3.1 percent pre-tax rate for 10-year Treasury notes in the A-4 guidance . Newell and Pizer (2003) find real interest rates between 3.5 and 4 percent for 30-year Treasury securities.

18 The positive approach reflects how individuals make allocation choices across time, but it is importan t to keep in mind that we wish to reflect preferences for societ y as a whole, which generally has a longer planning horizon.

19 Cambell et al (2001) estimates that the annual rea l return from stocks for 1900-1995 was about 7 perc ent. The annual real rate of return for the S&P 500 from 195 0 – 2008 was about 6.8 percent. In the absence of a better way to population-weight the tax rates, we use the midd le of the 20 – 40 percent range to derive a post-ta x interest rate (Kotlikoff and Rapson 2006).

20 The parameter ρ measures the **pure rate of time preference** : people’s behavior reveals a preference for an increase in utility today versus the future. Conse quently, it is standard to place a lower weight on utility in the future. The parameter η captures **diminishing marginal utility** : consumption in the future is likely to be higher than consumption today, so diminishing marginal utility of consumption implies that the same monetary damag e will21

rate of per-capita consumption) to equal the intere st rate at which future monetized damages are discounted: ρ + η∙g. 21 In the simplest version of the Ramsey model, with an optimizing representative agent with perfect foresight, what we are calling t he “Ramsey discount rate,” ρ + η∙g, will be equal t o the rate of return to capital, i.e., the market int erest rate.

A review of the literature provides some guidance o n reasonable parameter values for the Ramsey discounting equation, based on both prescriptive an d descriptive approaches.

• η. Most papers in the climate change literature adopt values for η in the range of 0.5 to 3 (Weitzman cites plausible values as those ranging f rom 1 to 4), although not all authors articulate whether their choice is based on prescri ptive or descriptive reasoning. 22 Dasgupta (2008) argues that η should be greater than 1 and m ay be as high as 3, since η equal to 1 suggests savings rates that do not conform to obser ved behavior.

• ρ. With respect to the pure rate of time preference, m ost papers in the climate change literature adopt values for ρ in the range of 0 to 3 percent per year. The very low rates tend to follow from moral judgments involving intergenerati onal neutrality. Some have argued that to use any value other than ρ = 0 would unjustly discriminate against future gen erations (e.g., Arrow et al. 1996, Stern et al. 2006). However, ev en in an inter-generational setting, it may make sense to use a small positive pure rate of tim e preference because of the small probability of unforeseen cataclysmic events (Stern et al. 2006).

• g. A commonly accepted approximation is around 2 pe rcent per year. For the socio-economic scenarios used for this exercise, the EMF models as sume that g is about 1.5-2 percent to 2100.

Some economists and non-economists have argued for constant discount rates below 2 percent based on the prescriptive approach. When grounded in the Ramsey framework, proponents of this approach have argued that a ρ of zero avoids giving preferential treatment to one generation over another. The
choice of η has also been posed as an ethical choice linked to the value of an additional dollar in poorer

cause a smaller reduction of utility for wealthier individuals, either in the future or in current gen erations. If η = 0, then a one dollar increase in income is equally val uable regardless of level of income; if η = 1, then a one percent increase in income is equally valuable no matter th e level of income; and if η > 1, then a one percent increase in income is less valuable to wealthier individuals.

21 In this case, g could be taken from the selected E MF socioeconomic scenarios or alternative assumptio ns about the rate of consumption growth.

22 Empirical estimates of η span a wide range of values. A benchmark value of 2 is near the middle of the range of values estimated or used by Szpiro (1986), Hall and Jones (2007), Arrow (2007), Dasgupta (2006, 2008), Weitzman (2007, 2009), and Nordhaus (2008). However, Chetty (2006) developed a method of estimating η using data on labor supply behavior. He shows that existing evid ence of the effects of wage changes on labor supply imposes a tight upper bound on the curvature of utility over wealth (CRRA < 2) with the mean implied value of 0. 71 and concludes that the standard expected utility model cannot generate high levels of risk aversion withou t contradicting established facts about labor supply. Recent work has jointly estimated the components of the Ramsey equation. Evans and Sezer (2005) estimate **η** = 1.49 for 22 OECD countries. They also estimate **ρ** = 1.08 percent per year using data on mortality rates. Ant hoff, et al. (2009b) estimate **η** = 1.18, and **ρ** = 1.4 percent. When they multiply the bivariate probability distri butions from their work and Evans and Sezer (2005) together, they find **η** = 1.47, and **ρ** = 1.07.22

countries compared to wealthier ones. Stern et al. (2006) applies this perspective through his choice of

ρ = 0.1 percent per year, η = 1 and g = 1.3 percent per year, which yields an a nnual discount rate of 1.4 percent. In the context of permanent income saving s behavior, however, Stern’s assumptions suggest that individuals would save 93 percent of their inc ome. 23

Recently, Stern (2008) revisited the values used in Stern et al. (2006), stating that there is a case to be made for raising η due to the amount of weight lower values place on damages far in the future (over 90 percent of expected damages occur after 2200 with η = 1). Using Stern’s assumption that ρ = 0.1 percent, combined with a η of 1.5 to 2 and his original growth rate, yields a discount rate greater 2
percent.

We conclude that arguments made under the prescript ive approach can be used to justify discount rates between roughly 1.4 and 3.1 percent. In light of c oncerns about the most appropriate value for η , we find it difficult to justify rates at the lower end of this range under the Ramsey framework.

**Accounting for Uncertainty in the Discount Rate**

While the consumption rate of interest is an import ant driver of the benefits estimate, it is uncertai n over time. Ideally, we would formally model this u ncertainty, just as we do for climate sensitivity. Weitzman (1998, 2001) showed theoretically and Newe ll and Pizer (2003) and Groom et al. (2006) confirm empirically that discount rate uncertainty can have a large effect on net present values. A m ain result from these studies is that if there is a per sistent element to the uncertainty in the discount rate (e.g., the rate follows a random walk), then it wil l result in an effective (or certainty-equivalent) discount rate that declines over time. Consequently, lower discount rates tend to dominate over the very long term (see Weitzman 1998, 1999, 2001; Newell and Piz er 2003; Groom et al. 2006; Gollier 2008; Summers and Zeckhauser 2008; and Gollier and Weitzm an 2009).

The proper way to model discount rate uncertainty r emains an active area of research. Newell and Pize r (2003) employ a model of how long-term interest rat es change over time to forecast future discount rates. Their model incorporates some of the basic features of how interest rates move over time, and its parameters are estimated based on historical observ ations of long-term rates. Subsequent work on this topic, most notably Groom et al. (2006), uses more general models of interest rate dynamics to allow f or better forecasts. Specifically, the volatility of interest rates depends on whether rates are current ly low or high and variation in the level of persistence o ver time.

While Newell and Pizer (2003) and Groom et al (2006 ) attempt formally to model uncertainty in the discount rate, others argue for a declining scale o f discount rates applied over time (e.g., Weitzman 2001, and the UK’s “Green Book” for regulatory anal ysis). This approach uses a higher discount rate

23 Stern (2008) argues that building in a positive ra te of exogenous technical change over time reduces the implied savings rate and that η at or above 2 are inconsistent with observed behavi or with regard to equity. (At the same time, adding exogenous technical change—all else eq ual—would increase g as well.)23

initially, but applies a graduated scale of lower d iscount rates further out in time. 24 A key question that has emerged with regard to both of these approaches is the trade-off between potential time inconsistency and giving greater weight to far futu re outcomes (see the EPA Science Advisory Board’s recent comments on this topic as part of its review of their **Guidelines for Economic Analysis** ). 25

**The Discount Rates Selected for Estimating SCC**

In light of disagreement in the literature on the a ppropriate market interest rate to use in this cont ext and uncertainty about how interest rates may change over time, we use three discount rates to span a plausible range of certainty-equivalent constant di scount rates: 2.5, 3, and 5 percent per year. Base d on the review in the previous sections, the interagenc y workgroup determined that these three rates reflect reasonable judgments under both descriptive and prescriptive approaches.

The central value, 3 percent, is consistent with es timates provided in the economics literature and OMB’s Circular A-4 guidance for the consumption rat e of interest. As previously mentioned, the consumption rate of interest is the correct discoun ting concept to use when future damages from elevated temperatures are estimated in consumption- equivalent units. Further, 3 percent roughly corresponds to the after-tax riskless interest rate . The upper value of 5 percent is included to repr esent the possibility that climate damages are positively correlated with market returns. Additionally, thi s discount rate may be justified by the high interest rates that many consumers use to smooth consumption across periods.

The low value, 2.5 percent, is included to incorpor ate the concern that interest rates are highly uncertain over time. It represents the average cer tainty-equivalent rate using the mean-reverting and random walk approaches from Newell and Pizer (2003) starting at a discount rate of 3 percent. Using this approach, the certainty equivalent is about 2. 2 percent using the random walk model and 2.8 percent using the mean reverting approach. 26 Without giving preference to a particular model, the average of the two rates is 2.5 percent. Further, a rate below the riskless rate would be justified i f climate investments are negatively correlated with the overall market rate of return. Use of this low er value also responds to certain judgments using the prescriptive or normative approach and to ethical objections that have been raised about rates of 3 p ercent or higher.

24 For instance, the UK applies a discount rate of 3. 5 percent to the first 30 years; 3 percent for year s 31 - 75; 2.5 percent for years 76 - 125; 2 percent for years 126 - 200; 1.5 percent for years 201 - 300; and 1 perc ent after 300 years. As a sensitivity, it recommends a discount rate of 3 percent for the first 30 years, also decr easing over time.

25 Uncertainty in future damages is distinct from unc ertainty in the discount rate. Weitzman (2008) argu es that Stern’s choice of a low discount rate was “right fo r the wrong reasons.” He demonstrates how the damag es from a low probability, catastrophic event far in the futu re dominate the effect of the discount rate in a pr esent value calculation and result in an infinite willingness-t o-pay for mitigation today. Newbold and Daigneault, (2009) and Nordhaus (2009) find that Weitzman’s result is sens itive to the functional forms chosen for climate se nsitivity, utility, and consumption. Summers and Zeckhauser (2 008) argue that uncertainty in future damages can a lso work in the other direction by increasing the benefits o f waiting to learn the appropriate level of mitigat ion required.

26 Calculations done by Pizer et al. using the origin al simulation program from Newell and Pizer (2003).24

IV. Revised SCC Estimates

Our general approach to estimating SCC values is to run the three integrated assessment models (FUND, DICE, and PAGE) using the following inputs agreed u pon by the interagency group:

• A Roe and Baker distribution for the climate sensit ivity parameter bounded between 0 and 10 with a median of 3 °C and a cumulative probability between 2 and 4.5 °C of two-thirds.

• Five sets of GDP, population and carbon emissions t rajectories based on EMF-22.

• Constant annual discount rates of 2.5, 3, and 5 per cent.

Because the climate sensitivity parameter is modele d probabilistically, and because PAGE and FUND incorporate uncertainty in other model parameters, the final output from each model run is a distribution over the SCC in year **t**

.
For each of the IAMS, the basic computational steps for calculating the SCC in a particular year **t** are:

1. Input the path of emissions, GDP, and population fr om the selected EMF-22 scenarios, and the extrapolations based on these scenarios for post-2100 years.

2. Calculate the temperature effects and (consumption- equivalent) damages in each year resulting from the baseline path of emissions.

a. In PAGE, the consumption-equivalent damages in each period are calculated as a fraction of the EMF GDP forecast, depending on th e temperature in that period relative to the pre-industrial average tempe rature in each region.
b. In FUND, damages in each period depend on both the level and the rate of temperature change in that period.

c. In DICE, temperature affects both consumption and i nvestment, so we first adjust the EMF GDP paths as follows: Using the Cobb -Douglas production function with the DICE2007 parameters, we extract t he path of exogenous technical change implied by the EMF GDP and populat ion paths, then we recalculate the baseline GDP path taking into accou nt climate damages resulting from the baseline emissions path.

3. Add an additional unit of carbon emissions in year **t.** (The exact unit varies by model.)

4. Recalculate the temperature effects and damages exp ected in all years beyond **t** resulting from this adjusted path of emissions, as in step 2.

5. Subtract the damages computed in step 2 from those in step 4 in each year. (DICE is run in 10 year time steps, FUND in annual time step s, while the time steps in PAGE vary.)

6. Discount the resulting path of marginal damages bac k to the year of emissions using the agreed upon fixed discount rates.25

7. Calculate the SCC as the net present value of the d iscounted path of damages computed in step 6, divided by the unit of carbon emissions used to shock the models in step 3.

8. Multiply by 12/44 to convert from dollars per ton o f carbon to dollars per ton of CO 2 (2007 dollars) in DICE and FUND. (All calculations are done in tons of CO 2 in PAGE).

The steps above were repeated in each model for mul tiple future years to cover the time horizons anticipated for upcoming rulemaking analysis. To m aintain consistency across the three IAMs, climate damages are calculated as lost consumption in each future year.

It is important to note that each of the three mode ls has a different default end year. The default t ime horizon is 2200 for PAGE, 2595 for DICE, and 3000 f or the latest version of FUND. This is an issue fo r the multi-model approach because differences in SCC est imates may arise simply due to the model time horizon. Many consider 2200 too short a time horiz on because it could miss a significant fraction of damages under certain assumptions about the growth of marginal damages and discounting, so each model is run here through 2300. This step required a small adjustment in the PAGE model only. This step also required assumptions about GDP, populatio n, and greenhouse gas emission trajectories after 2100, the last year for which these data are availa ble from the EMF-22 models. (A more detailed discussion of these assumptions is included in the Appendix.)

This exercise produces 45 separate distributions of the SCC for a given year, the product of 3 models, 3 discount rates, and 5 socioeconomic scenarios. Thi s is clearly too many separate distributions for consideration in a regulatory impact analysis.

To produce a range of plausible estimates that stil l reflects the uncertainty in the estimation exerci se, the distributions from each of the models and scena rios are equally weighed and combined to produce three separate probability distributions for SCC in a given year, one for each assumed discount rate. These distributions are then used to define a range of point estimates for the global SCC. In this wa y, no integrated assessment model or socioeconomic scenar io is given greater weight than another. Because the literature shows that the SCC is quite sensitiv e to assumptions about the discount rate, and becau se no consensus exists on the appropriate rate to use in an intergenerational context, we present SCCs based on the average values across models and socio economic scenarios for each discount rate.

The interagency group selected four SCC values for use in regulatory analyses. Three values are based on the average SCC across models and socio-economic and emissions scenarios at the 2.5, 3, and 5 percent discount rates. The fourth value is includ ed to represent the higher-than-expected economic impacts from climate change further out in the tail s of the SCC distribution. For this purpose, we use the
SCC value for the 95 th percentile at a 3 percent discount rate. (The ful l set of distributions by model and scenario combination is included in the Appendix.) As noted above, the 3 percent discount rate is the central value, and so the central value that emerge s is the average SCC across models at the 3 percent discount rate. For purposes of capturing the uncer tainties involved in regulatory impact analysis, we emphasize the importance and value of considering t he full range.26

As previously discussed, low probability, high impa ct events are incorporated into the SCC values through explicit consideration of their effects in two of the three models as well as the use of a probability density function for equilibrium climat e sensitivity. Treating climate sensitivity probabilistically results in more high temperature outcomes, which in turn lead to higher projections of damages. Although FUND does not include catastroph ic damages (in contrast to the other two models), its probabilistic treatment of the equilibrium clim ate sensitivity parameter will directly affect the noncatastrophic damages that are a function of the rat e of temperature change.

In Table 3, we begin by presenting SCC estimates fo r 2010 by model, scenario, and discount rate to illustrate the variability in the SCC across each o f these input parameters. As expected, higher disc ount rates consistently result in lower SCC values, whil e lower discount rates result in higher SCC values for each socioeconomic trajectory. It is also evident that there are differences in the SCC estimated acr oss the three main models. For these estimates, FUND p roduces the lowest estimates, while PAGE generally produces the highest estimates.

Table 3: Disaggregated Social Cost of CO 2 Values by Model, Socio-Economic Trajectory, and Di scount Rate for 2010 (in 2007 dollars)

**Discount rate:** 5% 3% 2.5% 3%
**Model Scenario**  Avg Avg Avg 95th

IMAGE 10.8 35.8 54.2 70.8

MERGE 7.5 22.0 31.6 42.1

Message 9.8 29.8 43.5 58.6

MiniCAM 8.6 28.8 44.4 57.9DICE

550 Average 8.2 24.9 37.4 50.8

IMAGE 8.3 39.5 65.5 142.4

MERGE 5.2 22.3 34.6 82.4

Message 7.2 30.3 49.2 115.6

MiniCAM 6.4 31.8 54.7 115.4PAGE

550 Average 5.5 25.4 42.9 104.7

IMAGE

- 1.3 8.2 19.3 39.7

MERGE

- 0.3 8.0 14.8 41.3

Message

- 1.9 3.6 8.8 32.1

MiniCAM

- 0.6 10.2 22.2 42.6FUND

550 Average

- 2.7

- 0.2 3.0 19.4

These results are not surprising when compared to t he estimates in the literature for the latest versi ons of each model. For example, adjusting the values from the literature that were used to develop inter im27

SCC values to 2007 dollars for the year 2010 (assum ing, as we did for the interim process, that SCC grows at 3 percent per year), FUND yields SCC estim ates at or near zero for a 5 percent discount rate and around $9 per ton for a 3 percent discount rate . There are far fewer estimates using the latest versions of DICE and PAGE in the literature: Using similar adjustments to generate 2010 estimates, we calculate a SCC from DICE (based on Nordhaus 2008) of around $9 per ton for a 5 percent discount rate, and a SCC from PAGE (based on Hope 2006, 2008) clos e to $8 per ton for a 4 percent discount rate. Note that these comparisons are only approximate since t he literature generally relies on Ramsey discounting, while we have assumed constant discoun t rates. 27

The SCC estimates from FUND are sensitive to differ ences in emissions paths but relatively insensitive to differences in GDP paths across scenarios, while th e reverse is true for DICE and PAGE. This likely o ccurs because of several structural differences among the models. Specifically in DICE and PAGE, the fracti on of economic output lost due to climate damages incr eases with the level of temperature alone, whereas
in FUND the fractional loss also increases with the rate of temperature change. Furthermore, in FUND
increases in income over time decrease vulnerabilit y to climate change (a form of adaptation), whereas
this does not occur in DICE and PAGE. These struct ural differences among the models make FUND more sensitive to the path of emissions and less sensiti ve to GDP compared to DICE and PAGE.

Figure 3 shows that IMAGE has the highest GDP in 21 00 while MERGE Optimistic has the lowest. The ordering of global GDP levels in 2100 directly corr esponds to the rank ordering of SCC for PAGE and DICE. For FUND, the correspondence is less clear, a result that is to be expected given its less dire ct relationship between its damage function and GDP.

Figure 3: Level of Global GDP across EMF Scenarios

0 50 100 150 200 250 300 350 400 450

2000 2010 2020 2030 2050 2100 Global GDP (trillions of U.S. dollars) IMAGE
MERGE Optimistic

MESSAGE

MiniCAM
3.7 W/m2 radiative forcing

27 Nordhaus (2008) runs DICE2007 with ρ = 1.5 and η = 2. The default approach in PAGE2002 (v ersion 1.4epm) treats ρ and η as random parameters, specified usin g a triangular distribution such that the min, mode , and max = 0.1, 1, and 2 for ρ, and 0.5, 1, and 2 for η, respe ctively. The FUND default value for η is 1, and To l generates SCC estimates for values of ρ = 0, 1, and 3 in many rec ent papers (e.g. Anthoff et al. 2009). The path of per-capita consumption growth, g, varies over time but is trea ted deterministically in two of the three models. In DICE, g is endogenous. Under Ramsey discounting, as economic g rowth slows in the future, the large damages from c limate change that occur far out in the future are discoun ted at a lower rate than impacts that occur in the nearer term.28

Table 4 shows the four selected SCC values in five year increments from 2010 to 2050. Values for 2010

, 2020, 2040, and 2050 are calculated by first combin ing 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 calculat ed using a simple linear interpolation.

Table 4: Social Cost of CO 2 , 2010 – 2050 (in 2007 dollars)

Discount Rate 5% 3% 2.5% 3%
Year Avg Avg Avg 95th

2010 4.7 21.4 35.1 64.9
2015 5.7 23.8 38.4 72.8

2020 6.8 26.3 41.7 80.7

2025 8.2 29.6 45.9 90.4

2030 9.7 32.8 50.0 100.0

2035 11.2 36.0 54.2 109.7

2040 12.7 39.2 58.4 119.3

2045 14.2 42.1 61.7 127.8

2050 15.7 44.9 65.0 136.2

The SCC increases over time because future emission s are expected to produce larger incremental damages as physical and economic systems become mor e stressed in response to greater climatic change. Note that this approach allows us to estim ate the growth rate of the SCC directly using DICE, PAGE, and FUND rather than assuming a constant annu al growth rate as was done for the interim estimates (using 3 percent). This helps to ensure t hat the estimates are internally consistent with ot her modeling assumptions. Table 5 illustrates how the growth rate for these four SCC estimates varies ove r time. The full set of annual SCC estimates between 2010 and 2050 is reported in the Appendix.

Table 5: Changes in the Average Annual Growth Rates of SCC Estimates between 2010 and 2050

5% 3% 2.5% 3.0% Average Annual Growth Rate (%) Avg Avg Avg 95th

20 10

- 2020 3.6% 2.1% 1.7% 2.2%

2020

- 2030 3.7% 2.2% 1.8% 2.2%

2030

- 2040 2.7% 1.8% 1.6% 1.8%

2040

- 2050 2.1% 1.4% 1.1% 1.3%

While the SCC estimate grows over time, the future monetized value of emissions reductions in each year (the SCC in year **t**

multiplied by the change in emissions in year **t** ) must be discounted to the present to determine its total net present value fo r use in regulatory analysis. Damages from future
emissions should be discounted at the same rate as that used to calculate the SCC estimates themselves to ensure internal consistency—i.e., future damages from climate change, whether they result from emissions today or emissions in a later year, shoul d be discounted using the same rate. For example,29

climate damages in the year 2020 that are calculate d using a SCC based on a 5 percent discount rate al so should be discounted back to the analysis year usin g a 5 percent discount rate. 28

V. Limitations of the Analysis

As noted, any estimate of the SCC must be taken as provisional and subject to further refinement (and possibly significant change) in accordance with evo lving scientific, economic, and ethical understandings. During the course of our modeling, it became apparent that there are several areas in particular need of additional exploration and resea rch. These caveats, and additional observations in the following section, are necessary to consider wh en interpreting and applying the SCC estimates.

**Incomplete treatment of non-catastrophic damages.** The impacts of climate change are expected to be widespread, diverse, and heterogeneous. In additio n, the exact magnitude of these impacts is uncertai n because of the inherent complexity of climate proce sses, the economic behavior of current and future populations, and our inability to accurately foreca st technological change and adaptation. Current IA Ms do not assign value to all of the important physica l, ecological, and economic impacts of climate chan ge recognized in the climate change literature (some o f which are discussed above) because of lack of precise information on the nature of damages and be cause the science incorporated into these models understandably lags behind the most recent research . Our ability to quantify and monetize impacts wil l undoubtedly improve with time. But it is also likel y that even in future applications, a number of potentially significant damage categories will rema in non-monetized. (Ocean acidification is one example of a potentially large damage from CO 2 emissions not quantified by any of the three model s. Species and wildlife loss is another example that i s exceedingly difficult to monetize.)

**Incomplete treatment of potential catastrophic dama ges.**  There has been considerable recent discussion of the risk of catastrophic impacts and how best to account for extreme scenarios, such as the collaps e of the Atlantic Meridional Overturning Circulation or the West Antarctic Ice Sheet, or large releases of methane from melting permafrost and warming oceans. Weitzman (2009) suggests that catastrophic damages are extremely large—so large, in fact, that the damages from a low probability, catastrophic
event far in the future dominate the effect of the discount rate in a present value calculation and re sult in an infinite willingness-to-pay for mitigation to day. However, Nordhaus (2009) concluded that the
conditions under which Weitzman's results hold “are limited and do not apply to a wide range of potential uncertain scenarios."

Using a simplified IAM, Newbold and Daigneault (200 9) confirmed the potential for large catastrophe risk premiums but also showed that the aggregate be nefit estimates can be highly sensitive to the shapes of both the climate sensitivity distribution and the damage function at high temperature changes. Pindyck (2009) also used a simplified IAM to examine high-impact low-probability risks, usin g a right-skewed gamma distribution for climate sensiti vity as well as an uncertain damage coefficient, bu t in most cases found only a modest risk premium. Gi ven this difference in opinion, further research in this area is needed before its practical significan ce can be fully understood and a reasonable approac h developed to account for such risks in regulatory a nalysis. (The next section discusses the scientifi c evidence on catastrophic impacts in greater detail. )

28 However, it is possible that other benefits or cost s of proposed regulations unrelated to CO 2 emissions will be discounted at rates that differ from those used to develop the SCC estimates.30

**Uncertainty in extrapolation of damages to high tem peratures:**  The damage functions in these IAMs are typically calibrated by estimating damages at moder ate temperature increases (e.g., DICE was calibrate d at 2.5 °C) and extrapolated to far higher temperatu res by assuming that damages increase as some power of the temperature change. Hence, estimated damages are far more uncertain under more extreme climate change scenarios.

**Incomplete treatment of adaptation and technologica l change:**  Each of the three integrated assessment models used here assumes a certain degree of low- o r no-cost adaptation. For instance, Tol assumes a great deal of adaptation in FUND, including widesp read reliance on air conditioning ; so much so, tha t the largest single benefit category in FUND is the reduced electricity costs from not having to run ai r conditioning as intensively (NRC 2009).

Climate change also will increase returns on invest ment to develop technologies that allow individuals to cope with adverse climate conditions, and IAMs t o do not adequately account for this directed technological change. 29 For example, scientists may develop crops that ar e better able to withstand higher and more variable temperatures. Although DI CE and FUND have both calibrated their agricultural sectors under the assumption that farmers will chan ge land use practices in response to climate change (Mastrandrea, 2009), they do not take into account technological changes that lower the cost of this adaptation over time. On the other hand, the calib rations do not account for increases in climate variability, pests, or diseases, which could make a daptation more difficult than assumed by the IAMs f or a given temperature change. Hence, models do not a dequately account for potential adaptation or technical change that might alter the emissions pat hway and resulting damages. In this respect, it is difficult to determine whether the incomplete treat ment of adaptation and technological change in these IAMs under or overstate the likely damages.

**Risk aversion:** A key question unanswered during this interagency p rocess is what to assume about relative risk aversion with regard to high-impact o utcomes. These calculations do not take into accou nt the possibility that individuals may have a higher willingness to pay to reduce the likelihood of lowprobability, high-impact damages than they do to re duce the likelihood of higher-probability but lower

impact damages with the same expected cost. (The i nclusion of the 95 th percentile estimate in the final set of SCC values was largely motivated by this con cern.) If individuals do show such a higher willin gness to pay, a further question is whether that fact sho uld be taken into account for regulatory policy. E ven if individuals are not risk-averse for such scenarios, it is possible that regulatory policy should inclu de a degree of risk-aversion.

Assuming a risk-neutral representative agent is con sistent with OMB’s 

### Circular A-4, which advises that the estimates of benefits and costs used in regulat ory analysis are usually based on the average or the expected value and that “emphasis on these expe cted values is appropriate as long as society is ‘risk neutral’ with respect to the regulatory alter natives. While this may not always be the case, [analysts] should in general assume ‘risk neutralit y’ in [their] analysis.”

Nordhaus (2008) points to the need to explore the r elationship between risk and income in the context of climate change across models and to explore the role of uncertainty regarding various parameters in

29 However these research dollars will be diverted fr om whatever their next best use would have been in the absence of climate change (so productivity/GDP woul d have been still higher).31

the results. Using FUND, Anthoff et al (2009) expl ored the sensitivity of the SCC to Ramsey equation parameter assumptions based on observed behavior. T hey conclude that “the assumed rate of risk aversion is at least as important as the assumed ra te of time preference in determining the social cos t of
carbon.” Since Circular A-4 allows for a different assumption on risk preference in regulatory analysi s if it is adequately justified, we plan to continue invest igating this issue.

V. A Further Discussion of Catastrophic Impacts and Da mage Functions

As noted above, the damage functions underlying the three IAMs used to estimate the SCC may not capture the economic effects of all possible advers e consequences of climate change and may therefore lead to underestimates of the SCC (Mastrandrea 2009 ). In particular, the models’ functional forms may not adequately capture: (1) potentially discontinuo us “tipping point” behavior in Earth systems, (2) inter-sectoral and inter-regional interactions, inc luding global security impacts of high-end warming, and (3) limited near-term substitutability between dama ge to natural systems and increased consumption.

It is the hope of the interagency group that over t ime researchers and modelers will work to fill thes e gaps and that the SCC estimates used for regulatory analysis by the Federal government will continue t o evolve with improvements in modeling. In the meanti me, we discuss some of the available evidence.

**Extrapolation of climate damages to high levels of warming** 

The damage functions in the models are calibrated a t moderate levels of warming and should therefore be viewed cautiously when extrapolated to the high temperatures found in the upper end of the distribution. Recent science suggests that there a re a number of potential climatic “tipping points” at which the Earth system may exhibit discontinuous be havior with potentially severe social and economic consequences (e.g., Lenton et al, 2008, Kriegler et al., 2009). These tipping points include the disr uption of the Indian Summer Monsoon, dieback of the Amazon Rainforest and boreal forests, collapse of the
Greenland Ice Sheet and the West Antarctic Ice Shee t, reorganization of the Atlantic Meridional Overturning Circulation, strengthening of El Niño-S outhern Oscillation, and the release of methane fro m melting permafrost. Many of these tipping points a re estimated to have thresholds between about 3 °C and 5 °C (Lenton et al., 2008). Probabilities of s everal of these tipping points were assessed throug h expert elicitation in 2005–2006 by Kriegler et al. (2009); results from this study are highlighted in Table 6. Ranges of probability are averaged across core experts on each topic.

As previously mentioned, FUND does not include pote ntially catastrophic effects. DICE assumes a small probability of catastrophic damages that increases with increased warming, but the damages from these risks are incorporated as expected values (i.e., ig noring potential risk aversion). PAGE models catastrophic impacts in a probabilistic framework ( see Figure 1), so the high-end output from PAGE potentially offers the best insight into the SCC if the world were to experience catastrophic climate change. For instance, at the 95 th percentile and a 3 percent discount rate, the SCC estimated by PAGE across the five socio-economic and emission traject ories of $113 per ton of CO 2 is almost double the value estimated by DICE, $58 per ton in 2010. We c annot evaluate how well the three models account for catastrophic or non-catastrophic impacts, but t his estimate highlights the sensitivity of SCC valu es in the tails of the distribution to the assumptions ma de about catastrophic impacts.32 Table 6: Probabilities of Various Tipping Points fr om Expert Elicitation

Additional Warming by 2100
Possible Tipping Points Duration
before effect is fully realized (in years) 0.5-1.5 C 1.5-3.0 C 3-5 C

Reorganization of Atlantic Meridional Overturning C irculation about 100 0-18% 6-39% 18-67%

Greenland Ice Sheet collapse at least 300 8-39% 33 -73% 67-96%

West Antarctic Ice Sheet collapse at least 300 5-4 1% 10-63% 33-88%

Dieback of Amazon rainforest about 50 2-46% 14-84% 41-94%

Strengthening of El Niño-Southern Oscillation about 100 1-13% 6-32% 19-49%

Dieback of boreal forests about 50 13-43% 20-81% 34 -91%

Shift in Indian Summer Monsoon about 1 Not formall y assessed

Release of methane from melting permafrost Less tha n 100 Not formally assessed.

PAGE treats the possibility of a catastrophic event probabilistically, while DICE treats it determinis tically (that is, by adding the expected value of the damag e from a catastrophe to the aggregate damage function). In part, this results in different prob abilities being assigned to a catastrophic event ac ross the two models. For instance, PAGE places a probability near zero on a catastrophe at 2.5 °C warming, whil e DICE assumes a 4 percent probability of a catastrop he at 2.5 °C. By comparison, Kriegler et al. (2009 ) estimate a probability of at least 16-36 percent of crossing at least one of their primary climatic ti pping points in a scenario with temperatures about 2-4 ° C warmer than pre-Industrial levels in 2100.

It is important to note that crossing a climatic ti pping point will not necessarily lead to an economi c catastrophe in the sense used in the IAMs. A tippin g point is a critical threshold across which some aspect of the Earth system starts to shifts into a qualitatively different state (for instance, one wi th dramatically reduced ice sheet volumes and higher s ea levels). In the IAMs, a catastrophe is a lowprobability environmental change with high economic impact.

**Failure to incorporate inter-sectoral and inter-reg ional interactions** 

The damage functions do not fully incorporate eithe r inter-sectoral or inter-regional interactions. F or instance, while damages to the agricultural sector are incorporated, the effects of changes in food supply on human health are not fully captured and d epend on the modeler’s choice of studies used to calibrate the IAM. Likewise, the effects of climat e damages in one region of the world on another reg ion are not included in some of the models (FUND includ es the effects of migration from sea level rise). These inter-regional interactions, though difficult to quantify, are the basis for climate-induced nat ional and economic security concerns (e.g., Campbell et a l., 2007; U.S. Department of Defense 2010) and are particularly worrisome at higher levels of warming. High-end warming scenarios, for instance, project water scarcity affecting 4.3-6.9 billion people by 2050, food scarcity affecting about 120 million33

additional people by 2080, and the creation of mill ions of climate refugees (Easterling et al., 2007; Campbell et al., 2007).

**Imperfect substitutability of environmental ameniti es** 

Data from the geological record of past climate cha nges suggests that 6 °C of warming may have severe consequences for natural systems. For instance, du ring the Paleocene-Eocene Thermal Maximum about 55.5 million years ago, when the Earth experienced a geologically rapid release of carbon associated with an approximately 5 °C increase in global mean temperatures, the effects included shifts of about 400-900 miles in the range of plants (Wing et al., 2005), and dwarfing of both land mammals (Gingerich

, 2006) and soil fauna (Smith et al., 2009).

The three IAMs used here assume that it is possible to compensate for the economic consequences of damages to natural systems through increased consum ption of non-climate goods, a common assumption in many economic models. In the context of climate change, however, it is possible that the damages to natural systems could become so great th at no increase in consumption of non-climate goods would provide complete compensation (Levy et al., 2005). For instance, as water supplies become scarcer or ecosystems become more fragile an d less bio-diverse, the services they provide may become increasingly more costly to replace. Uncali brated attempts to incorporate the imperfect substitutability of such amenities into IAMs (Stern er and Persson, 2008) indicate that the optimal deg ree of emissions abatement can be considerably greater than is commonly recognized.

VI. Conclusion

The interagency group selected four SCC estimates f or use in regulatory analyses. For 2010, these estimates are $5, $21, $35, and $65 (in 2007 dollar s). The first three estimates are based on the aver age SCC across models and socio-economic and emissions scenarios at the 5, 3, and 2.5 percent discount rates, respectively. The fourth value is included to represent the higher-than-expected impacts from temperature change further out in the tails of the SCC distribution. For this purpose, we use the SCC
value for the 95 th percentile at a 3 percent discount rate. The cent ral value is the average SCC across models at the 3 percent discount rate. For purpose s of capturing the uncertainties involved in regulatory impact analysis, we emphasize the import ance and value of considering the full range. These SCC estimates also grow over time. For instance, t he central value increases to $24 per ton of CO 2 in 2015 and $26 per ton of CO 2 in 2020.

We noted a number of limitations to this analysis, including the incomplete way in which the integrate d assessment models capture catastrophic and non-cata strophic impacts, their incomplete treatment of adaptation and technological change, uncertainty in the extrapolation of damages to high temperatures, and assumptions regarding risk aversion. The limit ed amount of research linking climate impacts to economic damages makes this modeling exercise even more difficult. It is the hope of the interagency group that over time researchers and modelers will work to fill these gaps and that the SCC estimates used for regulatory analysis by the Federal governm ent will continue to evolve with improvements in modeling.34

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Appendix

Table A1: Annual SCC Values: 2010–2050 (in 2007 dol lars)

Discount Rate 5% 3% 2.5% 3%
Year Avg Avg Avg 95th

2010 4.7 21.4 35.1 64.9
2011 4.9 21.9 35.7 66.5
2012 5.1 22.4 36.4 68.1
2013 5.3 22.8 37.0 69.6
2014 5.5 23.3 37.7 71.2
2015 5.7 23.8 38.4 72.8
2016 5.9 24.3 39.0 74.4
2017 6.1 24.8 39.7 76.0
2018 6.3 25.3 40.4 77.5
2019 6.5 25.8 41.0 79.1
2020 6.8 26.3 41.7 80.7
2021 7.1 27.0 42.5 82.6
2022 7.4 27.6 43.4 84.6
2023 7.7 28.3 44.2 86.5
2024 7.9 28.9 45.0 88.4
2025 8.2 29.6 45.9 90.4
2026 8.5 30.2 46.7 92.3
2027 8.8 30.9 47.5 94.2
2028 9.1 31.5 48.4 96.2
2029 9.4 32.1 49.2 98.1
2030 9.7 32.8 50.0 100.0
2031 10.0 33.4 50.9 102.0
2032 10.3 34.1 51.7 103.9
2033 10.6 34.7 52.5 105.8
2034 10.9 35.4 53.4 107.8
2035 11.2 36.0 54.2 109.7
2036 11.5 36.7 55.0 111.6
2037 11.8 37.3 55.9 113.6
2038 12.1 37.9 56.7 115.5
2039 12.4 38.6 57.5 117.4
2040 12.7 39.2 58.4 119.3
2041 13.0 39.8 59.0 121.0
2042 13.3 40.4 59.7 122.7
2043 13.6 40.9 60.4 124.4
2044 13.9 41.5 61.0 126.1
2045 14.2 42.1 61.7 127.8
2046 14.5 42.6 62.4 129.4
2047 14.8 43.2 63.0 131.1
2048 15.1 43.8 63.7 132.8
2049 15.4 44.4 64.4 134.5

2050 15.7 44.9 65.0 136.240

This Appendix also provides additional technical in formation about the non-CO 2 emission projections used in the modeling and the method for extrapolati ng emissions forecasts through 2300, and shows the full distribution of 2010 SCC estimates by mode l and scenario combination.

1. Other (non-CO 2 ) gases

In addition to fossil and industrial CO 2 emissions, each EMF scenario provides projections of methane (CH 4 ), nitrous oxide (N 2 O), fluorinated gases, and net land use CO 2 emissions to 2100. These assumptions are used in all three IAMs while retain ing each model’s default radiative forcings (RF) du e to other factors (e.g., aerosols and other gases). Specifically, to obtain the RF associated with the nonCO 2 EMF emissions only, we calculated the RF associate d with the EMF atmospheric CO 2 concentrations
and subtracted them from the EMF total RF. 30 This approach respects the EMF scenarios as much a s possible and at the same time takes account of thos e components not included in the EMF projections.
Since each model treats non-CO 2 gases differently (e.g., DICE lumps all other gase s into one composite exogenous input), this approach was applied slightl y differently in each of the models.

FUND : Rather than relying on RF for these gases, the ac tual emissions from each scenario were used in FUND. The model default trajectories for CH 4 , N 2 0, SF 6 , and the CO 2 emissions from land were replaced
with the EMF values.

PAGE : PAGE models CO 2 , CH 4 , sulfur hexafluoride (SF 6 ), and aerosols and contains an "excess forcing" vector that includes the RF for everything else. T o include the EMF values, we removed the default CH 4 and SF 6 factors 31 , decomposed the excess forcing vector, and constru cted a new excess forcing vector
that includes the EMF RF for CH 4 , N 2 0, and fluorinated gases, as well as the model defa ult values for
aerosols and other factors. Net land use CO 2 emissions were added to the fossil and industrial CO 2 emissions pathway.

DICE : DICE presents the greatest challenge because all forcing due to factors other than industrial CO 2 emissions is embedded in an exogenous non-CO 2 RF vector. To decompose this exogenous forcing pa th
into EMF non-CO 2 gases and other gases, we relied on the references in DICE2007 to the Intergovernmental Panel on Climate Change’s (IPCC) Fourth Assessment Report (AR4) and the discussion
of aerosol forecasts in the IPCC’s Third Assessment Report (TAR) and in AR4, as explained below. In DICE2007, Nordhaus assumes that exogenous forcing f rom all non-CO 2 sources is -0.06 W/m 2 in 2005, as reported in AR4, and increases linearly to 0.3 W/m 2 in 2105, based on GISS projections, and then stays
constant after that time.

30 Note EMF did not provide CO 2 concentrations for the IMAGE reference scenario. Thus, for this scenario, we fed the fossil, industrial and land CO 2 emissions into MAGICC (considered a "neutral arbit er" model, which is tuned to emulate the major global climate models) and the re sulting CO 2 concentrations were used. Note also that MERGE assumes a neutral biosphere so net land CO 2 emissions are set to zero for all years for the ME RGE Optimistic reference scenario, and for the MERGE component of the average 550 scenario (i.e., we add up the land use emissions from the other three models and divide by 4).

31 Both the model default CH 4 emissions and the initial atmospheric CH 4 is set to zero to avoid double counting the effect of past CH 4 emissions.41

According to AR4, the RF in 2005 from CH 4 , N 2 0, and halocarbons (approximately similar to the F- gases in the EMF-22 scenarios) was 0.48 + 0.16 + 0.34 = 0 .98 W/m 2 and RF from total aerosols was -1.2 W/m 2

. Thus, the -.06 W/m 2 non-CO 2 forcing in DICE can be decomposed into: 0.98 W/m 2 due to the EMF nonCO 2 gases, -1.2 W/m 2 due to aerosols, and the remainder, 0.16 W/m 2 , due to other residual forcing.

For subsequent years, we calculated the DICE defaul t RF from aerosols and other non-CO 2 gases based on the following two assumptions:

(1) RF from aerosols declines linearly from 2005 to 2100 at the rate projected by the TAR and then stays constant thereafter, and (2) With respect to RF from non-CO 2 gases not included in the EMF-22 scenarios, the sh are of nonaerosol RF matches the share implicit in the AR4 su mmary statistics cited above and remains
constant over time.

Assumption (1) means that the RF from aerosols in 2 100 equals 66 percent of that in 2000, which is th e fraction of the TAR projection of total RF from aer osols (including sulfates, black carbon, and organi c carbon) in 2100 vs. 2000 under the A1B SRES emissio ns scenario. Since the SRES marker scenarios were not updated for the AR4, the TAR provides the most recent IPCC projection of aerosol forcing. We rely on the A1B projection from the TAR because it provi des one of the lower aerosol forecasts among the
SRES marker scenarios and is more consistent with t he AR4 discussion of the post-SRES literature on
aerosols:

**Aerosols have a net cooling effect and the represen tation of aerosol and aerosol precursor emissions,**  **including sulphur dioxide, black carbon and organic carbon, has improved in the post-SRES scenarios.**  **Generally, these emissions are projected to be lowe r than reported in SRES. {WGIII 3.2, TS.3, SPM}.**  **32**

Assuming a simple linear decline in aerosols from 2 000 to 2100 also is more consistent with the recent literature on these emissions. For example, Figure A1 shows that the sulfur dioxide emissions peak ov er the short-term of some SRES scenarios above the upp er bound estimates of the more recent scenarios. 33 Recent scenarios project sulfur emissions to peak e arlier and at lower levels compared to the SRES in part because of new information about present and p lanned sulfur legislation in some developing countries, such as India and China. 34 The lower bound projections of the recent literat ure have also shifted downward slightly compared to the SRES scen ario (IPCC 2007).

32 AR4 Synthesis Report, p. 44, http://www.ipcc.ch/pdf/assessment-report/ar4/syr/ar 4_syr.pdf

33 See Smith, S.J., R. Andres, E. Conception, and J. Lurz, 2004: Historical sulfur dioxide emissions, 18 50-2000: methods and results. Joint Global Research Institut e, College Park, 14 pp.

34 See Carmichael, G., D. Streets, G. Calori, M. Aman n, M. Jacobson, J. Hansen, and H. Ueda, 2002: Chang ing trends in sulphur emissions in Asia: implications for acid deposition, air pollution, and climate. Environmen tal Science and Technology, 36(22):4707- 4713; Streets, D., K. Jian g, X. Hu, J. Sinton, X.-Q. Zhang, D. Xu, M. Jacobson, and J. Hansen, 2001: Recent reductions in China’s greenhou se gas emissions. Science, 294(5548): 1835-1837.42

With these assumptions, the DICE aerosol forcing ch anges from -1.2 in 2005 to -0.792 in 2105 W/m 2 ; forcing due to other non-CO 2 gases not included in the EMF scenarios declines f rom 0.160 to 0.153 W/m 2

.43 Figure A1: Sulphur Dioxide Emission Scenarios

.
Notes: Thick colored lines depict the four SRES mar ker scenarios and black dashed lines show the media n, 5 th and 95 th percentile of the frequency distribution for the f ull ensemble of 40 SRES scenarios. The blue area (and the thin dashed lines in blue) illustrate s individual scenarios and the range of Smith et al . (2004). Dotted lines indicate the minimum and maximum of SO 2 emissions scenarios developed pre-SRES. Source: IPCC (2007), AR4 WGIII 3.2, http://www.ipcc.ch/publications_and_data/ar4/wg3/en /ch3-ens3-2-
2-4.html

.

Although other approaches to decomposing the DICE e xogenous forcing vector are possible, initial sensitivity analysis suggests that the differences among reasonable alternative approaches are likely to be minor. For example, adjusting the TAR aerosol p rojection above to assume that aerosols will be maintained at 2000 levels through 2100 reduces aver age SCC values (for 2010) by approximately 3 percent (or less than $2); assuming all aerosols ar e phased out by 2100 increases average 2010 SCC values by 6-7 percent (or $0.50-$3)–depending on th e discount rate. These differences increase slight ly for SCC values in later years but are still well wi thin 10 percent of each other as far out as 2050.

Finally, as in PAGE, the EMF net land use CO 2 emissions are added to the fossil and industrial C O 2 emissions pathway.

2. Extrapolating Emissions Projections to 2300

To run each model through 2300 requires assumptions about GDP, population, greenhouse gas emissions, and radiative forcing trajectories after 2100, the last year for which these projections ar e available from the EMF-22 models. These inputs wer e extrapolated from 2100 to 2300 as follows:

1. Population growth rate declines linearly, reach ing zero in the year 2200. 2. GDP/ per capita growth rate declines linearly, reaching zero in the year 2300.
3. The decline in the fossil and industrial carbon intensity (CO 2 /GDP) growth rate over 2090-2100 is maintained from 2100 through 2300.
4. Net land use CO 2 emissions decline linearly, reaching zero in the y ear 2200.
5. Non-CO 2 radiative forcing remains constant after 2100.44

Long run stabilization of GDP per capita was viewed as a more realistic simplifying assumption than a linear or exponential extrapolation of the pre-2100 economic growth rate of each EMF scenario. This i s based on the idea that increasing scarcity of natur al resources and the degradation of environmental sinks available for assimilating pollution from eco nomic production activities may eventually overtake the rate of technological progress. Thus, the over all rate of economic growth may slow over the very long run. The interagency group also considered al lowing an exponential decline in the growth rate of GDP per capita. However, since this would require an additional assumption about how close to zero the growth rate would get by 2300, the group opted for the simpler and more transparent linear extrapolation to zero by 2300.

The population growth rate is also assumed to decli ne linearly, reaching zero by 2200. This assumpti on is reasonably consistent with the United Nations lo ng run population forecast, which estimates global population to be fairly stable after 2150 in the me dium scenario (UN 2004). 35 The resulting range of EMF population trajectories (Figure A2) also encomp ass the UN medium scenario forecasts through 2300 – global population of 8.5 billion by 2200, an d 9 billion by 2300.

Maintaining the decline in the 2090-2100 carbon int ensity growth rate (i.e., CO 2 per dollar of GDP) through 2300 assumes that technological improvement s and innovations in the areas of energy efficiency and other carbon reducing technologies ( possibly including currently unavailable methods) will continue to proceed at roughly the same pace t hat is projected to occur towards the end of the forecast period for each EMF scenario. This assump tion implies that total cumulative emissions in 230 0 will be between 5,000 and 12,000 GtC, which is with in the range of the total potential global carbon
stock estimated in the literature.

Net land use CO 2 emissions are expected to stabilize in the long ru n, so in the absence of any post 2100 projections, the group assumed a linear decline to zero by 2200. Given no a priori reasons for assumi ng a long run increase or decline in non-CO 2 radiative forcing, it is assumed to remain at the 2100 levels for each EMF scenario through 2300.

Figures A2-A7 show the paths of global population, GDP, fossil and industrial CO 2 emissions, net land
CO 2 emissions, non-CO 2 radiative forcing, and CO 2 intensity (fossil and industrial CO 2 emissions/GDP) resulting from these assumptions.

35 United Nations. 2004. **World Population to 2300**

. http://www.un.org/esa/population/publications/longr ange2/worldpop2300final.pdf45

Figure A2. Global Population, 2000-2300 (Post-2100 extrapolations assume the population growth

rate changes linearly to reach a zero growth rate b y 2200.)

5.5 6.5 7.5 8.5 9.5 10.5 11.5

2000 2050 2100 2150 2200 2250 2300 IMAGE
MERGE
MESSAGE
MiniCAM
5th scenario ExtrapolationsGlobal Population [billion]

Year
Note: In the fifth scenario, 2000-2100 population i s equal to the average of the population under the 550 ppm
CO 2 e, full-participation, not-to-exceed scenarios cons idered by each of the four models.

Figure A3. World GDP, 2000-2300 (Post-2100 extrapol ations assume GDP per capita growth declines linearly, reaching zero in the year 2300)

0 500 1000 1500 2000

2000 2050 2100 2150 2200 2250 2300

IMAGE

MERGE
MESSAGE

MiniCAM
5th scenario Extrapolations

YearWorld GDP [$trillion]

Note: In the fifth scenario, 2000-2100 GDP is equal to the average of the GDP under the 550 ppm CO 2 e, fullparticipation, not-to-exceed scenarios considered b y each of the four models.46

Figure A4. Global Fossil and Industrial CO 2 Emissions, 2000-2300 (Post-2100 extrapolations assu me growth rate of CO 2 intensity (CO 2 /GDP) over 2090-2100 is maintained through 2300.)

0 50 100 150 200

2000 2050 2100 2150 2200 2250 2300

IMAGE

MERGE

MESSAGE

MiniCAM

5th scenario
ExtrapolationsFossil&Industrial CO2 Emissions [GtCO2/decade]

Year

Note: In the fifth scenario, 2000-2100 emissions ar e equal to the average of the emissions under the 5 50 ppm CO2e, full-participation, not-to-exceed scenarios c onsidered by each of the four models.

Figure A5. Global Net Land Use CO 2 Emissions, 2000-2300 (Post-2100 extrapolations ass ume emissions decline linearly, reaching zero in the year 2200) 36

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00

2000 2050 2100 2150 2200 2250 2300 IMAGE
MERGE
MESSAGE
MiniCAM
5th scneario ExtrapolationsNet land CO2 emissions [GtCO2/yr]

Year z

Note: In the fifth scenario, 2000-2100 emissions ar e equal to the average of the emissions under the 5 50 ppm CO2e, full-participation, not-to-exceed scenarios c onsidered by each of the four models.

36 MERGE assumes a neutral biosphere so net land CO 2 emissions are set to zero for all years for the ME RGE Optimistic reference scenario, and for the MERGE co mponent of the average 550 scenario (i.e., we add u p the land use emissions from the other three models and divid e by 4).47

Figure A6. Global Non-CO 2 Radiative Forcing, 2000-2300 (Post-2100 extrapolat ions assume constant
non-CO 2 radiative forcing after 2100.)

0.00 0.75 1.50 2.25 3.00 3.75

2000 2050 2100 2150 2200 2250 2300

IMAGE

MERGE

MESSAGE
MiniCAM
5th scenario ExtrapolationsnonCO2 RF [W/m^2]

Year
Note: In the fifth scenario, 2000-2100 emissions ar e equal to the average of the emissions under the 5 50 ppm CO2e, full-participation, not-to-exceed scenarios c onsidered by each of the four models.

Figure A7. Global CO 2 Intensity (fossil & industrial CO 2 emissions/GDP), 2000-2300 (Post-2100 extrapolations assume decline in CO 2 /GDP growth rate over 2090-2100 is maintained throu gh 2300.)

0 0 0 0 0 1 1 1 1

2000 2050 2100 2150 2200 2250 2300 IMAGE

MERGE

MESSAGE

MiniCAM

5th scenario
ExtrapolationsFossil & Industrial CO2 intensity [GtCO2/trillion $]

Year
Note: In the fifth scenario, 2000-2100 emissions ar e equal to the average of the emissions under the 5 50 ppm
CO 2 e, full-participation, not-to-exceed scenarios cons idered by each of the four models.48 Table A2. 2010 Global SCC Estimates at 2.5 Percent Discount Rate (2007$/ton CO 2 )

**Percentile** 1st 5th 10th 25th 50th Avg 75th 90th 95th 99th
**Scenario** PAGE
IMAGE 3.3 5.9 8.1 13.9 28.8 65.5 68.2 147.9 239.6 563.8 MERGE optimistic 1.9 3.2 4.3 7.2 14.6 34.6 36.2 79.8 124.8 288.3 Message 2.4 4.3 5.8 9.8 20.3 49.2 50.7 114.9 181.7 428.4 MiniCAM base 2.7 4.6 6.4 11.2 22.8 54.7 55.7 120.5 195.3 482.3 5th scenario 2.0 3.5 4.7 8.1 16.3 42.9 41.5 103.9 176.3 371.9

**Scenario** DICE
IMAGE 16.4 21.4 25 33.3 46.8 54.2 69.7 96.3 111.1 130.0 MERGE optimistic 9.7 12.6 14.9 19.7 27.9 31.6 40.7 54.5 63.5 73.3 Message 13.5 17.2 20.1 27 38.5 43.5 55.1 75.8 87.9 103.0 MiniCAM base 13.1 16.7 19.8 26.7 38.6 44.4 56.8 79.5 92.8 109.3 5th scenario 10.8 14 16.7 22.2 32 37.4 47.7 67.8 80.2 96.8

**Scenario** FUND
IMAGE -33.1 -18.9 -13.3 -5.5 4.1 19.3 18.7 43.5 67.1 150.7 MERGE optimistic -33.1 -14.8 -10 -3 5.9 14.8 20.4 43.9 65.4 132.9 Message -32.5 -19.8 -14.6 -7.2 1.5 8.8 13.8 33.7 52.3 119.2 MiniCAM base -31.0 -15.9 -10.7 -3.4 6 22.2 21 46.4 70.4 152.9 5th scenario -32.2 -21.6 -16.7 -9.7 -2.3 3 6.7 20.5 34.2 96.8

Table A3. 2010 Global SCC Estimates at 3 Percent Di scount Rate (2007$/ton CO 2 )

**Percentile** 1st 5th 10th 25th 50th Avg 75th 90th 95th 99th
**Scenario** PAGE
IMAGE 2.0 3.5 4.8 8.1 16.5 39.5 41.6 90.3 142.4 327.4 MERGE optimistic 1.2 2.1 2.8 4.6 9.3 22.3 22.8 51.3 82.4 190.0 Message 1.6 2.7 3.6 6.2 12.5 30.3 31 71.4 115.6 263.0 MiniCAM base 1.7 2.8 3.8 6.5 13.2 31.8 32.4 72.6 115.4 287.0 5th scenario 1.3 2.3 3.1 5 9.6 25.4 23.6 62.1 104.7 222.5

**Scenario** DICE
IMAGE 11.0 14.5 17.2 22.8 31.6 35.8 45.4 61.9 70.8 82.1 MERGE optimistic 7.1 9.2 10.8 14.3 19.9 22 27.9 36.9 42.1 48.8 Message 9.7 12.5 14.7 19 26.6 29.8 37.8 51.1 58.6 67.4 MiniCAM base 8.8 11.5 13.6 18 25.2 28.8 36.9 50.4 57.9 67.8 5th scenario 7.9 10.1 11.8 15.6 21.6 24.9 31.8 43.7 50.8 60.6

**Scenario** FUND
IMAGE -25.2 -15.3 -11.2 -5.6 0.9 8.2 10.4 25.4 39.7 90.3 MERGE optimistic -24.0 -12.4 -8.7 -3.6 2.6 8 12.2 27 41.3 85.3 Message -25.3 -16.2 -12.2 -6.8 -0.5 3.6 7.7 20.1 32.1 72.5 MiniCAM base -23.1 -12.9 -9.3 -4 2.4 10.2 12.2 27.7 42.6 93.0 5th scenario -24.1 -16.6 -13.2 -8.3 -3 -0.2 2.9 11.2 19.4 53.649 Table A4. 2010 Global SCC Estimates at 5 Percent Di scount Rate (2007$/ton CO 2 )

**Percentile** 1st 5th 10th 25th 50th Avg 75th 90th 95th 99th
**Scenario** PAGE
IMAGE 0.5 0.8 1.1 1.8 3.5 8.3 8.5 19.5 31.4 67.2 MERGE optimistic 0.3 0.5 0.7 1.2 2.3 5.2 5.4 12.3 19.5 42.4 Message 0.4 0.7 0.9 1.6 3 7.2 7.2 17 28.2 60.8 MiniCAM base 0.3 0.6 0.8 1.4 2.7 6.4 6.6 15.9 24.9 52.6 5th scenario 0.3 0.6 0.8 1.3 2.3 5.5 5 12.9 22 48.7

**Scenario** DICE
IMAGE 4.2 5.4 6.2 7.6 10 10.8 13.4 16.8 18.7 21.1 MERGE optimistic 2.9 3.7 4.2 5.3 7 7.5 9.3 11.7 12.9 14.4 Message 3.9 4.9 5.5 7 9.2 9.8 12.2 15.4 17.1 18.8 MiniCAM base 3.4 4.2 4.7 6 7.9 8.6 10.7 13.5 15.1 16.9 5th scenario 3.2 4 4.6 5.7 7.6 8.2 10.2 12.8 14.3 16.0

**Scenario** FUND
IMAGE -11.7 -8.4 -6.9 -4.6 -2.2 -1.3 0.7 4.1 7.4 17.4 MERGE optimistic -10.6 -7.1 -5.6 -3.6 -1.3 -0.3 1.6 5.4 9.1 19.0 Message -12.2 -8.9 -7.3 -4.9 -2.5 -1.9 0.3 3.5 6.5 15.6 MiniCAM base -10.4 -7.2 -5.8 -3.8 -1.5 -0.6 1.3 4.8 8.2 18.0 5th scenario -10.9 -8.3 -7 -5 -2.9 -2.7 -0.8 1.4 3.2 9.2

Figure A8. Histogram of Global SCC Estimates in 201 0 (2007$/ton CO 2 ), by discount rate

0 2000 4000 6000 8000 10000 12000 14000 16000-25-12114274053667992105118131144157170183196209222235248261274

All 2010, 5.0% All 2010, 3.0% All 2010, 2.5%

* The distribution of SCC values ranges from -$5,19 2 to $66,116 but the X-axis has been truncated at approximately the 1 st and 99 th percentiles to better show the data.50Table A5. Additional Summary Statistics of 2010 Global SCC Estimates**Disc ount rate:** 5%3%2.5%**Scenario**MeanVarianceSkewnessKurtosisMeanVarianceSkewnessKurtosisMeanVarianceSkewnessKurtosisDICE9.013.10.80.228.3209.81.10.942.2534.91.21.1PAGE6.5136.06.372.429.83,383.78.6151.049.39,546.08.7143.8FUND-1.370.128.21,479.06.016,382.5128.018,976.513.6150,732.6149.023,558.3