Country-level social cost of carbon

The social cost of carbon (SCC) is a commonly employed metric of the expected economic damages from carbon dioxide (CO2) emissions. Although useful in an optimal policy context, a world-level approach obscures the heterogeneous geography of climate damage and vast differences in country-level contributions to the global SCC, as well as climate and socio-economic uncertainties, which are larger at the regional level. Here we estimate country-level contributions to the SCC using recent climate model projections, empirical climate-driven economic damage estimations and socio-economic projections. Central specifications show high global SCC values (median, US$417 per tonne of CO2 (tCO2); 66% confidence intervals, US$177–805 per tCO2) and a country-level SCC that is unequally distributed. However, the relative ranking of countries is robust to different specifications: countries that incur large fractions of the global cost consistently include India, China, Saudi Arabia and the United States. Global estimates of the economic impacts of CO2 emissions may obscure regional heterogeneities. A modular framework for estimating the country-level social cost of carbon shows consistently unequal country-level costs.

T he social cost of carbon (SCC) represents the economic cost associated with climate damage (or benefit) that results from the emission of an additional tonne of carbon dioxide (tCO 2 ). One way to compute it is by taking the net present value of the difference between climate change damages along with a baseline climate change pathway and the same pathway with an additional incremental pulse release of CO 2 . The SCC provides an economic valuation of the marginal impacts of climate change. It has been estimated hundreds of times in the past three decades 1 using a range of assumptions about uncertain parameters (such as social discount rate, economic growth and climate sensitivity). Recent estimates [2][3][4][5][6][7] of SCC range from approximately US$10 per tCO 2 to as much as US$1,000 per tCO 2 . A recent report issued by the US National Academies highlighted the many challenges and opportunities associated with improving estimates of SCC 8 .
Among the state-of-the-art contemporary estimates of the SCC are those calculated by the US Environmental Protection Agency. The latest figures equal to US$12, US$42 and US$62 per tCO 2 emitted in 2020 for 5, 3 and 2.5% discount rates, respectively 2 . These estimates are used, among other purposes, to inform US environmental rule-making. Various alternative approaches to estimate the SCC have been employed over the years, and include more sophisticated treatments of time, risk and equity preferences [9][10][11][12][13][14] , as well as those that incorporate more recent representations of climate damage and feedback [15][16][17][18] . A recent expert elicitation of climate scientists and economists 3 found a mean SCC of approximately US$150-200 per tCO 2 .
The global SCC (GSCC) captures the externality of CO 2 emissions, and is thus the right value to use from a global welfare perspective. Nonetheless, country-level contributions to the SCC are important for various reasons. Mapping domestic impacts can allow us to quantify non-cooperative behaviour, and thus better understand the determinants of international cooperation. The governance of climate agreements 19,20 is a key issue for climate change. The nationally determined architecture of the Paris climate agreement-and its vulnerability to changing national interestsis one important example. Country-level estimates can also allow us to better understand regional impacts, which are important for adaptation and compensation measures. Finally, a higher spatial resolution estimation of climate damage and benefits can impact estimates of net global climate damage 21,22 and its sensitivity to climate and socio-economic drivers.
Existing studies agree on the significant gap between domestic and global values of the SCC, but provide limited agreement on the distribution of the SCC by region 23 . Due to limitations on the availability of country-level climate and economic inputs, no previous analysis has partitioned GSCC into country-level contributions from each individual nation. In this article, we draw upon recent developments in physical and economic climate science to estimate country-level SCC (CSCC) and aggregate SCC and quantify the associated uncertainties. The CSCC captures the amount of marginal damage (or, if negative, the benefit) expected to occur in an individual country as a consequence of additional CO 2 emission. Although marginal impacts do not capture all the information relevant to climate decision-making, the distribution of the CSCC provides useful insights into distributional impacts of climate change and national strategic incentives.

A modular framework
Following the recommendations of the recent report by the US National Academies, we executed our calculations of the social cost of carbon through a process with four distinct components 8 : a socio-economic module wherein the future evolution of the economy, which includes the projected emissions of CO 2 , is characterized without the impact of climate change; a climate module wherein the earth system responds to emissions of CO 2 and other anthropogenic forcings; a damages module, wherein the economy's response to changes in the Earth system are quantified; and a discounting module, wherein a time series of future damages is compressed into a single present value. In our analysis, we explored uncertainties associated with each module at the global and country level. We focused only on climate impacts, and did not carry out a fully fledged cost-benefit analysis, which would require modelling mitigation costs.
We developed a method to calculate SCC that is oriented towards partitioning and quantifying uncertainties. Although it follows the same module structure as the integrated assessment models that are conventionally used to calculate SCC, rather than build reduced-form models of the climate or economy, we used country-level climate projections taken directly from gridded ensemble climate model simulation data as well as country-level economic damage relationships taken directly from empirical macroeconomic analyses. As climate and economic quantities are empirical in this analysis, these uncertainties are probabilistic in our output. Socio-economic and discounting uncertainties are assessed parametrically using five socio-economic scenarios and twelve discounting schemes.
Socio-economic module. For the socio-economic projections, we used the shared socio-economic pathway scenarios (SSPs) 24 . The SSPs provide five different storylines of the future (Supplementary Table 1). We used the GDP and population assumptions of the SSPs as well as subsequent work to estimate the emissions associated with each SSP without the climate mitigation policies 25 .
Climate module. We matched emission profiles of the SSPs to those of the representative concentration pathways (RCPs) 26 modelled in the Fifth Coupled Model Intercomparison Project (CMIP5) 27 to estimate baseline warming (Methods).To estimate the response of the climate system to a pulse release of CO 2 , we combined results from CMIP5 and a carbon cycle model intercomparison project 28 (Supplementary Tables 2 and 3). Carbon cycle uncertainty is represented by using the global-scale decay of atmospheric CO 2 after a pulse release of CO 2 into the present-day atmosphere. The climate system response uncertainty is calculated at the populationweighted country level using gridded output from the CMIP5 abrupt4× CO 2 experiment in which atmospheric CO 2 is instantaneously quadrupled from the preindustrial level. By convoluting the results from these experiments (as in Ricke and Caldeira 29 , but at the population-weighted country-mean level), we derived a range of country-specific transient warming responses to an incremental emission of CO 2 . To test the sensitivity of our results to the uncertain feedbacks between economic growth and emissions, we performed the calculations for RCPs 4.5, 6.0 and 8.5 for all the SSPs.
Damages module. We converted country-level temperature and precipitation changes into country-level damages using empirical macroeconomic relationships derived by Burke et al. 30 and Dell et al. 31 . Their econometric approaches exploit interannual climate variability in historical observations to estimate the impact of climate on economic growth. Estimating the economic damages associated with a given level of warming is a notoriously challenging problem for which there is no perfect state-of-the-art solution 8,32 . Gross domestic product (GDP) is an informative, but highly imperfect measure of welfare 33 . Among its advantages, an empirical macroeconomic approach captures the interactions and feedbacks among sectors of the economy, captures the effects of climate on the economy that have been neglected or are difficult to partition and quantify, has a higher geographical resolution (country level) than existing alternatives, is empirically validated and has confidence intervals that allow uncertainty analysis, and is completely transparent and replicable. As results are sensitive to the econometric specifications, for example, whether lags are included to capture long-run effects, and countries are distinguished between rich and poor to account for different capabilities to adapt 30 , we compared all the existing empirical specifications (Methods and Supplementary Information).
Discounting module. We applied these damage functions to our country-level temperature pulse response, SSP and RCP projections, including associated climate and damage function uncertainty bounds (Methods and Supplementary Fig. 1) and then compressed the time series of output into country-level contributions to the SCC (CSCCs) using discounting. Discounting assumptions are consistently one of the biggest determinants of differences between estimations of the SCC 10,34 . Although intuitive, the use of a fixed discounting rate is not appropriate, particularly when applied universally to countries with highly disparate growth rates and with significant economic losses due to climate change. We thus used growth-adjusted discounting determined by the Ramsey endogenous rule 35 , with a range of values for the elasticity of marginal utility (μ) and the pure rate of time preference (ρ), but we also report fixed discounting results to demonstrate the sensitivity of SCC calculations to discounting methods.

global results
The GSCC is the sum of the CSCC values. We calculated CSCC for each set of scenario, parameter and model specification assumptions, and established an uncertainty range based on a bootstrap resampling method (Methods and Supplementary Information) and then aggregated to the global level. The median estimates of the GSCC (Fig. 1) are significantly higher than the Inter-agency Working Group estimates, primarily due to the higher damages associated with the empirical macroeconomic production function 30 , although similar SCC values have been estimated in the past using other methodologies 11,18 . Under the 'middle-of-theroad' socio-economic scenario (SSP2) and its closest corresponding climate scenario (RCP6.0), and with the central specification of Burke-Hsiang-Miguel (BHM) damage function (short run, no income differentiation) we estimated a median GSCC of US$417 per tCO 2 (ρ, 2%; μ, 1.5).
The choice of both socio-economic and climate scenario has an impact on the estimated GSCC ( Fig. 1 and Supplementary Fig. 2). For a given RCP, scenarios with strong economic growth and reduced cross-country inequalities (SSP1 and SSP5) have a smaller GSCC than do scenarios with low productivity and persistent or even increasing global inequality (SSP3 and SSP4). For a given SSP, higher emission scenarios lead to a higher GSCC. When fixed time discounting is used ( Supplementary Fig. 2), the results are significantly different. In particular, the GSCC values are lower across the scenarios, and the ranking to SSPs and RCPs is often reversed. This highlights the importance of using the appropriate endogenous discounting rules to capture the feedback of climate on the economy. Figure 1 also shows the sensitivity to the impact function specification. Under most socio-economic scenarios, the GSCC is significantly higher and more uncertain when calculated with a long-run (lagged) damage model specification (BHM-LR). This somewhat counterintuitive result indicates that whether climate's primary impact on the economy is through growth or level effects, the negative cumulative effect of climate change on long-term growth is substantial and robust. The GSCC tends to be similar in both pooled and rich/poor specifications of the damages model, with the exception of SSP3, in which the estimated GSCC is much higher in the rich/poor specifications. The DJO specification of the economic impact function 31 yields significantly higher GSCC values.
The confidence intervals (CIs, 66%) illustrated in Fig. 1 emphasize the large degree of empirical uncertainty that surrounds SCC estimates, even if scenario and structural uncertainties are disregarded. These stem from both the uncertainties of the climate system response to CO 2 (climate sensitivity) and uncertainties in the economic harm expected from climate change (damage function). The latter are especially significant for the long-run specifications, which, by construction, have larger confidence intervals.

Country-level results
These global estimates conceal substantial heterogeneity in CSCCs. Figure 2a shows the spatial distribution of CSCCs under a reference scenario (SSP2-RCP6, standard BHM specification). All the fixed discounting, alternative scenario, parameterization and specification results are available as part of the database included in the Supplementary Information.
India's CSCC is the highest (US$86 per tCO 2 (49-157); 21% of the GSCC (20-30%); CIs are given in parentheses), followed by the United States (US$48 per tCO 2 (1-118); 11% of the GSCC (0-15%)) and Saudi Arabia (US$47 per tCO 2 (27-86); 11% of the GSCC (11-16%) of the GSCC). Three countries follow at above US$20 per tCO 2 : Brazil (US$24 (14-41) per tCO 2 ), China (US$24 (4-50) per tCO 2 ) and the United Arab Emirates (US$24 (14-48) per tCO 2 ). Northern Europe, Canada and the Former Soviet Union have negative CSCC values because their current temperatures are below the economic optimum. These results are among the most sensitive in the analysis, as under the BHM long-run and DJO damage model specifications all countries have positive CSCC. Under the reference case and other short-run model specifications, about 90% of the world population has a positive CSCC. Although the magnitude of CSCC varies considerably depending on the scenario and discount rate, the relative distribution is generally robust to these uncertainties. Damage function uncertainty is a larger contributor to the overall uncertainty, but at the country level, either climate or damages uncertainty may be larger. The alternative economic damage functions confirm the broad heterogeneity of CSCCs and relative country ranking ( Fig. 2b and Supplementary Fig. 5).
Consistent with past work on the geography of climate damages 5,30,36 , we found that the international distribution of SCC is inequitable (Lorenz curves in Fig. 3). The magnitude of the inequality is sensitive to the model specification of the economic impact function. As discussed above and in the Supplementary Discussion, there is an unsettled debate as to whether empirical evidence points toward the influence of climate on the economy operating primarily via growth or level effects, something that has been analysed without definitive conclusion in BHM and follow-up work 37 . Our results indicate that this uncertainty is consequential from a strategic perspective (that is, in determining the relative gains and losses to particular countries). In particular, with long-run and Dell-Jones-Olken (DJO) specifications, all countries have a positive CSCC. This results in higher (almost twice as much) global values of the SCC (as already observed in Fig. 1) and lower inequality with respect to the short-term specification. The distinction between income groups in the impact function (rich and poor countries) has smaller impacts, reducing GSCC and either leaving inequality unchanged (for the short-term specification) or lowering it (for the long-term specification). Figure 3b summarizes the inequality of the CSCC across all scenarios through Gini coefficients 38,39 , a synthetic measure of global heterogeneity. Under the short-run pooled BHM impact function (BHM-SR) specification, Gini values are slightly higher for SSP1 and SSP5, and significantly lower for SSP3, which is also the socioeconomic scenario with the highest GSCC value. Damage model specification is the most important uncertainty factor to future outcomes, as under long-run economic impact models, inequality (Gini value) is considerably lower (where GSCCs are higher), whereas the rich/poor distinction plays a smaller role. The discounting method also plays an important role-fixed discounting leads to significantly lower inequality (Gini coefficients) in the distribution of CSCC for most specifications. Figure 4 highlights a mapping of the winners and losers from climate change among the G20 nations. Although the magnitude of the CSCC is subject to considerable uncertainty, the shares of the GSCC allocated among world powers remains relatively stable  in all short-run impact model specifications. Russia dominates all the other nations in gains from emissions, whereas India is consistently dominated by all the other large economies with large losses. Other developing economies, such as Indonesia and Brazil, will accrue a significantly greater share of the GSCC than their current share of global emissions. The world's biggest emitters (China and the United States) both stand to accrue a smaller share of the GSCC than their share of emissions, but are consistently dominated by the European Union, Canada, South Korea and-in the case of the United States-Japan.
The relative ranking of the SCC is highly consistent among most of the 276 scenario-impact-discounting uncertainty cases with the notable exception of the change in relative positions of major world powers that occurs under the long-run impact model specifications . Countries like Russia, Canada, Germany and France that have negative CSCC under the reference case switch to having among the highest positive CSCCs ( Supplementary  Fig. 9). After the short-and long-run differences, the largest shifts in country order relative to our reference case occur under the highemissions SSP5 scenario and in the transition between growthadjusted and fixed discounting (Supplementary Fig. 8).

Discussion
The discord between country-level shares in CO 2 emissions and country-level shares in the SCC illustrates an important reason why significant challenges persist in reaching a common climate agreement. If countries were to price their own carbon emissions at their own CSCC, approximately 5%, a small amount, of the global climate externality would be internalized. At the same time, our results consistently show that the three highest-emitting countries (China, the United States and India) also have the among the highest countrylevel economic impacts from a CO 2 emission. These high-emitter CSCCs are on a par with carbon prices foreseen by detailed process integrated assessment models for climate stabilization scenarios ( Supplementary Fig. 10). That is, internalizing the domestic SCC in some major emitters could result in emissions pathways for those countries that are consistent with the 1.5-2 °C temperature pathways. Fully internalizing the CO 2 externality (that is, pricing carbon at the GSCC) would allow the Paris Agreement goal to be met, and beyond. Empirical macroeconomic damage functions have advantages and disadvantages compared to the approaches typically used to estimate the SCC in the past. The strengths include transparency, a strong empirical basis and the capacity to account for interactions among all the sectors of the economy as well as for impacts that are difficult to isolate and quantify. However, a number of long-term effects of climate change are not captured by this type of relationship. We present a number of these excluded contributors in Supplementary Table 5, along with an indication of the likely sign of impacts on the CSCCs and the GSCC. For example, adjustment costs associated with adaptation are not accounted for in this model. Such costs could be high or, given that climate change is not a surprise, could be modest compared to the type of effects that are represented (and which are demonstrably large). Already in our analysis, impacts from climate change are large enough in some countries to lead to negative discount rates ( Supplementary  Fig. 11). Most of these additional contributors would be expected to increase the GSCC.
Globalization and the many avenues by which the fortunes of countries are linked mean that a high CSCC in one place may result in costs as the global climate changes even in places where the CSCC is nominally negative. For many countries, the effects of climate change may be felt more greatly through transboundary effects, such as trade disruptions 40 , large-scale migration 41 or liability exposure 42 than through local climate damage. Although the CSCC in 2020 is negative for many rich northern countries, if the non-linear climate damages hold over time, the CSCC will become positive in most countries as the planet continues to warm. Furthermore, reducing greenhouse gas emissions can yield positive synergies on other environmental goals, such as improving air quality, which already have large welfare impacts 43 . These considerations suggest that country-level interests may be more closely aligned to global interests than indicated by contemporary country-level contributions to the SCC. Furthermore, climate decision-making does not occur in a vacuum. Some countries, such as northern Europe and Canada, are leaders on climate policy despite potentially negative SCCs, whereas other countries with the highest CSCCs, like the United States and India, lag behind. Clearly, a host of other strategic and ethical considerations factor into the international relations of climate change mitigation.
In the recent US National Academy of Sciences report on SCC, the Working Group cites three essential characteristics for future SCC estimates: scientific basis, uncertainty characterization and transparency 8 . Our work includes improvements upon past estimates of SCC on all three counts. Past estimates of SCC were based on reduced form climate modules and damage function calibration with limited empirical support 44 , whereas ours uses output from an ensemble of state-of-the-art coupled climate model simulations and two independently generated empirical damage functions. Past estimates of the SCC have included limited uncertainty analysis focused mostly on a limited set of parameters such as the social discount rate, whereas our estimates include quantified uncertainty bounds for carbon cycle, climate, economic and demographic uncertainties, and also provide disaggregation to the national level. In addition, past estimates of the SCC were often generated using opaque models and/or proprietary software. We provide all of our source code and the full output of our analysis for complete transparency (Supplementary Data).
The high values and profound inequalities highlighted by the country-level estimates of the social costs of carbon provide a further warning of the perils of unilateral or fragmented climate action. We make no claim here regarding the utility of the CSCC in setting climate policies. CO 2 emissions are a global externality. Despite 'deep uncertainty' 45 about discounting, socio-economic pathways and appropriate models of coupling between climate and economy, by all accounts the estimates of the GSCC made by the Interagency Working Group on Social Cost of Greenhouse Gases 2 appear much too low. More research is needed to estimate the geographical diversity of climate change impacts and to help devise policies that align domestic interests to the global good. However, large uncertainties in the precise magnitudes of the SCC, both national and global, cannot overshadow the robust indication that some of the world's largest emitters also have the most to lose from their effects.