nature sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Compensation for atmospheric appropriation Received: 20 August 2022 Andrew L. Fanning 1,2 & Jason Hickel 3,4 Accepted: 18 April 2023 Published online: xx xx xxxx Research on carbon inequalities shows that some countries are overshooting their fair share of the remaining carbon budget and hold Check for updates disproportionate responsibility for climate breakdown. Scholars argue that overshooting countries owe compensation or reparations to undershooting countries for atmospheric appropriation and climate-related damages. Here we develop a procedure to quantify the level of compensation owed in a ‘net zero’ scenario where all countries decarbonize by 2050, using carbon prices from IPCC scenarios that limit global warming to 1.5 °C and tracking cumulative emissions from 1960 across 168 countries. We find that even in this ambitious scenario, the global North would overshoot its collective equality-based share of the 1.5 °C carbon budget by a factor of three, appropriating half of the global South’s share in the process. We calculate that compensation of US$192 trillion would be owed to the undershooting countries of the global South for the appropriation of their atmospheric fair shares by 2050, with an average disbursement to those countries of US$940 per capita per year. We also examine countries’ overshoot of equality-based shares of 350 ppm and 2 °C carbon budgets and quantify the level of compensation owed using earlier and later starting years (1850 and 1992) for comparison. Global carbon emissions have continued to rise over the past several fair and equitable use5–8. Scholars have drawn on this principle to argue decades, and concentrations of atmospheric CO2 have increased dra- that carbon budgets should be shared equitably9–12 and that cumulative matically. The ‘safe’ planetary boundary for emissions—understood emissions in excess of fair shares represent a form of appropriation of as atmospheric concentration of 350 ppm CO2—was crossed in 19881. atmospheric commons, which has been framed in the language of ‘cli- As of 2022, atmospheric concentrations are now 415 ppm (ref. 2), and mate debt’ and ‘climate coloniality’13–15. Acknowledging issues of equity global temperatures have reached 1.1 °C over preindustrial levels3. The is essential to establishing trust and buy-in to the negotiation process16. Paris Agreement commits the world’s governments to limiting global Researchers and climate negotiators have argued that overemit- temperature rise to 1.5 °C, or well below 2 °C4. The remaining carbon ting countries owe compensation or reparations to low-emitting coun- budgets associated with these boundaries are being rapidly depleted, tries for atmospheric appropriation and climate-related damages, and climate damages are accelerating. which fall disproportionately on poorer countries that have contrib- Not all countries are equally responsible for the depletion of car- uted little or nothing to the crisis17–21. Paragraph 51 of the Paris Agree- bon budgets, however; some nations have contributed more to causing ment decision document states that the agreement “does not involve this crisis than others. This disproportionate historical responsibility or provide a basis for any liability or compensation”4. Nonetheless, is problematic from a climate justice perspective that recognizes the legal scholars argue that options remain open for the development of atmosphere as a shared commons, to which all people are entitled to a a compensation and liability system under the Warsaw International Doughnut Economics Action Lab, Oxford, UK. 2Sustainability Research Institute, School of Earth and Environment, University of Leeds, Leeds, UK. 1 3 Institute of Environmental Science and Technology, Autonomous University of Barcelona, Barcelona, Spain. 4International Inequalities Institute, London School of Economics and Political Science, London, UK. e-mail: j.e.hickel@lse.ac.uk Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 a World b Global South c Global North 4.5 4.5 4.5 4.0 4.0 4.0 Business as usual (1 = fair share of 1.5 °C budget) 3.5 3.5 3.5 Cumulative CO2 emissions 3.0 3.0 3.0 Net zero 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 2 °C fair share 1.0 1.0 1.0 1.5 °C fair share 0.5 0.5 0.5 350 ppm fair share 0 0 0 1975 2000 2025 2050 1975 2000 2025 2050 1975 2000 2025 2050 Year Year Year Fig. 1 | World and regional cumulative CO2 emissions with respect to fair 350 ppm (green line) and 2 °C budgets (red line) also shown. World and regional shares of global carbon budgets, historical trends (1960–2019) and scenario totals are aggregated from national values. Likely (66%) prediction intervals are trends (2020–2050). a, World. b, Global South region. c, Global North region. shown in lighter tint around the business-as-usual projections. See Extended The historical emissions (black area), business-as-usual projected pathway Data Figs. 1 and 2 for results with cumulative emissions starting from 1850 and (dashed line) and net-zero pathway (blue line) show cumulative emissions 1992, respectively. relative to fair shares of the 1.5 °C carbon budget (yellow line), with fair shares of Mechanism for Loss and Damage, which was created in 201322. Calls fair shares of the 350 ppm, 1.5 °C and 2 °C carbon budgets across 168 for payments for loss and damage have gained momentum, notably countries from 1960 to 2019, together with two forward-looking esti- during the twenty-sixth Conference of the Parties (COP26) summit mates between 2020 and 2050, namely (1) business-as-usual projec- in Scotland23 and the COP27 summit in Egypt24, which formally estab- tions based on historical trends (with ‘likely’ or 66% prediction intervals) lished a loss and damage fund, with details to be clarified at COP28. and (2) net-zero scenarios with country-specific mitigation rates that This Article adds to this literature—and the broader public debate— bring CO2 emissions in each country from 2020 levels to 0.1 tonnes per by offering an empirical method for quantifying compensation owed capita in 2050 (see Extended Data Fig. 1 for country-specific mitigation for the appropriation of atmospheric commons. Building on earlier rates). We also analyse the sensitivity of our cumulative results to the work, we use an equality-based fair-share approach to calculate coun- 1960 start date by conducting two parallel analyses starting in 1850 and tries’ use of established carbon budgets, including for 350 ppm, 1.5 °C 1992 (the year the United Nations Framework Convention on Climate and 2 °C (refs. 9,12). This analysis allows us to determine the extent to Change was established), respectively. The estimation procedures are which nations have exceeded their fair shares of the carbon budgets described in detail in Methods. and appropriated atmospheric commons. We then assess countries’ At the global scale, we find that cumulative emissions since 1960 projected future use of the carbon budgets if they carry on with busi- are currently around three times beyond the 350 ppm carbon budget ness as usual, as well as if they pursue ambitious emissions reductions (exhausted in 1988), and a global emissions mitigation rate of more than to reach ‘net zero’ by 2050, consistent with limiting warming to 1.5 °C. 10% per year between 2020 and 2050 is needed for net zero, which would The world must make every effort to respect the 1.5 °C limit, as per respect the 1.5 °C carbon budget (Fig. 1a). However, our business-as-usual the Paris Agreement. If some countries appropriate more than their fair projections suggest the world will likely deplete the 1.5 °C carbon budget shares of the carbon budget, this has important implications. It means by 2030 (2028–2032) and the 2 °C carbon budget by 2044 (2039–2049). overemitters are disproportionately responsible for damages caused We note that the 1.5 °C carbon budget and the 2 °C carbon budget are both by global warming but also that other countries must effectively forgo substantially larger—and therefore riskier—than the safe 350 ppm carbon the full use of their own fair shares to keep the world on track for 1.5 °C, budget that respects the climate change boundary proposed by ref. 1. mitigating more rapidly than would otherwise be required. One way to We performed a regional analysis to assess the depletion of carbon quantify the monetary value of atmospheric appropriation is by repre- budgets by the global North and global South: the global North here senting overshoot emissions in terms of carbon prices. In this Article, refers to the United States, Europe, Canada, Australia, New Zealand, we use marginal abatement costs from the Intergovernmental Panel Japan and Israel, while the global South refers to the rest of Asia, Africa on Climate Change Sixth Assessment Report (IPCC-AR6) scenarios and the Americas. consistent with limiting global warming to 1.5 °C. There are 129 countries from the global South in our analysis, Our results provide an indication of how compensation for atmos- which are home to more than 80% of the total population, but their pheric appropriation can be quantified in a way that accounts for his- aggregate cumulative emissions surpassed fair shares of the 350 ppm torical and current responsibilities, but it is beyond the scope of this carbon budget only in 2012—more than two decades after the world as study to provide a framework for practical implementation. However, a whole (Fig. 1b). If this group of countries collectively pursued ambi- we note that the climate reparations literature is increasingly consid- tious mitigation following our net-zero scenario between 2020 and ering the politics, governance and practicalities of such an approach, 2050, it would use only 50% of its 1.5 °C fair share. Our business-as-usual and our results may be useful inputs to inform the ongoing ‘Glasgow projections suggest this group of global South countries would likely Dialogue on Loss and Damage’ established during COP2617,23–26. remain within its fair share of the 2 °C carbon budget by 2050 but would likely overshoot its fair share of the 1.5 °C carbon budget in 2048 Results (2043–2053), judging from historical trends. Our first step is to estimate levels of atmospheric appropriation by The remaining 39 countries in our analysis are from the global tracking historical cumulative emissions with respect to equality-based North, and we find this group of high-emitting countries used up its Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 a b c Historical Business-as-usual Net zero Cumulative overshoot or undershoot of 1.5 °C fair share (GtCO2) 1,500 United States India 1,500 1,500 European Union and United Kingdom China United States 1,200 Rest of global North Sub–Saharan Africa 1,200 1,200 Global South overshoot Rest of global South European Union and Global North undershoot United Kingdom 900 900 900 Rest of global North 600 600 600 United States China overshoot European Union and 300 300 300 United Kingdom Rest of global North Rest of global South overshoot Global South overshoot 0 0 0 India India Sub-Saharan Africa China –300 –300 –300 Sub-Saharan Africa Rest of global South –600 –600 –600 Rest of global South –900 –900 –900 –1,200 –1,200 –1,200 –1,500 –1,500 –1,500 –1,800 –1,800 –1,800 1960 1970 1980 1990 2000 2010 2020 2050 2050 Year Year Year Fig. 2 | Cumulative CO2 emissions overshoot and undershoot by country group with respect to 1.5 °C fair shares. a, Historical 1960–2019 period. b, Business-as- usual median projection in 2050. c, Net-zero scenario in 2050. See Extended Data Figs. 3 and 4 for results with cumulative overshoot and undershoot starting from 1850 and 1992, respectively. collective fair share of the 350 ppm carbon budget by 1969, then over- process to balance the excess emissions of overshooting countries. We shot its 1.5 °C fair share by 1986 and then surpassed its 2 °C fair share by find broadly similar results with cumulative emissions starting from 1995 (Fig. 1c). As of 2019, this group of countries has already exceeded 1850 or from 1992, although the fair shares appropriated from under- its collective fair share of the 1.5 °C carbon budget by more than 2.5 shooting countries are somewhat higher from 1850 (60%; Extended times, with cumulative emissions measured from 1960. If this group Data Fig. 3) and somewhat lower from 1992 (48%; Extended Data Fig. 4). collectively pursues ambitious mitigation to reach net zero by 2050—as We use these findings as inputs for the next step in our analysis; to many of these countries have pledged in their Nationally Determined quantify the compensation owed by overshooting countries to under- Contributions under the Paris Agreement—our findings suggest its shooting countries for the appropriation of atmospheric commons. cumulative emissions would still be nearly three times over its 1.5 °C It is well established that there is a strong positive relationship fair share. However, our business-as-usual projections suggest this between affluence and ecological pressures, including carbon emis- group of global North countries will likely increase the extent of its sions27,28. We investigate this relationship further for our cumulative cumulative overshoot further to 4.0 times (3.7–4.3) over its fair share analysis by comparing the historical level of cumulative emissions of the 1.5 °C carbon budget by 2050. (with respect to 1.5 °C fair shares) with cumulative gross domestic We find all global North countries overshooting their 1.5 °C fair product (GDP) per capita from 1960 to 2018 (the most recent year with shares, and they collectively hold responsibility for the majority (91%) comparable data for a large number of countries; N = 151). of cumulative overshoot between 1960 and 2019. The only countries We find nearly 70% of cross-national variability in cumulative that stay within their 1.5 °C fair shares over the same period are all in the GDP per capita can be explained solely by differences in cumulative global South (Fig. 2a). Alarmingly, total cumulative overshoot is likely emissions with respect to fair shares (adj-R2 = 0.69; Fig. 3). There is to triple in absolute terms by 2050 under business-as-usual projections some variability across countries, notably among former USSR and (Fig. 2b). Although we find cumulative overshoot of 1.5 °C fair shares in Eastern European countries, which tend to have relatively higher levels the United States, Europe and the rest of the global North would likely of overshoot at lower levels of income. However, our linear estimates double in absolute terms by 2050 under business-as-usual projections, suggest each additional unit of cumulative overshoot beyond a coun- their share of total overshoot would fall to 60% due to increasing levels try’s 1.5 °C fair share is significantly associated with an increase of more of overshoot from countries in the global South. Notably, we find that than US$10,000 cumulative GDP per capita (P < 0.001; we report all China would likely switch from holding 15% of total 1.5 °C undershoot monetary values throughout in constant 2010 prices). These findings in 2019 to contributing 27% of total overshoot in 2050, according to support the view that overshooting countries have tended to enrich historical trends. themselves through appropriating more than their fair shares of the By contrast, stabilizing carbon emissions by 2050 under net-zero atmospheric commons. scenarios could limit warming to 1.5 °C, and would likewise stabilize Building on these results, we develop a procedure for allocating national responsibility for both averting and causing climate break- financial compensation from overshooting countries to undershooting down (Fig. 2c). We find total undershoot in our net-zero scenario countries based on each country’s cumulative emissions with respect would be held entirely by countries in the global South (including to 1.5 °C fair shares in a world that achieves net zero by 2050. Each China), and 89% of total overshoot would be held by the global North overshooting country’s cumulative excess emissions in 2050 under (with the remaining overshoot held by high-emitting countries in the its net-zero pathway were annualized and valued in monetary terms global South). from 2020 to 2050 using median (and interquartile range) marginal Overall, ambitious mitigation to reach net zero by 2050 in all coun- abatement costs derived from IPCC-AR6 mitigation pathways that limit tries could limit warming to 1.5 °C, but more than half (53%) of the warming to 1.5 °C with no or limited overshoot (N = 73) (ref. 29). The undershooting global South’s fair shares would be appropriated in the marginal abatement costs of carbon increase over time, for example, Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Qatar Switzerland 50,000 Norway Cumulative GDP per capita, 1960–2018 (US$) Denmark United States 40,000 Sweden Australia Canada Japan Netherlands France Iceland Finland United Arab Emirates Ireland Germany 30,000 New Zealand Austria Singapore United Kingdom Kuwait Israel Italy Hong Kong SAR Spain 20,000 Slovenia Greece Portugal Syria South Korea Saudi Arabia Bahrain Venezuela Slovak Republic Czech Republic United States Brazil Turkey Croatia European Union and United Kingdom Lithuania 10,000 Oman Latvia Poland Russia Rest of global North Mexico South Africa Kazakhstan Iran Hungary Global South overshoot Nigeria Bulgaria Ukraine India Romania Serbia China 0 China Georgia Sub–Saharan Africa India Rest of global South 0 1 2 3 4 5 Cumulative CO2 emissions with respect to 1.5 °C fair shares, 1960–2018 (1 = fair share) Fig. 3 | Cumulative CO2 emissions with respect to 1.5 °C fair shares versus with slope and intercept coefficient standard errors of 585 and 809, respectively cumulative GDP per capita, 1960–2018. Only countries with available GDP data (adj-R2: 0.69; F statistic: 333.8 on 1 and 149 d.f.; P < 2.2 × 10−16). One country covering the 1960–2018 analysis period are included (N = 151). GDP is expressed (Luxembourg) lies beyond the chart area; see Supplementary Data 1 for results in constant 2010 prices. A statistical model estimated using two-sided ordinary for all countries. least squares regression finds the following linear relationship: y = 10, 688x − 31 US$198 (158–242) per tonne of CO2 in 2030 and US$547 (394–887) per 200 tonne of CO2 in 2050. We then distributed the cumulative monetary value of excess emissions from each overshooting country to each Cumulative compensation in 2050, net-zero scenario undershooting country on the basis of the latter’s share of total under- India shoot emissions in 2050 under our net-zero scenario. The procedure (US$57 trillion) United States is described in detail in Methods. 150 (US$80 trillion) We find that cumulative financial compensation from overshoot- China ing countries to undershooting countries in a world that achieves (US$15 trillion) net zero between 2020 and 2050 can be valued at US$192 (141–298) (trillion US$) Compensation trillion (Fig. 4). The average annual compensation for each year over due for 100 Sub–Saharan Africa the 31-year period is equivalent to US$6.2 (4.5–9.6) trillion per year, atmospheric (US$45 trillion) European Union and appropriation or approximately 8% (6%–11%) of world GDP in 2018. Importantly, this United Kingdom (US$46 trillion) value should be seen as compensation for the appropriation of under- shooting countries’ 1.5 °C fair shares to avoid climate breakdown and is therefore additional to fairness considerations surrounding the costs 50 Rest of global North incurred by countries to actually transition to net-zero emissions or to (US$44 trillion) Rest of global South adapt to a 1.5 °C warmer world30. (US$74 trillion) Total financial compensation due to undershooting countries Global South decreases when historical responsibility for climate breakdown is overshoot (US$22 trillion) ‘forgiven’ by assessing cumulative emissions from a later start date (and 0 vice versa for an earlier start date), ranging from US$109 (80–170) tril- Overemitters Within fair shares lion from 1992 and US$238 (175–371) trillion from 1850 (Extended Data Fig. 4 | Cumulative compensation due from overshooting country groups to Fig. 5). We find the United States, the European Union and the United undershooting country groups (relative to 1.5 °C fair shares) based on the Kingdom owe around two-thirds of the total financial compensation historical period from 1960 to 2019 and net-zero scenario from 2020 to 2050. from overshooting countries, irrespective of the start year. Conversely, Cumulative compensation is expressed in constant 2010 prices. See Extended India and the undershooting countries of sub-Saharan Africa are owed Data Fig. 5 for results with cumulative financial compensation by country around half of the total financial compensation for giving up their group starting from 1850 and 1992 and Supplementary Data 1 for results for 1.5 °C fair shares to achieve net zero, regardless of when cumulative all countries. emissions start. By contrast, our results for China are more sensitive to the start year, ranging from 2% of total overshoot from 1992 to 16% of total undershoot from 1850. of their regional GDP in 2018 (Fig. 5b). Financial compensation to India We find the United States holds the single largest climate debt on a yearly basis would be equivalent to 66% (48–102%) of its GDP to undershooting countries at US$2.6 (1.9–4.0) trillion per year, on in 2018, and compensation to the rest of the undershooting global average, which is equivalent to 15% (11–23%) of its annual GDP in 2018 South, excluding China, would represent 22% (16–34%) of its regional (Fig. 5a). Other overshooting regions owe non-trivial amounts, ranging GDP. The climate credit due to China for achieving net zero would from 6% to 19% of their annual GDP on a yearly basis. be US$0.5 (0.4–0.8) trillion per year on average, or 6% (4–9%) of its Meanwhile, the annual financial compensation to undershooting GDP in 2018. countries in sub-Saharan Africa for achieving net zero by 2050 would At the country scale, we find the average monetary value of be US$1.4 (1.0–2.2) trillion per year, which represents 111% (82–173%) excess emissions appropriated by the 67 overshooting countries in Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 a Overemitters b Within fair shares 175 175 150 150 Annual compensation owed by region, Annual compensation owed to region, net-zero scenario (% of GDP) net-zero scenario (% of GDP) 125 125 100 100 75 75 50 50 25 25 0 0 United States Global South Rest of European Union Sub–Saharan India Rest of China overshoot global North and United Africa global South Kingdom Region Region Fig. 5 | Average annual compensation by country group relative to average and lower bounds of the interquartile range of carbon prices, derived from GDP by region in 2018 based on the historical period from 1960 to 2019 IPCC-AR6 scenario pathways that limit warming to 1.5 °C with no or limited and net-zero scenario from 2020 to 2050. a, Overemitting country groups. overshoot (N = 73). See Extended Data Figs. 6 and 7 for results starting from b, Country groups within their fair shares. Annual compensation is calculated 1850 and 1992, respectively. from median carbon price values, with error bars calculated from the upper a Within fair shares b Overemitters 8,000 8,000 United States 7,000 7,000 Annual compensation per capita owed by country, Annual compensation per capita owed to country, Kuwait Qatar 6,000 6,000 Czech Republic Canada net-zero scenario (US$) net-zero scenario (US$) 5,000 5,000 Germany Australia Russia 4,000 4,000 Finland Norway United Arab Emirates Japan Ukraine United Kingdom Austria Bahamas 3,000 3,000 Greece France Sweden Bahrain Italy Saudi Arabia 2,000 Bangladesh India 2,000 Latvia Ireland Haiti Vietnam Indonesia Spain New Zealand Mali South Korea Peru Brazil Thailand China Israel 1,000 Cuba 1,000 Croatia Kenya Pakistan Iraq Turkey South Africa Nigeria Malaysia Libya Egypt Algeria Georgia Iran 0 Jordan 0 Venezuela Mexico Argentina 0 0.25 0.50 0.75 1.00 1 2 3 4 5 6 Cumulative CO2 emissions in 2050 with respect to 1.5 °C fair shares, Cumulative CO2 emissions in 2050 with respect to 1.5 °C fair shares, net-zero scenario (1 = fair share) net-zero scenario (1 = fair share) Fig. 6 | Cumulative CO2 emissions in 2050 relative to 1.5 °C fair shares versus countries (N = 67). Compensation is expressed in constant 2010 prices. Colours average compensation per capita across countries, based on the historical are as per Fig. 3. Country circles are sized according to population. Two countries period from 1960 to 2019 and net-zero scenario from 2020 to 2050. a, Average (Hong Kong SAR (China) and Luxembourg) lie beyond the chart area; see annual per capita compensation owed to countries within their fair shares Supplementary Data 1 for results for all countries. (N = 101). b, Average annual per capita compensation owed by overemitting our analysis would be US$2,700 (1,980–4,200) per capita per year in a countries in our analysis that would have had their fair shares appropri- world that achieves net zero between 2020 and 2050. Our results sug- ated, which are home to most of humanity. gest that this monetary value converts to an average compensation of Ten countries would have more than 95% of their fair shares of US$940 (690–1,470) per capita per year across the 101 undershooting the 1.5 °C budget appropriated to stabilize global emissions under Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 our net-zero scenario—all in sub-Saharan Africa—and the majority of latest IPCC-AR6 synthesis report indicates that existing government undershooting countries (N = 55) would sacrifice more than 75% of policies have the world on track for 3.2 °C warming by 210036. This their fair shares, including India. We find this group of low-emitting under­scores the need for much more dramatic action than governments countries would be entitled to receive an average annual financial are presently planning. Relying on supply-side efficiency improvements compensation of US$1,160 (850–1,800) per capita from overshooting and technological change alone are likely to be inadequate37. countries to begin making reparations for the appropriation of nearly There is growing consensus that demand-side options that reduce the entirety of their fair shares of the 1.5 °C budget (88%, on average; unnecessary production and consumption, and shift to already-existing Fig. 6a). Meanwhile, undershooting countries that would have less of low-carbon technologies, could substantially reduce emissions while their fair shares appropriated would likewise be entitled to less financial reducing inequality and improving human well-being38. In addition, compensation. For example, countries with less than 25% of their fair mitigation consistent with 1.5 °C will probably require global North shares appropriated in a world that achieves the net-zero target by governments to adopt transformative post-growth and degrowth 2050, including China, would be entitled to receive US$280 (200–430) policies that reduce aggregate energy use directly and enable faster per capita per year, on average (N = 13). decarbonization39–44. Ultimately, we should understand net-zero Similarly, Fig. 6b shows overshooting countries closer to their fair policy as a minimum and aspire for regenerative economic systems shares would owe less compensation than countries who are far beyond that generously store carbon, cycle water and nurture biodiversity their fair shares under our net-zero scenario. We find overshooting by consciously emulating nature’s designs and processes45,46. countries with excess emissions more than three times beyond their The analysis presented here is necessarily limited by our metho­ fair shares, such as Qatar and the United States, would owe US$5,750 dological choices, which could be improved with further research. (4,220–8,950) per capita per year to undershooting countries, on aver- First, while national fair shares are calculated on the basis of the age (N = 12). Meanwhile, overshooting countries with excess emissions equality-based principle of atmospheric commons, other sharing less than 50% beyond their fair shares, such as Iran and Venezuela, principles exist and could be explored47. Second, we use carbon prices would be entitled to pay US$520 (380–800) per capita per year, on from scenarios that limit warming to 1.5 °C to quantify the value of average (N = 18). overshoot emissions and compensation because they are consist- ent with our net-zero scenario and readily available in IPCC-AR6, but Discussion other approaches may be equally valid. These could include other Our results reveal the global North has already more than exhausted ‘loss-based’ approaches (focusing on the value of appropriated fair its equality-based fair share of both the 1.5 °C and 2 °C carbon budgets, shares in terms of GDP gains and losses, for example) or ‘damage-based’ regardless of whether fair shares are calculated from 1850, 1960 or 1992. approaches (focusing on the costs of climate-related damages)18. Third, Any further emissions on their part will entail further appropriation our compensation estimates are based on historical and projected of the fair shares of other countries. By contrast, the global South as responsibility for emissions with no adjustments for country-specific a region remains well within its fair share of the 1.5 °C budget. In an needs or capabilities10,48. Fourth, although our business-as-usual pro- ambitious net-zero-by-2050 mitigation scenario, 50% of the South’s jections include uncertainty ranges, our analysis does not fully explore fair shares would be appropriated by wealthy nations. We find that uncertainties in historical estimates of emissions, population or GDP. compensation worth US$192 trillion would be owed to the undershoot- Finally, while emissions are normally calculated at the national ing nations of the global South by 2050, with an average disbursement level, the aggregate figures obscure significant inequalities within to those countries of US$940 per capita per year. countries. There is evidence that per capita emissions among the The compensation framework we propose here is in line with exist- poorest half of the populations in wealthy countries, such as France, ing calls for reparations in payment of climate debts, which could be the United Kingdom and the United States, are already close to the adapted and applied in practice on a yearly basis using observed carbon 2030 climate targets set by these countries49. Responsibility for excess emission values and rigorous scenario analyses hosted by a competent emissions is held largely by the wealthy classes who have high lifestyle international authority, such as the Warsaw International Mechanism emissions and who wield disproportionate power over provisioning for Loss and Damage. The benefits of this country-specific framework systems and national policy50. are (1) it acknowledges historical responsibility by overemitting coun- tries, (2) it provides fair compensation to countries still within their fair Methods shares and (3) it can accommodate changes in emissions trajectories This section summarizes how we collected historical data, estimated and carbon prices over time. The financial contributions that we quan- forward-looking projections and scenarios, calculated fair shares and tify here should be seen as rough first approximations. distributed financial compensation to (from) countries on the basis of There are debates about what year to use as a baseline for calculat- their cumulative undershoot (overshoot) of fair shares. ing responsibility for historical emissions, with studies often providing a range of different start dates7,10,31. We take a similar approach, consider- Time-series data ing 1960 to be a reasonable mid-range baseline while providing parallel We collected publicly available time-series data on population51,52, CO2 analyses of cumulative emissions from 1850, a common early baseline, emissions53–56, GDP57,58 and carbon prices29 from international sources. and from 1992, the year that the United Nations Framework Convention We combined data from multiple sources to create country-level time on Climate Change was established. We consider 1960 to be a reasonable series spanning the relatively long 1850–2019 historical period covered basis for compensation given that scientific understanding of the influ- by our analysis (see Supplementary Table 1 for summary descriptions ence on atmospheric CO2 and temperature from burning fossil fuels was of each indicator used in our analysis). well understood32–34, and beginning to be communicated to the general Following refs. 9,12, our approach prioritizes consumption-based public35, by the 1950s. Notably, we agree with the view that disregarding CO2 emissions data available for a large number of countries from emissions before the 1990s represents an unjust way to measure histori- the Eora Multi-Regional Input–Output database (excluding land cal responsibility10,11 given the importance of historical emissions noted use, land-use change and forestry)54,56. Unlike territorial emissions in the preamble of the convention itself. Nevertheless, our results show accounting, consumption-based accounting accounts for the upstream undershooting countries would be entitled to substantial compensa- emissions embodied in imports and exports and better reflects tion—more than US$100 trillion—even with a 1992 baseline. the principle of equal access to atmospheric commons. However, We note that the net-zero scenarios shown in Fig. 1 look highly consumption-based data were available only from 1970, so we obtained unlikely, as indicated by our business-as-usual projections. Indeed, the territorial CO2 emissions from the PRIMAP-HISTTP dataset (v.2.3.1)53,55 Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 for the earlier 1850–1969 period. We acknowledge that our analysis We converted these mitigation rates into annual net-zero CO2 does not fully explore uncertainties in the historical estimates of CO2 time series between 2020 and 2050 for each country n in each year t emissions, which can vary substantially across countries and tend to be by solving the exponential function on an annual basis and multiplying larger for consumption-based emissions due to the additional reliance this per capita series by UN population projections (medium fertility on multi-regional input–output tables to account for trade flows59. variant) over the same period, or Overall, our methods yielded a balanced panel of 168 countries with CO2 emissions and population data spanning the 1850–2019 period and a NetZeron,t = (CO2 n,t × e(t−2020)rn ) × populationn,t 2020 slightly smaller balanced panel of 151 countries with GDP data (in constant 2010 US$) spanning the 1960–2018 period. See Supplementary Data 1 for We joined these scenario values to 2050 with our historical data- results for all countries and Supplementary Information for additional base and calculated cumulative emissions for each country, starting indicator-specific methods that we used to construct each series. from 1850, 1960 and 1992. Projecting business-as-usual trends Deriving remaining global carbon budgets We projected business-as-usual trends in CO2 emissions for each coun- We obtained global carbon budgets remaining from 2020 with a 66% try on the basis of annual observations over the 1960–2019 period, likelihood of limiting global warming to 1.5 °C and 2 °C from IPCC-AR6 following the dynamic statistical forecasting methods described by (400 GtCO2 and 1,150 GtCO2, respectively)3. However, the IPCC-AR6 ref. 12. These methods selected the best-fitting estimate from two carbon budgets include CO2 sources from both fossil fuel combustion distinct model classes for each country—(1) an exponential smoothing and land-use change, but our country-level data exclude emissions (ETS) state space model and (2) an autoregressive integrated moving from land-use change. averages (ARIMA) model—based on an automatic forecasting proce- To account for this difference, we obtained data on the shares of dure described in detail by ref. 60 and enabled by the forecast package fossil fuel and land-use change in total anthropogenic emissions from in R61. These time-variant nonlinear statistical models are preferable to ref. 62 and calculated ten-year averages over the most recent decade linear estimation models (such as ordinary least squares regression) (90% and 10%, respectively). On the basis of these shares, we disag- because they can account for patterns within the data and give greater gregated the fossil fuel component of the IPCC global carbon budgets weight to more recent observations. remaining from 2020 for 1.5 °C and 2 °C (360 GtCO2 and 1,035 GtCO2, For each country, the best-fitting estimate within each model respectively) and calculated 1.5 °C and 2 °C carbon budgets starting class (ETS and ARIMA) was selected by using an automated procedure from 1850, 1960 and 1992. that estimates and compares a large number of defined parameter In contrast to the 1.5 °C and 2 °C boundaries, there is no carbon variations to fit the historical data of each country (30 for ETS and at budget remaining from 2020 for the 350 ppm climate boundary (CO2 least 17 for ARIMA)60 and chooses the model that minimizes Akaike’s concentrations are already greater than 415 ppm and rising2). We set information criterion, corrected for small-sample bias (AICc). Follow- the 350 ppm carbon budgets starting from 1850 and 1960 equal to ing ref. 61, the final best-fitting estimate across model classes for each their respective cumulative global totals in 1988 (the year that CO2 country was selected on the basis of a time-series cross-validation concentrations crossed this boundary). See Supplementary Table 2 for algorithm that minimizes mean standard error (as AICc cannot be used the numerical global carbon budgets that we derived for the different to select models across different classes). This best-fitting model for climate boundaries and start years used in the analysis. each country was used to project median estimates of CO2 emissions from 2020 to 2050, together with 66%, or ‘likely’, prediction intervals. Distributing national fair shares of global carbon budgets We joined these projected values to 2050 with our historical database There are different ‘top-down’ sharing principles that could be used to and calculated cumulative emissions for each country, starting from distribute global carbon budgets to countries, including equality, 1850, 1960 and 1992. historical responsibility, respective capabilities, geographical needs and sovereignty47. Building on refs. 9,12, we developed an equality-based Calculating net-zero scenarios method that considers historical responsibility and distributes a given We calculated net-zero scenarios by reducing each country’s 2020 global carbon budget into national fair shares according to a given level of CO2 emissions per capita to converge at 0.1 tonnes per capita in country’s population as a share of the global population, with popula- 2050. We derived country-specific mitigation pathways that reduced tions averaged over a given analysis period ( population ), or emissions at a constant rate using a simple exponential function, or b b populationn,t [start∶end] ln(0.1n,t2050 /CO2n,t ) fair-sharen,tstart∶end = CO2 budgetworld,t ×( ) 2020 start rn = populationworld,t (2050 − 2020) + 1 [start∶end] where r is the mitigation rate required for country n to reach 0.1 tonnes where the fair share for each country n is a function of the given climate CO2 per capita in 2050, starting from its initial projected level in 2020. boundary, b, and the cumulative analysis period, tstart:end. In our case, we Although this per capita approach reduces global emissions by analysed three climate boundaries (b = 350 ppm, 1.5 °C and 2 °C) and 97% over the 31-year period, we note that it allows 0.9 GtCO2 emissions three analysis periods with distinct starting years that each ended in in 2050 due to the asymptotic nature of the exponential function 2050 (tstart = 1850, 1960 and 1992; tend = 2050). combined with a global population of ~9.4 billion people, which would On the basis of the available parameter combinations, we cal- need additional carbon dioxide removal technologies to truly achieve culated a total of eight separate fair-share values for each country net zero. We have chosen this formula for transparency and simplicity using the preceding equation. Overall, our approach is underpinned (we use the same method for all countries), but we acknowledge that by the view that all people hold a right to an equitable and fair use of country-specific mitigation pathways can be derived in many ways, the atmospheric commons. It is motivated by our specific research ideally considering respective national needs and capabilities. See question, which asks whether the level of cumulative overshoot Extended Data Fig. 1 for country-specific mitigation rates, which range beyond a country’s fair share of global carbon budgets could serve from 17–20% per year in the highest-emitting countries, such as Qatar as the basis for making climate reparations to others who are unable and the United States, to 0–3% per year in the lowest-emitting countries to make full use of their own fair shares in a net-zero world. Notably, of sub-Saharan Africa, such as Malawi and Somalia. national fair shares may change depending on the analysis period, Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 as population shares can change with respect to the global popula- cumulative overshoot of 1.5 °C fair shares for each analysis period in a tion over time. world that achieves net zero between 2020 and 2050. We then distributed the monetary overshoot debt from each over- Comparing cumulative emissions with respect to fair shares shooting country to each undershooting country as a credit, or We present cumulative emissions with respect to fair shares of global undershootcreditj carbon budgets in two ways. In the first case, we follow a normalization procedure similar to that employed by ref. 12, which involves dividing ik cumulativeundershootj,t=2050 = ∑ (overshootdebti × ( )) national cumulative emissions values by a given fair-share value on i1 cumulativeundershoottotal,t=2050 an annual basis. More specifically, all the cumulative emissions and fair-shares data for a given country, climate boundary and year were where the sum of the overshoot debt from each overshooting country normalized for each cumulative analysis period by dividing them by i1, i2, …, ik was distributed to undershooting country j on the basis of the that country’s 1.5 °C fair share, so this fair share is always assigned latter’s share of total undershoot emissions in 2050 in each analysis the value of one. This normalization approach anchors the 1.5 °C fair period under our net-zero scenario. share in absolute terms (it is always one, regardless of the data), which is useful to illustrate and compare cumulative emission pathways with Additional limitations respect to fair shares of multiple budgets across diverse countries and Some additional methodological limitations are worth noting. The regions on an equivalent scale, as shown in Fig. 1 (and Extended Data data used in our analysis include only CO2 emissions and no other Figs. 1 and 2). greenhouse gases; they do not include emissions from land-use change. In the second case, national fair shares of each global carbon Our business-as-usual projections consider time trends, but additional budget were subtracted from countries’ cumulative emission path- variables could be explored to unpack our country-specific trends, such ways on an annual basis to calculate the extent to which these countries as population, affluence and technology63. Notably, the net-zero con- have either overshot or stayed within their fair shares in each analysis vergence scenario we have used here does not account for the principle period, building on the approach described by ref. 9, or of common but differentiated responsibilities in light of respective national capabilities, by which countries with greater means, and with b,s b cumulative over(under)shootn,t = fair sharen,tstart∶end higher cumulative emissions, must decarbonize faster than the rest of b,s the world (and vice versa for countries with lesser means). Although −cumulative emissionsn,t methods that consider respective capabilities are emerging10, often based on an income-based minimum threshold that excludes poorer where cumulative overshoot (or undershoot) for each country n in each countries from mitigation requirements, we have not applied them year t is a function of the given climate boundary b and the given sce- to our analysis for simplicity. It is not clear whether excluding poorer nario pathway s (business as usual or net zero). This approach provides countries from mitigation would be beneficial for them in our frame- a quantification of national responsibility for overshooting fair shares work, given that they would be entitled to additional compensation for of a given climate boundary in absolute terms of each country’s excess achieving net zero by 2050, and these funds could go towards improv- emissions (or undershoot emissions). These values were summed to ing respective capabilities. A useful step for future research could be give total overshoot (or undershoot), and responsibility was defined on to account for country-specific decarbonization trajectories and/or the basis of the proportion of this total held by each country, as shown to account for existing national commitments of varying strengths. in Fig. 2 (and Extended Data Figs. 3 and 4). Reporting summary Compensation from overshooting to undershooting countries Further information on research design is available in the Nature Port- We distributed financial compensation from overshooting countries to folio Reporting Summary linked to this article. undershooting countries (both with respect to 1.5 °C fair shares) using median carbon prices from 2020–2050 derived from the IPCC-AR6 Data availability scenario database29 and each country’s net-zero scenario pathway. Data sources for each indicator are described in the Time-series data We derived median (and interquartile range) marginal abatements subsection of Methods in the manuscript and summarized in Supple- costs of carbon over the 2020–2050 period on the basis of the 73 sce- mentary Table 1. The databases used in the study include (1) population narios in the IPCC-AR6 database that report 5-year values from 2025 data from Gapminder and UN Population Division World Population with a 50% likelihood of limiting warming to 1.5 °C with no or limited Prospects 2019, (2) CO2 emissions data from the PRIMAP-hist database overshoot. Notably, these year-specific carbon prices account for the and the EORA MRIO database, (3) GDP data from the Maddison project expectation of increasing marginal abatement costs over the coming database and the World Bank World Development Indicators data- decades. See Supplementary Table 3 for a summary of the numerical base and (4) carbon price data from the IPCC-AR6 scenarios database. values we used over the 2020–2050 period and Supplementary Infor- The data produced in the analysis are included in the Supplementary mation for additional details. Information spreadsheet accompanying this article. The data are also We used these carbon prices to quantify the climate debt incurred available via an interactive webpage (https://goodlife.leeds.ac.uk/ by overshooting countries’ cumulative excess emissions beyond their atmospheric-appropriation/) that allows users to query the dataset and 1.5 °C fair shares under our net-zero scenario as follows: visualize charts similar to Fig. 1 and Fig. 6 for all countries. overshootdebti Code availability 2050 cumulativeovershooti,t=2050 The data analysis was conducted using R (v.4.0.2). Beyond this base R = ∑ (( ) × carbonpricet ) t=2020 (2050−2020)+1 version, our analysis is dependent on several R packages. We used the tidyverse suite of packages (v.1.3.0) for organizing, manipulating and where each overshooting country i’s cumulative overshoot emissions visualizing the data. We also used the zoo package (v.1.8-8) and the in 2050 were annualized uniformly over the 31-year period and mul- forecast package (v.8.13) for time-series analysis functionality and the tiplied by the respective carbon price in year t. Summing country ggpubr package (v.0.4.0) for additional data visualization functionality. i’s excess emissions valued in monetary terms over the 2020–2050 The source data and custom R code used to generate the analysis are period yielded an estimate of the total overshoot debt incurred by its archived on Zenodo (v.1.0.0) at https://doi.org/10.5281/zenodo.7779453. Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 References 26. Grasso, M. & Heede, R. Time to pay the piper: fossil fuel 1. Steffen, W. et al. 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Structural production layer decomposition: a new method to Publisher’s note Springer Nature remains neutral with measure differences between MRIO databases for footprint regard to jurisdictional claims in published maps and assessments. Econ. Syst. Res. 30, 61–84 (2018). institutional affiliations. 60. Hyndman, R. J. & Khandakar, Y. Automatic time series forecasting: the forecast package for R. J. Stat. Softw. 27, 1–22 (2008). Open Access This article is licensed under a Creative Commons 61. Hyndman, R. J. & Athanasopoulos, G. Forecasting: Principles and Attribution 4.0 International License, which permits use, sharing, Practice (OTexts, 2019). adaptation, distribution and reproduction in any medium or format, 62. Friedlingstein, P. et al. Global carbon budget 2021. Earth Syst. Sci. as long as you give appropriate credit to the original author(s) and the Data 14, 1917–2005 (2022). source, provide a link to the Creative Commons license, and indicate 63. York, R., Rosa, E. A. & Dietz, T. STIRPAT, IPAT and ImPACT: analytic if changes were made. The images or other third party material in this tools for unpacking the driving forces of environmental impacts. article are included in the article’s Creative Commons license, unless Ecol. Econ. 46, 351–365 (2003). indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended Acknowledgements use is not permitted by statutory regulation or exceeds the permitted We are grateful to K. Raworth for providing comments on an earlier use, you will need to obtain permission directly from the copyright manuscript. J.H. was supported by the European Research Council holder. To view a copy of this license, visit http://creativecommons.org/ REAL—ERC-2022-SYG reference number 101071647 and the María de licenses/by/4.0/. Maeztu Unit of Excellence (CEX2019–374 000940-M) grant from the Spanish Ministry of Science and Innovation. © The Author(s) 2023 Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Qatar Hong Kong SAR, China Liechtenstein Saudi Arabia United States Iceland United Arab Emirates Singapore Australia Kuwait Canada Brunei Darussalam Norway Luxembourg Korea, Rep. San Marino Finland Kazakhstan Bahrain Austria Netherlands Ireland Belgium Switzerland Germany Oman Japan New Zealand Turkmenistan Israel Russian Federation Bahamas, The Sweden Denmark Andorra Cyprus United Kingdom Slovak Republic Antigua and Barbuda Iran, Islamic Rep. 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Zambia Senegal Tajikistan Cameroon Nepal Benin Myanmar Kenya Afghanistan Mozambique Togo Haiti Guinea Mali Gambia, The Tanzania Liberia Eritrea Niger Burkina Faso Uganda Sierra Leone Madagascar Rwanda Central African Republic Malawi Congo, Dem. Rep. Chad Somalia Burundi −0.20 −0.15 −0.10 −0.05 0.00 Net zero by 2050 mitigation rate (%) Extended Data Fig. 1 | Mitigation rates for country-specific levels of CO2 specific levels of emissions at a constant rate from 2020 levels to 0.1 tonnes emissions to converge to 0.1 tonnes CO2 per capita in all countries over per capita in 2050 using a simple exponential function, as described in Methods the 2020–2050 period. Mitigation rates are calculated by reducing country- (N = 168 plus World). Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Extended Data Fig. 2 | World and regional cumulative emissions with respect to fair shares of global carbon budgets, historical trends (1850–2019) and scenario trends (2020–2050). a, world, b, global South region, and c, global North region. The lines and colours are used as per Fig. 1 in the Main text. Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Extended Data Fig. 3 | World and regional cumulative emissions with respect to fair shares of global carbon budgets, historical trends (1992–2019) and scenario trends (2020–2050). a, world, b, global South region, and c, global North region. The lines and colours are used as per Fig. 1 in the Main text. Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Extended Data Fig. 4 | Cumulative emissions overshoot and undershoot by country group with respect to 1.5 °C fair shares, from 1850 start year. a, historical 1850–2019 period, b, business-as-usual median projection in 2050, and c, net zero scenario in 2050. Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Extended Data Fig. 5 | Cumulative emissions overshoot and undershoot by and c, net zero scenario in 2050. Note that the wedge showing overshoot in country group with respect to 1.5 °C fair shares, from 1992 start year. China under the net zero scenario in 2050 (7 Gt CO2) is very small relative to a, historical 1992–2019 period, b, business-as-usual median projection in 2050, the axis scale, and is not labelled in the figure due to a lack of space. Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Extended Data Fig. 6 | Cumulative compensation due from overshooting the wedge showing cumulative compensation owed by China starting from 1992 country groups to undershooting country groups (relative to 1.5 °C fair ($2 trillion) is very small relative to the axis scale, and is not labelled in the figure shares), based on different historical start years to 2019 and net zero due to a lack of space. scenario from 2020–2050. a, 1992–2050 period, and b, 1850–2050. Note that Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Extended Data Fig. 7 | Average annual compensation by country group calculated from median carbon price values, with error bars calculated from the relative to average GDP by region in 2018, based on the historical period from upper and lower bounds of the interquartile range of carbon prices, derived 1850–2019 and net zero scenario from 2020–2050. a, overemitting country from IPCC-AR6 pathways that limit warming to 1.5 °C with no or limited groups, and b, country groups within fair shares. Annual compensation is overshoot (N = 73). Nature Sustainability Article https://doi.org/10.1038/s41893-023-01130-8 Extended Data Fig. 8 | Average annual compensation by country group is calculated from median carbon price values, with error bars calculated from relative to average GDP by region in 2018, based on the historical period the upper and lower bounds of the interquartile range of carbon prices, from 1992–2019 and net zero scenario from 2020–2050. a, overemitting derived from IPCC-AR6 pathways that limit warming to 1.5 °C with no or country groups, and b, country groups within fair shares. Annual compensation limited overshoot (N = 73). Nature Sustainability nature portfolio | reporting summary Corresponding author(s): Jason Hickel Last updated by author(s): Mar 23, 2029 Reporting Summary Nature Portfolio wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Portfolio policies, see our Editorial Policies and the Editorial Policy Checklist. Statistics For all statistical analyses, confirm that the following items are present in the figure legend, table legend, main text, or Methods section. n/a Confirmed The exact sample size (n) for each experimental group/condition, given as a discrete number and unit of measurement A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedly The statistical test(s) used AND whether they are one- or two-sided Only common tests should be described solely by name; describe more complex techniques in the Methods section. A description of all covariates tested A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals) For null hypothesis testing, the test statistic (e.g. F, t, r) with confidence intervals, effect sizes, degrees of freedom and P value noted Give P values as exact values whenever suitable. For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settings For hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomes Estimates of effect sizes (e.g. Cohen's d, Pearson's r), indicating how they were calculated Our web collection on statistics for biologists contains articles on many of the points above. Software and code Policy information about availability of computer code Data collection Data was collected manually from publicly available online international datasets using Google Chrome. Data analysis The data analysis was conducted using R (v4.0.2). Above and beyond this base R version, our analysis is dependent on several R packages. We used the "tidyverse" suite of packages (v1.3.0) for organising, manipulating, and visualising the data. We also used the "zoo" package (v1.8-8) and the "forecast" package (v8.13) for time series analysis functionality, and the "ggpubr" package (v0.4.0) for additional data visualisation functionality. The source data and custom R code used to generate the analysis are archived on Zenodo (v1.0.0) at https://doi.org/10.5281/ zenodo.7779453. For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors and reviewers. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Portfolio guidelines for submitting code & software for further information. March 2021 1 nature portfolio | reporting summary Data Policy information about availability of data All manuscripts must include a data availability statement. This statement should provide the following information, where applicable: - Accession codes, unique identifiers, or web links for publicly available datasets - A description of any restrictions on data availability - For clinical datasets or third party data, please ensure that the statement adheres to our policy Data sources for each indicator are described in the 'Time-series data' sub-section of Methods in the manuscript and summarised in Supplementary Table 1. The databases used in the study include (i) population data from Gapminder and UN Population Division World Population Prospects 2019, (ii) CO2 emissions data from the PRIMAP-hist database and the EORA MRIO database, (iii) GDP data from the Maddison project database and the World Bank World Development Indicators database, and (iv) carbon price data from the IPCC-AR6 scenarios database. The data produced in the analysis are included in the Supplementary Information spreadsheet accompanying this article. The data are also available via an interactive webpage (https://goodlife.leeds.ac.uk/atmospheric-appropriation/), which allows users to query the dataset and visualise charts similar to Figure 1 and Figure 6 for all countries. Human research participants Policy information about studies involving human research participants and Sex and Gender in Research. Reporting on sex and gender There is no reporting by sex or gender in this study. Population characteristics This study includes reporting by total national population, aggregate national carbon dioxide emissions, and national gross domestic product. The national data were collected from existing datasets that are publicly available. National populations were categorised into global North and global South groups using the same protocol employed by Hickel et al. (2022) "National responsibility for ecological breakdown: a fair-shares assessment of resource use, 1970–2017", which is based on a core-periphery understanding of the global capitalist economic system as proposed by theories of underdevelopment, such as dependency theory and world systems theory. In general, the global North here refers to the United States, Europe, Canada, Australia, New Zealand, Japan, and Israel, while the global South refers to the rest of Asia, Africa, and the Americas. The specific categorisation of each country included in the study is defined in the Supplementary Information spreadsheet. Recruitment There were no participants recruited for this study. Ethics oversight This study uses publicly available secondary data from existing datasets, and therefore does not require formal ethics oversight. Note that full information on the approval of the study protocol must also be provided in the manuscript. Field-specific reporting Please select the one below that is the best fit for your research. If you are not sure, read the appropriate sections before making your selection. Life sciences Behavioural & social sciences Ecological, evolutionary & environmental sciences For a reference copy of the document with all sections, see nature.com/documents/nr-reporting-summary-flat.pdf Behavioural & social sciences study design All studies must disclose on these points even when the disclosure is negative. Study description This study includes a (desk-based) quantitative time series analysis of national carbon emissions relative to population-based fair shares, using secondary data obtained from publicly available international datasets. Research sample The national-level research sample (N = 168) was collected from existing datasets and it includes as many countries in the world as possible, given the availability of comparable time series data starting from 1850 for carbon dioxide emissions and total population. There is no reporting by demographic characteristics in this study (e.g. age, sex, etc.) All the existing dataset sources used in this March 2021 study are described in Methods and summarised in Supplementary Table 1. Sampling strategy Given the finite number of countries in the world, the cross-country sampling strategy for this study followed a non-probability purposive sampling procedure aiming to include as many countries as the availability of internationally comparable quantitative time- series data would allow. No within-country sample size calculation was performed in order to project the dynamic statistical "business-as-usual" trends to 2050 for CO2 emissions for each country, based on historical data between 1960 and 2019. According to Hyndman and Athanasopoulos' (2019) "Forecasting: Principles and Practice", rules-of-thumb minimum sample sizes for various time series models are unsubstantiated in theory and practice -- minimum sample sizes for time series forecasts will depend on the number of parameters to be estimated and the amount of randomness in the data. We followed these authors' suggestion that choosing the model with the minimum AICc value is the best approach for relatively short time series, like our 60-year period, 2 because it allows both the number of parameters and the amount of noise to be taken into account (see Methods for a full description of our estimation procedure). nature portfolio | reporting summary Data collection National data were collected from secondary sources provided by international datasets publicly available to download as spreadsheets (.csv or .xslx file formats). There were no participants involved in the desk-based study and the researchers were not blinded to the study hypothesis. The data sources and time series used for each indicator are described in Methods and summarised in Supplementary Table 1. Timing The data used in our analysis were collected online from publicly available sources during the first half of 2022, and the overall time series start date (1850) and stop date (2019) were determined by the earliest and most recent years of comparable data available with near-global country coverage at the time of data collection. Notably, although more recent territorial-based CO2 emissions were available for 2020, there is a 1-year lag on reliable consumption-based carbon dioxide emissions estimates for a large number of countries. However, we considered this lag acceptable for our purposes as consumption-based estimates that account for international trade are widely recognised to better reflect responsibility for environmental burdens than territorial estimates. Data exclusions We excluded 42 countries due to wholly missing observations in at least one of the carbon dioxide emissions and population indicator series, often countries with very small populations (N = 33), or due to very poorly modelled consumption-based CO2 emissions series estimated by the Eora MRIO compared to territorial values, which we detected using statistical outlier tests and box plots (N = 9). In addition, we also removed several within-country negative values in the consumption-based emissions data, and adopted a protocol developed by Fanning et al. (2022) "The social shortfall and ecological overshoot of nations" to test for within- country extreme statistical outlier spikes and troughs relative to the territorial emissions data (defined as 4 times beyond the interquartile range), interpolating linearly to fill the missing values in both cases. Non-participation The analysis uses national-level data; no participants were recruited to take part in this study. Randomization The analysis uses national-level data; there was no recruitment of participants for allocation into experimental groups. Randomization was not relevant because the study does not allocate countries into experimental control and treatment groups. Reporting for specific materials, systems and methods We require information from authors about some types of materials, experimental systems and methods used in many studies. Here, indicate whether each material, system or method listed is relevant to your study. If you are not sure if a list item applies to your research, read the appropriate section before selecting a response. Materials & experimental systems Methods n/a Involved in the study n/a Involved in the study Antibodies ChIP-seq Eukaryotic cell lines Flow cytometry Palaeontology and archaeology MRI-based neuroimaging Animals and other organisms Clinical data Dual use research of concern March 2021 3