Table 1 Alternative interpretations of the three equity principles (responsibility, capability, and equality) as applied in this work, in line with ref. ¹⁰ Table 6.5.

C1- EU implementation (EU-capability)

Corresponds to the 2021 EU policy proposal that puts a cap on the relevance of countries’ per capita GDP differences for the required emission reductions and is derived empirically from the 2021 proposal. The distribution is estimated in a regression based on GDP per capita from 2015–2018 and the previous (2018) ESR distribution (which builds on GDP/capita).

C2- GDP per capita (GDP/cap)

Weighs the relevance of all per capita GDP differences equally in specifying countries’ required emission reductions, increasing or reducing emission allocations based on the deviation from the EU-average GDP per capita. Countries with a higher GDP per capita (in 2019) are allocated a smaller emission budget, i.e., a stricter emission reduction target. For each percent above or below average, reductions are increased (reduced) by an equivalent share.

C3- Government effectiveness (Governance)

Takes into account additional factors which contribute to the ability of countries to reduce emissions using a governance indicator (government effectiveness). Similarly to C2, countries with higher indicator values are allocated a smaller emission budget. The indicator takes into account a number of considerations, from institutional effectiveness to infrastructure, human capital, and policy efficacy.

C4- Renewable growth capacity (RES-cap)

Reflects the ability of countries to reduce emissions via development of renewable energy sources, similar to C3. As countries that have recently (since 2005) more strongly developed their RES capacity are more likely to have the capital, institutional framework, and first-mover advantages to enable further growth in the future, we allocate greater emissions reduction burdens to those countries, and comparatively less reductions to countries with less capacity.

E1- Basic needs

Separates allocation of emission budgets into two stages. States are allocated emissions required to meet the basic needs energy demands of the fraction of the population at risk of poverty to reflect the satisfiers of meeting needs as people typically require, as meeting such needs cannot be directly measured. Second, the remainder of the budget is distributed in an equal-per-capita manner, so that all states are assigned at least enough emissions to reach the basic needs threshold, and then move beyond them.

E2- ES-sector EPC convergence (ES-EPC)

Reflects a convergence to equal-per capita emissions by 2030 (beginning at today’s unequal levels of emissions), based on country emissions in effort-sharing (ES) sectors (i.e., emissions not covered under the Emission Trading System).

E3-Full-EPC convergence (Full-EPC)

Reflects convergence to equal-per capita emissions by 2030 (beginning at today’s unequal level of emissions), based on all sectors’ emissions (sectors in and outside the Emission Trading System).

R1- Historical emissions from 1995 (Hist-emi)

Reflects emissions generation since 1995, when countries were liable to know the impacts of GHG emissions on climate and had the ability to abate. The point of time at which the remaining budget is allocated on an equal-per capita basis is shifted back to 1995. The EU GHG budget for 2020-2030 is extended by EU past emissions 1995-2019. Per capita budgets are allocated to countries as though budgeting began in 1995. The budget already used up by each country in 1995-2019 is subtracted to give the remaining national budgets for 2020-2030.

R2- Inherited benefits of emissions (Benefits)

Incorporates the benefits a country has obtained due to emissions prior to 1995, interpreted as the emissions embodied in national capital stock. Using capital stock estimates, GHG budgets are scaled similarly to R1 above, but based on pre-1995 emissions embodied in each country’s capital stock in 1995.

R3- C-budget

The total emissions budget for the ES sector (calculated by a fictitious linear path from 2020 to 2030) is split among states according to population without any convergence period, thus eliminating any aspect of grandfathering.

R4 - Expansion of renewables (RES expansion)

Reflects the differing change in renewable share from 2005 to 2019 of countries compared to the EU average. Countries with a higher relative change are allocated a larger emission budget, i.e., a more relaxed reduction target. Similar to C2, countries receive more (less) emissions at an equal rate as their increase (decrease) in RES share relative to the EU average.

R5- Cumulative emissions per capita (Budget/cap)

Proposes an alternative method to address historic emissions as compared to R1, by scaling future emission allowances based on differences in historical cumulative emissions per capita. Countries with a higher than EU-average cumulative historic emissions per capita from 1995 to 2019 are assigned higher reduction targets in 2030, and vice versa.