Cities, Lights, and Skills in Developing Economies∗
Jonathan I. Dingel†
Chicago Booth and NBER

Antonio Miscio‡
BCG

Donald R. Davis§
Columbia and NBER

May 2019

Abstract
In developed economies, agglomeration is skill-biased: larger cities are skill-abundantand exhibit higher skilled wage premia. This paper characterizes the spatial distributions of skills in Brazil, China, and India. To facilitate comparisons with developedeconomy findings, we construct metropolitan areas for each of these economies by
aggregating finer geographic units on the basis of contiguous areas of light in nighttime
satellite images. Our results validate this procedure. These lights-based metropolitan
areas mirror commuting-based definitions in the United States and Brazil. In China
and India, which lack commuting-based definitions, lights-based metropolitan populations follow a power law, while administrative units do not. Examining variation in
relative quantities and prices of skill across these metropolitan areas, we conclude that
agglomeration is also skill-biased in Brazil, China, and India.

Keywords: cities, metropolitan areas, satellite images, skill-biased agglomeration, Zipf’s
Law
JEL classification: R1, O1, O18, C8∗

We are grateful to Stuart Rosenthal and two anonymous referees for very valuable suggestions. We
thank Luis Costa, Kevin Dano, Shirley Yarin, Yue Yuan, and especially Dylan Clarke for excellent research
assistance. We thank Andrei Potlogea for a helpful discussion and Juan Pablo Chauvin for sharing suggestions
and data. Dingel thanks the Kathryn and Grant Swick Faculty Research Fund and the James S. Kemper
Foundation Faculty Research Fund at the University of Chicago Booth School of Business for supporting
this work.
†
jdingel@chicagobooth.edu‡
miscio.antonio@bcg.com§
drdavis@columbia.edu

11Introduction

This paper studies the distribution of skills across and within cities in three large developing
economies: Brazil, China, and India. These three countries jointly account for approximately
40% of the world’s population and are diverse in their levels of income. The process ofurbanization in developing economies is important due to both the number of people involved
and the opportunity to shape outcomes. The World Bank projects that 2.7 billion additional
people will live in cities in developing economies by 2050. While urbanization does notnecessarily imply growth, the two are nonetheless strongly linked (Henderson, 2014).
In developed economies, agglomeration appears to be skill-biased. There is a well-known
positive relationship between metropolitan population and the share of the population possessing a college degree (Costa and Kahn, 2000; Moretti, 2004; Bacolod, Blum and Strange,2009). Davis and Dingel (2017) study more narrowly defined educational categories and document that larger cities are skill-abundant and specialize in skill-intensive activities. Despite
this greater relative supply of skill in larger cities, the college wage premium is also higher
in larger cities (Baum-Snow and Pavan, 2013; Davis and Dingel, 2019). The implied greater
relative demand for skill in larger cities suggests that agglomeration complements skill in
production (Giannone, 2018). Within US metropolitan areas, more skilled residents haveincreasingly moved to city centers in the last two decades (Couture and Handbury, 2017).
Do the urban systems of developing economies also exhibit these spatial patterns? This
paper is a first step in characterizing the spatial distributions of skills and sectors in Brazil,
China, and India. Cities in developing economies will not necessarily mirror corresponding
characteristics of developed economies. The existence of cities still requires agglomerationand dispersion forces, but the technologies and conditions of production and consumption incities can diverge sharply. It is an empirical question whether developing economies’ larger
cities are populated by more skilled residents who earn relatively higher wages and live near
the city center. We begin to tackle this question by examining some of these patterns inthree large developing economies.
Studying the distribution of skills across and within metropolitan areas in Brazil, China,
and India necessitates constructing metropolitan areas consistent with our economic inquiry.
Economic theory treats a city as a highly – if imperfectly – integrated labor market. For
this and other reasons, statistical agencies in developed economies overwhelmingly define
metropolitan areas on the basis of commuting flows (Duranton, 2015). Unfortunately, such
commuting flow measures are not always available to define metropolitan areas in developing economies. This is the case in China and India. In practice, researchers studying cities
in developing economies have employed a variety of measures of the relevant geographies,
often using off-the-shelf administrative definitions of cities. These spatial units often do notcorrespond to the metropolitan areas employed in research describing cities in developed
economies. Administrative or political boundaries can fragment economically integrated areas into distinct cities or circumscribe places, including rural areas, that are not integrated
metropolises. Assessing whether developing economies exhibit spatial patterns of skills similar to those of developed economies requires an appropriate geography defining cities’ sizes
and economic characteristics.
In Section 2, we develop a method to define metropolitan areas in the absence of commuting data by using satellite images. Our approach aggregates spatial units into metropolitan2areas on the basis of lights at night. When municipalities or towns are part of a sufficiently
bright, contiguous area of light, they belong to that metropolitan area. We demonstrate thefeasibility and value of such an approach in three steps. First, we show that, with appropriately selected light-intensity thresholds, our night-lights–based method produces metropolitan areas that match commuting-defined US metropolitan areas very well. Second, we showthat this is also true in a developing-economy setting, Brazil, where data on both commuting
flows and night lights are available. Third, the application of our night-lights–based approachto China and India eliminates anomalies in their city-size distributions. While spatial units
defined by administrative boundaries in these countries seem to deviate from a power-law
distribution (Chauvin et al., 2017), our night-lights–based definitions of cities accord muchbetter with the empirical regularity exhibited in developed economies.
Using these definitions of metropolitan areas, we aggregate census data to characterize
the spatial distributions of skills across metropolitan areas in Section 3. We characterizespatial variation in relative quantities of skill by employing a linear regression implied by
the theory of Davis and Dingel (2017). In all three developing economies, larger cities are
skill-abundant. This result is robust to our choice of the light-intensity threshold employedin our algorithm defining metropolitan areas. However, we obtain substantially different
population elasticities in some cases when using the administrative definitions of spatial
units that have been commonly used in previous research.
We also characterize within-metro variation in quantities of skill for Brazil and China(Section 4) and spatial patterns of wages for Brazil (Section 5). In both Brazil and China,
more skilled residents tend to live closer to the center of metropolitan areas. In Brazil, college
wage premia are higher in more populous cities, consistent with developed-economy patterns
and the hypothesis that agglomeration increases productivity in a skill-biased manner. The
limited scope of this part of our investigation is dictated by data availability. Studies that use
satellite imagery to both define urban markets and measure outcomes, such as Baragwanath
Vogel et al. (2018), do not face such limitations. But in the absence of satellite-based meansof measuring skill-related outcomes, we must employ both satellite and administrative data
to answer fundamental questions about the urban systems of developing economies.
Our paper belongs to a growing literature on urbanization in developing economies.
Perhaps most closely related are Henderson (1991) and Chauvin et al. (2017), who also focus
on urban development in Brazil, China, and India, and Hu, Brakman and van Marrewijk(2014), who study China. In particular, Chauvin et al. (2017) examine whether stylized
facts about metropolitan areas in the United States also hold true in Brazil, China, andIndia using administrative spatial units commonly available in government data releases.
Hu, Brakman and van Marrewijk (2014) examine the predictions of Davis and Dingel (2017)
for China using administrative spatial units. Our investigation complements these studies
by focusing on the spatial distribution of skills and developing definitions of metropolitan
areas that are more comparable to the economically integrated entities studied in researchon developed-economy cities.
Our night-lights–based approach to defining metropolitan areas is distinct from the administrative units defined by government statistical agencies, a commuting-based algorithm
introduced by Duranton (2015), and a distance-based clustering algorithm introduced by
Rozenfeld et al. (2011). The administrative units defined by government agencies often do notcorrespond to the integrated metropolitan areas of interest to economists. The commuting3

based approach is ideal, but its application is constrained by the absence of economy-widecommuting data in many countries. The city-clustering algorithm of Rozenfeld et al. (2011)
aggregates adjacent spatial units on the basis of proximity without exploiting information
about the contiguity of economic activity. We use night lights, which are available at veryfine spatial resolution, to inform the aggregation of spatial units for which socioeconomic
data are available.
Our employment of satellite imagery to define metropolitan areas belongs to a rapidly
expanding economics literature exploiting satellite data, recently surveyed by Donaldson andStoreygard (2016). The use of satellite imagery to infer urban extent dates at least to Welch(1980), who inferred Chinese cities’ populations from their built-up areas in the absenceof a population census. Much of the recent economics research, such as Bleakley and Lin(2012), Henderson, Storeygard and Weil (2012), and Storeygard (2016), has utilized night
lights as a proxy for local economic activity at a finer resolution than typically documented
in administrative data. We use night lights as a basis for identifying contiguous areas of
economic activity that define metropolitan areas and then characterize those metropolitan
areas’ socioeconomic characteristics by aggregating spatial units available in more traditional
data sources. Our application to India is similar to Harari (2017), who defines Indian cities’
spatial extent using night lights, aggregates population counts for these footprints, andrelates cities’ economic outcomes to their compactness. Relative to her work, we validate
the lights-based approach by comparing it to commuting-based definitions, show that lightsbased metropolitan areas differ substantially from the geographic units used in much priorresearch on Brazil, China, and India, and characterize the spatial distributions of skills inthese three economies.

2

Defining metropolitan areas

In order to characterize the spatial distribution of skills and sectors, we construct metropolitan areas from finer geographic units for Brazil, China, and India. Research describing
cities in the United States and other developed economies typically uses spatial units defined by economic integration rather than legal jurisdictions or administrative boundaries.
Agglomeration forces, commuting flows, and other economic linkages do not stop at municipal, county, or state borders, so using these boundaries to define the unit of analysis would
fragment economically integrated metropolitan areas.1 In Brazil, China, and India, however, prior research describing urbanization has used spatial units defined by administrative
boundaries due to the absence of spatial units analogous to US metropolitan statistical areasin these countries.
We propose a method for constructing metropolitan areas from smaller geographic units
based on night lights. First, we validate our method by showing that applying it to theUnited States yields spatial units very similar to those defined by the government statistical1

As described by Duranton (2015), most commonly used definitions of metropolitan areas emphasize
commuting flows as the relevant economic linkage, treating metropolitan areas as integrated labor markets.
Employing administrative definitions that fragment these entities can alter research conclusions. For example,
when workplaces employ a mix of skills but there is residential sorting by skill, calling such units cities would
overstate between-city skill differences and understate within-city skill sorting.

4

agency based on commuting flows. Second, we apply both our night-lights–based method
and a commuting-flow method to Brazil, for which both types of data are available, andfind that they yield similar outcomes. Third, we construct metropolitan areas for China andIndia using satellite images of night lights, since commuting data are not available in thesetwo countries.
In a number of cases, these metropolitan areas differ from urban units defined by political boundaries. These differences are sufficiently large that they affect conclusions about
the distribution of population and economic activity across space. For example, we showthat the city-size distribution in China conforms reasonably well to Zipf’s law when we usenight-lights–based metropolitan areas, while Chauvin et al. (2017) have shown substantial
deviations from Zipf’s law when using administrative units that incorporate substantial rural
territories.2

2.1

Building metropolitan areas from satellite data

We propose a method for aggregating spatial units into a “metropolitan area” defined bya contiguous area of lights at night. Figure 1 illustrates the procedure for a portion of theeastern coast of China along the East China Sea in 2000.
The two inputs to the algorithm are a satellite (raster) image of the country at night anda shapefile of the administrative units for which socioeconomic characteristics are reported.
In the raster image, each pixel has a light intensity that is reported as an integer between
0 (no light) and 63 (top-coded value). The left panel of Figure 1 depicts these values as a“heatmap” over the administrative boundaries of Chinese townships.
Upon selecting a light-intensity threshold, we identify contiguous areas of light brighter
than the selected threshold. This yields polygons, as demonstrated in the middle panel of
Figure 1, which uses a light-intensity threshold of 30. Note that the polygons themselves areformed without reference to administrative boundaries. The largest polygon in that panel
corresponds to the city of Shanghai. Our assumption is that contiguity of lights at night is
informative about integration of economic activity.
We use the intersection of the night-lights–based polygons and the spatial units to construct metropolitan areas. A township that intersects one light polygon is assigned to thatpolygon. In the case of multiple intersections, a township is assigned to the light polygon containing the greatest area of the township.3 The union of the spatial units assigned
to a light polygon constitutes a metropolitan area. The right panel of Figure 1 depicts themetropolitan areas that result from applying our procedure to Chinese townships. Note that,
unlike a distance-based clustering algorithm, our procedure often assigns adjacent townships
to different metropolitan areas.
2

Zipf’s law for cities (the number of cities larger than L is proportionate to 1/L) is an empirical regularity found to hold in many countries and time periods (Gabaix and Ioannides, 2004), although numerous
deviations have also been documented (Ades and Glaeser, 1995; Soo, 2005; Findeisen and Südekum, 2008).
Theoretical models attribute this power-law distribution to random growth (Gabaix, 1999), a process ofurban industrial churn (Duranton, 2007), or the product of multiple random factors (Lee and Li, 2013).
3
Since townships are the finest spatial unit available, land area is the only characteristic upon whichassignment criteria can depend. Our assignment of the entire township to one polygon makes our procedurecomparable to other algorithms doing likewise, such as Duranton (2015).

5

Figure 1: Building metropolitan areas by aggregating smaller units based on lights at night(a) Inputs(b) Forming polygons(c) Metropolitan areas

Notes: This figure illustrates our procedure for combining satellite imagery of lights at night withadministrative spatial units to build metropolitan areas. These panels depict a portion of the eastern
coast of China in 2000. The administrative spatial units are townships. The polygons in the middle
panel are areas of contiguous light brighter than 30. Aggregating the townships that intersect thesepolygons produces the metropolitan areas depicted in the right panel. Adjacent townships are often
assigned to distinct metropolitan areas.

Finally, we impose a minimum population size to include a metropolitan area in our
analysis of metropolitan economic outcomes. Following the literature (e.g., Chauvin et al.
2017), we focus on metropolitan areas with populations greater than 100,000. A metropolitan
area’s population is the sum of the constituent spatial units’ populations.
The choice of the light-intensity threshold, which governs the definitions of the resulting
metropolitan areas, is not pinned down by economic theory or prior empirical research. The
relationship between the threshold and the number of metropolitan areas defined is ambiguous. On the one hand, a lower threshold aggregates more spatial units into a given polygon,
potentially defining more metropolitan areas with populations greater than 100,000. On
the other hand, a lower threshold may cause distinct areas of light to be combined into
one polygon, reducing the number of metropolitan areas. Table 1, discussed below, demonstrates that the number of metropolitan areas is indeed non-monotone in the light-intensity
threshold. Beyond this extensive margin, the choice of threshold affects the compositionof these metropolitan areas’ characteristics. To address this issue, we report results for avariety of light-intensity thresholds and examine whether they are sensitive to this choice.
Our qualitative conclusions about the spatial distribution of skills do not depend upon theparticular threshold used.
As shown in the middle panel of Figure 1, the night-lights–based polygons can intersectwith sets of townships in a variety of ways. Given the spatial resolution of these polygons
and administrative units, the edges of the resulting metropolitan areas may be defined withsignificant error.4 We cannot really improve upon this, given the absence of data on within4

This concern seems intuitively sensible, although we lack a precise notion of the urban boundary that6

township variation in economic characteristics. While we show that our empirical results
are not sensitive to the choice of light-intensity threshold, research questions particularly
focused on the “urban fringe” of metropolitan areas may be more sensitive to such choices.

2.2

US metropolitan areas

While this paper focuses on the spatial distribution of economic activity in developing
economies, we use the United States as a testing ground to validate the night-lights–based
method we develop to construct metropolitan areas in the absence of commuting data. In
the United States, the Office of Management and Budget (OMB) aggregates US counties
that meet certain requirements into a set of core-based statistical areas (CBSAs), which aredesignated metropolitan or micropolitan statistical areas depending on their size. The coreis an urban population area of sufficiently large size. Outlying counties are adjoined to thecentral counties constituting this urban core on the basis of commuting ties.5 Counties that
do not meet these requirements are not included in any CBSA.
Recently, Duranton (2015) proposed an algorithm for defining metropolitan areas by theiterative aggregation of spatial units on the basis of commuting ties without requiring theinitial designation of an urban core. Duranton applied this method to Colombia; here weapply it to US data to construct an alternative geography of US metropolitan areas. Our
purpose is to establish that the Duranton (2015) method, which we will apply to Brazil,
produces metropolitan areas similar to those defined by the OMB.6
We aggregate US counties into metropolitan areas on the basis of county-to-county commuting flows reported in the 2009-2013 American Community Survey.7
Our night-lights–based approach is a departure from these commuting-based methods.
When we apply our night-lights–based method to the US, aggregating counties to build
metropolitan areas, we obtain definitions of US metropolitan areas that are very similar
to OMB-defined core-based statistical areas. To demonstrate this, we take the 377 OMBdefined CBSAs with a population above 100,000 as our baseline and match each one ofthem to the best corresponding metropolitan areas defined by the alternative methods basedon commuting flows and night lights.8 We then compare log population and log land area
we would define even if we possessed ideal data.
5
An outlying county is aggregated into a CBSA if either of the following criteria is met: (i) at least 25%of the workers living in the outlying county work in the CBSA core; or (ii) at least 25% of the employment in
the county is accounted for by workers who reside in the CBSA core. See Office of Management and Budget(2010) for a complete explanation. Prior to 2010, “local opinion” was an input into defining CBSAs.
6
In cases of disagreement, it is not obvious which one should prefer. While the OMB definitions arewidely used, Duranton (2015) provides reasons to prefer an algorithmic approach that does not require thedesignation of an initial core.
7
The iterative algorithm requires the choices of a minimum commuting threshold to combine counties
that are sufficiently connected by commuting ties. As discussed in Duranton (2015), the choice of a thresholddepends on the size of the units to be aggregated as well as the level of economic development and qualityof transportation systems. While a threshold of 10% was deemed appropriate for Colombian municipios(median land area 288 km2 ), these criteria suggest that higher thresholds seem appropriate for the UnitedStates despite the much larger size of its counties (median land area 1,594 km2 ). We report the results ofconstructing metropolitan areas using a range of commuting thresholds.
8This matching is not one-to-one in all cases. Counties from multiple CBSAs may be assigned to the samelight-based metro, and different counties within one CBSA may be assigned to different light-based metros.

7

1
.95
.75
.7

.7

.75

.8

.85

.9

Correlation with OMB-defined CBSAs
.8
.85
.9
.95

1

Figure 2: Comparing population and land area across US metropolitan-area definitions, 2010

30

40
50
Threshold for light intensity

60

10%

Population

15%
20%
25%
30%
Threshold for commuting flows

35%

Land area

Notes: The left panel depicts correlations of log population and log land area between metropolitan areas defined by contiguous areas of lights at night and 377 OMBdefined core-based statistical areas (CBSAs) with population above 100,000 in the 2010
US Census of Population. The right panel depicts correlations of log population andlog land area between metropolitan areas defined by commuting flows and the OMBdefined CBSAs. The horizontal axes vary the thresholds for light intensity (left panel)and commuting flows (right panel) used to define metropolitan areas in our procedureand the Duranton (2015) procedure, respectively. Footnote 8 describes how we pair
CBSAs with comparison counterparts.

across agglomeration schemes, a comparison made by Rozenfeld et al. (2011) to validate
their method.
The left panel of Figure 2 shows that the correlation of log population between CBSAs
and their night-lights–based counterparts is about 0.98 and relatively insensitive to the choiceof light-intensity threshold. Similarly, the right panel shows that the correlations of log population between CBSAs and their commuting-flow-based counterparts exceed 0.96 and vary
little with the minimum commuting threshold used in the Duranton (2015) algorithm. Boththe night-lights–based and commuting-based metropolitan areas exhibit larger discrepancies
with OMB-defined CBSA in terms of land area, where the correlations average about 0.8.
This is natural, given that definitions of these metropolitan areas are more likely to differ
in their inclusion of boundary areas that have low population densities. Given our focus on
the pattern of economic activity in terms of skills and sectoral employment, the alignmentof population levels is more important for our purposes than the alignment of land area.
We compare each of our light-based metropolitan areas to the CBSA with the largest population assigned tothat metro, provided that CBSA does not have a greater population assigned to another light-based metro.

8

Our summary of these outcomes is that the US metropolitan-area population distribution can be well approximated by either of the alternative geographies and the quality ofthis approximation is not particularly sensitive to the threshold employed to define the agglomerations. This is our first finding validating our night-lights–based method, albeit in adeveloped-economy context. The fact that these methods are not particularly sensitive totheir threshold parameters is encouraging for their application to settings where we cannot
tune those parameters to replicate some (non-existent) official definition.

2.3

Brazilian metropolitan areas

Among the three developing economies that we study, only Brazil makes nationwide commuting data available, permitting us to implement more than one approach to defining
metropolitan areas there. We will use this setting to compare our night-lights–based approach to the results of the approach based on commuting flows in a developing-economy
context. Validating our night-lights–based approach in this setting is important because
commuting-flow data is not available in the Chinese and Indian contexts.
Brazil is partitioned by a hierarchy of increasingly fine geographic units: states (26),mesoregions (137), microregions (558), and municipios (5565). The states and municipios
are political entities. The mesoregions and microregions are areas defined by the Brazilian
Institute of Geography and Statistics (IBGE) for statistical purposes and do not constituteautonomous political or administrative entities. The IBGE defines microregions according
to shared forms of economic activity but not explicitly on the basis of commuting.9 Our
commuting-based and night-lights–based methods will be applied to municipios, the finest
geographic unit available, in order to define metropolitan areas.
Prior research on local labor markets in Brazil has used four different geographic units.
First, a number of papers have used microregions as the unit of analysis.10 We will compareand contrast microregions with our commuting- and night-lights–based metropolitan areas
below in Section 2.6. Second, a few researchers (e.g., Bustos, Caprettini and Ponticelli
2016; Cavalcanti, Mata and Toscani 2016) have used municipios as their spatial unit. Thisis appropriate for some research questions, but raises potential problems if the outcomesof interest depend on economic interactions at a supra-municipio level (e.g., local labormarkets linked by commuting). Third, the IBGE recently defined arranjos populacionais byaggregating municipios on the basis of urban density and flows to work or school (IBGE,
2016). A few researchers have employed these units (Chauvin, 2017; Dı́az-Lanchas et al.,2018; Scherer and Folch, 2017), and we will compare them to our metropolitan areas whendescribing the spatial distribution of skills in Sections 3 and 4.
Fourth, a less popular approach has employed definitions of metropolitan areas that thestates themselves have developed.11 These are known as Regiões metropolitanas. This has
9

See the criteria employed at http://www.ngb.ibge.gov.br/Default.aspx?pagina=divisao.
See for instance Kovak (2013); Dix-Carneiro and Kovak (2015); Costa, Garred and Pessoa (2016);
Chauvin et al. (2017).
11
See, for instance, Hoffmann (2003). More generally, any study that relies on data from the Brazilian
statistical agency (IBGE) aggregated by metropolitan area has indirectly used this definition, includingcommonly used data such as the National Sample Survey of Households (PNAD) and the Urban Labor
Force Survey (PME).
109three problems. The first, again, is that agglomerations may cross state borders and thedefinitions of metropolitan areas do not include these cross-boundary areas. This problem
was officially recognized by federal authorities in 1998 and solved with the introduction of a
new type of metropolitan area that may cross state boundaries. The latter are called Regiões
integradas de desenvolvimento econômico or RIDE. The second problem is that the criteria
for inclusion are state-specific. As the following example illustrates, these legal definitions are
subject to the vagaries of the legislative process, so they are not consistent across states nortime: the southern state of Santa Caterina suppressed five of its six Regiões metropolitanasin 2007, only to re-create all of them and a few more in 2010. The third problem is that bydefinition each Região metropolitana and RIDE must contain at least two municipios. This
results in the exclusion of large agglomerations contained within one municipio. Finally,
most states have used a high population cutoff for inclusion as a metropolitan area, withthe consequence that many agglomerations, including some with populations of nearly halfa million people, are excluded from these data.
Our first approach to building metropolitan areas in Brazil applies the Duranton (2015)
method to 2010 Brazilian Census data on commuting flows between municipios.12 We aggregate municipios into endogenously defined metropolitan areas using an iterative process that
depends on our choice of a minimum commuting threshold. In our preferred specification,
we use a threshold of 10% of the local working population.13 We work with metropolitan
areas with a minimum population of 100,000.14
Our second approach to building metropolitan areas in Brazil is based on satellite datacharacterizing lights at night, as described in Section 2.1. We construct encompassing polygons that depend on the choice of a light-intensity threshold. We then assign municipios tothese polygons in order to define metropolitan areas. If a municipio intersects with a single
polygon, it is assigned to the corresponding metropolitan area. If a municipio intersects
multiple polygons, it is assigned to the polygon with which it has the largest overlap.
Our commuting-based and night-lights–based methods produce quite similar metropolitan areas. Taking the 10% commuting threshold as our preferred specification, we compare
metropolitan areas defined by night lights and alternative commuting thresholds in termsof the correlation of log population and log land area. As Figure 3 shows, the correlations
for population are very high, exceeding 97%, across all the reported thresholds. That is, interms of population, the commuting-based and night-lights–based metropolitan areas withpopulations above 100,000 are quite robust to the choice of agglomeration-method parameters. As in the US case, the correlations for land area are weaker but still quite informative,
exceeding 80% for all light-intensity thresholds and 90% for all commuting thresholds. Thisis quite sensible because the municipios included or excluded are those at the boundary of
12

These commuting-flow data are not available for earlier years.
As mentioned in footnote 7, the threshold choice depends on economic development, transport infrastructure, and geographic size. Compared to Colombia, Brazil’s larger municipios (median area 416 km2 vs
288 km2 ) suggest a lower threshold, while its higher GDP per capita ($8,600 vs $6,000 in 2015) pushes in
the opposite direction. Hence, we choose to apply to Brazil the same 10% threshold applied to Colombia by
Duranton (2015).
14
With the 10% threshold, we obtain 4,807 metropolitan areas with populations ranging from 805 residents
to 19 million. 192 of these metropolitan areas have populations greater than 100,000, and they contain 60%
of Brazil’s total population and 68% of its urban population.
13

10

1
.8

.85

.9

.95

Correlation with 10%-commuting-based metropolitan areas
.8
.85
.9
.95
1

Figure 3: Comparing population and land area across Brazilian metropolitan-area definitions, 2010

10

20
30
40
50
Threshold for light intensity

60

5%Population

10%
15%
20%
Threshold for commuting flows

25%

Land area

Notes: The left panel depicts correlations of population and land area between
metropolitan areas defined by contiguous areas of lights at night using different thresholds. The right panel depicts the same for metropolitan areas defined by commuting flows using different thresholds. The baseline for comparison in both panels is
metropolitan areas defined by commuting flows in 2010 with a 10% threshold, per Duranton (2015). Thus, the perfect correlation at the 10% threshold in the right panel istautological. Footnote 8 describes how we pair metropolitan areas with their baselinecounterparts. The sample is restricted to metropolitan areas with population above
100,000.

the metropolitan areas, which typically have lower population densities and larger physical areas. The correlation is greater than in the US case because Brazilian municipios are
typically smaller geographic areas than US counties.
The key result of our comparison of Brazilian metropolitan areas constructed on the basisof commuting and satellite data is their similarity. There is a close correspondence between
the preferred approach based on commuting data, which we will use as our baseline definition in our work on Brazil, and the night-lights–based approach that can be applied to all
countries. This correspondence is relatively insensitive to the light-intensity threshold used.
This should give us confidence that when we use satellite data in China and India, where
we do not have commuting data, we will obtain sensible definitions of metropolitan areas.
The weaker relation with physical area is of little consequence for the research questions we
address here, as they do not depend on densities in an important way.
11

2.4

Chinese metropolitan areas

The basic geographical units in mainland China are provinces (31), prefectures (333, as of2013), counties (2853), and townships (40,497). The first three are geographic partitions of
the country. Townships, roughly speaking, partition the populated geography of the country,
since the only areas excluded from townships have very small populations. Urban administrative units mirror this hierarchical governance structure: there are provincial-level cities,
deputy-provincial cities, provincial capitals, prefecture-level cities, and county-level cities(Chan, 2010). These designations are time-varying and endogenous, as local jurisdictions
can be promoted to higher administrative ranks as they grow. The four provincial-level
cities, Beijing, Chongqing, Shanghai, and Tianjin, have the same administrative status asprovinces and span many thousands of square kilometers in area. Prefecture-level cities
are equivalent in administrative status to prefectures, span similarly large areas, and overtime have come to dominate this administrative level as prefectures have been converted
to prefecture-level cities. Today, nearly 300 of China’s prefecture-equivalent administrative
units are prefecture-level cities; less than a dozen are designated as prefectures.15
The spatial units most commonly used in prior research on Chinese urbanization havebeen the urban administrative units ranked as prefecture-level cities or higher. These offer
one huge advantage: administrative cities are often the most conveniently available data
(and in early periods may be the only form available). Yet there are large downsides.
First, because prefectures differ dramatically in population, the set of prefecture-level cities
includes some very small prefecture-level cities and does not recognize some very large cities
that lack the prefecture-level designation. Second, provincial-level and prefecture-level cities
incorporate both substantial rural areas and distinct urban areas not necessarily economicallyintegrated with the prefecture-level city’s urban core.16 Third, the prefecture-level cities arenecessarily bounded by the prefecture, whereas economically integrated metropolitan areas
need not be. A particularly problematic example is the pair of prefecture-level cities of
Guangzhou and Foshan. While administratively separate, they are geographically proximate;
the distance from downtown Guangzhou to downtown Foshan is only about 18 miles. The
two cities share connected subway lines, and it is not uncommon for people to live in Foshan
and work in Guangzhou.
We use night lights to build Chinese metropolitan areas. While the preferred approachto defining an economically integrated labor market in economies such as the United States
relies on commuting data, this method cannot be applied to China due to Chinese commuting data only being available for a quite limited set of areas. Based on our finding that
commuting-based and night-lights–based methods delivered similar results when applied toBrazil, we apply the night-lights–based approach to China. We build metropolitan areasby aggregating counties or townships.17 The latter is preferable, because it addresses the15

In addition to prefectures and prefecture-level cities, this administrative level includes “leagues” of Inner
Mongolia and “autonomous prefectures.” Chan (2007) warns that the “system of urban definitions used in
Mainland China. . . appears to be the world’s most complicated and confusing.”
16
Chan (2007) reports that “the current administrative boundaries of a great majority of large Chinese
cities extend far beyond the familiar ‘metropolitan area’ or ‘city proper’ patterns by including rural counties,some with dense farming populations.”17
In year 2000 definitions, the median township had a land area of 72 km2 . In year 2000 definitions, themedian county had a land area of 1,582 km2 .

12

Table 1: Comparing Chinese township- and county-based metropolitan areas, 2000
Correlation with township-based
Intensity: 10 Intensity: 30 Intensity: 50
Metropolitan scheme

N

Pop’n

Land

Pop’n

Land

Pop’n

Land

County-based, intensity 10
County-based, intensity 20
County-based, intensity 30
County-based, intensity 40
County-based, intensity 50
County-based, intensity 60
Township-based, intensity 10
Township-based, intensity 20
Township-based, intensity 30
Township-based, intensity 40
Township-based, intensity 50
Township-based, intensity 60

1705
1464
1167
811
501
185
1139
960
805
599
405
151

0.76
0.71
0.70
0.74
0.77
0.84

0.41
0.28
0.20
0.08
0.05
0.09

0.92
0.90
0.89
0.86
0.84

0.81
0.75
0.66
0.60
0.50

0.78
0.73
0.70
0.72
0.75
0.85
0.93
0.98

0.42
0.31
0.27
0.22
0.15
0.22
0.76
0.87

0.95
0.90
0.88

0.82
0.74
0.62

0.81
0.82
0.78
0.76
0.75
0.86
0.91
0.95
0.96
0.98

0.38
0.35
0.28
0.24
0.26
0.26
0.66
0.75
0.80
0.88

0.91

0.65

Notes: The first column reports the number of metropolitan areas with population exceeding
100,000 that are defined by that row’s metropolitan scheme. Each cell in the following six columns
reports the correlation coefficient for log population or log land area between the metropolitan
scheme identified in the row and the metropolitan scheme identified in the column pairs for China
in 2000. We pair metropolitan areas for comparison as described in footnote 8.

problems of erroneously including economically disconnected areas and rural areas in thedefined metropolitan areas. Unfortunately, township-level data for 2010 are not yet publicly
available for many socioeconomic characteristics of interest.
There are substantial differences between metropolitan areas obtained by aggregating
townships and those obtained by aggregating counties. Table 1 illustrates these differencesin two dimensions, reporting the correlations of log population and log land areas acrosscomparable locations under different metropolitan-area definitions. The metropolitan areas
obtained by aggregating townships are relatively consistent across different choices of thelight-intensity threshold. The level of correlation typically exceeds 0.8 for population and
0.6 for land area. In contrast, the correlation between county-based and township-based
metropolitan areas are typically below 0.8 for population and 0.4 for land area. This is
unsurprising, as there are an order of magnitude more townships than counties in China,
and townships cover only populated areas while counties partition the entire landmass. Thisstrongly favors using township- over county-based metropolitan areas when possible. For
total population and land area, Table 1 demonstrates the possibility that metropolitan characteristics may not be sensitive to the choice of light-intensity threshold.

13

2.5

Indian metropolitan areas

India is partitioned by a hierarchy of increasingly fine geographic units: states (35), districts(640), and sub-districts (5564).18 Distinctly, the Census of India divides the country into
urban and rural areas, with urban areas being comprised of two types of towns, “statutory
towns” defined by their political character and places that are sufficiently populous, nonagricultural, and dense to be declared “census towns.”19 The Census furthermore defines
an “urban agglomeration” (UA) as one or more physically contiguous towns with at least
20,000 residents. There were 384 UAs in 2001 and 475 UAs in 2011. Towns and urban
agglomerations can span subdistrict and district borders, but by definition they do not
cross state borders. This results in major metropolitan areas composed of multiple urban
agglomerations. For example, Chandigarh is a city and union territory that is the capital of
the states of Haryana and Punjab that is part of the “tricity” Chandigarh Capital Region,
which has a regional planning board to coordinate an economically integrated area thatspans three states.
Most prior research on urbanization in India has used (the urban population of) districts
as the geographic units of interest. This has two immediate shortcomings. The first isthat the towns within a district need not themselves be contiguous or have strong economic
connections. This is non-trivial since an Indian district is roughly twice the size of a US
county. The second is that there may be strong connections between contiguous urban areas
in different districts that are ignored in this approach. Each of these problems finds a partial
solution in the Indian statistical agencies’ definition of “urban agglomerations.”
We consider two different methods for defining Indian metropolitan areas, each imperfect in some respects. The first is to apply our night-lights–based approach to the urban
populations of subdistricts, the finest spatial unit for which both a geographic shapefile andsocioeconomic characteristics are publicly available.20 However, only a limited set of socioeconomic characteristics are reported for subdistricts.21 The second is to use administratively
defined urban agglomerations and cities, agglomerated across state borders on the basis ofnight lights.22 Socioeconomic characteristics are available for urban agglomerations’ component census towns of population greater than 100,000. Unfortunately, we are not aware
18

Here we use “states” to refer to “states and union territories.” There were 35 states prior to 2014, whena new state, Telangana, was created, constituted by ten districts formerly in northwestern Andhra Pradesh.
Sub-districts are known by names that vary across states, including mandal, tahsil, taluk, and block. See“Statement showing the Nomenclature and Number of Sub-Districts in States/UTs”.
19
Statutory towns are administrative units defined to be urban, such as municipal corporations, municipalities, and so forth. In 2011, a “census town” was a place with population greater than 5,000 persons,at least 75% of male laborers working outside agriculture, and population density greater than 400 persons
per square kilometer. See Census of India 2011, Provisional Population Totals, Urban Agglomerations andCities.
20
In year 2001 definitions, the median sub-district had a land area of 374 km2 .
21
Chauvin (2017), Harari (2017), and other researchers have addressed this shortcoming by using districtlevel averages as proxies for city-level averages when studying economic outcomes.
22
We aggregate urban agglomerations and towns across state borders using contiguous areas with lightintensity exceeding 20 defined by collections of subdistricts. When such a polygon crosses state borders,
we aggregate the urban agglomerations and sufficiently large towns belonging to that polygon into a single metropolitan area. This produces two metropolitan areas that span three states: Greater Delhi andChandigarh Tricity.

14

Figure 4: Brazilian microregions and commuting-based metropolitan areas, 2010

Notes: This figure depicts northeastern Brazil, including the states of Rio Grande
do Norte and Pernambuco. Microregion boundaries are depicted by black lines.
Commuting-based metropolitan areas (population greater than 100,000) are depictedby colored polygons. These metropolitan areas are defined by commuting ties between
municipios in 2010, using the Duranton (2015) algorithm with a 10% threshold.

of publicly available shapefiles for towns and villages, which we would need to apply ournight-lights–based approach to geographically finer administrative units.

2.6

Comparison with administrative units

Prior work on urbanization in Brazil, China, and India has typically relied upon administrative units, such as microregions in Brazil and prefecture-level cities in China, that do
not necessarily coincide with economically integrated metropolitan areas. In this section, we
compare our definitions of metropolitan areas to the geographic units employed in previous
research.
For Brazil, comparing our commuting-based metropolitan areas to the microregions usedin prior research reveals substantial discrepancies. Microregions may be defined too narrowly
or too broadly for such purposes. The former occurs frequently when agglomerations crossstate boundaries, since microregions are defined to be strict subsets within a single state.
The latter occurs when there are multiple small agglomerations of similar economic activity
grouped into a single microregion even though these components are not significantly integrated by commuting. For example, Figure 4 shows all the commuting-based metropolitan
areas (color-coded) with a population above 100,000 in northeastern Brazil and microregion
boundaries (dashed). We can spot several metropolitan areas that cross microregion boundaries, as well as one microregion that contains two distinct metropolitan areas. Moreover, we
can see that most microregions containing a metropolitan area also encompass large areasthat are not integrated to the metropolitan area by commuting ties. This mismatch between
microregion boundaries and commuting-based metropolitan areas occurs in other areas of
Brazil as well. 44 of the 192 metropolitan areas with population greater than 100,000, containing 59% of the population of such locations, span multiple microregions. 34 of the 208

15

Figure 5: City-size distributions with administrative units, 2010 (Chauvin et al., 2017)

Notes: These two panels are taken from Figure 2 in Chauvin et al. (2017). The left panel depicts 326
2citiesinpopulation
China (slope-0.91,= 0.79).
The right
495ondistricts
India (2011). Samples
Fig. 2. Zipf’s Law.prefecture-level
Urban populations andurban
ranks, 2010.
Note:RRegression
specifications
and panelstandarddepicts
errors based
Gabaix andin
Ibragimov
restricted to areas(slopewith urban
population
10 0,0 0 0 or larger.
-1.03,
R2 = of0.92).
Sources: See data appendix.

Table 4
distribution is, however, statistically different from the other three.
Gibrat’s Law: Urban population growth and initial urban population.
The primary difference is again that China has fewer ultra-large
microregions
containing
municipios
that
are
part
of a metropolitan
area with population
cities than the U.S. city size distribution would predict if it was
USA
BrazilChina
India(MSAs)(Microregions)applied to greater
the numberand 100,000
total populationof Chinese
cities. assigned to more than one metropolitan(Cities)
thancontainmunicipios
area. In-(Districts)
There aremany
explanations
for these
differences.implied∗∗∗
1980–2010
0.009−0.038 inform−0.447−0.052∗∗sofar
as possible
we think
the economic
integrationby commuting
shoulddefinitions
China’s population has exploded so rapidly that it may be far from(0.020)(0.023)(0.053)of China’s
metropolitan
areas,
thiscasts
on interpreting microregions
as metropolitan
areasN(0.023)
steady state.
governments
are farmore
activedoubt
in planning
N = 217N = 144
N = 187= 237
R2 = 0.001
R2 = 0.015
R2 = 0.280
R2 = 0.021
or localmarkets.
city populations
than labor
any of theother countries. The growth of ultra large Chinese
cities may
be blocked
by disamenities
of size our1980–1990
0.008−0.026−0.310∗∗∗0.063∗
Given
thealsoclose
correspondence
betweencommuting-basedand ∗∗night-lights–based(0.008)(0.013)(0.054)(0.034)that can become extreme for urban populations over 20 million. Fimetropolitan areas for Brazil, the contrasts between our Nnight-lights–based
metropolitan= 217
N = 144
N = 187
N = 237
nally, both China and India may be better seen as continents rather
R2 = 0.004
R2 = 0.020
R2 = 0.151
R2 = 0.015
areas
and microregions
similar.
than standard
countries
and this may alsoare
explainsome of the dif0.001−0.308∗∗∗0.005
1990–20 0 00.014∗∗
ference.
Prior work on China has used prefecture-level cities, the (0.007)
administrativedescribed(0.020)(0.010) capitals(0.036)
The differences between China and the other countries do raise= 217
N = 144
N = 187
in Section 2.4. Notably, Chauvin et al. (2017) find that theN Chinesecity-size
distribution
isN = 237
the possibility that in the long run China’s urban populations
R2 = 0.019
R2 = 0.0 0 0
R2 = 0.280
R2 = 0.00
poorlyby Zipf’s
lawareaswhencities.
The
left
panel
of
Figure∗∗will be much
more describedskewed towards
ultra large
likeusingBeijing prefecture-level
0.006
0.019
−0.01320 0 0–2010
0.012
and Shanghai.
The attempts
of many
localshows
governments
to boostrelationship that
(0.006)(0.006)(0.021)
5, takenfrom theirwork,
a rank-size
is more log-quadratic
than log-(0.015)= 217
N = 144
N = 187
N = 237
growth in middle(Tierdescribe
3 and Tierthis
4) cities
seem
have ledthat “China hasN fewer
linear.size
Theyresultastofinding
R2 = 0.018 ultra-large
R2 = 0.006 cities
R2 than= 0.005 theR2 = 0.004
to fiscal diﬃculties. Over time, more vertical construction and conUS city
would
predict”
a number of possible explanations. These
Note: All figures reported correspond to area-level regressions of the log change ingestion pricing
may sizeease distribution
the disamenities
of crowding
andandcon-suggest
urban
on the logstate,of initialmayurban bepopulationsin the specified period.
includethatdistribution
China’s may
city-size
distribution
may be farpopulationfrom steadysignificantly
gestion. China’s
city size
eventually
look far more
Regression restricted to areas with urban population of 10 0,0 0 0 or more in 1980.
like Zipf’s Law,
and to examinethat planning,
possibility we
nowbe
turnshaped
to the by disamenities unique to extreme
distortedby urbanmay
p<0.05, ∗ p<0.1.
Robust standard errors in parentheses. ∗∗∗ p<0.01, ∗∗ population
dynamics of city growth and Gibrat’s Law.
Sources: See data appendix.

sizes over 20 million, or that “China and India may be better seen as continents rather than
3.2. Gibrat’sstandard
Law across countries.”
four countries Another potential explanation is that the finding is simply a statistical
Gibrat’s Law does hold for the U.S. in recent decades, it does not
artifactofthe geographic
units used
to popucharacterize
Chinesedistribution.
Table 4 shows our resultson the mean reversionof city
appeartheto hold
well in city-size
Germany (Bosker
et al., 2008) or for the U.S.
There
considerable
differences
betweenadministrative
cities). and the metropolilations. In all cases,
we arereportcoeﬃcients where
the change
in the Chinese
historically(Glaeser et al., 2014b
logarithm ofarea
urbanwepopulationis regressedon the atlogarithm
Thetherefirst column
results foradministrative
the United States for 1980–
tan
areas
define basedon lights
night. While
are a shows
few hundredof initial area urban population. Gibrat’s Law implies that the co2010. We first show the coeﬃcient for the entire time period andcities, our aggregations of townships yield twicethen
as results
many foror eachmoreof metropolitan
areas with
eﬃcient should be statistically indistinguishable from zero. While
the three decades separately. Over the
population greater than 100,000. In addition, the metropolitan areas that correspond to
Please citelocations
this article as:
Chauvinet al., What is different
in richmeaningfully
and poor countries?
Cities in ofBrazil,China, India
forJ.P.which
prefecture-level
citiesabout
areurbanization
defined differ
in terms
theirand the UnitedStates,Journalof
Urban
Economics(2016),
http://dx.doi.org/10.1016/j.jue.2016.05.003
populations and land coverage. Figure 6 reports the correlation of log population and log
land area between metropolitan areas defined at various light-intensity thresholds and their16

0

Correlation with prefecture-level cities
.2
.4
.6
.8

Figure 6: Comparing Chinese night-lights–based metropolitan areas to prefecture-level cities,
2000

10

20

30
40
Threshold for light intensity
Population

50

60

Land area

prefecture-level-city counterparts. The correlation for log population never exceeds 0.8, andthe correlation for log land area is always below 0.4. Given these contrasts, using different geographic units may yield very different conclusions about the spatial distribution of
economic activity in China.
When measured using night-lights–based metropolitan areas, China’s city-size distribution is well described by a power law, and this fit is not very sensitive to the light-intensity
threshold used to construct the metropolitan areas. Figure 7 depicts China’s city-size distribution for a light-intensity threshold of 30. While the slope coefficient is statistically distinct
from the value of -1.0 that defines Zipf’s law, the rank-size relationship fits a log-linear powerlaw specification quite well, with an R2 of more than 99%.23 Table 2 shows that this result
is relatively invariant to the choice of light-intensity threshold. For threshold values from 10
to 50, the log-linear specification yields an R2 of 98% of higher. The log-quadratic shapefound by Chauvin et al. (2017) seems primarily due to their choice of geographic unit.24
Chauvin et al. (2017) suggest that China has a shortage of “ultra-large cities” relative
to a power-law distribution, but their use of administrative units plays an important rolein this result. The largest metropolitan area produced by our night-lights–based procedurecorresponds to the Pearl River Delta, the largest urban area in the world (World Bank
Group, 2015, 21). The Pearl River Delta is an administratively fragmented urban areaspanning Dongguan, Foshan, Guangzhou, and Shenzhen that has no dominant central city
but rather “several original centers that over time merge across boundaries” (World Bank
Group, 2015, 36). This multi-jurisdictional urban area, which by its nature does not appear
in prefecture-level city data, had about 42 million residents in 2010, and “is a unique kindof settlement in its immense scale as well as its form” (World Bank Group, 2015, 75).
23

Gabaix and Ioannides (2004) warn against excessive focus on statistically rejecting the null hypothesisof -1.0 and suggest focusing on fit.
24
To be clear, Zipf’s law is an empirical regularity observed in many countries, not a “law” that should
serve as the sole criterion for defining metropolitan areas in the Chinese context. The contrast in resultsshows that how one delineates metropolitan areas is important, but viewed in isolation it would not be astrong reason to prefer our approach.

178
Log (rank-0.5)
4

0

0

2

2

Log (rank-0.5)
4

6

6

8

Figure 7: China’s city-size distribution with night-lights–based units, 2000 and 2010

12

14

16

18

12

14

Log population

16

18

Log population

N = 805, β = -1.206, R = 0.997
Census 2000. Metropolitan areas defined by aggregating townships based on lights at night.

N = 1267, β = -1.180, R = 0.998
Census 2010. Metropolitan areas defined by aggregating townships based on lights at night.

22

Notes: The sample is Chinese metropolitan areas with population greater than 100,000.
Metropolitan areas defined by aggregating townships in areas of contiguous night lights withintensity greater than 30. Left panel depicts 2000; right panel 2010.

Table 2: China’s city-size distribution with night-lights–based units, 2000 and 2010

2000

2010

Metropolitan scheme

β

s.e.

R2

N

β

s.e.

Light intensity 10
Light intensity 20
Light intensity 30
Light intensity 40
Light intensity 50
Light intensity 60-1.175-1.211-1.206-1.157-1.091-0.859(0.049)(0.055)(0.060)(0.067)(0.077)(0.099)

0.998
0.996
0.997
0.994
0.989
0.945

1139
960
805
599
405
151

-1.033-1.150-1.180-1.163-1.091-0.987(0.044)(0.045)(0.047)(0.049)(0.052)(0.066)R2

N

0.995 1117
0.998 1313
0.998 1267
0.997 1140
0.995 876
0.988 454

Notes: This table reports the coefficient β, standard error, and R2 from a linear regression of
the formln(ranki − 0.5) = α + β ln populationi + ipwhere ranki is the population rank of metropolitan area i and the standard error is 2/N |β̂|
(Gabaix and Ibragimov, 2011). The sample for each regression is a set of Chinese metropolitan
areas in 2000 or 2010 with population greater than 100,000. Night-lights–based metropolitan
areas are defined by aggregating townships in contiguous areas with light intensity exceeding thelisted threshold.

18

-2

0

0

Log (rank-0.5)
2

Log (rank-0.5)
2
4

4

6

6

Figure 8: India’s city-size distribution, urban agglomerations, 2001 and 2011

12

14

16

18

12

14

Log population

16

18

Log population

N = 390, β = -1.085, R = 0.993

N = 465, β = -1.044, R = 0.990

2

2

Table 3: India’s city-size distribution, subdistrict-night-lights–based metropolitan areas

2001

2011

Metropolitan scheme

β

s.e.

R2

N

β

s.e.

R2

N

Light intensity 10
Light intensity 20
Light intensity 30
Light intensity 40
Light intensity 50
Light intensity 60-1.021-1.155-1.157-1.133-1.084-1.006(0.076)(0.078)(0.080)(0.083)(0.087)(0.117)

0.992
0.994
0.994
0.993
0.984
0.943

358
438
422
374
309
148

-0.967-1.096-1.125-1.122-1.104-1.035(0.072)(0.070)(0.071)(0.072)(0.075)(0.089)

0.995
0.992
0.992
0.991
0.988
0.968

359
494
503
481
436
272

Notes: This table reports the coefficient and R2 from a log-linear rank-size regression, as described in the notes of Table 2. The sample for each regression is a set of Indian metropolitan
areas in 2001 or 2011 with population greater than 100,000. Night-lights–based metropolitan
areas are defined by aggregating subdistricts in contiguous areas with light intensity exceeding
the listed threshold.

As in China, the Indian city-size distribution looks different when we use metropolitan
areas rather than administrative units. The distribution in Figure 5 depicting the urban
populations of Indian districts exhibits curvature, suggesting a log-quadratic rather thanlog-linear relationship between population size and population rank. Figure 8 depicts thisrelationship using urban agglomerations as the geographic units. This distribution is muchcloser to the expected power-law relationship, with the log-linear specification yielding an
R2 greater than 99% in both 2001 and 2011. Aggregating subdistricts’ urban populations
to define metropolitan areas based on night lights yields similar results, in the sense thatthe city-size distribution is well characterized by a power-law relationship with a very highR2 . As shown in Table 3, this result is quite stable across a broad range of light-intensity
thresholds used to define the metropolitan areas.
In all three developing economies we examine, there are substantial differences between
the administrative units typically employed in prior research and the metropolitan areas
19

that we construct on the basis of contiguous lights at night. In Brazil, we find that ournight-lights–based method produces metropolitan areas quite similar to those produced by
a commuting-flow-based algorithm. For both China and India, the power-law relationshipthat characterizes developed economies’ city-size distribution fits considerably better when
we use our night-lights–based approach to build metropolitan areas. Having built thesemetropolitan areas, we now turn to examining the distribution of skills across and withinthese metropolitan areas.

3

Skill distributions across metropolitan areas

For each country, we characterize the distribution of skill across metropolitan areas using four
categories of educational attainment. Following Davis and Dingel (2017), we regress eachskill’s log population in a city on that city’s log total population to estimate skill-specific“population elasticities.” These regressions are of the formln L(ν, c) = αν + βν ln L(c) + ν,c ,(1)

where L (ν, c) denotes the number of individuals in city c of skill ν, L(c) is that city’s total
population, αν are fixed effects, and βν is skill ν’s population elasticity. Where possible,
we report population elasticities for a variety of metropolitan-area definitions to assess thesensitivity of cross-metropolitan skill patterns to how metropolitan areas are constructed.
The theoretical model in Davis and Dingel (2017) implies that more skilled groups havehigher population elasticities, and our empirical estimates of βν are indeed monotonicallyincreasing in skill.25 In Appendix C.1, we also implement a non-parametric approach proposed in Davis and Dingel (2017) to characterize the distribution of skill across metropolitan
areas. Those results match the conclusion of the population-elasticities approach: larger
metropolitan areas are skill-abundant in all three countries.
Our focus on metropolitan-level variation in this section follows a large literature treating
cities as the relevant spatial unit for human capital externalities (Moretti, 2004). While thespatial scale of the skill-biased agglomeration economies may be much finer (c.f. Arzaghi andHenderson 2008, Rosenthal and Strange 2008, Ahlfeldt et al. 2015, and Kerr and Kominers2015), the large volume of research on cross-city variation makes this a natural starting
point. We will examine within-metropolitan variation in section 4.

3.1

BrazilFor Brazil, we construct metropolitan population counts for educational categories by aggregating (with appropriate sampling weights) individual-level observations from the 2010
Census. The four educational categories are “no schooling,” “elementary school graduate,”“high school graduate,” and “college graduate.” These four categories are unavoidably unequal in size due to the very large fraction of the population that has no schooling. As
25

In the frictionless model of Davis and Dingel (2017), all spatial difference in human capital are due
to individuals’ locational choices. When migration is costly, spatial variation in the production of humancapital may also contribute to these differences.

20

Table 4: Brazil: Population shares for educational categories, 2010
BrazilAll

Metro

No schooling
Elementary Graduate
High School Graduate
College Graduate

.49
.15
.25
.11

.40
.16
.29
.15

reported in Table 4, about half of Brazil’s population has no schooling. This number falls
to 40% when we restrict attention to metropolitan areas with at least 100,000 residents.
The contrast between the two columns in Table 4 already suggests that metropolitan
areas are more skilled, as the difference between the two columns is increasing in educational attainment. Our population elasticity regressions will, effectively, examine variationin population shares within the latter column across metropolitan areas of different sizes.
Table 5 reports population elasticities for these four skill groups for eight different definitions of metropolitan areas. The first three columns use commuting-based metropolitan
areas, and the next three use night-lights–based metropolitan areas. The final two columns
use the arranjos populacionais and microregions defined by the IBGE, the latter being thegeographic unit most commonly employed in prior studies of Brazil. A few patterns are
immediately evident. Within any column, the order of the population elasticities conforms
to the prediction of the model in Davis and Dingel (2017): more skilled groups exhibit
higher population elasticities. Comparing across the commuting-based and night-lights–
based columns, the estimated elasticities are quite stable. As suggested by the comparisonsin Figure 3, the patterns of economic activity are not sensitive to the threshold employed indefining the metropolitan areas and the two different methods yield metropolitan areas thatexhibit similar patterns. The results for arranjos populacionais are quite similar. There is anotable contrast between the results for microregions and the first seven columns. These population elasticities are also increasing in skill level, but that variation is considerably larger
in magnitude. These values suggest considerably larger difference in skill composition acrossmicroregions of different population sizes than across economically integrated metropolitan
areas of different sizes. Thus, conclusions about the spatial distribution of skills are sensitive
to whether and how we aggregate spatial units.
Figure 9 relaxes the linear specification employed in Table 5 by plotting a local meansmoother. The population level for each skill group is demeaned, so as to facilitate comparisons across metropolitan areas of different sizes. Plotting each series for commuting-based
metropolitan areas with a 10% commuting threshold amounts to a non-parametric versionof the log-linear regression slope coefficients reported in the second column of Table 5. The
slope at each point of the series is the “local population elasticity.” For almost all of thevariation, the log-linear approximation fits the data very well. Only at the extreme of thecity-size distribution, where there are only two metropolitan areas with population greaterthan 5 million and thus the local smoother amounts to little more than a data point, does the
local smoother deviate considerably from the log-linear approximation. Thus, the first-orderapproximation appears to be an apt summary of the relationship between metropolitan
population size and skill composition in Brazil, as Davis and Dingel (2017) found for US
21

Table 5: Brazil: Population elasticities for educational categories, 2010
Commuting5
No schooling (β1 )Elementary graduate (β2 )High school graduate (β3 )College graduate (β4 )15Nightlights
25

10

30

50

Arranjos

Microregions

NA

NA

0.912

0.921

0.914

0.931

0.915

0.912

0.917

0.858

(0.009)(0.010)(0.010)(0.011)(0.011)(0.011)(0.010)(0.009)

1.041

1.033

1.027

1.044

1.034

1.028

1.028

1.115

(0.010)(0.011)(0.011)(0.012)(0.011)(0.011)(0.011)(0.013)

1.102

1.087

1.086

1.092

1.095

1.096

1.090

1.217

(0.012)(0.012)(0.013)(0.014)(0.013)(0.013)(0.012)(0.016)

1.178

1.168

1.179

1.163

1.173

1.181

1.155

1.302

(0.024)(0.025)(0.026)(0.027)(0.026)(0.026)(0.023)(0.027)

Observations
816
768
880
616
676
728
740
1,672
Number of metropolitan areas
204
192
220
154
169
182
185
418
Notes: Each column reports OLS estimates of βν from a regression defined by equation (1). Skill fixed
effects αν are not reported. Standard errors are clustered by geographic unit. Each sample contains
geographic units with population greater than 100,000.

metropolitan areas.26
In sum, larger cities are skill-abundant in Brazil, and these differences are exaggerated if
one defines cities to be microregions.

3.2

China

For China, we construct metropolitan population counts for educational categories by aggregating township-level tabulations from the 2000 Census. While year-2010 township-level
population counts are available, year-2010 data describing educational attainment is currently only available at the county level. As we show below, characterizations of the spatial
distribution of skills are sensitive to whether we use metropolitan areas based on aggregating
townships or counties.
For China, the four educational categories are “primary school or less,” “middle school,”“high school,” and “college or university.” These four categories are unavoidably unequal insize due to the fact that, at the most granular level reported, the primary-school and middleschool categories have the two largest population shares and jointly account for about twothirds of the metropolitan population, as shown in Table 6. More detail is available for the“college or university” educational levels, but this skill group represents only 4% of China’s
total population.27
Table 7 reports population elasticities for these four skill groups for four different definitions of metropolitan areas. The first three columns use metropolitan areas obtained by
26

These results are not driven by the spatial distribution of age cohorts. Population elasticities monotonically increase with skill when estimated separately for ages 25-34, 35-44, and 45-54.
27
While average educational attainment is increasingly rapidly in China, the largest shift from 2000 to2010 is from primary school to middle school, so the population shares are also quite unequal in size in the2010 data.

22

150

.4
.3

100
Frequency

.2
.1

50

0
-.1
-.2

0

-.3

Log share of population (demeaned)

.5

200

Figure 9: Brazil: Non-parametric population elasticities for educational categories, 2010

12

14
16
Metropolitan log population
College Graduate
Elementary Graduate

18

High School Graduate
No schooling

Notes: Each series plots a local mean smoother using an Epanechnikov kernel.
Metropolitan areas are defined by commuting ties between municipios, using Duranton (2015) algorithm with 10% threshold. The histogram bars depict the number ofmetropolitan areas (on the right vertical axis).

Table 6: China: Population shares for educational categories, 2000
China

All

Metro

Primary school or less
Middle school
High school
College or university

.48
.37
.12
.04

.30
.38
.22
.10

23

Table 7: China: Population elasticities for educational categories, 2000

Township-based
Light intensity threshold:Primary school or less (β1 )Middle school (β2 )High school (β3 )College or university (β4 )Observations
Number of metropolitan areas

10

30

50

County-based
10

30

50

0.914

0.897

0.906

0.938

0.970

0.962

(0.008)(0.009)(0.010)(0.007)(0.012)(0.018)

1.003

0.985

0.970

1.066

1.017

1.021

(0.005)(0.006)(0.009)(0.007)(0.007)(0.009)

1.124

1.096

1.073

1.046

0.992

0.994

(0.012)(0.012)(0.013)(0.014)(0.021)(0.026)

1.344

1.327

1.314

1.140

1.090

1.105

(0.024)(0.027)(0.031)(0.026)(0.039)(0.050)

4,556
1139

3,220
805

1,620
405

6,820
1705

4,668
1167

2,004
501

Notes: Each column reports OLS estimates of βν from a regression defined by equation(1). Skill fixed effects αν are not reported. Standard errors are clustered by geographic unit.
Each sample contains geographic units with population greater than 100,000.

aggregating townships on the basis of night lights, while the fourth column aggregates counties. Using the township-based metropolitan areas, we find that more skilled groups exhibit
higher population elasticities. The estimated elasticities are not particularly sensitive tothe light-intensity threshold employed to define the metropolitan areas. The differences in
population elasticities across skill groups are comparable to those found for Brazil, though
this comparison should be tempered by the fact that the educational categories defining thefour skill groups are not necessarily comparable across countries.
The population elasticities estimated when employing county-based metropolitan areas
differ considerably. First, the elasticities vary much less, as the elasticities for the leastand most-skilled groups are both closer to one. Second, the population elasticities are nolonger monotonically increasing in educational attainment: the junior middle school andsenior middle school are not statistically distinguishable (and the point estimates are in the“wrong” order). By grouping together both urban and rural areas and possibly grouping
together distinct metropolitan areas of different sizes, the county-based metropolitan areas
would lead us to substantially understate spatial variation in skill distributions. Since at
the moment educational attainment data for 2010 is only available at the county level, we
cannot yet reliably characterize spatial variation in skill distributions using the 2010 Census
data.
In sum, we find that larger cities are skill-abundant in China when measuring skills using
four educational categories. These results are sensitive to the precision of the spatial units
used to define metropolitan areas and their characteristics. We find larger differences in24

population elasticities when building metropolitan areas from more precise geographic units.

3.3

India

For India, we construct metropolitan population counts for educational categories by aggregating town-level tabulations of main workers by educational level from the 2001 Census
for the metropolitan areas described in Section 2.5. The four educational categories are“illiterate,” “primary,” “secondary,” and “college graduate.” These four populations are ofroughly equal size, at least when we restrict attention to urban agglomerations and towns
with more than 100,000 residents, as shown in Table 8.
Table 8: India: Population shares for educational categories, 2001
India

All

Metro

No education
Primary
Secondary
College graduate

.43
.26
.24
.08

.22
.22
.36
.21

We face some data limitations imposed by the Census of India data describing educational
attainment. Educational attainment data are not available at the sub-district level, so wecannot use the metropolitan areas that were produced by aggregating sub-districts on thebasis of night lights. We therefore use the definition of metropolitan areas that is the union ofurban agglomerations (aggregated across state borders on the basis of night lights) and census
towns of sufficient population size. The data source that we employ describes educational
attainment for constituent components of these metropolitan areas when they are of sufficient
population size. We therefore report results for samples that differ in the degree to which we
require that the constituent components account for the total population of the metropolitan
area.
Table 9 reports population elasticities for the four skill groups for three different definitions of metropolitan areas. The first column includes all metropolitan areas regardless ofthe fraction of their population covered in the educational-attainment data, while the second and third columns impose minima of 80% and 95%, respectively. In all three columns,
skill groups’ population elasticities increase with the level of educational attainment. Thus,
India’s metropolitan areas that are more populous are more skill-abundant, and this finding is robust across various samples that we consider in order to address limitations of theunderlying data sources. The range of variation between the least- and most-skilled groups’
population elasticities is greater when we restrict the sample to observations with better
coverage.
In sum, when we examine whether the population distribution is log-supermodular in skill
and metropolitan population, we find that larger cities are indeed skill-abundant in Brazil,
China, and India. The quantitative magnitudes of these findings are, in some cases, sensitive
to using metropolitan areas defined by contiguity of night lights rather than administrativeor political boundaries. Relative to prior work characterizing the spatial distribution of25

Table 9: India: Population elasticities for educational categories, 2001

Inclusion threshold:None

No education (β1 )Primary (β2 )Secondary (β3 )College graduate (β4 )Observations
Number of metropolitan areas

0.8

0.95

0.960

0.980

0.970

(0.027)(0.018)(0.027)

0.972

0.987

1.009

(0.022)(0.020)(0.029)

1.014

1.035

1.049

(0.018)(0.015)(0.022)

1.027

1.063

1.061

(0.022)(0.018)(0.028)

1,320
330

1,152
288

808
202

Notes: Each column reports OLS estimates of βν from a regression defined by equation (1).
Skill fixed effects αν are not reported. Standard errors are clustered by geographic unit. Eachsample contains the union of urban agglomerations and census towns with population greaterthan 100,000. Across columns, there is variation in the inclusion threshold, which is the fractionof the urban agglomerations’ population for which educational attainment data on constituent
components is available.

26human capital in terms of two skill groups, we show that larger cities are skill-abundant ina high-dimensional sense.

4

Within-metropolitan variation in skills

In this section, we examine how the skill composition within metropolitan areas varies with
distance to the city center in Brazil and China.28 Even in the simplest monocentric citymodel, this skill gradient is theoretically ambiguous because it depends on the relative income
elasticities of housing demand and commuting costs (LeRoy and Sonstelie, 1983). Prior
empirical work on patterns of residential sorting within cities has overwhelmingly focusedon the United States and European countries (Duranton and Puga, 2015). In the UnitedStates, residents near the metropolitan center are typically poorer than suburban residents(Rosenthal and Ross, 2015), a pattern dating to at least 1930 (Lee and Lin, 2018). One
potential explanation for this pattern is that poor households locate in central cities toaccess public transport (Glaeser, Kahn and Rappaport, 2008).
In both Brazil and China, we find that residents living closer to the center of metropolitan areas are more skilled. For each metropolitan area, we define the city center as the
population-weighted average of the latitude-longitude coordinates of its constituent components.29 We then plot or regress the fraction of residents who are college graduates in eachconstituent component on its distance from the city center. To make these gradients comparable across metropolitan areas of different size and average skill, we measure the college
share relative to the metropolitan mean and distance relative to the most distant constituent
component in the metropolitan area.
For Brazil, Table 10 shows that the skill gradient is negative, precisely estimated, and notsensitive to the light-intensity threshold employed to define metropolitan areas. The nonparametric plot of this relationship in Figure 10 shows that the linear relationship imposedin the regression specification fits the data well. The skill gradient estimated when using
microregions is also negative but of substantially smaller magnitude.30
The skill gradient is also negative in China, as Table 11 shows. While the skill gradientsobserved in Chinese metropolitan areas are qualitatively similar whether we use township- or
county-level observations of educational attainment, they differ quantitatively. For intermediate light-intensity thresholds, the skill gradients obtained from township-based metropolitan areas in the upper panel of Table 11 are about 50% steeper than those obtained fromcounty-based metropolitan areas in the lower panel.

28

Unfortunately, Indian population counts by educational category are not reported for sufficiently finegeographic units to study this outcome for Indian urban agglomerations.
29
Alternatively, we could define the city center as the spatial unit within the metropolitan area with thehighest population density. Doing so yields qualitatively similar results, but the coefficients are about 20%
to 30% smaller in absolute magnitude than those reported in Tables 10 and 11.
30This is not merely due to the set of microregions containing many more places. Restricting attention to
microregions in which the largest municipio is also the largest municipio under the metropolitan areas definedby using a light-intensity threshold of 30 yields an estimated coefficient of -0.050, which is still meaningfully
less than -0.0715.

27

Table 10: Skill gradient in Brazilian metropolitan areas, 2010

Light threshold
Distance to metro center

Number of municipios
Number of metropolitan areas
Microregion p-value
Microregion Clusters
Arranjo p-value
Arranjo Clusters
ThresholdDistance to metro center

Number of municipios
Number of metropolitan areas

10

20

30

40

50

-0.0470-0.0747-0.0763-0.0794-0.0762(0.00834)(0.0121)(0.0111)(0.0107)(0.0129)

958
96
0.024
426
0.000
142

519
86
0.000
425
0.120
126

435
77
0.000
423
0.120
118

385
78
0.000
429
0.180
119

330
71
0.000
430
0.163
116

5

Commuting
15

25

ArranjosNA

Microregions
NA-0.0750-0.100-0.114-0.0921-0.0288(0.00348)(0.00604)(0.00789)(0.00506)(0.00178)

1,074
157

418
84

223
53

557
102

4,750
417

Notes: The dependent variable is the share of residents who are college graduates in a municipio.
Distance to metro center is measured from the municipio centroid to the population-weighted average of constituent-municipio centroids as a share of the greatest distance. The sample is restricted
to metropolitan areas containing at least two municipios. Standard errors, clustered by metropolitan area, are in parentheses. The reported p-values test the null hypotheses that the coefficients
estimated when using night-lights–based metropolitan areas are equal to the coefficients estimatedwhen using arranjos or microregions. The table also reports the number of clusters used when
computing those test statistics; see Appendix C.2 for details.

28

Table 11: Skill gradient in Chinese metropolitan areas, 2000

Light threshold:
10
20
Panel A: Township-based metropolitan areas
Distance to metro center

Number of townships
Number of metropolitan areas

30

40

50

60

-0.110-0.133-0.140-0.144-0.135-0.122(0.00934)(0.00712)(0.00733)(0.00823)(0.00944)(0.0117)

13,900
1116

9,672
901

7,761
720

6,224
501

4,775
332

2,584
135

-0.0841-0.0916-0.0988-0.0945-0.0970-0.107(0.0128)(0.0127)(0.0132)(0.0137)(0.0147)(0.0171)992
210
0.0386
1128

818
205
0.0001
950

719
186
0.0001780

663
173
0.0000578

556
143
0.0013395

335
79
0.0794173

Panel B: County-based metropolitan areas
Distance to metro center

Number of counties
Number of metropolitan areas
p-value for difference
Clusters

Notes: The dependent variable is the share of residents who are college graduates in a constituent
component, which is a township in the upper panel and a county in the lower panel. Distance to metro
center is measured from the component centroid to the population-weighted average of constituentcomponent centroids as a share of the greatest such distance in the metropolitan area. The sample
is restricted to metropolitan areas containing at least two constituent spatial units. Standard errors,
clustered by metropolitan area, in parentheses. The reported p-values test the null hypothesis that thecoefficients in the two panels within a column are equal. The last line reports the number of clusters
used in computing that test statistic. See Appendix C.2 for details.

29College graduate share (relative to MSA mean)
-.04
-.02
0
.02
.04

Figure 10: Skill gradient in Brazilian metropolitan areas, 2010

0

.2
.4
.6
.8
Distance to metro center (as fraction of metro radius)
All metros

1

Metros containing at least 7 municipios

Notes: The two series are local mean smoothers of the share of residents who arecollege graduates in a municipio as a function of distance to metro center using an
Epanechnikov kernel. Dashed lines depict 95% confidence intervals. Metropolitan
areas are defined by aggregating municipios using a light-intensity threshold of 30.

30

5Spatial variation in nominal wages across Brazil

In this section, we examine how spatial variation in nominal wages across Brazilian metropolitan areas relates to skills.31 A very robust finding of the empirical literature is that nominal
wages paid to observationally similar workers are higher in more populous and more skilled
cities (Moretti, 2004; Combes and Gobillon, 2015). We confirm this finding using our definitions of Brazilian metropolitan areas. A recent finding in developed economies is that therelative price of skill is higher in more populous cities (Baum-Snow and Pavan, 2013; Davisand Dingel, 2019). We also find this pattern in Brazil.
Table 12 shows that nominal wages are higher in Brazilian metropolitan areas with larger
populations and a higher share of residents with a college degree. These differences in nominal wages across metropolitan areas control for individual demographics (gender, age, race,and educational attainment). Such findings are usually interpreted as suggesting agglomeration economies and human capital externalities that increase productivity.32 The estimatedcoefficients are not sensitive to the thresholds used to define night-lights– and commutingbased metropolitan areas. While the coefficient on log population estimated when using
microregions is similar to the estimates obtained when using commuting- and night-lights–
based metropolitan definitions, the coefficient on the college graduate share is about 50%
greater when estimated using microregions.33
Are college wage premia higher in more populous metropolitan areas in Brazil? In the
United States, larger cities exhibit both higher relative quantities and higher relative pricesof skill, as measured by the share of college graduates and the college wage premium (Davisand Dingel, 2019). The implied greater relative demand for college graduates in larger cities
suggested that the productivity benefits of agglomeration are skill-biased.
Table 13 shows that college wage premia are higher in bigger cities in Brazil. We define
the college wage premium as the difference in average log hourly wages between college
graduates and high school graduates and estimate that its population elasticity is between
4% and 5%. Thus, the productivity benefits of agglomeration economies in Brazil appear
to be skill-biased. The population elasticity of the college wage premium in Brazil is larger
than the 3% elasticity estimated for US metropolitan areas in 2000 (Davis and Dingel, 2019).
Our estimates in Tables 12 and 13 are quantitatively similar across night-lights–based
metropolitan areas, commuting-based metropolitan areas, arranjos populacionais, and microregions. By contrast, our estimates describing spatial variation in the quantities of skill
in Tables 5 and 10 are substantially different when we employ microregions rather than our
preferred definitions of metropolitan areas. This contrast between spatial variation in quantities and prices of skill in their sensitivity to geographic definitions is interesting, but we do
not have reason to believe that this pattern will necessarily generalize to other countries.

31

Unfortunately, data on wages by educational category are not available for sufficiently fine geographic
units to study this outcome for Chinese and Indian metropolitan areas.
32
Glaeser and Mare (2001) and Rauch (1993) are early influential studies showing that metropolitan
population and educational attainment, respectively, are positively correlated with nominal wages after
controlling for individual characteristics.
33
The coefficient on the college graduate share estimated using microregions is comparable to that estimated by Chauvin et al. (2017, Table 10), who restrict their sample to prime-age males.

31

Table 12: Average nominal wages across Brazilian metropolitan areas, 2010

Light thresholdCollege graduate share
Log population

Observations
Full Sample
Number of metropolitan areas
ThresholdCollege graduate share
Log population

Observations
Number of metropolitan areas

10

20

30

40

50

0.02590.02300.02220.02090.0213(0.00270)(0.00283)(0.00281)(0.00281)(0.00276)

0.07070.07100.07230.07020.0688(0.00622)(0.00655)(0.00674)(0.00709)(0.00711)

139,6533600519
154

146,460
3170748
162

151,7713106347
169

160,9133056954
180

161,9362997105
182

5

Commuting
15

25

ArranjosNA

Microregions
NA

0.02460.02360.01640.02180.0354(0.00264)(0.00273)(0.00192)(0.00300)(0.00173)

0.07150.06940.07810.07320.0769(0.00677)(0.00732)(0.00809)(0.00718)(0.00815)

183,619204

171,273
192

195,235
220

166,919
185

372,908
418

Notes: The dependent variable is the average nominal hourly wage in a metropolitan-area × gender× age × race × education cell. The college graduate share takes values between 0 and 100. Unreported
controls are fixed effects for gender, age, race, and educational attainment. Standard errors, clusteredby metropolitan area, in parentheses.

32

Table 13: Skill premia in Brazilian metropolitan areas, 2010

Light threshold
Metro log population

Number of metropolitan areas
Threshold
Metro log population

Number of metropolitan areas

10

20

30

40

50

0.03990.04270.04560.05010.0497(0.00760)(0.00809)(0.00801)(0.00827)(0.00820)

154

162

169

180

182

5

Commuting
15

25

ArranjosNA

Microregions
NA

0.04690.0446

0.04890.04250.0517(0.00727)(0.00761)(0.00782)(0.00743)(0.00591)

204

192

220

185

418

Notes: The dependent variable is a metropolitan area’s difference in average log hourly wages
between college graduates and high school graduates.

33

6

Sectoral distributions across Brazilian cities

In the theoretical model of Davis and Dingel (2017), larger cities are relatively more skilled,
cities’ equilibrium productivity differences are Hicks-neutral, and sectors can be ordered bytheir skill intensity, so larger cities employ relatively more labor in skill-intensive sectors.
The results of Section 3 show that larger cities are relatively more skilled in Brazil, China,
and India. We now examine whether larger cities are relatively specialized in skill-intensive
sectors, using employment levels in both occupations and industries. Due to data limitations,
we restrict attention to Brazil.
To characterize the spatial distribution of occupational and industrial employment acrossBrazilian metropolitan areas, we plot each sector’s estimated population elasticity against
its skill intensity, measured as the average years of schooling of individuals employed in that
sector. Each sector’s bubble size is proportionate to its employment share.
Figure 11 depicts the results of using 10 occupational categories to define sectors. In theleft panel, the very low population elasticity of agricultural employment masks the rest of
the variation depicted, so the right panel omits agriculture and depicts the line of best fit.
The model of Davis and Dingel (2017) predicts that the population elasticity of occupational
employment should rise with skill intensity and indeed we see a clear positive relationshipin Figure 11.

Administrative services
Intermediary-leveltechnicians

1.15

1.2

Figure 11: Brazil: Occupational employment population elasticities, 2010

Scientists and intelectuals

Military and police force

Population elasticity.81Service & Commerce

Administrative services
Intermediary-level technicians

Managers and directors

Population elasticity
1.05
1.1

Machine operatorsServices
Construction/Mechanical

Military and police force

Managers and directors
Service & Commerce

1.6

Maintenance and repair

Scientists and intelectuals

Machine operators
Construction/Mechanical
Services.4.95

Agriculture

6

8
10
12
14
Skill intensity (employees' average years of schooling)

16

Maintenance and repair

8

10
12
14
Skill intensity (employees' average years of schooling)

16

Notes: Each observation is an occupational category. The population elasticity of employment is estimated by linear regression. Skill intensity is the average years of schoolingof persons employed in that occupational category. Bubble sizes are proportionate to theoccupational category’s share of employment. Metropolitan areas are defined by commuting
flows between municipios, using the Duranton (2015) algorithm with a 10% threshold. Leftpanel includes all occupations; right panel omits agriculture.

Figure 12 depicts the results of using 22 industrial categories to define sectors. Again,
we omit agriculture from the right panel in order to better depict the remaining variation
across industries. Industrial population elasticities generally increase with skill intensity.
The most notable outliers from the central tendency of the data are education (high skilled,
low elasticity) and administrative services (low skilled, high elasticity). The fact that the
population elasticity of education is quite close to one despite its employment of highly educated individuals may reflect the fact that educational services are typically non-traded. The
34

low skill intensity associated with administrative services as an industry contrasts with thehigher average years of schooling associated with administrative services as an occupation.

1.4

1.4

Figure 12: Brazil: Industrial employment population elasticities, 2010
Real Estate

Information & Communication
Information & Communication
Real Estate

Finance1.3

1.2

Administrative Services

Science & Technical Professions
Administrative Services

Science & Technical Professions
Arts, Culture & Sports
Ill-defined Activities
Health & Social Services
Extractive Industries
Other
services activities
Hospitality and Food
Services
Electricity and gas
Transportation
Public Administration
Domestic services.6

Sanitation

Commerce

Education

Construction

1

International institutions

FinancePopulation elasticity
1.1
1.2

Population elasticity.81Arts, Culture & Sports
Ill-defined Activities
Health & Social Services
Extractive
Industries
OtherServices
services
activities
Hospitality
and Food
Electricity and gas
Transportation
Public Administration
Domestic services
Sanitation
Commerce
Education
Construction
Transformation Industries

Transformation Industries.4.9Agriculture

8

10
12
14
Skill intensity (employees' average years of schooling)

16

International institutions

8

10
12
14
Skill intensity (employees' average years of schooling)

16

Notes: Each observation is an industrial category. The population elasticity of employment is estimated by linear regression. Skill intensity is the average years of schooling of
persons employed in that industrial category. Bubble sizes are proportionate to the industrial category’s share of employment. Metropolitan areas defined by commuting ties between
municipios, using Duranton (2015) algorithm with 10% threshold.

For both occupations and industries, the estimated population elasticities reveal a broadtendency for more populous metropolitan areas to employ relatively more individuals in skillintensive sectors. Using alternative commuting thresholds or any of the night-lights–based
metropolitan areas delivers very similar elasticity estimates. The population elasticities
estimated when using microregions are similarly ordered, but they exhibit substantiallygreater variation in magnitude, similar to the pattern in Table 5.

7

Conclusion

We study spatial variation in skills in Brazil, China, and India. Our goal is to characterize whether urban systems of developing economies exhibit spatial patterns similar to thosefound in developed economies, where agglomeration appears to be skill-biased. In order todo so, we aggregate smaller administrative spatial units, such as municipios and townships,
belonging to contiguously lit areas in satellite imagery to define metropolitan areas. We
intend these metropolitan areas to be comparable to those employed in research studying
developed economies. We find that larger cities are more skill-abundant, more skilled residents live closer to the city center, and larger cities exhibit higher skilled wage premia.
In short, the productivity benefits of agglomeration appear to be skill-biased in developing
economies.
Unlike research designs that employ satellite imagery to both define metropolitan areas
and measure economic outcomes, our strategy relies on both satellite imagery and conventional administrative data. Studying the relationship between skills and agglomerationnecessarily requires observing individuals’ educational attainment (or some other proxy forskills) and cannot be done using satellite imagery alone. Thus, our inquiry is constrained35

by the availability of data on socioeconomic outcomes for fine geographic units, and thislimitation is often binding in India.
Our use of satellite imagery to construct metropolitan areas is preferable to using administrative units that do not correspond to integrated economic entities and alleviates the needfor comprehensive commuting data, which are not available in many developing economies.
For Brazil and the United States, we find that our night-lights–based metropolitan areas are
similar to those defined based on commuting flows. For China and India, where commuting data are not available, our night-lights–based approach eliminates substantial deviations
from a power-law distribution for city sizes. Since satellite images cover the entire globe
and are becoming available in finer resolutions, our method for defining metropolitan areas
should facilitate studies of urbanization and local labor markets in many different contexts.
The spatial patterns that we observe suggest that agglomeration is skill-biased. In all
three developing economies, larger cities are skill-abundant. Across four educational categories, the estimated population elasticity monotonically increases with skill. This findingis robust to varying the light-intensity threshold used to define metropolitan areas, but theestimated elasticities can substantially differ from those obtained when using administrative definitions of cities. Where data permit we also study within-metropolitan variation inquantities and across-metropolitan variation in wages and sectoral employment. In Brazil,college wage premia and employment in skill-intensive sectors are relatively greater in more
populous cities. These patterns echo recent evidence that agglomeration is skill-biased in
the United States and other developed economies.

36References
Ades, Alberto F., and Edward L. Glaeser. 1995. “Trade and Circuses: Explaining Urban
Giants.” The Quarterly Journal of Economics, 110(1): 195–227.
Ahlfeldt, Gabriel M., Stephen J. Redding, Daniel M. Sturm, and Nikolaus Wolf. 2015. “TheEconomics of Density: Evidence From the Berlin Wall.” Econometrica, 83(6): 2127–2189.
Arzaghi, Mohammad, and J. Vernon Henderson. 2008. “Networking off Madison Avenue.”
The Review of Economic Studies, 75(4): 1011–1038.
Bacolod, Marigee, Bernardo S. Blum, and William C. Strange. 2009. “Skills in the city.”
Journal of Urban Economics, 65(2): 136 – 153.
Baragwanath Vogel, Kathryn, Ran Goldblatt, Gordon H Hanson, and Amit K Khandelwal. 2018. “Detecting Urban Markets with Satellite Imagery: An Application to India.”
National Bureau of Economic Research Working Paper 24796.
Baum-Snow, Nathaniel, and Ronni Pavan. 2013. “Inequality and City Size.” The Review of
Economics and Statistics, 95(5): 1535–1548.
Bleakley, Hoyt, and Jeffrey Lin. 2012. “Portage and Path Dependence.” The Quarterly Journal of Economics, 127(2): 587–644.
Bustos, Paula, Bruno Caprettini, and Jacopo Ponticelli. 2016. “Agricultural Productivity and Structural Transformation: Evidence from Brazil.” American Economic Review,106(6): 1320–65.
Cavalcanti, Tiago, Daniel Da Mata, and Frederik G Toscani. 2016. “Winning the Oil Lottery;
The Impact of Natural Resource Extraction on Growth.” International Monetary FundIMF Working Papers 16/61.
Chan, Kam Wing. 2007. “Misconceptions and Complexities in the Study of China’s Cities:
Definitions, Statistics, and Implications.” Eurasian Geography and Economics, 48(4): 383–
412.
Chan, Kam Wing. 2010. “Fundamentals of China’s Urbanization and Policy.” China Review,
10(1): 63–93.
Chauvin, Juan Pablo. 2017. “Gender-Segmented Labor Markets and the Effects of Local
Demand Shocks.”
Chauvin, Juan Pablo, Edward Glaeser, Yueran Ma, and Kristina Tobio. 2017. “What isdifferent about urbanization in rich and poor countries? Cities in Brazil, China, India andthe United States.” Journal of Urban Economics, 98: 17 – 49. Urbanization in Developing
Countries: Past and Present.

37

Combes, Pierre-Philippe, and Laurent Gobillon. 2015. “The Empirics of Agglomeration
Economies.” In Handbook of Regional and Urban Economics. Vol. 5 of Handbook of Regional and Urban Economics, , ed. Gilles Duranton, J. Vernon Henderson and William C.
Strange, 247 – 348. Elsevier.
Costa, Dora L., and Matthew E. Kahn. 2000. “Power Couples: Changes in the Locational Choice of the College Educated, 1940-1990.” The Quarterly Journal of Economics,
115(4): 1287–1315.
Costa, Francisco, Jason Garred, and João Paulo Pessoa. 2016. “Winners and losers from acommodities-for-manufactures trade boom.” Journal of International Economics, 102: 50– 69.
Couture, Victor, and Jessie Handbury. 2017. “Urban Revival in America, 2000 to 2010.”
National Bureau of Economic Research Working Paper 24084.
Davis, Donald R., and Jonathan I. Dingel. 2017. “The Comparative Advantage of Cities.”
Davis, Donald R., and Jonathan I. Dingel. 2019. “A Spatial Knowledge Economy.” American
Economic Review, 109(1): 153–170.
Dı́az-Lanchas, Jorge, Carlos Llano, Asier Minondo, and Francisco Requena. 2018. “Cities
export specialization.” Applied Economics Letters, 25(1): 38–42.
Dix-Carneiro, Rafael, and Brian K. Kovak. 2015. “Trade Reform and Regional Dynamics:
Evidence From 25 Years of Brazilian Matched Employer-Employee Data.” National Bureau
of Economic Research Working Paper 20908.
Donaldson, Dave, and Adam Storeygard. 2016. “The View from Above: Applications ofSatellite Data in Economics.” Journal of Economic Perspectives, 30(4): 171–98.
Duranton, Gilles. 2007. “Urban Evolutions: The Fast, the Slow, and the Still.” American
Economic Review, 97(1): 197–221.
Duranton, Gilles. 2015. “Delineating Metropolitan Areas: Measuring Spatial Labour Market
Networks Through Commuting Patterns.” In The Economics of Interfirm Networks. , ed.
Tsutomu Watanabe, Iichiro Uesugi and Arito Ono, 107–133. Tokyo:Springer Japan.
Duranton, Gilles, and Diego Puga. 2015. “Urban Land Use.” In Handbook of Regional and
Urban Economics. Vol. 5 of Handbook of Regional and Urban Economics, , ed. Gilles
Duranton, J. Vernon Henderson and William C. Strange, 467 – 560. Elsevier.
Findeisen, Sebastian, and Jens Südekum. 2008. “Industry churning and the evolution of
cities: Evidence for Germany.” Journal of Urban Economics, 64(2): 326–339.
Gabaix, Xavier. 1999. “Zipf’s Law For Cities: An Explanation.” The Quarterly Journal of
Economics, 114(3): 739–767.

38

Gabaix, Xavier, and Rustam Ibragimov. 2011. “Rank - 1/2: A Simple Way to Improve the
OLS Estimation of Tail Exponents.” Journal of Business & Economic Statistics, 29(1): 24–
39.
Gabaix, Xavier, and Yannis Ioannides. 2004. “The evolution of city size distributions.” In
Handbook of Regional and Urban Economics. Vol. 4. 1 ed., , ed. J. V. Henderson and J. F.
Thisse, Chapter 53, 2341–2378. Elsevier.
Giannone, Elisa. 2018. “Skill-Biased Technical Change and Regional Convergence.”Glaeser, Edward L, and David C Mare. 2001. “Cities and Skills.” Journal of Labor Economics,
19(2): 316–342.
Glaeser, Edward L., Matthew E. Kahn, and Jordan Rappaport. 2008. “Why do the poor livein cities? The role of public transportation.” Journal of Urban Economics, 63(1): 1 – 24.
Harari, Mariaflavia. 2017. “Cities in Bad Shape: Urban Geometry in India.”Henderson, J. Vernon. 1991. Urban Development: Theory, Fact, and Illusion. Oxford University Press.
Henderson, J. Vernon. 2014. “Urbanization and the Geography of Development.” WorldBank Policy Research Working Paper 6877, The World Bank.
Henderson, J. Vernon, Adam Storeygard, and David N. Weil. 2012. “Measuring Economic
Growth from Outer Space.” American Economic Review, 102(2): 994–1028.
Hoffmann, Rodolfo. 2003. “Inequality in Brazil: the contribution of pensions.” Revista
Brasileira de Economia, 57: 755 – 773.
Hu, Shiwei, Steven Brakman, and Charles van Marrewijk. 2014. “Smart Cities are Big Cities Comparative Advantage in Chinese Cities.” CESifo Group Munich CESifo Working Paper
Series 5028.
IBGE. 2016. Arranjos Populacionais e Concentrações Urbanas do Brasil, 2nd Edition. IBGE,
Rio de Janeiro.
Kerr, William R., and Scott Duke Kominers. 2015. “Agglomerative Forces and Cluster
Shapes.” The Review of Economics and Statistics, 97(4): 877–899.
Kovak, Brian K. 2013. “Regional Effects of Trade Reform: What is the Correct Measure of
Liberalization?” The American Economic Review, 103(5): 1960–1976.
Lee, Sanghoon, and Jeffrey Lin. 2018. “Natural Amenities, Neighbourhood Dynamics, andPersistence in the Spatial Distribution of Income.” The Review of Economic Studies,85(1): 663–694.
Lee, Sanghoon, and Qiang Li. 2013. “Uneven landscapes and city size distributions.” Journalof Urban Economics, 78: 19 – 29.
39

LeRoy, Stephen F., and Jon Sonstelie. 1983. “Paradise Lost and Regained: Transportation
Innovation, Income, and Residential Location.” Journal of Urban Economics, 13: 67–89.
Moretti, Enrico. 2004. “Human Capital Externalities in Cities.” In Cities and Geography.
Vol. 4 of Handbook of Regional and Urban Economics, , ed. J. Vernon Henderson and
Jacques-François Thisse, 2243 – 2291. Elsevier.
Office of Management and Budget. 2010. “2010 Standards for Delineating Metropolitan andMicropolitan Statistical Areas.” In Federal Register. Vol. 75, 37246–37252.
Rauch, James E. 1993. “Productivity Gains from Geographic Concentration of Human Capital: Evidence from the Cities.” Journal of Urban Economics, 34(3): 380–400.
Rosenthal, Stuart S., and Stephen L. Ross. 2015. “Change and Persistence in the Economic
Status of Neighborhoods and Cities.” In Handbook of Regional and Urban Economics.
Vol. 5 of Handbook of Regional and Urban Economics, , ed. Gilles Duranton, J. Vernon
Henderson and William C. Strange, 1047 – 1120. Elsevier.
Rosenthal, Stuart S., and William C. Strange. 2008. “The attenuation of human capital
spillovers.” Journal of Urban Economics, 64(2): 373 – 389.
Rozenfeld, Hernán D., Diego Rybski, Xavier Gabaix, and Hernán A. Makse. 2011. “The Area
and Population of Cities: New Insights from a Different Perspective on Cities.” American
Economic Review, 101(5): 2205–25.
Scherer, Clauber Eduardo Marchezan, and David C. Folch. 2017. “A Comparative Study of Urban Occupational Structure:
Brazil and United States.”
http://sisconev.com.br/Uploads/ENABER17/Trab01570036772017009 000000.pdf.
Soo, Kwok Tong. 2005. “Zipf’s Law for cities: a cross-country investigation.” Regional Science and Urban Economics, 35(3): 239 – 263.
Storeygard, Adam. 2016. “Farther on down the Road: Transport Costs, Trade and Urban
Growth in Sub-Saharan Africa.” The Review of Economic Studies, 83(3): 1263–1295.
Welch, R. 1980. “Monitoring urban population and energy utilization patterns from satellite
Data.” Remote Sensing of Environment, 9(1): 1 – 9.
World Bank Group. 2015. East Asia’s Changing Urban Landscape : Measuring a Decade of
Spatial Growth. World Bank.

40

A

Defining metropolitan areas

A.1

Building metropolitan areas from satellite data

This section provides a few more details of the procedure described in Section 2.1 of themain text.
We extract contour lines for selected light-intensity values from the night lights rasterlayer and convert those contour lines into polygons. To extract contour lines we project
the raster into an azimuthal equidistant projection defined by a latitude and longitude oforigin. This projection preserves distance and direction relative to the latitude and longitudeof the projection center that we specify for each country. Occasionally these contour lines
produce polygons-within-polygons, which can lead to erroneous assignments in subsequent
steps. This happens, for instance, when the night lights reveal a sufficiently large (dark)
park or lake entirely surrounded by a metropolitan area. We obtain contiguous areas bydissolving these smaller polygons into the larger ones that entirely contain them.
To obtain the intersection of these contiguous area with spatial units for which socioeconomic data is available, we perform a spatial join. Before joining them, we project boththe night-light polygons and the administrative spatial units into an Albers equal-area conic
projection centered on the same latitude and longitude of origin, specifying standard parallels for each country to minimize distortions. When an administrative spatial unit intersects
multiple night-light polygons, we assign the spatial unit to the polygon with which it has thelargest area of overlap. Thus, each administrative spatial unit is assigned to one metropolitanarea, if any.

A.2

Building metropolitan areas from commuting data

This section briefly describes the iterative algorithm introduced by Duranton (2015) to define
metropolitan areas on the basis of commuting flows between smaller geographic units, callthem “microunits,” which are in the US case and municipios in the Brazilian case. Using thealgorithm requires the choice of a minimum commuting threshold. We initialize the algorithm by aggregating the two microunits with the largest commuting tie. At each successive
iteration of the algorithm, we recompute the commuting flow between any microunit that is
not already assigned to a metropolitan area and each metropolitan area. We recursively aggregate microunits to the metropolitan area with which they share the strongest commuting
tie that exceeds the minimum commuting threshold. The algorithm stops when there are no
more microunits to be aggregated.

B

Data description

B.1

Satellite image data

Night lights raster data is available from NOAA’s Earth Observation Group. We use observations from the Version 4 DMSP-OLS Nighttime Lights Time Series for the years 2000,

41

2001, 2010, and 2011 from the “average visible, stable lights” series.34 These data have aresolution of 30 arc-seconds, which is roughly one square kilometer.

B.2

Brazil

B.2.1

Geography

We build metropolitan areas by aggregating municipios. In year 2010 definitions, the 5th ,50th , and 95th percentiles of municipio land area were 83, 416, and 5,344 km2 , respectively.
To construct metropolitan areas based on commuting flows, we use anonymized individuallevel microdata from the 2010 Census to construct a commuting flows matrix between origin
municipio and destination municipio. We then select a commuting share threshold andimplement the Duranton (2015) algorithm to construct metropolitan areas.
To construct metropolitan areas based on night lights, we use the night lights raster data
described above and shapefiles for Brazilian municipios. We use a spatial coordinate systemrecommended by the Instituto Brasileiro de Geografia e Estatı́stica (IBGE). Their website
recommends a latitude and longitude of origin (−12◦ , −54◦ ) and standard parallels of −2◦
and −22◦ . Our code pulls these parameters directly from https://spatialreference.org/
ref/sr-org/7823/. The azimuthal equidistant projection depends only on the latitude andlongitude of origin. The Albers conic projection employs this origin and also requires thestandard parallels.
B.2.2

Skills and Sectors

Anonymized individual-level microdata from the 2010 Census is available from the Instituto
Brasileiro de Geografia e Estatı́stica (IBGE) website. We aggregate these observations,using the individual sampling weights, to produce municipio-level counts of the population
older than 25 by educational attainment, industry, and occupation. We use these sameobservations to compute average years of schooling by industry and occupation. We computeaverage hourly wages and skill premia using income and hours at the main job for individuals
between 25 and 65 years old with an identified educational attainment and race with wages
between the 1st and 99th percentiles.

B.3

China

B.3.1

Geography

We build both county-based and township-based metropolitan areas for the years 2000 and2010. County- and township-level shapefiles are available via the China Data Center at
the University of Michigan. In year 2000 definitions, the 5th , 50th , and 95th percentiles
of township land area were 4, 72, and 435 km2 , respectively.
In year 2000 definitions,ththth
the 5 , 50 , and 95 percentiles of county land area were 42, 1,582, and 11,053 km2 ,
respectively. To implement our night-lights–based approach, we use the night lights rasterdata for 2000 and 2010 described above and apply light-intensity thresholds ranging from
34

These are filenames of the form F1?YYYY v4? stable lights.avg vis.tif for F152000, F152001,
F182010, and F182011.

42

10 to 60 in increments of 10. We use an azimuthal equidistant projection centered on(35◦ , 105◦ ) and an Albers equal-area conic projection centered on (35◦ , 105◦ ) with standard
parallels 27◦ and 45◦ , which is available at https://spatialreference.org/ref/sr-org/china-albers-equal-area-conic/proj4/.
B.3.2

SkillsData on township-level and county-level employment by educational level come from the2000 and 2010 Population Census. Townships are considerably smaller than counties andtherefore preferable where available. Population counts for both counties and townships areavailable for both 2000 and 2010. However, for the 2010 Census data, many socioeconomic
characteristics, such as educational attainment, are thus far only available at the level ofcounties. The Chinese population census enumerates the de facto population of these geographic units, not the de jure population of households given by the hukou (household
registration) system (Chan, 2007, p.392).

B.4

India

B.4.1

Geography

We define India metropolitan areas using two imperfect methods, due to the absence ofa shapefile for India’s towns and villages, which we have yet to acquire. First, we use
subdistricts, for which a shapefile is available, and aggregate these subdistricts using ournight-lights–based approach. In year 2001 definitions, the 5th , 50th , and 95th percentilesof sub-district land area were 92, 374, and 1,512 km2 , respectively.
Second, we use
urban agglomerations defined by the Census of India. The assignments of census towns
to urban agglomerations is available from the Census of India’s website. We use an azimuthal equidistant projection centered on (20◦ , 78◦ ) and an Albers equal-area conic projection centered on (20◦ , 78◦ ) with standard parallels 28◦ and 12◦ , which is available athttps://spatialreference.org/ref/sr-org/albers-india/proj4/.
B.4.2

SkillsTables from the 2001 Census are available via the Government of India’s website. Town-level
employment by educational level is reported in Table B-9, “Main Workers by Educational
Level, Age and Sex.”

B.5

United States

We define United States metropolitan areas by aggregating counties on the basis of lights
at night in 2010. We use an equidistant conic projection centered on −96◦ with standard
parallels 29.5◦ and 45.5◦ and an Albers equal-area conic projection centered on (37.5◦ , −96◦ )with standard parallels 29.5◦ and 45.5◦ for the contiguous United States, which is available athttps://spatialreference.org/ref/esri/usa-contiguous-albers-equal-area-conic/.
We use distinct azimuthal equidistant and Albers equal-area conic projections for Alaska and
Hawaii.
43

C

Additional empirical results

C.1

Pairwise comparisons of skills across metropolitan areas

Davis and Dingel (2017) introduce a theoretical model that predicts that larger cities are
skill-abundant and delivers two methods of examining these patterns for an arbitrary numberof skill groups. In Section 3, we report population elasticities estimated by linear regression.
In this appendix, we report non-parametric pairwise comparisons of relative population levelsof any two skills and any two cities, which test the theory’s prediction that the more skilledgroup should be relatively larger in the more populous city.
The pairwise-comparison prediction in Davis and Dingel (2017) says that, if cities are
divided into bins ordered by population sizes, then in any pairwise comparison of two bins
and two skills, the bin containing more populous cities will have relatively more of the moreskilled type.35 Our pairwise-comparison test therefore reports, among all possible pairs ofbins and pairs of skills, the fraction of comparisons in which the population of the moreskilled group is relatively larger in the more populous cities. We compare this observed
success rate to the null hypothesis that skills are uniformly distributed across cities. When
doing so, we can also weight the comparison outcome by the product of the difference inlog population sizes and the product of the educational categories’ population shares. Davisand Dingel (2017) show that, in the presence of additive random errors to ln L(ν, c), thelikelihood of a successful pairwise comparison increases with the difference in population
size and the number of cities assigned to each bin. In the interest of brevity, we only reportresults for one definition of metropolitan areas for each economy.
Table C.1 reports the success rates for these comparisons. In all three economies, thesuccess rate is higher when we use a smaller number of bins or weight the comparisonsby population differences. Thus, the central tendency of the data are consistent with thepatterns exhibited by the estimated population elasticities. More populous metropolitan
areas are more skill-abundant, as captured by four educational-attainment categories.
If we are willing to assume that the comparison of any two educational categories isequally informative across the three economies, we can also compare the success rates acrosscountries to gauge the degree to which larger cities are more skill-abundant. These comparisons are complicated by substantial cross-country differences in the size of geographic
units that we aggregate and the number of metropolitan areas with population greater than
100,000. With these caveats in mind, the general pattern is that Brazil’s pairwise-comparison
success rates are higher than China’s, which are higher than India’s. Thus, broadly speaking, the distribution of skills that most closely matches the theoretical predictions and US
empirical patterns in Davis and Dingel (2017) is that of Brazil, followed by China, and thenIndia. This is similar to the finding of Chauvin et al. (2017), who conclude that, in termsof a variety of spatial patterns, Brazil is more like the US than China, which is more like
Formally, if L (ν, c) is log-supermodular, C and C 0 are distinct sets, C is greater than C 0 (inf c∈C L(c) >supc0 ∈C 0 L(c0 )), and nC (nC 0 ) is the number of elements in C (C 0 ), then
35

1 X
1 X
1 X
1 X
ln L(ν, c) +ln L(ν 0 , c0 ) ≥ln L(ν 0 , c) +ln L(ν, c0 ) ∀ν > ν 0 .
nC
nC 0 0 0
nC
nC 0 0 0
c∈C

c ∈C

c∈C

44

c ∈C

Table C.1: Pairwise comparisons for educational categories
Brazil (2010)

China (2000)

India (2001)

Bins

Pairings Success rates Bins

Pairings

Success rates

Bins

Pairings

Success rates

2
8
16
64
96
192

6
168
720
12096
27360
110016

6
60
270
7350
67050
1941660

1.00
0.88
0.86
0.77
0.70
0.62

2
5
11
33
110
330

6
60
330
3168
35970
323736

1.00
0.78
0.65
0.58
0.53
0.52

Weighted

1.00
0.91
0.82
0.72
0.68
0.63

1.00
0.98
0.95
0.88
0.83
0.77

2
5
10
50
150
805

√

1.00
0.91
0.85
0.80
0.73
0.61
√

1.00
0.83
0.75
0.64
0.56
0.54
√

Notes: The samples contain geographic units with population greater than 100,000: 192 Brazilian
metropolitan areas defined by commuting with 10% threshold, 800 Chinese metropolitan areas definedby night lights with 30 intensity threshold, and 330 Indian urban agglomerations and census towns
for which educational attainment data are available. Weighted success rates are comparison outcomes
weighted by the product of the difference in log population sizes and product of educational category’s
population shares.

the US than India. In terms of the spatial distribution of skills, however, we find that all
three economies’ populations are well described by the stylized fact that larger cities are
skill-abundant.

C.2

Comparing skill gradients of different metropolitan definitions

The p-values reported in Table 11 test the null hypothesis that the skill gradient coefficients
estimated using township- and county-based metropolitan areas are equal. We implement
this test as a difference-in-differences regression. Let Yicg denote the college share of residents
in administrative unit i (either a town or a county) within metropolitan area c in group g.
A group g contains a county-based metropolitan area and the township-based metropolitan
areas with which it spatially overlaps. We regress the college share Yicg on a metropolitan
area fixed effect αc , the normalized distance to the metropolitan centroid Xicg , and theinteraction of Xicg with a dummy indicating that i is a township.
Yicg = αc + βXicg + γXicg × townshipi + icg
We allow icg to be correlated within group g when computing the standard error for γ. The
reported p-values test the hypothesis that γ = 0.
The analogous procedure is employed to produce the p-values reported in Table 10, whichtest the null hypothesis that the skill gradient coefficients estimated using night-lights–based
metropolitan areas are equal to those estimated using arranjos or microregions.

45