metadata: authors: 0: author: Lall,Somik V.
1: author: Lebrand,Mathilde Sylvie Maria
2: author: Soppelsa,Maria Edisa
count: World
docna: 0: docna: The Evolution of City Form : Evidence from
            Satellite Data
docty: Policy Research Working Paper
subtopic: Urban Governance and Management,Municipal Management and Reform,Urban Housing,Urban Housing and Land Settlements,Transport Services,Disaster Management,Hazard Risk Management,Social Risk Management
teratopic: Social Development,Communities and Human Settlements,Conflict and Development,Public Sector Development,Urban Development,Transport
abstracts: cdata!: This paper describes new global
            evidence—derived from satellite data—for rates and patterns
            of urban spatial development since 1990 along three margins:
            horizontal spread (outward extension), infill development
            (inward additions in the gaps left between earlier
            structures), and vertical layering (upward construction).
            The end product of this growth is floor space, the amount
            and distribution of which are central to understanding how a
            city becomes livable and sustainable. Over the quarter
            century between 1990 and 2015, urban built-up area worldwide
            grew by 30 percent through horizontal spread and infill.
            While most cities grow through a combination of horizontal
            spread and infill, the paper provides the first estimates of
            the relative prominence of each type of expansion at
            different stages of economic development. In low-income and
            lower-middle-income countries, 90 percent of urban built-up
            area expansion occurs as horizontal spread. The study also
            finds that increasing incomes are a uniquely necessary
            condition for a rise in floor space per person through
            vertical layering: the reason is that building tall is
            capital intensive. The analysis highlights that if a city’s
            population doubles but incomes stay constant, the city’s
            floor space per person declines by 40 percent; by contrast,
            if per capita income doubles but population stays constant,
            the city’s total floor space per person increases by 29 percent.
repnme: repnme: The Evolution of City Form : Evidence from
            Satellite Data
display_title: The Evolution of City Form :
            Evidence from Satellite Data
listing_relative_url: /research/2021/04/32986585/evolution-city-form-evidence-satellite-data
topicv3: Transport m1326661 135,Disaster Risk Management m1326682 820,Land and Housing m1327648 817,Population, Aging and Health m1327736 640,Coronavirus (COVID-19) m1939478 4828
publishtoextweb_dt: 2021-04-09T00:00:00Z
dois: 10.1596/1813-9450-9618
historic_topic: Social Development,Communities and Human Settlements,Conflict and Development,Public Sector Development,Urban Development,Transport
origu: URL Global Director (SURDR)
no_of_pages: 32
author_keys: 0: author_key: 124534
1: author_key: 1457978
2: author_key: 996678
model_extractions: Policy Research Working Paper 9618 The Evolution of City Form Evidence from Satellite Data _Somik V. Lall Mathilde Lebrand Maria Edisa Soppelsa_ Urban, Disaster Risk Management, Resilience and Land Global Practice April 2021
Policy Research Working Paper 9618

# **Abstract**

This paper describes new global evidence—derived from satellite data—for rates and patterns of urban spatial development since 1990 along three margins: horizontal spread (outward extension), infill development (inward additions in the gaps left between earlier structures), and vertical layering (upward construction). The end product of this growth is floor space, the amount and distribution of which are central to understanding how a city becomes livable and sustainable. Over the quarter century between 1990 and 2015, urban built-up area worldwide grew by 30 percent through horizontal spread and infill. While most cities grow through a combination of horizontal spread and infill, the paper provides the first estimates of the relative prominence of each type of expansion at different stages of economic development. In low-income and lower-middle-income countries, 90 percent of urban built-up area expansion occurs as horizontal spread. The study also finds that increasing incomes are a uniquely necessary condition for a rise in floor space per person through vertical layering: the reason is that building tall is capital intensive. The analysis highlights that if a city’s population doubles but incomes stay constant, the city’s floor space per person declines by 40 percent; by contrast, if per capita income doubles but population stays constant, the city’s total floor space per person increases by 29 percent.

This paper is a product of the Urban, Disaster Risk Management, Resilience and Land Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at slall1@worldbank.org and mlebrand@worldbank.org.

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

# **Evidence from Satellite Data**

Somik V. Lall* Mathilde Lebrand Maria Edisa Soppelsa World Bank

## JEL: O18, R52, R14

Key words: internal city structure; transport networks; satellite data; land-use policy

**Acknowledgments:** The authors thank Hogeun Park for supporting the spatial data analysis. They also thank Richard Damania, Lewis Dijkstra, William Maloney, Forhad Shilpi, Daniel Sturm, and Anthony Venables for helpful discussions. The authors appreciate the partnership with Thomas Esch and Mattia Marconcini of the German Aerospace Center (DLR) in developing measures of building heights. The authors acknowledge the generous financial support from the Global Platform for Sustainable Cities and the Government of Switzerland (SECO). The findings, interpretations, and conclusions expressed in this paper are entirely those of the author. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.

*Author for correspondence: Somik Lall, slall1@worldbank.org; Lead Urban Economist, World Bank
# 1. Background and Motivation

The United Nations projects that 2.3 billion people will be added to urban areas between 2020 and 2050, with 90 percent of this increase taking place in Asia and Africa (United Nations 2018). The pace of urban growth is projected to be the fastest in Sub-Saharan Africa, where the state has weak institutional and fiscal capabilities. Urban populations in Sub-Saharan Africa are expected to double from 458 million in 2020 to 1.2 billion in 2050. At the country level, China, India and Nigeria will account for 35 percent of the projected urban population growth. These are significant numbers and proactive planning and investments will be needed to help developing country cities prepare for such growth.

An important part in planning for the large urban population growth expected over the next three decades is to understand how city form has spatially evolved to accommodate people in the recent past and what have been the key drivers of urban spatial evolution. In this paper, we provide the first globally comparable estimates of the evolution of city form over the past three decades. We distinguish changes to city form along three margins: (a) horizontal spread (extensive margin), (b) infill development (inside a city’s edge), and (c) vertical layering (building taller structures).

The econometric analysis examines the proximate drivers of city form, showing the extent to which city form responds to the processes of economic development. City forms differ for cities at different stages of development; productivity enhancing agglomeration economies and supporting policies and infrastructure investment influence where people live, where firms locate, and how workers commute. As both the demand for space and economic proximity increase with income, the supply and spatial distribution of floor space is influenced by a city’s productivity and the capacity of cities to build higher and their transportation systems (Sturm, Takeda and Venables 2021a).

New transportation and building technologies have historically shaped urban form. Over the last two centuries, new transportation and building technologies have enabled the expansion of cities and increased the amount of living space consumed by households and firms (Glaeser, 2020). Horse-drawn omnibuses and subways enabled the spread of 19th century cities (for example London as discussed in Heblich et al. 2020). Elevators and other engineering innovations have enabled vertical growth which further expanded the supply of floor space (Ahlfeldt & Barr 2020). More recently highways and cars have had a large impact on density and living space as exemplified by sprawling cities in the United States.

Our research makes a significant contribution to the economics literature on the spatial structure of cities. First our analysis is global in scope and employs a new comparable measure – ‘the degree of urbanization’ (Dijkstra et al 2020) to assess city form. In our analysis, cities are defined as urban centers with at least 50,000 inhabitants in 2015. The universe of cities includes both small cities as well as giant megalopolises and covers cities across all incomes. Having a consistent definition of urban extent allows us to compare cities across countries and over time. While Jedwab et al. (2021) provide income elasticities for land area, population size and density for 1,773 urban agglomerations in 2010, we extend the coverage to about 10,000 cities in the world and construct a panel of data from 1990 to 2015. We also focus on built-up surface rather than total area as done in Jedwab et al. (2021), which is a better proxy for measuring available floor space and allows us to assess whether new built-up surface is done through infill construction or by spreading out.

Second, much of the existing research examines horizontal expansion, and rarely incorporates the vertical dimension. Even when the vertical dimension is considered, the focus has been on North American cities or restricted to very high buildings (Ahlfeldt and McMillen, 2018; Liu et al., 2018, Ahlfeldt & Barr, 2020; Jedwab et al., 2021). While Jedwab et al. (2021) use a data set which restricts the analysis to buildings 2
taller than 80m,<sup>1</sup> we use satellite height data for all buildings within the defined urban extent. We believe our approach provides a more representative measure of heights for the whole city.

Finally, we estimate income and population elasticities of the evolution of city form to understand how the spatial structures of cities change across the different stages of development and across countries and regions. We introduce novel estimates of density using floor area per resident in a city instead of traditional measures that use surface area or built-up area. We find that doubling of a city’s income is associated with a 11% increase in its built-up surface and 18% increase in average building height. The share of infill development is significantly higher for upper-middle-income and high-income countries.

Following this motivational section, the rest of the paper is organized as follows. Section 2 describes the satellite and economic data used in the research. Section 3 provides stylized facts on the three margins of city form evolution -- horizontal spread (extensive margin), infill development (inside a city’s edge), and vertical layering (building taller structures). Section 4 describes the econometric analysis on the proximate drivers of evolution of city form. Section 5 concludes.

# 2. Data

- 2.1 Defining a city

To measure city expansion and infill development, we use the Global Human Settlement Urban Center Database 2015 (GHS-UCDB) developed by the European Commission, Joint Research Centre (JRC). This data set defines urban centers applying the "Degree of Urbanization”, which is a new global definition of cities, urban and rural areas developed by the European Union and combines the previously developed Global Human Settlement Layer Built-up (GHS-BUILT) areas and Population (GHS-POP) grids. A city consists of "contiguous grid cells with a density of at least 1,500 inhabitants per km<sup>2</sup> of permanent land or with a built-up surface share on permanent land greater than 0.5 and has at least 50,000 inhabitants in the cluster with smoothed boundaries" (Florczyk et al., 2019).

The GHS-BUILT is derived from satellite imagery to measure the built-up area. The data set is constructed of a series of built-up layers across four different periods (i.e., 1975, 1990, 2000, and 2014). Each year of the data set is based on different collections of Landsat satellite imagery. A total of 33,202 scenes were captured to produce the multi-temporal layers of built-up (Florczyk et al. 2019). The GHS-BUILT uses a 30m spatial resolution, which is higher resolution compared to the Moderate Resolution Imaging Spectroradiometer (MODIS) Land Cover Type (MCD12Q1) and Global Land Cover (Globcover) that are available at 500m and 300m, respectively. Coarser resolution imagery may lead to the omission of small built-up areas (as in low income countries) and poor accuracy at the urban fringe.

The advantages of this data set are twofold. First, it uses a common definition of urban center across the world which is crucial for global level comparison. Although there has been a wide discussion in the literature on how to properly define cities, no definite consensus has been reached. Some studies have used a pre-defined pixel grid as a cookie-cutter and applied that to define each city (Mahtta et al., 2019) while others have used the cities' administrative boundaries or commuting zones (Roberts et al. 2017). Second, it defines the urban extent that corresponds to the most recent available data (2015). Having

> 11 Council on Tall Buildings and the Urban Habitat (CTBUH).

3
these fixed and recent boundaries is useful because it allows us to analyze changes in the same area aiming to answer the question of how city form has changed through time.

The Global Human Settlements population grid (GHS-POP) uses data from the Gridded Population of the World and reallocates these estimates using the GHS BUILT data set. An alternative would have been to use data from LandScan, which uses a proprietary algorithm to provide population estimates information on elevation, slope, and land cover, as well as locations of road and rail networks, hydrologic features and drainage systems, utility networks, airports, and populated urban places (Henderson et al 2020). While LandScan reports estimates of ambient population averaged throughout the day, GHS POP reports nighttime (residential) population estimates.

The entire data set consists of 13,135 cities with at least 50,000 inhabitants in 2015. The data set focuses on measures of city built-up and city population for four points in time: 1975, 1990, 2000, and 2015. It also includes other economic, geographic and environmental variables such as city GDP, elevation, precipitation and temperature, CO2 emissions, PM 2.5 emissions and concentration levels, for similar points in time. We construct a sample of cities that have recorded positive built-up and GDP since 1990. We drop the 1975 layer as it potentially underestimates built-up areas due to the coarser resolution of the Landsat2 Multispectral Scanner (60m compared to 30m). Using the 1975 data would introduce an upward bias in city growth estimates. To further reduce measurement errors and avoid outliers, we drop cities with population less than 10,000 inhabitants in 1990 and 2000, and those with a population/builtup coefficient larger than 500,000 in 1990. This gives us a final sample of 9,468 cities, which includes cities of all sizes (Table 1). More than half the cities in the sample have less than 200,000 inhabitants.

**Table 1: Distribution of Cities by City Size and Region**

|**Region**|**Less than**<br>**70k**|**70k -**<br>**100k**|**100k -**<br>**200k**|**200k -**<br>**500k**|**500k -**<br>**1m**|**1m- 10m**|**More**<br>**than 10m**|
|---|---|---|---|---|---|---|---|
|East Asia & Pacific|612|609|819|476|131|116|11|
|Europe & Central Asia|345|297|324|225|77|56|2|
|Latin America & Caribbean|267|228|255|158|60|51|3|
|Middle East & North Africa|221|137|199|113|43|40|2|
|North America|77|86|92|60|22|33|2|
|South Asia|312|362|588|390|122|84|7|
|Sub-Saharan Africa|300|290|439|217|55|52|1|

Source: GHS urban centers database One needs to keep in mind that our analysis uses cities as the unit of analysis and does not include urban agglomerations, which often include adjacent suburbs. However, to enable comparability, a density threshold of 1,500 people per km<sup>2</sup> is used as a cutoff. Figure 1 shows the boundaries for Casablanca, Cairo and Dakar with this approach. To check for robustness of this arbitrary cutoff, we selected the 50 fastest growing cities from 1990 to 2015 to assess the population variations across different sizes of urban areas. Multiple ring buffers (from negative 5km to positive 5km away from the edge of the urban boundary) were added to the urban boundary. Except for two outliers—Guangzhou, China, and Jakarta, Indonesia— 4
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between 2006 and 2011, but corresponds to only one point in time, which does not allow for examination of city height evolution.

As mentioned before, for each city, the data from the DLR provides average height of every pixel inside the defined urban extent, with a resolution of 90x90 meters. Table 3 provides summary statistics on building heights across cities at different income levels. These are average heights, covering the entire urban extent.

**Table 3: City Heights Measures - Summary Statistics by Income Group**

||**Low**<br>**Income**|**Lower-**<br>**Middle**<br>**Income**|**Upper-**<br>**Middle**<br>**Income**|**High**<br>**Income**|
|---|---|---|---|---|
|Ave Height (in m)|2.37|2.34|3.58|3.34|
||(0.53)|(0.77)|(1.32)|(1.14)|
|Ave q90 (in m)|3.63|3.72|6.24|5.93|
||(1.21)|(1.56)|(2.73)|(2.62)|
|Ave q95 (in m)|4.26|4.35|7.56|7.69|
||(1.58)|(2.00)|(3.43)|(3.88)|
|Ave max (in m)|10.52|13.26|25.12|31.78|
||(6.65)|(12.26)|(23.58)|(16.83)|
|Ave TFA (in m2)|78.65|140.75|354.58|707.37|
||(111.24)|(325.67)|(1,118.25)|(1,209.62)|
|Ave TFA/City Area|0.79|0.78|1.19|1.11|
||(0.18)|(0.26)|(0.44)|(0.38)|

Source: Analysis based on DLR WSF 3D data set Note: These are average heights for 90m x 90 m blocks, further averaged across the city’s extent

# 3. Stylized facts

In this section, we provide stylized facts on the magnitude and spatial distribution of built-up area growth and vertical layering in cities. As we have data on heights and can compute floor area, we provide a new measure of floor space adjusted density.

# 3.1 The growth of urban built-up area is slower than has been thought

Analysis of the satellite data show that between 1990 and 2015 the world’s total urban built-up area increased by 66,000 km<sup>2</sup> , or the size of Sri Lanka. Urban built-up area increased from 226,768 km<sup>2</sup> to 294,550 km<sup>2</sup> , a growth of 30 percent. In developing countries, urban built-up area increased from 117,977 km<sup>2</sup> to 166,231 km<sup>2</sup> over the same time period. That is a 34 percent growth in built-up expansion, an annual growth of 1.36%. While this is significant, it is not quite the explosive spread estimated by many recent studies. For example, the _Atlas of Urban Expansion_ (Angel et al, 2016) argued that during this period the area occupied by cities in less developed countries increased by a factor of 3.5—and that if this rate were to continue, the total amount of land taken over by urban land use would be equivalent to the entire country of India by 2050 (Angel et al 2016). Huang et al (2019) project urban land areas to expand 7
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| Expansion and Leapfrog Infill
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3.4 Floor area adjusted population densities can sort between crowded and livable cities Population density is the most common measure of urban concentration. Most measures of population density take the form of people/urban built-up area or people/total urban area. However, population density is an imperfect measure of urban proximity as it does not account for the quality of built structures.

Figure **8** a shows a scatter plot of population density and city incomes. Population density is measured as people per built-up area of the city, for 400 cities worldwide. Two striking features emerge. First, population densities decline with incomes, as countries move across stages of economic development. Kinshasa, Mumbai and Karachi are four to five time more densely populated than Shanghai, Tokyo or London. Second, naïve measures of population density can conflate crowding with livable densities. Kinshasa, Mumbai and Hong Kong are three cities with similar population density but at very different levels of income.

While Hong Kong’s residents can live in tall buildings with adequate floor space, over 50 percent of Mumbai’s population lives in slums. Most of Kinshasa’s population lives in squalid conditions. In low- and lower-middle-income countries, population densities in the range of 50,000 people per km2 are reflections of squalor and crowding, not livable densities. Such crowding has been associated with high degree of contagion risk during the COVID-19 pandemic, where residents do not have physical space to be socially distant and need to access shared toilets and water kiosks in their neighborhood (Lall and Wahba 2020).

To untangle crowding from livable densities, we introduce a new measure called the Floor-area adjusted population density (FAPD), which we measure using the heights data available from DLRs WSF 3D database. We first compute total floor area using the heights data as follows: Where TFA is the total floor area. The average floor height is assumed to be 3 meters. This measure can be compared across pixels in a city, or aggregates compared across cities. Using the TFA measure, we can compute FAPD as follows: 13
# **Figure 8:  Comparing naïve and floor area adjusted population densities (FAPD) across 400 global cities**

Figure a. Population density and city income, 2015. (population per km2 of built-up area, log scale) <!-- Start of picture text --> 150000<br>100000<br>Mumbai<br>50000<br>Kinshasa Karachi Hong Kong<br>Dhaka<br>Lagos Beijing<br>10000 Shanghai<br>Tokyo<br>London<br>5000<br>2000 Dallas<br>City income in 2015, log scale<br>Density (population per sq. km of built-up), log scale<br>500 1000 5000 10000 40000<br><!-- End of picture text --> Figure b. Floor Area Adjusted Population Density (FAPD) and city income, 2015 (population per km2 of floor space, log scale) <!-- Start of picture text --> 150000<br>100000<br>30000<br>Kinshasa<br>Karachi<br>Mumbai<br>10000 Dhaka<br>Lagos LondonHong Kong<br>5000<br>Tokyo<br>ShanghaiBeijing<br>2000<br>City income in 2015, log scale<br>Density (population per sq. km of floor space), log scale<br>500 1000 5000 10000 20000 40000<br><!-- End of picture text --> Source: Analysis based on DLR WSF 3D data set The FAPD in Figure 8b is a reasonable indicator of livability. Hong Kong’s FAPD is in line with that of a highincome city like London or Tokyo. FAPDs for low-income cities such as Kinshasa and Mumbai are also lower than their naïve population densities, with the correction making more of a difference for specific neighborhoods that have taller structures. While the FAPD makes intuitive sense, more work is needed to get better estimates of building heights. The DLR WSF3D data make a first contribution to such measurement. There are many measurement errors in the data coming from the ability of satellite sensors to measure height as well as noise introduced in the aggregation of the data collected at 12mx12m resolution. However, analysis of these data for the city of Dhaka shows remarkable correlation with predictions of heights based on productivity measures estimated through a general equilibrium urban model (Sturm, Takeda and Venables 2021b).

14
4. Evolution of urban form – econometric evidence The previous section provided descriptive statistics on built-up area growth, horizontal expansion and vertical layering of cities. In this section we expand on those stylized facts and provide econometric evidence to show how the evolution of urban form follows stages of a city’s economic development. There is a broader literature on institutions and economic development that makes the point that human capital, quality of institutions, and government effectiveness are strongly correlated with economic development (La Porta et al. 1999, Glaeser et al. 2004). More recently, Djankov and co-authors (2020) show that quality of institutions of land titling and transferring property across countries are generally much better in more developed countries.

Building and development choices are also shaped by institutions and regulations. Lack of clarity in land tenure creates a bias against sinking capital in formal structures and is a factor in the perpetuation of slum areas (Sturm, Takeda, and Venables 2021a). Building regulations, such as floor-area restrictions (FARs) often restrict density of both commercial and residential development, this lengthening commutes and weakening agglomeration spillovers between firms. Zoning can be done in ways that are damaging – locking in land-use patterns that become inappropriate as a city develops. Potential benefits could arise by regulating negative externalities that affect households, and possibly also by encouraging concentration of commercial activity, and so promoting positive spillovers and externalities between firms. Further, meeting the upfront capital costs of infrastructure and structures is more feasible in cities with higher incomes (Hommann and Lall 2019, White and Wahba 2019).

While we do not have comparable and representative data on institutional quality or regulatory regimes for individual cities, we use city incomes as a proxy for productivity as well as institutional and financial maturity. The econometric analysis examines how the evolution of urban form is closely tied to the processes of economic development. The econometric evidence is organized in three sub-sections. Section 4.1 examines the relationship between incomes and built-up area changes between 1990 and 2015. Section 4.2 examines links between income and city heights. Section 4.3 provides a new approach to look at the combined effect of population growth and income growth on floor space in a city.

# 4.1  The effects of income and population growth on built-up area

As population and income grow, cities expand by building more and occupying more land. We quantify the income and population elasticities of built-up using a panel of observations from the GHSL Urban Centers database. As described in section 2, built-up surface for all cities with more than 50,000 inhabitants in the world is available for four years: 1975, 1990, 2000, and 2015. City income and population estimates come from the same GHSL database.<sup>4</sup> Several econometric issues arise when estimating the impacts of a growing population and income on city built-up over the past decades. First endogeneity issues may arise as factors that are not observed may affect both the dependent variable, built-up surface, and the explanatory variables, population and income of the city. Second, there may be omitted variables that are key predictors of built-up but are not observed such as geographic or weather amenities. In each case, a simple OLS estimator will be biased. Therefore, the results from different specifications based on equation (1) are reported with each of them solving an econometric issue. The panel regression analysis is based on the following specification:

> 4 Similar estimates are obtained when using country income.

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For city c, at time t , + β<sup>b</sup> (1) With ln BBUU the built-up surface at time t for city c. cc,tt = αα+ γ<sup>b</sup> ln IIPPeeooIIaacc,tt ln FFooppCity Controlscc,tt + City Controls + TTFF+ εε include built-up surface in 1975. cc,tt include a series of fixed effects at the city or/and year levels. cc,tt BBUU Our very basic strategy was to use the ‘between’ estimator to capture variation based on changes across years, adding in country fixed effects. Results from this estimation are reported in table 4, column 1. Year fixed effects control for aggregate changes that have affected all cities at each period. The built-up of the city in 1975 is added as a control for unobserved variables like historical and geographic characteristics that are a main determinant of a city’s growth path.

A limitation with this specification is potential omitted variable bias. To address this, we estimate both the ‘between’ and ‘within’ estimator, we treat city heterogeneity as another variable, the fixed effect. This allows us to address unobserved city heterogeneity that do not vary with time. This reduces omitted variable bias. Results from this specification are reported in Table 4, column 2.

**Table 4: Determinants of built-up surface**

|**Dependent variable:**<br>**built-up**|**Between**<br>**Estimator**|**Between +**<br>**Within**<br>**Estimator**|**Between +**<br>**Within**<br>**Estimator**<br>**with lag**|**IV Between +**<br>**Within Estimator**|**Between +**<br>**Within**<br>**Estimator**<br>**with NTLs**|
|---|---|---|---|---|---|
|Ln Income<br>Ln Population<br>Built-up 1975|0.184<sup>***</sup><br>(0.00713)<br>0.509<sup>***</sup><br>(0.00846)<br>0.458<sup>***</sup><br>(0.00749)|**0.104**<sup>*******</sup><br>**(0.00483)**<br>**0.347**<sup>*******</sup><br>**(0.0176)**||0.149<sup>***</sup><br>(0.00439)<br>0.373<sup>***</sup><br>(0.00856)|0.307<sup>***</sup><br>(0.0179)|
|Ln lagged Income|||0.0982<sup>***</sup><br>(0.00453)|||
|Ln lagged population|||0.281<sup>***</sup><br>(0.0146)|||
|Ln NTLs per capita|||||0.0883<sup>***</sup><br>(0.00553)|
|FE|Year|**City + Year**|City + Year|City + Year|City + Year|
|Controls|Country|**No**|No|No|No|
|R-squared|0.913|**0.583**|0.471||0.572|
|N. of observations|28332|**28341**|18894|27460|27688|

Standard errors in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001 Another econometric problem is that incomes and population are endogenous to built-up. In addition, built-up might react with delays to changes in income. One way to address these endogeneity concerns is to introduce lagged variables. The first instrument is the lag of population and income. However, it reduces the sample of observations by a third. The second instrument used for income is the country GDP per capita. Column (3) and (4) report these results. Finally, we compare our measure of city income with 16
a commonly-used proxy for income, Nighttime Lights (NTL) per capita.<sup>5</sup> We process DMSP-OLS data for three years (1992, 2000, and 2012) for the areas matching with the GHS-UCDB urban areas used in the rest of the paper. Column (5) reports the results using Nighttime Lights per capita instead of the previous income measure. Our preferred specification is given by the between and within estimator in Column (2). Estimates are similar when using instrumental variables and Nighttime Lights as a proxy for income. Income and population elasticities can be inferred from the results of the regression.<sup>6</sup> As a city’s population doubles, its built-up surface increases by 34.7% when keeping income constant and controlling for unobserved city and year characteristics. This number is lower than previous estimates reported in the literature (Angel, et al., 2016) and shows that cities have not extended their built-up as much as their population growth would have suggested. As a city’s income doubles, the built-up surface increases by 10.4% when keeping population constant and controlling for unobserved city and year characteristics.

As a final robustness check, we run the same regression as in Table 4 using population, income and builtup from the Functional Urban Area (FUA) database developed by the OECD and the European Commission. The spatial entities represent the commuting areas of the urban centers in 2015, which are geographically larger than our urban extents as they often contain multiple urban centers. Annex 2 presents a similar table as in Table 4. The new coefficients are similar to the ones estimated using our urban centers.

**Table 5 : Determinants of built-up surface across income groups**

|**Dependent variable:**<br>**built-up**|**All**<br>**countries**|**Low income**|**Lower**<br>**middle**<br>**income**|**Upper**<br>**middle**<br>**income**|**High income**|
|---|---|---|---|---|---|
|Ln city Income|0.104***<br>(0.00483)|0.0488*<br>(0.0192)|0.0891***<br>(0.0134)|0.107***<br>(0.00594)|0.101***<br>(0.0187)|
|Ln Population|0.347***<br>(0.0176)|0.343***<br>(0.0474)|0.308***<br>(0.0371)|0.251***<br>(0.0207)|0.281***<br>(0.0261)|
|FE|City + Year|City + Year|City + Year|City + Year|City + Year|
|Controls|No|No|No|No|No|
|R-squared|0.583|0.597|0.612|0.611|0.549|
|N. of observations|28341|2139|10959|11124|4119|
|Standard errors in parentheses * p < 0.05,|** p < 0.01, **|* p < 0.001||||

> 5 While Defense Meteorological Satellite Program/Operational Linescan System (DMSP-OLS) was originally designed for military use, DMSP-OLS has been widely used in social science because of its low-light imaging capabilities to detect nighttime artificial lighting (Elvidge et al., 1997). Henderson et al. (2012) empirically prove the concept of using an annual composite of DMSP-OLS as a proxy measurement of economic growth across the national and/or local level. Many studies extensively use nighttime lights to estimate the national and sub-national GDP. These estimates are critically useful for developing countries and/or conflict-affected areas where official statistics are unavailable or limited.

> 6 Other possible specifications were considered but not reported in this note. A dynamic panel specification was considered but 3 years of data was not sufficient to report strong results for a dynamic panel.

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To examine how urban forms evolve across stages of development, we examine built-up area growth across income groups.

As a final robustness check, we run the same regression as in Table 4 using population, income and builtup from the Functional Urban Area (FUA) database developed by the OECD and the European Commission. The spatial entities represent the commuting areas of the urban centres in 2015, which are geographically larger than our urban extents as they often contain multiple urban centers. Annex 2 presents a similar table as in Table 4. The new coefficients are similar to the ones estimated using our urban centers.

Table 5 reports the results of the between and within estimator following equation (1) for cities per country income group as defined by the World Bank. The coefficients of each column can be interpreted as the income and population elasticities of built-up surface for cities in each income group.

Growing population is associated with a larger increase in built-up surface in poorer countries. As population doubles, cities’ built-up increases by 34% in low-income countries, 31% in lower-middle income countries, 25% in upper-middle-income countries and by 28% in high-income countries.<sup>7</sup> Cities in poorer countries grow more horizontally than cities in richer countries. In contrast, rising incomes are associated with slower built-up surface expansion in poorer countries than in richer ones. As urban population doubles, the city’s built-up area increases by 5 percent in low-income countries, 9 percent in lower-middle-income countries, 11 percent in upper-middle-income countries, and 10 percent in highincome countries. The significant jump in the income elasticities between low-income and middle-income countries is indicative that the evolution of urban form follows broader stages and processes of economic development.

Next, we examine the extent to which rising incomes and stages of economic development influence the shares of extensive margin and infill development. We build a panel of two periods of built-up growth: 1990-2000 and 2000-2015. We estimate the share of infill as : 1 2 (2) where denotes the share of infill built in the period between two years of our data (1990-2000 ln IIPPooeep cc,tt = αα+ ββ ln IIPPeecc,tt + ββ ln FFooppcc,tt + λλtt + γγcc + εεcc,tt 1 2 (2) where denotes the share of infill built in the period between two years of our data (1990-2000 and 2000-2015). cc,tt IIPPooeep Consistent with the stylized facts shown in Figure 5, the share of infill has reduced over time. Also consistent with the stylized facts, the share of infill increases with economic development. Within broad income groups, there is no association between income changes and infill in low-income countries. The positive relationship is strong and statistically significant for middle-incomes countries. We see a negative association between incomes and infill in high-income countries, presumably driven by the United States.

**Table 6: Determinants of infill development**

|**Dependent variable:**|**All**||**Lower**|**Upper**||
|---|---|---|---|---|---|
|**share of infill construction in total**|<br>**ti**|**Low income**|**middle**|**middle**|**High income**|
|**built-up area**|**counres**||**income**|**income**||

> 7 There is no contradiction in the fact that the estimated coefficients per income group are all lower than the estimated coefficient when including all cities.

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|Ln city Income|0.529***<br>(0.0458)|-0.181<br>(0.181)|0.517***<br>(0.104)|0.687***<br>(0.0590)|-1.115***<br>(0.223)|
|---|---|---|---|---|---|
|Ln Population|1.132***|1.427***|1.765***|0.675**|-0.915*|
||(0.143)|(0.388)|(0.248)|(0.216)|(0.390)|
|year=2015|-1.235***<br>(0.0293)|-1.945***<br>(0.124)|-1.306***<br>(0.0545)|-1.280***<br>(0.0467)|-0.655***<br>(0.0502)|
|FE|City + Year|City + Year|City + Year|City + Year|City + Year|
|Controls|No|No|No|No|No|
|R-squared|0.250|0.324|0.200|0.289|0.469|
|N. of observations|18787|1423|7233|7377|2754|

Standard errors in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001 The evolution of built-up area also has implications for population density. We estimate Income and population elasticities of naïve density measured as population over built-up area. Using the GHSL panel data, different specifications are estimated including nonlinear effects for the largest cities based on the following regression: 1 2 2 3 4 2 (3) ln FFaaPPsseettDD As shown previously, as cities become richer, they expand responding to a higher demand for space and cc,tt = αα+ ββ ln IIPPeecc,tt + ββ ln IIPPeecc,tt + ββ ln FFooppcc,tt + ββ ln FFooppcc,tt + λλtt + γγcc + εεcc,tt As shown previously, as cities become richer, they expand responding to a higher demand for space and supply for built-up, and therefore become less densely populated. The income elasticity of density is -0.10 using the between and within estimator; introducing instruments for incomes increases it to -0.15. Table 7 provides estimates of the income elasticity of density using various specifications. Figure 9plots out densities over incomes levels using the nonlinear specification for cities larger than 500,000 people (column 5, Table 7). The chart reveals that density declines rapidly between low and middle incomes, and it stabilizes as cities reach $20,000 per capita. As population keeps growing, some of these large cities will provide space through higher buildings, increasing the livability of its inhabitants while allowing for larger agglomeration gains.

**Table 7: Determinants of naïve population density (population over built-up)**

|**Dependent variable:**<br>**Population density**<br>**over**<br>**built-up**|**Between +**<br>**Within**<br>**Estimator**|**Between +**<br>**Within**<br>**Estimator**<br>**with lag**|**Between +**<br>**Within**<br>**Estimator**<br>**with NTLs**|**Between +**<br>**Within**<br>**Estimator**<br>**with IV for**<br>**income**|**For Cities >**<br>**500k only**|**Nonlinear**<br>**specification**<br>**for Cities >**<br>**500k**|
|---|---|---|---|---|---|---|
|Ln Income<br>Ln Population<br>Ln lagged Income|-0.105***<br>(0.00484)<br>0.649***<br>(0.0177)|-0.181***<br>(0.00650)|0.692***<br>(0.0180)|-0.149***<br>(0.00439)<br>0.627***<br>(0.00856)|-0.0762***<br>(0.0103)<br>0.784***<br>(0.0277)|-0.397***<br>(0.0946)<br>-0.446<br>(0.380)|
|Ln lagged population||0.478***<br>(0.0347)|||||
|Square Ln Income||||||0.0197***<br>(0.00584)|

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|Square Ln Population<br>Ln NTLs per capita<br>Constant|3.270***|5.699***|-0.0880***<br>(0.00553)<br>1.453***|3.860***|-0.615|0.0432**<br>(0.0132)<br>9.400***|
|---|---|---|---|---|---|---|
||(0.218)|(0.424)|(0.204)|(0.119)|(0.402)|(2.768)|
|FE|City + Year|City + Year|City + Year|City + Year|City + Year|City + Year|
|Controls|No|No|No|No|No|No|
|R-squared|0.415|0.328|0.420||0.466|0.477|
|N. of obs|28352|18856|27636|27460|2495|2495|

Standard errors in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001

# 4.2  The effects of income and population growth on vertical layering

Cities can add space by expanding their built-up surface as well as by building higher. We use the subsample of almost 400 cities, representative of the larger GHSL sample to assess the income and population elasticities of city height.<sup>8</sup> Height is measured as the average height of the city’s buildings within 5 kms of the highest point in the city.<sup>9</sup> Similar analysis is conducted using the average over the whole urban extent as defined by GHSL, or using quantiles over the whole distribution. Several specifications are reported in Table 5 adding regional dummies as additional controls and replacing city income by its Nighttime Light proxy or its equivalent at the country level.<sup>10</sup> Using the cross-section data for almost 400 cities, the following specification is estimated for all cities c: ln Average Height ln Income + β<sup>he</sup> ln Population cc<sup>eehtt</sup> (4)<sup>eehtt</sup> cc,2000 cc,2000 As city population doubles, the average height increases by 25% when keeping income constant. Such = αα+ γ<sup>he</sup> cc vertical growth adds up to the horizontal built-up growth previously measured. This elasticity is consistent + RRa eeooPP FFssI eeaass+ εε across the different specifications presented in Table 8.

As city income doubles, the average height increases by 18% when keeping population constant. While the population elasticity is lower for height than for built-up, the income elasticity is higher for height. Income is associated with a larger impact on vertical growth relatively to its impact on horizontal growth. This can be rationalized through different economic channels. As households get richer, more of them want to live close to where jobs are to reduce the time spent on commuting and can afford higher rents. Richer cities also tend to produce more tradable services which are intensive in knowledge workers and

> 8 The subsample of 400 cities was built to be as representative as possible at the global level of the GHSL sample of cities. As a first check, the same regression is run using both the universe and the subsample. The within-estimator of the income and population elasticities of built-up is obtained for each sample and are shown to be very similar. These estimates can be shared on request.

> 9 Given that most surface is expected to be built around the highest point of the city, the measured height per pixel in this 5-kilometer radius will correspond to both the average over the buildings and the average for the total area of the pixel. DLR data provide height averages over the area of the pixel.

> 10 Population and Income from year 2000 are used for two reasons. First, height data have been collected between 2007 and 2011, with the year of collection reported in the data. Second, adding some lag in the explanatory variable can be thought as an instrumental strategy to deal with the endogeneity issues associated with the initial specification.

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gain the most from agglomeration gains and density of activities, rising demand for higher buildings. On the supply side, the construction and real estate sectors are better equipped in richer cities to build high buildings which require advanced engineering technologies (Ahlfeldt & Barr, 2020).

Across geographic regions, there is a large heterogeneity in the heights of cities. Compared to cities in East Asia and Pacific, cities in Latin America & Caribbean have shorter buildings. The largest difference is however with cities in South Asia and Sub-Saharan Africa, which have the lowest building heights, when controlling for income and city population.

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**Table 8: Determinants of city height**

|**Dependent variable:**<br>**Average height**|**All with city income**<br>**[preferred specification]**|**All with NTLs**<br>**per capita**|**+ region**<br>**dummies**|**All with**<br>**country**<br>**income**|**+ region**<br>**dummies**|
|---|---|---|---|---|---|
|Ln Population 2000|0.251***|0.262***|0.266***|0.267***|0.269***|
||(0.0170)|(0.0155)|(0.0173)|(0.0171)|(0.0166)|
|Ln City Income 2000|0.185***<br>(0.0219)||0.0557<br>(0.0322)|||
|Ln NTLs per capita||0.209***<br>(0.0344)||||
|Ln Country Income 2000||||0.222***|0.102**|
|||||(0.0251)|(0.0352)|
|East Asia & Pacific|||0||0|
||||(.)||(.)|
|Europe & Central Asia|||-0.130<br>(0.0780)||-0.221*<br>(0.0874)|
|Latin America & Caribbean|||-0.139*||-0.195**|
||||(0.0693)||(0.0706)|
|Middle East & North Africa|||-0.197||-0.248*|
||||(0.104)||(0.111)|
|North America|||-0.198*||-0.315**|
||||(0.0876)||(0.0958)|
|South Asia|||-0.978***||-0.973***|
||||(0.111)||(0.110)|
|Sub-Saharan Africa|||-0.470***||-0.438***|
||||(0.0751)||(0.0776)|
|Constant|-4.047***|-1.650***|-2.880***|-4.683***|-3.328***|
||(0.286)|(0.254)|(0.289)|(0.352)|(0.362)|
|FE|No|No|No|No|No|
|Controls|No|No|Yes|No|Yes|
|R-squared|0.392|0.440|0.561|0.403|0.564|
|N. of observations|396|396|396|383|383|
|Standard errors in parentheses|* p < 0.05, ** p < 0.01, *** p|< 0.001||||

4.3 The combined impacts of built-up growth and vertical layering on floor area In the previous section, we introduced the concept of Floor Area Adjusted Densities (FAPD), which can help differentiate between crowded and livable cities. Floor area is critical for cities to accommodate families and firms. It can be added through horizontal spread, vertical layering, or infill development. Here, we combine the results from the previous estimates of horizontal and vertical growth to estimate income and population elasticities for the total floor area. Income and population elasticities are inferred using 22
the previous estimates for built-up area and vertical growth.<sup>11</sup> Income and population elasticities of total floor area are defined as the following:<sup>12</sup> A measure of area per person is a good proxy of livability for cities. While the slums in Mumbai and the East side of Manhattan have the same population density, the amount of space available per person is the relevant measure to compare these two areas. Based on the previous estimates, income and population elasticities of floor area per person are reported Table 9. The elasticities for total floor area per person with respect to income or population are then derived.<sup>13</sup> Income Elasticities of Floor Area per Capita = γ<sup>b</sup> + γ<sup>heeehtt</sup> Population Elasticities of Floor Area per Capita = β<sup>b</sup> + β<sup>he</sup> – 1<sup>eehtt</sup>

**Table 9: Elasticities of Total Floor Area**

|**ELASTICITIES**|**From**<br>|**the data**<br>|**Inferred from t**<br>|**heprevious elasticities**<br>|
|---|---|---|---|---|
|**Sample of estimation**|**Built-up**<br>**GHSL**|**Height**<br>**DLR**|**TFA**<br>**Combi**|**TFA per person**<br>**nation of both**|
|Population|0.347***|0.251***|0.598|-0.402|
|Income|0.104***|0.185***|0.289|0.289|

Source: Elasticities of income and population reported in earlier tables Table 9 shows these elasticities and confirms that as cities grow in population, in incomes, or in both, they add floor space by building both upward and outward. These estimates have profound implications for a growing city’s supply of floor area, and also for its tendency to sprawl outward—especially in the absence 11 We do not directly estimate the elasticities using our measures of total floor area as they only cover cities for which we have height data. Instead we use the estimates of elasticities for built-up calculated with the GHSL sample, which includes almost all cities.

sample, which includes almost all cities. 12 These properties come from the log properties. – cst ppPP(T The elasticities for total floor area with respect to income or population are then derived. TT) = ppPP(BBsseepptt−sspp ∗ HHaaeeaahtt/3) = ppPP(BBsseepptt−sspp) + ppPP(HHaaeeaahtt) ⇒ddppPP(TεT TT) = ddppPP(BBsseepptt−sspp) + ddppPP(HHaaeeaahtt)= εb + εhe T b he TT,eeiicc eebbtt−bbuu,eeiicc eehtt,eeiicc 13 The elasticities for total floor area per person with respect to income or population are then derived. The elasticities for total floor area per person with respect to income or population are then derived. TT,uuppuu eebbtt−bbuu,uuppuu eehtt,uuppuu εε = εε + εε

> T b he 13  The elasticities for total floor area per person with respect to income or population are then derived.    The elasticities for total floor area per person with respect to income or population are then derived. T b he T b he − 1 TT uueeppccppuu,eeiicc eebbtt−bbuu,eeiicc eehtt,eeiicc εε = εε + εε TT uueepp ccppuu,uuppuu eebbtt−bbuu,uuppuu eehtt,uuppuu εε = εε + εε

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5 Conclusion In this paper, we provided new estimates of the evolution of city form along three dimensions -- horizontal expansion, infill development and vertical layering. Our main finding is that the evolution of city form follows the broader processes of economic development. As cities go through economic development, they attract people, expand their footprint, and build upwards. Not only do rising incomes increase demand for built-up area and floor space among families and firms, but also rising incomes are associated with stronger land and market institutions, construction capabilities, as well as financial maturity to pay for the lumpy upfront cost of infrastructure.

We have used new sources of satellite data to describe devolution of city form over the past 25 years as well as provide the first glimpse at an exciting new data set that can tell us about the height distribution of cities. We have also provided a new measure of population density which we called the floor area adjusted population density (FAPD) that takes into account floor area based on heights of buildings. We find that distinguishing between FAPD and naive population density is important as one can distinguish between cities that are crowded and those that are livable. More broadly, we find that densities in general decline with economic development as people and firms demand more space and amenities and transportation improvements allow for the city to increase its spatial reach.

Our econometric analysis shows that incomes are a central driver for providing floor space. In fact, the heights of buildings are very sensitive to income growth. In the absence of income growth, cities with rising populations will accommodate people by crowding. The evidence we provide here is a first step towards understanding how new satellite data can help us understand the evolution of city form. These data can form the cornerstone of new and exciting research looking at the impact of urban regulations, construction costs, and transport improvements on city form and its implications for productivity, livability and sustainability.

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