# **3.2 The Construction of a Core-Periphery Typology**

This section describes the construction of a typology that we use to interpret changes in nighttime light emissions, so that we may estimate changes in economic activity within and across urban agglomerations. Our objective is to use a methodology that is easily interpretable and able to delineate urban agglomerations and their respective peripheries.

A traditional core-periphery model used by economists (e.g., Krugman (1991)) assumes a monocentric urban core and a surrounding periphery. However, urban agglomerations are often polycentric (e.g., Kloosterman and Musterd (2001)) with a given agglomeration able to benefit from the sizes of nearby agglomerations (e.g., Burger et al. (2015)). Further, the use of existing district boundaries to delineate urban areas suffers from two additional problems. First, as Fotheringham and Wong (1991) have shown, the modifiable areal unit problem makes statistical analysis of areal data dependent on the particular boundaries used. Second, urban boundaries are not consistent with administrative boundaries.

To our knowledge there is no standard method that is used to construct polycentric agglomerations. We employ the following two steps that combine the GHSL data and a clustering methodology to delineate urban agglomerations that are polycentric. First, starting with the individual raster pixels identified as being high-density (i.e., urban) by the GHSL for 2000, we construct a distance matrix, where the distance is computed using the cosine formula (to account for the Earth’s curvature). While the GHSL data is available every 5 years, we use the same typology for the entire 2000-2019 period, so that our results may be more easily interpreted.

Second, we employ hierarchical clustering methodology (Friedman, Hastie, and Tibshirani (2001)) to group the grid cells into urban agglomerations. The single linkage method we employ involves starting with every grid cell being marked as being in its own cluster. It then proceeds sequentially to combine clusters and stops when the nearest neighbor distance between a cluster and any other grid cell is greater than a parameter we define (discussed below). There are two advantages to using this approach. First, this allows the data to determine the number of clusters (i.e., urban agglomerations). Second, the approach and the results are easily interpretable because two different agglomerations are grouped based on a cut-off distance between the nearest neighbors between the groups. This is preferable to other approaches in our context, because agglomerations often cluster along highways or coasts.<sup>21</sup> Therefore, we view the requirement to select a parameter – the distance between the nearest neighbor grid cells across clusters — as a strength which allows us to make the analysis more interpretable. We chose 50 km., motivated by the idea that this distance corresponds to a relatively accessible commute, but one may imagine other choices. For Türkiye, a 25 km cut-off

> 21 In other contexts, compactness of clusters is desirable (e.g., Friedman, Hastie, and Tibshirani (2001)), and the possibility of forming a chain is seen as a weakness. But chains are useful in our context (i.e., we allow for urban corridors).

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