Chapter 14. The social cost of carbon
The social cost of carbon (SCC) is the central concept for the inclusion of climate change damages in the Cost-Benefit Analysis of public policy and public investments. It measures the present value in monetary terms of the damages incurred when an additional ton of carbon (or any other Greenhouse gas) is released into the atmosphere. The SCC can be added as a cost item for projects that induce carbon emissions, and as a benefit item for projects which induce a net reduction in carbon emissions. Most public projects have an impact on carbon emissions, but energy, transport and agriculture are key areas of concern where it will be important that the SCC is taken into account. In environmental policy, the SCC informs the optimal carbon price and the optimal level of emissions abatement. Implementation of carbon price (e.g. via a tax or permit system) will provide incentives for reduced carbon emissions across all sectors of the economy. Many countries now recognise the importance of the SCC and, as a result, have their own approaches to the estimation of the SCC. In this chapter the theoretical underpinnings of the SCC are explained, and the different approaches to the estimation of the SCC are elaborated upon. Since emissions of carbon have global impacts, which vary across time and space, and in many different sectors, calculation of the SCC is complex, requiring inputs from many different disciplines ranging from climate science, to agronomy, to social science, incuding economics. There are also considerable uncertainties at every stage of the process through which carbon causes damages. Three important questions which make the calculation of the SCC difficult are: What path will emissions take? How will emissions affect temperatures? How will temperatures cause damages? There are considerable uncertainties at each step of this calculation, which are compounded by the potentialfor ‘threshold effects’ and catastrophic outcomes. Yet the importance of climate change as a global problem, and the need to implement policies in line with commitments under international agreements means that many countries have already implemented carbon taxes or use the SCC routinely in their regulatory analysis. In this chapter the methods currently used to analyse and calculate the SCC are discussed. Some of the difficulties and disagreements on the issue are highlighted, and examples of current international practice on using the SCC in the CBA of public policy are explained.
14.1. Introduction
Anthropogenic climate change has been described as the “perfect storm” of environmental problems facing humanity. Part of this storm stems from the fact that the environmental and economic impacts of climate change are manifold and diffuse both across space and across time. Furthermore, despite the scientific consensus that temperatures are rising because of CO2 emissions, climate scientists and economists recognise that there is a huge amount of uncertainty associated with several aspects of climate change. The question for public policy and for CBA is how to include the expected damages into the analysis of public projects and regulations, and what value should be placed on these damages.
The social cost of carbon (SCC) or social cost of CO2 (SC-CO2) is one of the most important concepts for informing the public policy response to climate change.1 It represents the marginal damages of a unit of carbon or CO2. The value of the SCC provides information for the valuation of carbon damages associated with climate mitigation public projects and policies, and should be used to set the Pigouvian pollution tax, or carbon price for emissions. Carbon emissions contribute to a stock of CO2 (e.g. concentration) in the atmosphere and so the SCC reflects damages that are incurred as a result of the increasing stock over the lifetime of the emissions in the atmosphere. The SCC represents the present value of this stream of damages. With concentrations of CO2 evolving over time, the SCC will vary depending upon the point in time that it is evaluated. For this reason, the optimal carbon tax will also vary.
Estimating the damages associated with the marginal carbon emission is a complex exercise. 4 key estimation steps are required: 1) Future emissions; 2) the impact of emissions on geophysical outcomes like temperature and precipitation; 3) the impact of geophysical outcomes on economic damages; and, 4) a welfare calculation of the present value of the damages using social discounting. At each step the analyst is presented with considerable uncertainty about the structural and parametric relationships between variables. There is scientific uncertainty in relation to key response parameters such as equilibrium climate sensitivity (the long run impact on global temperatures resulting from a doubling of CO2) or transition sensitivity (the medium term response of temperatures to changes in CO2 emissions). Some elements of this uncertainty are considered to be irreducible, even if it is expected that new information will arrive in the future. Beyond the scientific uncertainties, the correlation between temperature changes and economic damages is a huge additional source of uncertainty. There is a burgeoning literature on the nature of climate damages, but for the long-run the accuracy of the damage function still remains questionable, in part because there is often no historical precedent to work from.
The scientific uncertainty, and uncertainty surrounding climate damages, represent problems of uncertainty in the strictest, “Knightian” sense, cf. Chapter 8.2 The tools of appraisal need to be mindful of the fact that effects of climate change are at best ambiguous and most likely are characterised by Knightian uncertainty. The estimation of the SCC needs to take into account these inherent risks and uncertainties, and reflect societal preferences concerning risks, uncertainty/ambiguity and the potential for catastrophic risks. Individual behaviour suggests that there is a preference for reducing risks, ambiguity and the probability of negative shocks. Many argue that the calculation of the SCC also should reflect such factors.
Climate change happens relatively slowly, with a long lead-time before damages occur, and significant inertia thereafter. Climate change is therefore an inter-generational issue whose impacts will affect future generations hundreds, possibly thousands, of years into the future. For this reason, any evaluation of the costs and benefits of climate change and associated mitigation strategies will be highly sensitive to the inter-temporal social welfare function used to evaluate societal well-being. As shown here and in Chapter 8, the SWF defines the social discount rate and hence the weight placed on future generations’ well-being. As the aftermath of the Stern Review illustrated, disagreement on the social discount rate can determine the outcome of an evaluation of policies to mitigate climate change.
Second, climate change raises the spectre of catastrophic outcomes for future generations. As will be seen, economic analysis of climate change has typically looked at the average damages. Due to the long-term consequences of climate change, a low discount rate is required for many mitigation strategies to pass a cost-benefit test when the average effects are the main concern. However, if the probability distribution of damages has “fat tails”, meaning that the likelihood of extremely bad outcomes is not vanishingly small, then these effects dominate any CBA, more or less irrespective of the discount rate. Reducing the likelihood of catastrophic events then becomes the main motivation for action on climate change.
This chapter discusses how, despite the apparent obstacles, the SCC has been estimated for use in CBA using a combination of the available climate science, climate models and economic models, evaluated using welfare economic approaches that underpin CBA. With a focus on the detailed procedures recommended in the US, the steps required to estimate the SCC will be explained and the values of the SCC that are in policy use described. In the main, estimates aimed at policy use have been derived from Integrated Assessment Models (IAM). The use of expert opinion and even simpler stylised models if climate and economy are also discussed.
Source: www.carbonbrief.org.
14.2. The social cost of carbon and the optimal carbon price: Some theory
The purpose of this section is to provide a clear definition of the social cost of carbon (SCC) and illustrate the relationship between the SCC and the optimal carbon price. The SCC is typically defined as the present value of the damages caused by the emission of a marginal unit of carbon (or other greenhouse gas) into the atmosphere. Sometimes this is expressed in units of carbon dioxide (CO2) as the social cost of carbon dioxide (SC-CO2) (e.g. NAS 2017).3 In the optimal first-best world of economic theory, the optimal carbon tax would be equated to the SCC. The SCC represents the optimal Pigouvian tax that should be applied to carbon emissions so that agents internalise the external cost of their decisions, and an optimal allocation is achieved in the economy. This section will show how in theory the optimal carbon tax and the SCC are linked in this optimal policy context. Subsequent sections will discuss the application of these principles and the different approaches that have been used to estimate the SCC. Once defined and estimated, the SCC can be used to inform the carbon price, or be used as the shadow price to value carbon in the evaluation via CBA of public policy (e.g. investment projects or regulatory change).
One important feature of carbon or carbon dioxide (CO2) emissions is that it is a stock-pollutant: it contributes to a stock of CO2 in atmosphere, which builds up and slowly dissipates over time. Climate change mitigation is therefore a dynamic problem, and the damages from CO2 emissions today are likely to evolve over time and be persistent. Hence the SCC has two key features. First, it reflects the future damages that evolve over time after a marginal change in change in carbon/greenhouse gas emissions today, or at a particular point in time. Second, the SCC will change over time to reflect the evolution of the stock of greenhouse gas pollutants and the marginal damages that entails. The optimal carbon price must therefore also reflect the dynamic nature of the pollutant and evolve over time. A formal presentation of these points makes these ideas concrete.
14.2.1. A formal theoretical analysis of the SCC and the optimal carbon price. A simplified exposition of Hoel and Kverndokk (1996)
There is an expansive theoretical literature analysing the properties of the social cost of carbon, the optimal carbon price, and their dynamics over time. This literature provides insights on the optimal carbon tax and its path over time in optimal economies with different characteristics. The basic insight, however, stems from the fact that carbon is a stock pollutant, rather than a flow pollutant like street-level Nitrogen Oxide or effluent flows in rivers. The fact that CO2 is a stock pollutant means that the social cost of carbon must reflect the damages over the entire planning horizon resulting from a marginal addition to the stock today.
In the framework of dynamic optimisation the social cost of carbon is represented by the negative shadow price on the CO2 stock. Box 14.1 shows that this shadow cost, the social cost of CO2 in this case, reflects the present value of the future damages of a marginal emission of CO2 today. In a steady state this present value is simply given by equation [14.1], which is reproduced here:
[14.1]
where S* is the stock of CO2 in the atmosphere, D¢(S*) is the flow of marginal damages at each point in time, r is a discount rate, and f is the decay rate of the stock of CO2 in the atmosphere. Equation [14.1], shows that the SC-CO2 is equivalent to the present value of an annuity of amount D¢(S*). The SC-CO2 increases in the marginal damages and decreases in the discount (r) and decay (f) rates.
In an optimising framework, marginal benefits of emissions (from manufacturing, transport etc.) should be equal to the marginal damages associated with CO2. This means that the optimal carbon tax should be equated to the SC-CO2 or SCC depending on the units. [14.1] provides an expression for an optimal (steady state) carbon tax. Outside of the steady state in which the stock of CO2 in constant over time, the optimal carbon tax should reflect the evolution of the carbon stock in the atmosphere, which in recent years has clearly been increasing (See Figure 14.1). Equation [14.3] in Box 14.1 represents the SC-CO2 in this case.
Although it is possible to define the SCC and the carbon tax in optimal terms, often estimates of the SCC will often be estimated or approximated using a non-optimal “business-as-usual” baseline (e.g. Nordhaus 2017; Stern, 2007). The definition of the SCC as the present value of damages remains the same in these cases.
14.2.2. The optimal path of the carbon tax
The optimal path of the carbon tax has been the subject of a great deal of investigation in the theoretical world. The recommended paths of the tax differ depending on the specific model analysed. Modelling CO2 emissions dynamically as a stock pollutant provides some important insights into the dynamic trade-offs that ought to be considered when thinking about the optimal path for the carbon tax. The details depend on the details of the specific modelling exercise. But there are some general findings which can inform the design of policy.
For instance, the model of Hoel and Kverndokk (1996) discussed in Box 14.1, a utility-maximising planner using a non-renewable resource which contributes to a stock pollutant, and which faces a backstop technology, would implement a carbon tax that would rise in the short run and fall in the long run. The associated stock of carbon emissions would follow a similar path, only with a delay, peaking later than the carbon tax would peak. These dynamics stem from their modelling assumptions, but the hump-shaped profile of taxes captures the trade-offs that are at stake when implementing policy. On the one hand, the static effect of a tax is to reduce resource extraction. On the other, the dynamic effect of a tax in the future is to reduce the present valuation of future extraction: the present value of the resource rent. Optimal extraction will adjust accordingly by increasing in the short run, and reducing in the future in order to satisfy the dynamics of the resource rent given by Hotelling’s rule. The decrease in the optimal tax in the future counteracts this dynamic extraction effect, thereby reducing the level of emissions at each point in time (See Figure 14.2). The time profile of the SCC reflects these dynamic considerations, and indicates that optimal climate policy must take into account the likely dynamic response of profit maximising fossil fuel extractors to policy interventions.
A simplified exposition of Hoel and Kvernndok (1996)
Hoel and Kverndokk (1996) is among the most straightforward theoretical models which can be used to illustrate the theoretical meaning of the social cost of carbon and the relationship with the optimal carbon tax. The social cost of carbon is analysed in the context of an economy reliant on an exhaustible resource (e.g. fossil fuels) that produces a stock pollutant (e.g. CO2). The problem is one of optimal depletion in the face of the stock pollutant that arises from the use of the non-renewable resource. This is a simplified representation of the problem of climate change being driven by fossil fuel use in the general economy. The following explanation provides some insights concerning the SCC and the optimal carbon tax.
The objective in Hoel and Kverndokk (1996) is to maximise present value of the sum of utility u(xt) over time (discounted at rate r) via the choice of the resource (pollutant) flow xt, given the fact that there is a finite stock of the non-renewable resource A0, the cumulative extraction of which induces a stock of atmospheric pollution, St which causes instantaneous damages D(St). The stock pollutant evolves over time according to the dynamic equation:
[14.2]
where xt is emissions of the pollutant, and f reflects the rate of decay of the pollution stock via natural atmospheric and
oceanic processes. The following Hamiltonian function captures the essential trade-off that is faced between the benefits
consuming the resource xt (e.g. oil) which provides instantaneous utility, u(xt), and the build-up of the pollutant St. which
causes damages D(St), and the dynamic effects of changes in the stock of pollution, 
. The Hamiltonian is maximised via the choice of the control variable xt:
The solution to this problem balances instantaneous flow of benefits that the economy obtains from the use of non-renewable resources, u(xt), against the costs incurred in the future due to the increased stock of pollution, D(St), which accumulates over time according to (14.2).1
The shadow price of a stock of CO2, μ, captures the marginal effect on inter-temporal well-being from a marginal increase in the pollution stock St. This will be negative, since pollution reduces welfare: it is a cost. This means that the social cost of carbon: SC-CO2 is equal to the θ = -μ. It is instructive to derive an expression for the SC-CO2. Using the Hamiltonian approach means that the shadow price μ evolves over time as follows:
[14.3]
With SC-CO2 defined as θ = -μ, the differential equation for θ implied by [14.2] yields the following expression for the SC-CO2 (θ) at time t (Hoel and Kverndokk, 1996, p. 119):
[14.4]
[14.3] is an accounting identity which allows the SC-CO2 to be defined explicitly as (14.4). The relationship holds for non-optimal paths too. [14.4] shows explicitly that the SC-CO2 (θ) is the present value of the sum of future marginal damages D’(St) arising from a marginal unit of CO2, discounted at the composite discount rate, (r + f), over the remaining planning horizon, 
.2
In an optimal solution, the marginal benefit of extraction today should be equated to the marginal cost in the future, θ. So the SC-CO2 equates to the optimal carbon tax. The SC-CO2 evolves over time according to the (14.3), and therefore so should the optimal carbon tax.
In the simpler steady state, in which Sτ = S* for all time, the carbon tax becomes the present value of the annuity D¢(S*):
[14.5]
Expressions (14.4) and (14.5) illustrate the general point that the SC-CO2 reflects the present value of all future marginal damages, discounted at the composite rate (f + r). The SC-CO2 decreases with a higher discount rate (r) and with more rapid decay of the pollutant (f). The discount rate reduces value of future the damages, whereas the decay reduces the quantity of future damages.
← 1. Hoel and Kverndokk (1996, p. 118) also include the extraction costs which depend on the cumulated extraction of the resource. Abstraction from this feature simplifies the discussion here.
← 2. The composite discount rate reflects the fact that there are two reasons to value future damages less than today’s damages. First, the opportunity cost, r. Second, the decay rate, f. Both are reasons to put less weight on the pollution stock in the future.
Source: Hoel and Kverndokk, 1996.
Similar results are found in other studies. Ulph and Ulph (1996) also argue for a hump-shaped profile of carbon taxes. In their case, the result is that emissions are higher in the short run and in the long run, but the optimal policy removes the peak emissions that arise in the medium run. In the Hoel and Kverndokk (1996) model, extraction continues for longer than without the optimal tax. See Figure 14.2, in which the “business-as-usual”, i.e. no carbon tax scenario has higher peak emissions but leads to a termination of the fossil fuel era at some point in finite time when the backstop technology becomes more economic. Alternatively, the “optimal carbon tax” scenario reduces emissions over in the medium term, but leads to an extended fossil era which overlaps with the use of the backstop technology. In each case, all economically viable resources are extracted. Many models of the optimal carbon tax lead to this essential point: optimal management of the stock pollutant involves smoothing out the time profile of emissions, possibly at the cost of longer fossil fuel eras.
14.2.3. Carbon policy and the Green Paradox
Analysis of the optimal path of the carbon tax illustrates the competing forces that policy must contend with, and the idea that, faced with a carbon tax, fossil fuel extractors have incentives to adjust their behaviour. The analyses suggest that naïve implementation of climate policies may induce unintended consequences. A literature related to the modelling of the social cost of carbon and the appropriate taxation policy concerns what is known as the Green Paradox. The Green Paradox states that certain policies that are aimed at reducing carbon emissions and abating climate change, may have the reverse effect of increasing emissions in the near-term, and potentially reducing welfare. The mechanism via which this can happen is that a steeply rising carbon tax, or rapidly falling cost of renewables (the backstop technology), has a similar effect as an expropriation risk: it makes fossil fuels worthless in the future and hence accelerates extraction by fossil fuel companies now (Sinn, 2008; van der Ploeg and Withagen, 2015). The Green Paradox concerns policies towards renewable resources and energy efficiency (Hoel, 2008), and even the enactment of successful international environmental agreements (Strand, 2007). In each case, the Green Paradox suggests that apparently helpful policies such as a carbon tax or renewable subsidies could have perverse effects on climate and welfare when mediated through existing markets and institutions.
A pivotal reference here is Sinn (2008) who analyses the impact of a carbon tax on a decentralised market economy. Sinn (2008) shows that in this context, a non-optimal tax on carbon, which rises at a constant rate over time, can increase the rate of extraction of non-renewable resources. The constant growth rate of the tax acts as an additional component of the discount rate, which quickens extraction. Underpinning this result is the idea that the property rights to subsoil assets are not perfect, so the tax essentially adds to the appropriation risk in the industry. The response to the tax moves the economy away from the optimal path of extraction. Sinn (2008) illustrates the potential for perverse outcomes of environmental policy, the importance of the existing institutions, and the insights from using dynamic frameworks. The rate of change of the tax is clearly an important consideration for taxation policy when it comes to carbon, as is the way in which taxes are internalised.
Starting from the perspective that not all fossil fuels can be used if the temperature targets of the Paris COP21 Accord are to be respected, Gerlagh (2011) shows that investment in alternative technologies is crucial to ensure that the era of fossil fuels ends, rather than being smoothed out over a longer horizon, as in other models. Ending the fossil fuel era might mean higher emissions in the short-term, but lower cumulative emissions overall. In such a context, the rate of reduction in the cost of the backstop technology determines how quickly non-renewables are “priced out’” of the market due to their increasing production costs and the rapidly falling backstop price. A similar result could be obtained when the deposits of non-renewables resources are of different qualities, and hence command different prices. In such cases it is likely that it will be inefficient to extract all reserves of fossil fuels, and the Green Paradox is no longer typically present (Gerlagh, 2011). Further analysis of the Green Paradox can be found in van der Ploeg and Withagen (2015).4 The general conclusion is that a carbon price is the best way in which to regulate carbon emissions, and that if subsidies to renewable technology (or fossil fuels) are put in place instead of carbon pricing, a Green Paradox is likely in which emissions rise and accelerate global warming.
14.3. Estimating the SCC or SC-CO2 using integrated assessment models (IAMs)
In order for climate damages to be considered in the analysis of public policy and public investments, or to inform the appropriate carbon price, an estimate of the SCC or SC-CO2 (henceforth SCC) is required. The National Academy of Sciences (NAS 2017, Chapter 2) provides a framework for the estimation of the SCC which relies on the use of integrated assessment models (IAMs) of climate and economy.
IAMs vary in their precise purpose and their level of modelling detail. NAS (2017) refers to two distinct types of IAM: 1) Detailed-structure IAMs; and 2) Reduced-form IAMs. Detailed-structure IAMs provide detailed decompositions of specific aspects of climate and economy depending on the core research questions they attempt to address. Technological change in the energy sector (e.g. the WITCH model of Bosetti et al., 2006), adaptation in the agricultural and manufacturing sector, feedbacks between land and oceans (e.g. Reilly et al., 2012), and climate change risks, are just some of the specific themes that have been addressed by these detailed-structure IAMS (NAS 2017, p. 40). Another aspect of these detailed models is their finer-grained spatial focus, with analysis taking place at the regional level (e.g. the Asian-specific Integrated Model (AIM) of Matsuika et al., 1995).
The detailed-structure IAMs typically have not been used to estimate the global value of climate damages and the SCC since they are often not sufficiently developed to place an economic value of the damages, and then aggregate these damages to the global level. For this purpose, the typical approach has been to use more reduced-form IAMs. Reduced-form IAMs provide representations of the economy, climate and the carbon cycle that are highly aggregated. For instance, the complexity of global production is typically represented by one aggregate production function. This function transforms aggregate capital and labour into output, via exogenous technological change, and abstracts from the specifics of any particular sector or industry. Similarly on the climate side, the relationship between carbon emissions, temperature and economy are represented in simplified relational expressions. The advantage of these models is that they represent global aggregate measures of climate change and economic welfare, and therefore can be used to estimate the SCC.
A handful of reduced-form IAMs (henceforth simply IAMs) have been used to calculate the SCC. In each case there are four essential steps required to calculate the SCC (e.g. NAS 2017, p. 39):
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Emissions: Projecting of the future path of output and CO2 emissions;
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Climate Impact: Projection of the impact of emissions on the physical world: including atmospheric and oceanic temperature change, changes in ecosystems and biomass productivity;
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Damages: Calculation of the economic damages associated with the future path of emissions and the changes in the physical world that are projected to occur;
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Discounting: Discount the stream of economic damages to obtain a present value (see Chapter 8)
The next section discusses how these steps can be undertaken in the context of a particular reduced form IAM, the DICE model (Nordhaus, 2017). Estimates from other IAMs are then presented followed by estimates that have been proposed for use in practice.
14.3.1. IAMs: 4 steps to estimate the SCC using the DICE model
The social cost of carbon: As discussed in the previous section, the social cost of carbon is the present value of the damages associated with an additional
tonne of carbon or tonne of CO2 emitted into the atmosphere.5 The DICE model, and most reduced-form IAMs, uses the discounted utilitarian inter-temporal welfare function of the form:
, to evaluate the climate change damages, where δ is the utility discount rate and U(Ct) is the instantaneous utility of a representative agent at time t. With emissions reflected by Et and consumption represented by Ct, and inter-temporal welfare represented by W, the general expression for the SCC is:
[14.6]
The numerator of [14.6] is the impact of emissions on welfare (the present value of utility) and the denominator is the marginal utility of consumption, which means that the SCC is measured in terms of consumption, rather than utility. Typically the calculation is undertaken by perturbing the model with a non-marginal pulse of carbon emissions (or removal thereof) to a well-established baseline scenario, and then dividing by the magnitude of the pulse to obtain the per unit value of the SCC in monetary terms (Newell and Pizer, 2003; Nordhaus, 2014; 2017). The way in which emissions diffuse over time and affect the wider climate and economy varies from one modelling approach to another.
14.3.2. Step 1: Emissions: Projection of global output and emissions
The socio-economic module of the DICE model consists of the welfare function above and the productive sector which produces aggregate output and emissions of carbon. In its measure of global welfare, utility is multiplied by global population, L(t) and a discount factor R(t) at each point in time:
[14.7]
CO2 Emissions come from aggregate output, Y(t) and from exogenous land use emissions, Eland(t):
[14.8]
where σ(t) is the carbon intensity of output and μ(t) is the emissions reduction rate, reflecting technological and policy interventions. Output, Y(t), is modelled as aggregate production function of technology, A(t) and diminishing marginal product in capital, K(t), and labour, L(t):
[14.9]
Aggregate output is either consumed, C(t), or invested. Projections of output and emissions are governed by these relationships, with the essential parameters and functions (σ(t), m(t), f(.)) estimated using the best available knowledge, and growth of population, output and technological change projected using historical evidence or expert opinion (see Nordhaus, 2016). In the DICE model (DICE 2016R), growth in per capita output is assumed to be 2.1% per annum until 2050, and then 1.9% per annum until 2100. Population growth is assumed to follow the United Nations population predictions.
14.3.3. Step 2: Climate impact: the impact of emissions on the physical world
Each IAM defines an explicit relationship between emissions and the physical world based on information from climate science. One of the key aspects is the change in temperature that emissions will induce. In the DICE 2016R model, the relationship is characterised by several simple reduced-form expressions for the geophysical relationships. These expressions (which are omitted here for simplicity, see Nordhaus, 2017, p. 1519-1520) characterise: 1) the flow of CO2 to and from atmosphere to upper ocean and biosphere, to deep ocean carbon reservoirs; 2) the radiative forcing (temperature effect) of CO2 emissions in the atmosphere; and 3) the effect of radiative forcing on atmospheric and lower ocean temperatures.
The process of estimating parameters, calibrating the models and making projections is made difficult because there is a great deal of uncertainty surrounding the estimates. One particularly important parameter which is used to characterise the relationship between CO2 emissions and atmospheric temperature change is the equilibrium climate sensitivity (ECS). ECS describes a long-run equilibrium relationship which indicates the change in temperature (positive or negative) as a result of the doubling of CO2 concentrations in the atmosphere. This parameter is inherently uncertain (Roe and Baker, 2007), and there have been many different attempts to estimate its probability distribution using climate modelling, empirical estimates using historical data on temperature-CO2 relationships, or interviews of expert opinion. Figure 14.3 shows the wide variety of estimates that are currently in circulation. The DICE 2016R model uses a mean value of 3.1°C based on Olsen et al. (2012). A related parameter is the transitory climate sensitivity (TCS). TCS describes shorter-run (50-100 years) relationships between CO2 emissions and temperature change. The DICE model uses a value of 1.7°C for TCS.
Source: Heal and Millner (2014).
The ECS of 3.1°C used in DICE 2016R lies within the range of 1.5°C-4.5°C that the IPCC’s 5th assessment report (IPCC-AR5) considers with medium confidence to be likely (IPCC 2013, p. 16).6 Reflecting the uncertainties surrounding this parameter, and based on numerous studies, the IPCC-AR5 continues to say that the ECS is “…very unlikely less than 1°C (high confidence), and very unlikely to be greater than 6°C (medium confidence)” (IPCC, 2013, p. 16). Furthermore, the IPCC-AR5 states that the TCS is likely in the range of 1°C and 2.5°C (high confidence). These statements are made based on a probability distribution which summarises many studies, including those in Figure 14.3, using Bayesian statistics.
The reduced-form IAMs model the complex geophysical relationships between emissions and the physical world in a very simplified and aggregated way, although the estimation of the parameters and relationships is informed by more detailed studies. For a more complete discussion of the issues surrounding the relationship between carbon emssions, the physical world and temperature, see the IPCC AR5 Working Group 1 report (IPCC, 2013).
14.3.4. Step 3: Damages: Predicting and valuing climate damages
The way in which expected temperature changes translate into economic damages, and how these damages are monetised, is another component of any economic analysis of climate change. Damages associated with climate change can take several possible forms (NAS 2017):
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Damages to consumption: climate change affects the bundle of goods and services that are consumed;
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Damages to capital stocks: damage to capital stocks can affect consumption indirectly e.g. via reductions in productivity. Applies to man-made, natural, human capital stocks.
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Damage to non-marketed capital stocks: non-marketed benefits of human and natural capital stocks that affect welfare directly, not via consumption. Includes some amenity values, landscape values, cultural heritage, the onset of violence and disease, are good examples (NAS 2017, p. 152).
Climate damages may manifest themselves in changes in the level of consumption and GDP. However, climate damages to capital stocks (broadly defined) are likely to affect growth. Hence, these long-term consequences which need to be estimated in order to get a complete picture. Another element of the cost of climate change is the induced investment costs (e.g. flood defences), while an important mediating factor is the ability to adapt to climate change. The damage functions that are used in IAMs to estimate the SCC should take all of these factors into account. Of course, as the NAS (2017, p. 139) makes plain, IAMs are “constrained by the available literature and typically need to extrapolate beyond the relationships characterised in supporting evidence”. Nevertheless, the IAMs damage functions do attempt to include many aspects of climate damages, reflecting micro-level, industry level, sectoral level studies aggregated to the economy, region and global level (Metcalf and Stock, 2017; Dell et al., 2014).
At the macro-economic level, several studies have attempted to estimate the costs of climate change either for the economy as a whole, by looking at the empirical relationship between GDP, as a supposed “catch-all” for climate damages, and climatic variables such as temperature (Metcalf and Stock, 2017). By looking at aggregated measures of economic performance such as country-level of region GDP, these studies overcome some of the difficulties in aggregating micro-level studies at the sector or industry level, which requires strong assumptions about the interactions between sectors. A recent example of this can be found in Dell et al. (2014) who estimate the relationship between country level GDP and temperature and precipitation fluctuations. They find that higher temperatures lead to large reductions in the level and growth rates of GDP, albeit only in poor countries. The impact on growth suggests that climate change may damage productive capital.
A number of studies have disaggregated the analysis to look at the impact of climate change (e.g. temperature and precipitation) on particular sectors of the economy. This is a natural line of enquiry since some sectors are likely to be more climate sensitive than others (e.g. agriculture and forestry). Dell et al. (2014) find that while a 1°C increase in temperature is associated with a short-run reduction of 2.7 percentage points in the growth rate, industrial productivity is similarly affected with a 2.0 percentage reduction in growth. This reduction in growth in industry is not among “downstream” agricultural industries, and accords with findings in other regions (e.g. Hsiang, 2010). Hence, the negative productivity effects of climate are not the exclusive reserve of what are traditionally thought of as climate-sensitive sectors, such as agriculture.
Another way in which macro-economic costs of climate change have been estimated is via structural economic models such as computable general equilibrium (CGE) models. Such models are IAMs in their own right, and include detailed structural relationships between environment and the economy. Since they capture general equilibrium effects between sectors, the CGE approach partially overcomes the aggregation problems associated with the sector level empirical approaches. For instance, Bosello et al. (2012) use a multi-country multi-sector CGE model to estimate the impacts for coastal regions (migration and land loss), tourism, agriculture (yield loss), energy (change in demand for oil and gas), floods (capital, land and labour productivity loss) and human health (productivity loss dues to heat humidity). The World Bank, using a similar CGE approach, estimated that the cost of adaptation alone to developing countries is at least USD 81 billion (World Bank, 2010).7
The structural relationships found in these CGE models are often informed by numerous empirical studies which take place at different levels of aggregation. There are macro-level studies, like Dell et al. (2014), which look at growth, possibly in some sub-sectors of the economy. Other studies use aggregated data for particular sectors, e.g. agriculture (Cline, 2007). Mendelsohn (2012) undertakes cross-sectional analysis in several regions of the developing world to estimate the impact of climate on the agricultural sector, by looking at the relationship between long-term climate variables and productivity levels (e.g. measured by land-rents) across different countries. Then there are micro-level studies within countries which have looked at the impact of climate change on adaptation on agriculture (Kurukulasuriya and Mendelsohn, 2008; Gorst et al., 2016; Di Falco and Veronesi, 2011; Deschenes and Greenstone, 2007; Schlenker and Roberts, 2009), on labour productivity (e.g. Zivin and Neidell, 2010) and on other socio-economic factors such as crime (Ranson, 2014; Hsiang et al., 2011) and mortality (Deschenes and Greenstone, 2011).8 Adaptation in agriculture has been shown to increase yields in some cases (Di Falco and Veronesi, 2011; Gorst et al., 2016), and at the very least reduce the impact of climate change in others (e.g. Mendelsohn et al., 1994; Mendelsohn, 2012). Some have argued that in some regions, climate change is expected to increase agricultural productivity even without adaptation, and provide net benefits (e.g. Cline, 2007). Analogous adaptations are possible to avert productivity losses in industry also, such as the introduction of air conditioning.
One key distinction in the empirical literature concerns the empirical strategies used to estimate the relationships. Many studies use panel data approaches which rely on short-term fluctuations in temperature and precipitation to identify the effects. Longer term effects of climate change are at best captured by distinguishing between short-term and long-term effects in their dynamic analysis of these fluctuations. Some argue that short-term weather fluctuations (even if they reflect 5-10 year mean values) capture changes in weather but not climate. One chief weakness of the panel studies could therefore be that they fail to adequately capture adaptive responses which happen over longer periods of time (Burke and Emerick, 2016). These arguments have motivated the continued study of the relationship between longer-term average temperatures and economic aggregates in cross-sections of countries and regions (e.g. Mendelsohn et al.; 1994; Schlenker et al., 2005; Mendelsohn, 2012). The implication is that panel studies could over-estimate the cost of climate change because they ignore the full extent of adaptation. Yet cross-sectional studies suffer from the weakness in identification, since a third variable could be mediating the relationship between climate and, say, productivity such as institutional quality.
There are many other areas of research that have informed the damage functions used in IAMs. Sea-level rise is predicted to lead to loss of productive land, increased flooding, and possibly an increase in disease and migration (e.g. Stern, 2007). The nature of these damages, and the nature of the adaptive response, is often difficult to predict. There are many studies at the micro and macro-economic level which attempt to understand the likely economic damages in each case. NAS (2017, Chapter 5) and the IPCC-AR5 WGII report (IPCC, 2013b) provide excellent summaries of what is known so far about the damages and adaptation in different sectors of the economy.
Another important aspect of climate damages is abrupt, non-gradual, and possibly catastrophic damages. Such damages would occur if ecosystems cross a threshold, or reach a ‘tipping point’ beyond which they shift into another equilibrium. Examples of such potential tipping points include: i) the shifting of the Atlantic Gulf Stream; ii) the changing of the monsoonal circulation patterns; iii) the melting of the polar ice-sheets; iv) melting of the Arctic perma-frost and the associated carbon and methane emissions; and v) the collapse of the Amazon rainforest (e.g. Weitzman, 2009). A related aspect to climate damages is feedback effects. For instance, the melting of the Arctic perma-frost will lead to the release of large amounts of carbon currently stored in the frozen ground. This will cause a positive feedback which exacerbates climate change.9 Beyond these geophysical tipping points, some have argued that even gradual climate change could lead to socio-economic tipping points, in which countries or regions slip into conflict traps, which could consequently stifle development (Hsiang et al., 2011; Hsiang et al., 2013).
Each of these events would cause abrupt damages and such catastrophic events, as well as the other sources of climate damage, need to be captured in the evaluation of the SCC and in the IAMs that attempt to estimate it. The problem for IAMs is that despite a growing literature and some robust estimates in some sectors, many aspects of the nature of climate damages, e.g. conflict and migration, are not known with a great degree of certainty. This is particularly so with regard to tipping points, catastrophic events and the probabilities associated with them (NAS 2017).10
Damages in the DICE model: The nature of climate related damages is a burgeoning area of research. Despite this on some key aspects there is a great deal of uncertainty: e.g. in relation to tipping points, and predictions over time. Nevertheless, the DICE model represents climate damages as an aggregation to the global level over regional level damage functions (NAS, 2017, Chapter 2) which attempts to capture the key features of what is known about the economic impact of climate change in a specific structural relationship.
The DICE model (Nordhaus, 2017) uses a highly aggregated damage function which translates atmospheric temperature change (TAT) at time t into economic damages D(T(t)) of the following form:
[14.10]
Damages are assumed to be quadratic in temperature. The fraction of global output lost due to climate damages becomes is defined as:
. [14.11]
Consequently, global output, net of damages (and mitigation costs), is then equal to total production, Y(t), multiplied by Ω(T(t)) and 
:
[14.12]
where 
reflects mitigation costs. The parameters of the damage function in Nordhaus (2017) were estimated based on an update of
a survey of damage studies undertaken by Tol (2009, 2012), and updated to include non-marketed factors, omitted sectors and
an estimate of catastrophic damages according to Nordhaus and Sztorc (2014).11 The function leads to damages of 2.1% of global output at 3°C of warming, and 8.5% of output at 6°C of warming.
Given the complexity of estimating economic damages, the quadratic form used in the DICE model is the subject of debate, particularly in relation to catastrophic risks. One implication of (14.9) is that although the marginal damages of temperature change are increasing, the increase is quite modest within the expected range of temperature change.
In discussing this point, Weitzman (2010) proposes a greater emphasis on catastrophic damages and “tipping points”, beyond which climate damages increase rapidly, and are possible irreversible. Weitzman (2010) argues that such damages could be better reflected by a damage function with a higher order polynomial form. Botzen and van den Bergh (2012) undertake a simulation of the sensitivity of the damages function to the changes in the functional form implied by Weitzman (2010). Their analysis uses the DICE model of Nordhaus and compares the damages found in Nordhaus (2008; 2017):12
[14.13]
to the higher order polynomial proposed by Weitzman (2010):
[14.14]
These are but two possible characterisations of the damage function. The implications of each damage function are reproduced in Figure 14.4. For temperature changes in the region of 3°C, the two damage functions lead to similar predictions: a loss of around 2-2.5% of global income. For temperature change in the region of 6°C, the Nordhaus (2008) damage function leads to a 10% loss of output, whereas the Weitzman calibration leads to a 50% loss. The Weitzman calibration was based on expert opinion of the temperature changes required to exceed various climatic tipping points, such as the release of methane from the Arctic perma-frost (Tundra), and changes in the flow of Thermohaline Circulation (e.g. Gulf Stream) (Botzen and van den Bergh, 2012, p. 373; Weitzman, 2010).
Yet, as Pindyck (2013) points out, the extent of damages given a temperature rises in excess of 6°C are really unknown, and calibrating the damage function is an exercise involving guesswork and a certain amount of speculation. Differences between models arise as a result of the modelling assumptions that are used to resolve this issue and the generate projections. The FUND model, for instance, has detailed sector-specific damage functions, which in aggregate, using baseline parameters, lead to lower levels of damage at each temperature increase than the DICE model, and even leads to benefits over the range 0 to 3°C of temperature increase (Greenstone et al., 2013, p. 27). Alternatively, Howard and Sterner (2017) provide a meta-analysis of damage functions for climate change which concludes that damages are likely to be more severe than the DICE-2016R model.
14.3.5. Step 4: Discounting
Chapter 8 contains a detailed description of discounting issues. In the context of reduced-form IAMs, the issue of discounting reduces
to how to calibrate the social welfare function in (14.7). The typical modelling assumption is to assume a constant utility
discount rate, δ, and a utility function with a constant elasticity of marginal utility: 
, where the parameters δ and η are components of the Ramsey Rule for the social discount rate: SDR = d + hgc, where gc, is the growth of consumption (see Chapter 8). Climate change is a non-marginal change to the economy. In the DICE model therefore, growth of consumption is an endogenous
component that is an outcome of the optimisation procedure with and without climate policies. The only question remaining
is how to choose the two welfare parameters δ and η? Disagreement on this issue alone has led to different policies on climate change being proposed (e.g. Stern 2007; Nordhaus
2008). In the DICE model Nordhaus proposes a positivist approach to the calibration which assumes that the social discount
rate should reflect observed rates of return in the market place. This, it is argued, reflects the opportunity cost of investment
in climate change mitigation, and the parameters of the social welfare function should be calibrated to ensure that the Ramsey
Rule holds as follows: 
. This approach requires an empirical estimate of η and g. δ is estimated as a residual Nordhaus (2017, p. 1520). The SCC in the DICE model assumes that the global real rate of return on investment will be 4.25% until 2100, which is a global average of observed historical rates in the United States and the rest of the world.
Source: Botzen and van den Bergh, 2012.
Other IAMs estimates of the SCC take alternative approaches to discounting. The Stern Review, which used the PAGE IAM, calibrated the social welfare function using a prescriptive or normative approach, which pointedly did not use market rates of interest to define the social discount rate (see Chapter 8 for more on this).
14.3.6. Summary
Each step of the process of calculating the SCC is subject to uncertainty in the relationships modelled, be they between economy and emissions, between emissions and climate or between climate and damages. Uncertainty surrounds climatic parameters such as ECS and TCS, as well as in relation to the spatial, temporal and probabilistic nature of climate damages. In addition to which, projections hundreds of years into the future are made on the basis of assumptions made today. The estimates of the SCC therefore need to be accompanied by a clear strategy for dealing with uncertainty, and be presented in a manner that makes it clear that uncertainty exists. Most estimates focus on central values yet provide summary statistics of the distribution of estimates based on consideration of different aspects of parameter uncertainty, e.g. the ECS parameter. Before discussing how uncertainty is dealt with in practice, SCC estimates from some important reduced form IAMs are presented. Above all, these estimates confirm the position of most researchers that the SCC is definitely not zero.
14.4. Uncertainty, catastrophic risk and Weitzman’s dismal theorem
14.4.1. Uncertainty in the SCC and IAMs
There are many sources of uncertainty at each step of the calculation of the SCC. In step 1, the emissions that are likely in the future depend on unknown and uncertain future policies on climate and technology, for instance. In step 2, the parameters which map emissions into changes in the climate are not known with certainty, as discussed in relation to the Equilibrium Climate Sensitivity and Transitory Response Sensitivity described above (See Figure 14.3). In step 3, the translation of climatic changes into physical and economic damages is perhaps one of the largest sources of uncertainty. Finally in step 4, the components of the discount rate are either difficult to predict (interest rates, returns to capital and so forth) or the source of a great deal of disagreement (Drupp et al., 2017).
A key distinction when discussing uncertainty in the calculation of the SCC is between structural uncertainty and parametric uncertainty. Structural uncertainty refers to the uncertainty about which model, or indeed if any model, is the most suitable for capturing the relationships necessary to calculate the SCC. One key uncertainty here is in relation to the abrupt damages, thresholds and tipping points which may lead to potentially catastrophic outcomes. Parametric uncertainty relates to what goes on inside the models, for instance, Figure 14.3 illustrates the uncertainty surrounding the ECS parameter that is used to calibrate the relationship between emissions and temperature change in all IAMs. But parametric uncertainty extends to all parameters used, from economic relationships, e.g. technological change and growth, to aspects of the damage function, such as the elasticity of damages with respect to output and temperature particularly at higher temperatures, as seen in the damage functions shown in Figure 14.3 (NAS 2017).
From a policy perspective these uncertainties are important to understand and incorporate in the estimates of the SCC. The current practice in dealing with structural uncertainty is to use several models to estimate the SCC. In the US, as discussed below, the DICE, FUND and PAGE models are used and variation between them reflects the different modelling assumptions. In terms of parametric uncertainty, the standard approach is to assign probability distributions to parameters (as in Figure 14.3) and undertake Monte Carlo analysis. The US Interagency Working Group for the Social Cost of Carbon is estimated the SCC using 3 IAMs using 10000 draws from the distribution of the ECS proposed by Roe and Baker (2012) to build a distribution of estimates of the SCC (IWG 2016). The NAS (2017) report recommends undertaking this analysis at each of the 4 steps outlined above. Nordhaus (2017) undertakes Monte Carlo analysis for all the parameters in the model. Such approaches assume that probability distributions can be defined for all parameters. In many cases probabilities are at best ambiguous and often unknown, e.g. the likelihood of a catastrophic outcomes and tipping points. Such risks can dominate the welfare analysis of climate change since avoiding them can be highly valuable in welfare terms from an insurance perspective.
14.4.2. Catastrophic risk and Weitzman’s dismal theorem
Weitzman’s dismal theorem (Weitzman, 2009) is the proposal that the standard framework for CBA is not fit for purpose for evaluating the costs and benefits of climate change. The reason for this position stems from the uncertainty surrounding the damages associated with climate change. Weitzman argues that the probability distribution associated with uncertain factors such climate sensitivity are “fat-tailed”. A normal distribution, for instance, is not fat-tailed since the probability of extreme events converges quickly to zero as one moves away from the central location of the distribution. Yet, by the best estimates, extreme values of climate sensitivity, e.g. values in excess of 6°C, do not have vanishingly small probabilities associated with them. Indeed, the IPCC fourth assessment report (IPCC AR4) concludes that the probability that climate sensitivity is in excess of 6°C is around 10%, with a fat-tailed distribution. With large climate sensitivity comes large potential economic damages, and potentially disastrous outcomes for humanity. It is these extreme events, Weitzman argues, that push standard CBA to the limits of its sensible use.
The argument contained in Weitzman (2009) is somewhat complex, but in a critique of the dismal theorem, Nordhaus (2011) provides a simple exposition of the basic principle. A more detailed analysis of the implications of the Dismal Theorem can be found in Millner (2013).
Suppose that social welfare is evaluated at each point in time using the standard expected utility framework:
[14.15]
In this framework, a catastrophic outcome would be captured by situations when consumption, C, is approximately zero. Weitzman’s dismal theorem argues that the expected utility in such a situation will not converge because the expected marginal utility will become negative infinity. From a welfare perspective, what this means is that society would be willing to reallocate the entire wealth towards avoiding such catastrophic events. In the context of climate change, if future generations are subject to fat-tailed risks of catastrophic outcomes, the smooth trade-off between current and future generations disappears as the calculus of CBA would argue for an infinite investment in future well-beings.
The argument has caused great deal of interest in climate economics. Weitzman (2007) argued that arguments such as these could be used to justify the conclusions of the Stern Review: deep cuts in emissions are required now to avoid climate change, stating that the Stern Review might be right, but for the wrong reasons. It is extreme, and works only for particular utility functions and probability distribution functions. Nordhaus (2009) provides a simple explanation of these points.
Suppose that utility is iso-elastic in consumption, C, a typical assumption in applied work in economics and finance: 
. This implies that marginal utility is given by: 
. If the probability distribution for C is a power law, then as C approaches zero, as it would in a catastrophic state, the probability density is given by the approximation:
. In this case small values of k mean fatter tails, and large values of k, e.g. powers much greater than 1, mean thin tails. Figure 14.5 provides an illustration of how this might look in the vicinity of C = 0.
The upper graph shows the entire probability density function (pdf) for consumption. The lower graph magnifies the lower end of the pdf in the vicinity of C equal to zero, for alternative values of the parameter k. What Nordhaus calls the conditional marginal utility in the vicinity of zero is then given by:
[14.16]
The expected utility in the vicinity of zero, between C = 0 and some (arbitrary) positive level of consumption, 
, is given by:
[14.17]
Finding the definite solution to this integral is only possible if k + 2 – η > 0. If k + 2 – η < 0, expected utility converges to minus infinity, since C to the power of a negative exponent is infinite when evaluated at C = 0. Both cases are possible with plausible parameter values for k and η, but the latter (k + 2 – η < 0) is a simple illustration of Weitzman’s dismal theorem.
Weitzman’s point is that when the tails of the distribution are fat, k is small in this example, then the welfare criterion fails to provide useable information, since it provides an infinitely negative valuation of catastrophic states of the world. Taken literally, a CBA along these lines would imply that all possible resources should be reallocated to averting the catastrophic risk. Yet, Nordhaus (2011) makes the point that the dismal theorem is not inevitable, even with fat-tailed distributions, since it depends on the preferences of the representative agent. Nevertheless, if k + 2 – η < 0, as it would be if society was very risk averse and η was very large, and the tails of the distribution are fat (k small) then the expected utility criterion fails to provide a useful measure of welfare. Under similar conditions, expected marginal utility becomes infinite, which becomes critical when evaluating marginal changes in consumption induced by public investment as would be the case in CBA. Expected marginal utility is infinite when k + 1 < η.
The basic intuition presented by Nordhaus (2011) was developed more comprehensively elsewhere and is discussed in detail by Millner (2013). Many authors have pointed out that non-convergence of the expected welfare criterion is not a general problem, but one that is more likely with iso-elastic utility functions. Yet, the problem remains a theoretical illustration of the frailties of particular frameworks when they are pushed to extremes. The consideration of fat tailed distributions and the welfare valuation of catastrophic risks is widely regarded to be the major concern in climate change economics, even if Weitzman’s dismal theorem is an extreme case (e.g. Wagner and Weitzman 2013; Pindyck, 2013).
14.5. Estimates of SCC from integrated assessment models
The four steps for calculating the SCC have been outlined and the specific example of the DICE model has been used to illustrate the modelling assumptions used in each step, and the background studies that assist with the calibration of the model. There are many IAMs in use in the academic and policy world, and each differs in the assumptions it uses to undertake each of the 4 steps described above. Furthermore, while many IAMs exist for the purpose of analysing climate change policy, as Nordhaus (2014) points out, most of the estimates of the SCC that are in circulation in the policy literature have come from three of these models: Dynamic Integrated Climate and Economy model (DICE) written by William Nordhaus and colleagues at Yale, the Framework for Uncertainty, Negotiation and Distribution (FUND) model, by Richard Tol at the University of Sussex, and the Policy Analysis of Greenhouse gas Emissions (PAGE) model of Chris Hope of Cambridge University (Hope, 2007), which provided the basis for the results presented in the Stern Review (Stern, 2007). Comparing the SCC calculated from these different models highlights some of these fundamental differences.
Tol (2011) summarised estimates of the SCC from these and other IAMs and the results of this summary are shown in Table 14.1. Another recent summary of estimates can be found in Greenstone et al. (2013), in which similar models are compared under different scenarios.
The summary statistics in Table 14.1 are raw and un-weighted statistics among the models selected. What these distributions illustrate is the wide variety of estimates of the SCC that exist in the literature. The variation stems from the different assumptions, both economic and in relation to the climate science, that are embodied in each of the models. The fact that many of the different estimates stem from the same models illustrates the different policy simulations that were undertaken, and the different parametric and other assumptions that have been deployed within each model, sometimes for sensitivity analysis. In short though, the weighted average estimate of the SCC across the three main models in 2011 was USD 62 per tonne of carbon, in 1995 dollars, or USD 92 per tonne of carbon in 2015 dollars.13 The estimates vary tremendously and the distribution has a long tail extending to thousands of dollars. Two measures of the uncertainty in the estimates of the SCC in Table 14.1 are the standard deviation and the probability that the models report an SCC that is less than zero. As Tol (2011) shows, such is the uncertainty in the estimates, the standard deviations are large and there is a 25% chance that the models produce negative estimates of the SCC when summarising the models across all the assumptions that have been deployed in their many applications.
To illustrate the determinants of the variation, consider the estimates of the SCC obtained from Nordhaus (2014), which compares a variety of scenarios which differ in their policy target and parameters such as the discount rate in Table 14.2.
The estimates in Table 14.2 are undertaken using the 2013 version of the DICE model: DICE-2013R. The basic economic and climatic assumptions remain constant across the scenarios. The differences between the scenarios are as follows. The baseline model assumes no additional climate policies are enacted henceforth. The optimal model optimises the response to climate change assuming that emissions reductions and international agreements are possible. The “Stern Review discounting” scenario uses the discounting parameters used in Stern Review (Stern, 2007) while the “High discount” scenario has a pure rate of time preference (δ ) of 3.5%. The value of the SCC varies in fairly obvious ways in response to these scenarios.
First, in the DICE model, optimal emissions reductions do not manage to reach the 2°C target given the way in which damages are modelled. The 2°C scenario adjusts damages so that it is optimal to reduce emissions and meet this target. Inevitably, with damages increased, the SCC increases accordingly. This illustrates the importance of the damage function in determining the SCC, but also the view that the 2°C limit (let alone the 1.5°C agreed in the Paris Accord) is not necessarily what Nordhaus (2014) would recommend for climate policy: the costs are too high compared to the avoided damages.
The Stern Review used the PAGE model to evaluate the benefits and costs of climate change mitigation (Stern, 2007). The Review’s analysis assumed that the rate of pure time preference (utility discount rate) ought to be equal to zero for reasons of intergenerational equity. This assumption places equal weight on utilities that accrue in the future as utilities that accrue today in the calculation of overall inter-temporal welfare. The normative calibration of the discount rate, which implies equal treatment of utilities, was debated both on normative and positive grounds (see e.g. Nordhaus, 2007; Weitzman, 2007; Dasgupta 2008). Practically speaking, the social cost of carbon is highly sensitive to the level of the discount rate, and its influence is plainly seen in Table 14.2, where the SCC of USD 90 per tonne of CO2 in 2015 is nearly five times larger than the DICE-2013R optimal scenario. As a further illustration of the sensitivity of the SCC to the discount rate, the High discount scenario uses a pure rate of time preference of 3.5%, and the associated SCC is USD 6.4 per tonne of CO2 in 2015. Finally, the optimal path of the SCC is rising with the time horizon in the DICE model.
What these simulations illustrate is the sensitivity of the estimates of the SCC to some crucial assumptions concerning the IAM. The two sources of sensitivity here are the damage function (which is increased to make the 2C scenario optimal) and the pure rate of time preference. The former is the source of deep uncertainty (See e.g. Millner et al., 2013; Pindyck, 2013), and the latter is a source of disagreement (Drupp et al., 2017).
A more recent review of the SCC by Nordhaus (2017) illustrates some additional sensitivities of the estimates of the SCC by IAMs, and also how scientific advances can be incorporated into the IAMs in order to update the estimates to reflect the latest science. Table 14.3 shows how the estimates of the SCC have changed as a result of updates to 5 elements contained in in the DICE-2016R model which affect steps 1-4 above: 1) Damages; 2) Population growth; 3) Temperature sensitivity; 4) Decarbonisation assumptions; and, 5) The carbon cycle.
Table 14.3 shows the most recent estimates of the SCC and the path of SCC over time for similar scenarios as in Table 14.2. Nordhaus (2017) has the usual baseline and optimal scenarios, but the 2C scenario is replaced with a more realistic 2.5°C scenario. Nordhaus (2017) concludes that a maximum temperature increase of 2°C is unfeasible with the current level of technology, hence the 2.5°C scenario in the 2017 update (Nordhaus 2017, p. 1522). The 2.5°C scenario again adjusts damages so that it is optimal to reduce emissions and meet this target. This increases the SCC as before, from USD 31 per tonne of CO2 to USD 184 per tonne of CO2. This SCC is also sensitive to the discount rate, increasing over 6‐fold in 2015 if a 2.5% discount rate is favoured over a 5% discount rate.
Tables 14.2and 14.3 are not measured in the same units of the same base year. Yet Nordhaus (2017) shows that the updates to the DICE-2016R model affected the calculation of the SCC in the following way (% change in parentheses):
-
Damages (-14%);
-
Population growth (+6%);
-
Temperature sensitivity (+8%);
-
Economic assumptions on decarbonisation (+31);
-
The carbon cycle (+25%).
Ultimately, Nordhaus’ preferred value of the SCC from the DICE model is USD 31 per tonne of CO2 in 2015, rising to USD 102.5 in 2100. Yet there remains is a great deal of uncertainty surrounding these estimates. For instance, Howard and Sterner (2017) find an SCC almost 4 times this value after undertaking their meta-analysis of the damage function and showing that a higher damage function which better accounts for catastrophic risks and non-marketed damages is more appropriate.
14.6. The social cost of carbon: International experience
Several countries have enacted legislation or policies to ensure that carbon emissions are incorporated into the analysis of public projects and regulations (e.g. United States, United Kingdom and Canada). In some cases carbon emissions are regulated by carbon taxes (Finland, Sweden) or cap and trade instruments (e.g. European Emission Trading Scheme (ETS), California (ETS) in the United States, Alberta ETS Canada).14 The United States uses the SCC in CBA of public projects and regulations while France recommends the abatement costs approach. In 2009, the United Kingdom moved away from SCC and focused on the abatement costs of meeting a specified emissions reduction under the Climate Change Act of 2008. Some of these cases are discussed below, starting with the United States.
14.6.1. Calculating the SCC in the United States: The Interagency Working Group
In the United States, a series of legal rulings have led to the Environmental Protection Agency having authority to regulate greenhouse gas emissions under the Clean Air Act (CAA), along with other air pollutants (Metcalf and Stock, 2017). In 2007, the case of Massachusetts vs EPA (549 U.S. 497) the Supreme Court ruled that the CAA gives the EPA authority to regulate tailpipe emissions of greenhouse gasses. In 2008, the U.S. 9th Circuit Court of Appeals ruled that the National Highway and Transport Safety Commission had acted “arbitrarily” when it refused to value carbon emissions due to the uncertainty surrounding the value of the SCC. Executive Order 12866 required agencies “to assess both the costs and the benefits of the intended evaluation and, recognising that some costs and benefits are difficult to quantify, propose or adopt a regulation on upon a reasoned determination that the benefits of the regulation justify its cost” (Section 1, part 6).15 According to the Inter-Agency Working group Technical Support Document, the purpose of the SCC is to “allow agencies to incorporate the social benefits of reducing carbon dioxide (CO2) emissions into cost benefit analyses of regulatory actions.” (IWG 2016, p. 3).
The process by which the SCC is calculated is most developed in the United States. In 2010 an Interagency Working Group (IWG) was convened by the Council of Economic advisors (CEA) to develop estimates of the SCC that could be applied in accordance with Executive Order 12866. This resulted in a Technical Support Document (IWG 2010). In the interim the estimates were updated in 2013, as summarised by Greenstone et al. (2013), and in 2016 leading to an updated Technical Support Document (IWG 2016). These updates were in accordance with Executive Order 13563, which commits the agency to use the best available science in any regulatory decision making (IWG 2016, p. 6). Finally, a recent report by the National Academy of Sciences (NAS, 2017) responded to a request by the IWG for advice on how to approach future updates of the SCC to ensure that estimates are based on the best available science. Several important recommendations have been made which are discussed below.
The US Interagency Working Group (IWG, 2016) estimated the SCC using three IAM models: FUND, DICE and PAGE. The IWG used the most up-to-date versions of these models at that time and followed the procedure set out in Greenstone et al. (2013):16
-
The emissions trajectory EMF-22 from the Stanford Energy Modelling Forum was used to define the emissions scenarios;
-
5 scenarios were defined: 4 business-as-usual scenarios resulting in high concentrations of CO2 between 600 and 900 ppm, and a 5th scenario which involves mitigation and stabilisation of emissions at around 450 ppm;
-
The Equilibrium Climate Sensitivity (ECS) was drawn as a random parameter the distribution recommended by Roe and Baker (2007), calibrated to the IPCC-AR4 consensus statement. This resulted in a distribution with a “median of 3°C, a 2/3 probability of being between 2°C and 4.5°C and zero probability of being outside of the range zero to 10°C” (Greenstone et al., 2013).
-
Three discount rate scenarios were chosen by fixing the real rates of return in different emissions scenarios to 2.5%, 3% and 5%.17
-
Welfare effects were evaluated using a global welfare function (Equation [14.7]).
Following these steps the IWG (2016) estimated a schedule values for the SC-CO2 which are presented in Table 14.4. This work led to a value of USD 40 per tonne of CO2 being proposed for inclusion in cost-benefit analysis of public works and regulations, based on the 3% discount rate scenarios and year 2020. Once again, variation in the estimates across the 3 models stems from different modelling assumptions, but the estimates are clearly sensitive to the discount rate. Furthermore, as in the summary undertaken by Tol (2011), the values in Table 14.4 represent unweighted averages across models and scenarios.
Following these procedures and repeating 10 000 times, a range of estimates of the SCC were obtained reflecting the repeated sampling of the climate sensitivity parameter (IWG 2016; Greenstone et al., 2013). As shown in Chapter 9, Monte Carlo analysis: drawing parameters from a distribution and collating the estimates, is commonplace in CBA. It is also typical in the reduced form IAM models as a means of dealing with parameter uncertainty. While for 2020 the estimates had a 5%-95 percentile range of – USD 11 (FUND) per tonne of CO2 to + USD 370 (PAGE) per tonne of CO2, using a 3% discount rate, the mean across all models was USD 42 per tonne of CO2, in 2007 dollars. These estimates of the SCC are expected to increase over time as emissions become more damaging. For regulatory analysis, sensitivity of the SCC was recommended at USD 12 and USD 62 (in 2020, for discount rates 5% and 2.5% respectively). The 95th percentile value of USD 123 in 2020 reflects a damage function more akin to the Weitzman damage function in Figure 14.4. At the time these estimates represented the latest recommendations for the value of the SCC for regulatory analysis (IWG 2016).
Calculating the SCC in the United States: The NAS (2017) report responds to requests made by the IWG to provide advice on how to improve and update the calculation of the SCC in the future for regulatory analysis. It makes several recommendations for future updates of the SCC.
14.6.2. The SCC in the United States: Policy impact and future
Hahn and Ritz (2017) ask whether the use of the SCC in the US has had any effect on national policy, and undertake a systematic analysis of all federal regulations since 2008. Nordhaus (2017) notes that the SCC has been used in Federal Regulations with estimated benefits of up to USD 1 trillion, while Greenstone et al. (2013, p. 43) claims that three key policy areas in the United States have been influenced by the presence of SCC estimates: 1) US Department of Transport and the Environmental Protection Agency’s standards for GHG emissions and fuel efficiency; 2) Colorado Public Utility Commission’s hearing on retiring 900 MW of coal-fired power stations; 3) Declaration before the US Court of Appeals for the District of Columbia Circuit regarding EPA’s GHG regulations.
Yet Hahn and Ritz (2017) find that the ranking of projects within the United States was unchanged by the presence of the SCC, despite making up approximately 15% of the benefits on average among the 53 regulatory policies that they analysed. Of course, there could be many internal reasons for such a finding, Hahn and Ritz (2017) argue this result could have many causes, ranging from non-maximising behaviour from regulatory agencies, to expectations that SCC will rise in the future. The lack of influence could have been deliberate, with the SCC chosen as a visible but ineffectual policy on carbon emissions, which allowed the administration to be seen to do something. Only 1 in 8 projects reviewed were significantly affected by the inclusion of the SCC (Hahn and Ritz 2017, p. 245).
The future of the SCC as part of the decision-making apparatus in the US became uncertain in March 2017 when Executive Order 13783 was signed by the incumbent president. Among other things, this Executive Order disbanded the Interagency Working Group on the Social Cost of Carbon, and nullified all of their Technical Support Documents (E.O. 13783, Section 5). Furthermore, the US administration is now looking more closely at an SCC that includes only domestic damages and includes the upper bound 7% discount rate for sensitivity (USEPA 2017, p. 1). With domestic benefits only, the SCC reduces to USD 7 per tonne of CO2 (USD 1 per tonne of CO2) for discount rates of 3% (7%), with 95th percentiles of USD 28 per tonne of CO2 (USD 5 per tonne of CO2), compared to the figures shown in Table 14.4. These figures represent reductions of between 80-95%.
14.6.3. The United Kingdom
In the United Kingdom, for instance, the use of the SCC in regulatory analysis was recommended in 2002, with values of between GBP 35 and GBP 140 per tonne of carbon proposed, with a central value of GBP 70 per tonne of carbon (approximately USD 250 per tonne of CO2), to be used across government. In 2009, the way in which the UK government included carbon values in CBA changed from the SCC approach towards values based on the European Emissions Trading System (ETS) if the source was included in the ETS, or an abatement cost approach otherwise. All government projects and regulatory changes that have carbon impacts, which include those in transport, energy and energy efficiency, are advised to refer to the Government’s short-term carbon values. These values are regularly updated with the most recent update taking place in 2016.18 Table 14.5 shows the current estimates of traded and non-traded carbon emissions, and the predictions from 2010-30.
The switch from an SCC approach to the abatement cost approach stems from the passing of the 2008 Climate Change Act (Act of Parliament c 27) which makes it the duty of the secretary of state to ensure that net carbon emissions in the UK are 80% lower in 2050 than the baseline level in 1990, in line with the commitments under the Kyoto Protocol and subsequent agreements. The Climate Change Committee, made up of experts from relevant disciplines and civil servants, oversees the commitments under the Act and makes recommendations in the case that the targets are not being met.
14.6.4. France
In France the “carbon value”, which is the estimate of the SC-CO2, is now one of the “unit values” that appears in the CBA guidance alongside the value of statistical life and the discount rate. The values used start at approximately USD 27 (EUR 32) per tonne of CO2 and rise at rate of 5.8% per year until 2030 and at the rate of discount (4.5%) thereafter. These increases over time reflect Hotelling’s Rule for non-renewable resources which is an attempt to define the optimal time path of carbon values, as discussed in Section 14.2, and reflect the increasing damages associated with carbon emissions (Quinet, 2013). The carbon value is used to inform the carbon tax which applies to ETS and non ETS industries alike.
14.7. Other approaches to calculating the SCC
14.7.1. Expert opinions on the SCC
In a series of critical articles, Pindyck (2012, 2013, 2016) discusses the weaknesses of integrated assessment models. The chief complaint is not that IAMs cannot be a useful tool for increasing the broad understanding of the likely impacts of climate change, and the efficacy of different policies on e.g. mitigation and technology. Rather, Pindyck criticises the use of these models as an input to actual policy measures, such as estimates of the SCC of the kind undertaken by the IWG (2016) for the US.
The reason for this criticism is that in some critical areas the models and their parameterisation is based on what Pindyck (2013) describes as “pure guesswork” on matters which are subject to a great deal of scientific uncertainty. The most crucial example of this is in the damage function for climate change emissions. As if equilibrium climate sensitivity (ECS: the long-run response to the climate of a doubling of CO2 emissions) and the transitory climate response were not uncertain enough (e.g. see Figure 14.2), the way in which temperature change is translated into damages in the long-run is very difficult to define with any certainty, despite the burgeoning empirical literature on the estimation of climate damages. The problem is that projections of damages into the future are uncharted territory since they require temperature changes that have not been yet been witnessed. Particularly uncertain are the risks of catastrophic outcomes.
Pindyck (2013, 2016) also argues that in addition to these uncertainties and unknowable factors, should be coupled the general complexity and hence opacity of the models. Typically this means that the reason that policy or climate simulations lead to particular outcomes is often not easy to determine: one cannot tell what is driving what, and whether the outcomes are in a sense “real” or artefacts of some hidden-away assumption. In short, most IAMs can be thought of as black-boxes. Finally, there is a tendency for IAMs to analyse averages in temperature and hence average damages. The present value damages arising from changes in the central tendencies of climate typically do not amount to much more than 5-10% of GDP, equivalent to a moderately sized recession. This is because climate damages accrue only slowly when measured in this way, hence the sensitivity of these damage estimates to the social discount rate. For these reasons: i) parameter and model uncertainty; ii) opacity or lack of transparency; and, iii) focus on central tendencies of climate change, Pindyck is sceptical of the usefulness of IAMs.
As an alternative, Pindyck proposes simply asking experts for their opinion on the SCC, not by asking them directly, but by asking a range of simple questions about climate damages that allow a simplified model of climate to be calibrated and the SCC to be calculated based on the removal of catastrophic risks, rather than based upon average changes in temperature. The Annex provides some details of the approach and the questions that were asked. The key information required from the experts was: i) Emissions trajectories; ii) % reduction in GDP due to climate in 50 years; iii) the probability of X% reduction in GDP 50 and 150 years in the future; iv) the reduction in emissions required to reduce the risk of a 20% loss to zero; v) the discount rate. Together with some simple transparent modelling relationships between damages and emissions (See Annex 14.A1), the answers to these questions lead to an SCC based on expert opinions.
For instance, the answers to the probabilistic questions about reductions in GDP (iii above) allow the researcher to build a rudimentary probability distribution function for damages. Table 14.6 and Figure 14.6 provide an example of the probability distribution that could be drawn from an expert’s responses to the Pindyck survey.19
Note: Each point on the blue line graph represents a point at which the survey asked for the probability of GDP loss being larger than x%, except the furthest left point. The orange line is one minus this probability: the survivor function, which gives the probability of GDP loss being greater than x%.
The SCC can now be approximated by using the expert opinions. The estimate of the social cost of carbon proposed in Pindyck (2016) is composed of two parts. First, the expected benefits of the reduction in costs from eliminating damages greater than 20% of GDP. Second, the benefits are divided by the emissions reductions required to eliminate the prospect of extreme damages. It should be evident that this is an estimate of average SCC, rather than the typical SCC which values the damage from a marginal change in emissions.
The advantages of this estimate of the unit damages of carbon emissions are that it is transparent in the sense that it is parsimonious while capturing some of the most salient features of climate change and the evolution of damages. Furthermore, the focus is clearly on the most disastrous tail events that might be associated with climate change, rather than the gradual and moderate damages associated with changes in the central tendencies of temperature, e.g. the mean. With a few additional assumptions on the distribution of opinions it is easy to calculate the benefits of truncating disastrous outcomes.
The survey of experts in Pindyck (2016) calibrates the average SCC using responses from around 1 000 experts drawn from different disciplines, including economics and climate science. The SCC estimates were extremely heterogeneous but the average SCC was typically well in excess of USD 200 per tonne of carbon (USD 54.6 per tonne of CO2) among all groups. The average across all groups was USD 290 per tonne of carbon (USD 79.1 per tonne of CO2). Once outliers were removed, and those who claimed insufficient expertise, the average SCC was reduced to about USD 200 per tonne of carbon.
The simplified model of climate change and climate damages in Pindyck (2016) is in many ways a triumph of Occam’s razor.20 The transparency of the expression for the average SCC, and the assumptions that lie behind it, is obvious. Yet, the charge of there being a black-box behind these estimates arguably still remains, only in this case the black-box being deployed for each response is inside the head of the expert respondent. There may be offsetting errors in the aggregation process which make this survey approach more accurate, but there may be biases also. In the end it is not entirely clear that this approach is better in the sense of providing more sensible numbers, despite its obvious elegance and simplicity.
Perhaps the most important message that can be taken from the approach is that the social cost of carbon estimated from this approach is well in excess of the USD 42 per tonne of CO2 that was the focus of regulatory guidance in the United States in the Obama presidency, and way above the USD 1 per tonne of CO2 currently being proposed.
14.7.2. Simplified expressions for the SCC
Another approach to the estimation of the SCC is to develop a relatively simple closed-form expression for the SCC which depends on relatively few components and can be easily estimated for policy purposes. In some ways, Pindyck (2016) provides a simple understandable representation of the SCC (See Equation [14.A1.1] in Annex 14.A1) but this expression is not based on any clear distinct economic assumptions and a strong connection to climate science and economic theory is not its purpose. The research discussed in this section attempts to obtain parsimonious representations of the SCC than the IAMs, which are still strongly rooted in economic theory and climate science.
A number of papers have taken this approach using highly simplified/stylised models of climate and economy that capture the salient features of the climate change problem without deriving a closed form solution for the SCC (Golosov et al., 2014; Gerlagh and Liski, 2012). Van den Bijgaart et al. (2016) go further in providing a closed-form solution for the SCC in a deterministic framework, while showing that the approximation to more complicated (deterministic) IAMs is good.
The chief motivation for such expressions overlaps somewhat with Pindyck’s critique of IAMs: the need for transparency and parsimony. One advantage of having simplified and transparent estimates of the SCC is that policy-makers and practitioners are more able to understand the principles behind it and generally engage with the concept, without the need for high level or technical knowledge about the model itself. Van den Bijgaart et al. (2016, p. 75-76) state that a major problem with IAMs is that they are “not accessible” to policy makers and members of the public. Inaccessibility is a major determinant of the SCC is often “accepted or not accepted on the basis of trust or mistrust” in its estimates and procedures.
The simple formula provided by van den Bijgaart et al. (2016) is as follows:
[14.18]
where Y is income/output, L is population, and 
is a reference consumption level. The other terms are all parameters relating to the 4 steps outlined above for estimating the SCC: 1) Output to emissions; 2) Emissions to temperatures; 3) Temperatures to damages; 4) Discounting. Table 14.6 provides details.
This representation of the SCC is extremely transparent and closely maps the SCC that emerges from many reduced form IAMs (See van den Bijgaart et al., 2016, p. 81-88), while remaining extremely transparent. Rather than being based on expert opinion it is based upon parsimonious functional relationships in the economic and geophysical domains, and well defined economic assumptions. Compared to an IAM, this expression for the SCC is relatively easy to explain to policy makers, while a publicly available excel spreadsheet allows practitioners to gain a sense of the relative sensitivity of the SCC to different parameter choices.21
Using typical parameter distribution assumptions for the DICE model, the SCC stemming from [14.18] turns out to be strongly right skewed, with a mean of approximately USD 40 per tonne of CO2, a median of USD 17 per tonne of CO2 and a 90th percentile of USD 84 per tonne of CO2. These values closely map the estimates found in Table 14.3and 14.4.
|
Table 14.7. Parameters for the simple SCC expression in equation [14.18]
|
|
|---|---|
|
Parameter |
Meaning |
|
ω |
At reference consumption level |
|
μ |
Pre-industrial emissions levels |
|
ɸ |
The decay parameter for the stock of CO2 (as in Box 14.1) |
|
ɛ |
Temperatures adjust at rate e to their long run equilibrium level. |
|
σ |
The climate discount rate:
Where l is population growth and ζ is described below. |
|
ψ |
The elasticity of damages with respect to temperature, T. |
|
ζ |
The elasticity of damages with respect to output, Y. |
|
Source: van den Bijgaart et al. (2016). |
|
a 1ºC rise in temperature leads to relative damages ω.
14.8. SCC: Global or domestic values?
Another policy relevant issue when it comes to calculating the SCC is whether an individual country should use the global value of the SCC or whether it should focus solely on the present value of domestic damages of climate change (Fraas et al., 2016; Dudley and Mannix, 2014; Gayer and Viscusi, 2016). The convention has typically been to estimate the global SCC for use in public policy at the domestic level (IWG, 2016; NAS, 2017, Chapter 2). The argument for focussing on the global values is that CO2 is a global pollutant, and so in order to internalise the global externality, all countries need to internalise that externality. It has also been argued that the international cooperation required to limit global warming is also more likely to be achieved if a global stance is taken (Revesz et al., 2017). In its discussion of the SCC, the Interagency Working Group (IWG 2010) estimated that the domestic SCC is between 7% and 23% of the global SCC for the US. Many caveats were placed on this measure, including the fact that many of the models used to estimate the SCC are not sufficiently spatially detailed to attribute damages at the country level. Furthermore, it was acknowledged that such estimates tend to ignore indirect damages to the US that occur via countries that are trading partners, for instance. The issue of domestic versus global damages is an active area of research (e.g. Kotchen, 2016).
Nevertheless, the idea of using domestic SCC has gained policy traction. In October 2017, the US EPA recalculated the SCC to be used for regulatory analysis on the basis of domestic damages only, coupled with a new sensitivity test to the highest discount in the range of discount rate recommended by the OMB (2003) guidelines: 7%. At a 7% discount rate, and using only domestic damages, the US SCC falls from USD 40 per tonne of CO2 to USD 1 per tonne of CO2 as a consequence (US EPA, 2017).22
14.9. Conclusions
For regulatory analysis and the evaluation of public projects, it is essential that the cost of carbon emissions is taken into account. An estimate of the SCC is required in order to include these damages in CBA and to inform the optimal carbon tax. Estimation is made difficult due to the complexity of the problem and the uncertainties that the future of climate change holds in relation to climate sensitivity, future economic growth and emissions paths, and the damages that can be expected as a consequence. Theory shows that care is needed in regulating carbon and setting the appropriate carbon tax over time, and that sub-optimal policies could lead to perverse outcomes like the Green Paradox, although such outcomes are not guaranteed.
On the estimation side, the United States has clear guidance on how to estimate the SCC for these purposes and up until recent policy changes, the SCC was routinely used in regulatory analysis and the analysis of policies, with a value of around USD 40 per tonne of CO2 rising to over USD 100 per tonne of CO2 in 2050. Many OECD countries use an estimate of the SCC in their appraisal of public projects and to inform their carbon taxes.
Integrated assessment models (IAM) are typically used to estimate the SCC, and these have been shown to be sensitive to the assumptions concerning climate sensitivity, climate damages and the welfare treatment of uncertainty and ambiguity. In particular the way in which catastrophic risks are treated in IAMs, both on the damages side and in the measurement of welfare side, is as strong determinant of the aggressiveness of the climate policy response. Greater uncertainty and ambiguity, coupled with fat-tailed probabilities of catastrophic events, leads to recommendations for more stringent climate policy, and larger estimates of the SCC.
In recent years the use of exert opinions on the SCC, and the development of simple transparent formulae for the SCC have been developed. Some argue that these approaches are better since they are more transparent and democratic, sometimes at no cost in terms of the range of values of the SCC that they produce. The calibration of IAMs for public policy advice is an area of active debate and further research due to the uncertainty associated with the science and economics of climate change, and disagreement concerning some of the crucial parameters that determine the SCC (e.g. the discount rate or ECS). The main success from the perspective of CBA is that estimates of SCC are currently appearing in the analysis of public policy, and are influencing decisions in ways that are likely to improve long-run social welfare.
The price of carbon is very unlikely to be zero. Evidence of the general agreement that the SCC is non-zero can be found in the widespread inclusion of monetary values of carbon in policy analysis across the OECD countries (Smith and Braathen 2015; ITF 2015).
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Pindyck’s survey questions attempted to define the baseline emissions scenario and then the likelihood of particular damages occurring in terms of proportional losses in GDP. The questions were as follows:
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What is the average GHG emissions growth rate under Business-as-Usual (BAU) over the next 50 years (i.e., no additional steps are taken to reduce emissions)?;
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In the absence of any climate mitigation policy, what is the most likely climate-caused reduction (in %) in world GDP that will be witnessed in 50 years?
Then, the questions tried to get experts to specify the probability distribution associated with climate damages, in particular the likelihood of extreme tail events. The following questions were posed:
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In the absence of climate mitigation, what is the probability that 50 years from now, climate change will cause a reduction in world GDP of at least 2, 5, 10, 20 and 50%?
The same questions were then asked in relation to the far-distant future, 150 years hence. Experts were further asked:
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What reduction in the growth of emissions would be required to eliminate the tail of the distribution and push the probability of climate damages being greater than 20% of GDP to zero 50 and 150 years in the future?
The answers to question 3 implicitly specify a cumulative probability distribution function and survivor function for GDP damages in percentage terms like the one tabulated in Table 14.3, and plotted in Figure 14.6. Experts provided responses such as these for the two time horizons: 50 and 150 years. These are the kinds of inputs that would typically be produced by an Integrated Assessment Model, but in this case are produced from expert opinions.
The benefits of reducing extreme damages are calculated as follows (Pindyck, 2016):
[14.A1.1]
where the numerator is composed of two terms:
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[E1(z1)-E0(z1)]: the change in the expected percentage reduction in GDP resulting from eliminating the tail risk. Expectation E0(z1) is taken over the reduced range of values (probabilistic support) of damages, whereas E1(z1) is the expectation over the entire support of damages;
and;
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b Y0: the proportion in 1.) is multiplied by the initial level of GDP, Y0, and the assumed growth rate of damages, β.
The numerator divided by the term (1 – exp(– b T)) yields the instantaneous flow of benefits from reducing climate damages for the horizon T. The present value of this flow is given by dividing through by the effective discount rate, which is given composed of the discount rate on consumption, r, net of growth in GDP, g, and the growth of damages, β : (r – g) (r + b – g) (Pindyck, 2016, p. 11).
The emission reductions required to obtain this expected reduction in damages is calculated from the answers to question 4 above. The expert opinions on emission reductions imply a particular change in the growth rate of emissions: a reduction from μ0 to μ1. The differences between these trajectories in present value terms over an infinite horizon are given by (Pindyck, 2016, p. 11):
where r is the discount rate and E0 is the initial emissions level. Dividing through the experts’ view of the gross benefits of the damage reduction by their opinion of the emissions reduction required provides an estimate of the average social cost of carbon. Combining the two equations yields the average social cost of carbon:
[14.A1.2]
Notes
← 1. Despite being called the SCC, it typically measures the damages associated with all greenhouse gases. This chapter assumes this throughout.
← 2. Knightian uncertainty describes a circumstance in which the risk associated with events cannot be represented by well-defined probability distributions. Events which are rare, or previously not experienced, are examples of Knightian uncertainties since the probability of these events occurring is not known. At best probabilities are ambiguous, and can be defined within some interval.
← 3. A tonne of CO2 contains 0.273 tonnes of carbon, so the SC-CO2 will be 0.273*SCC
← 4. van der Ploeg and Withagen (2015) is part of a symposium on the Green Paradox in the Review of Environmental Economics and Policy.
← 5. A tonne of CO2 contains 0.273 tonnes of carbon.
← 6. In the IPCC (2013) a distinction is made between confidence and likelihood in relation to uncertainty. Medium confidence meansa 5 out of 10 chance, high confidence mean an 8 out of 10 chance. Alternatively, likely means > 66% probability, and unlikely means < 33% probability, and very unlikely means < 10% confidence. For a full description see: www.ipcc.ch/publications_and_data/ar4/wg1/en/ch1s1-6.html.
← 7. See Perry and Ciscar (2014) for a summary of structural modelling approaches.
← 8. NAS (2017, Chapter 5) and Dell et al. (2014) have good summaries of damage-related studies. A symposium on adaptation in agriculture can be found in a symposium edition of the Review of Environmental Economics and Policy, July 2017.
← 9. For an analysis of cloud formation, see IPCC (2013), Chapter 7. For an analysis of feedback and irreversible impacts of climate change, see IPCC (2013), Chapter 12. See-level change is analysed in IPCC (2013), Chapter 13.
← 10. NAS (2017, p. 138) quotes the IWG (2010) report that highlighted the incomplete treatment of catastrophic damages as well as non-catastrophic damages in the current formulations of damages. Damage functions have been updated since 2010, e.g. Nordhaus (2017), but difficulties still remain in relation to the way reduced-form IAMs embody catastrophic risk and tipping points according to NAS(2017, p. 144).
← 11. Some arithmetic errors that appeared in Tol (2009; 2012) were corrected in recent DICE updates. See Tol (2014) and Nordhaus and Moffatt (2017).
← 12. Strictly speaking, for reasons of goodness of fit, the estimation uses a one parameter function, assuming j1 = 0, hence the formulation in (14.13).
← 13. At 2% inflation over 20 years.
← 14. Beyond this, a number of countries have implemented carbon taxes on different sectors of their economies. For example, Sweden and Finland have implemented carbon taxes, of USD 150 per tonne of CO2 and USD 89 per tonne of C respectively.
← 15. See www.epa.gov/laws-regulations/summary-executive-order-12866-regulatory-planning-and-review.
← 16. Updates included changes to damages modules such as sea-level rise, regional scaling factors, adaptation, and carbon cycle parameters.
← 17. The lower 2.5% scenario is motivated by the literature on declining discount rates stemming from Newell and Pizer (2003), Groom et al. (2007) and more recently Freeman et al. (2015). See IWG (2010) and Chapter 8 of this book.
← 18. The list of traded and untraded short-term carbon values can be found here: www.gov.uk/government/collections/carbon-valuation--2.
← 19. To sketch the probability distributions, the minimum bound is the only additional information required beyond the questions in Pindyck (2016).
← 20. See https://en.wikipedia.org/wiki/Occam’s_razor.
← 21. See: https://doi.org/10.1016/j.jeem.2016. 01.005.
← 22. www.federalregister.gov/documents/2017/03/31/2017-06576/promoting-energy-independence-and-economic-growth.