The remainder of our paper is structured as follows. Section 2 describes the four approaches for delineating metropolitan areas that we compare in this paper. Section 3 presents our application of these approaches to Indonesia. We document the data that we use to implement these approaches and present a basic descriptive comparison of Indonesia’s urban landscape generated by the different approaches. Section 4 then takes the definitions of metro areas from Section 3 to see whether the choice of definition makes a difference for the estimated strength of agglomeration economies. Section 5 concludes.

# **2. Approaches to defining metro areas**

The four approaches to defining metro areas that we compare in this paper are:

# **_Approach #1: Local labor market approach – Duranton (2015b) algorithm_**

This approach identifies a metropolitan area as an integrated local labor market. All else equal in terms of data availability, such a functional approach to defining a city is typically preferred by economists. Duranton’s (2015b) algorithm holds the advantage over other algorithms that similarly seek to delineate metro areas based on their functional areas in that it does not require the predefinition of metro cores nor the use of additional criteria beyond the specification of a simple commuting flow threshold (Duranton, 2015b). The algorithm is a simple iterative algorithm which uses sub-national administrative units (in our case, Indonesian districts) to “grow” metro areas through successive aggregation.

In the first round of running the algorithm, a district A will be aggregated to a second district, B, if the share of workers that live in A and commute daily for work to B is above a given threshold, T<sup>�</sup> . In the second round, the algorithm will then aggregate a third district, C, to the union of A and B, if the share of workers that live in C and commute daily to the spatial unit A + B exceeds T<sup>�</sup> , even though it may not have been possible to aggregate C to either A or B directly in round one. The algorithm then continues to run until no districts remain to be aggregated given the commuting flow threshold.<sup>8</sup> Based on his own application of the algorithm to Colombian municipalities, Duranton (2015b) notes that, given the gravitational nature of commuting, the algorithm’s preferred threshold for any application is likely to be decreasing in the sizes of the underlying subnational units being aggregated into metropolitan areas.

# **_Approach #2: The Agglomeration Index (AI)_**

The Agglomeration Index (AI) was originally developed by Uchida and Nelson (2009) for the World Bank’s 2009 World Development Report (WDR) on “Reshaping Economic Geography” and, since then, has been further applied in other World Bank reports, including in World Bank – IMF (2013) and Ellis and Roberts (2016). The AI was designed by Uchida and Nelson for global application. Given the absence of O-D commuting flow data for many countries – especially developing countries – it instead relies on estimated travel times to a set of pre-defined cores to

> 8 Prior to aggregating a given origin district to a given destination district, the algorithm checks that in cases where a district could be aggregated to several destinations, it is, in fact, uniquely added to the one to which it sends the greatest number of workers. When commuting flows between two districts are above the threshold in both directions, the algorithm also ensures that the smaller district is aggregated to the larger (see, Duranton, 2015b, p 184).

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