metadata: authors: 0: author: Bosker,Maarten
1: author: Park,Jane
2: author: Roberts,Mark
count: Indonesia
docna: 0: docna: Definition Matters : Metropolitan Areas and
            Agglomeration Economies in a Large Developing Country
docty: Policy Research Working Paper
subtopic: Railways Transport,Rural Labor Markets,Educational Sciences,Labor Markets
teratopic: Social Protections and Labor,Education,Transport,Rural Development
abstracts: cdata!: A variety of approaches to delineate
            metropolitan areas have been developed. Systematic
            comparisons of these approaches in terms of the urban
            landscape that they generate are however few. This paper
            aims to fill this gap. The paper focuses on Indonesia and
            makes use of the availability of data on commuting flows,
            remotely-sensed nighttime lights, and spatially fine-grained
            population, to construct metropolitan areas using the
            different approaches that have been developed in the
            literature. The analysis finds that the maps and
            characteristics of Indonesia’s urban landscape vary
            substantially, depending on the approach used. Moreover,
            combining information on the metro areas generated by the
            different approaches with detailed micro-data from
            Indonesia's national labor force survey, the paper
            shows that the estimated size of the agglomeration wage
            premium depends nontrivially on the approach used to define
            metropolitan areas.
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repnme: repnme: Definition Matters : Metropolitan Areas and
            Agglomeration Economies in a Large Developing Country
display_title: Definition Matters : Metropolitan
            Areas and Agglomeration Economies in a Large Developing Country
listing_relative_url: /research/2018/11/30595799/definition-matters-metropolitan-areas-agglomeration-economies-large-developing-country
topicv3: Labor Markets m1326488 855,Education m1327048 470,Population, Aging and Health m1327736 640,Jobs m1503931 2670,Urban Rail m1583571 4233
publishtoextweb_dt: 2018-11-07T00:00:00Z
historic_topic: Social Protections and Labor,Education,Transport,Rural Development
no_of_pages: 45
author_keys: 0: author_key: 997692
1: author_key: 1461319
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model_extractions: WPS8641 Policy Research Working Paper 8641

# Definition Matters

Metropolitan Areas and Agglomeration Economies in a Large Developing Country _Maarten Bosker Jane Park Mark Roberts_ Social, Urban, Rural and Resilience Global Practice November 2018
Policy Research Working Paper 8641

# **Abstract**

A variety of approaches to delineate metropolitan areas have been developed. Systematic comparisons of these approaches in terms of the urban landscape that they generate are however few. This paper aims to fill this gap. The paper focuses on Indonesia and makes use of the availability of data on commuting flows, remotely-sensed nighttime lights, and spatially fine-grained population, to construct metropolitan areas using the different approaches that have been developed in the literature. The analysis finds that the maps and characteristics of Indonesia’s urban landscape vary substantially, depending on the approach used. Moreover, combining information on the metro areas generated by the different approaches with detailed micro-data from Indonesia’s national labor force survey, the paper shows that the estimated size of the agglomeration wage premium depends nontrivially on the approach used to define metropolitan areas. .

This paper is a product of the Social, Urban, Rural and Resilience Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at mroberts1@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **_Definition Matters: Metropolitan Areas and Agglomeration Economies in a Large Developing Country_**<sup>**_1_**</sup>

Maarten Bosker<sup>2</sup> , Jane Park<sup>3</sup> , and Mark Roberts<sup>4</sup>

**Key words:** metro areas, urban definitions, agglomeration economies, Indonesia **JEL Codes:** O18, O47, C21

> 1 The authors thank Katie McWilliams, Benjamin Stewart and Andrii Berdnyk for their outstanding GIS support, as well as Brian Blankespoor and Shaun Zhang for supplemental GIS support. They also thank Gilles Duranton for very helpful comments and feedback provided during the preparation of the paper. Financial support from both SECO and DFID is furthermore very gratefully acknowledged.

> 2 Department of Economics, Erasmus University Rotterdam, The Netherlands and CEPR <bosker@ese.eur.nl>

> 3 Social, Urban, Rural and Resilience Global Practice, The World Bank, Washington, DC, USA <jpark16@worldbank.org>

> 4 Social, Urban, Rural and Resilience Global Practice, The World Bank, Washington, DC, USA <mroberts1@worldbank.org> (corresponding author).
# **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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commuting flow data – with the economist’s “first best” approach based on the identification of a city’s functional area using data on origin – destination (O-D) commuting flows. At the same time, while international organizations have developed global maps of consistently defined cities, there has been no effort to explore how the use of these maps to define cities affects key empirical results that are crucial to a proper understanding of the working of urban economies, such as, for example, the estimated strength of agglomeration economies.

Given the above, the aims of this paper are two-fold. First, we compare the results of different algorithms and approaches for delineating metropolitan areas in terms of the basic descriptions they provide of the urban landscape (notably, the number of metro areas, the sub-national administrative units that these areas cover, and their population sizes). And, second, we assess whether the choice of approach to defining metro areas matters when it comes to estimating the strength of agglomeration economies.

More specifically, we compare four different approaches. The first of these requires _O-D commuting flow_ data and adheres to the economist’s preferred approach of defining metro areas as functional local labor markets. Specifically, for this first approach, we make use of an algorithm recently developed by Duranton (2015b). The other three approaches are “second best” approaches which instead rely on global data sets derived, wholly or in part, from satellite imagery. These three approaches are the _Agglomeration Index_ (AI), which was originally developed by Uchida and Nelson (2009) for the World Bank’s 2009 World Development Report on “Reshaping Economic Geography” (World Bank, 2008); a “ _Cluster Algorithm_ ” developed by Dijkstra and Poelman (2014) which associates cities with dense clusters of population; and, finally, the identification and delineation of metro areas based on the “thresholding of _Night-Time Lights_ data _”_ (NTL), similar to, for example, Ellis and Roberts (2016) and CAF (2017). These latter three approaches all have the obvious advantage that they can be applied to any country in the world using readily available data sets, including those countries for which O-D commuting flow data are not available.

In all our empirics, we focus on the case of a single large developing country – Indonesia. Unlike many developing countries, Indonesia has the advantage that its national labor force survey ( _Survei Tenaga Kerja Nasional_ , SAKERNAS) allows for the derivation of an O-D matrix of commuting flows between sub-national areas (districts), which is the crucial input for the application of the Duranton (2015b) algorithm in defining metro areas. Beyond the main focus of this paper, however, Indonesia’s urban landscape is interesting to study in and of itself. Indonesia has, in recent decades, been one of the world’s most rapidly urbanizing countries and, within the country, there is intense policy interest in the issue of how to delineate metropolitan areas (see World Bank, 2018).<sup>7</sup> By focusing on Indonesia, our paper also contributes to the, to date, limited credible empirical evidence on the strength of agglomeration economies in developing countries. This is a knowledge gap that economists such as Overman and Venables (2005), Duranton (2015a), and Glaeser and Henderson (2017) have made recent calls for the profession to fill.

> 7 The Government of Indonesia has itself attempted to identify metropolitan areas. This began in 2008 with Government Regulation 26/2008 (Peraturan Pemerintah/PP) that specified nine multi-district urban areas (“ _kawasan perkotaan yang bersifat lintas wilayah_ ”). A further four multi-district urban areas were added in 2017 through Government Regulation 13/2017.

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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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delineate the extents of metro areas. Cores are pre-defined from a global settlement point layer<sup>9</sup> based on a population threshold. Rather than rely on sub-national administrative units, the AI instead relies on a globally gridded population data set. In such a data set, the underlying units that undergo aggregation are grid cells that are of a uniform geographic size – in practice, 30-arc seconds, which is approximately 1 km<sup>2</sup> at the equator.

Constructing the AI first requires the specification of three thresholds – a minimum population threshold to identify settlement points that qualify as metro cores, a travel time threshold, and a population density threshold. While Uchida and Nelson (2009) experimented with a range of thresholds, the AI has become synonymous with thresholds of 50,000 for the population of the core, 60 minutes for travel time, and 150 people per km<sup>2</sup> for population density. Hence, the AI defines a group of population grid cells as constituting a metro area if each of those grid cells have a population density of at least 150 people per km<sup>2</sup> and fall within a 60-minute travel time radius of a settlement point that has an associated population of at least 50,000. An important feature of the AI is that it, in contrast to the other two “satellite data based” approaches, _does not include a contiguity requirement_ . This means that, in principle, a metro area may not consist of a single contiguous block of grid cells. Another important feature of the AI is that if there are two or more cores that fall within 60 minutes travel time of each other then they, effectively, merge into a single extended metro area.

# **_Approach #3: The cluster algorithm_**

Rather than attempting to delineate a metro area based on its functional area, using either commuting flow data or estimated travel times, Dijkstra and Poelman’s (2014) cluster algorithm simply identifies a metro area as a dense population cluster. The algorithm was originally developed with the European Union in mind, but has since been applied globally and, given the simplicity of its data requirements, is emerging as the preferred algorithm of not only the European Commission, but also of a coalition of international agencies that further includes the Organisation for Economic Co-operation and Development (OECD) and the World Bank. As with the AI, the cluster algorithm relies on a gridded population data set of resolution 30 arc-seconds – i.e. approximately 1 km<sup>2</sup> at the equator – as input. Given these data, it identifies a _spatially contiguous_ set of population grid cells as a metro if each of those grid cells satisfies a population density threshold, T<sup>�</sup> �, and, collectively, the population of the grid cells exceeds a population threshold, T<sup>�</sup> �.

In practice, the cluster algorithm has become associated with two different sets of thresholds. The first set of thresholds is T<sup>�</sup> � = 300 people per km<sup>2</sup> and T<sup>�</sup> � = 5,000 with the resultant areas that are delineated being referred to as _“Urban Clusters”_ (UC). Meanwhile, the second set of thresholds is T<sup>�</sup> � = 1,500 people per km<sup>2</sup> and T<sup>�</sup> � = 50,000 with the areas that result being labelled _“High Density Clusters”_ (HDC) (Dijkstra and Poelman, 2014).

# **_Approach #4: Thresholding of nighttime lights (NTL) data_**

The use of nighttime lights (NTL) data to identify metro areas, and, more generally, urban settlements, originated in the remote sensing literature with early applications including Imhoff _et_

> 9 Namely, CIESIN’s Global Rural – Urban Mapping Project (GRUMP) Settlement Point layer (http://sedac.ciesin.columbia.edu/data/set/grump-v1-settlement-points-rev01).

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_al_ . (1997), Sutton (2003), and Small _et al_ . (2005). More recent applications at either a regional or a global scale include Zhang and Seto (2011), Zhou _et al_ . (2015), Ellis and Roberts (2016), and CAF (2017).

Applications of NTL data to delineate metro areas have invariably relied on data products that have been derived by the National Oceanic and Atmospheric Association (NOAA) from sensors (Optical Line Scanner, or OLS, sensors) on-board the Defense Meteorological Satellite Program (DMSP) constellation of satellites. The derived DMSP-OLS data products cover the entire globe and are available at a resolution of 30 arc-seconds, which is, again, equivalent to approximately 1 km<sup>2</sup> at the equator. One deficiency of DMSP-OLS NTL data, however, is that they suffer from a well-documented “overglow” or “blooming” problem, whereby the light emitted from a given point on the earth is recorded as covering an area that extends beyond that point.<sup>10</sup> This creates a tendency for the lit area of a metro to overstate its “true” extent – for example, the Pacific Ocean can be lit up as far as 50 km from the coastline near Los Angeles (Pinkovskiy, 2013). The most common approach to dealing with this overglow problem has been to threshold the NTL data, considering only pixels in the data that exceed a certain luminosity, or digital number (DN), value as part of the area of a city or metro (see, for example, Imhoff _et al_ ., 1997; Small _et al_ ., 2005; Zhou _et al_ ., 2015; Ellis and Roberts, 2016). A contiguous cluster of grid cells that falls above the applied threshold is then classified as constituting a “metro” area.

More recently, however, DMSP-OLS NTL data have been superseded by NTL data collected from a new satellite sensor, the Visible Infrared Imaging Radiometer Suite (VIIRS) sensor, launched in 2011. This sensor collects NTL data at a far higher resolution than the old DMSP-OLS sensors and the derived data products are also not subject to the overglow problem. We use the new VIIRS satellite data to delineate metro areas. Specifically, we use the 2015 annual composite product which has recently been released by NOAA.<sup>11</sup> This product reports luminosity values, calculated as an annual average over all cloud-free nights in 2015, at a resolution of 15 arc seconds, which is equal to 460 m<sup>2</sup> at the equator. Prior to averaging, NOAA applies filtering techniques to remove data that are affected by stray light, lightning, and lunar illumination. NOAA likewise filters out lights from aurora, fires, boats and other temporary lights. Although the VIIRS NTL data do not suffer from the same overglow problem as the DMSP-OLS NTL data, they, nevertheless, record light emitted to the nighttime sky by all human activities, including light at very low levels outside of what may be considered metro or even urban areas. For this reason, the use of a threshold may still be required to properly delineate metro from non-metro areas. As with papers that have used the DMSP-OLS data for the same purpose, we consider a contiguous cluster of grid cells that falls above any imposed threshold as representing a “metro” area.

# **3. Application to Indonesia**

# _3.1. Data sources_

The data that we use to apply the four approaches to delineating metro areas to Indonesia come from a variety of sources. For Duranton’s algorithm, we use data on O-D commuting flows between Indonesian districts that we derive from the August rounds of Indonesia’s national labor

> 10 See Doll (2008) for a description of the underlying causes of the overglow problem with DMSP-OLS NTL data.

> 11 This product is available for download from: https://ngdc.noaa.gov/eog/viirs/download_dnb_composites.html.

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force survey ( _Survei Tenaga Kerja Nasional,_ SAKERNAS) for the years 2013 – 2015.<sup>12</sup> In doing so, we measure the commuting flow from a given origin district _i_ to a destination district _j_ as the share of workers who live in _i_ but commute daily to work in _j_ , where – following SAKERNAS – workers are defined to include all employed wage workers including casual workers, selfemployed workers, and unpaid family workers, where anyone who worked for at least one hour consecutively in the previous week, including temporary non-workers who normally meet the condition, is considered employed.

Both the AI and the two cluster algorithms require a gridded population data set. We use the _Landscan-2012_ gridded population data set produced by Oak Ridge National Laboratory. This population grid has a resolution of 30 arc-seconds. An earlier version of the same population grid was used by Uchida and Nelson (2009) in their original application of the AI. More generally, the _Landscan_ population grid is the most established global gridded population data set and has been widely used in social scientific research.<sup>13</sup> This includes the paper by Henderson _et al_ . (2018), who use the same _Landscan-2012_ data in identifying urban areas and for constructing measures of population, and economic, density for six African countries. Importantly, Henderson _et al_ . (2018) “ground-truth” the _Landscan_ data, reaching the conclusion that the data do good job in estimating population at a fine spatial scale. The population grid is derived through distributing population data for sub-national administrative units across grid cells using a modeling process that relies on other geo-spatial data sources and high-resolution satellite imagery analysis.<sup>14</sup> In addition to gridded population data, the AI also requires data on estimated travel times. The travel time data originally used by Uchida and Nelson (2009) for the AI were based on “... _estimates of the time required to travel 1 km over different road and off-road surfaces...”_ and were derived from a cost surface that was constructed from a variety of Geographic Information System (GIS) data layers. These layers included data on road and rail networks, navigable rivers and water bodies, travel delays for crossing international borders, roughness of terrain and foot-based travel for off-road and paths.<sup>15</sup> The AI estimates used in this paper are taken from Roberts _et al._ (2017) and based on an updated version of this same cost surface layer from Berg _et al._ (2017). This updated layer is derived from more recent (i.e. _circa_ 2010 versus _circa_ 2000) data on roads, railroads, and land cover.<sup>16</sup> Finally, as already described in Section 2, the NTL data that we use in this paper are VIIRS NTL data taken from NOAA’s 2015 annual composite product.

# _3.2. Mapping to districts_

> 12 Importantly, the sampling strategy of the SAKERNAS August rounds is stratified at the district level for these years. We average the commuting flows over three years, rather than using a single year, to smooth out any temporary measurement error in the survey data.

> 13 Alternative population grids that we could have used are WorldPop (http://www.worldpop.org.uk/) and GHS-Pop

> (http://ghsl.jrc.ec.europa.eu/ghs_pop.php). Roberts _et al._ (2017) compare the level of agreement between maps of urban areas generated using the AI and cluster algorithms with different gridded population products. In general, the level of agreement is fairly high.

> 14 See http://web.ornl.gov/sci/landscan/landscan_documentation.shtml for more information.

> 15 See Appendix Table A.1 in Uchida and Nelson (2009) for more details.

> 16 One important limitation of the resultant travel time estimates is that they do not take account of travel time delays owing to traffic congestion.

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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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# _3.3. Key descriptives of identified metro areas_

Table 1 summarizes key statistics for metro areas delineated by each of the four approaches. For Duranton’s algorithm, we present statistics for commuting flow thresholds between 27 percent – which is when the first metro area appears using this algorithm – and 7 percent. Although we generated results for all commuting flow thresholds between these two values at 0.5 percent intervals, we only show results for selected thresholds. Meanwhile, for the cluster algorithm, we show results based on both the “Urban Cluster” (UC) set of thresholds (i.e. T<sup>�</sup> � = 300 people per km<sup>2</sup> , T<sup>�</sup> � = 5,000) and the “High Density Cluster” (HDC) set of thresholds (T<sup>�</sup> � =1,500 people per km<sup>2</sup> and T<sup>�</sup> � = 50,000). Finally, for the NTL approach, we present selected results based on the thresholding of the lights data at different points in the distribution of luminosity values.<sup>19</sup> In presenting results, we include information not only on the total number of metro areas, but also on the number of metro areas that belong to the official island-region of Java-Bali, which is where the majority of Indonesia’s urban population – approximately 70 percent in 2016 – resides and which, overall, is significantly more urbanized and densely populated than Indonesia’s other island-regions.<sup>20</sup>

**<u>Table 1: Comparison of key statistics</u>**

||<br>**No.**|<br>**No. me**|<br>**tro district**|**s**<br>**P**|**opulatio**|**n**|**Land**|<br>**area**|**Largest Metro**|
|---|---|---|---|---|---|---|---|---|---|
||**Metros**|||||||||
|**Threshold**|<br>**(Java-Bali)**|**total**|**avg per**<br>**Metro**|**Total**<br>**(mil.)**|**% IDN**|<br>**Urban**|**Total**<br>**(km**<sup>**2**</sup>**)**|**% IDN**|**Name**<br>**(no. districts)**|
||||**DU**|<br>**RANTON**|**ALGO**|**RITHM**||||
|27.0%|1 (1)|2|2.0|3.05|1.2|3.05|191|0.0|Bandung (2)|
|23.0%|2 (2)|4|2.0|6.71|2.7|6.71|513|0.0|Jakarta Selatan (2)|
|21.0%|3 (2)|6|2.0|10.88|4.3|10.40|3,405|0.2|Medan (2)|
|17.5%|4 (3)|8|2.0|12.36|4.9|11.75|3,921|0.2|Medan (2)|
|15.5%|8 (5)|17|2.1|19.31|7.7|16.99|17,616|0.9|Jakarta Selatan (3)|
|13.5%|11 (7)|23|2.1|25.45|10.1|20.86|24,483|1.3|Jakarta Selatan (3)|
|12.0%|14 (8)|31|2.2|32.81|13.0|27.18|35,205|1.9|Surabaya (3)|
|11.0%|20 (13)|43|2.2|49.55|19.7|41.18|41,529|2.2|Surabaya (3)|
|10.0%|24 (17)|58|2.4|64.51|25.6|51.13|54,181|2.9|Bogor (2)|
|9.0%|28 (16)|77|2.8|81.79|32.5|63.86|76,542|4.0|Jakarta (11)|
|8.0%|32 (17)|86|2.7|88.18|35.0|67.70|89,773|4.7|Jakarta (11)|
|7.0%|39(18)|103|2.6|97.09|38.5|72.70|110,197|5.8|Jakarta(13)|
||||**AGG**|**LOMER**|**ATION**|**INDEX**||||
|AI|12(4)|126|10.5|14170|56.2|89.38|126414|6.7|West-Central Java (38)|
|||<br>|<br>**CL**<br>|,<br>**USTER**<br>|<br>**ALGOR**<br>|<br>**ITHM**<br>|,<br>|<br>||
|HDC|9(8)|38|4.2|62.53|24.8|54.15|22,739|1.2|Jakarta(15)|

19 For the NTL approach, we experimented with a total of 19 thresholds by breaking the national range of NTL intensity values (from 0 to 1,340.44) at every 5<sup>th</sup> percentile. Despite the wide range, low values are prevalent in Indonesia and 95 percent of the values fall below 9.11.

20 In 2016, 60.8 percent of Indonesia’s population was classified as urban. For Indonesia’s other main island-regions, the shares of the population classified as urban were as follows: Kalimantan (43.5 percent), Sumatra (40.2 percent), Sulawesi (35.0 percent), Nusa Tenggara (31.6 percent), and Maluku-Papua (31.3 percent).

9
||**No.**<br>|**No. me**|**tro districts**|<br>**P**|**opulatio**|**n**|**Land**|<br>**area**|**Largest Metro**|
|---|---|---|---|---|---|---|---|---|---|
||**Metros**|||||||||
|**Threshold**|<br>**(Java-Bali)**|<br>**total**|**avg per**<br>**Metro**|**Total**<br>**(mil.)**|**% IDN**|<br>**Urban**|**Total**<br>**(km**<sup>**2**</sup>**)**|**% IDN**|**Name**<br>**(no. districts)**|
|UC|18(8)|135|7.5|144.24|57.2|88.37|145,260|7.7|Central-East Java(55)|
||||**THRES**<br>|**HOLDI**<br>|**NG OF N**<br>|**TL DAT**<br>|**A**<br>|||
|5th pct|8 (3)|118|14.8|130.89|51.9|86.00|109,702|5.8|Java (91)|
|10th pct|9 (4)|114|12.7|129.12|51.2|85.46|105,065|5.6|West-Central Java (33)|
|25th pct|9 (4)|109|12.1|125.66|49.9|83.76|97,858|5.2|West-Central Java (33)|
|30th pct|9 (4)|105|11.7|122.39|48.6|82.84|93,750|5.0|West-Central Java (33)|
|40th pct|9 (5)|89|9.9|111.68|44.3|78.79|78,113|4.1|West-Central Java (31)|
|50th pct|9 (6)|83|9.2|107.16|42.5|77.49|69,036|3.6|West-Central Java (31)|
|60th pct|9 (6)|69|7.7|92.05|36.5|71.72|50,125|2.6|Northwest Java (26)|
|70th pct|10 (7)|52|5.2|76.42|30.3|63.20|35,424|1.9|Jakarta-Bandung (22)|
|80th pct|8 (7)|41|5.1|64.42|25.6|55.39|25,382|1.3|Jakarta (15)|
|90th pct|5 (4)|21|4.2|38.16|15.1|36.24|8,110|0.4|Jakarta (11)|
|95thpct|3(3)|13|4.3|26.18|10.4|25.99|2,633|0.1|Jakarta(9)|

**_Notes:_** (Urban) Population data based on the 2014 Indonesian household survey (Survei Sosial Ekonomi, SUSENAS).

# **_Duranton Algorithm_**

As expected, the number of metro areas, the total number of districts that compose those metro areas, the total (urban) population living in metros, as well as the total land area covered by them, all steadily increase as the commuting flow threshold is lowered from 27 percent to 7 percent. At a threshold of 27 percent, we find a single metro area (Bandung) comprised of two districts that has an entirely urban population of just over 3 million and an area of 191 km<sup>2</sup> . A second metro area (Jakarta Selatan), also comprising two districts, then appears at a threshold of 23 percent, more than doubling the overall urban population that lives in metro areas to 6.7 million and the total land area covered by metro areas to 513 km<sup>2</sup> . By the time the threshold reaches 10 percent, which is Duranton’s preferred threshold in his application to Colombia, the number of metro areas has increased to 24, 17 of which are located on Java – Bali. The aggregate population of these metro areas is 64.5 million (25.6 percent of Indonesia’s population) with an urban population of 51.1 million. Together, the metro areas cover just over 54,000 km<sup>2</sup> or 2.2 percent of Indonesia’s total land area. At the lowest threshold of 7 percent, the number of metro areas has reached 39, 18 of which are on Java – Bali, with an aggregate population of 97 million and an overall urban population of 72.7 million. These metro areas collectively cover 110,197 km<sup>2</sup> .

Interestingly, regardless of the threshold used, the average number of districts per metro area remains small, increasing steadily from two at a threshold of 27 percent to 2.8 at a threshold of 9 percent before subsequently declining to 2.6 at a threshold of 7 percent. This turns out to be a defining feature of this approach: reducing the commuting threshold mainly has the effect of increasing the number of metro areas rather than the spatial extent of those metro areas. Finally, it is also notable that only as the threshold is lowered below 10 percent, more and more metros start appearing outside of Java – Bali. Using the 10% threshold identifies 24 metro areas of which 17 are on Java-Bali. Reducing the threshold further from 10 to 7 percent adds 15 additional metro areas, of which only 1 is on Java – Bali (see also Figure A2 in Appendix A). Also, it is not until a 10
threshold of 9 percent that the five constituent districts of DKI Jakarta – which is the recognized core of Indonesia’s capital city – aggregate into a single metro area. And, only at the lowest threshold of 7 percent does Duranton’s algorithm aggregate the districts that belong to Jabodetabek, the official Jakarta metropolitan area (see also Figure 1b).

# **_The Agglomeration Index_**

The AI approach generates highly implausible results at the standard thresholds with which it has become synonymous (i.e. a core population of 50,000, a travel time radius of 60 minutes, and a population density threshold of 150 people per km<sup>2</sup> ).<sup>21</sup> It yields 12 metro areas with an aggregate population of 141.6 million (equivalent to 56.2 percent of the Indonesian population), of which 89.4 million is urban. Out of these 12 metro areas, however, only four are located on Java – Bali. The small number of metros on Java – Bali is a consequence of the low population and population density thresholds associated with the AI, as well as the fact that cores that are within 60 minutes travel time of each other merge together in extended metro areas. Given that Java – Bali, overall, is very densely populated, this results in a small number of exceptionally large metro areas. The low population density threshold results in the algorithm picking up development along Indonesia’s major roads that connect cities, contributing to the grouping together of large numbers of districts. As Figure 1c shows, the largest metro generated by the AI covers much of West and Central Java and consists of 38 districts with a total aggregate population of 63 million, which is more than double the population of the largest metro generated by Duranton’s algorithm at the 7 percent threshold, which corresponds to the official Jabodetabek area and consists of only 13 districts.

# **_The Cluster Algorithms_**

A similar story to that for the AI holds for the cluster algorithm under the _Urban Cluster_ set of thresholds (i.e. T<sup>�</sup> � = 300 people per km<sup>2</sup> , T<sup>�</sup> � = 5,000). With these thresholds we obtain an aggregate metro population – 144.2 million (equivalent to 57.2 percent of Indonesia’s overall population) – that is remarkably close to that generated by the AI. This population is spread over 135 districts which form 18 separate metro areas, eight of which are located on Java – Bali (Table 1). Again, the largest metro, which, in this case, covers much of East and Central Java, is implausibly large. Thus, it covers 38 districts with a total population of 53.7 million (Figure 1d).

When we turn, however, to the cluster algorithm with the _High-Density Cluster_ set of thresholds (i.e. T<sup>�</sup> � =1,500 people per km<sup>2</sup> and T<sup>�</sup> � = 50,000), the results look more reasonable (Figure 1(e)). The most populous metro area in this case corresponds, in a recognizable manner, to Jakarta; although, with 33 million people, it has a slightly larger population than the official Jabodetabek area that Duranton’s algorithm successfully replicates when using a commuting threshold of 7 percent. Meanwhile, the overall population that lives in metro areas is 62.5 million, which is close to Duranton’s algorithm at a threshold of 10 percent (Table 1). Compared to Duranton’s algorithm at this threshold, however, the total number of metro areas is far fewer (9 versus 24) and the average number of districts per metro area is correspondingly larger (4.2 versus 2.4).

> 21 Of course, the approach may potentially yield more plausible results if different thresholds are applied or if delays due to traffic congestion are incorporated into the travel time estimates.

11
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# **_Nighttime Lights_**

As expected, both the total number of districts that form metro areas and the aggregate metro population decline as the NTL intensity threshold for delineating metro areas is increased. Increasing the threshold from the 25<sup>th</sup> to the 80<sup>th</sup> percentile thus almost halves the aggregate metro population from 125.7 million to 64.4 million while cutting the number of districts that form metro areas from 109 to 41. It is only when the threshold is set at the 80<sup>th</sup> percentile that Jakarta really adopts a recognizable form as the largest metro (Figure 1g). Compared to Duranton’s algorithm, where the number of metro areas detected depends strongly on the threshold, it is notable that the number of metros identified using the NTL approach remains – at between 8 and 10 – relatively stable between thresholds set at the 5<sup>th</sup> and 80<sup>th</sup> percentiles of the distribution of NTL intensity values. Reducing the NTL intensity threshold tends to result in the adding of more districts to existing metros rather than, as with Duranton’s algorithm, creating new metros.

Summarizing, the different approaches to delineating metro areas generate often very different results in terms of, _inter alia_ , the number of metro areas, the aggregate population of those metro areas, and the characteristics of the largest identified metro area. Both the AI and the cluster algorithm under the urban cluster set of thresholds generate results that appear implausible. This is because their low population density thresholds contribute to generating implausibly large metro areas – in both cases, almost the entirety of Java – Bali is split into a small number of metros, as is most evident from Figures 1c and 1d. Results look more reasonable under the other approaches. Most notably, at a commuting flow threshold of 7 percent, Duranton’s algorithm – which represents an example of a commuting data–based approach to defining metro areas of the kind that economists tend most to favor – successfully re-creates the official Jabodetabek metro area. The cluster algorithm using the high-density cluster set of thresholds and the NTL approach with a threshold set at the 80<sup>th</sup> percentile of the distribution of NTL intensity values generate an overall population living in metro areas similarly to Duranton’s algorithm with a 10 percent commuting flow threshold. However, in both these cases, this population lives in a much smaller number of metro areas.

In fact, a defining feature of using an O-D commuting flow–based approach, at least in the case of Indonesia, is that it generates a much larger number of separate metro areas, each consisting of only a few districts. All the other “satellite data-based” approaches tend to “overagglomerate” a larger number of districts into fewer metro areas.

# _3.4. Jaccard indices and a closer look at levels of agreement_

To provide further insights into the spatial level of agreement between the different approaches, Figure 2 presents values of the Jaccard index for pairwise comparisons of the “metro maps” generated by the different approaches. And, Figure 3 provides a visualization of the level of agreement between the different approaches for four selected metro areas – namely, Jakarta, Surabaya, Denpasar, and Makassar.

First, the Jaccard index. This index measures the proportion of districts that belong to metro areas in the two maps among districts that belong to metro areas in at least one of the maps. More formally, if we denote the set of districts that are classified as metro districts in one map by _A_ and 13
the set of districts that are classified as metro districts in a second map by _B_ then the Jaccard index is given the size of the intersection of the two sets divided by the size of the union – i.e. J�A, B�� |A∩B|/|A∪B|. As can be seen from comparing Figure 2, the highest levels of agreement are obtained when comparing the maps associated with the AI, the cluster algorithm with the urban cluster set of thresholds and the NTL approach with the 25<sup>th</sup> percentile threshold. For these comparisons, the Jaccard index exceeds 0.65. These high levels of agreement are driven by the low population density and NTL intensity thresholds associated with these maps, which, as described earlier, lead to much of Java – Bali being classified as “metro” (compare also Figures 1d, 1e, and 1f).

**Figure 2: Jaccard index for pairwise map comparisons**

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A reasonably high Jaccard index is also found when comparing the map associated with the Duranton approach at a 10 percent commuting flow threshold with the map associated with the same approach at a 7 percent commuting threshold. This is, again, driven by the high level of agreement between the maps for Java-Bali (see also Figure A2 in the Appendix – and the discussion in the previous subsection). For the remaining pairwise comparisons, the levels of agreement between the maps associated with different approaches and thresholds are much lower. This is generally simply so because these comparisons involve comparing one map with a strict set of thresholds, generating only few metro districts, with another map that has a much more relaxed set of thresholds, generating many metro districts.

Figure 3 adds to this general comparison provided by the Jaccard indexes, by zooming in on specific (large) metro areas and visualizing the level of agreement between the different approaches on the exact spatial extent of these specific metro areas. It clearly shows that for large metros such as Jakarta and Surabaya on Java, all approaches typically agree on a specific sub-set of core districts. However, the level of agreement declines as we move further away from these core districts. This happens because approaches with stricter thresholds (i.e. higher commuting flow, population density or NTL intensity thresholds) tend to classify as metro only sub-sets of 14
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While there exists a large and well-established literature that empirically examines the strength of agglomeration economies for developed countries,<sup>22</sup> there have been comparatively very few papers that have done likewise for developing countries. The main exceptions are recent papers by Duranton (2016), Chauvin _et al_ . (2017), and Quintero and Roberts (2018). Duranton provides estimates of the strength of agglomeration economies for Colombia, while Chauvin _et al_ . do likewise for Brazil, China and India.<sup>23</sup> Quintero and Roberts, meanwhile, present estimates of the strength of agglomeration economies for 16 Latin American and Caribbean countries.<sup>24</sup> In all three cases, these papers estimate the strength of agglomeration economies using either individual or pooled cross-sections of data on workers drawn from either household or labor force surveys. They estimate the strength of agglomeration economies by regressing a worker’s nominal wage on a measure of either the size or density of the city in which the worker lives while controlling for observable characteristics of the worker, including, most notably, the worker’s level of education and workforce experience, as proxied by the worker’s age.

In what follows below, we follow a similar approach to Duranton (2016), Chauvin _et al._ (2017) and Quintero and Roberts (2018) in estimating the strength of agglomeration economies for Indonesia.<sup>25</sup> Hence, we draw on micro-data for Indonesian workers from the same survey – SAKERNAS – that we used to measure commuting flows, to estimate the size of the agglomeration wage premium in a simple cross-sectional regression framework.<sup>26</sup> Importantly, in doing so, we estimate the size of this premium based on each of the different approaches – Duranton’s algorithm, the AI, the two cluster algorithms, and the NTL approach – to defining metro areas.

# _4.1. Empirical framework_

4.1.1. Estimation strategy Similar to previous papers for other countries (Duranton, 2016; Chauvin _et al_ ., 2017; Quintero and Roberts, 2018), we identify the strength of Indonesia’s agglomeration wage premium, using the following basic regression:

> 22 See Rosenthal and Strange (2004) and Combes and Gobillon (2015) for excellent reviews of this literature.

> 23 Chauvin _et al_ . (2017) also present estimates of the strength of agglomeration economies for the United States for purposes of comparison.

> 24 See also Roberts (2018a).

> 25 We do not attempt to distinguish between the possible different underlying sources of agglomeration economies. These sources include the various matching, sharing and learning mechanisms and are discussed in detail by e.g., Duranton and Puga (2004).

> 26 Specifically, we use data from the August 2014 round of SAKERNAS. These data are representative for Indonesian districts. This cross-sectional framework leaves us unable to control for sorting of workers based on time-invariant unobservable characteristics as their ability (as distinct from their level of education) and motivation. In this sense, we fall short of the standards of what researchers have been able to achieve in terms of the identification of agglomeration effects for countries such as the United States (Glaeser and Mare, 2001), France (Combes _et al_ ., 2008), or Spain (De la Roca and Puga, 2017) where detailed panel data sets allow the researcher to control for time-invariant unobservable characteristics of workers.

16
where our dependent variable ln w���� denotes the hourly nominal wage of individual _i_ , working in occupation _o_ , in industry _j_ that is in district _d_ .<sup>27</sup> It is important to note that _d_ denotes the district where the job, and not necessarily the worker is located. α� denotes a full set of 186 3-digit industry dummies (with industries as defined in the 2000 Indonesian Standard Industrial Classification, KBLI 2000), and α� a full set of 241 occupation dummies (with occupations as defined in the 1982 Indonesian Classification of Occupations, KJI 1982). Xi denotes a vector of individual worker characteristics that we can control for in our regressions. Specifically, we control for a worker’s age and age<sup>2</sup> , which can (among others) be considered as an (imperfect) measure of his/her overall workforce experience. We do not have information on the latter, but we always include a worker’s experience on his/her _current job_ and its square, which is measured as the number of years he/she has been working on the job, as well as a dummy variable indicating whether he/she ever held a job before his/her current job. Next, we control for a worker’s highest completed level of education,<sup>28</sup> as well as two dummy variables indicating whether he/she completed at least one, respectively two, additional formal training courses for which he/she got a certificate. Finally, we include a dummy variable indicating whether a worker is an “own account worker” or an employee.<sup>29</sup> Xd is a set of dummy variables for the 8 main Indonesian islands (groups)<sup>30</sup> that the district is located on, and ε���� captures all other unobserved nominal wage determinants.

Finally, S�� denotes our main independent variable of interest. In our main specification, we follow De la Roca and Puga (2017) in the specification of this variable. For all districts that belong to a metro area, it is defined as “ _the number of people living within 10 km of the average person in the metropolitan area, m, to which district, d, belongs_ ”, i.e. it takes the same value for all districts belonging to the same metro area. For all districts that do not belong to a metro area, it is defined as _“the number of people living within 10 km of the average person in the district, d”_ . Crucially, this variable varies depending on the algorithm/approach used to define metro areas. We use this variable instead of a simpler density measure, as it is (see De la Roca and Puga, 2017, p.112) better able to deal with the noise introduced by urban boundaries that vary across urban areas in their tightness around built-up areas. We calculate this variable using the same _Landscan_ - _2012_ gridded population data that we used to define metro areas using the AI and cluster algorithms (see Section 3.1 above).

27 SAKERNAS reports monthly income for sampled individuals. Based on this, and a person’s reported total working hours during the last week, we calculate his/her hourly wage as: (monthly income / (365/12))  (7/hours worked last week). SAKERNAS reports both monthly income earned in cash as well as in goods. In all results reported here, we use total monthly income, i.e. total monthly income in cash and in goods combined. All our findings are robust to using only total monthly income in cash (see e.g. Table A8 in Appendix A). This is not that surprising as the share of income earned in cash is 0.981 (1.0) for the average (median) worker. Only for less than 0.75 percent of workers does non-cash income make up more than 50 percent of their total income.

> 28 SAKERNAS indicates a worker’s highest level of completed education in one of 13 different categories of (completed) education. From lowest to highest level of education, these categories are: no schooling, incomplete primary school, primary school, package A, general junior high school, vocational junior high school, package B, general senior high school, vocational senior high school, package C, diploma I/II, diploma III, div/S1, and S2/S3 (university).

> 29 In our main sample, which we define below, the share of “own account workers” is about 30 percent. Our results are robust to only considering employees in our regressions. See e.g. Table A7 in Appendix A.

> 30 These islands (groups) are: Bali, Java, Kalimantan, Maluku, Nusa Tenggara, Papua, Sulawesi, and Sumatera.

17
In extensions, we also use four other independent variables at the same “ �� ” level as our main city size variable. First, we obtain the total urban population of each metro area / district from the 2014 Indonesian household survey ( _Survei Sosial Ekonomi_ , SUSENAS). Our main city size variable is essentially a weighted density measure. Using total urban population instead we can assess how sensitive our results are to the use of a simple overall population size measure. Second, we constructed two other agglomeration variables from the information in SAKERNAS that measure: (i) the sectoral specialization of the metro area/district, i.e. the share of a metro’s total employment in the same sector as the worker him/herself; and (ii) the share of skilled workers in a metro/district’s total employment, where we define skilled workers as those that have completed general senior high school or higher. Note that, similar to our main size variable, these two variables, as well as the earlier discussed “ _total urban population measure_ ” are defined at the district level for all districts that are not part of a metro area. Finally, we have calculated each district’s market access that captures a district’s accessibility to the markets of all other districts within Indonesia taking estimated travel times into account.<sup>31</sup> Taking a metro/district’s sectoral specialization, share of skilled workers and access to other districts’ markets into account, we can assess to what extent our findings are sensitive to taking explicit account of alternative explanations for agglomeration economies.

In all our regressions, _β_ is our main coefficient of interest. It measures the size of Indonesia’s agglomeration wage premium. This coefficient is of interest in and of itself, but for the purposes of this paper, we are particularly interested in seeing how the estimated size (and significance) of _β_ depends on the approach used to define metro areas. In establishing its significance, it is important to note that we always cluster our standard errors at the metro or district level (depending on whether a district belongs to a metro area or not), i.e. at the same level at which our main independent variable of interest varies.

We estimate equation (1) using ordinary least squares (OLS) regression, so that we can interpret the estimated _β_ as a consistent estimate of Indonesia’s agglomeration wage premium under the assumption that ε���� is uncorrelated with the included independent variables in the regression. But, in an attempt to deal with the possible endogeneity of the metro/urban size measure (which, if present, would clearly violate this assumption), we also employ a Two-stage Least Squares (2SLS) regression strategy inspired by De la Roca and Puga (2017), Combes _et al._ (2010), and Saiz (2010), where in the first stage, we instrument our size measure with several geographic and climate variables that, historically, (may) have constrained urban development, but that, today, are unlikely to have an important influence on workers’ wages. Hence, we use a district’s elevation, ruggedness, temperature (both its monthly average as well as its standard deviation over the year) and rainfall (both total monthly rainfall as well as its standard deviation over the year) as

> 31 Following, for example, Jedwab and Storeygard (2015), Blankespoor _et al_ . (2017) and Berg _et al._ (2018), we measure market access as MA� �∑��� P�τ���� where MA� is a district _i_ ’s level of market access, P� is the population of district _j_ , and τ�,� is the estimated road travel time between districts _i_ and _j_ . Population data are from the 2014 round of SUSENAS. To estimate road travel time, we construct a road data set by transferring the 2014 road categories on a paper map published by NELLES to a geo-referenced network-enabled road data set (DeLorme) and assume uniform travel time speeds by road category identical to those assumed by Jedwab and Storeygard (2015) and Berg _et al._ (2018): expressway 105km/h, principal highway 100km/h, highway 90km/h, secondary road 75km/h, track 50km/h, 6 km/h for the unknown category and 5 km/h in the absence of a road. For the elasticity of trade, _θ_ , we assume 3.8 following Donaldson (2018).

18
instruments.<sup>32</sup> These variables are either related to a location’s agricultural potential and/or the constraints its geography poses on urban expansion (ruggedness, elevation). Especially when focusing on the urban workers in our sample only (see the next sub-section), these instruments should plausibly satisfy the exclusion restriction.

# 4.1.2. Main Sample

In estimating equation (1), we follow De la Roca and Puga (2017) as closely as possible, and restrict attention to working age (15 - 64) males that report a non-zero income in the August 2014 round of SAKERNAS. This initial sample consists of 116,156 workers. Next, we further exclude workers employed in agriculture, forestry, livestock and fishing, mining and quarrying, public administration and defense, education, health and social work. These activities are typically rural or much more controlled / regulated by the national and local governments in Indonesia. Also, we only focus on workers who have worked at least 32 hours (four working days) during the last week. These restrictions reduce the sample to 56,577 workers. In several robustness checks to these choices, we also show results when extending the sample to females; workers who have worked at least 24 hours (3 working days) in the previous week; workers in public administration and defense, education, health and social work; and/or non-production occupations in agriculture, forestry, livestock, fishing and mining and quarrying. We also perform robustness checks based on restricting the sample to employees or prime age (25-54) males only, or measuring the hourly wage using cash income only.

# _4.2. Baseline results_

Table 2 and Figure 4 show our main results using De la Roca and Puga’s (2017) preferred measure of metro/urban size as our main independent variable of interest – i.e. the number of people within 10 km of the average person in the metro area or district. Table 2, as well as Tables A1 – A10 in Appendix A that contain various robustness check to our main specification, show the estimated agglomeration wage premia when relying on seven different ways to define Indonesia’s metro areas – namely, Duranton’s algorithm based on commuting flow thresholds of 10 percent and 7 percent; the AI; the cluster algorithm using both the UC (i.e. T<sup>�</sup> � = 300 people per km<sup>2</sup> ; T<sup>�</sup> � = 5,000) and the HDC (T<sup>�</sup> � = 1,500 people per km<sup>2</sup> ; T<sup>�</sup> � = 50,000) sets of thresholds; and the NTL approach using the 25<sup>th</sup> and 80<sup>th</sup> percentile thresholds.<sup>33</sup> We focus on these seven based on our discussion in 32 We derived our temperature and rainfall measures from 2013 data produced by the University of East Anglia’s Climate Research Unit (https://crudata.uea.ac.uk/cru/data/hrg/). Meanwhile, we derived out elevation and ruggedness variables using data that were originally generated by NASA's Shuttle Radar Topography Mission (SRTM). Terrain ruggedness at the central point of a grid cell is defined as the mean of the absolute differences in elevation of the central point between the central grid cell and its eight adjacent grid cells, i.e., grid cells in the north, northeast, east, southeast, south, southwest, west, and northwest of the central grid cell. That is, TRI� �∑�����E� �E��⁄8, where _TRIi_ denotes the ruggedness in the central grid cell _i_ , _Ei_ and _Ej_ represent the values of elevation in the central grid cell _i_ and neighboring grid cell _j_ , respectively (Wilson _et al._ , 2007). Using our elevation data, we ran the TRI command from a Python library (GDAL: https://docs.qgis.org/2.8/en/docs/user_manual/processing_algs/gdalogr/gdal_analysis.html) and generated a single-band output raster with the index values. The resultant raster was subsequently used as an input value layer for the zonal statistics to obtain the mean terrain ruggedness for Indonesian district.

33 All tables and figures in this section, as well as the tables showing various robustness checks to our main results (see Appendix A), only report the estimated agglomeration wage premium, _β_ in equation (1). All regressions always include the full set of controls discussed in Section 4.1.1. Table A1 in Appendix A shows the estimated effect of the 19
Section 3.3. Besides this, we also show results when using a “naïve” metro area definition, which simply takes each Indonesian administrative district as its own metro area. Figure 4 complements these results by plotting the estimated agglomeration wage premia for metro area definitions calculated using all the different thresholds for Duranton’s algorithm and the NTL approach that were analyzed in Section 3.3.

For each of these definitions, we show results when estimating equation (1) on four different samples. These samples become ever stricter in terms of what we consider as _cities_ in our sample. In column [1], we include all districts and all workers (i.e., both urban and rural) in the sample. As discussed before, metro districts get assigned the relevant population size measure of the entire metro area that they belong to, and non-metro districts simply the relevant population size measure of their own district. In column [2], we again include all districts but restrict the sample to “urban workers” only. The SAKERNAS classifies each worker as living in an urban or rural area.<sup>34</sup> If anything, we expect the agglomeration premium to be prevalent primarily in an urban context.<sup>35</sup> .In column [3], we drop non-metro districts and only consider those districts that belong to a metro area. In these columns, however, we do include both urban and rural workers. Effectively, we hereby focus entirely on the variation in the size of the metro areas defined by each of the different approaches discussed in Sections 2 and 3. Finally, in columns [4], we focus on the urban workers in metro-districts only.<sup>36</sup> First of all, Table 2 and Figure 4 show that we always find a positive agglomeration wage premium, regardless of the approach used to define metro areas, or whether we restrict the sample to urban workers and/or metro areas only. Compared to recent estimates of this premium for India (7.6%) and China (19.2%), Colombia (about 5%), and several other Latin American countries (1.2%) - see Chauvin et al., 2017; Duranton (2016) and Roberts (2018b), respectively -, our estimates are on the larger side, especially when including only metro-districts.

Also, regardless of the approach used to define metro areas, we always find a higher agglomeration wage premium when focusing on urban workers only. This is as expected, as agglomeration economies are expected to be, if anything, stronger for urban workers. Finally, and again regardless various worker characteristics that we include as controls. They all have the expected impact on nominal wages. These coefficients are very stable and do not vary with the metro definition used, nor do they change substantially across the various robustness checks we perform.

34 This classification is based on a composite scoring system which assesses Indonesian villages as either urban or rural based on their possession of certain “urban characteristics” (BPS Regulation 37/2010). The urban characteristics assessed are: (i) population density; (ii) the structure of the local economy (specifically, the share of agricultural households); (iii) the percentage of households with certain types of infrastructure (i.e. electricity and telephone networks); and (iv) the availability of urban facilities (those considered are schools, hospitals, a market, shops, a cinema, and, finally, recreational facilities such as a hotel, a salon, a billiard hall, a discothèque or a massage parlor). Each sub-national administrative unit in Indonesia at the 4<sup>th</sup> level (i.e. each “village”) is assigned a score from 1 to 8 for (i) and (ii), respectively, while scoring 1 or 0 for each of eight infrastructure/urban facilities in (iii) and (iv) depending on the availability within a certain distance. If a village’s total score is 10 or higher, it is classified as urban; and rural, otherwise.

35 Alternatively, we restrict the sample to those districts designated as “Kota”, or city. Districts are either coded as “Kota”, city, or as “Kabupaten”, village. Results, which are available on request, are very similar to those where we focus on “urban workers.” 36 When simply defining our population size measures for each separate district, we do not report results in columns [3] – [4]. These results would simply be identical to those shown in columns [1] – [2].

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of the approach used to define metro areas, we always find a much higher agglomeration wage premium when restricting the sample to metro districts only. Again, this is not surprising considering that the agglomeration wage premium is expected to be, if anything, stronger in the (much) larger, denser metro-areas defined by the various approaches to delineating these areas. The agglomeration wage premium _does_ , however, _differ_ quite substantially in size depending on the approach used to delineate metro areas. Importantly, these differences exist regardless of whether we restrict the sample to urban workers only or not. Also, we find the above-described patterns in any of our robustness checks as well (see Tables A2 – A10 in Appendix A).

**<u>Table 2: Estimated agglomeration wage premium using Ordinary Least Squares (OLS) regressions</u>**

||**[1]**|**[2]**|**[3]**|**[4]**|
|---|---|---|---|---|
|**District sample:**|**All**|**All**|**Metro**|**Metro**|
|**Worker sample:**|**All**|**Urban**|**All**|**Urban**|
|**Metro definition:**||**Weighted p**|**opulation**||
|District|0.066***|0.083***|||
||[0.010]|[0.012]|||
|Duranton: 10 %|0.065***|0.081***|0.161***|0.170***|
||[0.011]|[0.013]|[0.035]|[0.039]|
|Duranton: 7 %|0.066***|0.082***|0.125***|0.141***|
||[0.021]|[0.024]|[0.045]|[0.048]|
|NTL: 80<sup>th</sup>percentile|0.065***|0.080***|0.372***|0.420***|
||[0.019]|[0.023]|[0.073]|[0.082]|
|NTL: 25<sup>th</sup>percentile|0.053***|0.069***|0.260***|0.297***|
||[0.014]|[0.018]|[0.025]|[0.026]|
|AI|0.047***|0.062***|0.215***|0.243***|
||[0.014]|[0.018]|[0.027]|[0.033]|
|Cluster algorithm|0.063***|0.079***|0.354***|0.372***|
|(High density)|[0.019]|[0.022]|[0.045]|[0.049]|
|Cluster algorithm|0.050***|0.065***|0.210***|0.240***|
|(Urban cluster)|[0.016]|[0.020]|[0.039]|[0.046]|
|n|47,513|33,243|13,610|11,018|

**_Notes:_** The dependent variable in all columns is the log of hourly wage. Standard errors clustered at the metro level are reported in brackets. ***, **, *, denotes significance at the 1 percent, 5 percent and 10 percent levels respectively. All results include the full set of job and worker characteristics discussed in Section 4.1.1. Number of observations varies by metro definition used. To give an idea of the relative sample size across the different (restricted) samples, the reported number of observations denotes the number of observations using the “Duranton: 10 %” approach to define metro areas.

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**Figure 4: Estimated agglomeration wage premium across thresholds**

<!-- Start of picture text --> (a) Commuting shares (Duranton) in combination (b) Nighttime lights in combination with<br>with weighted population weighted population<br><!-- End of picture text -->

**_Notes:_** In panel (a), the use of a commuting threshold larger than 17 percent would result in estimates of _β_ that are larger than 2. We do not show these in the figures as including them would blur the pattern observed when using thresholds smaller than 17 percent. Furthermore, using thresholds above 17 percent results in an unrealistic delineation of metro areas (as discussed in Section 3.3).

# _4.2.1 Including all districts in the sample_

Interestingly, the differences in the estimated agglomeration wage premium, i.e. the estimate of  , across approaches and thresholds are smallest when including all districts in the sample (see columns [1] – [2] in Table 2). Furthermore, the estimated agglomeration premium is always smaller than that estimated using a naïve district-based metro area definition (i.e. where we simply define each district as a metro). The largest differences can be found across the different approaches to delineating metro areas. Within approaches, i.e. for the different commuting share or NTL thresholds used, results are very stable when including all districts in the sample (see the blue and red lines in Figure 4). The estimated agglomeration wage premium is smallest when using the AI or the cluster algorithm with the UC set of thresholds to define metro areas, followed by the NTL approach using below median intensity (up to the 50<sup>th</sup> percentile). Using Duranton’s algorithm with a commuting threshold lower than 17 percent, the NTL approach using above median percentile of intensity, and the cluster algorithm with the HDC thresholds to delineate metro areas all give us estimated agglomeration wage premia that are only slightly smaller than that obtained using a naïve district-based metro area definition.

Of course, it may not be that surprising that the estimated agglomeration wage premia using the different approaches to delineating metro areas is not that different from that obtained when simply taking each district for a metro area. The number of metro-districts is at most 135 (when using the cluster algorithm with the UC thresholds) and can be as small as 38 (when using the cluster algorithm with the HDC thresholds). The total number of districts in our sample is 497, so that, at most, 27 percent of all districts get assigned a different “city size variable” than when using the naïve district-based metro area definition. Moreover, for the metro-districts, a district’s own “city size variable” is typically not very different from that defined for the entire metro area that the district is part of. Table 3 below illustrates this by reporting the correlation between the “city size 22
variable” at the district level and that at each of the seven main metro area levels for which we also show results in Table 2. It shows these correlations for each of the two main city size variables (i.e. weighted population and urban population) used in our analysis, as well as when including all, or only urban, workers in the sample.

**<u>Table 3: Correlation between city size variable defined at the district and at the metro area levels</u>**

|**City size variable:**|**Weighted**|**population**|
|---|---|---|
|**Sample:**|**All workers**|**Urban workers**|
|Commuting share: 10 percent|0.80|0.83|
|Commuting share: 7 percent|0.84|0.86|
|NTL: 80<sup>th</sup>percentile|0.56|0.58|
|NTL: 25<sup>th</sup>percentile|0.58|0.59|
|Agglomeration Index|0.58|0.59|
|Cluster algorithm – HDC|0.60|0.61|
|Cluster algorithm – UC|0.65|0.65|

These correlations can also partly explain the differences in estimated agglomeration wage premia in columns [1] – [2] of Table 2 discussed above. They are strongest when using Duranton’s algorithm to delineate metro areas that also produced agglomeration wage premia that are (very) close to that estimated when simply taking each district as a metro area. This is not so surprising when considering that the use of this approach (except when using the highest commuting thresholds) crucially differs from all the other approaches in the much larger number of metro areas, that, importantly, each consist of a much smaller number of districts (see Table 1 in Section 3.3): the variation in the city size measure is simply much smaller when using this method to delineate metro areas. As a result, the metro area-based “city size variables” are strongly correlated to that using a simple district-based “city size variables”. The other two approaches that resulted in estimated agglomeration wage premia closest to that obtained using a naïve district-based metro area definition, share this feature, but to a lesser extent. Both the cluster algorithm with the HDC thresholds and the NTL approach using the 80<sup>th</sup> percentile threshold have fewer districts per metro area compared to, for example, the cluster algorithm with the UC thresholds or the AI (but far fewer metro areas overall compared to Duranton’s algorithm using a 10 percent or 7 percent commuting threshold).

# _4.2.2 Including only metro districts_

We observe much more variation in the estimated agglomeration wage premium when we restrict the sample to metro districts only. This can be explained by the fact that now we do not only change the “city size variable” for each of the metro districts from its own to that of the metro area it is part of, but we also run our regressions on often very different samples. These samples range from all workers in the 138 metro districts based on the UC algorithm, to those in only about 40 metro districts based on the HDC algorithm or the 80<sup>th</sup> percentile of NTL intensity (and even fewer when considering some of the results in Figure 4).

Interestingly, the variation in the estimated agglomeration wage premium appears to be (at least partly) related to both the total number of metro districts identified by the approach used, as well 23
as the average number of metro districts _per metro area_ . It is largest when using either the cluster algorithm with the HDC thresholds or the 80<sup>th</sup> percentile of NTL intensity. These are exactly the approaches resulting in the fewest metro districts (see Table 1 and Figure 1 in Section 3.3). The cluster algorithm with the UC thresholds and the AI, as well as the NTL approach using a 25<sup>th</sup> percentile threshold identify many more districts as metro-districts, and result in a smaller estimated agglomeration wage premium.<sup>37</sup> However, the number of metro districts per metro area identified also appears to play an important role in explaining the variation in results shown in columns [3] and [4] of Table 2: the agglomeration wage premium is smallest when using Duranton’s algorithm, which is characterized by fewer districts per metro area than any of the other approaches.

# _4.3. Accounting for potential endogeneity of our main city size variables_

All results discussed so far were obtained by estimating equation (1) using OLS regressions. This section aims to mitigate any remaining endogeneity concerns that one may have regarding these results. These concerns include the omission of other important determinants of nominal wages that are correlated with any of the included regressors in equation (1), or reverse causality issues, i.e. higher nominal wages attracting workers/people instead of larger/denser cities generating agglomeration rents.

To do this, we instead estimate equation (1) using 2SLS, where, in the first stage, we instrument our city size measure with several geographic and climate variables that, historically, (may) have constrained urban development, but that, today, are unlikely to have an important influence on workers’ wages. These variables are either related to a location’s agricultural potential (temperature, rainfall) and/or the constraints its geography poses on urban expansion (ruggedness, elevation) - see the discussion at the end of Section 4.2.1 for the exact variables used. Especially when focusing on the particular (urban) workers in our sample (see the next subsection), these instruments should plausibly satisfy the exclusion restriction.

Table 4 below shows the resulting estimated agglomeration wage premia using the same approaches to delineating metro areas for which we showed results in Table 2. Figure A3 in Appendix A further complements Table 4 by showing the estimated agglomeration wage premiums across different thresholds both for Duranton’s algorithm (panels (a) and (b)) and for the NTL approach (panels (c) and (d)) to delineating metro areas. The estimated agglomeration wage premium is typically (much) larger when using this IV-approach.<sup>38</sup> However, most important for our purposes, our main findings as to how this estimated wage premium differs depending on the approach used to define metropolitan areas hold up.

> 37 When using the NTL approach to delineate metro areas, the estimated agglomeration wage premium also decreases with the number of metro districts identified (i.e. it increases with the NTL intensity threshold). See Figure 4(b).

> 38 A potential explanation for OLS underestimating the agglomeration wage premium would be sorting on unobservables that are negatively (positively) related to wages and positively (negatively) to urban density.

24
**-** **<u>Table 4: Estimated agglomeration wage premium using 2 Stage Least Squares Regressions</u>**

||**[1]**|**[2]**|**[3]**|**[4]**|
|---|---|---|---|---|
|**District sample:**|**All**|**All**|**Metro**|**Metro**|
|**Worker sample:**|**All**|**Urban**|**All**|**Urban**|
|**Metro definition:**||**Weighted**|**population**||
|District|0.141***<br>[0.026]|0.153***<br>[0.025]|||
|Duranton: 10 %|0.151***|0.164***|0.168***|0.179***|
||[0.023]|[0.025]|[0.038]|[0.044]|
|Duranton: 7 %|0.172***|0.192***|0.204***|0.217***|
||[0.041]|[0.048]|[0.052]|[0.045]|
|NTL: 80<sup>th</sup>percentile|0.165***|0.183***|0.682**|0.796**|
||[0.046]|[0.054]|[0.278]|[0.285]|
|NTL: 25<sup>th</sup>percentile|0.195***|0.220***|0.547***|0.584***|
||[0.072]|[0.083]|[0.065]|[0.109]|
|AI|0.199**|0.224**|0.389**|0.123**|
||[0.080]|[0.093]|[0.127]|[0.051]|
|Cluster algorithm|0.161***|0.178***|0.452***|0.490***|
|(High density)|[0.042]|[0.049]|[0.091]|[0.099]|
|Cluster algorithm|0.207***|0.234***|0.409***|0.466***|
|(Urban cluster)|[0.073]|[0.085]|[0.127]|[0.132]|
|n|47,513|33,243|13,610|11,018|

**_Notes:_** The dependent variable in all columns is the natural log of hourly wage. Standard errors clustered at the metro level are reported in brackets. ***, **, *, denotes significance at the 1 percent, 5 percent and 10 percent levels respectively. All results include the full set of job and worker characteristics discussed in Section 4.1.1. Number of observations varies by metro area definition used. To give an idea of the relative sample size, the reported number of observations denotes the number of observations using the “Duranton: 10 %” approach to define metro areas. In all regressions, the population measure (in natural log) is instrumented using the set of instruments set out in the text above Table 4. Instruments are generally relevant, and pass the usual overidentification tests. First stage results are available upon request.

# _4.4. Extension – Controlling for human capital, sectoral specialization and market access_

As a final extension, or robustness check (see also Tables A2 – A10 in the Appendix), to our findings, we also include three other, frequently used agglomeration variables in our regressions. Specifically, we add a metro/district’s sectoral specialization, a measure of its overall level of human capital, and its market access to other Indonesian districts’ markets to equation (1). This allows us to verify the extent to which our findings are sensitive to taking explicit account of these alternative explanations for agglomeration economies.

25
Table 5 below shows the resulting estimated agglomeration wage premiums using the same approaches to delineating metro areas for which we showed results in Table 2.<sup>39</sup> Columns [1] – [4] show that all results for our main city size measure, i.e., the population within 10 km of the average person in the metro area/district, are close to those we found before. The main difference with our baseline results in Table 2 is a generally slightly smaller estimated agglomeration wage premium.

**Table 5. Estimated agglomeration wage premium using Ordinary Least Squares regressions after** **<u>controlling for overall human capital, sectoral specialization, and market access</u>**

||**[1]**|**[2]**|**[3]**|**[4]**|
|---|---|---|---|---|
|**District sample:**|**All**|**All**|**Metro**|**Metro**|
|**Worker sample:**|**All**|**Urban**|**All**|**Urban**|
|**Metro definition:**||**Weighted**|**population**||
|District|0.039***<br>[0.013]|0.051***<br>[0.017]|||
|Duranton: 10 %|0.036***|0.045***|0.156***|0.164***|
||[0.013]|[0.016]|[0.048]|[0.054]|
|Duranton: 7 %|0.034**|0.043**|0.065|0.068|
||[0.017]|[0.021]|[0.054]|[0.057]|
|NTL: 80<sup>th</sup>percentile|0.048**|0.060**|0.308**|0.345***|
||[0.019]|[0.023]|[0.095]|[0.097]|
|NTL: 25<sup>th</sup>percentile|0.046**|0.054**|0.132*|0.154*|
||[0.018]|[0.022]|[0.069]|[0.073]|
|AI|0.038**|0.046**|0.128***|0.123***|
||[0.018]|[0.022]|[0.034]|[0.033]|
|Cluster algorithm|0.040**|0.052**|0.337***|0.364***|
|(High density)|[0.019]|[0.023]|[0.068]|[0.074]|
|Cluster algorithm|0.039*|0.047*|0.180**|0.206*|
|(Urban cluster)|[0.020]|[0.025]|[0.082]|[0.098]|
|n|47,513|33,243|13,610|11,018|

**_Notes:_** The dependent variable in all columns is the natural log of hourly wage. Standard errors clustered at the metro level are reported in brackets. ***, **, *, denotes significance at the 1 percent, 5 percent and 10 percent levels respectively. All results include the full set of job and worker characteristics discussed in Section 4.1.1, as well as the share of skilled workers in the metro area’s workforce, the share of workers in the metro area’s workforce employed in the same sector as the worker him/herself, as well as the natural log of a district’s market access to all other Indonesian districts. See Section 4.1.1 for a detailed definition of these variables. The number of observations varies by metro area definition used. To give an idea of the relative sample size, the reported number of observations denotes the number of observations using the “Duranton: 10 %” approach to define metro areas.

> 39 Results for the three additionally included agglomeration variables are available upon request. Generally, we find that a district’s market access to other Indonesian districts, if significant, negatively affects nominal wages, and, if significant, a positive effect of a metro area’s share of skilled people in the workforce, and a mostly insignificant negative effect of a metro area’s degree of sectoral specialization.

26
# **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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