Estimating a social cost of carbon for global energy consumption

Estimates of global economic damage caused by carbon dioxide (CO2) emissions can inform climate policy1–3. The social cost of carbon (SCC) quantifies these damages by characterizing how additional CO2 emissions today impact future economic outcomes through altering the climate4–6. Previous estimates have suggested that large, warming-driven increases in energy expenditures could dominate the SCC7,8, but they rely on models9–11 that are spatially coarse and not tightly linked to data2,3,6,7,12,13. Here we show that the release of one ton of CO2 today is projected to reduce total future energy expenditures, with most estimates valued between −US$3 and −US$1, depending on discount rates. Our results are based on an architecture that integrates global data, econometrics and climate science to estimate local damages worldwide. Notably, we project that emerging economies in the tropics will dramatically increase electricity consumption owing to warming, which requires critical infrastructure planning. However, heating reductions in colder countries offset this increase globally. We estimate that 2099 annual global electricity consumption increases by about 4.5 exajoules (7 per cent of current global consumption) per one-degree-Celsius increase in global mean surface temperature (GMST), whereas direct consumption of other fuels declines by about 11.3 exajoules (7 per cent of current global consumption) per one-degree-Celsius increase in GMST. Our finding of net savings contradicts previous research7,8, because global data indicate that many populations will remain too poor for most of the twenty-first century to substantially increase energy consumption in response to warming. Importantly, damage estimates would differ if poorer populations were given greater weight14. Using global data, econometrics and climate science to estimate the damages induced by the emission of one ton of carbon dioxide, climate change is projected to increase electricity spending but reduce overall end-use energy expenditure.

Quantifying the benefits of greenhouse gas mitigation is a topic of considerable importance to researchers and policymakers alike. The 'social cost of carbon' (SCC)-defined as the dollar value of climate change damages imposed globally by an additional (that is, 'marginal') ton of carbon dioxide (CO 2 ) emissions (or its equivalent)-provides a means to determine the global social benefits of mitigation policies 6 . So far, our understanding of the SCC has been informed by theoretical-numerical integrated assessment models (IAMs) [9][10][11] . These pioneering models have produced numerous valuable insights and guided research and policy for decades 1,5 . For instance, SCC estimates derived from these models have been used by the US federal government to assess over 80 policies so far, with a combined value of US$1 trillion in estimated benefits 15 . Yet as research has progressed with advances in data and computing, new challenges and opportunities have emerged 3,13 .
Recent assessments 2,3,6,7 have raised concerns that the category of current IAMs used to perform aggregate benefit-cost analyses related to climate change 16 are not tightly constrained by data. They also do not utilize the best-available Earth-system models, do not capture many known linkages between climate change and society, and only resolve damages at the geographic scale of large regions (for example, continents). We address these concerns by designing a fully modular 'bottom up' architecture, the Data-driven Spatial Climate Impact Model (DSCIM) 17 , to develop 'partial' SCC estimates for individual subsectors of the global economy (for example, agriculture, health and labour), using representative data and detailed climate models 7,[18][19][20][21][22][23][24][25] . Each global partial SCC is built up from econometrically derived, probabilistic, local damage estimates for thousands of geographic regions. In ongoing work, we are integrating these partial SCC estimates 17 to compute a total SCC, taking into account intersector linkages. Previously, 'top down' econometric results describing the gross domestic product (GDP) impacts of warming 26,27 have been translated into SCC values 28,29 ; however, to our knowledge, no existing IAM transparently assembles a bottom-up and globally representative SCC based on local econometric-based projections of damage 6 .

Climate-driven energy expenditures
Here we develop empirically derived estimates of the net change in global energy expenditures associated with an additional ton of CO 2 emissions, that is, a partial SCC for energy expenditure. IAM developers have themselves argued that the uncertainty over this number is the most important uncertainty to resolve in the total SCC 8 , in part because some models predict that increasing energy expenditures will be the single largest global cost from warming 16 . Previous econometric studies have measured the effect of local temperatures on local electricity consumption [30][31][32][33][34] , although they often omit non-electric energy consumption (for example, natural gas used for heating) because the data are difficult to obtain. Moreover, these studies generally focus on residential end uses in regions that are wealthy and thus not globally representative (for example, California). In contrast, an appealing feature of non-econometric studies using process-based models is that they simulate how climate change will affect all aspects of the production, conversion, delivery and use of energy [35][36][37][38] . However, similar to IAMs, their drawback is that they are not generally constrained by plausibly causal econometric estimates of consumption behaviour in response to warming. This analysis recovers globally representative measurements of total energy consumption in response to increasing temperatures, accounting for economic development and adaptive behaviour, and uses these results to compute a partial SCC for energy expenditure.
As there remains debate on how best to aggregate costs across populations over time 39,40 (that is, discounting), here we present results using multiple approaches and a range of parameter values 6 . When aggregating costs between different populations within a time period, we treat all individuals equally, consistent with guidance to US federal agencies 6 , although alternative approaches that upweight costs to poor populations have been proposed 14 .

Computing a social cost of carbon
Our modular approach to computing partial SCC values using DSCIM has five steps, each of which can be implemented for each sector of the global economy. Here we apply these steps to compute the energy expenditure component of the SCC.
First, we match globally representative, longitudinal data on energy consumption with 0.25° × 0.25° globally harmonized historical climate data 41 . This represents, to our knowledge, the most comprehensive global dataset compiled on energy consumption and temperature ('Data assembly' in Methods, Supplementary Section A). Energy consumption data are derived from International Energy Agency (IEA) data files 42 that describe electricity and direct fuel consumption across residential, commercial, industrial and agricultural end-uses (excluding transportation) in 146 countries during 1971-2010. To make these data usable for global analysis, we harmonize data across diverse reporting systems and use econometric methods that minimize the influence of errors in record keeping ('Data assembly' in Methods, Supplementary Section A.1).
Second, we econometrically estimate the effect of historical temperature distributions on national annual per-capita energy consumption using random year-to-year variation 24 , and measure how this energytemperature response differs across energy types (electricity and other fuels), income levels and climate zones 17 . This allows us to observe the effects of adaptive behaviours that populations undertake as they become richer 31 and/or are exposed to warmer climates 34 (for example, the adoption of air conditioning). Our approach accounts for all permanent differences between countries in energy consumption (for example, due to geography or history) and all common trends in energy consumption (for example, due to macroeconomic fluctuations, price changes or technological innovations) to identify a plausibly causal effect 30 of temperature distributions on energy consumption. We then use the variation in income level and climate zone to predict how the energy-temperature relationship may change in association with these two factors ('Econometric estimation of energy-temperature responses' in Methods, Supplementary Section B).
Third, we project impacts of climate change in 24,378 globally comprehensive geographic regions (roughly the size of US counties; Extended Data Fig. 1) to 2099 (the final-year high-resolution climate simulations are available) by combining the econometric results above with a probabilistic ensemble of downscaled climate projections (Extended Data Fig. 2) 43 based on Coupled Model Intercomparison Project phase 5 (CMIP5) models 19 . When projecting these impacts, we account for how the energy-temperature response will evolve as populations become richer and exposed to warmer climates ('Projecting the impacts of climate change' in Methods). Standard socioeconomic scenarios 22 forecast that over 90% of the end-of-century population will still remain within the range of historical temperatures and incomes that we currently observe around the world (Extended Data Fig. 3). In isolating the impact of future climate change on energy consumption, we hold constant the current energy supply mix, an assumption that should be relaxed in future work.
Fourth, we monetize and pool the empirically derived damage estimates from the previous step and fit global energy expenditure damage functions by aggregating impacts across locations and indexing them against the global mean surface temperature anomaly (ΔGMST) expressed in each climate model realization 18 . These functions describe the full distribution of global damage conditional on ΔGMST. We estimate damage functions up to 2100 that evolve over time to reflect expected changes in socioeconomics and adaptation, and extrapolate their continuing evolution forward to 2300 ('Estimating global energy damage functions' in Methods, Supplementary Section D) 17 .
Fifth, we adapt a probabilistic, simple climate-carbon cycle model 25 to project the distribution of annual ΔGMST up to 2300 that results from the release of an additional 1 GtC of CO 2 ('Calculating the partial SCC' in Methods, Supplementary Section E). Applying the distribution of the impulse responses of ΔGMST to the damage functions from the previous step generates a probability distribution for the stream of total global damages that result from the emission of a marginal ton of CO 2 today. This probability distribution accounts for uncertainty in our econometric estimates at all stages of the analysis as well as climatological uncertainty. Finally, the value of the flow of damage is discounted 6 to capture the partial SCC for global energy expenditure.

Energy consumption and temperature
The role of income Empirically, we find that a population's average income per capita is a key determinant of how its end-use energy consumption responds to temperature. Electricity-temperature responses (Fig. 1a) are U-shaped (that is, increasing with hot and cold temperatures), but only in the seventh decile or higher of the global income distribution (annual per-capita income ≥US$11,258, 2019 purchasing power parity (PPP)), whereas the other fuels-temperature response is L-shaped (that is, increasing with cold temperatures) in the third decile or higher (annual per-capita income ≥US$ 2,849, 2019 PPP). Above these thresholds, increasing incomes appear to amplify both responses, such that in the top decile, electricity consumption increases by 0.017 GJ per capita (4.6 kWh per capita, 66% of 2010 global average per-capita daily consumption) on a 35 °C day (relative to a 20 °C day) and by 0.0068 GJ per capita (1.9 kWh per capita, 27% of 2010 global average per-capita daily consumption) on a 0 °C day, on average, whereas direct consumption of other fuels increases by 0.034 GJ per capita (50% of 2010 global average Article per-capita daily consumption) on a 0 °C day. These differing responses probably reflect the use of electricity for cooling and heating, compared with the use of other fuels (for example, natural gas, oil and coal) for heating. Previous research has documented similarly U-shaped electricity-temperature responses in the top decile 30,32-34 (see Supplementary Section H for comparisons), but our data reveal that such responses do not generalize to other income levels nor do they capture the substantial other fuels-temperature response, which dominates on cold days (Fig. 1b). These findings represent an empirical demonstration of how economic development shapes energy-temperature responses on a global, macroeconomic scale. The differing income thresholds at which electricity and other fuels consumption start to respond to temperature are consistent with microeconomic evidence that air conditioning is widely adopted only at very high income levels 31,44 , whereas solid fuels are burned for heating even in lower-income settings 45,46 .

Adaptation to local long-run climate
Although income per capita is the dominant driver of the energytemperature response, long-run climate also has a smaller role in how populations adapt. For instance, higher air-conditioning adoption in hot locations may increase electricity use on hot days 31,34 . We empirically recover how income and long-run climate continuously and jointly shape the energy-temperature response (Methods, equation (3), Supplementary Section B.3), thereby accounting simultaneously for the effects of economic development and climate (Fig. 1c). We find evidence that populations adapt to their long-run climate in ways that change their energy consumption during hot and cold periods, conditional on their income level. For instance, on a 35 °C day, per-capita electricity consumption is 0.004 GJ (16% of 2010 global average per-capita daily consumption) greater in the hottest climate tercile relative to the coldest. Conversely, on a 0 °C day, per-capita consumption of electricity and other fuels are 0.0002 GJ (1% of 2010 global average per-capita daily consumption) and 0.027 GJ (40% of 2010 global average per-capita daily consumption) greater, respectively, in the coldest tercile relative to the hottest. These results are consistent with populations adopting more heating or cooling technologies when their climate is cooler or hotter, respectively.

Impacts of future climate change
Accounting for local adaptation globally Combining the measured relationships estimated using country-by-year energy consumption observations (Fig. 1c) with projections for how incomes and climate will change over the next century in each of 24,378 globally comprehensive geographic units, we project how the structure of energy-temperature responses will evolve ('Projecting the impacts of climate change' in Methods, Supplementary Section B.3). This spatial granularity contrasts with existing IAMs used to develop SCC estimates, which partitioned the world into at most 16 units 10 (Extended Data Fig. 1). Previous analysis 18 has demonstrated that accounting for this spatial granularity is crucial to capture the unequal impacts of climate change within countries. Applying the ensemble of downscaled climate models and surrogates ('Data assembly' in Methods, Supplementary Section A.2.2) to our evolving projections of local energy-temperature responses, we isolate the additional energy consumption in each region caused by changes in the temperature distribution, over and above any changes to consumption that would occur without climate change, such as those increases associated with economic development (Methods, equation (4)).

Impacts on energy consumption
In a high-emissions scenario (representative concentration pathway (RCP) 8.5), we project that by the end of the century, most of the world is expected to increase net annual per-capita electricity consumption and decrease consumption of other fuels due to climate change (Fig. 2a). The amplitude of these effects reflects differences in incomes and climates across locations. Hot and wealthy locations show large net increases in electricity consumption, although very cold locations show net declines where warming does not increase the number of hot days enough to offset the loss of cold days. Low-income regions, such as much of sub-Saharan Africa, do not increase electricity consumption as dramatically because they are projected to still have relatively low incomes at the end of the century (for example, see Ethiopia in Fig. 1a). Declines in the consumption of other fuels are projected throughout the world, consistent with the use of these fuels for heating across a wider range of incomes.
To understand the scale of these impacts, they can be compared with current levels of energy consumption (Fig. 2b). In many of today's rich countries, impacts at the end of the century are projected to be modest relative to current consumption, for example, a +2.7% relative increase in annual US electricity consumption. This small magnitude is due to high current consumption levels in conjunction with the fact that many rich countries are in temperate climates, where large projected increases and decreases in electricity consumption-from more hot and fewer cold days, respectively-offset one another. In contrast, in many of the poorest and/or most populous countries, the additional consumption imposed by climate change is projected to be substantial relative   22 . b, Overlay of fuel-specific responses for the richest decile on a common scale. c, Estimated energy-temperature relationship as simultaneously influenced by income and local long-run climate (Methods, equation (3)). Each cell within a matrix illustrates a predicted energytemperature relationship for a level of income and long-run climate. The rows separate income terciles (increasing income from bottom to top) and the columns separate climate terciles based on annual cooling degree days (increasingly warm climate from left to right; 'Econometric estimation of energy-temperature responses' in Methods, Supplementary Section B.3).
to current consumption, for example, a +2,000% relative increase in annual Nigerian electricity consumption. This is due both to uniformly hot temperatures and very low levels of current energy use.
Aggregating energy impacts globally, we project that in a high-emissions scenario, annual electricity consumption will increase due to climate change by 1.21 GJ per capita (90% confidence interval (CI) = [0.54, 2.43], P < 0.001) in 2099 (RCP 8.5), whereas consumption of other fuels will decline by 2.94 GJ per capita ([1.02, 6.15], P < 0.01) (Fig. 2c). Estimates in a moderate emissions scenario (RCP 4.5) are 0.44 GJ per capita and 1.16 GJ per capita, respectively. (Electricity impacts do not include the primary energy lost in conversion to electricity.) It is notable that ignoring the effects of income growth and climate adaptation on the energy-temperature response would have resulted in dramatic underestimation of projected changes to global energy consumption due to warming (green lines in Fig. 2c, Supplementary Section D).

Impacts on total energy expenditures
We monetize the climate change-induced changes in total energy consumption (electricity and other fuels combined) to develop a measure of the economic damages from climate change, that is, all economic resources that would be available for other purposes in the absence of warming. In a baseline scenario of future real energy price growth of 1.4% per year (the historical growth rate of US energy prices), we project that end-of-century warming will cause net energy expenditure declines in much of the world, although there are net increases in many tropical and subtropical middle-income regions, such as portions of India, China, Indonesia and Mexico (Fig. 3a). This pattern occurs because currently low-income countries will probably be rich enough by the end of the century to consume other fuels on cold days but not rich enough to consume electricity on hot days; thus, they experience savings from warming because it reduces other fuel costs (for example, Ethiopia in Fig. 1a). Hot middle-income countries will be rich enough to spend on electricity for cooling in the future, so in some regions, the additional spending on electricity during hot days outweighs the savings on cold days (for example, India in Fig. 1a). The largest overall savings are projected to occur among today's richest countries; however, net savings are projected across most of the present-day income distribution (Extended Data Fig. 4).
Aggregating costs globally, we project modest net savings at the end of the century due to climate change, amounting to 0.17% ([−0.1%, 0.53%], P < 0.3) and 0.08% ([−0.03%, 0.21%], P < 0.25) of 2099 world GDP in RCP 8.5 and RCP 4.5, respectively (Fig. 3b). The magnitude of net global savings is similar across alternative pricing scenarios (Extended Data Fig. 5, Supplementary Section C). This result differs qualitatively from the increased energy spending reported in previous studies 16,18,30,[32][33][34] that focused on electricity consumption in wealthy regions. As low-income and middle-income populations spend little on electricity to cool and other fuels are consumed everywhere almost exclusively for heating, projections that use only electricity-temperature responses from high-income populations will overestimate new cooling expenditures and underestimate savings from reduced heating, leading to systematic overestimation of the total energy damages from climate change.

Future damages from CO 2 emissions today
Damage functions describe the relationship between ΔGMST and global aggregate costs in a sector or the economy as a whole-they are at the centre of all IAMs used to develop SCC estimates 4,[9][10][11] , informing mitigation policy implications by summarizing the costs of additional warming. We construct empirically based global damage functions for energy consumption using the method in refs. 17,18 , organizing global aggregate costs into functions of realized ΔGMST across 33,000 simulations (Fig. 3c). These damage functions evolve over time, thereby capturing the influence of changing demographics, increasing incomes and warming local climates ('Estimating global energy damage functions' in Methods). Damages are slightly quadratic in ΔGMST, although essentially linear, with an additional +1 °C ΔGMST warming at the end of the century

Article
As CO 2 is long lived in the atmosphere, the US National Academy of Sciences recommends computing SCC values that capture damages to the year 2300 6 . To do this, we combine our empirically derived damage functions with the Finite Amplitude Impulse Response (FAIR) climate model 25 to project to 2300 the distribution of ΔGMST responses to the emission of a marginal 1 GtC of CO 2 (Supplementary Section E) (The high-resolution CMIP5 model runs used above to project spatially granular impacts end in 2100.) A CO 2 pulse emitted today perturbs the future trajectory of atmospheric CO 2 concentrations nonlinearly, affected by the half-life of CO 2 in the atmosphere as it is stored and released in the oceans and biosphere (Fig. 4a, b). This results in future ΔGMST that deviates from the baseline scenario, which in turn causes a stream of energy damages in future years (Fig. 4c, d). The partial SCC from energy expenditure is the net present value (NPV) of these annual damages. As there are multiple views on how best to discount future damages into an NPV (see refs. 39,40 ), we present multiple estimates using both constant discount rates and rates that evolve with economic growth 6 ('Ramsey' discounting 47 ; 'Calculating the partial SCC' in Methods).
We find that 1 t of CO 2 emitted today generates a total energy expenditure burden valued at −US$13.93 to −US$0.69 in NPV under the high-emissions RCP 8.5 scenario and −US$4.16 to −US$0.76 under the moderate-emissions RCP 4.5 scenario (central estimates, 1.4% price growth scenario, Fig. 4e), with most estimates between −US$3 and −US$1. Our finding that the partial SCC from energy expenditure is negative and small in magnitude is broadly robust across multiple pricing scenarios (Fig. 4e, Extended Data Tables 1, 2).

Discussion
Our estimates make use of globally comprehensive data and empirical relationships to compute a global partial SCC for energy expenditure. This approach reveals the critical role of economic development in shaping how energy consumption patterns respond to climate change, as we find that much of the world will remain too poor in the coming decades to spend substantially on energy-intensive cooling technologies. Our approach also demonstrates the importance of accounting for non-electricity energy consumption as global populations use other fuels to cope with cold temperatures even at low income levels. Together, these two factors explain why our analysis indicates that total global energy expenditures are not likely to increase dramatically in response to warming, and why marginal emissions today may in fact produce savings in global energy expenditures.
The modest magnitude of the aggregate global impacts, however, masks substantial important shifts in projected energy consumption. Most notably, projected impacts of warming in many of today's emerging economies may impose substantial costs and represent a large fraction of current consumption. For instance, we project that climate change will increase end-of-century electricity consumption in India by over 100% of its current consumption (Fig. 2b). Future work should  0 1 2 3 4 5 6 7 8 9 10  0 1 2 3 4 5 6 7 8 9 10  0 1 2 3 4 5 6 7 8 9 10  0 1 2 3 4 5 6 7 8 9 10   5  explore alternative approaches to valuing global damages across space and time when costs are distributed unequally, as we find 14 .
Our approach is designed to isolate the effect of future climate change on energy consumption under given emissions and socioeconomic pathways. However, a natural area for future exploration is to account for feedback effects that climate change and climate policy may introduce via changes in the energy supply mix, the trajectory of global CO 2 and local air pollutant emissions, and technological innovation 48,49 . Although future work should explore the potential for these factors to alter the partial SCC for energy consumption, we believe at least the CO 2 emissions feedbacks are probably immaterial, given the small size of our aggregate estimated impacts (Extended Data Table 3).
Another extension to this analysis would be to account for additional types of future technological advancement that may affect the energy consumption response to climate change (for example, changes in the relative cost of cooling technologies). As we allow energy-temperature responses to evolve with increasing incomes and temperatures in our projection, our estimates reflect historical trends in advancement and diffusion of technology that occur with changes in these two factors. Theoretically, larger values of the partial SCC for energy consumption can arise if the price of cooling technology falls indefinitely relative to other goods and services without a corresponding trend in efficiency. However, these assumptions are unlikely to hold and we do not observe evidence of such a trend historically. The difficulty of predicting the direction and magnitude of unprecedented technological innovation under climate change underscores the critical need for further research in this area.
The results of our analysis contrast with estimates derived from alternative approaches. For example, the numerical-theoretical Climate Framework for Uncertainty, Negotiation and Distribution (FUND) IAM 10 -the only modelling framework where direct comparison is possible-estimates a partial SCC for energy expenditure 16 of US$10 per ton of CO 2 , which constitutes 90% of that model's total SCC estimate (high-emissions scenario, 3% discount rate) and is considered uncertain by its developers 8 . Our findings using DSCIM differ from this estimate, in part, because FUND projects very large increases in energy expenditures due to warming across many middle-income and low-income regions, such as China, North Africa, Southeast Asia and sub-Saharan Africa; in contrast, we project small or negative changes in these regions (Supplementary Section I). This divergence can be explained by the data used to inform these projections. In FUND, these regional projections are driven by parameters (for example, the income elasticity of cooling and heating energy demand) that are calibrated using data from a single high-income country (the United Kingdom) 10 , which we found shows energy consumption behaviour that is fundamentally different from these regions (Fig. 1a). Our findings thus underscore the importance of employing a representative empirical approach when estimating global impacts of climate change.
We demonstrate the feasibility of combining global data, econometrics, detailed climate models and modern computing within DSCIM to estimate a partial SCC for energy expenditure. Although implementing such an approach substantially reduces the energy expenditure partial SCC relative to previous estimates, this does not necessarily hold for all sectors of the economy. Although focusing on data from only wealthy locations can lead to large estimates of certain climate change damages (for example, energy expenditures), a similarly limited data focus has been shown to severely underestimate damages in other areas (for example, human health 17 ). A total SCC, composed of many partial SCCs for different sectors of the economy, would be required to determine the full social cost of warming to global society. Our approach can be extended to the full range of outcomes potentially affected by climate (for example mortality 17 , agriculture and labour), thereby providing an empirically based characterization of the total SCC.

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Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-021-03883-8.

Methods
Here we provide an overview of the data and methods used to complete each of the five stages of analysis that compose DSCIM, our modular approach to constructing a partial SCC. Details on each stage can be found in Supplementary Information.

Data assembly
In the first step, we compile a comprehensive dataset on historical energy consumption, climate and income, as well as future projections of climate, income, populations and energy prices (Supplementary Section A). Historical data are used to econometrically estimate the energy-temperature response, and how it differs by energy type (electricity and other fuels), income and climate. Future projection data are used to generate high-resolution projected impacts of climate change, accounting for the effects of income growth and warming on the shape of the energy-temperature response.
Historical datasets. Annual data on final consumption of electricity and other fuels for 146 countries from 1971 to 2010 were obtained from the IEA's World Energy Balances dataset 42 . We take electricity consumption directly from the dataset, whereas other fuels consumption is constructed by aggregating over coal, peat, oil shale and oil sands, oil products, natural gas, solar, wind, goethermal, biofuels and waste, heat, and heat production from non-specified combustible fuels. For both electricity and other fuels, we aggregate over the industrial, commercial/public services, residential, agricultural, forestry, fishing and non-specified sectors. Data inconsistencies and quality issues in the IEA's records are extensively documented 42 . We classify every such change in record-keeping methodology and employ specific data preparation and econometric techniques to address each individually (Supplementary Section A.1). Historical data on daily average temperature and precipitation, as well as historical climatologies, are obtained from the Global Meteorological Forcing Dataset, v1 (GMFD) 41 , a global gridded (0.25° × 0.25°) daily climate record available from 1948 to 2010 20 . We link high-resolution daily climate data to country-level annual energy consumption data using a procedure detailed in Supplementary Section A.2.4 that preserves nonlinearity in the energy consumption response to daily temperature.
We obtain historical values of country-level annual income per capita (constant dollar PPP) from within the IEA's World Energy Balances dataset, which in turn sources these data from the World Bank.
Datasets of future projections. We use a set of 21 high-resolution (0.25° × 0.25°) bias-corrected global climate projections that provide daily temperature and precipitation to the year 2099 from the NASA Earth Exchange (NEX) Global Daily Downscaled Projections (GDDP) dataset 51 . We obtain climate projections based on two standardized emissions scenarios: RCP 4.5 (an emissions stabilization scenario) and RCP 8.5 (a scenario with intensive growth in fossil fuel emissions) [52][53][54] . As this set of 21 climate models systematically underestimates tail risks of future climate change 43,55 , we assign probabilistic weights to climate projections and use 12 surrogate models that describe local climate outcomes in the tails of the climate-sensitivity distribution 43 . The 21 models and 12 surrogate models are treated identically in our calculations and are referred to as the surrogate/model mixed ensemble (SMME). We utilize the probabilistic weights when calculating and reporting summary statistics of impact estimates across the 33 models and surrogates (Extended Data Fig. 2, Supplementary Section B.5). Full details on the SMME climate projections are in Supplementary Section A.2.3. The gridded output from these projections is aggregated to 24,378 globally comprehensive agglomerated political units that we call impact regions using the same method applied to historical climate data (Supplementary Section A.2.4). Impact regions are constructed to (1) respect national borders, (2) be roughly equal in population across regions and (3) have approximately homogenous within-region climatic conditions (Extended Data Fig. 1).
Projections of national populations and income per capita are derived from the shared socioeconomic pathways (SSPs) 56 , a set of scenarios of socioeconomic development over the twenty-first century in the absence of climate impacts. We utilize population 57 and country-level GDP 58,59 projections for scenarios SSP1, SSP2, SSP3, SSP4 and SSP5 60 . These projections have been used as inputs to IAM-based projections of other social and economic outcomes, such as land-cover changes or air pollution, through the SSP research programme 56 , although we do not utilize these outputs in our main calculations. However, we do examine the sensitivity of our results to assuming alternative energy price projections that are output from these IAM exercises. National population projections are respectively allocated to 24,378 impact regions based on current satellite-based within-country population distributions 61 (Supplementary Section A.3.3) or an alternative, time-varying scenario of within-country population distributions that reflects projected urbanization 62,63 (Supplementary Section G.1).
The price trajectories we use to monetize estimated impacts of climate change are constructed based on either of two distinct data sources-present-day statistics from the IEA are used for our main estimates and price projections from IAMs are used in the sensitivity tests. We obtain present-day average electricity generation costs by region of the world from the IEA's World Energy Outlook 2017 (Figure 6.25); prices for other fuels are obtained from the IEA's Energy Prices and Taxes Statistics dataset. Price projections of electricity and other fuels' prices from five IAMs were obtained from the International Institute for Applied Systems Analysis (IIASA) Scenario Explorer database 64 . Price projections from IAMs are used only to examine the sensitivity of our results to alternative pricing assumptions; however, we note that they are derived using models that express market equilibria different from the projected changes in energy consumption that we estimate here. Details on how prices are assigned across countries and over time can be found in Supplementary Section C.

Econometric estimation of energy-temperature responses
In the second step, we use historical data on national annual per-capita energy consumption, climate and income to flexibly model electricity and other fuels consumption each as a function of daily average temperatures within a year, while accounting for heterogeneity in energytemperature responses along the dimensions of both income and long-run climate. Importantly, our econometric procedure is designed to recover nonlinear changes in local per-capita energy consumption at the grid-cell-by-day level, in response to locally experienced daily temperatures and these other factors. Accounting for such local nonlinearity is crucial in this context, as different locations within a country on the same day, or the same location on different days within a year, may show very different temperatures, which generate divergent energy consumption responses.
We apply methods from previous research that has demonstrated that the local effect of climate variables on many outcomes (including energy consumption) may be nonlinear in important ways 65 . These outcome variables are sometimes measured at the same temporal and spatial resolution as that at which these nonlinear effects manifest (for example, refs. 66,67 ). However, in most contexts, nonlinear effects emerge over timescales and spatial scales (for example, for individual grid cells on single days) that are much finer than the scale at which outcome data are available 24,30,68 (for example, for entire countries over a year). Yet, despite only observing spatially and temporally aggregated outcomes (that is, annual national per-capita energy consumption), it is possible to empirically recover the nonlinear relationships that take place at the spatial and temporal scale at which the climate variables are recorded (that is, the effect of daily grid-cell temperature on daily grid-cell per-capita energy consumption), provided that the climate variables are themselves aggregated in a way that preserves nonlinearities 24,68 .
Recovering such high-resolution energy consumption-temperature responses is only possible because we observe the temperature on each day in each grid cell. Conceptually, these data enable us to search for the grid-cell-level energy-temperature consumption relationship that, if applied to every grid cell for every daily temperature, would generate predicted per-capita energy consumption at the country-by-year level that best matches observed consumption. This approach is established in the broader literature; for example, ref. 68 estimates nonlinear local effects of daily temperature on crop yields using annual aggregate yields, and the approach is derived in the review by ref. 24 . Here we implement this approach through a country-year-level regression of per-capita energy consumption on specific population-weighted nonlinear climate variables (described below). A crucial step in implementation is properly constructing weighted aggregates of nonlinear transformations of local daily temperature (Supplementary Section A.2.4).
Specifically, let E zjdtc denote consumption in GJ per capita in grid cell z of country j, on day d of year t, for fuel category c (electricity, other fuels), and let T zjdt denote the daily average temperature at grid cell z on day d. Let T zjdt denote an M-element vector in which each element (T zjdt1 , …, T zjdtM ) is a nonlinear transformation of grid-cell-level daily temperature (for example, polynomial terms, We assume per-capita fuel category c energy consumption at grid cell z on day d is a function of the grid cell's temperature on that day, where this function, f c (T zjdt ), is a linear combination of the nonlinear elements in T zjdt : where β c1 , …, β cM are assumed to be constant average coefficients. Daily grid-cell-level per-capita energy consumption (E zjdtc ) is unavailable to us, but we observe national annual per-capita energy consumption (E jtc ), which is the population-weighted average of daily per capita consumption across grid cells in the country, summed over days in the year 24 . Let w zj denote the share of a country j's population that falls into grid cell z. Country j's per-capita annual consumption in the year t is thus the weighted average of daily per capita consumption across grid cells in j, aggregated over all 365 days d in year t: (2) The second line of equation (2) is obtained by substitution from equation (1) and interchanging the order of summation, expressing national annual per-capita energy consumption as f (~) c jt T , where T jt is an M-element vector in which the mth element, T jtm , is a country-by-year aggregation of the corresponding element from the grid-cell-level daily vector T zjdt (Supplementary Section A.2.4). Removing the coefficients β c1 , …, β cM from the summation over grid cells and days is possible given that these coefficients are assumed homogenous within a country and year. Thus, a regression of country-level annual per-capita energy consumption (E jtc ) on variables that are country-year weighted aggregates of the nonlinear temperature terms (T T , …,j t jtM 1 ) recovers the same coefficients, β c1 , …, β cM , that describe the primitive grid cell-by-day relationship described by equation (1). (See Extended Data Fig. 6 for a simplified, graphical illustration of this concept.) In practice, we allow energy-temperature responses to vary by income and long-run climate, estimating the function f c (⋅) conditional on these covariates. If this conditional function is homogenous within a country and year, then we can recover a grid cell-by-day relationship, as demonstrated above. To model heterogeneity by income, we use the 15-year moving average of a country j's natural log of per-capita GDP in year t (logGDPPC jt ). To model heterogeneity by long-run climate, we use average annual cooling degree days and heating degree days over the sample period (CDD j and HDD j , respectively). Annual cooling (heating) degree days are a common measure of exposure to warm (cold) temperatures and are defined as the cumulative deviations of daily average temperatures from a benchmark of 20 °C, over all days in the year where the average temperature exceeded (fell below) 20 °C. As these measures do not change substantially over the historical record, we do not rely on long-run temporal variation within the timespan of the sample and instead use the average over the sample period (Supplementary Section B.3).
Our estimating equation takes the following form: In our main specifications,T jt contains linear and quadratic terms for a spline in daily average temperatures (allowing a kink at 20 °C), each averaged over grid cells and summed across the year, as shown in equation (2). Exploiting flexible interactions between the three income and long-run climate covariates (logGDPPC jt , CDD j and HDD j ) and all terms in the temperature vector (~) jt T , we estimate an energy-temperature response f c for fuel category c that is conditional on income and long-run climate. Details of this procedure can be found in Supplementary Section B.3. Importantly, the interactions involving the long-run climate covariates are country-by-year aggregations of grid-cell-level interactions, allowing us to recover heterogeneity in the energy-temperature response due to long-run climate at the grid-cell level. In contrast, because our income data are available only at the country level, we recover heterogeneity in the energy-temperature response due to income only at the country level.
All our econometric specifications control for the effects of precipitation through the function g c (⋅), constructed analogously to f c (⋅); the vector ~j t P contains linear and quadratic terms of daily cumulative precipitation, each averaged over grid cells and summed annually. We also include a full set of country-by-reporting regime intercepts, referred to here as 'fixed effects' (α jic ), where reporting regimes (i) are time spans within a country where observations for a given fuel category are documented by the IEA to be comparable (Supplementary Section A.1). These fixed effects flexibly account for all permanent differences in energy consumption across country regimes. In addition, we include world region-by-year fixed effects (δ wtc ) for each fuel category, where w indexes world regions based on United Nations classifications (Oceania, N. America, N. Europe, S. Europe, W. Europe, E. Europe, E. Asia, S.E. Asia, Central America/Caribbean, South America, sub-Saharan Africa, N. Africa/W. Asia, S. Asia). These fixed effects flexibly account for all world region-level trends and shocks in energy consumption. The use of fixed effects is more reliable than trying to individually control explicitly for determinants of energy consumption because it accounts for time-invariant and time-trending factors non-parametrically. We thus exploit random within-country-regime, year-to-year variation in realized daily temperatures to identify a plausibly causal effect of historical temperature distributions on energy consumption, and we use variation in income and long-run climate to predict how the energy-temperature relationship may change in association with these two factors (Supplementary Section B.3). It should be noted that because our long-run climate measures (CDD j and HDD j ) do not vary over time within a country, their direct effect on energy consumption is absorbed in the fixed effects α jic . However, our objects of interest in equation (3) are the interactions of income and longrun climate with temperature, and not their direct effect on the level of energy consumption. Finally, ε jtc denotes the stochastic error term.
Owing to evidence of unit root behaviour in the dependent variable, we estimate equation (3) in first differences (Supplementary Section A.1). Furthermore, we employ inverse variance weighting to address differences in data quality across reporting regimes (Supplementary Section B.1). Standard errors are clustered by country-fuel category-reporting regime.
Although equation (3) is designed to causally identify the effect of daily temperatures on per-capita energy consumption, it does not identify overall levels of per-capita energy consumption as these are absorbed in the spatial and temporal fixed effects. We therefore express estimated electricity-temperature or other fuels-temperature responses as predicted consumption relative to a 'mild' day with an average temperature of 20 °C. The matrices of electricity-temperature and other fuels-temperature responses in Fig. 1c summarize the results from estimating equation (3), whereas Fig. 1a, b displays responses that are estimated for each decile of the in-sample income distribution, but do not differ by long-run climate (Supplementary Section B.2).

Projecting the impacts of climate change
In the third step, we estimate future per-capita energy consumption impacts of climate change. We first use estimates from equation (3) along with observable characteristics (logGDPPC, CDD and HDD) to predict energy-temperature responses at different points in time for each of 24,378 impact regions. For each impact region r in country j at year t, we use the estimated function f ( ⋅ ) c from equation (3), along with 15-year moving averages of the covariates (logGDPPC jt , CDD rjt and HDD rjt ), to predict energy-temperature responses for each fuel category. Responses evolve over time as 15-year moving averages of the covariates change for a given impact region r in country j, thereby reflecting the effects of adaptive behaviours that populations undertake as they become richer and/or are exposed to warmer climates. Because equation (3) estimates the interaction between temperature and country-level income as well as the interaction between temperature and grid-cell-level climate, our projections reflect changes in income and climate at these two corresponding spatial scales for internal consistency (Supplementary Section B.3).
We then apply a set of probabilistic climate change projections to the spatially and temporally heterogeneous energy-temperature responses to compute per-capita consumption impacts for each fuel category c and impact region r in country j for each year from 2015 to 2099. The distribution of future daily average temperatures under a given emissions scenario (RCP 8.5 or RCP 4.5) is obtained from the 33 projections in the SMME (Supplementary Section A.2.3).
Let rjt T ∼ represent a vector containing impact region-by-year aggregations of nonlinear grid-cell-level transformations of daily temperature in a future year t, under a warmer climate. In contrast, let ∼ rjt 0 T represent the counterfactual temperature vector for the same impact region under a climatology that is the same as that of a historical baseline period t 0 (Supplementary Section B.4). These vectors are constructed in exactly the same way as for the temperature vectors used in estimating equation (3), except that we take a weighted aggregation only over grid cells z within the impact region rather than the entire country; for example, element m of T rjt ∼ is The object Impact of climate change per capita crjt in equation (4) represents the change in annual per-capita electricity or other fuels consumption due to a shift in the temperature distribution under climate change, accounting for the evolution of energy-temperature responses as locations warm and incomes increase. It isolates the additional impact of climate change net of other factors (for example, income) that will change in the future. The two projections (A) and (B) are identical in every way, except for the climate. Thus, we evaluate (B) using future levels of income but use ∼ T, CDD and HDD values from a historical baseline t 0 (Supplementary Section B.4). All fixed effects and other controls cancel out and are therefore omitted.
We construct estimates of equation (4) for all impact regions up to 2099 under emissions scenarios RCP 8.5 and RCP 4.5, using each of the 33 climate projections in the SMME. Figure 2a maps mean impact estimates across these 33 climate projections at year 2099 under RCP 8.5, whereas Fig. 2b, c shows impacts aggregated to the country and global levels, respectively. Confidence intervals around the means are constructed to reflect both climatological and econometric sources of uncertainty. The distribution of impacts across 33 climate projections captures uncertainties in the climate system to 2099, and we additionally capture uncertainty arising from econometric estimation of equation (3) using the delta method 69 . Supplementary Section B.5 details the method used to combine both these independent sources of uncertainty.
To highlight the critical importance of income growth and climate-driven adaptation in shaping future energy-temperature responses, we also consider a 'no adaptation' impact projection that ignores these factors (green lines in Fig. 2c). To do this, we project

Estimating global energy damage functions
Our fourth step is to pool empirical estimates of climate change impacts constructed using equation (4) to fit global energy damage functions, which express global energy consumption costs of climate change as a function of the change in global mean surface temperature relative to the 2001-2010 average level (ΔGMST) 4 . These damage functions summarize the economic costs of all impacts measured in the detailed empirical analysis, demonstrating how they vary with the change in global mean surface temperature.
Damage functions to 2099 are directly built from estimates of global costs (D tlps , denominated in either EJ or dollars) in each year (t) using 33 climate models (l), two emissions scenarios (p) and a resampling of estimates (s) that captures uncertainty in the estimation of equation (3). We interpret each of the resulting 33,000 simulation outputs D tlps as a potential realization of damages that result from the spatial distribution of warming in model l, given the overall ΔGMST that is shown by that model under the emissions scenario p. Multiple simulations lead to an empirically derived distribution of potential outcomes that are conditional on the ΔGMST value for the year, climate model and emissions scenario used to generate that projection. To construct damage functions, we use these outcomes to estimate a conditional distribution of damages 17,18 using ordinary least squares, to obtain expected values, and quantile regressions, to capture uncertainty in damages conditional on ΔGMST.
In our projections of the future, the underlying population distribution and level of per-capita income are evolving over time, thereby shaping the sensitivity of energy consumption to warming and through it, global damages. These changes over time require the construction of year-specific damage functions. Thus, we separately estimate a quadratic damage function in each year: ). The right panel shows a damage function for total energy expenditure, denominated in dollars. To monetize the projected impacts of climate change on energy consumption, we apply country-specific real prices for electricity and other fuels to the projected quantity impacts, thus reflecting differential costs across geographies and fuels. Hence, a realization of D tlps in the right panel is W ρ ∑ ∑ ∑ × × Impact of climate change per capita j r j c rjt cjt c rjt lps ∈ , , where ρ cjt denotes a country-year-specific price for fuel category c. Price trajectories up to 2099 are constructed in one of two ways: (1) by extrapolating present-day prices under various price-growth-scenario assumptions or (2) by utilizing price projections developed in existing IAMs (Supplementary Section C).
In addition to estimating expected damages, we estimate 19 quantile regressions (for every 5th quantile from the 5th to 95th quantiles) to capture the full distribution of damages conditional on ΔGMST (Supplementary Section E.4). Quantile regressions also use a quadratic functional form (equation (6)), but with different coefficients and residuals. The resulting conditional distribution reflects econometric uncertainty in the impact estimates from which damages are constructed, as well as differences in the spatial patterns of warming exhibited across different climate models within the SMME. The 5th-95th quantile ranges from this conditional distribution are indicated by the shaded areas in Fig. 3c.
As described in the next step, we use the estimated dollardenominated damage functions to compute the net change in global energy expenditures associated with an additional ton of CO 2 . As CO 2 is long lived in the atmosphere, the US National Academy of Sciences recommends computing SCC values that capture damages to the year 2300 6 . As CMIP5 models are not run beyond 2099, the SMME sample ends in 2099. Therefore, it is necessary to develop a separate approach to extend these damage functions beyond 2099. Details of this approach can be found in Supplementary Section D. Figure 3d depicts damage functions for every ten years up to the end of the century (orange and black curves, estimated using equation (6)), as well as extended damage functions for every 50 years post-2100 (grey curves).

Calculating the partial SCC
In the final step, we combine a probabilistic, simple climate-carbon cycle model with the set of damage functions described above to compute the partial SCC. The partial SCC at time t 0 is defined as the marginal social cost from elevated energy expenditures imposed by the emission of a marginal ton of CO 2 at t 0 holding all other factors fixed (including the forecast trajectory of baseline greenhouse gas emissions). This is expressed as: dΔGMST t are the marginal damages at each moment in time that occur as a result of this small change in future global temperatures; they are computed using the damage functions described in equation (6). The discount factor, DF t , converts damages in future year t into an NPV.
To calculate the change in ΔGMST t due to a marginal pulse of CO 2 in 2020, we adapt a version of the FAIR simple climate model that has been developed especially for this type of calculation (Supplementary Section E) 25,70 . Specifically, we use FAIR to calculate ΔGMST t trajectories for emissions scenarios RCP 4.5 and RCP 8.5, both with and without an exogenous impulse of 1 GtC (equivalent to 3.66 GtCO 2 ) in the year 2020, an approximation of a marginal emission for which the model numerics are stable. In FAIR, this emissions impulse perturbs the trajectory of atmospheric CO 2 concentrations and ΔGMST t for 2020-2300, with dynamics that are influenced by the baseline RCP scenario. In each scenario, the trajectory of damages in the 'RCP + pulse' simulation is differenced from the baseline RCP simulation to compute D t d^(ΔGMST, ) dΔGMST dΔGMST dCO t t t 2, 0 , and the resulting damages are converted into US$ per 1 tCO 2 and discounted to the present.
As there are multiple views on how best to discount future damages (see refs. 6,39,40 for reviews and discussions of various options and their implications), we present multiple estimates using both constant discount rates and 'Ramsey' discounting 6 . In the case of a constant discount rate r, DF = e t r t t − ( − ) 0 . We use the range of values r ∈ {0.02, 0.025, 0.03, 0.05} to explore the influence of the discount rate. The value r = 0.02 is consistent with ten-year US Treasury rates over the past two decades 71,72 and the remaining values are recommended by ref. 1 .
In the case of Ramsey discounting, , where r s denotes the time-varying discount rate for year s, and s t > 0 I is an indicator variable taking a value of one if year s > t 0 . Time-varying discount rates are calculated according to the Ramsey equation r s = δ + ηg s , where the parameter δ measures the pure rate of time preference, g s measures the growth rate of consumption in year s, and η is the elasticity of marginal utility of consumption 47 . We use global per-capita income growth from the SSP scenarios to obtain annual values for g s , and explore a range of parameter values for δ and η based on previous literature 29,39,47,73-79 and guidance from the US National Academy of Sciences 6 .
To capture uncertainty in the climate physics represented in FAIR, we generate a distribution of future temperature trajectories by resampling the equilibrium climate sensitivity, the transient climate response, the short thermal adjustment time and the timescale of rapid carbon uptake by the ocean mixed layer from a joint distribution that we constrain using findings from the literature (Supplementary Section E.2). The solid lines in Fig. 4 indicate the median trajectories when sampling from this constrained joint distribution (Fig. 4b,c) or when sampling jointly from both this conditional joint distribution and quantiles of the damage function (Fig. 4d); shaded areas indicate interquartile ranges. The final range of uncertainty in projected damages (shaded area in Fig. 4d) thus combines uncertainty in climate sensitivity with uncertainty in damages, conditional on the climate sensitivity. Figure 4e and Extended Data Tables 1 and 2 present partial SCC estimates under RCP 8.5 and RCP 4.5, assuming various discount rates and future energy price scenarios. The 5th-95th percentile ranges (in parentheses) account for econometric and climatological uncertainty (Supplementary Section E.4). Additional partial SCC estimates demonstrating sensitivity to alternative approaches for estimating post-2100 damages, and alternative socioeconomic scenarios can be found in Supplementary Section F.

Data availability
The data for replicating the findings of this study are available on Zenodo at https://doi.org/10.5281/zenodo.5099834.

Code availability
The code for replicating the findings of this study is available on GitHub at https://github.com/ClimateImpactLab/energy-code-release-2020/.