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This study consists of a six-scenario protocol run by eight models representing four different theoretical paradigms (methods): detailed process-based IAMs (two models), cost-benefit IAMs (CB-IAMS; two models), CGE models (two models) and one macro-econometric model. The diversity in representing economic processes, in the solution concept and in technological, sectoral and regional resolution, is a primary added value of this modeling exercise, given the very diverse results available in the literature on the economics of decarbonization45,46,47. The representation of economic inequality varies by model type and characteristic: from parametric assumptions such as log-normal consumption in ReMIND, through income and consumption deciles and disaggregated consumption patterns in CGE models, to elasticity-based approaches based on deciles in CB-IAMs (see additional information A for a detailed description of participating models). A dataset collected for this study, which includes housing and transportation energy expenditure by household deciles, is used by several participating models (Supplementary Information B).

Participating IAM

A total of eight state-of-the-art IAMs were used in this study, with a notable focus on adding the distributional consideration of mitigation costs, potential redistribution of carbon revenues, and climate impacts. This section presents the main features of the models used, as well as their main characteristics in terms of modeling inequalities within countries.

Although most models examined have a global focus, regional disaggregation varies. Moreover, when different countries are combined into macro-regions, income distribution becomes a mixture of between- and within-country distributions. Because wage distributions, net consumer prices, income taxes, and transfer arrangements are designed at the country level, the aggregation of income distributions is challenging. In particular, distributional effects within countries could be overshadowed by differences between countries due to economic growth, convergence or potential transfers between countries. Because we wanted to isolate the domestic dimension of climate change and policy here, we chose to focus on individual countries modeled in at least three IAMs, resulting in a set of ten major countries (Brazil, Canada, China, France, India, Japan, Mexico, Russia, South Africa and the United States). All models have a time horizon of at least 2100, except E3ME, which runs until 2050.

Scenario protocol

The scenario protocol includes a reference scenario (Reference) without new climate policy and a scenario compatible with the objectives of the Paris Agreement (Paris), modeled on the basis of a reduction in cumulative CO2 emissions.2 emissions (from 2020 to 2100) of 650 GtCO2consistent with the Paris target of staying well below 2°C (1.5°C with a one-third chance, or 1.7°C with a more than two-thirds chance, according to IPCC Sixth Assessment Group Working Group 1 (AR6 WG1). For robustness, we also investigate a carbon budget of 1,150 GtCO2 consistent with a warming of 2°C.

The carbon budget is achieved using a uniform carbon price for all sectors and countries, without overshooting. The carbon price is also applied to non-CO22 greenhouse gases, if represented in the models. As a result, we do not consider regionally differentiated carbon pricing, nor transfers (implicit or explicit) and carbon allowance trading.48. Therefore, these scenarios serve as benchmarks in the absence of international transfers that could, however, significantly increase redistributive power in developing countries. Although politically unrealistic, this makes it possible to separate distribution within countries from the discussion of transfers between countries, which can interact with redistribution within countries.15.

Orthogonal to the climate policy dimension, the models implemented two redistributive policies on the revenues generated by the carbon price: climate dividends are neutrally recycled within each country or returned to households on an EPC basis. The resulting scenario matrix allows quantification of both the distributive implications of carbon pricing within countries and the effectiveness of offset policies. To isolate the domestic dimension of climate change and policy, we focus on the ten major countries mentioned above that are represented as a whole in at least three models. Finally, we exploit the large model ensemble for the quantification of uncertainty: we quantify an index of model agreement as the proportion of models that agree with respect to the sign of the policy response.

Key scenario details

Reference

This is a counterfactual scenario with relaxed or absent climate policy. Each model is left free to choose a business-as-usual policy or implement the current policy until the year 203049. The default reference scenario of your model (after 2020, no (further) climate policy: this could be a business-as-usual scenario if you do not implement the current policy, or the current policy until 2020 without further reinforcement (preferred).

Paris

Until 2020, fixed to Reference. After 2020, implement a global uniform carbon price, with the time profile set at the discretion of the models (e.g. the Hotelling rule grows at a social discount rate or, if not available, set at 5% per year). Target: peak carbon budget (2020–2100) of 650 GtCO2 for CO2 emissions, including fossil fuels as well as industry and land use. Carbon budgets cannot be exceeded – that is, no net negative emissions are allowed. This design is consistent with the most recent practices in the modeling community49.50. Non-CO2 gases are prices at the same CO2 price using the global warming potential from AR6 WG1 (www.ercevolution.energy/ipcc-sixth-assessment-report/) or, alternatively, the standard global warming potential model if not available.

Paris with EPC

Same as Paris. Now all domestic carbon income is redistributed to households on an EPC basis. Note that in some cases (small) negative emissions can imply negative transfers, resulting in an increase in inequality. We rule this out and set the transfers in these years to zero.

In addition, for robustness we also implemented two scenarios based on CO2 emissions of 1,150 Gt2 carbon budget (Weak Paris). This means that we have a total of five different policy scenarios. Furthermore, we have a series of these five runs without climate effects, and (where models do implement climate effects) also with climate effects, for a total of ten scenarios (Supplementary Figure 2).

An important distinction in measuring inequality is income versus consumption or expenditure inequality. All teams were asked to focus on consumption inequality, where available, because data on expenditure or total consumption inequality is more reliable than income inequality, especially in studies from developing countries. This seems justified when assessing the impact of climate policy, as carbon pricing particularly affects energy and food expenditure. Nevertheless, the impact on factor prices, including wages, may lead to additional consequences for income distribution36.51which are particularly taken into account in the macroeconometric/post-Keynesian and CGE models (E3ME, GEM-E3 and Imaclim).

Postprocessing of climate effects for models without climate effects

In addition to the distributional effects of climate policy, the models also address inequality in climate risks. Although three of the models in this study have their own distributive impact implementations (NICE, RICE50+ and ReMIND), for the other models we apply the impact function at the income decile level as estimated in recent empirical work32. The damage function is based on the degree of warming at country level, taking into account heterogeneity between countries, and implies an income elasticity of damage of 0.6 on average. This damage function suggests that damage is less than proportional to income, indicating modest regressive effects within countries.

We focus on the impact of future temperature changes, controlling for precipitation, on income growth in deciles by estimating the following equations via ordinary least squares:

$$\begin{array}{l}\Delta {y}_{{iqt}}=\Delta {\,y}_{{iqt}-1}+{\beta }_{1}^{q} {\mathrm{{Temp}}}_{{it}}+{\beta }_{2}^{q}{\mathrm{{Temp}}}_{{it}}^{2}\\\ qquad\quad+{\gamma }_{1}^{q}{\mathrm{{Temp}}}_{{it}}\, {y}_{{it}-1}+{\gamma }_{ 2}^{q}{\mathrm{{Temp}}}_{{it}}^{2}\, {y}_{{it}-1}\\\qquad\quad+\pi {{\bf {P}}}_{{it}}^{{\prime } }+{\alpha }_{i}+{\lambda }_{t}+{\vartheta }_{i}t+{\varepsilon } _{{iqt}}\end{array}$$

Where \({y}_{{iqt}}\) is the logarithm of decile income Q = 1, …, 10 in country iper year T ; Temp is the average annual temperature; \({y}_{{it}-1}\) is the log of the country’s GDP per capita i during the sample period; \({{\bf{P)}_{{it}}^{{\prime} }\) is a vector of cumulative annual precipitation variables (linear and quadratic, and respective interactions with them \({y}_{{it}-1}\)regarding temperature); \({\alpha }_{i}\) its country fixed effects; \({\lambda }_{t}\) are usual time fixed effects; \({\vartheta }_{i}\) is a linear time trend per country; And \({\varepsilon }_{{iqt}}\) is an error term assumed to be orthogonal to the temperature dependent on the controls. We thus estimate separate sets of coefficients for each income decile. The damage function is then defined by a change in income at the decile level, specified as

$${\delta }_{{iqt}}={f}_{q}\left({{{\mathrm{Temp}}}}_{{it}},{y}_{{it}- 1}^{{{{impacts}}}}\right)-{f}_{q}\left({{{\mathrm{Temp}}}}_{0},{y}_{{it} -1}^{{{{Reference}}}}\right)$$

Where \({f}_{q}\) is the approximate function defined above, and \({y}_{{it}-1}^{\,s}\) is the GDP per capita in the country i either under the Reference Scenario without climate effects (Reference) or under Reference with effects \((s={{\mathrm{\it has influence}}})\). This specification follows from the above equation, where the climate impacts depend on the country’s GDP, which in turn is also affected by the realized temperature changes over time.

The income of decile Q per year Tso evolves accordingly

$${y}_{{iqt}}=(1+{g}_{{iqt}}+{\delta }_{{iqt}}){y}_{{iqt}-1}$$

Where \({g}_{{iqt}}\) is the counterfactual growth rate without climate effects, which is taken from the submitted GDP and deciles calculated by the different IAMs. To obtain country-level projections of future temperatures given an emissions path, we first calculate the global mean surface temperature anomaly as a function of cumulative emissions.

We convert cumulative emissions to global temperature increase using the estimated transient climate response to cumulative carbon dioxide emissions of 0.44 °C per 1,000 GtCO2. We then downscale the global mean surface temperature to country level following the linear scaling procedure based on the CMIP6 database32 (Supplementary Figure 14).

Reporting overview

More information on study design is available in the Nature Portfolio Reporting Summary linked to this article.

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