Dividing countries into five bins based on per capita GDP (from $0-$2,000 to _>_ $8,000, all USD2015) we find that within every bin the range of correlations spans strongly negative to strongly positive (Figure SI-3a) suggesting that income alone does not explain the observed patterns. When we group countries based on their primary sources of particulate emission we observe similar patterns. Heterogeneity persists whether the primary source of pollution is the power, transport, industrial, or agricultural sectors (Figure SI-3c). While re-estimating the correlation between wealth and ambient pollution using the measure of PM2 _._ 5 that removes dust and sea salt substantially reduces the number of countries with a negative relationship across all categories, there still do not appear to be clear patterns in the relationship between wealth and anthropogenic pollution across GDP or primary pollution sources (Figure SI-3b & d).

# **SI-1.3 City level heterogeneity**

In seeking to explain the observed heterogeneity across cities we first classify city heterogeneity separately by strength (proxied by statistical significance) and by sign (whether relationship is positive or negative). We do this to account for the possibility that the drivers of these two different measures of heterogeneity may not be the same. For example, cities in which the relationship is weak and positive may be more qualitatively similar to cities with a weak but negative relationship than to cities with a strong positive relationship.

To better understand these dimensions of heterogeneity we focus on understanding three components of cities - the degree of pollution inequality, the degree of wealth inequality, and the proximity of wealthy neighborhoods to high pollution areas. In some cities pollution and wealth vary dramatically across neighborhoods while in other cities both are more uniformly distributed. Among cities with large ranges of wealth and pollution levels, settlement patterns could have resulted in highly different proximities of wealthy neighborhoods to polluted areas. Ultimately, understanding city-level heterogeneity requires understanding why some cities have high levels of variation in pollution while others do not, why there is large variation in wealth levels in some cities and not others, and, in cities with large variation in both wealth and pollution, why settlement patterns have resulted in the wealthy living in relatively higher pollution neighborhoods in some cities and relatively lower pollution neighborhoods in other cities.

We explore several potential answers to these questions.

In the main text we highlight that elevation does appear to be an important determinant in some cities, especially those with substantial changes in elevation within the city limits. This is because pollution is consistently lower at higher elevations. How wealth sorts across the elevation gradient varies by city however. In some, like Santiago, Chile the wealthy live at higher elevations.<sup>2</sup> In others, like Tbilisi, Georgia, the opposite is true. As a result, sometimes cities with a large change in elevation exhibit a positive relationship between wealth and pollution 21