In this study, we have estimated a quantitative link between cumulative CO 2 emissions and potential socioeconomic impacts resulting from changing extreme weather conditions. As such, we are able to quantify the causal relationship between units of CO 2 that we emit and the effect of increasing heat exposure on labour productivity loss in vulnerable economic sectors based on health recommendations.

In our analysis, we used a simplified version of the WBGT indicator, though our projections of WBGT are similar to those of other studies who have used a more complex version of the indicator [e.g.37,38]. Given that temperature and humidity are the main components of the WBGT that change over time with climate change, the assumption of unchanging (average) solar radiation and wind speed does not have a large influence on our results. Furthermore, as the findings of our study are based on the difference over time relative to pre-industrial conditions (rather than on absolute values at particular points in time), the use of a simplified indicator is a reasonable approximation that nevertheless allows us to produce relevant results.

It is worth noting that we have not applied any bias correction to the climate model data that we have used to calculate the WBGT indicators. Though this approach is consistent with other studies that have quantified the response of different climate variables to cumulative emissions [e.g.9,10,19], we acknowledge that bias correction is a standard approach for impact studies, and that our study is therefore limited as an assessment of the absolute impacts on labour productivity. However, our primary intent is to calculate a socioeconomic impact per additional emission of CO 2 , and we suggest that this calculation has less sensitivity to bias correction as compared to an estimate of the total impact at a given level of climate change. Furthermore, there are several practical reasons why we consider this to be a reasonable approach. First, corrections to both temperature and humidity data can produce results that are physically inconsistent, and can alter the variability of the modelled time series; as a result, we prefer to use the uncorrected data so as to maintain a clean estimate of modelled change per unit of CO 2 emissions. In addition, a full bias correction would also require considering model-specific carbon cycle biases that would need to be corrected to account for differences between simulated and observed historical CO 2 emissions. This is a non-trivial task that has not yet been tackled in the literature.

Another important assumption of our study is that socioeconomic conditions remain static at present-day values. Of course in the real world, socioeconomic conditions continuously evolve over time, and such changes have the potential to either amplify or moderate the economic impacts of climate change. In this sense, our analysis should be interpreted as a “no-adaptation” case, that excludes proactive socioeconomic changes that might decrease the overall impact of increased heat exposure. For example, societies could find ways to adapt to increasing heat exposure by redistributing the workforce within different economic sectors or shifting working hours to seasons or times of day when heat exposure is lower. In a similar manner, we have assumed that the labour output elasticity of all vulnerable sectors is equal to 1, meaning that we assume working hours are lost in direct proportion to elevated heat exposure, and again are not counterbalanced by any short-term adaptation measures [similar to Kjellstrom et al. (2009), Hsiang (2010), Wenz and Levermann (2016)2,39,40]. There are some previous studies that have considered similar hypotheses to ours, but with evolving socioeconomic conditions4,41. These studies estimated an annual loss of 2 to 3% of total GDP at global scale under the RCP8.5 scenario in 2100, which is smaller than our estimates, indicating that there is some potential for adaptation in labour practices to decrease the economic impacts that would be expected without such measures.

A similar caveat applies to the fact that health recommendations are not obligatory and are not always seriously (or consistently) respected at actual work sites. Given this, our estimated loss of GDP is technically what would occur as from worker breaks that are consistent with projected heat exposure, provided that health recommendations are strictly followed [similarly to Takakura et al. (2017)41].

Another point worth noting is that in our analysis of labour productivity loss, spatial differences of climate conditions and distribution of population are not considered within a country, but are rather averaged for each country. Indeed, statistics of workforce, economic sectors and GDP are only available at a country level25. In many cases, this assumption does not have a large bearing on our results: for example, some of the largest countries with uneven population distribution, such as Russia and Canada, are also only marginally affected by productivity loss given their colder climate conditions. Some other large countries such as Brazil and Australia are substantially affected by productivity loss due to the increase in heat exposure, but in these cases the evolution of climate conditions is quite similar over the entire country. The two instances where the effect of within-country population distributions may be important are: (i) countries such as the United States, which span a range of climate changes, have the potential to be sensitive to the distribution of population within the country, though, the changes we find in our study for the United States (Fig. 5) are generally consistent with national estimates found in previous studies42, which gives us some confidence that our results are not overly biased by assuming a uniform population and therefore impact distribution within countries; and (ii) we have not considered the distribution of population among urban vs rural areas within a country. It is possible that impacts on productivity loss might be greater in urban areas than what we have estimated based on average national values. However, it is also the case that access to air conditioning is more common in urban workplaces, where the majority of workers do their job indoors.

Similarly to the labour productivity loss that we assessed, the number of productive days lost per year (i.e. the days for which it is supposed to be physically impossible to work) exhibit a clear link to income classes: the lower the income class, the higher the number of days lost (Supplementary Table S4 and Fig. S10). However, the number of days lost computed for low-income countries is (only) 3 to 4 times higher than for high-income countries (compared to a factor of 9 higher for the labour productivity loss), meaning that the fraction of output generated by vulnerable sectors within a country has an influence on our indicator of productivity loss. Indeed, low-income countries generate 73% of their output in vulnerable sectors, unlike higher-income countries (54, 41 and 30%, respectively of the income class)25. High-income countries might therefore be better adapted to face the increase in heat exposure on workers2.