# **1. Introduction**

Traditionally, except for the United States, for which data on metropolitan statistical areas (MSAs) are readily available, urban economists have relied on data for cities as defined by their administrative boundaries. However, administrative boundaries often fail to adequately delineate the “true” boundaries of a city, leading to cities being, sometimes substantially, _“under-”_ or _“overbounded”_ (administrative boundaries under- or, respectively, overstating the true city area). This issue has been highlighted for developing and developed countries alike, especially in situations where urbanization has been rapid, and cities have been growing quickly in terms of not only population, but also in the land area which they cover (see, for example, Ellis and Roberts, 2016).

In reaction to this, there have been a growing number of attempts in recent years to develop and apply algorithms that enable the better delineation of cities and metropolitan areas. These attempts have been led not just by economists, but also by both geographers and the remote sensing community, in which there is a very long tradition of using satellite imagery to help define a city’s “true” extent (see, for example, Danko, 1992; Elvidge _et al_ ., 1996). Moreover, many of them have been driven by international organizations such as the Development Bank of Latin America (CAF), The European Commission (EC), the Organisation for Economic Co-operation and Development (OECD), and the World Bank. The ambition of these organizations has been to construct consistently defined global data sets of cities to facilitate the uniform measurement of urbanization.<sup>5</sup> While the preferred approach of economists to defining cities and metropolitan areas tends to be rooted in a labor market perspective based on the use of commuting flow data, as with the definition of MSAs in the US, such data is hard to come by for many countries in the world, especially for many developing countries. As such, attempts to define globally consistent data sets of cities based on the “true” extents of these cities have instead relied on either the use of estimated travel times to approximate commuting sheds (World Bank, 2008; Uchida and Nelson, 2009; Ellis and Roberts, 2016); approaches that associate cities with dense clusters of population (Dijkstra and Poelman, 2014; Roberts, 2018b); or approaches that rely on global satellite imagery and which identify cities based on their built-up area or the amount of light they emit at night (Ellis and Roberts, 2016; CAF, 2017).

While, however, much effort has been expended in developing and applying algorithms and approaches for the better delineation of cities and metro areas, little effort has been made to systematically compare these approaches in terms of the results that they yield (e.g., in the number of metro areas identified, or in the populations and areas of those metros).<sup>6</sup> There has likewise been little effort to compare the results of “second best” approaches to defining metro areas – i.e. approaches which rely on global data sets and which proxy or otherwise forego the use of

> 5 The development of global data sets of cities based on their “true” extents has been greatly facilitated by the increased availability of global satellite imagery, both optical and nighttime, and the derivation from this imagery of global data sets of built-up area, including the Global Human Settlement Layer (https://ghsl.jrc.ec.europa.eu/about.php) and the Global Urban Footprint (https://www.dlr.de/eoc/en/desktopdefault.aspx/tabid-9628/16557_read-40454/) built-up area data sets. It has also been facilitated by the development of increasingly accurate globally gridded population data.

> 6 Exceptions are Rozenfield _et al._ (2011) who, for the United States, compare results derived from a population clustering algorithm for identifying cities with cities as defined by their MSAs, and Roberts _et al_ . (2017), who compare the maps associated with three different global approaches to delineating urban areas.

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