The concepts Social Cost of Carbon (SCC) and Marginal Abatement Cost (MAC) represent two mainstream approaches for estimating the carbon cost. The SCC represents the economic cost (damage value) that society incurs for emitting an additional ton of CO₂ into the atmosphere for the time it will remain there (or the benefit for reducing it). SCC includes considerations of climate change damages to agriculture, human health, and property, and non-market damage such as the services that natural ecosystems provide to society ^[1][12]. SCC has been used primarily by national government agencies or international organizations to calculate the impact of climate policies based on a cost–benefit analysis. Researchers initially used the concept of SCC for the global scale and over time discussed it at large regional and national scales ^[2][3][4][13,14,15]. SCC is generally considered to have some major weaknesses, namely: complexity, subjectivity of discount rate, and the uncertainty of climate change impacts. Stern proposed that the discount rate should be zero as an attempt to solve this variability of the SCC and to avoid disproportionate burdens for the future caused by climate damage today due to overestimation of the present value of economic damage caused. The SCC approach to mitigate or explain the uncertainty elements results in a large variability of values, depending on the parameters, ranging from less than 0 to 1909 EUR/tCO₂ (0 to 2300 USD/tCO₂) ^[5][16] (assuming 1 US$ = 0.82 €; and CO₂ and carbon are used here interchangeably), and with concentration of results between 8.3 and 166 EUR/tCO₂ (10 and 200 USD/tCO₂). Pindyck ^[6][7][17,18] proposed the average SCC from an elicitation with experts after criticism of the “pure guesswork” on critical matters of climate and social science that are themselves uncertain (e.g., tipping points). His large survey of climate economists and scientists showed that the highest average value (163 EUR/tCO₂ (200 USD/tCO₂)) for economists was the lowest value for climate scientists. Wang et al. ^[5][16] proposed a revised SCC calculation method, and Tian, Ye and Zhen ^[8][19] created a new simplified model for SCC calculation. When assessing the SCC at the country level, Ricke et al. ^[9][20] identified inequality in climate change impacts geographically as well as the contribution of each country to global emissions and the risk of unilateral climate action. Tol ^[10][21] estimated the national SCC and the penalty on the poorest and most populous countries. An important criticism also comes from the environmental science: SCC leads to an underestimation of fundamental costs of climate change such as ocean acidification and humanitarian and social impacts ^[11][22], which are not quantified in terms of GDP.

The other method for carbon cost estimation is the MAC—the cost of reducing an additional unit of emissions and the basis for measuring the capacity of an economy to support the cost of decarbonization, in relation to energy technology sectors. It is cost-effective-driven and does not consider the climate damage cost component. The MAC approach was developed following the oil shocks of the 1970s and the need to reduce energy consumption (fossil fuels and electricity) and air pollutants. Afterwards, researchers started to integrate carbon emissions and other sectors with strong climatic impacts into analyses using the MAC approach, such as agriculture and water.

Interest in MAC increased dramatically when the Paris Agreement in 2015 shifted the political focus from a carbon tax extracted from SCC to a committed timeframe, CO₂ concentration, and temperature targets ^[6][17], and even more so when nations began to commit to carbon neutrality by mid-century. Carbon neutrality corresponds to a state of “balance between anthropogenic emissions by sources and removals by sinks of greenhouse gases” ^[12][23]. One MAC model that the International Energy Agency (IEA) has been developing is TIMES, in collaboration with member countries and academic institutions in open source and for several decades. Country members of the IEA use TIMES to simulate short-term average technology costs from the energy transition to carbon neutrality in 2050.

Pezzey ^[13][24] points out that it is preferable to estimate the carbon price closer to the target-based climate policies, while also recognizing uncertainties that remain in the MAC. The focus on reduction targets strengthens the adequacy of MAC to capture the effort of emissions reduction. Kaufman et al. ^[14][25] advocate for an alternative to the carbon price definition in a carbon-neutral horizon in 2050, based on a short-term MAC model (near-term to net-zero, or NT2NZ). The approach results in prices around 103.75 EUR/tCO₂ (125 USD/tCO₂) in 2030. Stern and Stiglitz ^[15][26] considered this approach as imperfect and transparent, as the SCC is uncertain and complex, proposing an alternative approach to the classic SCC that puts it at 83 EUR/tCO₂ (100 USD/tCO₂) (Table S1 in the Supplementary Information). They include the 2 °C increase limit as an additional constraint to the model, assuming that climate damage from the maximum limit drawn in the Paris Agreement costs more than 2% of GDP/year.

Much of the literature on the complexity, uncertainty, and subjectivity of the SCC and the limitations of the MAC shows that there is not an ideal approach, and policymakers should instead use a set of tools to assess climate policy. The problems pointed out with the SCC at the global or country levels are amplified when applied at a subnational level and smaller scales. As a global value harmonized to maximize efficiency, SCC is highly aggregated, and the smaller the scale (from global to regional, from regional to national, or from national to local), the greater the possible error margin. Although Pindyck ^[7][18] finds a general preference among economists for the SCC, the complexity of the estimates represents a barrier for policymakers and practitioners to understand ^[16][17][27,28].

As for the impacts of carbon pricing, Best, Burke and Jotzo ^[18][29] found evidence that in countries with carbon pricing, the average annual growth rate of CO₂ emissions from fossil fuel consumption is 2% lower than in countries that do not have carbon pricing. Green ^[19][30] found that most studies concern Europe, and that the aggregate reductions range is modest, ranging from 0% to 2% per year. Lilliestam, Patt, and Bersalli ^[20][31] state that there is still no empirical evidence of carbon pricing effectiveness in promoting the technological change necessary for full decarbonization.

To summarize, both methods share the economic concept of marginal cost, and while the SCC is the marginal cost of damages associated with carbon emissions (when emitting less, the cost decreases), the MAC is the marginal cost of reducing emissions (when emitting less, the cost rises). Both have advantages and disadvantages. Comparing SCC and MAC, economists agree that MAC is not as sensitive to the discount rate as SCC is and does not use the damage function. MAC responds to how to decarbonize a sector in a given time constraint, and it allows for the modeling of regions/countries, as Ibrahim and Kennedy ^[21][32] as well as others have previously shown.

Integrated Assessment Models (IAM) as a type of science and policymaking interface have been developed to estimate the cost of carbon, in the form of SCC or MAC. They simulate and calculate the optimal level of implementation of decisions/policies, while dealing with highly complex natural (climate) and social (economic) systems. Historically, an IAM includes key elements of the climate change mitigation and climate impacts systems in order to project alternative future climates with and without various types of policies ^[22][33]. When IAMs began to be increasingly used in climate policy analysis and policymaking in the 1990s, the rationale was to support policy on climate change mitigation and adaptation at the global level ^[23][34]. Today, IAMs are increasingly needing to be improved to suit analysis at the regional, national, or subnational levels, especially since the shift of focus of the Paris Agreement from global action to bottom-up initiatives and national mitigation policies ^[24][35]. An example of IAM adaptations to incorporate specific characteristics is the new single-region model—DEMETER-CCPE (previously a global IAM), which addresses regional climate policies from the perspective of cost–benefit efficiency ^[25][36]. The current diversity of IAM reflects different perspectives of analysis supporting climate policy decisions, such as cost-effectiveness, cost–benefit efficiency, and technology abatement contribution ^[26][27][37,38], which are useful to estimate the cost of carbon. The main limitations pointed out for IAM (assumptions uncertainty, transparency, replicability, and information) derive from the complexity of the climate puzzle (tipping points) and the policy decision (discount rate). Their detractors call them a “black box”. The strength of these newly adapted models is the systematic exploration of model, value, and parameter uncertainties, which improves the transparency of results and is thereby more useful for subnational decision makers ^[22][33].