Controlling for size, the existence of a positive relationship between a country’s level of GDP per capita and its level of urbanization continues to hold when, instead of using official definitions of urban areas, we define urban areas as cities using the dartboard approach. However, the share of population that lives in cities tends to be significantly _larger_ for more populous SSA countries, the opposite of what we found for official definitions of urban areas. This tendency for more populous SSA countries to have a larger share of their populations living in cities is driven by the extensive margin – i.e., by area rather than by population density. GDP per capita, area and overall average population density alone account for almost half of the variation in the shares of population that live in cities across SSA countries.

For the share of a country’s land area that is occupied by cities, the results are very different. Hence, neither a country’s level of development nor its area is correlated with this share (col. [3]). However, countries that are more densely populated on average tend to have larger shares of their areas dedicated to cities, suggesting that cities are more “sprawling” for these countries, perhaps because of stronger congestion forces that bid-up the price of land and push cities outward. Consistent with this, more densely populated countries also tend to have more densely populated cities, irrespective of whether we control for a country’s level of development (cols. [2] and [3]). Unsurprisingly, countries that are more populous at either the intensive or extensive margins tend to have more cities, although there is no correlation between a country’s level of development and its number of cities. This suggests that, as SSA countries become richer, they also become urbanized not because of the emergence of new cities, but because the existing set of cities become more populous. Consistent with this, both the average population and average area of a country’s cities are significantly positively correlated with its GDP per capita, controlling for country size (col. [3]).

In terms of the size distribution of cities, more developed and geographically smaller SSA countries tend to exhibit higher levels of urban primacy (i.e., have larger shares of their populations living in the largest city) (col. [3]). The positive relationship with GDP per capita, conditional on controlling for a country’s overall size, is consistent with SSA countries being on the upward sloping section of a spatial Kuznets curve in which population concentration at first increases with GDP per capita at low levels of development before starting to decline above some critical level of development. Such a relationship is, in turn, rationalized by the tendency of population and resources to first concentrate in a few cities as countries start to develop before later deconcentrating to secondary and other smaller cities as, _inter alia_ , rising land costs and improved transportation networks incentivize relatively land intensive industries to deconcentrate to smaller cities (World Bank 2009). We also observe that more populous countries tend to have a smaller spread of population sizes across cities, regardless of whether we look at the inter-quartile or inter-decline ratio. There is, however, no correlation between a country’s estimated Zipf coefficient and any of the three country characteristics – average population density, area, or GDP per capita – examined.

# **5. Spatial Concentration within Cities**

Having described patterns of urbanization across SSA countries, at both the aggregate and urban area levels in Sections 3 and 4, we now turn to describe features of the _internal structures_ of cities and how these differ across SSA countries and cities. Given that comprehensive evidence is generally lacking on the internal structures of cities, especially for SSA, this arguably represents the most novel part of our analysis. Tables 6-8 present our results. Tables 6 and 7 provide descriptive evidence on population and built-up density gradients within cities respectively. Meanwhile, Table 8 provides descriptive evidence on the numbers of centers within cities. For brevity, we, again, only focus on cities in this section of the paper. This is because the internal structures of cities are likely to be more complicated than those of towns.<sup>28,29</sup>

**_5.1. City population density gradients_** The first row of Table 6 presents summary statistics for triplets of values for the following three sets of _grid cell level_ regressions, which are estimated separately for each country, pooling all cities within a 2 2 2 country (i.e., the first-row reports e e e ]): RR<sup>2</sup> ee.[4] ee.[5] ee.[6] [RR , RR , RR [4] ii cc(ii) 1ii llRR(D DD ) = αα+ θθ + εε

> 28 Results have also been generated for towns and are available on request.

> 29 Table A4 in the Annex reports results from OLS regressions which examine the correlation, across SSA countries, between average within-city characteristics and country size. We do not focus on these results in the main text because we lack clear theory on these relationships.

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