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).

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