8 Globally, conditional on country indicator variables capturing country-specific factors, we also find that this is the case (correlation about 0.7 and adjusted R-squared of 0.83). Note that we consider 12,516 world (GHS-UCBD) cities in 168 countries for this analysis.

## **C5. Decomposing built-up volumes at the city level**

The higher levels of volume per capita in richer/larger cities are driven by both larger areas and taller buildings in them. To obtain their respective contributions to total volumes, we rely on equation (C4.1) and use simple econometric regressions where the dependent variable is the unlogged per capita volume variable considered and the variable of interest is the per capita income measure based on night lights in 2015 (N = 12,516 world cities).

Total Volume = outward volume (area) + upward volume (heights) (C4.1) We obtain the following slopes for total volume, outward volume and upward volume: 444***, 152*** and 292***, respectively (*** implies significance at 1%). Using country populations as weights, we get 283***, 74*** and 209***, respectively. The implication of these results is that heights contribute to between two thirds and three fourths of the volume-income relation.

We then obtain the following slopes for upward volumes based on low-rises or high-rises: 281*** (184*** with population weights) and 12*** (25***), respectively. Giving more weight to larger cities since they account for most of the world’s urban population, low-rises and highrises respectively account for 88% and 12% of the heights-income relation, hence 65% and 10% of the volume-income relation (25% for areas). In contrast, at the country level and including rural areas, we found 60% for high-rises, 5% for low-rises, and 35% for areas.

**C6. Classifying regions into 4 groups for primate & secondary cities & rural areas**

For each subregion, Appx. Fig. C.7-C.9 show the (locality) population-weighted average residuals when only considering large cities (defined as cities in the top 15 of each country), small and medium-sized cities (cities not in the top 15 of each country) or rural areas & towns (localities _<_ 50,000 c. 2015). Comparing the three figures, one can see how some regions exhibit similar patterns for each type of locality. The coefficient of correlation between the pro-height residuals based on large cities and the same residuals but based on small and medium-sized cities or rural areas & towns is _∼_ 0.7-0.9. Correlation is less high but still positive, at _∼_ 0.45-0.6, for the pro-highrises residuals. Thus, regions tend to be similarly “specialised” across all localities.

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