One issue that we face in generating results that can be compared across the different approaches for delineating metro areas is that while Duranton’s algorithm uses sub-national administrative units – in our case, Indonesian districts – as the “building blocks” for metro areas, the remaining approaches rely on much higher resolution gridded data sets. This means that while the outer perimeters of the metro areas defined by Duranton’s algorithm are constrained to follow district boundaries, this is not the case for the metro areas generated by the other approaches. The latter is, in principle, a highly attractive feature of using the AI, cluster algorithm or NTL data to define metro areas. But, importantly, it poses difficulties for any empirical analysis that wishes to use the metro areas based on these approaches as the unit of observation. This is because other data that the researcher might wish to match to these metro areas with will often only be available for subnational administrative areas or, in the case of household and firm survey micro-data, include location identifiers for such areas only, or have been obtained using a random sampling strategy stratified at the level of sub-national administrative areas. This is also the case for Indonesia.

Given the above, we need to map the urban extents generated by the AI, cluster algorithm and NTL approach to (aggregations of) Indonesian districts. We do this by always applying the same basic rule: we associate two or more districts with a single urban extent if at least 50 percent of the district’s population belongs to that urban extent. In this way, we construct approximations of the “true” urban extents implied by a given approach through the aggregation of districts.<sup>17</sup> Analogous to Duranton’s algorithm, we only consider a given urban extent generated by each of the AI, cluster algorithm and NTL approach to represent a metro area if that extent maps to two or more districts. This implies, for example, that where an urban extent is smaller in area than a district, we do not consider this to be a metropolitan area.<sup>18</sup> The Indonesian districts in our analysis are defined by their official 2013 boundaries. On average, such districts are large. The median area of an Indonesian district in our data is 1,943 km<sup>2</sup> with a range that goes from a minimum of 9.6 km<sup>2</sup> to a maximum of 44,177 km<sup>2</sup> . However, 76.4 percent of Indonesia’s urban population in 2014 lived in districts of below median area, while 53 percent lived in districts of area less than 1,000 km<sup>2</sup> . As shown in Figure 1 in Section 3.3 below, despite the large average size of Indonesian districts, the maps of metro areas generated using the different approaches appear to map very well to districts.

> 17 We have experimented with the sensitivity of our results to the 50 percent threshold by increasing it, in steps of 5 percentage points, up to 80 percent. As one might expect, increasing the threshold tends to primarily lead to excluding an increasing number of districts on the peripheries of the identified metro areas such that they become composed of fewer districts. This is particularly the case for the AI, the cluster algorithm with the urban cluster set of thresholds, and the NTL approach with a low luminosity threshold for identifying metro areas. The number of identified multidistrict metro areas itself also falls when increasing the threshold but to a lesser extent (and may even go up when using a higher threshold “breaks” a metro area identified using a lower threshold in two. Figure A1 in the Appendix illustrates this for the AI, HDC, UC and two NTL based approaches to define metro areas. Importantly, using a higher threshold does not, qualitatively, affect any of our main findings in the next Sections. See e.g. Table A10 in the Appendix.

> 18 This does not mean that we completely discard all districts that are home to urban extents that are wholly contained within their boundaries. We do include such “single-district urban areas” in our regressions that estimate the agglomeration wage premium (see Section 4 for more detail).

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