of a population threshold. As with the OECD algorithm for identifying FUAs, the AI typically relies on gridded population data as input.<sup>20</sup> To see more formally how the AI measures a country’s level of urbanization, let � index a cell in a population grid for that country, and �� and �� the population and population density respectively associated with that cell. Furthermore, let ��1, ... , � index a settlement point within the country that has an associated population of ��, where �� ��<sup>�</sup> and �<sup>�</sup> denotes the threshold population level that defines a “sizeable” settlement. Given this, associated with each of these � settlement points there will be an agglomeration �� and grid cell � will be classified as belonging to agglomeration � _iff_ �� ��<sup>�</sup> and ��� ��<sup>�</sup> , where �<sup>�</sup> is a threshold population density level, ��,� is the estimated travel time from grid cell _i_ to the settlement point _j_ , and �<sup>�</sup> is a threshold travel time level.<sup>21</sup> Based on this, a country’s level of urbanization, as measured by the share of its population living in urban areas, is given by: From this, it is clear that there are three key thresholds to which values need to be assigned in the implementation of the AI methodology: namely, �<sup>�</sup> , �<sup>�</sup> , and �<sup>�</sup> . Following Uchida and Nelson (2010) and World Bank (2008), it has become standard to set �<sup>�</sup> �50,000, �<sup>�</sup> �150 people per km<sup>2</sup> , and �<sup>�</sup> �60 minutes.<sup>22</sup> In other words, an area is defined as urban if it has a population density of at least 150 people per km<sup>2</sup> and falls within a 60 minute travel time radius of a settlement which itself has a population of at least 50,000. A country’s level of urbanization is then given by the sum of the population living within all such areas.

# 2.2.2. The cluster method

In contrast to the AI, the cluster method adopts a more spatio-demographic approach to the consistent cross-country measurement of urbanization. In doing so, it follows a long tradition of using population size and density thresholds to define urban areas. As noted above, over a hundred countries use population size to define urban areas, while 11 use population density. The US Census Bureau began using population size, population density, and contiguity criteria to standardize the definition of metropolitan areas as far back as the early 20th century (Berry, Goheen and Goldstein, 1969).

More specifically, the cluster method classifies cells in a population grid according to density, and then groups them into “urban clusters.” Again using the notation �� to denote the population of a grid cell and �� its population density, a grid cell � is classified as belonging to an urban cluster �

> 20 Although, as demonstrated by Day _et al._ (2017) for Sri Lanka, the approach can also be feasibly implemented using polygon data which correspond to sub-national administrative units.

> 21 In principle, the areas of two or more different agglomerations can overlap so that, in effect, they merge into a single agglomeration that contains multiple settlement points.  In this case, the number of “merged” agglomerations will be less than _J_ .  To avoid double-counting pixels, population should then be summed over the number of merged agglomerations to arrive at an estimate of the national urban share of the population.

> 22 Uchida and Nelson (2010) also report results from other combinations of assumed values for the three thresholds.

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