# Technical Support Document: ­ Social Cost of Carbon for Regulatory Impact Analysis ­ Under Executive Order 12866 ­

Interagency Working Group on Social Cost of Carbon, United States Government

With participation by

Council of Economic Advisers Council on Environmental Quality Department of Agriculture Department of Commerce

Department of Energy Department of Transportation Environmental Protection Agency
National Economic Council Office of Energy and Climate Change

Office of Management and Budget Office of Science and Technology Policy Department of the Treasury



## February 2010Executive Summary

Under Executive Order 12866, agencies are required, to the extent permitted by law, “to assess both the costs and the benefits of the intended regulation and, recognizing that some costs and benefits are difficult to quantify, propose or adopt a regulation only upon a reasoned determination that the benefits of the intended regulation justify its costs.” The purpose of the “social cost of carbon” (SCC) estimates presented here is to allow agencies to incorporate the social benefits of reducing carbon dioxide (CO 2 ) emissions into cost-benefit analyses of regulatory actions that have small, or “marginal,” impacts on cumulative global emissions. The estimates are presented with an acknowledgement of the many uncertainties involved and with a clear understanding that they should be updated over time to reflect increasing knowledge of the science and economics of climate impacts.

The SCC is an estimate of the monetized damages associated with an incremental increase in carbon emissions in a given year. It is intended to include (but is not limited to) changes in net agricultural productivity, human health, property damages from increased flood risk, and the value of ecosystem services due to climate change.

This document presents a summary of the interagency process that developed these SCC estimates. Technical experts from numerous agencies met on a regular basis to consider public comments, explore the technical literature in relevant fields, and discuss 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 uncertainties and model differences transparently and consistently 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 higher-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 65.0 136.2

1I. 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 limited to) changes in net agricultural productivity, human health, property damages from increased flood risk, and the value of ecosystem services. We report estimates of the social cost of carbon in dollars per metric 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 report from the National Academies of Science (NRC 2009) points out that any assessment will suffer from uncertainty, speculation, and lack of information 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 climate 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 climate change will raise serious questions of science, economics, and ethics and should be viewed as provisional.

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

For such policies, the benefits from reduced (or costs from increased) emissions in any future year can 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 then be calculated by multiplying each of these future benefits by an appropriate discount factor and summing across all affected years. This approach assumes that the marginal damages from increased emissions 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 global carbon dioxide emissions. For policies that have a large (non-marginal) impact on global cumulative emissions, there is a separate question of whether the SCC is an appropriate tool for calculating the benefits 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 inputs and assumptions in order to generate SCC estimates. Agencies that actively participated in the interagency 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 between mass of
CO 2 and the mass of carbon is 3.67 (the molecular weight of CO 2 divided by the molecular weight of carbon = 44/12 = 3.67). 2Agency, and the Departments of Agriculture, Commerce, Energy, Transportation, and Treasury. This process was convened by the Council of Economic Advisers and the Office of Management and Budget, with active participation and regular input from the Council on Environmental Quality, National Economic Council, Office of Energy and Climate Change, 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 input assumptions that are grounded in the existing literature. 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 for use in regulatory analyses. For 2010, these estimates are $5, $21, $35, and $65 (in 2007 dollars). The first three estimates are based on the average 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 central value is the average SCC across models at the 3 percent discount rate. For purposes of capturing the uncertainties involved in regulatory impact analysis, we emphasize the importance and value of considering the full range. These SCC estimates also grow over time. For instance, the 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 annual SCC estimates from

2010 to 2050.

It is important to emphasize that the interagency process is committed to updating these estimates as the science and economic understanding of climate change and its impacts on society improves over time. Specifically, we have set a preliminary goal of revisiting the SCC values within two years or at such time as substantially updated models become available, 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 Regulatory Analyses

To date, economic analyses for Federal regulations have used a wide range of values to estimate the benefits associated with reducing carbon dioxide emissions. In the final model year 2011 CAFE rule, the Department of Transportation (DOT) used both a “domestic” 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), increasing 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 in 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 domestic SCC value of $7 per ton CO 2 (in 2006 dollars) for 2011 emission reductions (with a range of $0-$14 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). In addition, EPA’s 2008 Advance Notice of Proposed Rulemaking for Greenhouse Gases identified what it described as “very preliminary” SCC estimates subject to revision. EPA’s global mean values were $68 and $40 per ton CO 2 for discount rates of approximately 2 percent and 3 percent, respectively (in 2006 dollars for 2007 emissions).

3In 2009, an interagency process was initiated to offer a preliminary assessment of how best to quantify the benefits from reducing carbon dioxide emissions. To ensure consistency in how benefits are evaluated across agencies, the Administration sought to develop a transparent and defensible method, specifically designed for the rulemaking process, to quantify avoided climate change damages from
reduced CO 2 emissions. The interagency group did not undertake 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 interagency 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 published estimates produced from the most recently available versions of three integrated assessment 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, respectively. The $19 value was chosen as a central value between the $5 and $33 per ton estimates. All of these 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 for 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, interagency group has reconvened on a regular basis to generate improved SCC estimates. Specifically, the group has 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 uncertainties remain, and that current SCC estimates should be treated as provisional and revisable since 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 (2009) points out that there is tension between the goal of producing quantified estimates of the economic damages from an incremental ton of carbon and the limits of existing efforts to model these effects. Throughout this document, we highlight a number of concerns and problems that should be addressed by the research community, including research programs housed in many of the agencies participating in the interagency process to estimate the SCC.

The U.S. Government will periodically review and reconsider estimates of the SCC used for cost-benefit analyses to reflect increasing knowledge of the science and economics of climate impacts, as well as improvements in modeling. In this context, statements recognizing the limitations of the analysis and calling for further research take on exceptional significance. The interagency group offers the new SCC values with all due humility about the uncertainties embedded in them and with a sincere promise to continue work to improve them.
4A. 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-reviewed literature and used in the IPCC assessment. Each model is given equal weight in the SCC values developed through this process, bearing in mind their different limitations (discussed below).

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

The three IAMs translate emissions into changes in atmospheric greenhouse concentrations, atmospheric concentrations into changes in temperature, and changes in temperature into economic damages. The emissions projections used in the models are based on specified socio-economic (GDP and population) pathways. These emissions are translated into concentrations using the carbon cycle built into each model, and concentrations are translated 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 about how to discount them.

Each model takes a slightly different approach to model how changes in emissions result in changes in economic damages. In PAGE, for example, the consumption-equivalent damages in each period are calculated as a fraction of GDP, depending on the temperature in that period relative to the pre

industrial 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 detail here. In a later section, we discuss key gaps in how the models account for various scientific and economic processes (e.g. the probability of catastrophe, and the ability to adapt to climate change and the physical changes it causes).

2 The DICE (Dynamic Integrated Climate and Economy) model by William Nordhaus evolved from a series of energy models and was first presented in 1990 (Nordhaus and Boyer 2000, Nordhaus 2008). The PAGE (Policy Analysis of the Greenhouse Effect) model was developed by Chris Hope in 1991 for use by European decision-makers in 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, originally 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). 5The parameters and assumptions embedded in the three models vary widely. A key objective of the interagency process was to enable a consistent exploration of the three models while respecting the different approaches to quantifying damages taken by the key modelers in the field. An extensive review of the literature was conducted to select three sets of input parameters for these models: climate sensitivity, socio-economic and emissions trajectories, and discount rates. A probability distribution for climate sensitivity was specified as an input into all three models. In addition, the 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 were left unchanged, relying on the model developers’ best estimates and judgments. In DICE, these parameters are handled deterministically and represented by fixed constants; in PAGE, most parameters are represented 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 function) 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 are 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 natural capital today through reductions in emissions— implying reduced consumption—harmful effects of climate 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 latter declining over time due to technological progress. The DICE damage function links global average temperature 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 climate change, and is calibrated to include the effects of warming on the production of market and nonmarket 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 climate-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 includes the expected value of damages associated with low probability, high impact “catastrophic” climate change. This last component is calibrated based on a survey of experts (Nordhaus 1994). The expected value of these impacts is then added to the other market and non-market impacts mentioned above.

No structural components of the DICE model represent adaptation explicitly, though it is included implicitly through the choice of studies used to calibrate the aggregate damage function. For example, its agricultural impact estimates assume that farmers 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, water systems, construction, fisheries, and outdoor recreation imply optimistic and costless adaptation in these sectors (Nordhaus and Boyer, 2000; Warren

6et al., 2006). Costs of resettlement due to sea level rise are incorporated into damage estimates, but their magnitude is not clearly reported. Mastrandrea’s (2009) review concludes that “in general, DICE assumes very effective adaptation, and largely ignores adaptation costs."

Note that the damage function in DICE has a somewhat different meaning from the damage functions in FUND and PAGE. Because GDP is endogenous in DICE and 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 damages in any given year do not propagate forward. 3

**The PAGE Model**

PAGE2002 (version 1.4epm) treats GDP growth as exogenous. It divides impacts into economic, non

economic, and catastrophic categories and calculates these impacts separately for eight geographic regions. Damages in each region are expressed as a fraction of output, where the fraction lost depends on the temperature change in each region. Damages are expressed as power functions of temperature change. The exponents of the damage function are the same in all regions but are treated as uncertain, with values ranging from 1 to 3 (instead of being fixed at 2 as in DICE).

PAGE2002 includes the consequences of catastrophic events in a separate damage sub-function. Unlike DICE, PAGE2002 models these events probabilistically. The probability of a “discontinuity” (i.e., a catastrophic event) is assumed to increase with temperature above a specified threshold. The threshold temperature, the rate at which the probability of experiencing a discontinuity increases above the threshold, and the magnitude of the resulting catastrophe 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 countries and 0°C for developing countries for economic impacts, and 0°C for all regions for non-economic impacts), but adaptation is assumed to reduce these impacts. Default values in PAGE2002 assume that the developed countries can ultimately eliminate up to 90 percent of all economic impacts beyond the tolerable 2°C increase and that developing countries can eventually eliminate 50 percent of their economic impacts. All regions are assumed to be able to mitigate 25 percent of the non-economic impacts through adaptation (Hope 2006).

**The FUND Model**

Like PAGE, the FUND model treats GDP growth as exogenous. It includes separately calibrated damage functions for eight market and nonmarket sectors: agriculture, forestry, water, energy (based on heating and cooling demand), sea level rise (based on the value of land lost and the cost of protection),

3 Using the default assumptions in DICE 2007, this effect generates an approximately 25 percent increase in the SCC relative to damages calculated by fixing GDP. In DICE2007, the time path of GDP is endogenous. Specifically, the path of GDP depends on the rate of saving and level of abatement in each period chosen by the optimizing representative agent in the model. We made two modifications to DICE to make it consistent with EMF GDP trajectories (see next section): we assumed a fixed rate of savings of 20%, and we re-calibrated the exogenous path of total factor productivity so that DICE would produce GDP projections in the absence of warming that exactly matched the EMF scenarios.

7ecosystems, human health (diarrhea, vector-borne diseases, and cardiovascular and respiratory mortality), and extreme weather. Each impact sector has a different functional form, and is calculated separately for sixteen geographic regions. In some impact sectors, the fraction of output lost or gained due to climate change depends not only on the absolute temperature change but also on the rate of temperature change and level of regional income. 4 In the forestry and agricultural sectors, economic damages also depend on CO 2 concentrations.

Tol (2009) discusses impacts not included in FUND, noting that many are likely to have a relatively small effect on damage estimates (both positive and negative). However, he characterizes several omitted impacts as “big unknowns”: for instance, extreme climate 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 studies of climate change have examined these issues.”

Adaptation is included both implicitly and explicitly in FUND. Explicit adaptation is seen in the agriculture and sea level rise sectors. Implicit adaptation is included in sectors such as energy and human health, where wealthier populations are assumed 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 region and temperature); and (3) those from CO 2 fertilization (damages are generally negative but diminishing to zero).

Adaptation is incorporated into FUND by allowing damages 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 climate 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 (represented 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 these representations are incomplete and highly uncertain. But given the paucity of data linking the physical impacts to economic damages, we were not 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 conditioning demand, while reduced cold stress in Europe, North America, and Central and East Asia results in health benefits in those regions at low to moderate levels of warming (Warren et al., 2006). 8Figure 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 models 5

The damage functions for the three IAMs are presented in Figures 1A and 1B, using the modeler’s default scenarios and mean input assumptions. There 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 temperature 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 greater proportion of the SCC value is due to damages in years with lower temperature increases. For example, 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 approximately 55 percent and 80 percent at discount rates of 3 and 5 percent, respectively.

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

5 The x-axis represents increases in annual, rather than equilibrium, temperature, while the y-axis represents the annual stream of benefits as a share of global GDP. Each specific combination of climate sensitivity, socio

economic, and emissions parameters will produce a different realization of damages for each IAM. The damage functions represented in Figures 1A and 1B are the outcome of default assumptions. For instance, under alternate assumptions, the damages from FUND may cross from negative to positive at less than or greater than 3 °C. 9Figure 1B: Annual Consumption Loss for Lower Temperature Changes in DICE, FUND, and PAGE ­

B. Global versus Domestic Measures of SCC

Because of the distinctive nature of the climate change problem, we center our current attention on a global measure of SCC. This approach is the same as that taken for the interim values, but it otherwise represents a departure from past practices, which tended to put greater emphasis on a domestic measure of SCC (limited to impacts of climate change experienced within U.S. borders). As a matter of law, consideration of both global and domestic values is generally permissible; the relevant statutory provisions are usually ambiguous and allow selection 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 change problem is highly unusual in at least two respects. First, it involves a global externality: emissions of most greenhouse gases contribute to damages around the world even when they are emitted in the United States. Consequently, to address the global nature of the problem, the SCC must incorporate the full (global) damages caused by GHG emissions. Second, climate change presents a problem that the United States alone cannot solve. Even if the United States were to reduce its greenhouse gas emissions to zero, that step would be far from enough to avoid substantial climate change. Other countries would also need to take action to reduce emissions if

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 does not intrude on such interests. 10significant changes in the global climate are to be avoided. Emphasizing the need for a global solution to a global problem, the United States has been actively involved in seeking international agreements to reduce emissions and in encouraging other nations, including emerging major economies, to take significant steps to reduce emissions. When these considerations are taken as a whole, the interagency group concluded that a global measure of the benefits from reducing U.S. emissions is preferable.

When quantifying the damages associated with a change 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 reductions in wealth in different regions of the world. A per-capita loss of $500 in GDP, for instance, is weighted 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 reduction in utility or welfare than does the same loss in a wealthy nation. Notwithstanding the theoretical claims on behalf of equity weighting, the interagency group concluded that this approach would not be appropriate for estimating a SCC value used in domestic regulatory analysis. 7 For this reason, the group concluded that using the global (rather than domestic) value, without equity weighting, is the appropriate approach.

**Domestic SCC**

As an empirical matter, the development of a domestic 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 parameter 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, across the scenarios analyzed. Alternatively, if the fraction of GDP lost due to climate change is assumed to be similar across countries, the domestic benefit would 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 workgroup determined that a range of values from 7 to 23 percent should be used to adjust the global SCC to calculate domestic effects. Reported domestic values should use this range. It is recognized that these values are approximate, provisional, and highly speculative. There is no a priori reason why domestic benefits should be a constant fraction of net global 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 methods 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 serious harm on a poor nation than on a wealthy one, but development of the appropriate "equity weight" is challenging. Emissions reductions also impose costs, and hence a full account would have to consider that a given cost of emissions reductions imposes a greater utility or welfare loss on a poor nation than on a wealthy one. Even if equity weighting—for both the costs and benefits of emissions reductions—is appropriate when considering the utility or welfare effects of international action, the interagency group concluded that it should not be used in developing an SCC for use in regulatory policy at this time.

8 Based on 2008 GDP (in current US dollars) from the **World Bank Development Indicators Report**

. 11C. 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 finding: methane, nitrous oxide, hydrofluorocarbons, perfluorocarbons, and sulfur hexafluoride. The climate impact of these gases is commonly discussed in terms of their 100-year global warming potential (GWP). GWP measures the ability of different gases to trap heat in the atmosphere (i.e., radiative forcing per unit of mass) over a particular timeframe relative to CO 2 . However, because these gases differ in both radiative forcing and atmospheric lifetimes, their relative damages are not constant over time. For example, because methane has a short lifetime, its impacts occur primarily in the near term and thus are not discounted as heavily as those caused by longer-lived gases. Impacts other than temperature change also vary across gases in ways that are not captured by GWP. For instance, 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 feed 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 input 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 (or stabilization at a concentration of approximately 550 parts per million (ppm)). Uncertainties in this important parameter have received substantial attention in the peer-reviewed literature.

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 independent lines of evidence...including observed climate change and the strength of known feedbacks simulated in [global climate models],**  **we conclude that the global mean equilibrium warming for doubling CO 2**  **, or ‘equilibrium climate**

9 The equilibrium climate sensitivity includes the response of the climate system to increased greenhouse 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 scale of many hundreds to thousands of years (e.g. Hansen et al. 2007). 12**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 larger than 1.5 °C.**  10

**For fundamental physical reasons as well as data limitations, values substantially higher than 4.5 °C still cannot be excluded, but agreement with observations 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 workgroup selected four candidate probability distributions and 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 distributions.

Table 1: Summary Statistics for Four Calibrated Climate 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 greater than 10°C (see Hegerl et al. 2006, p. 721).

We selected the calibrated Roe and Baker distribution from the four candidates for two reasons. First, the Roe and Baker distribution is the only one of the four that is based on a theoretical understanding of the response of the climate system to increased greenhouse gas concentrations (Roe and Baker 2007,

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

11 Strictly speaking, “most likely” refers to the mode of a distribution rather than the median, but common usage would allow the mode, median, or mean to serve as candidates for the central or “most likely” value and the IPCC report is not specific on this point. For the distributions we considered, the median was between the mode and the mean. For the Roe and Baker distribution, setting the median equal to 3°C, rather than the mode or mean, gave a 95 th percentile that is more consistent with IPCC judgments 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 the truncated distributions selected by the IPCC (Hegerl, et al., 2006); the average median is 3.1 °C and the average mode is 2.3 °C, which is most consistent with a Roe and Baker distribution with the median set equal to 3 °C. 13Roe 2008). In contrast, the other three distributions are mathematical functions that are arbitrarily chosen based on simplicity, convenience, and general 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 factors are proportional to the change in surface temperature; and (3) uncertainties in feedback factors are normally 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 better reflects the IPCC judgment that “values substantially higher than 4.5°C still cannot be excluded.” Although the IPCC made no quantitative judgment, the 95 th percentile of the calibrated Roe & Baker distribution (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 Newbold 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 equilibrium climate sensitivity “is very likely larger than 1.5°C.” Although the calibrated Roe & Baker distribution, for which the probability of equilibrium climate sensitivity being greater than 1.5°C is almost 99 percent, is not inconsistent with the IPCC definition of “very likely” as “greater than 90 percent probability,” it reflects a greater degree of certainty about very low values of ECS than was expressed by the IPCC.

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

Calibrated Roe & Baker

To show how the calibrated Roe and Baker distribution compares to different estimates of the� probability distribution function of equilibrium climate sensitivity in the empirical literature, Figure 2� (below) overlays it on Figure 9.20 from the IPCC Fourth Assessment Report. These functions are scaled�

14to integrate to unity between 0 °C and 10 °C. The horizontal 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 group is how to select the set of socio-economic and emissions parameters for use in PAGE, DICE, and FUND. Socio-economic pathways are closely tied to climate damages because, all else equal, more and wealthier people tend to emit more greenhouse gases and also have a higher (absolute) willingness to pay to avoid climate disruptions. For this reason, we consider how to model several input parameters in tandem: GDP, population, CO 2 emissions, and

non-CO 2 radiative forcing. A wide variety of scenarios have 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 scenarios that span most of the plausible ranges of
outcomes for these variables.

To accomplish this task in a transparent way, we decided to rely on the recent Stanford Energy Modeling Forum exercise, EMF-22. EMF-22 uses ten well-recognized models to evaluate substantial, coordinated global action to meet specific stabilization targets. A key advantage of relying on these data is that GDP, population, and emission trajectories are internally consistent for each model and scenario evaluated. The EMF-22 modeling effort also is preferable to the IPCC SRES due to their age (SRES were developed in 1997) and the fact that 3 of 4 of the SRES scenarios are now extreme outliers in one or more variables. Although the EMF-22 scenarios have not undergone the same level of scrutiny as the SRES scenarios, they are recent, peer-reviewed, published, and publicly 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 emission trajectories that span a range of plausible scenarios. Five trajectories were selected from EMF-22 (see Table 2 below). Four of these represent potential business-as-usual (BAU) growth in population, 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 used by MiniCAM, MESSAGE, IMAGE, and the optimistic scenario from MERGE. For the BAU pathways, we used the GDP, population, and emission trajectories from each of these four models. For the 550 ppm CO 2 e scenario, we averaged the GDP, population, and emission trajectories implied by these same four models.

12 The estimates based on instrumental data are from Andronova and Schlesinger (2001), Forest et al. (2002;� dashed line, anthropogenic forcings only), Forest et 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). Hegerl et al. (2006)� are based on multiple palaeoclimatic reconstructions of north hemisphere mean temperatures over the last 700� years. Also shown are the 5-95 percent approximate ranges for two estimates from the last glacial maximum� (dashed, Annan et al. 2005; solid, Schneider von Deimling et al. 2006), which are based on models with different� structural properties.� 13 Such an emissions path would be consistent with widespread action by countries to mitigate GHG emissions,� though it could also result from technological advances. It was chosen because it represents the most stringent� case analyzed by the EMF-22 where all the models converge: a 550 ppm, not to exceed, full participation scenario.� 15Table 2: Socioeconomic and Emissions Projections from 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 trillion 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 assumptions about how the future will evolve without prejudging what is likely to occur. The interagency group considered formally assigning probability weights to different states of the world, but this proved challenging to do in an analytically rigorous way given the dearth of information on the likelihood of a full range of future socio-economic pathways.

There are a number of caveats. First, EMF BAU scenarios 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 views 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 account the different price levels across countries, so it more accurately describes relative standards of living across countries. MERs tend to make low-income countries 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 higher economic growth in low income countries. There is an ongoing debate about how much this will affect estimated climate impacts. Critics of the use of MER argue that it leads to overstated economic growth and hence a significant upward bias in projections of greenhouse gas emissions, and unrealistically high future temperatures (e.g., Castles and Henderson 2003). Others argue that convergence of the emissions-intensity gap across countries at least partially offset the overstated income gap so that differences in exchange rates have less of an effect on emissions (Holtsmark and Alfsen, 2005; Tol, 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 national accounts price and quantity indexes for time-series extrapolations). However, he notes that it important to keep this debate in perspective; it is by no means clear that exchange-rate-conversion issues are as important as uncertainties about population, technological change, or the many geophysical uncertainties. 16from the more optimistic (e.g. abundant low-cost, low-carbon energy) to more pessimistic (e.g. constraints on the availability of nuclear and renewables). 15 Second, the socio-economic trajectories associated with a 550 ppm CO 2 e concentration scenario are not derived from an assessment of what policy is optimal from a benefit-cost standpoint. Rather, it is indicative of one possible future outcome. The emission trajectories underlying some BAU scenarios (e.g. MESSAGE’s 612 ppm) also are consistent with some modest policy action to address climate change. 16 We chose not to include socio-economic trajectories that achieve even lower GHG concentrations at this time, given the difficulty many models had in converging to meet these targets.

For comparison purposes, the Energy Information Agency in its 2009 Annual Energy Outlook projected that global carbon dioxide emissions will grow to 30.8, 35.6, and 40.4 gigatons in 2010, 2020, and 2030, respectively, while world GDP is projected to be $51.8, $71.0 and $93.9 trillion (in 2005 dollars using market exchange rates) in 2010, 2020, and 2030, respectively. 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 2000 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 net 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 other factors (e.g. aerosols and other gases). See the Appendix 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, economics, philosophy, and law. Although it is well understood that the discount rate has a large influence on the current value of future damages, there is no consensus about what rates to use in this context. Because carbon dioxide emissions are long-lived, subsequent damages occur over many years. In calculating the SCC, we first estimate the future damages to agriculture, human health, and other market 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 temperatures, as represented in each of the three IAMs. Then we discount the stream of future damages to its present value in the year when the additional unit of emissions was released using the selected discount rate, which is intended to reflect society's marginal rate of substitution between consumption in different time periods.

For rules with both intra- and intergenerational effects, agencies traditionally employ constant discount 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 case total primary energy production from nuclear, biomass, and non-biomass renewables is projected to increase from about 15 percent of total primary energy in 2000 to 54 percent in 2100. In comparison, the MiniCAM reference case shows 10 percent in 2000 and 21 percent in 2100.

16 For example, MiniCAM projects if all non-US OECD countries reduce CO 2 emissions to 83 percent below 2005 levels by 2050 (per the G-8 agreement) but all other countries continue along a BAU path CO 2 concentrations in 2100 would drop from 794 ppmv in its reference case to 762 ppmv. 17problems and presents considerable challenges. After reviewing those challenges, Circular A-4 states, “If your rule will have important intergenerational benefits or costs you might consider a further sensitivity analysis using a lower but positive discount rate in addition to calculating net benefits using discount rates of 3 and 7 percent.” For the specific purpose 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 “prescriptive.” The descriptive approach reflects a positive (non-normative) perspective based on observations of people’s actual choices—e.g., savings versus consumption decisions over time, and allocations of savings among more and less risky investments. Advocates of this approach generally call for inferring the discount rate from market rates of return “because of a lack of justification for choosing a social welfare function that is any different than what decision makers [individuals] actually use” (Arrow et al. 1996).

One theoretical foundation for the cost-benefit analyses in which the social cost of carbon will be used— the Kaldor-Hicks potential-compensation test—also suggests that market rates should be used to discount future benefits and costs, because it is the market interest rate that would govern the returns potentially set aside today to compensate future individuals for climate damages that they bear (e.g., Just et al. 2004). As some have noted, the word “potentially” is an important qualification; there is no assurance that such returns will actually be set aside to provide compensation, and the very idea of compensation is difficult to define in the intergenerational 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 and other physical capital.

The prescriptive approach specifies a social welfare function that formalizes the normative judgments that the decision-maker wants explicitly to incorporate into the policy evaluation—e.g., how inter

personal comparisons of utility should be made, and how the welfare of future generations should be weighed against that of the present generation. Ramsey (1928), for example, has argued that it is “ethically indefensible” to apply a positive pure rate 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 generations with regard to consumption versus environmental amenities may not be the same as those today, making the current market rate on consumption an inappropriate metric by which to discount 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 intergenerational transfers of wealth, which in the Kaldor-Hicks logic are presumed to compensate future generations for damage (a potentially controversial assumption, as noted above) (Arrow et al. 1996, Weitzman 1999).

Further, a legitimate concern about both descriptive and prescriptive approaches is that they tend to obscure important heterogeneity in the population. The utility function that underlies the prescriptive approach assumes a representative agent with perfect foresight and no credit constraints. This is an artificial rendering of the real world that misses many of the frictions that characterize individuals’ lives

18and indeed the available descriptive evidence supports this. For instance, many individuals smooth consumption by borrowing with credit cards that have relatively high rates. Some are unable to access traditional credit markets and rely on payday lending operations or other high cost forms of smoothing consumption. Whether one puts greater weight on the 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 the descriptive approach to inform the choice of discount rate. With recognition of its limitations, we find this approach to be the most defensible andtransparent 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 derive the appropriate discount rate(s), we note the inherent conceptual and practical difficulties of adequately capturing consumption trade-offs over many decades or even centuries. While relying primarily on the descriptive approach in selecting specific discount rates, the interagency group has been keenly aware of the deeply normative dimensions of both the debate over discounting in the intergenerational context and the consequences of selecting
one discount rate over another.

**Historically Observed Interest Rates**

In a market with no distortions, the return to savings would equal the private return on investment, and the market rate of interest would be the appropriate choice for the social discount rate. In the real world risk, taxes, and other market imperfections drive a wedge between the risk-free rate of return on capital and the consumption rate of interest. Thus, the literature recognizes two conceptual discount concepts—the consumption rate of interest and the opportunity cost of capital.

According to OMB’s Circular A-4, it is appropriate to use the rate of return on capital when a regulation is expected to displace or alter the use of capital in the private sector. In this case, OMB recommends Agencies use a discount rate of 7 percent. When regulation is expected to primarily affect private consumption—for instance, via higher prices for goods and services—a lower discount rate of 3 percent is appropriate to reflect how private individuals trade-off current and future consumption.

The interagency group examined the economics literature and concluded that the consumption rate of interest is the correct concept to use in evaluating the benefits and costs of a marginal change in carbon emissions (see Lind 1990, Arrow et al 1996, and Arrow 2000). The consumption rate of interest also is appropriate when the impacts of a regulation are measured 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 that vary with risk level, time horizon, and tax characteristics. The standard analytic framework used to develop intuition about the discount rate typically assumes a representative agent with perfect foresight and no credit constraints. The risk-free rate is appropriate for discounting certain future benefits or costs, but the benefits calculated by IAMs are uncertain. To use the risk-free rate to discount uncertain benefits, these benefits first must be

19transformed into "certainty equivalents," that is the maximum certain amount that we would exchange for the uncertain amount. However, the calculation of the certainty-equivalent requires first estimating 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 not equal the risk-free rate. If the benefits of thepolicy tend to be high in those states of the world in which consumption is low, then the certaintyequivalent benefits will be higher than the expected benefits (and vice versa). Since many (though not necessarily all) of the important impacts of climate change will flow through market sectors such as agriculture and energy, and since willingness to pay 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. Alternatively, a negative correlation between the returns 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 riskless and risky rates can be used to capture individuals’ consumption-equivalent interest rate. As a measure of the post-tax riskless rate, we calculate the average real return from Treasury notes over the longest time period available (those from Newell and Pizer 2003) and adjust for Federal taxes (the average marginal rate from tax years 2003 through 2006 is 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 recommendation to use 3 percent to represent the consumption
rate of interest. 18 A measure of the post-tax risky rate for investments whose returns are positively correlated with overall equity market returns can be obtained by adjusting pre-tax rates of household returns to risky investments (approximately 7 percent) for taxes yields a real rate of roughly 5 percent. 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 elasticity 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 government bonds as an appropriate measure of the consumption 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 important to keep in mind that we wish to reflect preferences for society as a whole, which generally has a longer planning horizon.

19 Cambell et al (2001) estimates that the annual real return from stocks for 1900-1995 was about 7 percent. The annual real rate of return for the S&P 500 from 1950 – 2008 was about 6.8 percent. In the absence of a better way to population-weight the tax rates, we use the middle of the 20 – 40 percent range to derive a post-tax 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. Consequently, 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 damage will 20rate of per-capita consumption) to equal the interest 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 the “Ramsey discount rate,” ρ + η∙g, will be equal to the rate of return to capital, i.e., the market interest rate.

A review of the literature provides some guidance on reasonable parameter values for the Ramsey discounting equation, based on both prescriptive and 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 from 1 to 4), although not all authors articulate whether their choice is based on prescriptive or descriptive reasoning. 22 Dasgupta (2008) argues that η should be greater than 1 and may be as high as 3, since η equal to 1 suggests savings rates that do not conform to observed behavior.

• ρ. With respect to the pure rate of time preference, most 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 intergenerational neutrality. Some have argued that to use any value other than ρ = 0 would unjustly discriminate against future generations (e.g., Arrow et al. 1996, Stern et al. 2006). However, even in an inter-generational setting, it may make sense to use a small positive pure rate of time preference because of the small probability of unforeseen cataclysmic events (Stern et al. 2006).

• g. A commonly accepted approximation is around 2 percent per year. For the socio-economic scenarios used for this exercise, the EMF models assume 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 generations. If η = 0, then a one dollar increase in income is equally valuable regardless of level of income; if η = 1, then a one percent increase in income is equally valuable no matter the 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 EMF socioeconomic scenarios or alternative assumptions 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 evidence 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 without 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. Anthoff, et al. (2009b) estimate **η** = 1.18, and **ρ** = 1.4 percent. When they multiply the bivariate probability distributions from their work and Evans and Sezer (2005) together, they find **η** = 1.47, and **ρ** = 1.07. 21countries 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 annual discount rate of 1.4 percent. In the context of permanent income savings behavior, however, Stern’s assumptions suggest that individuals would save 93 percent of their income. 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 prescriptive approach can be used to justify discount rates between roughly 1.4 and 3.1 percent. In light of concerns 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 important driver of the benefits estimate, it is uncertain over time. Ideally, we would formally model this uncertainty, just as we do for climate sensitivity. Weitzman (1998, 2001) showed theoretically and Newell and Pizer (2003) and Groom et al. (2006) confirm empirically that discount rate uncertainty can have a large effect on net present values. A main result from these studies is that if there is a persistent element to the uncertainty in the discount rate (e.g., the rate follows a random walk), then it will 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 Pizer 2003; Groom et al. 2006; Gollier 2008; Summers and Zeckhauser 2008; and Gollier and Weitzman 2009).

The proper way to model discount rate uncertainty remains an active area of research. Newell and Pizer (2003) employ a model of how long-term interest rates 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 observations 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 for better forecasts. Specifically, the volatility of interest rates depends on whether rates are currently low or high and variation in the level of persistence over 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 of discount rates applied over time (e.g., Weitzman 2001, and the UK’s “Green Book” for regulatory analysis). This approach uses a higher discount rate

23 Stern (2008) argues that building in a positive rate of exogenous technical change over time reduces the implied savings rate and that η at or above 2 are inconsistent with observed behavior with regard to equity. (At the same time, adding exogenous technical change—all else equal—would increase g as well.) 22initially, but applies a graduated scale of lower discount 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 future 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 appropriate market interest rate to use in this context and uncertainty about how interest rates may change over time, we use three discount rates to span a plausible range of certainty-equivalent constant discount rates: 2.5, 3, and 5 percent per year. Based on the review in the previous sections, the interagency workgroup determined that these three rates reflect reasonable judgments under both descriptive and prescriptive approaches.

The central value, 3 percent, is consistent with estimates provided in the economics literature and OMB’s Circular A-4 guidance for the consumption rate of interest. As previously mentioned, the consumption rate of interest is the correct discounting 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 represent the possibility that climate damages are positively correlated with market returns. Additionally, this 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 incorporate the concern that interest rates are highly uncertain over time. It represents the average certainty-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 if climate investments are negatively correlated with the overall market rate of return. Use of this lower value also responds to certain judgments using the prescriptive or normative approach and to ethical objections that have been raised about rates of 3 percent or higher.

24 For instance, the UK applies a discount rate of 3.5 percent to the first 30 years; 3 percent for years 31 - 75; 2.5 percent for years 76 - 125; 2 percent for years 126 - 200; 1.5 percent for years 201 - 300; and 1 percent after 300 years. As a sensitivity, it recommends a discount rate of 3 percent for the first 30 years, also decreasing over time.

25 Uncertainty in future damages is distinct from uncertainty in the discount rate. Weitzman (2008) argues that Stern’s choice of a low discount rate was “right for the wrong reasons.” He demonstrates how 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 result in an infinite willingness-to-pay for mitigation today. Newbold and Daigneault, (2009) and Nordhaus (2009) find that Weitzman’s result is sensitive to the functional forms chosen for climate sensitivity, utility, and consumption. Summers and Zeckhauser (2008) argue that uncertainty in future damages can also work in the other direction by increasing the benefits of waiting to learn the appropriate level of mitigation required.

26 Calculations done by Pizer et al. using the original simulation program from Newell and Pizer (2003). 23IV. 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 upon by the interagency group:

• A Roe and Baker distribution for the climate sensitivity 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 trajectories based on EMF-22.

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

Because the climate sensitivity parameter is modeled 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 from 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 the temperature in that period relative to the pre-industrial average temperature 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 investment, so we first adjust the EMF GDP paths as follows: Using the Cobb-Douglas production function with the DICE2007 parameters, we extract the path of exogenous technical change implied by the EMF GDP and population paths, then we recalculate the baseline GDP path taking into account 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 expected 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 steps, while the time steps in PAGE vary.)

6.� Discount the resulting path of marginal damages back to the year of emissions using the agreed upon fixed discount rates.

247. Calculate the SCC as the net present value of the discounted 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 of 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 multiple future years to cover the time horizons anticipated for upcoming rulemaking analysis. To maintain 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 models has a different default end year. The default time horizon is 2200 for PAGE, 2595 for DICE, and 3000 for the latest version of FUND. This is an issue for the multi-model approach because differences in SCC estimates may arise simply due to the model time horizon. Many consider 2200 too short a time horizon 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, population, and greenhouse gas emission trajectories after 2100, the last year for which these data are available 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. This is clearly too many separate distributions for consideration in a regulatory impact analysis.

To produce a range of plausible estimates that still reflects the uncertainty in the estimation exercise, the distributions from each of the models and scenarios 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 way, no integrated assessment model or socioeconomic scenario is given greater weight than another. Because the literature shows that the SCC is quite sensitive to assumptions about the discount rate, and because no consensus exists on the appropriate rate to use in an intergenerational context, we present SCCs based on the average values across models and socioeconomic 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 included to represent the higher-than-expected economic impacts from climate 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 full 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 emerges is the average SCC across models at the 3 percent discount rate. For purposes of capturing the uncertainties involved in regulatory impact analysis, we emphasize the importance and value of considering the full range.

25As previously discussed, low probability, high impact 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 climate 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 catastrophic damages (in contrast to the other two models),its probabilistic treatment of the equilibrium climate sensitivity parameter will directly affect the noncatastrophic damages that are a function of the rate of temperature change.

In Table 3, we begin by presenting SCC estimates for 2010 by model, scenario, and discount rate to illustrate the variability in the SCC across each of these input parameters. As expected, higher discount rates consistently result in lower SCC values, while lower discount rates result in higher SCC values for each socioeconomic trajectory. It is also evident that there are differences in the SCC estimated across the three main models. For these estimates, FUND produces 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 Discount 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 the estimates in the literature for the latest versions� of each model. For example, adjusting the values from the literature that were used to develop interim�

26SCC values to 2007 dollars for the year 2010 (assuming, as we did for the interim process, that SCC grows at 3 percent per year), FUND yields SCC estimates 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) close to $8 per ton for a 4 percent discount rate. Note that these comparisons are only approximate since the literature generally relies on Ramsey discounting, while we have assumed constant discount rates. 27

The SCC estimates from FUND are sensitive to differences in emissions paths but relatively insensitive to differences in GDP paths across scenarios, while the reverse is true for DICE and PAGE. This likely occurs because of several structural differences among the models. Specifically in DICE and PAGE, the fraction of economic output lost due to climate damages increases 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 vulnerability to climate change (a form of adaptation), whereas this does not occur in DICE and PAGE. These structural differences among the models make FUND more sensitive to the path of emissions and less sensitive to GDP compared to DICE and PAGE.

Figure 3 shows that IMAGE has the highest GDP in 2100 while MERGE Optimistic has the lowest. The ordering of global GDP levels in 2100 directly corresponds 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 direct relationship between its damage function and GDP.

Figure 3: Level of Global GDP across EMF Scenarios

450

400

350

Global 300 GDP (trillions 250 of U.S. dollars) 200

150

100

50

0

2000 2010 2020 2030 2050 2100 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 (version 1.4epm) treats ρ and η as random parameters, specified using 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, respectively. The FUND default value for η is 1, and Tol generates SCC estimates for values of ρ = 0, 1, and 3 in many recent papers (e.g. Anthoff et al. 2009). The path of per-capita consumption growth, g, varies over time but is treated deterministically in two of the three models. In DICE, g is endogenous. Under Ramsey discounting, as economic growth slows in the future, the large damages from climate change that occur far out in the future are discounted at a lower rate than impacts that occur in the nearer term.

27Table 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 combining all outputs (10,000 estimates per model run) from all scenarios and models for a given discount rate. Values for the years in between are calculated using 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 emissions are expected to produce larger incremental damages as physical and economic systems become more stressed in response to greater climatic change. Note that this approach allows us to estimate the growth rate of the SCC directly using DICE, PAGE, and FUND rather than assuming a constant annual growth rate as was done for the interim estimates (using 3 percent). This helps to ensure that the estimates are internally consistent with other modeling assumptions. Table 5 illustrates how the growth rate for these four SCC estimates varies over 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

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

20 10

- 2020

2020

- 2030

2030

- 2040

2040

- 2050 3.6%
3.7%

2.7%

2.1% 2.1%
2.2%

1.8%

1.4% 1.7%
1.8%

1.6%

1.1% 2.2%
2.2%

1.8%

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 for 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, should be discounted using the same rate. For example,

28climate damages in the year 2020 that are calculated using a SCC based on a 5 percent discount rate also should be discounted back to the analysis year using 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 evolving 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 research. These caveats, and additional observations in the following section, are necessary to consider when 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 addition, the exact magnitude of these impacts is uncertain because of the inherent complexity of climate processes, the economic behavior of current and future populations, and our inability to accurately forecast technological change and adaptation. Current IAMs do not assign value to all of the important physical, ecological, and economic impacts of climate change recognized in the climate change literature (some of which are discussed above) because of lack of precise information on the nature of damages and because the science incorporated into these models understandably lags behind the most recent research. Our ability to quantify and monetize impacts will undoubtedly improve with time. But it is also likely that even in future applications, a number of potentially significant damage categories will remain non-monetized. (Ocean acidification is one example of a potentially large damage from CO 2 emissions not quantified by any of the three models. Species and wildlife loss is another example that is exceedingly difficult to monetize.)

**Incomplete treatment of potential catastrophic damages.** There has been considerable recent discussion of the risk of catastrophic impacts and how best to account for extreme scenarios, such as the collapse 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 result in an infinite willingness-to-pay for mitigation today. 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 (2009) confirmed the potential for large catastrophe risk premiums but also showed that the aggregate benefit 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, using a right-skewed gamma distribution for climate sensitivity as well as an uncertain damage coefficient, but in most cases found only a modest risk premium. Given this difference in opinion, further research in this area is needed before its practical significance can be fully understood and a reasonable approach developed to account for such risks in regulatory analysis. (The next section discusses the scientific evidence on catastrophic impacts in greater detail.)

28 However, it is possible that other benefits or costs of proposed regulations unrelated to CO 2 emissions will be discounted at rates that differ from those used to develop the SCC estimates. 29**Uncertainty in extrapolation of damages to high temperatures:** The damage functions in these IAMs are typically calibrated by estimating damages at moderate temperature increases (e.g., DICE was calibrated at 2.5 °C) and extrapolated to far higher temperatures 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 technological change:** Each of the three integrated assessment models used here assumes a certain degree of low- or no-cost adaptation. For instance, Tol assumes a great deal of adaptation in FUND, including widespread reliance on air conditioning ; so much so, that the largest single benefit category in FUND is the reduced electricity costs from not having to run air conditioning as intensively (NRC 2009).

Climate change also will increase returns on investment to develop technologies that allow individuals to cope with adverse climate conditions, and IAMs to do not adequately account for this directed technological change. 29 For example, scientists may develop crops that are better able to withstand higher and more variable temperatures. Although DICE and FUND have both calibrated their agricultural sectors under the assumption that farmers will change 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 calibrations do not account for increases in climate variability, pests, or diseases, which could make adaptation more difficult than assumed by the IAMs for a given temperature change. Hence, models do not adequately account for potential adaptation or technical change that might alter the emissions pathway and resulting damages. In this respect, it is difficult to determine whether the incomplete treatment of adaptation and technological change in these IAMs under or overstate the likely damages.

**Risk aversion:** A key question unanswered during this interagency process is what to assume about relative risk aversion with regard to high-impact outcomes. These calculations do not take into accountthe possibility that individuals may have a higher willingness to pay to reduce the likelihood of lowprobability, high-impact damages than they do to reduce the likelihood of higher-probability but lowerimpact damages with the same expected cost. (The inclusion of the 95 th percentile estimate in the final set of SCC values was largely motivated by this concern.) If individuals do show such a higher willingness to pay, a further question is whether that fact should be taken into account for regulatory policy. Even if individuals are not risk-averse for such scenarios, it is possible that regulatory policy should include a degree of risk-aversion.

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

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

Nordhaus (2008) points to the need to explore the relationship 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 from whatever their next best use would have been in the absence of climate change (so productivity/GDP would have been still higher). 30the results. Using FUND, Anthoff et al (2009) explored the sensitivity of the SCC to Ramsey equation parameter assumptions based on observed behavior. They conclude that “the assumed rate of risk aversion is at least as important as the assumed rate of time preference in determining the social cost of carbon.” Since Circular A-4 allows for a different assumption on risk preference in regulatory analysis if it is adequately justified, we plan to continue investigating this issue.

V. A Further Discussion of Catastrophic Impacts and Damage 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 adverse 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 discontinuous “tipping point” behavior in Earth systems, (2) inter-sectoral and inter-regional interactions, including global security impacts of high-end warming, and (3) limited near-term substitutability between damage to natural systems and increased consumption.

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 government will continue to evolve with improvements in modeling. In the meantime, we discuss some of the available evidence.

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

The damage functions in the models are calibrated at 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 are a number of potential climatic “tipping points” at which the Earth system may exhibit discontinuous behavior with potentially severe social and economic consequences (e.g., Lenton et al, 2008, Kriegler et al., 2009). These tipping points include the disruption of the Indian Summer Monsoon, dieback of the Amazon Rainforest and boreal forests, collapse of the Greenland Ice Sheet and the West Antarctic Ice Sheet, reorganization of the Atlantic Meridional Overturning Circulation, strengthening of El Niño-Southern Oscillation, and the release of methane from melting permafrost. Many of these tipping points are estimated to have thresholds between about 3 °C and 5 °C (Lenton et al., 2008). Probabilities of several of these tipping points were assessed through 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 potentially 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., ignoring 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 trajectories of $113 per ton of CO 2 is almost double the value estimated by DICE, $58 per ton in 2010. We cannot evaluate how well the three models account for catastrophic or non-catastrophic impacts, but this estimate highlights the sensitivity of SCC values in the tails of the distribution to the assumptions made about catastrophic impacts.

31Table 6: Probabilities of Various Tipping Points from Expert Elicitation ­

Possible Tipping Points Duration
before effect is fully realized (in years) Additional Warming by 2100

0.5-1.5 C 1.5-3.0 C 3-5 C

Reorganization of Atlantic Meridional Overturning Circulation 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 5-41% 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 formally assessed

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

PAGE treats the possibility of a catastrophic event probabilistically, while DICE treats it deterministically (that is, by adding the expected value of the damage from a catastrophe to the aggregate damage function). In part, this results in different probabilities being assigned to a catastrophic event across the two models. For instance, PAGE places a probability near zero on a catastrophe at 2.5 °C warming, while DICE assumes a 4 percent probability of a catastrophe 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 tipping 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 tipping point will not necessarily lead to an economic catastrophe in the sense used in the IAMs. A tipping point is a critical threshold across which some aspect of the Earth system starts to shifts into a qualitatively different state (for instance, one withdramatically reduced ice sheet volumes and higher sea levels). In the IAMs, a catastrophe is a lowprobability environmental change with high economic impact.

**Failure to incorporate inter-sectoral and inter-regional interactions**

The damage functions do not fully incorporate either inter-sectoral or inter-regional interactions. For instance, while damages to the agricultural sector are incorporated, the effects of changes in food supply on human health are not fully captured and depend on the modeler’s choice of studies used to calibrate the IAM. Likewise, the effects of climate damages in one region of the world on another region are not included in some of the models (FUND includes the effects of migration from sea level rise). These inter-regional interactions, though difficult to quantify, are the basis for climate-induced national and economic security concerns (e.g., Campbell et al., 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 million

32additional people by 2080, and the creation of millions of climate refugees (Easterling et al., 2007; Campbell et al., 2007).

**Imperfect substitutability of environmental amenities**

Data from the geological record of past climate changes suggests that 6 °C of warming may have severe consequences for natural systems. For instance, during 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 consumption 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 that 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 and less bio-diverse, the services they provide may become increasingly more costly to replace. Uncalibrated attempts to incorporate the imperfect substitutability of such amenities into IAMs (Sterner and Persson, 2008) indicate that the optimal degree of emissions abatement can be considerably greater than is commonly recognized.

VI. Conclusion

The interagency group selected four SCC estimates for use in regulatory analyses. For 2010, these estimates are $5, $21, $35, and $65 (in 2007 dollars). The first three estimates are based on the average 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 central value is the average SCC across models at the 3 percent discount rate. For purposes of capturing the uncertainties involved in regulatory impact analysis, we emphasize the importance and value of considering the full range. These SCC estimates also grow over time. For instance, the 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 integrated assessment models capture catastrophic and non-catastrophic impacts, their incomplete treatment of adaptation and technological change, uncertainty in the extrapolation of damages to high temperatures, and assumptions regarding risk aversion. The limited 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 government will continue to evolve with improvements in modeling.

33References

Andronova, N., and M. Schlesinger. 2001. “Objective estimation of the probability density function for climate sensitivity.” **J. Geophys. Res** ., 106(D19), 22605–22611.

Annan, J., et al., 2005. “Efficiently constraining climate sensitivity with paleoclimate simulations.” **Scientific Online Letters on the Atmosphere** , 1, 181–184.

Anthoff D, C. Hepburn, and R. Tol. 2009a. “Equity Weighting and the Marginal Damage Costs of Climate Change.” **Ecological Economics** 68:836-849.

Anthoff, D., R. Tol, and G. Yohe. 2009b. “Risk aversion, time preference, and the social cost of carbon.” **Environmental Research Letters** 4: 024002 (7pp).

Arrow, K. 2007. “Global climate change: a challenge to policy.” **Economist’s Voice** 4(3):Article 2.

Arrow, K. 2000. “A Comment on Cooper.” **The World Bank Research Observer** . vol 15, no. 2.

Arrow, K., et al. 1996. **Benefit-Cost Analysis in Environmental, Health, and Safety Regulation: A Statement of Principles**  . Washington, D.C., AEI Press. pp. 13-14.

Arrow, K.J., et al. 1996. ”Intertemporal equity, discounting and economic efficiency,” in Climate Change 1995: Economic and Social Dimensions of Climate Change, Contribution of Working Group III to the **Second Assessment Report of the Intergovernmental Panel on Climate Change**

. Campbell, J., P. Diamond, and J. Shoven. 2001. “Estimating the Real Rate of Return on Stocks Over the Long Term.” Presented to the Social Security Advisory Board. August.

Campbell, K. et al. 2007. **The age of consequences: The foreign policy and national security implications of global climate change**  . Center for Strategic & International Studies, 119 pp.

Castles, I. and D. Henderson. 2003. “The IPCC Emission Scenarios: An Economic-Statistical Critique.” **Energy and Environment** 14(2-3): 159-185.

Chetty, R. 2006. “A New Method of Estimating Risk Aversion.” **American Economic Review** 96(5):
1821–1834.

Dasgupta P. 2006. “Comments on the Stern Review’s economics of climate change.” University of Cambridge working paper.

Dasgupta P. 2008. “Discounting climate change.” **Journal of Risk and Uncertainty** 37:141-169.

Easterling, W., et al. 2007. **Climate Change 2007: Impacts, Adaptation, and Vulnerability**

. Intergovernmental Panel on Climate Change, 976 pp. http://www.ipcc.ch/publications_and_data/publications_ipcc_fourth_assessment_report_wg2_report_i mpacts_adaptation_and_vulnerability.htm , last accessed March 25, 2010.

Evans D., and H. Sezer. 2005. “Social discount rates for member countries of the European Union.” **J. Econ. Stud**  . 32 47–59.

34Forest, C., et al. 2002. “Quantifying uncertainties in climate system properties with the use of recent
observations.” **Science** 295, 113.

Forest, D., P. Stone, and A. Sokolov. 2006. “Estimated PDFs of climate system properties including natural and anthropogenic forcings.” **Geophys. Res. Lett** ., 33, L01705.

Forster, P., and J. Gregory. 2006. “The climate sensitivity and its components diagnosed from Earth radiation budget data.” **J. Clim** ., 19, 39–52.

Frame, D., et al. 2005. “Constraining climate forecasts: The role of prior assumptions.” **Geophys. Res.**

**Lett** ., 32, L09702.

Gingerich, P. 2006. “Environment and evolution through the Paleocene-Eocene thermal maximum.”
**Trends Ecol. Evol.** 21: 246-253.

Gollier, C. 2008. “Discounting with fat-tailed economic growth.” **Journal of Risk and Uncertainty** 37:171

- 186.

Gollier, C. and M. Weitzman (2009). "How Should the Distant Future be Discounted When Discount Rates are Uncertain?" Harvard University, mimeo, Nov 2009.

Gregory, J., et al. 2002a. “An observationally based estimate of the climate sensitivity.” **J. Clim** ., 15(22),
3117–3121.

Groom, B., Koundouri, P., Panipoulou, E., Pantelidis, T. 2006. “An econometric approach to estimating long-run discount rates.” **Journal of Applied Econometrics.**

Hall R, and C. Jones . 2007. “The value of life and the rise in health spending.” Quarterly **Journal of**
**Economics** 122(1):39-72.

Hansen, J.,M. Sato, P. Kharecha, G. Russell, D. W. Lea and M. Siddall. 2007. “Climate change and trace gases.” **Phil. Trans. Roy. Soc. A** 365: 1925-1954.

Hegerl G, et al. 2007. “Understanding and attributing climate change.” in Solomon S, et al. (eds) **Climate Change 2007: the physical science basis. Contribution of Working Group I to the Fourth Assessment**  **Report of the Intergovernmental Panel on Climate Change** . Cambridge, UK: Cambridge University Press. http://www.ipcc.ch/publications_and_data/ar4/wg1/en/contents.html

Hegerl, G., T. Crowley, W. Hyde, and D. Frame. 2006. “Constraints on climate sensitivity from temperature reconstructions of the past seven centuries.” **Nature** 440.

Holtsmark, B., and K. Alfsen. 2005. “PPP Correction of the IPCC Emission Scenarios – Does it Matter?” **Climatic Change** 68(1-2): 11-19.

Hope C. 2006. “The marginal impact of CO2 from PAGE2002: an integrated assessment model incorporating the IPCC’s five reasons for concern.” **The Integrated Assessment Journal** 6(1):19-56.

Hope C. 2008. “Optimal carbon emissions and the social cost of carbon under uncertainty.” **The Integrated Assessment Journal**  8(1):107-122.

35Intergovernmental Panel on Climate Change (2007). “Summary for Policymakers.” In **Climate Change 2007: The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the**  **Intergovernmental Panel on Climate Change** . Cambridge University Press.

Just, R., D. Hueth, and A. Schmitz. 2004. **The Welfare Economics of Public Policy** . Glos UK: Edward Elgar Publishing Limited.

Knutti, R., T. Stocker, F. Joos, and G. Plattner. 2002. “Constraints on radiative forcing and future climate change from observations and climate model ensembles.” **Nature** , 416, 719–723.

Kriegler, E. et al. 2009. “Imprecise probability assessment of tipping points in the climate system.” **Proc. Natl. Acad. Sci.**  106: 5041-5046.

Kotlikoff, L. and D. Rapson. 2006. “Does It Pay, at the Margin, to Work and Save? – Measuring Effective Marginal Taxes on Americans’ Labor Supply and Saving.” National Bureau of Economic Research, Working Paper, No. 12533.

Le Treut H., et al. 2007. “Historical Overview of Climate Change.” in Solomon et al., **Climate Change**
**2007**

.
Lenton, T., et al. 2008. “Tipping elements in the Earth’s climate system.” **Proc. Natl. Acad. Sci.** 105: 1786

- 1793.

Levy, M., et al. 2005. “Ecosystem conditions and human well-being.” In: **Ecosystems and Human Well**

  ** being: Current State and Trends, Volume 1.** [R. Hassan, R. Scholes, and N. Ash, eds.] Washington: Island Press. pp. 123-164.

Lind, R. 1990. “Reassessing the Government’s Discount Rate Policy in Light of New Theory and Data in a World Economy with a High Degree of Capital Mobility.” **Journal of Environmental Economics and Management**  18, S-8-S-28.

Mastrandre, M. 2009. “Calculating the benefits of climate policy: Examining the assumptions of Integrated Assessment Models.” Pew Center on Global Climate Change Working Paper, 60 pp.

Meehl, G, et al. 2007. “Global Climate Projections.” in Solomon et al., **Climate Change 2007**

.
National Research Council (2009). **Hidden Costs of Energy: Unpriced Consequences of Energy Production**
**and Use** . National Academies Press.

Newbold S, Daigneault A. 2009. “Climate response uncertainty and the benefits of greenhouse gas emissions reductions.” **Environmental and Resource Economics** 44:351-377.

Newell, R., and W. Pizer. 2003. Discounting the distant future: how much do uncertain rates increase valuations? **Journal of Environmental Economics and Management** 46: 52-71.

Nordhaus, W. 1994. “Expert Opinion on Climate Change.” **American Scientist** 82: 45-51.

Nordhaus, W. 2007a. **Accompanying notes and documentation on development of DICE-2007 model: notes on DICE-2007.delta.v8 as of September 21, 2007.** 

36Nordhaus, W. 2007b. “Alternative measures of output in global economic-environmental models: Purchasing power parity or market exchange rates?” **Energy Economics** 29: 349-372.

Nordhaus W. 2008. **A Question of Balance: Weighing the Options on Global Warming Policies** . New Haven, CT: Yale University Press.

Nordhaus, W. 2009. “An Analysis of the Dismal Theorem. Cowles Foundation Discussion Paper. No. 1686. January.

Nordhaus W., and Boyer J. 2000. **Warming the World: Economic Models of Global Warming** . Cambridge,
MA: MIT Press.

Pindyck, R. 2009. “Uncertain Outcomes and Climate Change Policy.” NBER Working Paper, No. 15259. August.

Ramsey, F. 1928. “A Mathematical Theory of Saving.” **The Economic Journal** 38(152): 543-559.

Roe, G. 2008. “Feedbacks, timescales, and seeing red.” **Annual Review of Earth and Planetary Sciences**
37:5.1-5.23

.
Roe, G., and M. Baker. 2007. “Why is climate sensitivity so unpredictable?” **Science** 318:629-632.

Schneider von Deimling, T., H. Held, A. Ganopolski, and S. Rahmstorf. 2006. “Climate sensitivity estimated from ensemble simulations of glacial climate.” **Clim. Dyn** ., 27, 149–163.

Smith, J. et al. 2009. “Transient dwarfism of soil fauna during the Paleocene-Eocene Thermal
Maximum.” **Proc. Natl. Acad. Sci.** 106: 17665-17660.

Stern, N., et al. (2006), **Stern Review: The Economics of Climate Change** , HM Treasury, London. See http://www.hm-treasury.gov.uk/stern_review_report.htm , last accessed March 25, 2010.

Stern N. 2008. “The economics of climate change.” **American Economic Review** 98(2):1-37.

Sterner, T., and U. Persson. 2008. An even Sterner review: Introducing relative prices into the discounting debate. **Rev. Env. Econ. Pol.** 2: 61-76.

Summers, L., and R. Zeckhauser. 2008. “Policymaking for Posterity.” Journal of Risk and Uncertainty 37:
115-140.

Szpiro, G. 1986. “Measuring Risk Aversion: An Alternative Approach.” **The Review of Economics and**
**Statistics** 68(1): 156-9.

Tol, R. 2002a. “Estimates of the damage costs of climate change. Part I: benchmark estimates.” **Environmental and Resource Economics** 21:47-73.

Tol, R. 2002b. “Estimates of the damage costs of climate change. Part II: dynamic estimates.” **Environmental and Resource Economics** 21:135-160.

Tol, R. 2006. “Exchange Rates and Climate Change: An Application of FUND.” **Climatic Change** 75(1-2):
59-80.

37Tol, R. 2009. “An analysis of mitigation as a response to climate change.” Copenhagen Consensus on Climate. Discussion Paper.

U.S. Department of Defense. 2010. Quadrennial Defense Review Report. February.

Warren, R., et al. 2006. “Spotlight Impact Functions in Integrated Assessment.” Tyndall Center for Climate Change Research, Working Paper 91.

Weitzman, M. 2009. “On modeling and interpreting the economics of catastrophic climate change.” **Review of Economics and Statistics** 91:1-19.

Weitzman, M. 2007. “A review of The Stern Review of the Economics of Climate Change **.” Journal of**
**Economic Literature** 45:703-724.

Weitzman, M. 1999. In Portney P.R. and Weyant J.P. (eds.), **Discounting and Intergenerational Equity**

, Resources for the Future, Washington, D.C.

Weitzman, M. 1998. “Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate.” **Journal of Environmental Economics and Management** 36 (3): 201-208.

Wing, S. et al. 2005. “Transient floral change and rapid global warming at the Paleocene-Eocene boundary.” **Science** 310: 993-996.

38Appendix

Table A1: Annual SCC Values: 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
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 65.0 136.2 39This Appendix also provides additional technical information about the non-CO 2 emission projections used in the modeling and the method for extrapolating emissions forecasts through 2300, and shows the full distribution of 2010 SCC estimates by model 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 retaining each model’s default radiative forcings (RF) due to other factors (e.g., aerosols and other gases). Specifically, to obtain the RF associated with the non

CO 2 EMF emissions only, we calculated the RF associated with the EMF atmospheric CO 2 concentrations
and subtracted them from the EMF total RF. 30 This approach respects the EMF scenarios as much as possible and at the same time takes account of those components not included in the EMF projections.
Since each model treats non-CO 2 gases differently (e.g., DICE lumps all other gases into one composite exogenous input), this approach was applied slightly differently in each of the models.

FUND : Rather than relying on RF for these gases, the actual 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. To include the EMF values, we removed the default CH 4 and SF 6 factors 31 , decomposed the excess forcing vector, and constructed a new excess forcing vector
that includes the EMF RF for CH 4 , N 2 0, and fluorinated gases, as well as the model default 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 path
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 from 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 arbiter" model, which is tuned to emulate the major global climate models) and the resulting 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 MERGE 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. 40According 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 non

CO 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 default 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 share of nonaerosol RF matches the share implicit in the AR4 summary statistics cited above and remains
constant over time.

Assumption (1) means that the RF from aerosols in 2100 equals 66 percent of that in 2000, which is the fraction of the TAR projection of total RF from aerosols (including sulfates, black carbon, and organic carbon) in 2100 vs. 2000 under the A1B SRES emissions 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 provides one of the lower aerosol forecasts among the SRES marker scenarios and is more consistent with the AR4 discussion of the post-SRES literature on
aerosols:

**Aerosols have a net cooling effect and the representation 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 lower than reported in SRES. {WGIII 3.2, TS.3, SPM}. 32** 

Assuming a simple linear decline in aerosols from 2000 to 2100 also is more consistent with the recent literature on these emissions. For example, Figure A1 shows that the sulfur dioxide emissions peak over the short-term of some SRES scenarios above the upper bound estimates of the more recent scenarios. 33 Recent scenarios project sulfur emissions to peak earlier and at lower levels compared to the SRES in part because of new information about present and planned sulfur legislation in some developing countries, such as India and China. 34 The lower bound projections of the recent literature have also shifted downward slightly compared to the SRES scenario (IPCC 2007).

32 AR4 Synthesis Report, p. 44, http://www.ipcc.ch/pdf/assessment-report/ar4/syr/ar4_syr.pdf� 33 See Smith, S.J., R. Andres, E. Conception, and J. Lurz, 2004: Historical sulfur dioxide emissions, 1850-2000:� methods and results. Joint Global Research Institute, College Park, 14 pp.� 34 See Carmichael, G., D. Streets, G. Calori, M. Amann, M. Jacobson, J. Hansen, and H. Ueda, 2002: Changing trends� in sulphur emissions in Asia: implications for acid deposition, air pollution, and climate. Environmental Science and� Technology, 36(22):4707- 4713; Streets, D., K. Jiang, X. Hu, J. Sinton, X.-Q. Zhang, D. Xu, M. Jacobson, and J.� Hansen, 2001: Recent reductions in China’s greenhouse gas emissions. Science, 294(5548): 1835-1837.�

41With these assumptions, the DICE aerosol forcing changes 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 from 0.160 to 0.153 W/m 2

.

42Figure A1: Sulphur Dioxide Emission Scenarios ­

.

Notes: Thick colored lines depict the four SRES marker scenarios and black dashed lines show the median,

th th 5 and 95 percentile of the frequency distribution for the full ensemble of 40 SRES scenarios. The blue� area (and the thin dashed lines in blue) illustrates 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 exogenous 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 projection above to assume that aerosols will be maintained at 2000 levels through 2100 reduces average SCC values (for 2010) by approximately 3 percent (or less than $2); assuming all aerosols are phased out by 2100 increases average 2010 SCC values by 6-7 percent (or $0.50-$3)–depending on the discount rate. These differences increase slightly for SCC values in later years but are still well within 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 CO 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 are available from the EMF-22 models. These inputs were extrapolated from 2100 to 2300 as follows:

1. Population growth rate declines linearly, reaching 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 year 2200.

5. Non-CO 2 radiative forcing remains constant after 2100.

43Long 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 is based on the idea that increasing scarcity of natural resources and the degradation of environmental sinks available for assimilating pollution from economic production activities may eventually overtake the rate of technological progress. Thus, the overall rate of economic growth may slow over the very long run. The interagency group also considered allowing 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 decline linearly, reaching zero by 2200. This assumption is reasonably consistent with the United Nations long run population forecast, which estimates global population to be fairly stable after 2150 in the medium scenario (UN 2004). 35 The resulting range of EMF population trajectories (Figure A2) also encompass the UN medium scenario forecasts through 2300 – global population of 8.5 billion by 2200, and 9 billion by 2300.

Maintaining the decline in the 2090-2100 carbon intensity growth rate (i.e., CO 2 per dollar of GDP) through 2300 assumes that technological improvements 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 that is projected to occur towards the end of the forecast period for each EMF scenario. This assumption implies that total cumulative emissions in 2300 will be between 5,000 and 12,000 GtC, which is within 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 run, 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 assuming 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/longrange2/worldpop2300final.pdf
44Figure A2. Global Population, 2000-2300 (Post-2100 extrapolations assume the population growth ­ rate changes linearly to reach a zero growth rate by 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 is equal to the average of the population under the 550 ppm

CO 2 e, full-participation, not-to-exceed scenarios considered by each of the four models.

Figure A3. World GDP, 2000-2300 (Post-2100 extrapolations 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 by each of the four models.

45Figure A4. Global Fossil and Industrial CO 2 Emissions, 2000-2300 (Post-2100 extrapolations assume 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 are equal to the average of the emissions under the 550 ppm CO2e, full-participation, not-to-exceed scenarios considered by each of the four models.

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

4.00

IMAGE

MERGE

MESSAGE
MiniCAM
5th scneario Extrapolations

2050 2100 00 2150 z

2200 2250 20Net land CO2 emissions [GtCO2/yr] 3.00

2.00

1.00

0.00

2300

-1.00

-2.00

-3.00

Year Note: In the fifth scenario, 2000-2100 emissions are equal to the average of the emissions under the 550 ppm CO2e, full-participation, not-to-exceed scenarios considered 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 MERGE 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). 46Figure A6. Global Non-CO 2 Radiative Forcing, 2000-2300 (Post-2100 extrapolations assume constant

non-CO 2 radiative forcing after 2100.)nonCO2 RF [W/m^2] 3.75

3.00

2.25

1.50

0.75

0.00 IMAGE

MERGE

MESSAGE
MiniCAM
5th scenario Extrapolations

2000 2050 2100 2150 2200 2250 2300

Year
Note: In the fifth scenario, 2000-2100 emissions are equal to the average of the emissions under the 550 ppm CO2e, full-participation, not-to-exceed scenarios considered 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 through 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 are equal to the average of the emissions under the 550 ppm

CO 2 e, full-participation, not-to-exceed scenarios considered by each of the four models.

47Table 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 Discount 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 53.6

48�Table A4. 2010 Global SCC Estimates at 5 Percent Discount Rate (2007$/ton CO 2 )

**Percentile** 1st 5th 10th 25th 50th Avg 75th 90th 95th 99th
**Scenario** PAGE
IMAGE 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 2010 (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 -$5,192 to $66,116 but the X-axis has been truncated at

st th approximately the 1 and 99 percentiles to better show the data.

49Table 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-1.370.128.21,479.06.016,382.5128.018,976.513.6150,732.6149.023,558.350