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The social cost of carbon in U.S. regulatory impact analyses: an introduction and critique

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Abstract

In 2010, as part of a rulemaking on efficiency standards, the U.S. government published its first estimates of the benefits of reducing CO2 emissions, referred to as the social cost of carbon (SCC). Using three climate economic models, an interagency task force concluded that regulatory impact analyses should use a central value of \$21 per metric ton of CO2 for the monetized benefits of emission reductions. In addition, it suggested that sensitivity analysis be carried out with values of \$5, \$35, and \$65. These estimates have been criticized for relying upon discount rates that are considered too high for intergenerational cost–benefit analysis, and for treating monetized damages equivalently between regions, without regard to income levels. We reestimate the values from the models (1) using a range of discount rates and methodologies considered more appropriate for the very long time horizons associated with climate change and (2) using a methodology that assigns “equity weights” to damages based upon relative income levels between regions—i.e., a dollar’s worth of damages occurring in a poor region is given more weight than one occurring in a wealthy region. Under our alternative discount rate specifications, we find an SCC 2.6 to over 12 times larger than the Working Group’s central estimate of \$21; results are similar when the government’s estimates are equity weighted. Our results suggest that regulatory impact analyses that use the government’s limited range of SCC estimates will significantly understate potential benefits of climate mitigation. This has important implications with respect to greenhouse gas standards, in which debates over their stringency focus critically on the benefits of regulations justifying the industry compliance costs.

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Notes

  1. Models are being developed for other gases as well; in the meantime, their impacts are approximated by multiplying the SCC by a gas’s CO2 equivalency, or its “global warming potential.” See the Intergovernmental Panel on Climate Change’s Fourth Assessment Report (2007).

  2. All figures in this article are given in 2007 dollars, and rounded to the nearest dollar.

  3. As discussed further below, other variables are also important in explaining the Working Group’s low SCCs, including the limited number of damages represented in the SCC models, a limited representation of catastrophic risks, and a lack of accounting for risk aversion—which generally increases the SCC (Kousky and Kopp, 2011). Unfortunately, re-estimating the SCC along any of these lines would require additional data currently unavailable, methodologies that are only in early stages of development within the literature, or both.

  4. The PAGE model used by the Working Group (see below) does include potential damages from tipping points. For any given temperature increase above some tolerable threshold, the model assigns a positive probability of reaching a tipping point. It then specifies a percentage of world GDP that would be lost in that instance. See Hope (2006, 2008) for a more detailed description.

  5. These impacts refer to interactions between events, where one type of climate damage can lead to, or exacerbate, another. For example, extreme weather events could lead to various public health damages (“inter-sectoral”) or mass migration, which in turn could lead to sociopolitical international conflicts (“inter-regional”).

  6. In the case of downward biases, the Working Group notes several ways in which the models may be overly optimistic with respect to adaptation and technology assumptions. DICE, for example, assumes healthcare technologies improve over time, so that health impacts are reduced. In PAGE, an explicit parameter specifies the percentage of damages that can be adapted to, with especially large amounts assumed in the version of PAGE used by the Working Group, so much so that Ackerman et al. (2009) questioned whether so much adaptation would actually occur in reality (the model has since been updated with reduced percentages). In both DICE and FUND, assumed changes in agricultural practices mitigate some climate impacts, but these calibrations do not account for negative effects of increased climate variability, pests, or diseases.

  7. David Anthoff now co-develops revised versions of FUND with Tol.

  8. While similar in overall architecture, the models differ in some important ways that explain the different SCCs they produce. A discussion of these is beyond the scope of this article. A summary can be found in the Working Group’s analysis; Ackerman and Stanton (2011) also provide a comprehensive overview of climate economics that includes a detailed discussion and critique of the three models. Full descriptions of the models published by their developers are available as cited above.

  9. The Working Group chose the EMF scenarios over those developed by the United Nation’s Intergovernmental Panel on Climate Change (IPCC) on the rationale that they were more recent (the IPCC scenarios date back to the 1997 Second Assessment Report), while at the same time also peer-reviewed, published, and publicly available. See http://emf.stanford.edu/ for a description.

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

  11. For example, in a 2009 regulation of fuel economy standards, the Department of Transportation calculated a separate \$2 domestic SCC and a \$33 global SCC (US Government 2010, p. 3).

  12. The CNA Corporation, (2007). National Security and the Threat of Climate Change. http://securityandclimate.cna.org.

  13. National Intelligence Council, (2008). National Intelligence Assessment on the National Security Implications of Global Climate Change to 2030. As presented at the Permanent Select Committee on Intelligence and the Select Committee on Energy Independence and Global Warming, 25 June 2008, in the testimony of Dr. Thomas Fingar, Deputy Director of National Intelligence for Analysis and Chairman of the National Intelligence Council. http://www.dni.gov/testimonies/20080625_testimony.pdf.

  14. Public goods failure in this context refers to a situation in which it is in one’s self interest to ignore negative externalities s/he is imposing on others; with everyone behaving this way, everyone is worse off than they would have been had they taken into account the effects of their choices on others.

  15. The U.S. Office of Management and Budget distinguishes between projects that impact consumption verses investment flows. Specifically: “…the average before-tax rate of return to private capital in the U.S. economy…is a broad measure that reflects the returns to real estate and small business capital as well as corporate capital. It approximates the opportunity cost of capital, and it is the appropriate discount rate whenever the main effect of a regulation is to displace or alter the use of capital in the private sector…The effects of regulation do not always fall exclusively or primarily on the allocation of capital. When regulation primarily and directly affects private consumption (e.g., through higher consumer prices for goods and services), a lower discount rate is appropriate…This simply means the rate at which a society discounts future consumption flows to their present value.” (OMB 2003, p. 33).

  16. The Stern Review (2007) used a rate of pure time preference of 0.1 % per year, based on an arbitrary estimate of the annual probability that the human race will not survive.

  17. Put another way, if there is any uncertainty in future consumption levels, mitigation pays off the most in bad states of the world, increasing its value. For a mathematical derivation of the relationship between uncertainty in income and marginal utility, see Cochrane (2001). Howarth (2003) also provides a helpful discussion.

  18. EPA’s Guidelines for Preparing Economic Analyses (2000) also note that estimates of intergenerational discount rates “generally range from one-half to three percent (p50).” Interestingly, the most recently published Guidelines (2010) do not provide estimates of intergenerational discount rates.

  19. Technical support document, U.S. EPA (2008). EPA notes in the beginning of the document that it began developing most of the information in the report in support of the Executive Order 13432, for developing Clean Air Act regulations that would reduce GHG emissions from motor vehicles. The report does not reflect an official agency decision and, to the authors’ knowledge, EPA has not since released any documents specifying an official range for intergenerational discount rates. We also note that the 2000 guidelines discussion of intergenerational discount rates, similar to OMB, is not an agency directive specifying these discount rates must be used in agency analysis.

  20. On Treasury notes, OMB cites evidence of a 3.1 % average pre-tax rate (2003); after adjusting for Federal taxes, the Working Group (p20) estimates a post-tax return of about 2.7 %; Newell and Pizer (2003) find pre-tax interest rates between 3.5 and 4 %, while Arrow (2000) suggests roughly 3–4 %.

  21. Newell and Pizer estimated two declining discount that gave equivalent constant discount rates of 2.2 and 2.8 %; the Working Group took 2.5 as a mid-point.

  22. As shown in the next section, using either alternative discount rate schedule produces higher SCC estimates than the Working Group’s at 2.5 %.

  23. Goodstein summarizes Nordhaus and Tobin (1972), who estimate a 0.7 percentage point difference in annual per capita growth between 1929 and 1965, and a 1.8 percentage point difference between 1947 and 1965; Zolatas (1981), who estimates 1.8 % (1947–1965), 1.6 % (1950–1965), and 1.5 % (1965–1977) differences; and Daly and Cobb (1989), who estimate differences of 0.2 (1950–1960), 0.6 (1960–1970), 3 (1970–1980) and 3.1 (1980–1986).

  24. Though a majority of these regions are expected to remain poor in the future, some inequality will be mitigated by the fact that a few countries are projected to grow so rapidly that they eventually catch up with today’s wealthier countries.

  25. Although not the focus of this paper, it is important to note that the Working Group’s use of constant discount rates is internally inconsistent the EMF-22 scenarios in the IAM models specifying growth rates that vary by regions.

  26. An extensive discussion of questions related to equity weighting can be found in Dietz et al. (2009).

  27. Theoretically, it is possible that U.S. regulations could increase prices of internationally consumed goods, but we would argue such effects would be orders of magnitude smaller than costs to the U.S., if any at all.

  28. The UK declining discount rate schedule (Lowe, 2008) is as followsa,b:

     

    0–30 years

    31–75 years

    76–125 years

    126–200 years

    201–300 years

    301+ years

    UK Treasury discount rate schedule, zero rate of time preference

    3.00 %

    2.57 %

    2.14 %

    1.71 %

    1.29 %

    0.86 %

    aThere are two declining discount rate schedules in UK guidelines, one that includes a positive value for the rate of time preference and one that excludes it. This schedule is the one that excludes it.

    bThe Stern Review used a constant discount rate of 1.4 %.

  29. The Weitzman (2009) schedule is as follows:

     

    1–5 years

    6–25 years

    26–75 years

    76–300 years

    300+ years

    Weitzman schedule

    4 %

    3 %

    2 %

    1 %

    0 %

    In addition, new versions of the models would need to be re-coded to use the socioeconomic scenarios used by the Working Group.

  30. See, for example, Nordhaus (2011), Stern (2007), Hope (2008), and Anthoff et al. (2009).

  31. As discussed in the Appendix, while our equity weighting increases the Working Group SCCs, alternative values for eta could produce both higher and lower equity weighted estimates than those presented here.

  32. FUND is the only model of the three used by the Working Group to estimate a negative SCC. This is a result of a controversial benefit included in FUND that predicts CO2 fertilization will significantly increase agricultural yields in the early stages of warming. For research finding counterbalancing negative impacts of climate change on agriculture, see Lobell et al. (2011), Fisher et al. (2012), Roberts and Schlenker (2012), and Schlenker and Roberts (2009). Because these benefits come early, higher discount rates can have the effect of reversing the sign of the SCC, as relative to damages that occur much later in time, these benefits are less impacted by the compounding effect of discounting.

  33. The authors are currently examining whether this result holds for other values of η.

  34. These emission rates are for a model 600-MW plant operating at an assumed 85 % capacity factor and built in 2016. Capacity factor is the actual output of a power plant relative to the maximum generation it can produce if operating at full capacity over a given period of time.

  35. These figures are for plants built in 2017, and take into account factors that vary widely by technology, such as capacity factors, transmission costs, and operation and maintenance expenses. Tax incentives or subsidies that would lower costs are not included, i.e., these are generation costs before applying any subsidies that would lower cost.

  36. Calculations for a given pollution damage were as follows: $ damages/kWh = (total annual tons of emissions for unit type × $ damage/ton)/total number of annual kilowatt hours for a model 600 megawatt (MW) power plant operating at an 85% capacity factor. For example, a model 600 MW coal plant emits 3.6 million tons of CO2 per year and generates 4,467.6 million KWhs of electricity (1.7 million tons of CO2 for a comparable natural gas plant). An SCC of \$35 thus generates 2.8 cents/kWh in carbon pollution damages for a coal plant, while an SCC of \$65 generates 5.2 cents/kWh in damages. Corresponding to this, the 4 cents/kWh generation cost differential in Table 6 for solar photovoltaic versus coal falls between 2.8 and 5.2 cents/kWh, and the \$50/ton break even SCC between \$35/ton and \$65/ton.

  37. We use the midpoint of damage estimates for SO2 and NOx provided in the RIA. SO2 and NOx damages are large for coal and negligible for natural gas; SO2 damages account for the majority of costs from these two pollutants.

  38. 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.

  39. Benefits of the 1990 amendments to the Clean Air Act (CAA) are estimated to exceed costs by a ratio of 26 to 1 in 2010, and 30 to 1 in 2020 (EPA 2011).

  40. EPA summarizes this measure as follows: “[W]hen conducting a benefit–cost analysis of new environmental policies, the Agency uses estimates of how much people are willing to pay for small reductions in their risks of dying from adverse health conditions that may be caused by environmental pollution…This is best explained by way of an example. Suppose each person in a sample of 100,000 people were asked how much he or she would be willing to pay for a reduction in their individual risk of dying of 1 in 100,000, or 0.001 %…[if the average willingness to pay for this reduction in risk were \$100] [t]hen the total dollar amount…to save one statistical life in a year would be \$100 per person × 100,000 people, or \$10 million” (http://yosemite.epa.gov/ee/epa/eed.nsf/pages/MortalityRiskValuation.html#whatisvsl).

  41. Early economic theory estimated the value of a life using foregone earnings (i.e., the value of a lost life was equal to the individual’s remaining lifetime earnings), which produced estimates far lower than today’s that use VSL methodology. EPA currently uses \$7.6 million per life. (http://yosemite.epa.gov/ee/epa/eed.nsf/pages/MortalityRiskValuation.html#whatvalue, converted from 2006$ to 2007$).

  42. More precisely, let g s be the actual consumption growth rate at time s, then g t is defined by the following equation \( {\left( {1 + {g_t}} \right)^{{ - t}}} = \prod\nolimits_{{s = 0}}^t {{{\left( {1 + {g_s}} \right)}^{{ - 1}}}} \), i.e., g t is the geometric mean growth from the present to time t.

  43. Ideally, the models would be constructed at a more disaggregated level such that inequalities within countries could also be accounted for. At present, however, the models are not sufficiently developed to do so, and it would be challenging to modify them due to limited inequality data in many parts of the world.

  44. It is important to note that equity weighted results can be presented using different per capita consumption levels for normalization, as long as the costs of mitigation (and any other costs and benefits in the U.S.) are similarly weighted. Regardless of the normalization weight chosen, if it is consistently applied across all costs and benefits the conclusion of a cost–benefit analysis will not change (i.e., the cost–benefit ratio will stay the same). In calculating an SCC for any given region, using that region’s per capita income as the normalization weight reduces the likelihood of errors in a cost–benefit analysis. If a social cost of carbon that is equity weighted and normalized with world average per capita consumption is used in a U.S. cost–benefit analysis, one consequently has to equity weight the other costs and benefits the same way, with a weight also less than 1. In practice this would be highly cumbersome, confusing, and prone to error. Alternatively one can pick U.S. per capita income as the normalization for the equity weighting, as was done in Anthoff et al. (2009) and for the FUND results presented in this paper. With this normalization, the equity weight for the U.S. is 1, and the need to equity weight any other costs or benefits in the U.S. to which the benefits of emission reductions might be compared is not necessary, given that a weight of 1 would not change these estimates.

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Acknowledgments

The authors would like to thank David Anthoff, Blair Beasley, Dallas Burtraw, Dan Lashof, Antony Millner, and several anonymous reviewers for their helpful comments. Any errors are our own.

Author information

Authors and Affiliations

  1. Natural Resources Defense Council, Washington, DC, USA

    Laurie T. Johnson

  2. Judge Business School, University of Cambridge, Cambridge, UK

    Chris Hope

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Correspondence to Laurie T. Johnson.

Appendix

Appendix

The FUND model uses the Ramsey discounting formula to apply regional equity weights to damages based upon whether they occur in poorer versus wealthier regions.

To understand the methodology in more detail, this Appendix describes the discounting equations themselves—both the one used by the Working Group, and the Ramsey formulation we used to apply regional equity weights. We include here a review of some of the concepts discussed in “The social cost of carbon models used by the Working Group” section.

Equation 1 below shows the Working Group’s discount rate formula, where δ is the constant discount rate, t the time period, r a given region, and D tr damages in region r in time period t caused by one additional ton of CO2 emitted today. T is the number of years considered for the analysis.

$$ \matrix{ {{\text{SCC}}\;{\text{with}}\;{\text{constant}}\;{\text{discounting}}\left( \delta \right)} \\ { = \sum\limits_r {\sum\limits_{{t = 0}}^T {{D_{{tr}}}{{\left( {\frac{1}{{1 + \delta }}} \right)}^t}} } = \sum\limits_{{t = 0}}^T {{{\left( {\frac{1}{{1 + \delta }}} \right)}^t}} \sum\limits_r {{D_{{tr}}}} } \\ }<!end array> $$
(1)

In layman’s terms, Eq. 1 discounts all damages by the same discount rate δ, regardless of the region in which they occur, and then sums them over time.

Equation 2 describes Ramsey discounting, without an equity weight applied between regions.

$$ \begin{array}{*{20}{c}} {{\text{SCC}}\:{\text{with}}\:{\text{Ramsey}}\:{\text{discounting}}\:{\text{without}}\:{\text{regional}}\:{\text{equity}}\:{\text{weights}}\left( {\rho ,\eta ,{{g}_{t}}} \right)} \hfill \\ { = \sum\limits_{r} {\sum\limits_{{t = 0}}^{T} {{{D}_{{tr}}}} } \underbrace{{{{{\left( {\frac{1}{{1 + \rho + \eta {{g}_{t}}}}} \right)}}^{t}}}}_{{\begin{array}{*{20}{c}} {{\text{Ramsey discount}}} \\ {{\text{factor}}} \\ \end{array} }}} \hfill \\ \end{array} $$
(2)

where η is the elasticity of marginal utility, ρ the pure rate of time preference (PRTP), and g t average per capita world consumption growth between the present and time t.Footnote 42 The PRTP is the most controversial parameter, as it captures a tendency to prefer experiencing utility from consumption today rather than delaying it into the future—thus discounting future damages to individuals simply because they have the misfortune of being born later. The parameter η represents the idea that as one’s income increases, each additional dollar brings less utility; correspondingly, one dollar’s worth of climate damages causes more “disutility” to a poor individual than it does to a wealthier one. The growth term, g t , correspondingly captures changes in income. If g t is positive, the discount rate increases; if it is negative, it decreases.

Finally, we apply a regional equity weight to Eq. 2

$$ {\text{SCC}} = \sum\nolimits_r {{{\underbrace{{\left( {\frac{{{C_n}}}{{{C_{{0r}}}}}} \right)}}_{{\matrix{ {\text{equity}} \\ {\text{weight}} \\ }<!end array> }}}^{\eta }}} \sum\nolimits_{{t = 0}}^T {{D_{{tr}}}\underbrace{{{{\left( {\frac{1}{{1 + \rho + \eta {g_{{tr}}}}}} \right)}^t}}}_{{\matrix{ {{\text{Ramsey}}\;{\text{discount}}} \\ {\text{factor}} \\ }<!end array> }}} \approx \sum\nolimits_r {\sum\nolimits_{{t = 0}}^T {{D_{{tr}}}{{\left( {\frac{{{C_n}}}{{{C_{{tr}}}}}} \right)}^{\eta }}{{\left( {\frac{1}{{1 + \rho }}} \right)}^t}} } $$
(3)

where C n is consumption per capita in time 0 in the region to which other regions’ damages are weighted, C or per capita consumption at time 0 for a given region r for which the equity weight is computed, and C tr per capita consumption at time t in region r. g tr now stands for the average consumption growth between the present and time t in region r (the precise definition follows the same method as outlined in the footnote above).

We set C n equal to U.S. per capita income, so that the equity weight for impacts in the U.S.A. is 1, i.e., that impacts in the U.S.A. are valued the same way as any other cost or benefit within the U.S.A. would be valued.Footnote 43 , Footnote 44

To estimate a regionally equity weighted SCC corresponding to a given constant consumption discount rate used by the Working Group, we first solved for the value of ρ in Eq. 2 that gave us the same SCC as obtained for a given consumption discount rate δ in Eq. 1, assuming a value of 1 for η and the realized consumption growth rates corresponding to the given EMF-22 socioeconomic scenario for different regions. For each EMF-22 scenario, we obtained a value for ρ, denoted hereafter \( \overline \rho \). After solving for \( \overline \rho \), we then substituted that value into Eq. 3, to get the final regionally equity weighted SCCs corresponding to the different consumption discount rates. In effect, we isolate the impact of adding equity weights from the time discounting component of the Working Group’s SCCs.

We set η equal to 1 because it was the simplest way to do the calculation, and because it is the most used value in the literature. It is important to note, however, that in this exercise we are not advocating any particular value of η (or ρ); rather, we are demonstrating the importance of imposing regional equity weights on the Working Group’s SCC estimates for a given consumption discount rate.

Different values of η would produce different SCCs and corresponding \( \overline \rho \,{\text{s}} \), so the equity-weighted estimates presented here should not be interpreted as the only possible values the Working Group would have obtained had it used regional equity weights. In general, damages can increase or decrease as η increases, depending upon how incomes for rich versus poor regions compare relative to one another in a given time period (equity weighting between regions in a given time period), and relative to their starting values (“marginal utility” weighting for a given region over time via the discount rate). The latter effect, however, does not impact our SCCs, as we held that constant by varying ρ (see above). The effect of η can also vary depending upon whether regions are assumed to get benefits from climate change (e.g., through CO2 fertilization) and the income level of regions obtaining such benefits.

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Johnson, L.T., Hope, C. The social cost of carbon in U.S. regulatory impact analyses: an introduction and critique. J Environ Stud Sci 2, 205–221 (2012). https://doi.org/10.1007/s13412-012-0087-7

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