7 Finally, log(city GDP) / log (city pop.) is our income measure instead of log (city GDP / city pop.). We believe that the latter measure does not properly capture city incomes due to non-linearities in the relation between lights and population (see Appendix Section C3. below).

Appendix Figure C.3 shows a positive volume-income relation. For a given income level, there is more variation across cities than across countries. For example, volume per capita dramatically varies across U.S. cities despite them having similar incomes when compared to other world cities (e.g., 311m<sup>3</sup> per resident in New York vs. 569 in Dallas).

Note that this analysis indirectly controls for the effect of city population size. In the U.S., city incomes and sizes strongly correlate (Appendix Fig. C.5). That is also true globally conditional on country indicator variables (see Appendix Section C4. below). Indeed, within the same economy, higher-wage cities attract workers. Conversely, larger cities are denser, which generates productivity-enhancing agglomeration economies (Combes and Gobillon, 2015).

Based on the same analysis as at the country level, heights explain between two thirds and three fourths of the volume-income relation (vs. 65% at the country level) (Appx. Section C5. and Appx. Fig. C.4-C.6). Low-rises and high-rises account for 88% and 12% of the heights-income relation, hence 65% and 10% of the volume-income relation (25% for areas). At the country level and including rural areas, we found 60% for high-rises, 5% for low-rises, and 35% for areas.

**C3. City per capita income measure** To study how city stocks vary with respect to income, we use the 2015 city GDP data from Chen et al. (2022). More precisely, they provide high-resolution “real GDP” data (in 2017 dollars) based on (not top-coded) night lights data as reported by the NPP/VIIRS satellite series. While night lights data could capture infrastructure (including electrification) and past economic development in addition to current economic development as infrastructure and urban structures are durable, we use this data in the absence of better data on city incomes for the whole world. To obtain a measure of city GDP, we rely on the total sum of lights within each city’s boundary as defined by GHS-UCDB (Florczyk et al., 2019). Finally, we use log(city GDP) / log (city pop.) as our city per capita income measure instead of log (city GDP / city pop.).

Indeed, the latter measure does not, in our view, properly capture city incomes due to nonlinearities in the relationship between lights and population. As shown for 324 U.S. metro areas in Appendix Figure C.5, log (city GDP / city pop.) decreases with city population size for larger cities, for example due to street lighting being a non-rivalrous good. Indeed, the use of street lighting by some individuals does not diminish its availability to other individuals. As such, the number of street lights per capita should increase less than proportionally with respect to population. There could be of course other reasons. In contrast and as can be seen in Appendix Figure C.5, log (city GDP) / log(city pop.) increases (slightly concavely) with city size.

# **C4. Relation between city per capita income and city population size**

As shown in Appendix Figure C.5 for 324 U.S. metro areas, city per capita incomes and city population sizes are very strongly correlated (correlation about 0.9 and R-squared of 0.90). That is also the case in large countries with many cities, for example China and India (not shown).