Our approach is threefold: (1) Estimate national contributions to GMST change using a simple emissions-driven climate model; (2) Propagate these GMST changes into country-level temperatures using pattern scaling methods trained on output from coupled climate models; and (3) Calculate the resulting economic damages using empirical temperature-growth relationships.
National contributions to global temperature change in a simple climate model
To simulate the contributions of individual countries to global climate change, we use FaIR in a set of “leave-one-country-out” experiments. We run FaIR from 1850 to 2014 with total historical emissions to represent the historical scenario (Fig. 1a). Then, for each country in the CEDS data (N = 174), we simulate the same historical period with all emissions except those from that country (Fig. 1a). In each of the 174 sets of simulations, we remove a single country’s contributions to fossil fuel and LULCC carbon dioxide, methane, and nitrous oxides; we leave other chemical species, along with solar and volcanic forcing, unchanged. We also run a “natural” simulation where all emissions are fixed at 1861–1880 averages (Smith et al., 2018).
When we use consumption-based emissions, we scale the original CEDS territorial fossil fuel CO2 emissions by the ratio of consumption-to-territorial emissions from GCP. This procedure generates consumption-based emissions data that are internally consistent with the CEDS data, which avoids propagating absolute differences in emissions amounts between GCP and CEDS into our results.
To match our calculations of economic damage from temperature change, which are performed from 1990 to 2014 and from 1960 to 2014, our leave-one-out simulations with FaIR are forced with total historical emissions from 1850 until either 1990 or 1960, at which point the forcing removes a nation’s emissions. A start date of 1990 examines the counterfactual in which countries had phased out fossil fuels once the scientific consensus on climate change became clear; a start date of 1960 examines the counterfactual in which postwar economic development had occurred with renewable energy rather than fossil fuels. Note that global emissions include processes with ambiguous national affiliations, such as international shipping and aviation. We include these emissions in the global total, but CEDS does not assign them to individual nations, so they are never subtracted from that global total. As such, our leave-one-out simulations may not precisely sum to global totals.
Further discussion of the appropriateness of the “leave-one-out” method, explanation of the choice to use total emissions instead of per capita emissions, and details on how we implement the perturbed-parameter FaIR simulations are available in the Supplementary Information.
Propagating national contributions to warming to the country level
To extend the results of our FaIR simulations to the country level, we use a “pattern scaling” approach that relates GMST to country-level temperatures (Mitchell, 2003; Santer, BD et al., 1990; Tebaldi & Arblaster, 2014). We first calculate annual GMST from each model by averaging surface temperature, weighting by the square root of the cosine of latitude. We then take the difference between the historical and natural simulations for each model for both GMST and each country’s annual temperature, and we smooth these differences with an 11-year centered running mean to reduce interannual variability, a method which has been previously used to reduce the influence of internal variability in pattern scaling (Mitchell, 2003). The centered running mean means that the value for 2014 represents the average from 2009 to 2019, inclusive, which is why we splice the historical CMIP6 simulations with the SSP5-8.5 projections to allow this calculation.
We then linearly regress the simulated 1960–2014 country-level temperature change values onto the simulated 1960–2014 GMST change values for each model (Beusch et al., 2020; Mitchell, 2003; Tebaldi & Arblaster, 2014), motivated by the strong linear relationship between GMST change and local temperature change (Seneviratne et al., 2016). Other pattern scaling approaches use a “delta” method that compares epoch differences rather than fitting a regression (Tebaldi & Arblaster, 2014), but the regression method has been found to outperform delta method approaches (Lynch et al., 2017; Mitchell, 2003). This approach yields a regression coefficient for each country that describes its sensitivity to changes in GMST; coefficients range from 0.6 to 0.7 °C in the tropics, indicating slower warming than the global mean, to > 1.5 °C in the poles, indicating faster warming than the global mean and consistent with the classic “Arctic amplification” pattern (Fig. 1b, inset). We perform this regression over the model-simulated 1960–2014 period to maintain consistency in time periods with the rest of the analysis.
We then predict the time evolution of country-level temperatures in each FaIR realization using the FaIR GMST values and the above coefficients, in both the historical and leave-one-out simulations (Fig. 1c). Note that the predicted time series do not contain realistic interannual variability; in the next section, we show how we reference these predicted time series to observed temperatures to impute realistic variability to the counterfactual time series.
Attribution of climate damages to each country
The final step in our analysis is to extend these reconstructed country-level temperature changes into income changes. Here we apply existing methods for empirically estimating the effect of temperature changes on economic growth rates. Our main analysis uses the global nonlinear approach developed by Burke et al. (2015), though we also test several alternative functional forms (Supplementary Information). We apply the regression specification of Burke et al. (2015) to our data, rather than relying on their published parameter estimates, so that each step of our analysis uses the same data and spatiotemporal scale and so that we can easily propagate uncertainty through our analysis. Specifically, we estimate the following model with ordinary least squares:
$${g}_{ct}={\upbeta }_{1}{T}_{ct}+{\upbeta }_{2}{T}_{ct}^{2}+{\uppi }_{1}{P}_{ct}+{\uppi }_{2}{P}_{ct}^{2}+{\upgamma }_{c}+{\upmu }_{t}+{\uptheta }_{c1}t+{\uptheta }_{c2}{t}^{2}+{\upepsilon }_{ct}$$
(1)
In Eq. 1, g denotes GDPpc growth, T denotes population-weighted country-mean annual mean temperature, and P denotes population-weighted country-mean precipitation (annual mean of monthly total rainfall). The country fixed effect γ controls for time-invariant country-specific factors such as geography and the year fixed effect μ controls for common global shocks. θ denotes country-specific linear and quadratic time trends, which account for secular trends in output due to factors such as technological change. To sample uncertainty in the β parameters, we use 250 bootstrap iterations to re-estimate the parameters after resampling with replacement by country, which accounts for autocorrelation in errors within each country (Burke et al., 2018). Our results may differ from the exact parameter values found in Burke et al. (2015) due to different data and a slightly longer period of analysis, but the quadratic relationship between temperature and growth we find is very similar to previous estimates (Fig. 1c).
To calculate the marginal effect of an additional degree in the annual mean temperature (Fig. 1c, inset), we differentiate Eq. 1 with respect to temperature.
$$\frac{\partial {g}_{ct}}{\partial {T}_{ct}}={\upbeta }_{1}+2*{\upbeta }_{2}*{T}_{ct}$$
(2)
We use this temperature-growth relationship to compare observed growth in each country with the counterfactual growth that would have occurred without each other country’s emissions. ∆Thist denotes the historical temperature change from FaIR and ∆Thist−a denotes the temperature change induced by the leave-one-out simulations for country a, with distinct values for each GCM, FaIR realization, country, and year.
For each country, GCM, and FaIR realization, we construct two counterfactual temperature time series:
$$\updelta {T}^{\mathrm{hist}}=T-\Delta {T}^{\mathrm{hist}}$$
(3)
$$\updelta {T}^{a}=T-\left(\Delta {T}^{\mathrm{hist}}-\Delta {T}^{\mathrm{hist}-a}\right)$$
(4)
Here, T refers to observed temperatures, δThist refers to temperatures that would have occurred without any anthropogenic climate change, and δTa refers to temperatures that would have occurred without country a’s emissions. Supplementary Fig. 3 provides a schematic of this calculation. These counterfactual temperatures are referenced to the observed time series to: (1) impute realistic interannual variability to these smooth counterfactual time series; and (2) bias-correct the model output by using differences rather than absolute temperatures.
To calculate the resulting economic damage for each country, year, FaIR realization, GCM, and damage function bootstrap, we first calculate the effect of temperature change on economic growth ∆g using the parameters β1 and β2, where ∆g is positive when countries would have grown faster without climate change:
$$\Delta {g}^{\mathrm{hist}}=\left[{\upbeta }_{1}\left(\updelta {T}^{\mathrm{hist}}\right)+{\upbeta }_{2}{\left(\updelta {T}^{\mathrm{hist}}\right)}^{2}\right]-\left[{\upbeta }_{1}\left(T\right)+{\upbeta }_{2}{\left(T\right)}^{2}\right]$$
(5)
Calculating the change in growth this way subtracts out the non-climate determinants of growth and isolates the change associated with temperature. This difference in growth is then applied to the beginning of the observed GDPpc time series and integrated to calculate a counterfactual GDPpc time series (cGDPhist) for each country, model, FaIR realization, and damage function bootstrap:
$$cGD{P}_{t}^{\mathrm{hist}}=cGD{P}_{t-1}^{\mathrm{hist}}+\left[cGD{P}_{t-1}^{\mathrm{hist}}*\left({g}_{t}+\Delta {g}_{t}^{\mathrm{hist}}\right)\right]$$
(6)
Economic damage D is calculated as the difference between a country’s actual GDPpc time series and this counterfactual time series. GDPpc values are multiplied by population to convert to absolute GDP where appropriate.
We first perform the above calculation using the historical counterfactual time series δThist and the observed time series T, yielding total historical damage Dhist. We then compute the leave-one-out damage value Dhist−a, which refers to the damage done by all emissions other than those of country a, by repeating the counterfactual growth and GDP calculation using δThist and δTa (Supplementary Fig. 3). The economic damage attributable to country a (Da) for each country, year, GCM, FaIR realization, and damage function bootstrap is the difference between these damage values:
$${D}^{a}={D}^{\mathrm{hist}}-{D}^{\mathrm{hist}-a}$$
(7)
Note that Da can take on both negative and positive values, representing economic damages and benefits resulting from country a’s emissions, respectively. Once we determine total dollar effects in individual nations, we aggregate them to total global income changes; where appropriate, we show cumulative attributable damages, which refer to the sum over time of attributable income changes.
One key caveat in our work relates to the emission of anthropogenic aerosols, which have a cooling effect. Based on analysis presented in detail in the Supplementary Information, the varied treatment of aerosols across models does not drive model differences in attributable damages (Supplementary Fig. 4).
Statistical tests of significant national contributions to damages
To determine whether attributable damage for country a is statistically significant, we compare the distributions of damage with (Dhist) and without (Dhist−a) the emissions of country a. For each country and year, we use a Kolmogorov–Smirnov (K-S) test to determine whether these two distributions are statistically distinguishable (Fig. 1d). P-values less than 0.05 are considered significant, indicating that the “with a” and “without a” distributions are not likely drawn from the same underlying distribution. When aggregating total attributable damages, we only aggregate from countries and years that pass this significance test.
We use a K-S test both because it is nonparametric and because it incorporates both the location and shape of the damage distributions, allowing us to leverage our uncertainty quantification analysis. However, repeating our analysis using a Student’s t-test yields similar results, so our results are not sensitive to this choice (Supplementary Fig. 5).
Uncertainty partitioning
Our analysis yields an array Da, which refers to the cumulative effect of country a’s emissions on country c, with uncertainty from the FaIR carbon cycle parameters, the global-to-local pattern scaling, and the empirical temperature-growth parameters. Each type of uncertainty is calculated as the standard deviation of Da across that dimension and the mean of all other dimensions, for example, the standard deviation of Da across all FaIR carbon cycle parameters and the mean across the pattern scaling coefficients and temperature-growth parameters. We split out CMIP6 and CESM1-LE in this calculation to represent global-to-local pattern scaling uncertainty from model structure and internal variability, respectively.
We then follow previous uncertainty partitioning work by calculating additive 95% uncertainty ranges around the mean (Hawkins & Sutton, 2009; Lehner et al., 2020). The component of the 95% range due to carbon cycle uncertainty R, for example, is calculated as:
$$\pm \frac{1.96*R}{F}$$
(8)
where F is calculated as:
$$F=\frac{R+B+MS+IV}{\sqrt{{R}^{2}+{B}^{2}+M{S}^{2}+I{V}^{2}}}$$
(9)
Here B denotes temperature-growth parameter uncertainty (i.e., the standard deviation of the damage estimates across the temperature-growth parameters with the other dimensions held at their mean values), R denotes FaIR carbon cycle uncertainty, MS denotes uncertainty in the pattern scaling from model structure, and IV denotes uncertainty in the pattern scaling from internal variability. The sum of all four sources of uncertainty is shown as the range of the bars in Fig. 2b, c, with the components of total uncertainty colored by type.