11 and 13).<sup>36</sup> Consistent with this, when we estimate Zipf’s law for the populations of centers for cities with multiple centers, we find an estimated Zipf coefficient that is, on average across cities and countries, negative (row 14), with even lower absolute values than those presented above for cities. By contrast, the estimated elasticity of the number of centers with respect to a city’s population is, on average across cities and countries, positive (row 15), although these estimates, as with the estimated Zipf coefficients, need to be treated with care given that most cities only have a single center.

# **6. Comparison with Degree of Urbanization**

Our analysis so far has relied on the dartboard approach to both identify and delineate urban areas for SSA countries. However, there are other approaches to urban area identification and delineation. One of these is the “degree of urbanization” approach of Dijkstra and Poelman (2014) and Dijkstra et al. (2021). While, compared to the dartboard approach, this approach has the shortcoming of being more reliant on arbitrary thresholds to identify and delineate urban areas, it is, nevertheless, an approach that has been widely applied both in academic papers (see, for example, Henderson et al. 2019) and policy reports by international agencies, including by the World Bank (Ferreyra and Roberts 2018; Lall et al. 2021; Mukim and Roberts 2023). Given this, in this section we provide a brief comparison of our results from the dartboard approach with those obtained from the alternative use of the degree of urbanization. In doing so, we focus, for brevity, on results for differences in levels of urbanization across countries.

The degree of urbanization defines an urban area as a contiguous set of 1 km<sup>2</sup> gridded population cells in which each cell has a population density of at least 300 people per km<sup>2</sup> and the overall population of the set of cells is at least 5,000. As such, unlike the dartboard approach, which is a relative approach, the degree of urbanization is an absolute approach to urban area identification and delineation.<sup>37</sup> It will also be noted that the use of a 1 km<sup>2</sup> gridded population layer is part of the definition of the degree of urbanization. In applying the degree of urbanization, we therefore aggregate the constrained WorldPop data to this resolution rather than the 250 m*250 m resolution that we use for the dartboard approach.

**Figure 2: Correlation with official urban population shares across 46 SSA countries – dartboard approach and degree of urbanization**

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**Note:** In each graph, the x-axis shows the share of a country’s population that lived in officially defined urban areas in 2015 based on data from the United Nations World Urbanization Prospects: 2018 Revision database (https://population.un.org/wup/). The y-axis in part (a) shows a country’s urbanization rate based on the dartboard approach, while the y-axis in part (b) shows a country’s urbanization rate based on the degree of urbanization. Results exclude São Tomé Príncipe.

As Figure 2 shows, as with the dartboard approach, estimates of urbanization rates – i.e., of the share of a country’s population that is urban – derived from the degree of urbanization tend to be higher than urbanization rates based on official national definitions of urban areas. Therefore, according to both

> 36 Consistent with this, the shares of population and area accounted for by all centers within a city are, on average across countries, not much higher than the shares accounted for by a city’s largest center (results available on request). 37 A related difference between the two approaches is that our application of the dartboard approach takes account of the presence of significant desert areas, which the degree of urbanization does not. Hence, the dartboard approach identifies urban grid cells based on their density _relative to the density of all cells within a country that are potentially habitable_ , where the potentially habitable areas exclude deserts.

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