rather save some for investing and savings. There will likely always be some individuals with very low or negative income each year due to a negative capital shock or for other reasons. Yet this may not imply that their consumption falls below any problematic threshold. This poses a challenge for our study because it is not obvious that income poverty can be ended. For that reason, we convert income distributions to consumption distributions by applying the following formula: ln(c m m m )) cc) = llcc(iic<sup>0.93</sup> + 0.68 + 0.26 ∗ln(iic (1) This is derived by exploiting 150 surveys spanning 16 countries where for a given year, there exists both an income aggregate and consumption aggregate in the World Bank’s Poverty and Inequality Platform. For each of these surveys, the distributions are converted to 100 quantiles of matching income-consumption pairs (i.e. the income and consumption level at a particular quantile for a particular country-year). The functional form in equation (1) is chosen as it reflects a scenario where both the consumption and income distributions follow a 3-parameter log normal distribution while allowing for these distributions to differ based on a country’s median income. The fit gives an R<sup>2</sup> of 0.965 and hence highly accurately converts income to consumption distributions. Note that the conversion is not done at the household level, meaning that we do not convert a particular household’s income level to a consumption level. Rather, we convert the 2022 distributions to 1,000 quantiles and convert each of the income quantiles to consumption based on the equation above. More details about the income-consumption conversion are available in the appendix.

For about 50 economies home to less than 2% of the world’s population, we have no prior income or consumption data at all. These tend to be small high-income countries that do not share microdata as well as very closed countries, such as Cuba and the Democratic People’s Republic of Korea. To make the exercise truly global, we impute consumption distributions for these countries by taking the median value of the 1,000 consumption quantiles of their respective World Bank income group and region. For region-income group pairs with fewer than five countries with data, we take the median from the income group for the country with missing data.

Finally, we winsorize the consumption distributions at 50 cents per person per day. Consumption levels below that would reflect a daily caloric intake that likely is impossible to sustain over periods of time, and hence likely reflect measurement error. This winsorization affects 0.4% of the observations. If we do not winsorize consumption, our baseline additional emissions in 2050 relative to 2019 levels for the three poverty lines go from 4.9% to 5.6% ($2.15), from 15.3% to 16.3% ($3.65), and from 45.7% to 47.5% ($6.85). If we winsorize consumption at $1, our results decrease to 3.7%, 13.4%, and 42.5% for the three lines, respectively.

# **1.2 Poverty lines**

We are primarily interested in the greenhouse gases necessary to end extreme poverty, currently measured as falling short of a daily consumption of $2.15 in 2017 purchasing power parity adjusted dollars.<sup>27</sup> This is the international poverty line used for the first target of the Sustainable Development Goals and the poverty line used for the World Bank’s mission goal. It reflects the typical national poverty line of low-income countries. These low-income countries tend to define their national poverty lines as the expenditure necessary to consume about 2,200 calories per day and a small non-food allotment.

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