Summary
The social cost of carbon (SC-CO2) for a given year is an estimate, in dollars, of the present discounted value of the future damage caused by a 1 metric ton increase in carbon dioxide (CO2) emissions into the atmosphere in that year or, equivalently, the benefits of reducing CO2 emissions by the same amount in that year. The SC-CO2 is intended to provide a comprehensive measure of the net damages—that is, the monetized value of the net impacts—from global climate change that result from an additional ton of CO2.1 Those damages include, but are not limited to, changes in net agricultural productivity, energy use, human health, property damage from increased flood risk, as well as nonmarket damages, such as the services that natural ecosystems provide to society. Many of these damages from CO2 emissions today will affect economic outcomes throughout the next several centuries. Federal agencies are required to use the SC-CO2 to value the CO2 emission reduction benefit of proposed regulations, including emission and fuel economy standards for vehicles; emission standards for industrial manufacturing, power plants, and solid waste incineration; and appliance energy efficiency standards.
The Interagency Working Group on the Social Cost of Greenhouse Gases2 (IWG) developed a methodology for estimating the SC-CO2. That
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1 Here and throughout this report, “damage” represents the net effects of both the negative and positive economic outcomes of climate change.
2 Until 2016 the name of the group was the Interagency Working Group on the Social Cost of Carbon.
methodology has been applied to produce estimates that U.S. government agencies use in regulatory impact analyses under Executive Order 12866. The IWG requested the National Academies of Science, Engineering, and Medicine to undertake a study examining potential approaches, along with their relative merits and challenges, for a comprehensive update to the SC-CO2 estimates.
AN INTEGRATED MODULAR APPROACH
The committee’s conclusions and recommendations highlight four components of analysis or “modules” involved in estimating the SC-CO2—socioeconomic and emissions projections, climate modeling, estimation of climate impacts and damages, and discounting net monetary damages. Each module comprises conceptual formulations and theory, computer models, and other analytical frameworks; each is supported by its own specialized disciplinary expertise. The SC-CO2 estimation framework put forward by the committee integrates these four modules, and, when possible, taking into account the interdependencies among them.
Current estimates of the SC-CO2 are obtained by pooling estimates of monetized damages produced by three reduced-form integrated assessment models (IAMs) that feature prominently in the literature assessing the benefits and costs of climate change mitigation: the committee refers to these as SC-IAMs. Each SC-IAM contains its own modeling components along the lines of the four modules described. The IWG ran each SC-IAM with a common set of socioeconomic scenarios and a common distribution of the equilibrium climate sensitivity, as well as model-specific distributions for other parameters.
CONCLUSION 2-1 For at least some steps in the SC-CO2 estimation framework, using a common module—rather than averaging the results from multiple models—can improve transparency and consistency of key assumptions with the peer-reviewed science and can improve control over the uncertainty representation, including structural uncertainty. This rationale underlies the Interagency Working Group’s use of the same socioeconomic scenarios, discount rates, and distribution for climate sensitivity across IAMs, as well as the committee’s suggestion in its Phase 1 report that the IWG develop or adopt a common climate module.
CONCLUSION 2-2 An integrated modular framework for SC-CO2 estimation can provide a transparent identification of the inputs, outputs, uncertainties, and linkages among the dif-
ferent steps of the SC-CO2 estimation process. This framework can also provide a mechanism for incorporating new scientific evidence and for facilitating regular improvement of the framework modules and resulting estimates by engaging experts across the varied disciplines that are relevant to each module.
RECOMMENDATION 2-1 The Interagency Working Group should support the creation of an integrated modular SC-CO2 framework that provides a transparent articulation of the inputs, outputs, uncertainties, and linkages among the different steps of SC-CO2 estimation. For some modules within this framework, the best course of action may be for the government to develop a new module, while for other modules the best course of action may be to adapt one or more existing models developed by the scientific community.
RECOMMENDATION 2-2 The Interagency Working Group should use three criteria to evaluate the overall integrated SC-CO2 framework and the modules to be used in that framework: scientific basis, uncertainty characterization, and transparency.
- Scientific basis: Modules, their components, their interactions, and their implementation should be consistent with the state of scientific knowledge as reflected in the body of current, peer-reviewed literature.
- Uncertainty characterization: Key uncertainties and sensitivities, including functional form, parameter assumptions, and data inputs, should be adequately identified and represented in each module. Uncertainties that cannot be or have not been quantified should be identified.
- Transparency: Documentation and presentation of results should be adequate for the scientific community to understand and assess the modules. Documentation should explain and justify design choices, including such features as model structure, functional form, parameter assumptions, and data inputs, as well as how multiple lines of evidence are combined. The extent to which features are evidence-based or judgment-based should be explicit. Model code should be available for review, use, and modification by researchers.
In the integrated modular CO2 framework, the first of the four modules would generate estimates of future population and gross domestic
product (GDP). From these, it would generate projections of greenhouse gas emissions. Each emissions path would serve as a baseline to which an emission pulse is added in order to estimate the incremental impact of an additional ton of CO2 released in a particular year. Given projected emissions, the climate module would generate estimates of CO2 concentrations in the atmosphere and ocean, surface temperature change, and sea level rise. Together with the associated population and GDP projections, these climate results would serve as inputs to the damages module that would calculate the monetary value, each year, of net climate damages due to projected emissions.
Each of these modules would include data inputs or structural elements that are treated as uncertain, leading to outputs in the form of distributions of estimates for each year rather than a single value. The discounting module would sum the future stream of monetized damage estimates to a single present value for each of the possible future “states of the world” that are embodied in the analysis in the earlier steps in the SC-CO2 estimation process.
In addition to recommendations regarding the incorporation of uncertainty in the modeling process, the committee reiterates its recommendations on the presentation of uncertainty from its Phase 1 report. Specifically, it is important that the sources of uncertainty in SC-CO2 estimation be made clear. In future updates to the technical support documentation of the SC-CO2 estimates, a discussion of various types of uncertainty and how they are handled in estimating the SC-CO2, as well as sources of uncertainty that are not captured in current SC-CO2 estimates, would improve transparency.
The main disadvantage of a focus on individual modules is the potential neglect of important feedbacks between components of the system. Successful implementation of a modular framework in the longer term will require attention to the interactions among the modules, and modification of the overall structure to incorporate findings and approaches from ongoing research on the human-environment-climate system.
RECOMMENDATION 2-3 The Interagency Working Group should continue to monitor research that identifies and explores the magnitude of various interactions and feedbacks in the human-climate system including those not represented in implementation of the proposed modular SC-CO2 estimation framework. The IWG should include interactions and feedbacks among the modules of the SC-CO2 framework if they are found to significantly affect SC-CO2 estimates.
Due to the global nature of the impacts that result from CO2 emissions regardless of where they originate, efforts to estimate the SC-CO2 by both the scientific community and the IWG have focused on total global damages, rather than the damages to an individual country such as the United States. At the same time, the IWG recognized that this approach “represents a departure from past practices, which tended to put greater emphasis on a domestic measure of SC-CO2 (limited to impacts of climate change experienced within U.S. borders)” (Interagency Working Group on the Social Cost of Carbon, 2010, p. 10). The IWG therefore provided rough estimates of the proportion of global damages attributable directly to impacts within U.S. borders.
Accurately estimating the damage of CO2 emissions for the United States involves more than examining the direct impacts of climate change that occur within U.S. physical borders. The IWG has noted that climate change in other regions of the world could affect the United States, through such pathways as global migration, economic destabilization, and political destabilization. In addition, the United States may be affected by changes in the economic conditions of its trading partners. The current SC-IAMs do not fully account for these types of interactions. The implications of U.S. emissions or mitigation thereof on levering actions by other countries is another consideration affecting the accurate estimation of the domestic, relative to the global, damages from U.S. CO2 emissions.
CONCLUSION 2-4 Estimation of the net damages per ton of CO2 emissions to the United States alone, beyond the approximations done by the IWG, is feasible in principle; however it is limited in practice by the existing SC-IAM methodologies, which focus primarily on global estimates and do not model all relevant interactions among regions. It is important to consider what constitutes a domestic impact in the case of a global pollutant that could have international implications that impact the United States. More thoroughly estimating a domestic SC-CO2 would therefore need to consider the potential implications of climate impacts on, and actions by, other countries, which also have impacts on the United States.
The committee recommends a regularized process for updating SC-CO2 estimates to enhance their scientific credibility and provide a way for experts to suggest both improvements for updates and priorities for research.
RECOMMENDATION 2-4 The Interagency Working Group should establish a regularized three-step process for updating
the SC-CO2 estimates. An update cycle of roughly 5 years would balance the benefit of responding to evolving research with the need for a thorough and predictable process. In the first step, the interagency process and associated technical efforts should draw on internal and external technical expertise and incorporate scientific peer review. In the second step, draft revisions to the SC-CO2 methods and estimates should be subject to public notice and comment, allowing input and review from a broader set of stakeholders, the scientific community, and the public. In the third step, the government’s approach to estimating the SC-CO2 should be regularly reviewed by an independent scientific assessment panel to identify improvements for potential future updates and research needs.
SOCIOECONOMIC MODULE
The purpose of a socioeconomic module is to provide a set of projections of population and GDP, which in turn drive projections of CO2 and other relevant climate-forcing emissions that are inputs to the calculation of a baseline climate trajectory. The baseline trajectory influences the response of the climate to a pulse of CO2 emissions. Estimates of population and GDP, possibly disaggregated by region and sector, are also direct inputs to the estimation of climate damages, and the trajectory of GDP per capita also feeds into the recommended discounting procedure.
RECOMMENDATION 3-1 In addition to applying the committee’s overall criteria for scientific basis, uncertainty characterization, and transparency (see Recommendation 2-2 in Chapter 2), the Interagency Working Group should evaluate potential socioeconomic modules according to four criteria: time horizon, future policies, disaggregation, and feedbacks.
- Time horizon: The socioeconomic projections should extend far enough in the future to provide inputs for estimation of the vast majority of discounted climate damages.
- Future policies: Projections of emissions of CO2 and other important forcing agents should take account of the likelihood of future emissions mitigation policies and technological developments.
- Disaggregation: The projections should provide the sectoral and regional detail in population and GDP necessary for damage calculations.
- Feedbacks: To the extent possible, the socioeconomic module should incorporate feedbacks from the climate and damages modules that have a significant impact on population, GDP, or emissions.
To produce a module satisfying the criteria in Recommendation 3-1, the committee offers a recommendation for the near term.
RECOMMENDATION 3-2 In the near term, to develop a socioeconomic module and projections over the relevant time horizon, the Interagency Working Group should:
- Use an appropriate statistical technique to estimate a probability density of average annual growth rates of global per capita GDP. Choose a small number of values of the average annual growth rate to represent the estimated density. Elicit expert opinion on the desirability of possible modifications to the implied projections of per capita GDP, particularly after 2100.
- Work with demographers who have produced probabilistic projections through 2100 to create a small number of population projections beyond 2100 to represent a probability density function. Development of such projections should include both the extension of existing statistical models and the elicitation of expert opinion for validation and adjustment, particularly after 2100. Should either the economic or demographic experts suggest that correlation between economic and population projections is important, this could be included.
- Use expert elicitation, guided by information on historical trends and emissions consistent with different climate outcomes, to produce a small number of emissions trajectories for each forcing agent of interest conditional on population and income scenarios.
- Develop projections of sectoral and regional GDP and regional population using scenario libraries, published regional or national population projections, detailed-structure economic models, SC-IAMs, or other sources.
In the longer term, there are many advantages to investing in the construction of a dedicated socioeconomic projection framework designed for the task. Existing detailed-structure models were formulated to meet objectives different from those of the IWG.
RECOMMENDATION 3-3 In the longer term, the Interagency Working Group should engage in the development of a new socioeconomic module, based on a detailed-structure model, that meets the criteria of scientific basis, uncertainty characterization, and transparency, is consistent with the best available judgment regarding the probability distributions of uncertain parameters and that has the following characteristics:
- provides internally consistent probabilistic projections, consistent with elicited expert opinion, as far beyond 2100 as required to capture the vast majority of discounted damages, taking into account the increased uncertainty regarding technology, policies, and social and economic structures in the distant future;
- provides probabilistic regional and sectoral projections consistent with requirements of the damage module, taking into account historical experience, expert judgment, and increasing uncertainty over time regarding the regional and sectoral structure of the global economy;
- captures important feedbacks from the climate and damage modules that affect capital stocks, productivity, and other determinants of socioeconomic and emissions projections. It should enable interactions among the modules to ensure consistency among economic growth, emissions, and their consequences; and
- is developed in conjunction with the climate and damage modules, to provide a coherent and manageable means of propagating uncertainty through the components of the SC-CO2 estimation procedure.
Development of such a framework, designed to satisfy the long-term needs of SC-CO2 estimation, would represent an advance in economic modeling. Chapter 7 includes a set of conclusions about the research needed on economic modeling frameworks and model development for the long term.
CLIMATE MODULE
The purpose of a climate module is to take outputs of the socioeconomic module (particularly emissions of CO2 and other climate forcing agents) and estimate their effect on physical climate variables, such as a time series of temperature change, at the spatial and temporal resolution required by the damages module. Thus, it must translate greenhouse
gas emissions into atmospheric concentrations, translate concentrations of CO2 and other climate forcers into their radiative effects (“forcing”), translate forcing into global mean surface temperature response, and generate other climatic variables that may be needed by the damage module. In so doing, it must accurately represent within a probabilistic context the current understanding of the climate and carbon cycle systems and associated uncertainties.
A simple Earth system model would be appropriate for the SC-CO2 setting, and it is important that such a model be considered for use in SC-CO2 calculations. Such a model would reflect current scientific understanding of the relationships between greenhouse gas emissions, concentrations, radiative forcing, and global mean surface temperature change, as well as their uncertainty and profiles over time.
RECOMMENDATION 4-1 In the near term, the Interagency Working Group should adopt or develop a climate module that captures the relationships between CO2 emissions, atmospheric CO2 concentrations, and global mean surface temperature change, as well as their uncertainty, and projects their profiles over time. The module should apply the overall criteria for scientific basis, uncertainty characterization, and transparency (see Recommendation 2-2 in Chapter 2). In the context of the climate module, this means:
- Scientific basis and uncertainty characterization: The module’s behavior should be consistent with the current, peer-reviewed scientific understanding of the relationships over time between CO2 emissions, atmospheric CO2 concentrations, and CO2-induced global mean surface temperature change, including their uncertainty. The module should be assessed on the basis of its response to long-term forcing trajectories (specifically, trajectories designed to assess equilibrium climate sensitivity, transient climate response and transient climate response to emissions, as well as historical and high- and low-emissions scenarios) and its response to a pulse of CO2 emissions. The assessment of the module should be formally documented.
- Transparency and simplicity: The module should strive for transparency and simplicity so that the central tendency and range of uncertainty in its behavior are readily understood, reproducible, and amenable to improvement over time through the incorporation of evolving scientific evidence.
The climate module should also meet the following additional criterion:
- Incorporation of non-CO2 forcing: The module should be formulated such that effects of non-CO2 forcing agents can be incorporated, which will allow both for more accurate reflection of baseline trajectories and for the same model to be used to assess the social cost of non-CO2 forcing agents in a manner consistent with estimates of the SC-CO2.
RECOMMENDATION 4-2 To the extent possible, the Interagency Working Group should use formal assessments that draw on multiple lines of evidence and a broad body of scientific work, such as the assessment reports of the Intergovernmental Panel on Climate Change, which provide the most reliable estimates of the ranges of key metrics of climate system behavior. If such assessments are not available, the IWG should derive estimates from a review of the peer-reviewed literature, with care taken so as to not introduce inconsistencies with the formally assessed parameters. The assessments should provide ranges with associated likelihood statements and specify complete probability distributions. If multiple interpretations are possible, the selected approach should be clearly described and justified.
An example of a simple Earth system model that satisfies the criteria set forth above is the Finite Amplitude Impulse Response (FAIR) model (see Chapter 4). FAIR includes a minor modification of the model used in the Intergovernmental Panel on Climate Change Fifth Assessment Report to assess the global warming potential of different gases. The committee notes that none of the current SC-IAM climate components fully satisfies the criteria above.
Global mean sea level rise is another key physical variable relevant for estimating climate damages. Global mean sea level rise results from both the transfer of water mass from continental ice sheets and glaciers into the ocean, and also from the volumetric expansion of ocean water as it warms.
RECOMMENDATION 4-3 In the near term, the Interagency Working Group should adopt or develop a sea level rise component in the climate module that (1) accounts for uncertainty in the translation of global mean temperature to global mean sea level rise and (2) is consistent with sea level rise projections
available in the literature for similar forcing and temperature pathways. Existing semi-empirical sea level models provide one basis for doing this. In the longer term, research will be necessary to incorporate recent scientific discoveries regarding ice sheet stability in such models.
CO2 dissolves in seawater to form carbonic acid. As the oceans have absorbed about one-quarter to one-third of anthropogenic CO2 emissions, the oceans have steadily become more acidic. Modeling of the consequences of ocean acidification is at an early stage, and is mainly carried out using Earth system or regional ocean models with comparable complexity.
RECOMMENDATION 4-4 The Interagency Working Group should adopt or develop a surface ocean pH component within the climate module that (1) is consistent with carbon uptake in the climate module, (2) accounts for uncertainty in the translation of global mean surface temperature and carbon uptake to surface ocean pH, and (3) is consistent with observations and projections of surface ocean pH available in the current peer-reviewed literature. For example, surface ocean pH can be derived from global mean surface temperature and global cumulative carbon uptake using relationships calibrated to the results of explicit models of carbonate chemistry of the surface ocean.
Simple Earth system models produce climate projections that are highly aggregated both spatially and temporally. For example, the FAIR model produces projections of climatological (multi-decadal-average) global mean temperature. Yet people do not live under 30-year global mean conditions. Rather, damages are caused by the day-to-day, place-specific effects of the weather, the statistical properties of which are described by the climate. The damages module will therefore either require geographically and temporally disaggregated climate variables as inputs or such disaggregation will need to occur in the calibration of the relationship between highly aggregated climate variables and resulting damages. The most straightforward approach to transforming global mean variables into more spatially disaggregated variables is to estimate linear relationships between local climate variables (e.g., temperature, precipitation) and global mean temperature, known as pattern scaling.
RECOMMENDATION 4-5 To the extent needed by the damages module, the Interagency Working Group should use disaggre-
gation methods that reflect relationships between global mean quantities and disaggregated variables, such as regional mean temperature, mean precipitation, and frequency of extremes, that are inferred from up-to-date observational data and more comprehensive climate models.
CONCLUSION 4-3 In the near term, linear pattern scaling, although subject to numerous limitations, provides an acceptable approach to estimating some regionally disaggregated variables from global mean temperature and global mean sea level. If necessary, projections based on pattern scaling can be augmented with high-frequency variability estimated from observational data or from model projections. In the longer term, it would be worthwhile to consider incorporating the dependence of disaggregated variables on spatial patterns of forcing, the temporal evolution of patterns under stable or decreasing forcing, and nonlinearities in the relationship between global mean variables and regional variables.
Research focused on improving the representation of the Earth system in the context of coupled climate-economic analyses would improve the reliability of estimates of the SC-CO2. A list of research topics needed to reach such a goal is outlined in Chapter 7.
DAMAGES MODULE
The purpose of the damages module is to translate a time series of socioeconomic variables (e.g., income and population) and physical climatic variables (e.g., changes in temperature and sea level) into estimates of physical impacts and, when possible, monetized damages over time. To do so, it must represent relationships among physical variables, socioeconomic variables, and damages. The SC-IAMs include damage representations that are either simple and global (e.g., global damages as a function of global mean temperature and gross world product), or are sectorally and regionally disaggregated (e.g., agricultural damages as a function of regional temperature, precipitation change, CO2 concentrations, and the economic value added or GDP of relevant sectors or regions).
RECOMMENDATION 5-1 In the near term, the Interagency Working Group should develop a damages module using elements from the current SC-IAM damage components and scientific literature. The damages module should meet the committee’s overall criteria for scientific basis, transparency, and
uncertainty characterization (see Recommendation 2-2, in Chapter 2) and include the following four additional improvements:
- Individual sectoral damage functions should be updated as feasible.
- Damage function calibrations should be transparently and quantitatively characterized.
- If multiple damage formulations are used, they should recognize any correlations between formulations.
- A summary should be provided of disaggregated (incremental and total) damage projections underlying SC-CO2 calculations, including how they scale with temperature, income, and population.
RECOMMENDATION 5-2 In the longer term, the IWG should develop a damages module that meets the overall criteria for scientific basis, transparency, and uncertainty characterization (see Recommendation 2-2, in Chapter 2) and has the following five features:
- It should disaggregate market and nonmarket climate damages by region and sector, with results that are presented in both monetary and natural units and that are consistent with empirical and structural economic studies of sectoral impacts and damages.
- It should include representation of important interactions and spillovers among regions and sectors, as well as feedbacks to other modules.
- It should explicitly recognize and consider damages that affect welfare either directly or through changes to consumption, capital stocks (physical, human, natural), or through other channels.
- It should include representation of adaptation to climate change and the costs of adaptation.
- It should include representation of nongradual damages, such as those associated with critical climatic or socioeconomic thresholds.
DISCOUNTING MODULE
The purpose of a discounting module is to integrate the future stream of monetized damage estimates into a single present value for each state of the world generated by the earlier steps of the SC-CO2 estimation pro-
cess. Discounting is the procedure by which costs and benefits in future years are made comparable with costs and benefits incurred today. The discount rate refers to a reduction (or “discount”) in value that a future cost or benefit is adjusted for each year in the future to be compared with a current cost or benefit. Because the impacts of CO2 emissions in any particular year persist for many years, the value of avoiding those impacts depends on how much society discounts those future impacts. Due to the power of compounding, small differences in the discount rate can have large impacts on the estimated SC-CO2.
CONCLUSION 6-1 In the current approach of the Interagency Working Group, uncertainty about future discount rates motivates the use of both a lower 2.5 percent rate and higher 5.0 percent rate, relative to the central 3.0 percent rate. However, this approach does not incorporate an explicit connection between discounting and consumption growth that arises under a more structural (e.g., Ramsey-like) approach to discounting. Such an explicit analytic connection is especially important when considering uncertain climate damages that are positively or negatively associated with the level of consumption. The Ramsey formula provides a feasible and conceptually sound framework for modeling the relationship between economic growth and discounting uncertainty.
In formulating its recommendations, the committee makes use of the Ramsey discounting formula, in which the discount rate equals the sum of the pure rate of time preference (δ) and the product of the value of an additional dollar as society grows wealthier (η) and the growth rate of per capita consumption (g).
RECOMMENDATION 6-1 The Interagency Working Group should develop a discounting module that explicitly recognizes the uncertainty surrounding discount rates over long time horizons, its connection to uncertainty in economic growth, and, in turn, to climate damages. This uncertainty should be modeled using a Ramsey-like formula, r = δ + η. g, where the uncertain discount rate r is defined by parameters δ and η and uncertain per capita economic growth g. When applied to a set of projected damage estimates that vary in their assumptions about per capita economic growth, each projection should use a path of discount rates based on its particular path of per capita economic growth. These discounted damage estimates can then be
used to calculate an average SC-CO2 and an uncertainty distribution for the SC-CO2, conditional on the assumed parameters.
To choose the parameters of a Ramsey-like approach, one could examine empirical assessments of pure time preference and utility curvature or one could choose those parameters to match empirical features of observed interest rates and the long-term relationship between interest rates and economic growth.
RECOMMENDATION 6-2 The Interagency Working Group should choose parameters for the Ramsey formula that are consistent with theory and evidence and that produce certainty-equivalent discount rates consistent, over the next several decades, with consumption rates of interest. The IWG should use three sets of Ramsey parameters, generating a low, central, and high certainty-equivalent near-term discount rate, and three means and ranges of SC-CO2 estimates.
In the regulatory impact analyses required under federal rules, the rate at which future benefits and costs are discounted can significantly alter the estimated present value of the net benefits of that rule. In accordance with guidance from the U.S. Office of Management and Budget, agencies have generally used sensitivity analysis with discount rates of 3.0 and 7.0 percent. The 7.0 percent rate is intended to represent the average before-tax rate of return to private capital in the U.S. economy. The 3.0 percent rate is intended to reflect the rate at which society discounts future consumption, which is particularly relevant if a regulation is expected to affect private consumption directly. Due to the atypically long time frame and important intergenerational consequences associated with CO2 emissions, the IWG has used alternative discount rates for the SC-CO2 of 2.5, 3.0, and 5.0 percent.
Incorporating estimates of the SC-CO2 in a regulatory impact analysis can present a challenge if the SC-CO2 calculation uses discount rates that are different from those used for other benefits and costs in the analysis (e.g., short-term air quality impacts).
RECOMMENDATION 6-3 The Interagency Working Group should be explicit about how the SC-CO2 estimates should be combined in regulatory impact analyses with other cost and benefit estimates that may use different discount rates.
