Detecting Urban Markets with Satellite Imagery:
An Application to India∗
Kathryn Baragwanath* , Ran Goldblatt† , Gordon Hanson‡ , and Amit K. Khandelwal§*

UCSD
New Light Technologies‡
UCSD & NBER§
Columbia GSB & NBER†

First Draft: July 2018
This Draft: May 2019

Abstract
We propose a methodology for defining urban markets based on builtup landcover classified
from daytime satellite imagery. Compared to markets defined using minimum thresholds fornighttime light intensity, daytime imagery identify an order of magnitude more markets, capture more of India’s urban population, are more realistically jagged in shape, and reveal morevariation in the spatial distribution of economic activity. We conclude that daytime satellite
data are a promising source for the study of urban forms.
Keywords: Satellite, Landsat, Nightlight Data, Market Access, Cities, Urbanization
JEL Classification: R1, O1, O18∗

We acknowledge funding from the World Bank, the International Growth Centre (Project 89448), and the Center for Global Transformation at UC San Diego. We thank the Editor, Gilles Duranton, and two anonymousreferees for valuable feedback. Additionally, we thank Somik Lall, Trevor Monroe, Rinku Murgai, Adam Storeygard, Siddharth Sharma, and seminar participants at University of Toronto, Berkeley Haas, 2018 Urban Economics
Association Meetings, the Urban and Regional/Spatial Zoom Seminar, MIT, McGill University, and the WorldBank for constructive comments. Khandelwal acknowledges support from The Council on Foreign Relations International Affairs Fellowship in International Economics. All errors are our own. E-mail: kbaragwa@ucsd.edu,
ran.goldblatt@newlighttechnologies.com, gohanson@ucsd.edu, ak2796@columbia.edu.

1Introduction

Core to the study of economic geography is explaining why cities exist and how their dimensions
are determined. It is standard to attribute the existence of cities to the benefits of agglomeration—be they conventional agglomeration economies (e.g., Henderson 1974, Duranton and Puga
2001), or home-market effects derived in new-economic-geography models (e.g., Fujita et al. 2001).
Where cities locate, in turn, is influenced by the availability of key resources, access to transportation routes, and historical accident (e.g., Bleakley and Lin 2012, Henderson et al. 2018). Withincities, the clustering of activity creates gradients in land prices and presents workers with a tradeoff
between housing costs and commute times (Duranton and Puga 2015). A rich and vibrant literature studies how the concentrating forces of agglomeration and the dispersing forces of congestion
combine to create urban systems (e.g., Duranton and Puga 2004, Desmet and Henderson 2015).
Empirical work on economic geography requires measuring the location and scale of urban
activity. A common approach to measurement is to use officially designated administrative units.
These may be as large as a metropolitan area (e.g., Duranton and Turner 2012), as small as atown or village (e.g., Eeckhout 2004), or an intermediately sized unit such as a county or a district(e.g., Hanson 2005, Ghani et al. 2014, Donaldson and Hornbeck 2016). Because administrative
boundaries are defined according to pre-existing legal jurisdictions, they may be noisy indicatorsof how cities are actually organized. In influential work, Rozenfeld et al. (2011) construct cities byclustering officially designated towns and villages into larger units based on geographic proximity.
This approach only works, however, if official sources measure activity for fine administrative units
on a frequent basis. In many countries, such data are available only decadally, if at all.
In this paper, we use remotely sensed data to detect urban markets in India for 2013. A market
is a set of contiguous, or near contiguous, pixels that contain economic activity according to daytime
or nighttime satellite imagery. Our practical approach approximates the conceptual definition ofa market in economic geography models: a set of locations that are highly integrated relative tooutside locations because of low internal trade costs (e.g., Redding 2016) and (or) low commuting
costs (e.g., Duranton 2015). We categorize a pixel as having economic activity if its nighttime
light intensity exceeds a given threshold or its spectral properties indicate builtup landcover. Ourmaintained assumption is that clusters of proximate pixels are integrated through internal tradeand commuting links, which we attempt to validate in external data.
Our first source of imagery is nighttime lights from the Defense Meteorological Satellite Program
Operational Linescan System, which indicates the presence of economically active agents (Henderson et al. 2012). Following Rozenfeld et al. (2011), we explore buffers that combine contiguous
sets of pixels if they lie within a radius of 1km, 2km, 4km or 8km. Defining urban land usingnightlights requires choosing a minimum threshold of light intensity for contiguous pixels. Harari(2017), for instance, in her analysis of urban sprawl in large Indian cities chooses a digital number(DN) of 35 (on a scale of 0 to 63) to designate urban areas. Our analysis reveals a tradeoff inchoosing the minimum light threshold for a market: while a strict threshold only captures majorurban agglomerations, lowering the threshold to include smaller cities explodes the size of larger
1cities with proximate satellites. This tradeoff is a consequence of the blooming effect of light, which
produces cities whose boundaries are too expansive and too smooth relative to actual cities.
We contrast the spatial extent of nightlight-based markets with those formed from high-resolution
daytime satellite imagery. These data are available at finer resolutions than nighttime lights databut require further image classification to detect urban land. We explore data on builtup landcoverfrom the MODIS layer constructed by Channan et al. (2014). We also examine two additional
daytime imagery layers: the Global Human Settlements Layer (Pesaresi et al. 2015) and a recent
layer produced by Goldblatt et al. (2018). We define landcover-based markets using an analogous
algorithm that clusters contiguous or near contiguous pixels of builtup landcover.
Our approach has three advantages over conventional methods to measure urban areas using
administrative data. First, it is scalable. Because our method is algorithmic and uses publicly
available imagery, it scales to detect markets globally and, in principle, over time. It also circumvents the need to reconcile differences across countries and time in how administrative units aredefined. Second, and relatedly, our data do not stop at national borders. Markets that straddle
national boundaries along transportation routes can be tracked. Third, the spatial resolution isadjustable. By altering the buffer used to aggregate proximate pixels, we can narrow the focus to
the rough equivalent of a town center or widen the focus to a metropolitan area. This versatility is
helpful for detecting within-metro area heterogeneity, a feature we explore.
To preview our results, the patterns of landcover-based markets are starkly different from thoseof nightlight-based markets. Using the definition of a market that buffers clusters of contiguous
pixels at 1km, we detect 1,669 and 469 markets using a nightlight threshold of DN33 and DN60,
respectively. The DN60 markets accurately capture India’s largest 470 cities according to official
Census data, which suggests that nightlight-based markets are reliable for tracking activity acrossIndia’s major urban areas. In contrast, we detect an order of magnitude more markets using
MODIS data: 12,953 in total. These markets are smaller, less compact, more closely fit a powerlaw in area size, and capture activity ranging from distinct areas within large metropolises to small
towns that are distant from India’s major cities. For example, within Delhi’s official administrative
boundary, we detect 579 distinct 1km MODIS markets. More remote, landcover-based markets havean average DN nightlight intensity of just 5, suggesting that we are able to capture many parts ofIndia that lack reliable access to electricity. While we could detect these markets with nightlightdata by lowering the light-intensity threshold, this would come at the cost of vastly increasing thearea of above-threshold contiguous pixels around India’s large cities, which is evident from visualinspection and from statistics on the maximum size of markets at different thresholds. Our results
suggest that landcover-based markets are able to capture small cities and towns in India while
preserving the spatial distribution of activity of the largest cities.
We perform several validation checks to demonstrate that our markets capture real economic
activity. Using shape files for the 2011 India Census, we allocate population across our market
boundaries. Collectively, the DN33 and DN60 1km markets contain 23.4% and 14.8% of India’s
total population and 75.3% and 47.6% of India’s urban population, respectively. The MODIS 1km

2markets capture 29.0% and 93.2% of India’s total and urban populations, respectively. Market
size correlates strongly with population, and the variance in population for smaller sized landcovermarkets reflects the fact that these markets include both dense areas within major metro areas andless populated peripheral towns. We detect strong correlations between market size and proximity
to public infrastructure, such as roads, railway stations and mobile phone towers. Additionally, we
find that larger landcover-based markets have higher nighttime light intensity. These correlations
are important for addressing a limitation of daytime satellite data. While these data are suitable
for measuring the spatial extent of markets, they may not reveal the intensity of economic activity.
However, the positive correlations reveal that the extensive margin—which is measured accurately
through daytime imagery—correlates well with proxies for the intensive margin. For example, a
MODIS market at the 10th percentile of the land-area distribution has a nightlight DN of 9.4
compared to 27.2 for a market at the 90th percentile of land area.1 Combining daytime imagery
to measure the boundary of markets with nighttime data to measure the intensity of activity is apromising approach to leverage two remotely sensed datasets that are publicly available, have along time span, and have global coverage.
Finally, we consider the potential to use landcover-based markets to study polycentric cities(Duranton and Puga 2015). The literature has long recognized that cities do not expand smoothly
along their margins but through the construction of outlying communities in the form of suburbs,
edge cities, or commercial hubs (e.g., Henderson and Mitra 1996, Anas et al. 1998). For example, theHyderabad metro area, which spans 650km2 and contains 6.8 million people, contains Hyderabad
and Secunderabad as major poles and substantial satellites in Ghatkesar and Kukatpally. As one
zooms in further, many more satellites appear and Hyderabad’s full polycentricity is revealed. We
examine polycentricity using the larger buffered markets, which we term “super-markets”. The
average MODIS 8km market spans an area of 63.4 km2 , but physical structures cover only 23% of
this area. On average, these super-markets contain 4.2 distinct 1km markets; the elasticity of thenumber of 1km buffered markets with respect to super-market area size is 0.36. This within-market
variation may be sufficient to study, for instance, how transportation investments, such as ring roads
or metro rail, impact the distribution of economic activity within large cities. To demonstrate thispossibility, we construct measures of market access based on Donaldson and Hornbeck (2016) andfind that a non-trivial portion of a market’s access is determined by other close-by markets thatare within the same larger buffered super-market.
The availability of satellite imagery and machine-learning techniques for image classification
have led to rapid advances in detecting land use in the remote sensing literature. In efforts toconstruct urban layers for the world as a whole, Pesaresi et al. (2015) use Landsat imagery todetect urban land for grid cells at a 38m resolution, Channan et al. (2014) use MODIS imagery
to detect multiple types of land use for grid cells at a 500m resolution, and Zhou et al. (2015) use
nightlight intensity to detect urban land at a 1km resolution.2 This work typically classifies land
1

Using the nightlight-GDP elasticity of 0.3 from Henderson et al. (2012) implies that the larger area would havea 56.8% higher GDP.
2
Alqurashi and Kumar (2013) discuss earlier work in remote sensing to detect land use. Recent papers that detect3use at the pixel level, where the dimensions of the pixels vary according to the source of the satellite
imagery. Pixel-level classifications, while important building blocks in urban analysis, are not inand of themselves informative for the study of economic geography. Without aggregating pixels toform larger markets, one cannot test theories of the size distribution of cities, evaluate the impactsof expanding national transportation grids, or identify the consequences of severe weather events,
plant closures, or other localized economic shocks.
Our results contribute most directly to the efforts to delineate urban areas that do not rely on
administrative boundaries. In addition to Rozenfeld et al. (2011), our paper has antecedents inEeckhout (2004), who uses U.S. Census Designated Places instead of (much larger) Metropolitan
Statistical Areas to re-examine Zipf’s law and Gibrat’s law; Burchfield et al. (2006), who use
contiguous pixels to measure sprawl in the U.S. based on Landsat satellite imagery from 1976-1992;
and Harari (2017), who uses nightlights to track urban sprawl in large Indian metropolitan areas.
Davis et al. (2019) also use clusters of pixels above nightlight thresholds to construct metro areas
in Brazil, China, and India. Recent work by Duranton (2015) proposes an alternative algorithm toconstruct markets based on commuting patterns for Colombia. de Bellefon et al. (2019) develop astatistical approach to detect urban areas using precise locational data covering 34 million buildings
in France. Our contribution to this literature is to develop and compare methods to detect markets
solely from remotely sensed data, and in particular daytime imagery.
More broadly, our paper builds on the increasing use of remotely sensed data for economic
analysis. Economists have used satellite data on the intensity of light emitted at night to study
national and regional economic growth (Henderson et al. 2012, Gennaioli et al. 2013, Pinkovskiy
and Sala-i Martin 2016), the political economy of regional development (Gennaioli et al. 2013,
Michalopoulos and Papaioannou 2013a, Michalopoulos and Papaioannou 2013b), spatial linkages
between cities (Storeygard 2016), and the global distribution of economic activity (Henderson et al.
2018), among a rapidly growing set of topics. Daytime satellite imagery, whose use in economics
was pioneered by Burchfield et al. (2006), is available at even higher spatial resolutions, down to
30m for data going back to the late 1990s and down to less than 1m for imagery from recently
launched proprietary satellites. Michaels et al. (2018) use an ensemble of remotely sensed imagery
to measure urbanization in Tanzania. For a comprehensive survey of recent work, see Donaldson
and Storeygard (2016).
Section 2 presents the method to detect markets from satellite imagery. Section 3 comparesnightlight-based markets and landcover-based markets and provides validation checks. Section 4
uses landcover-based markets to evaluate market access. Section 5 concludes.

2

Algorithmic Approach to Detect Markets
We define markets using two sources of remotely sensed data: (1) the intensity of light as

captured by nighttime lights data; and (2) classifications for builtup landcover based on daytime
urban land for individual countries include Pandey et al. (2013) on India; Bagan and Yamagata (2015) on Japan;
and Zhou et al. (2014), Huang et al. (2015), and Fu et al. (2017) on China. For literature that detects urban land
using daytime satellite imagery, see Trianni et al. (2015), Goldblatt et al. (2016), and Goldblatt et al. (2018).

4

satellite imagery. In this section, we describe the data sources and algorithms used to detect the
spatial extent of a market for each data source.

2.1

Detecting Markets from Nightlight Imagery

The US Air Force Defense Meteorological Satellite Program (DMSP) operates satellites thatcarry light sensors known as the Operational Linescan System (OLS). Originally used to detect
the global distribution of clouds and cloud-top temperatures, OLS sensors also detect visible andnear-infrared emissions at night from different sources on Earth, such as city lights, auroras, gasflares, and fires. Pixels have a resolution of 30 arc seconds, or approximately 1km × 1km. For
each pixel, the digital number of calibrated light intensity ranges from 0 to 63, which we refer toas the nightlight value or intensity. Because persistent light emitted at night is often associatedwith man-made structures, we assume that if the intensity of a pixel exceeds a given threshold, thispixel represents a populated location. Processed DMSP-OLS imagery is publicly available from
1992-2014, and can be analyzed on Google Earth Engine. We process lit pixels using data for 2013.
We use the stable light band of sensor F14, which discards ephemeral events, such as fires, but
remains sensitive to persistent lighting, including from gas flares or volcanoes. Since India has noactive volcanoes or gas flares on land (Elvidge et al. 1999), it is safe to assume that highly lit pixels
in India indicate builtup activity.
There are well-known limitations to DMSP-OLS data. These include saturation effects, in which
the amplification of light detection to capture low levels of light leads to right censoring in detection
in highly-lit areas (e.g., city centers); and blooming effects, in which reflection causes light emitted
in one pixel to be detected in nearby pixels, making highly lit areas appear to be larger than theyare. Blooming occurs due to several idiosyncratic features of the DMSP-OLS sensor: (1) field ofview variation, where the satellite’s round field of view morphs into an elliptical and larger shape as
it scans east and west of nadir; (2) geolocation errors, whereby the satellite miscalculates a pixel’s
location, so on each night not only is there a differently sized ellipse, but its centroid is shocked in arandom compass direction (Abrahams et al. 2018); and (3) on-board data management, where the1970s technology on board the satellites causes top-censoring of inputs. The highest possible DN
is 63, and because of this saturation, it is often impossible to differentiate between medium-density
cities and high-density cities.3 In our setting, saturation is not an issue because we measure theextent of markets through lower bounds of light intensity. However, blooming is problematic, as
we demonstrate below.
Nightlight-Based Markets: A nightlight-based market is a cluster of contiguous, or nearcontiguous pixels, with a DN that exceeds a specified threshold.
3

Blooming and saturation are less pronounced in data from recently launched satellites. The Visible Infrared
Imaging Radiometer Suite (VIIRS), imagery from which is only available since 2012, detects electric light at a higher
spatial resolution and at lower distortion than DMSP-OLS. See Elvidge et al. (2017) for a discussion of VIIRS imagery
and Shi et al. (2014) for an application of these data to detecting urban areas in China. Henderson et al. (2018) use aradiance-calibrated version of the nightlight data that alleviates the saturation effect (Elvidge et al. 1999) but thesedata are also available only for a subset of recent years. We use DMSP-OLS imagery in order to create methods formeasuring markets that can be extended backward in time.

5

To operationalize this definition of a market based on nightlight data, three choices are required:(1) the minimum number of pixels that constitute a market; (2) the parameter values that govern“near contiguity”; and (3) the minimum DN to be used. As mentioned, the DMSP-OLS sensor has
a 1km resolution. We set the minimum number of pixels to form a market at 1 pixel.4
To determine the minimum DN thresholds for our market definition, we examine the distribution of DNs across pixels in India for 2013 in Figure A1. Because light is not detected in large
expanses of the country—including bodies of water, farmland, deserts, forests, and villages withno electricity—the DN is zero (i.e., no detectable light) for the pixel at the 50th percentile of the
distribution. The DN is moderately higher at a value of 5 at the 63rd percentile, and rises sharply
as one moves into the upper tail, reaching 17.4 at the 95th percentile, 49 at the 99th percentile, and
60 at the 99.5th percentile; only a tiny fraction of pixels are right censored at the maximum DN of
63.5 Motivated by these patterns, we set the following alternative DN thresholds for a pixel to behighly lit: 17.4 (95th percentile), 33 (98th percentile), and 60 (99.5th percentile).
We designate as a market a cluster of contiguous highly lit pixels, which may consist of only asingle pixel. Many clusters of highly lit pixels lie in close proximity to each other, creating chainsof light islands that appear when we map our results. By the strict definition above, we would
treat each island, or polygon of pixels, as a separate market, whereas in truth clusters of proximate
polygons may share dense commercial and commuting ties (as in the case of U.S. counties thatcomprise commuting zones; e.g., Tolbert and Sizer 1996). Motivated by the method in Rozenfeld
et al. (2011) for agglomerating neighboring administrative units into larger units, we combine any
pair of highly lit clusters for which the minimum distance between their boundaries is less than
1km, 2km, 4km, or 8km.6 For a given threshold, larger buffers nest smaller buffers: 1km markets⊆ 2km markets ⊆ 4km markets ⊆ 8km markets.

2.2

Detecting Markets from High-Resolution Daytime Imagery

Daytime imagery offers alternative data to detect human activity from space. The major
challenge in working with daytime imagery is that one needs a classifier to convert the spectral
signature of an image into a categorization of landcover. In recent years, there has been substantial
4

The threshold pixel choice of 1 may appear to low. As a point of reference, Rozenfeld et al. (2011) use grid cellswith 200m resolution for Great Britain and FIPS units for the U.S., which range from 100m grid cells in Manhattan
to 100km grid cells in Wyoming. In recent work, de Bellefon et al. (2019) provide a statistical approach to choose
thresholds to define urban areas using detailed geocoded data on the location of buildings in France, and detect
distinct urban areas as small as 0.04km2 .
5
The bunching at 0 and 5 is an artifact of the stable light band of satellite F14, which removes noise and unstable
light removal. Cauwels et al. (2014) note that the number of pixels with DN greater than 0 and less than 5 isextremely low; for example, the satellite registers no pixels with a DN equal to 1 in the year 2000. Tuttle et al.
(2014) develop a mapping of DNs to wattage by placing portable high-pressure sodium lamps at uninhabited sites
in Colorado and New Mexico to check the DN recorded by the F16 and F18 sensors. They find that ninety-three
100-watt incandescent lamps could be detected (DN=1) at both fine (0.6km) and coarse (2.7km) resolutions. Eighttimes as many bulbs would saturate (DN=63) the sensor at the fine resolution but not at the coarser resolution.
6
We view a 0km buffer as extreme as it does not account for commuting or trade linkages and therefore do notconsider this buffer choice for our analysis. We use the Aggregate Polygons function in ArcGis to cluster the pixels.
Online Appendix A explains the procedure to aggregate pixels to markets.

6

progress in remote sensing to improve the precision of classification algorithms at scale. Use ofdaytime imagery is also facilitated by cloud-based computing engines, such as Google Earth Engine,which hosts the full library of Landsat, MODIS, Sentinel, and other satellite imagery.
We use the MODIS dataset as our benchmark source of landcover classification from daytime
imagery. MODIS uses a supervised machine learning method, which takes advantage of a global
database of training sites extracted from high-resolution imagery that contain 36 spectral bands.
We use the University of Maryland classification scheme version MCD12Q1 V006, which has aresolution of 500m (Friedl and Sulla-Menashe 2015). We use data from 2013 and take the takethe Urban and Builtup pixels (classification 13) to indicate builtup landcover. MODIS is publicly
available on Google Earth Engine and widely used in the remote sensing literature (e.g., Huang
et al. 2016, Mertes et al. 2015, Guo et al. 2015).7
We also examine two other landcover datasets as a robustness check against MODIS. The Global
Human Settlements Layer (GHSL, Pesaresi et al. 2015) combines satellite data from Global Land
Surveys datasets (GLS1975, GLS1990, GLS2000), Landsat 8, and other sources—–including OpenStreet Maps, WorldPop and MODIS—–to determine builtup pixels at a 38m spatial resolution.8
We use their “Builtup Confidence Grid”, which aggregates builtup data in 2014 and classifies pixels
as builtup if the confidence of being builtup is greater than 50%. GHSL contains landcover maps
from an earlier period but has less frequent temporal variation than MODIS. Although publicly
available, the GHSL is difficult to access, uses data beyond raw satellite bands, and is less widelyused. The third map of builtup landcover for India in 2013 is created using the methodology inGoldblatt et al. (2018). This layer, to which we refer as MIX, uses DMSP-OLS nightlight dataas quasi-ground truth and daytime satellite imagery as inputs to train a classifier for builtup land
cover in India. Appendix B summarizes their method for producing this layer.
Our motivation for using multiple layers of builtup landcover comes from rapid advances inremote sensing for classifying land use from satellite imagery. The accuracy with which existinglayers detect changes in urban landcover, rather than just cross-sectional features, is a subject ofon-going research (e.g., see Mertes et al. 2015, Song et al. 2016). We anticipate more advances
will be made in land-use classification in the near future, such that none of the existing layers
may become the standard source for builtup landcover. In light of this uncertainty, we use threedifferent layers, which allows us to assess the strengths and weaknesses of alternative approaches
to detecting urban activity. Our method would easily extend to new layers of builtup landcover.
Using the three layers that classify builtup landcover—MODIS, GHSL, and MIX—we adopt
7

MODIS (MCD12Q1 V006) classifies global land cover types at yearly intervals from 2001 to 2016. There are
six versions of MODIS. The most recent version, Collection 6, improves over previous versions by implementing ahierarchical classification approach, using a RandomForest classifier instead of a C4.5 decision tree, increasing thenumber of sites in the training data by 47% and updating sites that have changed their land use (about 31% of sites),
improving the feature set that now includes phenology metrics, and using Markov chain stabilization. Additionally,
we found that this version was slightly better at capturing urban land cover changes in time than its previous version.
See the MCD12Q1 V006 user manual for details.
8
The USGS Landsat 7 satellite, launched in 1999, contains seven spectral bands at a spatial resolution of 30m anda temporal frequency of 16 days. Landsat 8, launched in 2013, contains nine spectral bands with a spatial resolutionof 30m at a temporal frequency of 16 days.

7

the following definition for markets for daytime satellite imagery.
Landcover-Based Markets: A landcover-based market is a cluster of contiguous or nearcontiguous pixels whose spectral features in daytime satellite imagery indicate that the majority of
their land area consists of builtup landcover.
For MODIS markets, we impose a minimum number of pixels for a market to be 1 (0.25km2 ). For
GHSL and MIX, the minimum number of pixels is set to 40 (0.04km2 and 0.03km2 , respectively).
Choosing a minimum pixel size of 1 for GHSL and MIX would be extreme given the granularity ofthese data (and would be computationally cumbersome); the choice of 40 leverages the granularityof the data to detect small clusters of pixels while not creating markets so small that they would
rarely display well-defined internal trade or self-contained commuting patterns. Clusters of builtup
pixels are aggregated in a manner analogous to that described above (e.g., if two clusters of MODIS
pixels are separated by, say, 1.5km of non-builtup pixels, they would form two distinct markets
under the 1km buffer and a single market under the 2km buffer).

2.3

Visual Inspection of Market Definitions

To obtain a visual sense of the shape of urban markets identified by daytime versus nightlightdata sources under the four buffers, we plot the markets detected around three cities of different
sizes: Delhi (19 million, 2011 Census population), Ahmedabad (5.5 million), and Ajmer (0.5 million)
in Figures 1 to 3. We overlay road networks from OpenStreetMaps in 2018 to provide a sense of
how transportation networks may influence the shape of markets. Panels (a) to (d), in the firstrow, display results for MODIS-based markets, while panels (e) to (t), in the second through fifthrows, display results for nightlight-based markets. We include nightlight markets formed using a
DN threshold of 10 to understand better the consequences of varying light intensity thresholds but
we do not analyze DN10 markets in subsequent sections.
Consider first nightlight-based markets. Together, we have 16 alternative nightlight-based market definitions. The maps illustrate how changing the DN threshold and buffer sizes affects market
shape. At a DN of 10 (fifth row), Delhi is an immense blob that swallows cities across three statesin India, including Meerut (1.3 million, in Uttar Pradesh), Rohtak (0.4 million, in Haryana) andBhiwadi (0.1 million, in Rajasthan). The blob itself is 145,336km2 , which is close to the size of
the U.S. state of Iowa. At a higher DN of 17.4 (fourth row), Delhi takes the shape of a moreconventional urban market, but again swallows the city of Meerut (1.3 million), which is 75km
northeast of central Delhi. At a DN of 60 (second row), by contrast, Meerut appears as a separate market from Delhi. But this threshold fails to detect the small city of Hapur (0.2 million).
Moreover, the satellite cities of Gurgaon (0.9 million) and Noida (0.6 million), two vibrant areas of
economic activity in Delhi, are fused together with central Delhi to form one large market. Figure
2 for Ahmedabad shows a similar pattern: a high threshold separates the main city from its largest
satellite (Nadiad, 0.2 million), but fails to detect many smaller cities; lowering the threshold causes
the size of Ahmedabad to explode. Figure 3 shows the smaller city of Ajmer in the state of Ra-8jasthan. The road leading out of Ajmer towards the Northeast is part of the Golden Quadrilateral.
At lower DN thresholds, activity appears to coalesce along the artery. This is problematic as theselights are likely capturing lights along the road rather than stable clusters of economic activity.
To consider landcover-based markets, examine the top rows of Figures 1 to 3, which show
markets using the MODIS layer. In stark contrast to the nightlight-based definition in the bottom
four rows, landcover-based markets are jagged in shape and display large variation in the spatial
density of economic activity. Also, landcover-based markets show that within the outer envelopeof the market area there are substantial numbers of white pixel islands, indicating areas that are
not builtup. Whereas the blooming effect creates the perception that inside market boundaries
all pixels contain light-emitting structures, higher-resolution imagery indicates that cities containmany clusters of pixels that have not been builtup (e.g., undeveloped land, water, and parks). For
example, the Yamuna river in Northeast Delhi is visible in the landcover-based figures but masked
through the blooming of lights in the nightlight-based markets. The presence of undeveloped pixels
within cities in the top row and absence in the lower rows (which are especially apparent in Figures 1
and 2 for the larger cities of Delhi and Ahmedabad and would appear for the smaller city of Ajmer
were we to zoom in) indicates that nightlight-based markets tend to make urbanization insidemarket boundaries appear to be overly smooth. Notice also that within Delhi, we observe many
distinct neighborhoods that are fused together in nightlight-based markets. At higher distancebuffers, the small distinct markets within cities fuse together while remote towns remain visible.
Visual inspection illustrates the tradeoff in varying the DN threshold to detect markets usingnightlights. A strict DN threshold captures the most economically developed urban centers ofIndia. But this threshold misses smaller cities and towns. In attempting to capture these towns
through a lower DN threshold, the large cities mushroom in size and swallow neighboring satellite
cities. Lower thresholds also start to capture activity along roads which are likely emitted by street
lights and (or) the blooming effects from towns. Landcover-based markets detected through highresolution daytime imagery are not subject to this tradeoff. We observe distinct pockets of activity
within cities and detect smaller towns located at the periphery; increasing the buffer fuses together
markets within cities while preserving the shape of the smaller cities. Statistics reported in thenext section reinforce the descriptive results from this visual inspection.

3

Market Characteristics and Validation
This section explores the characteristics of nightlight- and landcover-based markets based solely

on the properties of the satellite data. We then validate that these markets do indeed capture
economic activity, by incorporating data from the Indian Census and open source platforms.

3.1

Market Characteristics

We document the following market characteristics. First, while nightlight-based markets capture
the largest cities in India, daytime imagery detect an order of magnitude more markets that, on
9average, are much smaller in size, are less compact, and have lower nightlight intensities. Second,landcover-based markets capture remote pockets of economic activity, as well as sub-centers withinlarger urban metropolises. Third, the distribution of landcover-based markets follow a power law
that more closely matches Zipf’s law than the distribution of nightlight-based markets.
3.1.1

Market Shape

Harari (2017) finds that the geometry of Indian cities affects economic outcomes. Her analysis
uses a novel geography-based identification strategy that predicts the compactness of cities, wherecompactness is measured by how close a city’s shape resembles a perfect circle. She determines theextent of cities using a procedure analogous to our nightlight-based markets, and finds that lesscompact Indian cities have higher commuting costs and lower economic welfare for residents. As
shown above, visual inspection suggests that nightlights will produce boundaries that are overly
smooth relative to the jagged boundaries of landcover-based markets. If shape determines thewelfare of residents, as her study finds, measuring it accurately is important. Her primary measureof urban shape is the disconnection index, based on Angel et al. (2010), which is the average distance
between all pairs of interior points within a market. In the absence of actual commuting data, theindex serves as a proxy for the average commute length within a market.
Figure 4 plots the disconnection index, measured in kilometers, for DN33, DN60 and MODIS
markets against market size.9 For nightlight markets, the disconnection index does not increase witharea size. This suggests that the shape of nightlight markets does not fundamentally change withthe overall expanse of a market. Increasing market size, by definition, will increase the bilateral
distances between some interior points. But the finding that the overall index does not change
implies that the market is including builtup pixels in close proximity with other builtup pixels.
Thus, the overall compactness appears to be invariant to total market land area. In contrast,
the shape of MODIS markets changes starkly with overall market size. As the market land area
increases, the disconnection index increases linearly, which reveals that larger MODIS markets aremuch less compact compared to both smaller MODIS markets and to all nightlight-based markets.
For example, the disconnection index of a 100km2 MODIS market, buffered at 1km, is 6.1km
compared to 3.4km and 0.8km for DN33 and DN60 markets, respectively. The figure also reveals
that disconnectedness increases more sharply for higher buffered markets. These patterns reinforce
the visual perception that landcover markets are more jagged and irregular, and therefore moredisconnected, than nightlight markets.
9
The computational burden of computing the disconnection index is very high since it is an average of all bilateralpixels within a market. We therefore only compute this index for the two nightlight-based markets and for MODIS
markets. For the same reason, we do not compute the index for 8km-buffered markets. Harari (2017) normalizes her
disconnection index by the average distance between points in a circle that has equivalent area of a given market.
We report the disconnection index without normalization, as it is more straightforward to interpret and insteadreport how the index changes with market size. Additionally, whereas nightlight-based markets consist largely ofcontinuous expanses of lit pixels, MODIS markets contain many undeveloped areas within their outer envelope. It
is thus instructive to compare average distances between points within a market without normalizing, since thenormalization factor for, say a 4km buffer, would be vastly different for MODIS and nightlight markets.

10

3.1.2

Number of markets

We next explore the number of markets detected through the alternative market definitions.
For context, Table A1 reports the official number of enumerations, at various levels of aggregation,according to the 2011 Census. The Census recognizes 6,171 “towns”, which are home to India’s 377
million urban residents (31% of India’s total population).10 Of the 6,171 towns, 468 are considered“Class 1” cities with more than 100,000 inhabitants; these are the largest cities in India, whichcollectively contain 22% of India’s population. There are 1,847 Class 1, 2 and 3 towns—localities
with at least 20,000 inhabitants.
The top panel of Table 1 reports the number of markets detected through nighttime lights. By
construction, the number of markets decreases as we raise either the distance buffer for joining pixel
clusters or the DN threshold for designating highly lit pixels. At a buffer of 1km, we observe 3,275
DN17.4 markets, 1,669 DN33 markets, and 469 DN60 markets. The two higher DN thresholds
exhibit little variation in the number of markets across buffers. Comparing Table 1 and Table A1,
we see that DN17.4 markets at a 1km buffer roughly match the number of officially recognizedIndian cities and towns with more than 10,000 residents. The DN60 markets accurately capture
Class 1 towns, which corroborates the finding in Harari (2017) that nighttime satellite imagery are
well-suited for tracking variation in urban form across India’s largest cities.
The bottom panel of Table 1 reports the number of markets detected from daytime imagery.
While the numbers vary across the three daytime satellite layers, the total number of markets
detected is substantially larger than the number of nightlight-based markets. For the MODIS
layer, the number of markets ranges from 12,953 at distance buffer of 1km to 3,073 at a distancebuffer of 8km. For the GHSL layer, the number of urban markets ranges from 26,202 at distancebuffer of 1km to 3,861 at a distance buffer of 8km. The corresponding numbers of markets for
the MIX layer are 17,304 and 3,417, respectively.11 At a distance buffer of 4km or less, the total
numbers of landcover-based markets are much larger than the number of towns in India with apopulation of 10,000 inhabitants or greater.
3.1.3

Land area

Column 2 of Table 1 reports the average land area for each market definition.

Considernightlight-based markets, first. For DN17.4, the average size ranges from 48.6km2 at a 1km buffer
to 97.8km2 for a distance buffer of 8km. These values fall, respectively, to 37.0km2 and 43.7km2
for DN60 markets. These statistics reinforce the tradeoff in choosing a light intensity threshold:lower thresholds detect more markets but the average market size increases. For landcover-based
10

These towns satisfy one of two criteria: (1) a place with a municipality, corporation, cantonment board, or
notified town area committee; or (2) a place that has a minimum of 5,000 inhabitants, at least 75 percent of the maleworking population engaged in non-agricultural pursuits, and a population density of at least 400 people per km2 .
11
The GHSL and MIX layers detect more distinct markets in part because the underlying resolution of these data
are finer than MODIS. We are unsure of the precise explanation for why the number of GHSL-based markets is sohigh. Unlike MODIS and MIX, GHSL combines raw daytime spectral bands with MODIS and data from open-sourced
platforms, which makes this layer quite different from the other two.

11

markets, the average market sizes are much smaller. At a 1km buffer, MODIS markets are 3.0km2 ,while the average size of GHSL and MIX markets are 1.4km2 and 1.9km2 , respectively. The smaller
sizes of landcover markets are a result both of the granularity of the daytime imagery and the exclusion of non-builtup land area (e.g., due to blooming), which we explore in more detail in Section
4. At a 4km buffer, the sizes of MODIS, GHSL and MIX landcover-based markets rise to 10.6km2 ,
10.9km2 , and 12.1km2 .
To further illustrate the tradeoffs in forming markets with nightlight data, it is useful to compare
maximum market sizes. The maximum area of MODIS markets at a 1km buffer is 1,582km2 . By
contrast, the maximum sizes of nightlight-based markets at a 1km buffer changes substantiallyacross the DN17.4, DN33, and DN60 thresholds: from 9,977km2 for DN17.4 to 4,681km2 for DN30
and to 2,223km2 for DN60. To see this further, consider Figures A3 and A4, which plot the
distribution of market area and average nightlight values within market boundaries, respectively.
Figure A3 reveals that landcover-based markets are able to capture the full range of market sizes.
The mode of each distribution effectively reveals the minimum number of pixels used to define amarket.12 Figure A4 illustrates that nightlight-based markets, by construction, are left censoredat their respective DN thresholds. Note that because of buffering these markets do capture pixels
below their respective thresholds, which is most apparent at the 8km buffer. By contrast, at all
buffers, landcover-based markets capture pixels that span the entire range of DNs. In particular,
these markets capture areas in India with average DNs well below 10.
These comparisons highlight the tradeoff in forming markets from nightlight data. As one lowers
the DN threshold to detect smaller markets, the area of larger markets expands dramatically. This
tradeoff is not present in the construction of landcover-based markets. Landcover-based markets,
because they are not subject to a blooming, span a relatively wide range of land areas and intensities
of economic activity (as captured by nightlight intensity per unit of land in these markets).
3.1.4

Power Law of Market Area

Economists have long been interested in the size distribution of cities. The standard approachin the literature is to gather population data using census counts for cities in a particular country
and to regress the log of city population on the log city population rank. Zipf’s Law holds if theslope of the regression is -1. Testing for Zipf’s Law requires confronting the thorny issues of whichdata sources to use, how to assess the quality of these sources and the accuracy of their implied
methods for designating administrative boundaries, and whether to truncate the distribution soas to focus on the properties of the upper tail (Gabaix and Ioannides 2004). The motivation for
the algorithmic approach developed by Rozenfeld et al. (2011) is to construct the extent of urban
markets without having to rely on seemingly arbitrary boundaries, and then to test for the presence
12
The right shift of the distribution of land area for nightlight-based markets is most pronounced at a buffer of
1km, because at this buffer only the high-resolution daytime imagery is able to isolate small urban markets. While
the right shift of market-size distributions for the lower-resolution imagery is preserved at higher distance buffers, therelative “peakiness” of the market-size distribution for landcover-based markets diminishes at higher buffers because
smaller market areas are joined into larger pixel clusters at these buffers.

12

of Zipf’s Law using cities whose boundaries are justified based on economic fundamentals (i.e., theproximity of their internal clusters of activity). In that paper, they show that the distribution ofcity land areas approximately obeys Zipf’s Law for the US and the UK, and explain that a Zipf’s
law in area can be rationalized by a model with Cobb-Douglas preferences for goods and housing
along with a proportional random growth process.
To connect our results with the literature, we examine the emergence of a power law in the
distribution of land areas for our market definitions. Our aim is a narrow one, to compare regularities regarding the size distribution of land area across our market definitions and those basedon conventional data sources, rather than to inquire into the origins of power laws more broadly.
Following Gabaix and Ibragimov (2011), Figure 6 plots the log of market rank minus 0.5, basedon land area, against the log of land area. The figure reveals three patterns. First, landcoverbased markets more closely follow the log-linear relationship dictated by a power law. The R2 ofthe regressions for landcover-based markets (which range from 0.90 to 0.98) are higher than fornightlight-based markets (which range from 0.84 to 0.91). For MODIS 1km markets, the R2 is 0.96.
That is, for landcover markets the entire distribution of market size appears to be Pareto, whereas
for nightlight markets the size distribution appears to be Pareto only in the upper tail. Second,
the figure also reveals that for nightlight-based markets the shape of the area-rank plot is roughly
stable across buffers. This suggests that increasing buffers simply increases the size of markets
proportionally, such that the rank-area relationship remains constant. In contrast, the linear slopesof the area-rank plots for landcover-based markets flatten out as the buffer size increases, indicating
greater dispersion. Finally, Figure 6 also reveals that for nightlight-based markets, the log-linear
relationship breaks down for the largest markets. For landcover-based markets, however, the curvethat fits the upper tail markets is close to linearity (as it is in the remainder of the distribution).
For the MODIS 1km markets, the slope of the line is -0.93.

3.2

Validation

The statistics presented above summarize the extensive margins of urban activity and are based
solely on satellite data. A limitation of satellite-inferred markets is that they convey uncertain information on the intensive margin of economic activity. This limitation may be less of a concern
with nightlight-based markets, since earlier work demonstrates a strong positive relationship between nightlight intensity and GDP, both in levels and in changes (e.g., Henderson et al. 2012).
Daytime satellite imagery, in contrast, provide unknown information on the intensity of economic
activity within markets. This is because in the landcover layers the pixels record only whether or
not a man-made impervious structure is present. One would need additional information, such as
the density and height of structures, to improve the prediction of economic activity based on theunderlying spectral signatures of those images.13
This subsection matches external datasets to the boundaries of markets to explore correlations
13

See Jean et al. (2016) for a recent application that predicts micro-spatial poverty headcount for five countries inAfrica using nighttime and daytime imagery and Demographic and Health Surveys.

13

between market area and different measures of economic activity. Since we are confident in measuring the land area of a market, the strength of these correlations provides an indication of whether
land area is also a reasonable proxy for the intensity of economic activity of cities. We examine correlations between market area, population, nightlight intensity per unit of land, and three granularmeasures of infrastructure provision—–roads, railway stations, and mobile phone towers.
3.2.1

Population

Our first approach to measure economic activity within our market boundaries is to overlay
the 2011 India Census to obtain population counts for each market.14 Census shape files are
disaggregated at the town and village level, which have an average area of 16.6km2 and 4.8km2 ,
respectively (see Table A1). Analogous to Davis et al. (2019), we overlay our markets with the
Census towns and villages shape files to spatially match each town to the market it lies inside or
overlaps. The population of each town is then assigned to the market it overlaps. If a market
overlaps more than one town, the population of all the towns it overlaps is assigned to that market.
If a town overlaps more than one market, we divide the population of the town by the number ofmarkets it overlaps, and assign this value to each market it overlaps. This ensures that we are notdouble counting the population of towns that overlap more than one market.
The third column of Table 1 reports the total population contained in the markets we detect.
According to our estimates, the DN60 markets, which as shown above find the Census’ Class 1
towns, collectively contain 14.8% of India’s population and 47.6% of the urban population. This islower than the official Class 1 total since DN60 markets identify the core urban area of cities (theDN60 markets are smaller, on average, than the average size of Class 1 towns). The DN33 markets
contain 23.4% and 75.3% of India’s total and urban populations, respectively.
Compared to these two DN thresholds, landcover markets capture a larger share of India’s
urban population. The 1km MODIS markets contain 29.0% and 93.2% of the total and urban
population. Total urban population share rises to 93.8%, 96.7%, and 111.1% for 2km, 4km and
8km markets. Thus, we find that landcover markets are able to capture the vast majority of India’s
urban population. The 8km MODIS markets also capture some of India’s population that do notreside in Census’ towns, which is why the share is above 100%.
The left axis of Figure 7 examines the correlation between population and area for 1km bufferedmarkets. For each market definition, there is a strong positive correlation between the area of themarket and its total population. This validates that the larger markets we detect are not simply
capturing pixels that appear builtup but contain no population. Instead, larger markets containmore people, as we would expect. A second message of the graph is that the population varianceacross smaller landcover-based markets can be large. This again reflects the fact that distinct
landcover based-markets can be found in both remote areas and large metropolises. (This variance14

An early version of this paper used WorldPop, a publicly available source of gridded population data. These datacontain measurement errors but are nevertheless useful because of their global coverage. These figures are available
in earlier versions of the paper and are available upon request.

14

decreases, but the positive correlation remains, at higher buffered 4km markets, as illustrated in
Figure A5). We also examine population density, defined as population divided by land area, as ameasure of economic activity on the right axis. The figure reveals a fairly constant density acrosssize for each market definition. However, the figure does show higher variation in population density
for smaller landcover markets for reasons just explained.
While the builtup pixels from daytime imagery undoubtedly contain man-made structures that
do not necessarily contain human settlements (e.g., roads, freeway overpasses, dams, and power
grids), the Census data serve as an important validation that the markets we identify do indeed
contain urban populations within their boundaries.
3.2.2

Nightlight Intensity

Previous work by Henderson et al. (2012) and Henderson et al. (2018) demonstrate that nightlight intensity is a good proxy for national or regional GDP. Inspired by this work, we compare
the average DN (nightlight intensity per unit of land) across markets. While the average DN fornightlight-based markets would be affected by blooming because of its impact on the extent ofmarket boundaries, blooming is less of an issue for landcover-based markets since those boundaries
are more accurately delineated.
Figure 8 reports the relationship between the average DN and the land area of a market (1kmbuffers). For each of the landcover-based markets, larger markets are associated with higher DNs.
Moreover, the change in DNs across market size is quite sharp. For example, a MODIS market atthe 10th percentile of the area distribution has a mean nightlight intensity of 9.4 compared to avalue of 27.2 at the 90th percentile. Henderson et al. (2012) report an elasticity of 0.3 for GDP
with respect to DN, which implies that there is a GDP difference of 56.8% between markets thatspan the interdecile range of land area.
The figure also reveals that landcover-based markets exhibit more variance in DN intensity at
smaller market sizes. For instance, for the smallest MODIS markets, we observe the full range ofmean DNs (as seen by examining the range of points spanned along the y-axis for given points justto the right of the origin along the x-axis). This regularity is again a result of the fact that we
detect small-in-area landcover-based markets both in remote regions of the country, where economic
intensity is low (as indicated by low DNs), and within large urban centers, where DNs are high.
This suggests that when using DN intensity as a proxy for the economic activity of landcover-based
markets, researchers may want to account for the characteristics of the surrounding markets.
The correlations in Figure 8 thus suggest that the pooling of daytime and nightlight imagery
may be a powerful means of characterizing the combined extensive and intensive margins of urban
markets. While researchers interested in the economic geography of specific cities may want to bringinformation from external datasets, these correlations are promising for researchers interested instudying urban market activity at national or global scales.

153.2.3

Proximity to Infrastructure

A third way to examine whether our markets capture economic activity is to merge them with
open-source data containing the locations of key infrastructure markers. We examine proximity ofmarkets to paved roads, railway stations, and mobile phone towers. A caveat with this exercise isthat these data reflect the current location of infrastructure. The road and railway station data
are from OpenStreetMaps.15 Because the road data are for a time period roughly five years after
our satellite imagery was collected, there is measurement error in matching markets to roads. Railstations are less susceptible to this problem since they are built at much lower frequencies. The
tower locations share the same caveat as the roads data, but have the advantage of being compiled
by a different data source (https://opencellid.org).
We construct the distance between market centroids to the nearest infrastructure type for eachmarket definition in Table 2. For nightlight-based 1km markets, the fractions of DN17.4, DN33
and DN60 markets that lie within two kilometers of a paved road are 96.7%, 97.0% and 97.4%,
respectively. This fact should not be surprising since these markets are relatively large, although
one caveat is that the nightlight data may capture street lights along the roads.
The more informative statistics are the fractions of landcover-based 1km markets that lie within
two kilometers of a paved road. For MODIS market, this fraction is 88.3% (the corresponding
numbers for GHSL and MIX markets are 89.4% and 90.8%). Since we believe that most urban
markets would be connected to a road of some kind, this regularity provides validation that thedaytime satellite imagery are capturing markets that contain economic activity. The table also
reports proximity to the nearest railway station (second panel) and mobile towers (third panel).
We find that 26.2% of MODIS 1km markets are within 5km of a railway station, which rises
to 81.7% for markets within 25km of a rail station. Proximity to mobile phone towers is also very
high across markets: 86.9% of MODIS 1km markets are within five kilometers of a mobile tower.
We also expect a positive relationship between market size and its proximity to paved roads(Storeygard 2016). The left axis of Figure 9 plots this relationship, which illustrates the potential
power of daytime imagery over nighttime imagery. Landcover-based markets exhibit a sharp negative elasticity of market area with respect to distance to the nearest road. For instance, comparedto markets that are bisected by a road, a MODIS market that is 2km away from a road is about
50% smaller in land area. Such a large difference in size is not detectable using nightlight-based
markets: for markets based on DN thresholds, the elasticity of size with respect to distance to aroad is an imprecisely estimated zero.
Figure 9 repeats the plots with average nightlight intensity on the second y-axis. These illustrate that for landcover-based markets, light intensity, which as discussed above is a proxy for theintensity of economic activity, falls sharply with distance to a paved road. For MODIS markets,the average light value falls from about 20 to 8 when one compares a market that lies on top of a15

We use the OpenStreetMaps road classifications. The major roads (511x) include motorways, freeways, andtrunk, primary, secondary and tertiary roads. We additionally include two minor road classifications: smaller local
roads (5121) and roads in residential areas (5112). For the railway stations, we include large rail stations (5601) andsmaller, local rail stations or subway stations (5602).

16

road to a market that is 2km from a road. As with land area, a decline in light intensity is notdetectable for nightlight-based markets between 0km-2km from a road.
As noted earlier, nightlight data have a relatively coarse spatial resolution compared to daytime images (1km vs 30m). The lights data are also subject to blooming which introduces measurement error in market size. Which of these two differences—spatial resolution or exposure toblooming—explains why the road-distance elasticities are less sharply negative for nightlight-based
markets when compared to landcover-based markets? We examine this question in the MODIS
data by changing the minimum cluster threshold from 1 pixel to 4 pixels, or roughly 1km gridcells, in order to match the minimum market area of nightlight-based markets. We then rebuild
the landcover-based markets using a 1km buffer. The procedure creates 5,527 markets (comparedto 12,953 using a minimum of one MODIS pixels at 1km buffer). We then compare the elasticity ofmarket area and average DN value to distance from the closest road in Appendix Figure A6. The
MODIS markets that impose a 1km minimum area still display a strong negative elasticity withrespect to road distance for both outcomes. With landcover-based markets and nightlight-based
markets now approximately equal in spatial resolution, the more negative road-distance elasticity
for the former relative to the latter would appear to be the result of blooming in nightlights andthe measurement error it introduces when trying to detect market size.

4Markets within Super-Markets
The literature has long recognized that actual structure of cities does not easily map into

static spatial models with a featureless geography. Instead, urban sprawl occurs unevenly at cityboundaries (Duranton and Puga 2014). As cities expand, there often remains undeveloped land
within city limits. This may be due to physical constraints imposed by geography (Harari 2017),
leapfrogging that occurs from dynamic city growth (Fujita 1982), municipalities wanting to control
how land is utilized, or, particularly relevant to India, disputes over land titles and coordination
failures across government agencies (Roy 2009). These features have led to a large literature on thepolycentric structure of cities (Duranton and Puga 2015). We next explore this polycentricity.

4.1

Properties of Super-Markets

Our market definitions have a recursive property that nests smaller buffered markets withinlarger buffered “super-markets”. This feature allows us to study the distribution of markets withinsuper-markets. Our results suggest a potential use of high-resolution daytime satellite imagery toevaluate policies that impact the intra-regional distribution of markets within these larger urban
forms. The granularity allows us to observe impacts both within markets (e.g., markets or neighborhoods within a larger super-market), and at high temporal frequencies (important for policymakers
loathe to wait years to evaluate the returns to public infrastructure investments).
To see that landcover-based markets have the potential to uncover local-level responses toshocks that would otherwise appear hidden by the coarseness and granularity of nightlight-based17

markets, consider Figure 10, which maps MODIS landcover-based markets at different buffers
for New Delhi. The outer ring is the official administrative boundary of New Delhi. The lightgray polygon represents the 60 8km buffered markets that lie within the administrative boundary.
These 8km super-markets further contain smaller 4km, 2km and 1km markets. Within the official
boundary, we detect 205, 435 and 579 markets buffered at 4km, 2km, and 1km.
Turning to the country as a whole, Table 3 reports the average number of i = {1, 2, 4}km
markets that are contained within their larger super-market buffer j = {2, 4, 8}km for all markets
in India. While the megacity of New Delhi unsurprisingly stands out for its large number ofmarkets, the presence of these markets is a general phenomenon detectable via landcover-based
market definitions. For example, an average of 1.9 buffered MODIS 1km markets lie within supermarkets defined at a 4km buffer, and an average of 4.2 markets lie within 8km super-markets. The
second column within each panel of Table 3 reports the elasticity of the number of markets to thesize of the super-market. The elasticity of the number of 1km MODIS markets with respect tothe size of 2km markets is 0.15 and increases to 0.31 and 0.36 for 4km and 8km super-markets,
respectively. These patterns suggests that there is substantial scope for using landcover-based
markets to evaluate theories of how polycentric cities are organized and grow. Markets definedaccording to administrative boundaries would likely be poorly suited for this purpose as official
boundary definitions may substantially lag urban structure.
The size of markets within super-markets is highly unequal. Table 4 reports the distributionof 1km market size shares within the super-markets for MODIS. For each 1km market, we rankthem within their respective super-market and compute their share of builtup area. The top panel
reports the distribution of shares within 2km super-markets; the middle and bottom panels reports
statistics for 4km and 8km super-markets, respectively. The table reveals that for 4km supermarkets that contain two 1km markets, the larger market accounts for about 72% of the builtuparea. For super-markets that contain 5 markets, the largest market accounts for 51% of the builtuparea of 4km super-markets, and 58% of the builtup area of 8km super-markets.
While super-markets contain many distinct markets, they also contain vast tracts of unbuilt
land. To demonstrate this regularity, we compute the area of builtup pixels that lie within theboundary. Figure 5 plots a non-parametric relationship for the developed land fraction against thesize of markets, by buffer. For the 1km and 2km buffers, a large fraction of market area is builtup
for both nightlight and MODIS markets. This is intuitive since the clustering algorithm builds
very small land bridges for these buffers. For larger buffers, the fraction of land area increases witharea for nightlight markets. However, for MODIS markets, the builtup area percentage falls witharea size; it levels off at around 50% for 4km markets, and falls continuously in 8km markets. The
fraction of builtup land area in the average 8km buffered DN33 and DN60 market is 78% and 87%,
respectively, compared to just 23% in the average 8km MODIS market.
These patterns reinforce several messages from earlier figures. The blooming of lights implies
that larger buffered nightlight-based markets will suggest that human activity is too expansive
within its boundaries. This is particularly an issue for the largest cities. Landcover-based markets

18instead reveal far more undeveloped land within boundaries. For large cities, daytime imagery
reveal a sizable fraction of undeveloped land within market boundaries. This suggests there may
be substantial within-market variation in builtup land across regions and over time.

4.2

Application to Market Access

How might we deploy data on landcover-based markets and super-markets? One application
is to detect the consequences of infrastructure development. Governments across the developingworld are making large-scale investments in improving internal transport connectivity. A growing literature studies the economic impacts of transportation (e.g, see Redding and Turner 2015).
Ghani et al. (2014), for instance, use across-district variation in the distance to the India’s Golden
Quadrilateral highways and find positive impacts on allocative efficiency within Indian manufacturing. Asher and Novosad (forthcoming) study India’s $40 billion in expenditures on rural roads anddo not find substantial effects on rural household welfare. Both analyses draw upon administrative
datasets to evaluate impacts of new roads. Satellite imagery offers the potential to complement
these studies by using remotely sensed data and by analyzing impacts on markets that lie within,for instance, larger buffered peri-urban areas.
In the spirit of such analysis, we examine the average distances to (the centroids of) othermarkets within given super-markets, which are reported in third column of each panel in Table 3.
Consider MODIS markets. Within a 8km buffer, the average distance between 1km sub-markets is52.1 kilometers, indicating that the typical 8km buffered super-market is an economic region unto
itself, which would utilize highways and railways in a manner that we may typically associate withinter-urban transport. The average distance between 1km sub-markets within a 4km buffer is 6.2
kilometers, which indicates that at a 4km buffer we are dealing with collections of interconnectedneighborhoods. The contrast in market distances between 4km and 8km buffered super-markets
illustrates the different market concepts that these designations represent. One might reasonably
conclude that 4km buffered markets approximately constitute commuting zones, while 8km bufferedmarkets approximately constitute economic regions that support dense internal trade in goods andservices. Differing urban market definitions may then be useful for evaluating the consequencesof reduced travel time on different aspects of economic integration, for goods markets at higher
distance buffers and for local labor markets at lower distance buffers.
To investigate such potential, we follow Donaldson and Hornbeck (2016) by calculating measuresof market access for the MODIS markets. For each market i, we calculate its market access as
M Ai =areaj+θ
distanceij
j∈S ,j6=i
X

X

ik

j ∈S
/ ik ,j6=i

areaj
distanceθij(1)where areaj is the land area of market j, distanceij is the great circle distance from market i tomarket j, and θ is a distance elasticity that we set to 1.4 (Redding and Turner, 2015). We exclude
the own market in the summation, as Donaldson and Hornbeck (2016) do in their analysis. We areparticularly interested in the contribution to market i’s term by the j markets that lie within i’s
19super-market Sik , buffered at k = {2, 4, 8}km. Figure 11 reports the contribution of the withinsuper-market component, across buffers and daytime imagery sources. We also report the resultsthat obtain for other distance elasticities by setting θ = 1 and θ = 1.8.
In the baseline case of θ = 1.4, the results indicate that, on average, 2.3%, 6.8% and 25.4% of
a 1km MODIS market’s access comes from other markets within the same super-market buffer of
2km, 4km, and 8km, respectively. At the higher elasticity of θ = 1.8, the corresponding percentages
increase to 5.2%, 14.4% and 40.1%. Whereas previous literature largely conceives of infrastructuredevelopment as integrating our equivalent of super-markets, examining landcover-based markets
reveals that a substantial share of a location’s market access is intra-urban in nature. With data on
combined infrastructure investments in inter-state highways, such as India’s Golden Quadrilateral,and in intra-urban investments in access roads, road widening, and related improvements, daytime
satellite imagery have the potential to provide a much higher resolution characterization of how
these changes in trade costs shape the spatial distribution of economic activity.

5

Conclusion
Economists have been utilizing satellite imagery for over a decade. Notable applications haveelucidated the dimensions of urban sprawl and the connection between GDP growth and the intensity of light emitted at night. In the last several years, the landscape, so to speak, has begun tochange rapidly. Dramatic reductions in storage costs have made vast troves of high-resolution daytime satellite imagery widely available, while advances in machine learning are making it possible
to deploy imagery to detect economic outcomes at previously unimaginable spatial resolutions.
Our results indicate the value of combining different types of satellite imagery in economic analysis. Daytime imagery is well suited for defining the spatial expanse of markets, the polycentricity
of urban areas, and the gaps in urban development that exist even within densely populated cities.
Nighttime imagery, in turn, is well suited for measuring the intensive margin of economic activity
within urban ares.
The creation of new methods for integrating alternative sources of satellite imagery is a promising avenue for research.With existing analytical tools, these data will make it possible to evaluate
the potentially highly spatially heterogeneous economic impacts of investments in infrastructure andother policy interventions. With the continents of Asia and Africa in the midst of a multi-trillion
dollar infrastructure investments, the arrival of such capabilities is well timed.
Although satellite imagery greatly expands the supply of data amenable to economic analysis,
their interpretation is, at this stage, still constrained by the supply of conventionally measured
economic quantities, which serve as ground truth in machine learning. Demand will be particularlyhigh for methods to validate satellite-based measures of economic activity using additional sourcesof micro data. We view this as an important area for future work.

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25

Figures and Tables
Figure 1: Delhi, Alternative Market Definitions

a. MODIS (1km)b. MODIS (2km)c. MODIS (4km)d. MODIS (8km)e. DN>60 (1km)f. DN>60 (2km)g. DN>60 (4km)h. DN>60 (8km)

i. DN>33 (1km)

j. DN>33 (2km)

k. DN>33 (4km)l. DN>33 (8km)

m. DN>17.4 (1km)n. DN>17.4 (2km)o. DN>17.4 (4km)p. DN>17.4 (8km)q. DN>10 (1km)r. DN>10 (2km)s. DN>10 (4km)t. DN>10 (8Km)

Notes: The figure displays markets around New Delhi for alternative distance buffers. Row 1 displays landcover-based markets using the MODIS layer. Row 2-5 displays nightlight-based markets.

Figure 2: Ahmedabad, Alternative Market Definitions

a. MODIS (1km)b. MODIS (2km)c. MODIS (4km)d. MODIS (8km)e. DN>60 (1km)f. DN>60 (2km)g. DN>60 (4km)h. DN>60 (8km)

i. DN>33 (1km)

j. DN>33 (2km)

k. DN>33 (4km)l. DN>33 (8km)

m. DN>17.4 (1km)n. DN>17.4 (2km)o. DN>17.4 (4km)p. DN>17.4 (8km)q. DN>10 (1km)r. DN>10 (2km)s. DN>10 (4km)t. DN>10 (8km)

Notes: The figure displays markets around Ahmedabad for alternative distance buffers. Row
1 displays landcover-based markets using the MODIS layer. Row 2-5 displays nightlight-based
markets.

Figure 3: Ajmer, Alternative Market Definitions

a. MODIS (1km)b. MODIS (2km)c. MODIS (4km)d. MODIS (8km)e. DN>60 (1km)f. DN>60 (2km)g. DN>60 (4km)h. DN>60 (8km)

i. DN>33 (1km)

j. DN>33 (2km)

k. DN>33 (4km)l. DN>33 (8km)

m. DN>17.4 (1km)n. DN>17.4 (2km)o. DN>17.4 (4km)p. DN>17.4 (8km)q. DN>10 (1km)r. DN>10 (2km)s. DN>10 (4km)t. DN>10 (8km)

Notes: The figure displays markets around Ajmer for alternative distance buffers. Row 1 displays
landcover-based markets using the MODIS layer. Row 2-5 displays nightlight-based markets.

Figure 4: Disconnection Index

Notes: Figure reports a non-parametric plot between a market’s disconnection index, measured inkilometers, and its area.

Figure 5: Builtup Land

Notes: Figure reports the fraction of builtup land area by buffer. The nonparametric curve for
MODIS markets displays 5%/95% confidence interval.

Figure 6: Land Area-Rank Relationship

Notes: The {b, N, R-squared} are reported for the regression: log(rank-0.5) = constant +b*log(area) + error.

Figure 7: Population versus Land Area

Notes: Figures report the relationship between market size, population and population density.
Markets are buffered at 1km. Population from 2011 Census.

Figure 8: Average DN Intensity versus Land Area

Notes: Figures report the relationship between market size and average light intensity. Markets
are buffered at 1km.

Figure 9: Land Area, Average DN and Proximity to Roads

Notes: Distance to road is the shortest distance from market centroid to a primary, secondary or
tertiary road. Road data obtained from OpenStreetMaps. Markets are buffered at 1km. Figure
shows 5% and 95% confidence intervals.

Figure 10: MODIS Landcover-Based Markets within New Delhi Metro Area

MODIS 1km
MODIS 2km
MODIS 4km
MODIS 8km
Delhi Metro

Notes: Map shows MODIS markets in the New Delhi metropolitan area. The black outline is theofficial administrative boundary of New Delhi from the 2011 Census. Within the administrative
boundary, there are 579 1km, 435 2km, 205 4km and 60 8km markets.

Figure 11: Share of Market Access within Super-Markets

Notes: Figure reports the average share of market access accounted by markets within supermarkets for different values of θ.

Table 1: Market Statistics

MarketNumberAvg Area(km2)

Population
Share

Urban
Population
Share

Panel A: Nightlight-based Markets
DN17.4
1km
2km
4km
8km
DN33
1km
2km
4km
8km
DN60
1km
2km
4km
8km

3,275
3,275
3,146
2,752

48.6
50.7
59.6
97.8

32.6%
32.6%
32.7%
33.5%

104.6%
104.6%
105.0%
107.6%

1,669
1,640
1,544
1,322

39.0
39.8
42.9
55.4

23.4%
23.4%
23.5%
23.8%

75.3%
75.3%
75.5%
76.5%

469
465
455
421

37.0
37.3
38.3
43.7

14.8%
14.8%
14.8%
14.9%

47.6%
47.6%
47.6%
47.7%

Panel B: Landcover-based Markets
MODIS
1km
2km
4km
8km
GHSL
1km
2km
4km
8km
MIX
1km
2km
4km
8km

12,953
10,836
6,921
3,073

3.0
4.2
10.6
63.4

29.0%
29.2%
30.1%
34.6%

93.2%
93.8%
96.7%
111.1%

26,202
18,753
10,371
3,861

1.4
2.9
10.9
77.5

33.3%
33.5%
34.8%
39.4%

106.9%
107.6%
111.8%
126.5%

17,304
11,816
7,225
3,417

1.9
4.3
12.1
54.5

27.1%
27.3%
28.4%
31.4%

87.1%
87.7%
91.1%
100.7%

Notes: Table reports the number and average area (in square kilometers) of markets and shareof total India population, by definition. Total 2011 India population is 1,210,854,977. Urban
population (population that resides in Census ”Towns”) is 377,106,125.

Table 2: Market Distances to Nearest Infrastructure
Road
Market
DN17.4
DN33
DN60
MODIS
GHSL
MIX

1km
91.9%
93.2%
94.7%
75.1%
81.3%
81.0%

2km
96.7%
97.0%
97.4%
88.3%
89.4%
90.8%

5km
98.2%
98.6%
98.7%
97.3%
97.1%
97.8%

10km
98.6%
99.0%
98.9%
99.1%
99.0%
99.1%

25km
98.7%
99.0%
98.9%
99.3%
99.2%
99.3%

50km
98.7%
99.0%
98.9%
99.3%
99.2%
99.3%

DN17.4
DN33
DN60
MODIS
GHSL
MIX

1km
12.2%
19.2%
22.0%
4.6%
5.1%
6.1%

2km
28.5%
42.7%
52.9%
12.8%
9.1%
11.3%

Rail Station
5km
10km
43.1%
55.0%
60.8%
70.1%
78.7%
88.1%
26.2%
46.2%
22.5%
45.2%
26.7%
50.0%

25km
83.4%
89.2%
97.0%
81.7%
82.1%
83.6%

50km
97.3%
98.6%
99.1%
96.8%
96.9%
97.3%

DN17.4
DN33
DN60
MODIS
GHSL
MIX

1km
59.7%
96.6%
98.9%
56.1%
55.3%
59.6%

2km
61.6%
97.7%
99.4%
68.2%
67.8%
72.2%

Mobile Phone Towers
5km
10km
64.4%
67.6%
99.0%
99.7%
99.8%
100.0%
86.9%
96.8%
86.8%
97.0%
89.6%
97.8%

25km
69.9%
100.0%
100.0%
99.9%
99.9%
99.9%

50km
70.0%
100.0%
100.0%
100.0%
100.0%
100.0%

Notes: Table reports the fraction of markets in which the centroid lies within a particular distanceof the noted infrastucture type.

Table 3: Markets within Super-Markets

Market
MODIS
1km
2km
4km
GHSL
1km
2km
4km
MIX
1km
2km
4km

2km Super-Market
Number Elasticity Distance

4km Super-Market
Number Elasticity Distance

8km Super-Market
Number Elasticity Distance

1.2

0.15%

1.9

1.9
1.6

0.31%
0.23%

6.2
5.0

4.2
3.5
2.3

0.36%
0.32%
0.24%

52.1
50.4
38.1

1.4

0.19%

5.1

2.5
1.8

0.28%
0.20%

20.8
13.5

6.8
4.9
2.7

0.32%
0.28%
0.22%

75.4
66.3
45.0

1.5

0.17%

3.9

2.4
1.6

0.25%
0.17%

11.1
7.2

5.1
3.5
2.1

0.30%
0.25%
0.18%

31.6
27.9
20.0

Notes: Table reports statistics for the 2km, 4km and 8km super-markets. Columns 1, 4 and 7 are
the average number of sub-markets within the super-market. Column 2, 5 and 8 is the average
distance between sub-markets. Column 3, 6 and 9 is the elasticity of the number of sub-markets tothe size of the super-market (e.g., a one percent increase in the size of the super-market increases thenumber of markets by the number reported in the cell). Blank cells indicate that the statistic is not
relevant (e.g., a blank cell for the number of 2km markets within the 2km or 4km super-market).

Table 4: Distribution of Market Size within Super-Markets

Rank
1
2
3
4
5
6+

Rank
1
2
3
4
5
6+

Rank
1
2
3
4
5
6+

1
100%

1
100%

1
100%

2
73%
27%

2km Super-Market
Number of Markets
3
4
66%
64%
22%
19%
12%
11%
6%

2
72%
28%

4km Super-Market
Number of Markets
3
4
62%
56%
24%
22%
14%
13%
9%

2
74%
26%

8km Super-Market
Number of Markets
3
4
64%
58%
23%
20%
13%
13%
9%

5
61%
16%
11%
7%
4%

6+
58%
12%
7%
5%
4%
14%

5
51%
20%
14%
10%
6%

6+
44%
11%
6%
5%
4%
30%

5
58%
18%
11%
8%
5%

6+
38%
11%
6%
5%
4%
37%

Notes: Table reports the distribution of area share of MODIS 1km markets within 2km, 4km and
8km super-markets. For example, in the first panel, for 2km super-markets that contain three
MODIS 1km markets, the largest market accounts for 67% of the markets’ area, the second largest
market for 22%, and the smallest market accounts for 12% of area. Numbers may not sum to one
because of rounding.

Online Appendix Tables and Figures
Table A1: Administrative Areas in India, 2011 Census

Villages
Towns
Class 1 (>100k)
Class 2 (50k-100k)
Class 3 (20k-50k)
Class 4 (10k-20k)
Class 5 (5k-10k)
Class 6 (<5k)

Number640,932
6,171

Total
Population
833,748,852
377,106,125

Population
Share
68.9%
31.1%

Mean
Population
1,301
61,109Mean Area
(km2)
4.8
16.6

468
474
1,373
1,683
1,749
424

264,745,519
32,179,677
41,833,295
24,012,860
12,656,749
1,678,025

21.9%
2.7%
3.5%
2.0%
1.0%
0.1%

565,696
67,89030,46914,268
7,237
3,958

97.6
20.4
14.4
9.3
5.5
4.1

Notes: Table reports official tabulations from 2011 Census of India.

41

Figure A1: Density of Nighttime Lights for 1km Pixels, All India

Notes: Vertical lines denote the 90th, 95th, 99th, 99.5th percentiles of DNs. Histogram formed
using a 3% random sample of pixels.

42

Figure A2: Combining Polygons to Form Markets

Bhatu

Bhatu

Karanpura

Karanpura

SidhmukhaSidhmukh

b
Bhatu

Bhatu

Karanpura

Karanpura

Sidhmukhc0

8

16 24 32

Sidhmukh

d

Km

0

5

Km

Notes: Panel (a) illustrates DN10 threshold markets. Panels (b-d) shows 2km, 4km and 8km
buffers, respectively. The last panel shows the aggregated 8km buffered markets.

Figure A3: Distribution of Land Area

Notes: Figure reports the distribution of market land area, by market definition.

Figure A4: Distribution of Minimum Nightlight DN Values

Notes: Figure reports the distribution of minimum DN values, by market definition.

Figure A5: Population versus Land Area, 4km Buffer

Notes: Figures reports relationship between market size, population and population density. Markets are buffered at 4km. Population from 2011 Census.

Figure A6: Proximity to Roads, Coarser MODIS Markets (1km2 minimum area)

Notes: Distance to road is the shortest distance from market centroid to a primary, secondary or
tertiary road. Road data obtained from OpenStreetMaps. Figure uses MODIS markets formed
using a minimum threshold of 1km and buffered at 1km. Figure shows 5% and 95% confidence
intervals.

Figure A7: MODIS Landcover-Based Markets within Ahmedabad Metro Area

MODIS 1km
MODIS 2km
MODIS 4km
MODIS 8km

Ahmedabad Metro

Notes: Map shows MODIS markets in the Ahmedabad metropolitan area. The black outline isthe official administrative boundary of Ahmedabad from 2011 Census. Within the administrative
boundary, there are 15 1km, 11 2km, 7 4km and 2 8km markets.

Figure A8: MODIS Landcover-Based Markets within Ajmer Metro Area

MODIS 1km
MODIS 2km
MODIS 4km
MODIS 8km

Ajmer Metro

Notes: Map shows MODIS markets in the Ajmer metropolitan area. The black outline is the official
administrative boundary of Ajmer from 2011 Census. Within the administrative boundary, there
are 1 1km, 1 2km, 1 4km and 1 8km markets.

A

Aggregating Pixels to Markets
To combine clusters of highly lit pixels, we use the Aggregate Polygons function in ArcGis. Thisfunction combines polygons within a specified buffer to form larger polygons. Appendix Figure A2
illustrates the tool with lit pixels, focusing the border between Rajasthan and Haryana, two states inIndia. The gray areas illustrate polygons that are contiguous sets of pixels with a DN that exceeds
10. Notice that there are many unconnected polygons. Merging two polygons forms a larger
polygon that contains the land area of the original two polygons plus a land bridge that connects
them, whose dimension is determined by the algorithm. The larger is the distance buffer, the larger
will be the land bridges that connect polygons. Figure A2a illustrates the results of implementing
a 1km buffer; Figures A2b through A2d implement 2km, 4km, and 8km buffers, respectively. For
a sub-area within the sample geographic region, Figure A2e illustrates the resulting markets when
we impose the 8km buffer. Notice that moving from the smallest to the largest buffer collapses thenumber of markets in this area from more than 20 to just 3.

B

Construction of the MIX Layer
This online appendix provides an overview of the builtup classification methodology developedby Goldblatt et al. (2018) for India, Mexico, and the U.S. The methodology uses DMSP-OLS
nightlight data as quasi-ground truth to train a classifier for builtup land cover using Landsat
8 imagery. The basic idea is that since lights indicate the presence of human activity, we cantrain a classifier that uses the spectral signature of daytime images to predict the presence ofhumans, as indicated by lights. The challenge of using nightlights as a source of ground truth isthe blooming of lights. Goldblatt et al. (2018) correct for this blooming as follows. Using theirapproach and imagery for 2013, we calculate the per-band median values from a standard topof-atmosphere calibration of raw Landsat 8 scenes. These per-pixel band values are then used toconstruct commonly used indices to detect vegetation (the normalized difference vegetation index,
NDVI), water (the normalized difference water index, NDWI), physical structures (the normalized
difference built index, NDBI), and other relevant features. We use these indexes to mask out pixels
that appear with high DN from the DMSP-OLS data; the assumption is that these pixels, because
they are composed mostly or entirely of water or vegetation, do not contain builtup activity andappear unlit only because of blooming. We then proceed with the classification.
The steps of the methodology are as follows:
1. Designate a pixel as builtup if its DN exceeds a threshold. This threshold is set at the 95th
percentile of pixels in the training set, which is 17.4 across all India but ranges is allowed tovary across hex-cells (discussed below).
2. Re-classify a builtup pixel as not builtup if the Landsat index bands (NDVI, NDWI, NDBI)
indicate presence of water, dense vegetation or not builtup activity (as noted above, thiscorrects for the blooming).

50

3. Use supervised machine learning to train a classifier (a random forest with 20 trees) with theadjusted builtup/not builtup binary pixels from steps 1 and 2, and the Landsat 8 median-bandvalues and index values as inputs.
4. Use the classifier to construct the posterior probability that a pixel is builtup, and then create
binary values of builtup/not builtup status based on this probability (discussed below).
5. Evaluate the accuracy of the classifier by comparing the predicted builtup status of a pixel toa ground-truth dataset that has 85,000 human-labeled pixels that were classified as builtup
or not builtup.
In (3), we allow for variation in how the reflectance of India’s heterogeneous land cover is associatedwith urbanization by partitioning the country into an equal-area hexagonal grid with hex-cells thathave center-to-center distances of 1-decimal degree, and then treat each hex-cell as an independent unit of analysis. (We also train classifiers for hex-cells that have distances of 4- or 8-decimaldegrees, but find that the 1-decimal degree hex-cell is most accurate.) After training the classifier separately within each hex-cell, we mosaic the resulting local classifications to map predictedbuiltup land cover for the entire country. In (4), we designate a pixel as builtup if its posterior
probability exceeds a given threshold that is determined by the Otsu algorithm (Otsu 1979), which
is a nonparametric and unsupervised method for automatic threshold selection originally developed
for picture segmentation. The method uses a discriminant criterion to identify an optimal threshold that maximizes the between-class variance. We choose the threshold to maximize the variance
between builtup and not-builtup classes. In (5), which compares our predicted values of builtup
status with human-labeled examples, we achieve an overall accuracy rate is 84%. The accuracy
rate is defined as the sum of true positives and true negatives divided by the total sample. Notethat this accuracy rate exceeds the MODIS classification accuracy by 2.5% in India; see Table 6 ofGoldblatt et al. (2018).

51