# **5. Conclusion**

While a variety of approaches have been developed in the literature for the delineation of metro areas, there has been little effort to compare these approaches and to assess how the choice of approach affects key empirical insights on the forces that determine the productivity and growth of urban areas. In this paper, we have attempted to fill this gap by focusing on Indonesia. Because Indonesia has a national labor force survey from which an origin – destination commuting flow matrix can be derived, this allows the implementation of an algorithm attributable to Duranton (2015b) that allows for the delineation of metro areas based on these flows. Such an algorithm represents an example of what most economists would consider a “first best” approach to defining metro areas. We compare results obtained from Duranton’s algorithm with those obtained using other prominent “satellite-data based” approaches that have been developed for delineating metro areas in the absence of commuting flow data. These approaches are the Agglomeration Index, the cluster algorithm, and the thresholding of nighttime lights data.

Overall, we find that definition matters. This is true both in terms of the basic description of Indonesia’s urban landscape that the adoption of a given definition gives rise to and the estimated size of the agglomeration wage premium. A defining feature of Duranton’s algorithm using commuting flow thresholds of 10 percent and 7 percent is that it generates a relatively large number of metro areas, each of which is typically comprised of a small number of districts. The other “satellite-data based” approaches tend to generate much smaller numbers of much larger metro areas. Given the country’s high average population density, both the Agglomeration Index and the cluster algorithm with the urban cluster set of thresholds even produce results that look implausible for Indonesia. The cluster algorithm with the high-density cluster set of thresholds and the nighttime lights approach with a threshold set at the 80<sup>th</sup> percentile of the distribution of luminosity values produce descriptions that look more reasonable, but which, nevertheless, differ significantly from those generated by algorithm based on O-D commuting flows. Similarly, the estimated agglomeration wage premium, while always positive, sizeable and significant, varies substantially with the exact approach used to define metro areas. This is especially true when estimating this premium based on districts belonging to the metro areas defined by the different algorithms only.

If a commuting flow–based approach to delineating metro areas is indeed to be preferred, one important implication of our findings is that one should not necessarily assume that, in the absence of commuting flow data, alternative approaches to defining metro areas should be preferred over the simple use of sub-national administrative units as defined by national statistical offices. Hence, the biases that result from choosing the “wrong” approach to delineating metro areas may well be worse than those associated with the simple use of sub-national admin units in the estimation of the agglomeration wage premium and other key empirical relationships in urban economics.

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