metadata: authors: 0: author: Esch,Thomas
1: author: Deininger,Klaus W.
2: author: Jedwab,Remi Camille
3: author: Palacios-Lopez,Daniela
count: World
docna: 0: docna: Outward and Upward Construction : A 3D
            Analysis of the Global Building Stock
docty: Policy Research Working Paper
abstracts: cdata!: The developing world has built
            structures on an unprecedented scale to accommodate
            population growth and urbanization. The horizontal and
            vertical structuring of the building stock resulting from
            this &#x201c;megatrend construction&#x201d; strongly
            influences urban and rural poverty, sustainability,
            resilience, and quality of life. However, due to data
            constraints, little is known about how and why 3D building
            patterns vary globally and in the developing world in
            particular. This study uncovers novel facts on global 3D
            building patterns as a result of outward and upward
            preferences in construction and investigates their
            relationship to the development process. To this end, new
            high-resolution data on the area, height, and volume of the
            global building stock are combined with various analyses
            undertaken at different spatial domains. The results show
            that building stock per capita increases convexly with
            income, but income only explains two-thirds of the
            differences in international volume. Additionally, while
            building upward systematically drives international volume
            differences, low-rise buildings still dominate construction
            patterns. Urbanization tends to reduce space consumption per
            capita as urban residents consume less volume than rural
            residents. Finally, the analyses of construction preferences
            may help to assess construction needs by forecasting volume
            requirements in developing Africa, Asia and Latin America.
display_title: Outward and Upward Construction : A
            3D Analysis of the Global Building Stock
listing_relative_url: /research/2024/08/34376490/outward-upward-construction-3d-analysis-global-building-stock
topicv3: Environmental Sustainability m1325984 1786,Urban Land Supply and Markets m1326023 868,Urban Development m1327371 699,Commercial Property and Housing m1504599 3779
publishtoextweb_dt: 2024-08-12T00:00:00Z
dois: 10.1596/1813-9450-10866
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 50
author_keys: 0: author_key: 2188420
1: author_key: 96410
2: author_key: 1140935
3: author_key: NA
model_extractions: Policy Research Working Paper 10866 Outward and Upward Construction A 3D Analysis of the Global Building Stock _Thomas Esch Klaus Deininger Remi Jedwab Daniela Palacios-Lopez_ Development Economics Development Research Group August 2024
Policy Research Working Paper 10866

# **Abstract**

The developing world has built structures on an unprecedented scale to accommodate population growth and urbanization. The horizontal and vertical structuring of the building stock resulting from this “megatrend construction” strongly influences urban and rural poverty, sustainability, resilience, and quality of life. However, due to data constraints, little is known about how and why 3D building patterns vary globally and in the developing world in particular. This study uncovers novel facts on global 3D building patterns as a result of outward and upward preferences in construction and investigates their relationship to the development process. To this end, new high-resolution data on the area, height, and volume of the global building stock are combined with various analyses undertaken at different spatial domains. The results show that building stock per capita increases convexly with income, but income only explains two-thirds of the differences in international volume. Additionally, while building upward systematically drives international volume differences, low-rise buildings still dominate construction patterns. Urbanization tends to reduce space consumption per capita as urban residents consume less volume than rural residents. Finally, the analyses of construction preferences may help to assess construction needs by forecasting volume requirements in developing Africa, Asia and Latin America.

This paper is a product of the Development Research Group, Development Economics. 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 thomas.esch@dlr.de; kdeininger@worldbank.org; jedwab@email.gwo.edu; and daniela.palacioslopez@dlr.de.

_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
# Outward and Upward Construction: A 3D Analysis of the Global Building Stock

Thomas Esch (DLR-DFD) Klaus Deininger (World Bank) Remi Jedwab (GWU)<sup>*</sup> Daniela Palacios-Lopez (DLR-DFD) Keywords: World Built Environment in 3D; Construction; Vertical and Horizontal Expansion; Global Socio-Economic Development; Urbanization; Housing; Poverty; Sustainability

> *Corresponding author: Remi Jedwab: George Washington University, D.C., USA. jedwab@gwu.edu. Thomas Esch: German Remote Sensing Data Center (DFD), German Aerospace Center (DLR); Oberpfaffenhofen, Germany. Klaus Deininger: Development Research Group, The World Bank; Washington D.C., USA. Daniela Palacios-Lopez: German Remote Sensing Data Center (DFD), German Aerospace Center (DLR); Oberpfaffenhofen, Germany. The authors thank Jampel Dell’Angelo and two anonymous referees for their comments. The authors acknowledge the contributions of Julian Zeidler, Mattia Marconcini and Elisabeth Brzoska (German Aerospace Center). Funding: European Space Agency [contract no. 4000126100/19/I-EF]. EU-funded ACP-EU Natural Disaster Risk Reduction Program, managed by the Global Facility for Disaster Reduction and Recovery of the World Bank [contract no. 7194331, contract no. 7196541]. World Bank Multi-Donor Trust Fund (TF055155) on Land Policies for Growth and Poverty Reduction. R. Jedwab is grateful to Andrew Durrer, Eleanor Greenbaum, Claudia Groeling and Madison Fallon for research assistance. The findings, interpretations, and conclusions expressed in this paper are entirely ours. 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 or the governments they represent.
1

# **1. Introduction**

Capturing the 3D characteristics of the building stock plays a key role in the development of sustainable and inclusive growth policies. On the one hand, a complete and accurate quantification of the building volume and density is essential to assess the efficiency, sustainability, and resilience of settlement development and urban growth (Mahendra and Seto, 2019; Bibri et al., 2020; The World Bank, 2023b). Making “cities and human settlements inclusive, safe, resilient and sustainable” is U.N. Sustainable Development Goal (SDG) 11. In addition, building volume and building density have a high influence on the local climate (Guo et al., 2022), carbon footprint (Sun et al., 2022), traffic, and mobility (Rode et al., 2017), or adaptability to natural hazards and climate change (UN Habitat, 2020). As such, these measures are also important for SDGs 12 (Responsible Consumption & Production) and 13 (Climate Action).

On the other hand, as population continues to grow rapidly in many developing regions of the world (UN, 2017), detailed information on the building volume available to residents is crucial for the provision of housing (Adetooto et al., 2022), preservation of livable cities (Lall et al., 2021), and promotion of economic development (Adabre et al., 2020). Furthermore, evidence on future construction needs is just as important as real estate (i.e., buildings) accounts for twothirds of global wealth (McKinsey, 2021) and two-fifths of carbon emissions (UN Habitat, 2020). Also, housing represents the largest consumption item (The World Bank, 2023a) and the lack of housing is one of the main factors, if not the main factor, of urban poverty (UN Habitat, 2020).

Today, satellite imagery and computer technology allow us to map and analyze the physical form, compactness, and built-up density of settlements in 3D based on a measurement of their horizontal extent and/or vertical extent (Angel et al., 2012; Mahtta et al., 2019; Angel et al., 2021; Blei and Angel, 2021; Jedwab et al., 2021b; Frolking et al., 2022). This is especially important for developing country municipalities that do not have the administrative capacity to generate and maintain cadasters, despite how essential these are for urban planning and development (Erba and Piumetto, 2016). Recently, Esch et al. (2022), Li et al. (2022), Pesaresi and Politis (2022) and Zhou et al. (2022) generated global 3D data of the built environment that provides insights into the worldwide patterns of built-up heights and volumes. However, despite this recent progress, there is still a lack of sufficient data and knowledge at the global scale related to three issues.

Firstly, existing 3D studies still only reflect the morphological characteristics of the built-up area in general (buildings but also roads and other paved areas). For many applications, the key information needed is precise and consistent knowledge about the building stock in 3D (e.g., for estimating economic production, population distribution, or energy consumption).

Secondly, to our knowledge, most of the globally available key figures on 3D settlement morphology are currently derived from input data or analysis kernels with coarse geometric resolutions of 500m-1000m (Frolking et al., 2022; Li et al., 2022; Zhou et al., 2022).
2 Thirdly, systematic 3D analyses of horizontal and vertical settlement extent are often derived from between a few hundred to a thousand selected city regions (Jedwab et al., 2021b; Lall et al., 2021; Li et al., 2022; Zhou et al., 2022). The resulting empirical evidence therefore tends to favor the characteristics of urban areas, and large cities among them, focusing on developed economies rather than developing economies where most of the data needs are.

To address these limitations, this research focuses on several major improvements. Based on a unique combination of area-wide information provided by the World Settlement Footprint 3D (WSF3D) raster layer (Esch et al., 2022), with the exceptional precision of the Emporis point database of high-rise buildings (Emporis, 2022), a new dataset (WSF3Dv2) is generated with detailed information on the area, height, and volume of the building stock worldwide today. Since the data does not rely on local administrative data, the low data capacity of less developed economies does not constrain our analysis. At the same time, our data is most useful where alternative sources of data are limited, which is the case of poorer economies.

This research derives information on building area and height with a geometric resolution of 12m*12m with global coverage. Biases in terms of income status (e.g., from over-relying on data from developed economies), geographic region (e.g., driven by selection of sample regions) or settlement type (e.g., megacities) are avoided and completeness, representativeness, and general validity of the analyses and findings are assured. To meet requirements of German data security regulations (Palacios-Lopez et al., 2021) and for an open dissemination of the novel WSF3Dv2 data and derived results, all outcomes are finally provided in the form of zonal statistics (building area, building height, and building volume) aggregated to a grid of 90m*90m.

We then use the data to investigate the role of economic development in construction. National building stocks per capita increase convexly with income. Small differences are observed between low-income and lower-middle-income economies and it is only when countries become upper-middle-income economies (i.e., reach a per capita GDP of _∼_ $4,000) that space consumption per capita significantly increases with income. Next, we rely on the globally estimated volume-income relation to quantify global construction needs.

Developing nations in Asia and Latin America & the Caribbean (LAC) respectively account for _∼_ 60% and _∼_ 20% of _current_ global construction needs (South Asia explains two-thirds of developing Asia’s gap). African nations do not have large construction gaps because they have low incomes, and little variation in space consumption per capita is observed at such incomes.

Developing Asia then accounts for about 75% of _future_ , growth-driven global construction needs when considering a horizon of five years. In developing Asia, the effects of population growth and income growth compound each other. African nations, having low incomes and low economic growth rates, do not appear prominently in the rankings despite their fast population
3 growth (developing LAC’s contribution is also small). Lastly, focusing on future construction needs by 2050, and only taking into account population growth, developing Africa, Asia and LAC now respectively account for _∼_ 50%, _∼_ 25% and _∼_ 5% of _current_ global construction needs.

We then use the data to unpack how outward construction (building area) and upward construction (building height) account for the volume-income relation observed globally. We find that vertical expansion is the main driver of international volume differences, as it accounts for _∼_ 60% of the global volume-income relation, including in the developing world. Low-rises below 50 m, not high-rises, then account for _∼_ 90% of the contribution of upward construction.

Given that urban residents consume less space per capita than rural residents, urbanization should tend to reduce per capita consumption, and thus cannot account for the higher levels of space consumption in more developed economies. We find that rural areas & small towns differ more across countries in terms of volumes than urban areas do, as a result of which rural areas & small towns explain _∼_ 60% of international volume differences. Lastly, upward construction and low-rises drive international volume differences in both types of areas.

Finally, we employ residualization procedures to classify large countries and cities with similar levels of economic development into pro-heights vs. pro-area and pro-high-rises vs. prolow-rises for their heights. Asian nations and megacities are more pro-heights than African or LAC nations and megacities. LAC is more pro-high-rises for its heights whereas Africa is more pro-low-rises. Asia has a more balanced height distribution. Eastern Europe is more pro-heights than Western Europe or North America (they are all pro-high-rises for their heights).

Policy-wise, the results suggest that: (i) economic development does not fully explain international volume differences, as one-third of volume differences can be attributed to other factors, which likely include land use regulations such as height restrictions and urban containment policies (e.g., greenbelts and urban growth boundaries); (ii) land-use regulations are likely not as consequential in lower income countries where little variation in space consumption levels are observed; (iii) existing land-use regulations may become more binding in the future as some regions of the world keep experiencing fast population growth, including Africa and South Asia; (iv) countries and cities with similar income levels vary in their upward vs. outward specializations, suggesting again an important role for height restrictions and urban containment policies; and (v) meeting construction needs could have important environmental implications because the construction sector accounts for _∼_ 40% of carbon emissions (UNEP, 2022). Likewise, a nation’s or city’s outward or upward specialization could have environmental implications if sprawl or skyscrapers disproportionately produce carbon emissions (e.g., either because of gasoline cars or the construction materials used) (The World Bank, 2023b).

In addition to literature on how construction patterns vary across world regions, countries,
4 and cities, we contribute to literature on the characteristics of the urbanization process globally, and in the developing world in particular. Urban areas only account for _∼_ 40% of global volumes and international volume differences. Given that urban residents typically consume less space per capita than rural residents, urbanization should reduce space consumption per capita. At the same time, many nations and cities have low levels of space consumption per capita, implying that they may need to build more vertically and/or horizontally. Studies have shown how historically crowded the cities of many developing countries are (Castells-Quintana, 2017; Jedwab et al., 2017; Jedwab and Vollrath, 2019). Many developing countries are also “urbanizing without growth” (Fay and Opal, 2000; Fox, 2012; Jedwab and Vollrath, 2015; Gollin et al., 2016; Fox and Goodfellow, 2016; Castells-Quintana and Wenban-Smith, 2020). At the same time, meeting global construction needs could have dramatic environmental consequences. There are thus trade-offs between promoting housing affordability and ensuring livability/sustainability.

There is then the question of whether it is more optimal to meet construction needs by building upward or outward. Verticality is associated with compact and economically dense cities (Lall et al., 2021; Ahlfeldt et al., 2023; The World Bank, 2023b), which favors economic efficiency and innovation as shown by a large literature on agglomeration economies (Duranton and Puga, 2004; Castells-Quintana and Royuela, 2014; Combes and Gobillon, 2015; Chauvin et al., 2017; Duranton and Puga, 2020). Horizontality produces sprawl and congestion (Duranton and Turner, 2011; Jedwab et al., 2022; Akbar et al., 2023). However, the skyscrapers of many developing countries constitute white elephant projects that are economically and environmentally inefficient (Gjerlow and Knutsen, 2019; Ianchovichina et al., 2022; Jedwab and Roberts, 2023). Finally, nations and cities of similar income levels can differ in their specialization in heights or areas. These specializations likely reflect differences in land-use regulations and institutions more broadly, as shown by studies on individual regions, countries, cities (Brueckner and Sridhar, 2012; Fox, 2014; Brueckner et al., 2017; Brueckner and Singh, 2020) or skyscrapers globally (Jedwab et al., 2022; Jedwab and Barr, 2023b,a). We instead consider the whole building distribution.

# **2. World Settlement Footprint 3D: From Version 1 to Version 2**

The first version of the World Settlement Footprint 3D (WSF3Dv1) dataset, released in 2017, provides information on the building fraction (BF), height (BH), and volume (BV) at 90 m spatial resolution (Esch et al., 2022). WSF3Dv1 was created based on a global coverage of 12 m digital elevation (TDX-DEM) and Synthetic Aperture Radar (SAR) data (TDX-AMP) collected by the TanDEM-X satellite mission in 2012-2013 (Zink et al., 2014), in combination with 10 m resolution multispectral Sentinel-2 (S2) satellite imagery. Although the analyses are performed at a gridding of 12 m, the final WSF3D products can only be made publicly available with a reduced resolution of 90 m due to German data security regulations (SatDSiG) related to the TanDEM-X mission.
5 The WSF3Dv1 analysis framework introduced by Esch et al. (2022) consists of three automated processing modules: a first workflow defines the building fraction (BF) within each 90 m grid cell based on TDX-DEM, TDX-AMP, and S2. The second module analyzes height differences occurring along building edges in the TDX-DEM elevation data to derive the average building height (BH) at 90 m gridding. A last processing workflow combines the previously derived BF and BH information to calculate the building volume (BV).<sup>1</sup> To determine the building fraction BF, the temporal maximum of the Normalized Difference Vegetation Index (NDVI ~~m~~ ax) is calculated for all WSF2019 pixels from a time series of _∼_ 2.27 million S2 granules with _<_ 60% cloud cover (level 2A, bottom of the atmosphere reflectance) acquired in 2018-2019 (Marconcini et al., 2020). Using NDVI ~~m~~ ax and building footprint data from OpenStreetMap (OSM, 2017), an ensemble of support vector regression models is trained separately for all K ̈oppen-Geiger climate zones to estimate the BF for each WSF2019 settlement pixel.<sup>2</sup> The resulting information on BF (%) can be employed to define the total building area BA (m<sup>2</sup> ) of each cell by applying BF as a multiplication factor to the cell’s 12*12 m ground area.

The generation of the building height (BH) product is based on analyzing local height differences at vertical edges (VE) in the 12 m resolution TDX-DEM within the settlement area of WSF2019. In the TDX-DEM, VEs appear as distinct punctual or linear height variations along the outlines of quasi vertical structures such as buildings, walls, trees, or hedgerows. A given pixel in TDX-DEM is considered as a VE candidate if the ratio between the height of the target pixel (above sea level) and the median height (ditto) in its immediate neighborhood (within a 5 x 5 moving window) is _>_ 1.0 (Esch et al., 2022). Since the natural slope of the local terrain also leads to height differences, the slope-induced height differences are factored out by normalizing the measured local edge height VE with the local slope of the terrain. The terrain slope is measured by first removing all local maxima and vertical edges (TDX-DEM pixels where VE _>_ 0.0) before filling the resulting local gaps in the TDX-DEM elevation data with a four-direction conic search distance weighting (Esch et al., 2022). This generates an edge-smoothed version of the TDXDEM that only shows height differences due to the local terrain, whereas previously included height structures in the original TDX-DEM that arose from local vertical objects are now leveled in. By subtracting the edge-smoothed version of TDX-DEM from the original TDX-DEM, the effect of slope-induced height differences is minimized so that the resulting VE layer only shows

> 1Note that all analyses are exclusively carried out for areas assigned as settlement by the World Settlement Footprint 2019 (WSF2019) human settlements mask (Marconcini et al., 2021).

> 2 Empirical tests with a WSF settlement mask and WSF-IMP layer generated on the basis of 30 m Landsat data collected in 2012 (meaning the exact time of the TDXDEM data acquisition) clearly indicated the superiority of the WSF mask and WSF-IMP information derived from the 10 m S2 data (not yet available in 2012), although the imagery was collected in 2019. Indeed, the WSF2019 settlement mask, although including additional settlement areas that arose between 2012 and 2019, still shows a higher accuracy compared to the settlement mask derived from the coarse 30 m Landsat imagery. Moreover, the imperviousness estimation at 10 m based on NDVI ~~m~~ ax from 2019 S2 data led to a more precise masking of urban green spaces compared to the results obtained from Landsat.
6 the actual height variations along local vertical structures. Since VE can still include vertical vegetation structures such as trees or hedges, all VE-candidate pixels dominated by vegetation are masked out. For this purpose, an ensemble of support vector regression models is trained separately on the NDVI ~~m~~ ax layer for all K ̈oppen-Geiger climate zones to estimate the percent impervious surface (IMP) within each WSF2019 pixel. Based on the resulting WSF-IMP, all VE candidate pixels showing a value _<_ 10 (meaning that more than 90 % of the pixel area is covered by vegetation) are masked out. To produce the final BH product, all local height differences observed for the remaining VE pixels are then spatially aggregated from their 12 m resolution to a 90 m cell by calculating the mean of all VE heights observed within this cell.

As reported in Esch et al. (2022), the BH layer of the WSF3Dv1 shows certain inaccuracies due to the systematic underestimation for the heights of high-rise ( _>_ 50 m) buildings. In dense, high-rise areas, complex and compact morphological structuring leads to multiple scattering, layover, and shadow effects causing ambiguities in the SAR signal, which ultimately results in errors in the absolute heights provided by TDX-DEM.

Thus, information from Emporis (EM) for the year 2019 is now integrated to create an enhanced version of World Settlement Footprint 3D (WSF3Dv2). EM is the most complete collection of global skyscraper and high-rise building data (see Appendix Section B for details). They rely on information provided by the industry for “thousands of cities worldwide. Emporis (2022) collects information about the full life-cycle of each building. The database (last accessed 09-07-2022) contains information for 781,136 completed tall buildings.

Technically, the improvement of the BH layer is based on a correction factor (fxy) calculated using the relative differences between spatially overlapping BH values derived from WSF3Dv1 (BHv1), and EM building height values (BHEM) provided for the exact geographical coordinates of all buildings as defined in eq. (1) and (2): The application of a 90% adjustment factor f _xy_ (instead of directly using the EM-provided height at the xy location) is dictated by the need to prevent the original, license-protected EM information from being reconstructed from the resulting BHv2 layer.

In a second processing step, EM is also used for BH outlier detection and removal. As EM is supposed to be globally complete for all buildings _>_ 100 m (see Appx. Section B), BHv1 pixels showing a BH _>_ 100 m and not having any EM point in a 3x3 neighborhood (BHv1xy _∈/_ EM), are considered as outliers. However, as the WSF2019 settlement mask indicates the presence of buildings at this location, the actual BH value is not completely removed, but drastically reduced by applying an adaptation factor of 0.01 to the current BH value as shown in eq. (3):
7 ( _BHv_ 2) _xy ∈/ EM_ = 0 _._ 01 _∗_ ( _BHv_ 1) _xy ∈/ EM ⇒_ ( _BHv_ 2) _xy ∈/ EM >_ 100 _m_ (3) Next, for BH pixels showing a height between 50-100 m without an EM point in their vicinity (meaning here, EM is still supposed to be reasonably complete), we assume that BH is overestimated because otherwise EM should indicate the presence of a high-rise. In this case, the BHv1 value is reduced by 90% of the difference between the current BHv2 value and a fixed virtual height of 50 m (see eq. (4)). The 50 m height is used because it represents the empirically determined completeness threshold for tall buildings in EM (see Appx. Section B): ( _BHv_ 2) _xy ∈/ EM_ = ( _BHv_ 1) _xy ∈/ EM_ +0 _._ 01(50 _−BHv_ 1) _xy ∈/ EM ⇒_ 50 _m <_ ( _BHv_ 2) _xy ∈/ EM >_ 100 _m_ (4) In order to generate the new building volume product BVv2 (m<sup>3</sup> ), the BHv2 building heights are merged with the building areas given by BAv1. See eq. (5).

The improvements in BH achieved by integrating EM are documented by a comprehensive global validation campaign (see Appx. Section A for details). The WSF3Dv2 data can be accessed free and open at: https://geoservice.dlr.de/web/maps/eoc:wsf3d. Likewise, the replication files for the analysis and the country- and city-level data sets can be found here: https://doi.org/10.7910/DVN/TQ1AS5.

In Figure 1 below, this improvement can be observed in Manhattan by comparing the BH (building height in m) layer of the original WSF3Dv1 (top-right panel B) and the EM-improved WSF3Dv2 (bottom-left panel C). The top-left panel A shows the BA (building area in m<sup>2</sup> ) layer, whereas the bottom-right panel D shows the BV (building volume in m<sup>3</sup> ) layer. Redder pixels have more buildings (A), taller buildings (B-C), or more voluminous buildings (D).<sup>3</sup> Figure 2 illustrates the distribution of WSF3Dv2 heights for selected areas. Redder bars indicate a higher frequency of taller buildings. Asia has more tall buildings than Africa and Latin America, and Europe has more tall buildings than North America. China has taller buildings than the U.S. India has almost as many tall buildings as the United Kingdom. Seoul appears as tall as New York. Bogota, Cairo, Karachi, Paris, and Lagos are relatively flat.

3Appendix Figures C.1 and C.2 show the maps for some of the world’s largest cities and at global scale, respectively.
8 Figure 1: Building Area, Height and Volume for New York City’s Region, 2012/2019 _Notes:_ The figure shows New York City’s region in WSF3D (90m*90m resolution). Building area is in m<sup>2</sup> (A). Height is in m in WSF3Dv1 (B) and WSF3Dv2 (C). WSF3Dv2 volume is in m<sup>3</sup> (D). Data is for the year 2012/2019.
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10

# **3. Background**

The total global building volume equals 1,593 billion m<sup>3</sup> ( _∼_ 1.52 million Empire State Buildings), resulting from a total building area of _∼_ 300,000 km<sup>2</sup> and a mean height of _∼_ 5 m. We obtain 1,558 billion m<sup>3</sup> in WSF3Dv1, implying that it missed 2% of global volumes. WSF3Dv2 mostly improves upon WSF3Dv1 for cities, where WSF3Dv1 missed 5% of global volumes (we get 9% for cities above 5 million today). Indeed, WSF3Dv1 disproportionately missed high-rise buildings and skyscrapers typically found in cities. This holds as well in the developing world where the same missing shares are 2%, 4%, and 8%, respectively. Focusing on cities, the volume discrepancy between WSF3Dv2 and WSF3Dv1 is then larger for the developing economies of Latin America & the Caribbean (LAC) (7%) than in developing Asia (3%) or Africa (1%).

Regional statistics from WSF3Dv2 are provided in Table 1. Developing economies account for two-thirds of global volumes. Upper-middle, lower-middle, and low income economies account for 70%, 25%, and 5% of total volumes in the developing world, respectively. Africa accounts for 9% of global volumes despite comprising almost 18% of the world’s population.

Table 1: Selected summary statistics for several groupings of countries, 2012/2019

|Economies|Volume km<sup>3</sup>|Per Cap. m<sup>3</sup>|% Outward|% Upward|% Low-Rise|% High-Rise|
|---|---|---|---|---|---|---|
|World|1593|207|52|48|46|2|
|Developed|577|467|43|57|53|4|
|Developing|1016|157|54|46|45|1|
|High-Income|577|467|43|57|53|4|
|Upper-Middle-Inc.|705|246|46|54|52|2|
|Lower-Middle-Inc.|254|87|59|41|40|1|
|Low-Income|55|83|68|32|32|0|
|Africa|148|113|65|35|35|0|
|Asia|749|164|50|50|48|2|
|Europe|372|498|43|57|55|2|
|Latin America & Carib.|115|177|54|46|43|3|
|North America|193|526|47|53|51|2|
|Pacifc|16|375|54|47|45|2|

_Notes:_ This table shows summary statistics for four groupings of countries. Developed Status is based on the World Bank (WB)’s classification of countries in 2019 (= high-income economies). Outward volume = built area x 2.5m. Upward volume = volume - outward volume. High-rise volume = from high-rises ( _≥_ 50 m). Low-rise volume = from low-rises (between 2.5m and 50m).

In general, the mean volume per capita in the world is 207m<sup>3</sup> . Assuming housing accounts for half the building stock and a ceiling height of 2.5m, the average resident occupies 40m<sup>2</sup> . But volume per capita in low- (LIC), lower-middle (LMIC), upper-middle (UMIC), and high-(HIC) income countries is 83, 87, 246, and 467m<sup>3</sup> , respectively. Thus, the average resident in LICs, LMICs, UMICs, and HICs possibly occupies 17, 17, 49, and 94m<sup>2</sup> of living space.
<!-- Start of picture text --> Upward Volume High-rises (>50m)<br>Total_Volume - Outward_Volume<br>Multi-Story<br>Low-rises (2.5m<H<50m)<br>Outward-volume<br>Single-Story | Building Area *2.5m<br>Building Area Building Area Building Area<br><!-- End of picture text -->
<!-- Start of picture text --> ro)<br>ro)<br>- LICs & LMICs | UMICs & HICs RURAL & TOWNS<br>cm | ——> ,<br>—/<br>a< //OVERALL<br>4 4<br>a. § / c<br>” / ¢<br>dd / 4<br>oo / ft CITIES7<br>i POL DE, ? 7<br>o © ae ¢<br>= 7. Y a<br>2 4. USAF 7<br>2 nuh ;Lions “v<br>& o ptsegeeFRA77 MEGACITIES<br>og UKR Ke oe KOR GBR<br>re) 7 Y- -<br>re 70 7 OPN <<br>2 UZB CHN° THA ve ara#& “5~7 (SAU<br>© ZA as EMS < ~<br>=aES Z7; Fae TUR ARG<br>S ~ Moz TZA Moy:VEN. AP>ay “BRAPER IRN<br>cop ~~ SGA — oaaeIND minm ION cot<br>oO a<br>7 8 9 10 11 12<br>Log per capita GDP (cst 2017 intl dol, PPP)<br><!-- End of picture text -->
<!-- Start of picture text --> Oo<br>oOoO 7<br>_ Western EuropeQ<br>€ (o) Australia/New Zealand? °<br>= Oo > North America<br>5 / Eastern Europe® Yo &<br>o Southern Europe? Northern Europe<br>g S Fa<br>o> y<br>E 7<br>aS) ¢<br>Do OCentral Asia Yo<br>ne) 7<br>—©7~ Eastern Asia 7<br>=Southern Africa 7<br>eo- oOS South ponéfica“ogyy Western“.<br>a. Northern Africa ~ Caribbean Central America<br>2 4 Western Africae OA<br>= r=) ou Afric? ooo South-Eastern Asia<br>3 — OEastern Africa = ~ .<br>S$ —_—_—--- o O Southern Asia<br>Melanesia<br>oO<br>7.5 8 8.5 9 9.5 10 10.5 11 11.6<br>Log per capita GDP (cst 2017 intl dol, PPP)<br>O Africa O Asia-Pacific 4 LAC © Other<br><!-- End of picture text -->
<!-- Start of picture text --> Switzerland<br>Saudi Arabia<br>Israel<br>Chile<br>Colombia<br>Dominican Rep<br>Sri Lanka<br>Turkiye<br>Costa Rica<br>Japan<br>Argentina<br>United Kingdom<br>Malaysia<br>Mexico<br>Philippines<br>Indonesia<br>Cuba<br>Iraq<br>Peru<br>Egypt<br>0 50 100 150 200<br>Per capita volume need 2019-2025 (cubic m per cap)<br><!-- End of picture text --> <!-- Start of picture text --> India<br>Indonesia<br>Japan<br>Mexico<br>Turkiye<br>Philippines<br>Bangladesh<br>Pakistan<br>Colombia<br>Brazil<br>Egypt<br>Saudi Arabia<br>United Kingdom<br>Argentina<br>Iran, Islamic Rep.<br>United States<br>Korea, Rep.<br>lraq<br>Malaysia<br>Sri Lanka<br>0 10 20 30 40 50 60<br>Total volume need 2019-2025 (billion cubic m)<br><!-- End of picture text -->
15 In per capita terms, the list includes many MICs (Argentina, Colombia, the Arab Republic of Egypt, Indonesia, Mexico, and T ̈urkiye). Focusing on total volume, the list is dominated by populated developing economies with large per capita needs (India, Indonesia, Mexico, T ̈urkiye, the Philippines, Bangladesh, Pakistan, Colombia, Brazil, and Egypt). LICs are absent from the lists as there is less variation in volumes per capita at low income levels than at intermediary income levels.

Only considering developing economies below the line, the mean per capita gap is 24 m<sup>3</sup> in Africa, 47 m<sup>3</sup> in Asia, and 65 m<sup>3</sup> in LAC (respectively 5 m<sup>2</sup> , 9 m<sup>2</sup> , and 13 m<sup>2</sup> assuming a housing share of 50% and a 2.5. m ceiling height). However, for total volume needs, we get 15 billion, 125 billion, and 36 billion m<sup>3</sup> , respectively. More generally, developing Asian economies account for _∼_ 60% of the world gap (vs. 17% for developing LAC and 7% for Africa), with South Asia explaining two-thirds of developing Asia’s gap, and India contributing to _∼_ 70% of South Asia’s gap. India might need to build 54 billion m<sup>3</sup> , more than half of its current stock. For Indonesia, it is 20 billion m<sup>3</sup> , one-third of its current stock. Globally, bridging the gap would increase stocks by _∼_ 14%.

However, other factors could affect the economic, social, and environmental “optimality” of construction patterns. Bridging the gap could have dramatic effects on the environment, given the building sector accounts for 39% of carbon emissions worldwide (UNEP, 2022). Meeting the estimated global needs would increase global carbon emissions by _∼_ 5%, implying trade-offs between promoting housing affordability and ensuring livability/sustainability.

# **4.3. Quantifying Future Global Construction Needs**

**4.3.1. Forecast until 2025**

The forecast of future, growth-driven construction needs is a crucial tool in view of a fasturbanizing world and unaffordable cities (UN Habitat, 2020; The World Bank, 2023b). With estimates of the future population and income of a country, we can quantify by how much the country’s volume must increase to match global construction trends. From the estimated quadratic fit in Figure 4, we obtain coefficients _α_ (2,209***), _β_ (-580***) and _γ_ (39***) in eq. (6): _V olume/Population_ = _α_ + _β ∗ log_ ( _GDP/Population_ ) + _γ ∗_ ( _log_ ( _GDP/Population_ ))<sup>2</sup> (6) Using data from the World Bank (2019), we obtained the predicted real GDP growth rate of each country in 2019-2022. We consider countries from the viewpoint of 2019, thus ignoring the unrelated economic effects of the COVID-19 pandemic. Using the average annual growth rates in 2019-2022, we estimate each country’s GDP in 2025. From the United Nations (2019), we obtained each country’s predicted population in 2025 (ignoring COVID-19 mortality).<sup>5</sup> Equation (6) is used to estimate how Volume/Population may need to change as

> 5The COVID-19 pandemic could reduce construction needs by increasing mortality and depressing economic growth. However, the remote work revolution has dramatically increased housing demand.
16 GDP/Population is changing between 2019 and 2025. Likewise, given that we know how population is predicted to change by 2025, we obtain the total volume change needed.
<!-- Start of picture text --> Maldives<br>China<br>Poland<br>Romania<br>Mongolia<br>Panama<br>Vietnam<br>Hungary<br>Armenia<br>Dominican Rep<br>India<br>Bulgaria<br>Mauritius<br>Malaysia<br>Bosnia<br>Philippines<br>Turkmenistan<br>Bhutan<br>Georgia<br>Ukraine<br>0 10 20 30 40 50 60<br>Per capita volume need 2019-2025 (cubic m per cap)<br><!-- End of picture text --> <!-- Start of picture text --> China<br>India<br>Indonesia<br>United States<br>Bangladesh<br>Egypt<br>Philippines<br>Vietnam<br>Brazil<br>Pakistan<br>Mexico<br>Russia<br>Thailand<br>Turkiye<br>Nigeria<br>Colombia<br>Germany<br>Kenya<br>Poland<br>Malaysia<br>0 25 50 15 100<br>Total volume need 2019-2025 (billion cubic m)<br><!-- End of picture text -->
18 Figure 7 lists the top 20 economies in terms of future, growth-driven construction needs. In per capita terms, the list includes fast-growing economies in Asia (China, Viet Nam and India), Eastern Europe (Poland, Romania and Hungary) and Latin America (Panama and the Dominican Republic). Focusing on total volume, China, India, Indonesia, Bangladesh, the Philippines and Viet Nam dominate the list. LICs are missing from the list because they were not as of 2019 forecasted to grow fast in terms of per capita GDP, or at least not fast enough to allow enough of these nations to pass the cut-off at which volumes per capita increase with incomes.

Developing Asia accounts for 77% of future global construction needs vs. 8% for Africa and 5% for Latin America. China alone might need to build 100 billion m<sup>3</sup> (3% of its current stock). Given their high income growth _and_ population growth, India and Indonesia might need to increase their current stock by 8% (77 billion m<sup>3</sup> ) and 6% (15 billion m<sup>3</sup> ), respectively. In both countries, the effects of fast income growth and fast population growth compound each other. Other large economies with significant future needs are Bangladesh (14% of its current stock), the Philippines (10%), Egypt (5%), Viet Nam (5%), and Pakistan (4%). In contrast, the U.S. might need to increase its stock by 1% only. However, that is high in absolute terms (14 billion m<sup>3</sup> in the U.S. vs. 15 billion m<sup>3</sup> in Indonesia), since the U.S. has a large building stock to start with.

Noticeably, the rankings are barely affected if we only consider the effects of income growth (not shown). That is because income growth is what is driving future construction in that exercise. Indeed, countries with the highest population growth rates today are low-income countries characterized by sluggish income growth rates. In addition, given the non-linearities seen in Figure 4, economic growth may not increase per capita volumes for LICs and LMICs.

Lastly, meeting the predicted needs would increase global carbon emissions by _∼_ 8%.

**4.3.2. Forecast until 2050** We obtain each country’s predicted population in 2050 (United Nations, 2019) and predict total construction needs by 2050. Not knowing future incomes, we cannot forecast construction needs per capita. We also ignore any potential impact of population growth/decline on per capita incomes, hence per capita volumes (which we take as given as of 2019). Figure 8 lists the top 20 economies in total needs. It includes many African LICs and LMICs with fast population growth (Nigeria, Tanzania, the Democratic Republic of Congo, and Mozambique). However, the list also includes LMICs and UMICs whose population is not growing as fast but whose volume per capita is higher given the higher incomes there (India, Egypt, Indonesia, and Mexico). Finally, the list includes developed economies with non-nil population growth and high volumes per capita (U.S., Canada, and Australia). Thus, population growth has larger effects when average consumption levels are higher, which may offset the fact that richer nations have slow population growth.

Africa, predicted to account for 58% of global population growth by 2050, now makes up 48% of future global construction needs vs. 26% for developing Asia (7% for developing LAC). Meeting
<!-- Start of picture text --> United States<br>Nigeria<br>India<br>Tanzania<br>Congo, Dem. Rep.<br>Egypt<br>Pakistan<br>Indonesia<br>Mexico<br>Mozambique<br>Angola<br>South Africa<br>Canada<br>Australia<br>Sudan<br>Iran, Islamic Rep.<br>Syrian Arab Republic<br>Brazil<br>Zambia<br>Mali<br>0 25 50 75 100 125 150 175 200 225 250<br><!-- End of picture text --> Total volume need 2019-2050 (billion cubic m)
<!-- Start of picture text --> LICs RURAL & TOWNS<br>& LMICs UMICs & HICs 7<br>——— ———-> /<br>/<br>e re)fo) //<br>coc // OVERALL<br>7 7 ¢<br>oO ¢<br>roe 4 ¢<br>E 4 ¢<br>low 7 ¢<br>a Rou / 2 ¢?<br>3s 8 )% _(USA34<br>a7 /. dEUcAy% CITIES<br>© & FRA ¢ 7<br>° RUSS“ o” o<br>2 028 - SATA <<br>a. UKR 7 ¢ o”<br>o© ZAR) ” 7 “6p 27 ~MEGA-CITIES-<br>raeo THAy& eo0 JPN 4 a o*<br>go ro) 7 ¢ = sau 2<br>~3 Moz aux SHIN7IREwy ARS="-7KoR = “*<br>‘3 ~ TZA SDN VEN@ aa ~~ “MYSL =<br>a . ~ >~ ~ S22 ae AGS oF DZA oo TURS - -<br>we Le Nea heen<br>con) = ssy LGA ue THT KENPAliyny © -MARhaL6G AON —_Cou Pod<br>ETHAFGYEM NPL gg) PHL<br>ro)<br>7 8 9 10 11 12<br>Log per capita GDP (cst 2017 intl dol, PPP)<br>=<br>2 HKG, MAC A<br>LICs & LMICs UMICs & HICs<br><—_——. ——————> KOR<br>os eet Ts x MEGA-CITIES<br>- eecccn<br>E © 7 —-— CITIES<br>— 7 7 = - --<br>x ¢ oc7<br>2 Yo - -<br>2 Vv<br>D / ) 4 “ecy MysTuR ) SR Gey OVERALL=<br>< 7 77 | CHN Seer" -<br>oa=5 Oo y Z oeMAR “RUSwwVsJPN sauUsm\e= & = -<br>®fo) /-yem/ cb Z NaCOLn * PD cake =RURAL-TOWNS<br>>© 77 y;Wr PHL.RO gy opmnPER BRAIRN@ THA Loe Sen ‘AN<br>oO yy 2 Wn VE yar<br>g cob 7 7” MMR) ie © IDN Bs<br>av YF79-AGao”_GHA>NealeINDRET eoIRQ Meg ARG<br>MOZ (EB etca KEN ; )UZB ZAR<br>-sof iAFG)me TZA PAK AGO.<br>“529<br>oe” Y SDN<br>7<br>N 7<br>7 8 9 10 11 12<br>Log per capita GDP (cst 2017 intl dol, PPP)<br><!-- End of picture text -->
<!-- Start of picture text --> ro)<br>ro)<br>©<br>‘/<br>& © )<br>oO<br>~S)<br>A<br>= ro)<br>; ‘<br>we) y<br>38<br>x+<br>= .<br>uu foo) ;<br>gS ye<br>e S ye<br>;a: en unannneneeee 1awewe [ol<br>, 9 10 44 5<br>Log per capita GDP (cst 2017 intl dol, PPP)<br>meneeenn! Outward === Outward + Upward - High-Rises === All<br><!-- End of picture text -->
22 respectively. In developing economies, changes in areas and heights similarly explain _∼_ 40% and _∼_ 60% of total volume differences, respectively. Therefore, vertical expansion is the main driver of international volume differences, both globally and in the developing world.

Low-rises and high-rises account for 93% and 7% of the upward volume-income relation, hence 60% and 5% of the total volume-income relation (we find similar patterns in developing economies). The volume added by high-rises is only 2%-3% in LAC and Asia and 0% in Africa (Table 1). While high-rises may visually appear as driving verticality globally, low-rises ( _<_ 50m) dominate construction patterns worldwide. This suggests that policies constraining low-rise development are more consequential than policies related to land expansion or highrise development. Also, low-rises have the added advantage that they are more likely to house the middle-class, whereas high-rises may more specifically cater to the needs of the wealthy.

Lastly, LAC and Asian buildings both provide _∼_ 50% more volume per capita than African buildings. However, LAC does so by providing more outward volume (+30% than Africa vs. +1% for Asia) whereas Asia uses more upward volume (+125% than Africa vs. +105% for LAC). The fact that world regions use various ways to provide space to their residents leads us in the next subsection to study the upward vs. outward specialization of countries and regions. Note that this specialization is obtained conditional on income, and thus does not address the role of the development process in construction. Instead, it asks, how is the space of a country provided relative to other countries with similar income levels. Policy-wise, this informs us on the type of settlements found in a country, which has economic, social, and environmental implications because outward expansion implies less compact settlements. Outward expansion may then be due to stringent height restrictions and/or public investments in transportation infrastructure (since lower commuting costs in a locality tend to decentralize its population patterns).

**5.2. Upward versus Outward Specializations**

We proceed in several steps for this analysis. First, outward volumes are residualized with respect to log per capita income, capturing whether a country provides a lot of area per capita given its income level. Second, upward volumes are residualized with respect to log per capita income, capturing whether a country provides a lot of height per capita given its income level. Overall, countries with higher area residuals have higher heights residuals (countries with “good” areas have “good” heights). Third, the upward volume residuals are residualized with respect to the outward volume residuals, with the resulting residuals indicating how relatively more pro-heights or pro-area the country is, given its income level and other similar countries’ specializations. Fourth, the final residuals that we estimate indicate whether a country is relatively pro-high-rises or pro-low-rises for a given income level (using the same procedure as for areas and overall heights). See Appx. Section C1. for details on these procedures.

Figure 12 plots the pro-high-rises/low-rises residuals against the pro-heights/area residuals. Nations in Asia (China and the Republic of Korea), Eastern Europe (Poland and the Russian
<!-- Start of picture text --> ° Va<br>| RUS KOR<br>o CAN |<br>2 BRA DEU<br>we GBR UPA |cPoL UKR<br>a! FRA JPN COL | ESP) TUR<br>iS ARG THA |<br>—fe) - VNM \ PHL<br>a. MEX | ITA CHN<br>(o>) ZAFee ee ee ee ee ee LC| ra<br>ON IND) |<br>N KEN<br>oO ~ IRN Dz MMFOX Yep<br>aI TZA | ey<br>s R<br>7j IRQ | MA<br>Oo PAK |<br>o NGA ETH|<br>SDN COD<br>oY AFG UGA | \<br>-.5 -.25 0 .25 ie)<br>Pro-Area Pro-Heights<br><!-- End of picture text -->
<!-- Start of picture text --> (7p) Sten QNorth America ' Eastern Europe<br>@ N wnt eee eaes, > estern Europe<br>rnd Australia/NewZealand Northern Eugope = T" ""oneeay P<br>< South America |<br>D> — Southern Europe<br>a7 | ° Eastem Asia<br>o =* _ South-Eastern Asi<br>7 Central Americas e777 oa ] aren S12 —_—'<br>oo ie) sutiem Aca et =”— — — — — WestenWester AsiaOAsia ee —_—2 __ __ ___ —<br>—_<br>Central Asia Ths = O Southern Asia<br>ow Caribbean |<br>D . OMelanesia<br>a orthern Africa, |<br>syI |<br>9S Eastern Africa °<br>e |<br>Oo «6 O Western Africa Middle Africa<br>' | 0<br>-.5 0 ne)<br>Pro-Area Pro-Heights<br><!-- End of picture text -->
25 pro-heights likely suggests looser height restrictions there.

# **6. The Influence of Urban and Rural Areas as Countries Develop**

We just found that upward construction and outward construction respectively account for 60%-65% and 40%-35% of international volume differences, with the contribution of upward construction almost entirely driven by low-rises. Since countries simultaneously urbanize as they develop, and since urban areas differ from rural areas in many dimensions, we investigate how construction patterns depend on urban status. We first show that low-rises and high-rises more strongly explain volume differences across world cities than across countries. This leads us to examine if cities drive international volume differences across countries. However, we find that rural areas and small towns, not cities, disproportionately influence the distribution of volume per capita at a global scale. Medium to small cities, not large cities, then dominate total urban volumes. More generally, we discuss how urbanization is not the primary factor underlying the building stock-income relation observed across countries. Finally, we use our city-level analysis to study the upward vs. outward specializations of selected urban systems and world megacities.

**6.1. International Volume Differences across Cities**

Our definition of _urban areas_ includes 12,831 cities above 50,000 people in 2015 as identified by GHS-UCDB (Florczyk et al., 2019). Therefore, in our analysis, _rural areas_ include small towns and villages below 50,000 people in 2015. Table 2 shows selected summary statistics for urban vs. rural areas. Comparing Tables 2 and 1, the volume per capita added by building upward makes a larger difference at the city level than at the country level. For example, upward building accounts for 55% of total city volumes as compared to 48% at the country level.

Similarly to what we found at the country level, city volume per capita increases with city incomes (Appx. Section C2.-C4. and Appx. Fig. C.3).<sup>6</sup> Using the same regression analyses as before, heights explain between two-thirds and three-fourths of the global city volume-income relation (we found 60%-65% at the country level) (Appx. Section C5. and Appx. Fig. C.4-C.6 for the scatterplots). Low-rises and high-rises account for _∼_ 90% and _∼_ 10% of the upward volumeincome relation, hence 65% and 10% of the total volume-income relation (25% for areas). At the country level, lower contributions of 60% were found for low-rises and 5% for high-rises. Lastly, we find very similar patterns and differences considering developing economies only.

Hence, upward construction appears relatively more important for cities than for rural areas. Combined with the fact that more developed economies are also more urbanized, this could

> 6We use the 2015 city GDP data from Chen et al. (2022) who provide high-resolution “real GDP” data (in 2017 dollars) based on (not top-coded) night lights data as reported by the NPP/VIIRS satellite series. While night lights data could capture infrastructure (including electrification) and past economic development in addition to current economic development as infrastructure and urban structures are durable, we use this data in the absence of better data on city incomes for the whole world. Nonetheless, the city-level results should be taken with caution.
26 explain why upward construction disproportionately explains international volume differences. However, we actually find the opposite as described in the next subsection.

# **6.2. Volumes from Urban Areas versus Rural Areas**

Urban areas account for 48% and 42% of the world’s population and volume. Therefore, rural areas comprise 52% of the world’s population _but_ 58% of the world’s volume (Table 2). This is due to cities being more compact, i.e. spatially efficient, than rural areas (193 and 238 m<sup>3</sup> per resident, respectively). That is the case in both developed and developing economies.

If anything, urbanization should reduce aggregate volume consumption per capita. The fact that volumes per capita increase with incomes suggests that forces other than urbanization itself are at play and dominate the urbanization effect. For example, the residents of wealthier nations could consume more space per capita regardless of their type of residence. Another possibility is that rural areas and small towns drive international volume differences.

Figure 4 (p. 12) gives credence to both hypotheses. Space consumption per capita increases with national income in all types of localities. However, rural volume per capita increases more steeply with income than city volume per capita (“rural-towns” line vs. “cities” line). In other words, world cities are more similar to each other than villages and small towns. Using the same regression analysis as before, we find that rural construction and urban construction respectively account for _∼_ 60% and _∼_ 40% of international volume differences (finding again broadly similar patterns when considering developing economies only).

The U.N. then defines megacities as agglomerations over 10m+ inhabitants (UN, 2017), which leads to 28 megacities being selected. In order to include more cities, we use a 5 million inhabitants cut-off. This selects 71 megacities (including 55 cities in developing economies) that concentrate 24% of the world’s total city population, but account for only 22.5% global building volume provided by cities. Thus, cities with 50k to 5m residents provide the remaining 77.5%.

Similarly, volume per capita increases less steeply for megacities than for all cities across different income levels (see Figure 4 on p. 12), which indicates that megacities are more similar to each other than cities overall. Thus, countries’ construction patterns differ more in their small and medium-sized cities than in their largest cities. Relatedly, regression analyses suggest that construction in megacities and construction in other cities respectively account for _∼_ 40% and _∼_ 60% of international urban volume differences (including in developed economies).

To conclude, rural areas, not cities, disproportionately influence the distribution of volume per capita at a global scale. Medium to small cities then actually dominate total urban volumes. **6.3. Decomposition of International Urban and Rural Volume Differences** Similarly to what we do at the country level, we can decompose international volume differences separately for urban and rural areas. Figures 9 and 10 show the respective built area-income
27 Table 2: Summary statistics for urban areas and rural areas, 2012/2019

|Economies<br>V|olume km<sup>3</sup>|Per Cap. m<sup>3</sup>|% Outward|% Upward|% Low-Rise|% High-Rise|
|---|---|---|---|---|---|---|
|_Panel A:_||Urban Areas<br>(De|fned as Cities|_≥_50,000 Inha|bitants in 2015|)|
|World|677|193|44|55|52|3|
|Developed|232|399|34|65|58|7|
|Developing|445|152|46|54|51|3|
|High-Income|232|399|34|65|58|7|
|Upper-Middle-Inc.|318|243|37|63|59|4|
|Lower-Middle-Inc.|109|81|51|49|47|2|
|Low-Income|17|65|63|37|37|0|
|Africa|54|99|58|41|41|0|
|Asia|352|165|42|58|55|3|
|Europe|127|439|30|70|64|6|
|Latin America & Carib.|56|160|47|53|47|6|
|North America|82|473|42|59|54|5|
|Pacifc|6|374|45|55|51|4|
|_Panel B:_|Rura|l Areas<br>(Defned a|s Villages and T|owns_≥_50,00|0 Inhabitants in|2015)|
|World|916|238|60|40|40|0|
|Developed|343|552|50|51|50|1|
|Developing|572|177|62|38|38|0|
|High-Income|343|552|50|51|50|1|
|Upper-Middle-Inc.|388|262|54|45|45|0|
|Lower-Middle-Inc.|145|104|67|32|32|0|
|Low-Income|38|112|73|27|27|0|
|Africa|94|147|72|28|28|0|
|Asia|398|174|60|40|40|0|
|Europe|245|540|50|50|49|1|
|Latin America & Carib.|58|215|61|39|39|0|
|North America|111|604|50|49|49|0|
|Pacifc|9|417|59|41|41|0|

_Notes:_ This table shows summary statistics for four groupings of countries. Developed Status is based on the World Bank (WB)’s classification of countries in 2019 (= high-income economies). Outward volume = built area x 2.5m. Upward volume = volume - outward volume. High-rise volume = from high-rises ( _≥_ 50 m). Low-rise volume = from low-rises (between 2.5m and 50m).
28 relation and average height-income relation separately for urban areas (“cities”) and rural areas (“rural & towns”). As seen, area increases more steeply with economic development for rural areas than for urban areas (incl. megacities). Conversely, average height increases more steeply with economic development for urban areas (incl. megacities) than for rural areas. However, even for rural areas, average height significantly increases with economic development.

When using regression analyses to decompose volumes per capita, we find that upward construction accounts for 70%-75% of the urban volume-income relation (whether in developed or developing economies) and 60% of the rural volume-income relation (50-55% in developing economies). With rural areas explaining 60% of global volume differences, it makes sense that upward construction explains _∼_ 60%-65% of global volume differences.

**6.4. Upward versus Outward Specializations: Urban and Rural Areas**

LAC and Asian cities provide two-thirds more volume per capita than African cities (Table 2). However, LAC cities do so by providing more outward volume, i.e. flat residential areas (+40% than in Africa vs. +4% for Asia), whereas Asian cities provide more upward volume/heights (+139% than in Africa vs. +89% for LAC). This leads us to examine the upward vs. outward specializations (conditional on income) of selected cities, which are interesting in and of themselves as (vertical and horizontal) land use regulations also vary across world cities.

We start with the 12,831 cities using the same residualization procedure as for countries (Appendix Section C6.). Figure 14 shows how the 15 largest cities are classified for six large economies. U.S. megacities are for the most part pro-area (exceptions include New York, Boston, and Washington) and most specialize in high-rises (top-left quadrant). Thus, when U.S. cities build upwards, they are tall. The pro-high-rises and pro-heights residuals are positively correlated, implying pro-height is achieved via high-rises. In contrast, Chinese megacities are clearly pro-heights. Most cities specialize in high-rises (top-right quadrant), and again, a positive relationship between the pro-high-rises and pro-heights residuals is found. Therefore, even if low-rises account for most of the upward volumes globally, high-rises may matter locally.

In India, there are pro-heights cities specialized in high-rises (Mumbai and Bangalore; topright quadrant), pro-area cities specialized in high-rises for their heights (Delhi and Chennai; top-left quadrant) and pro-area cities specialized in low-rises instead (Ahmedabad and Jaipur; bottom-left quadrant). Brazil is a middle ground between the pro-area U.S. (Rio de Janeiro) and pro-heights China (S ̃ao Paulo). Most cities specialize in high-rises (top quadrants).

South African megacities are all pro-area and either pro-high-rises (Johannesburg and Cape Town) or pro-low-rises (Port Elizabeth and Polokwane). Nigerian megacities are mostly proarea. All of them are then pro-low-rises (bottom quadrants). The results show how focusing on a few megacities can generate misleading country classifications. While Mumbai, New York, and S ̃ao Paulo are pro-heights, large cities in India, the U.S., and Brazil are on average pro-area.
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31 that regional/local governments emulate each other in implementing similar policies.

# **7. Conclusion**

Maps have been a major innovation in human history, contributing to nation building and trade globalization. Historically, maps showed the world in 2D. Given historical transportation and building technologies, human life itself was mostly functioning on a horizontal plane. With the advent of airplanes or skyscrapers in cities, our world verticalized. Today, satellite imagery and computer technology allow us to generate a detailed 3D picture of our global built environment.

The outcomes of this global 3D study of the building stock expand the body of research in this area. We have found that economic development accounts for two-thirds of international volume differences, with the remaining third probably due to policy-related factors. While Asian nations have large construction gaps based on current economic conditions, African nations’ construction gaps will dramatically increase in the future as the continent keeps experiencing fast population growth. International volume differences are disproportionately driven by upward construction and by rural areas and small towns instead of cities (including rural upward construction). Lastly, nations/cities with similar levels of economic development may specialize in heights or areas. Overall, the results suggest an important role for land-use regulations and highlight that construction patterns may have significant environmental implications.

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<!-- Start of picture text --> Building Fraction [%] | Building Height [m] Building Volume [m3]<br>Reference (mean of 20.78 7.77 11,798<br>19 reference cites)<br>CO<br>SME2.78 | 10.31MAE| RMSE14.09 | -230 | 356 | RMSE6.04 | -2,808 | 6,878 | 12,464RMSE |<br>Identical to v2.0 RMSE RMSE<br>ssGD OS (<br><!-- End of picture text -->
2 on skyscrapers and high-rise buildings only. Since 2003 Emporis has branched out, widening its database by collecting building information on all construction types.” As such, Emporis obtains data from its extensive member network of land developers, architectural firms, builders, city administrations, and banks to maintain the database. Emporis was recently bought by the CoStar group, a global leader in commercial real estate. As such, the data is confidential.

# **B2. First-step selection of the tall buildings**

We only consider “existing” or “demolished” buildings, thus ignoring “unbuilt” and “planned” buildings. We also exclude “under construction” buildings (as of 09-07-2022) since it means they did not exist as of 2019. This leaves us with 781,136 buildings. Next, we exclude buildings without geographical coordinates. This reduces the sample size to 764,343 buildings. Lastly, we exclude buildings for which we do not have any height information, which further reduces sample size to 748,651 tall buildings.

The main types of tall buildings are “high-rise buildings,” “low-rise buildings,” “skyscrapers,” and “building with towers.” Altogether, they account for 96% of buildings and almost 100% of total heights in the data. Other types of buildings include, for example, airport towers, openair structures, reactor buildings, and telecommunications towers. We do not exclude these as the satellite data that we also use cannot distinguish a building’s use. To be consistent with this other data set, we thus keep all buildings, noting that it should not be too consequential for the analysis given how little they contribute to overall heights globally.

**B3. Height variables used**

The main height variable used by Emporis is “architectural height” (meters), which “is the elevation from its base to its highest architectural element.” For some buildings where the information is missing, Emporis reports “architectural height (estimated),” which “is an automatic calculation of a probable approximation” of the architectural height based on other sources of height information and considering the building’s locality. Combining both variables, architectural height (incl. estimated) is only missing for 9,151 out of the 748,651 buildings. In contrast, the variable that we are most interested in is “roof height,” which is “the vertical elevation from the base of a building to the highest exterior portion of the shell enclosing its interior space.” Indeed, this type of height matches the most with what the satellite data captures. As such, it excludes spires and antennas, which do not occupy much volume. Roof height is missing for 724,655 of the 748,651 buildings. However, we can use “architectural height” (i.e., not including the observations for which we have “architectural height estimated” only) to recreate roof height since the two are very correlated with each other (additionally, almost all buildings do not have spires/antennas). More precisely, the coefficient of correlation between the two types of heights is 0.99 (N = 22,396). Next, to impute roof height based on architectural height, we use the following model for buildings b in locality c (N = 23,558): _ROOFHEIGHTbc_ = _α_ + _β ∗ ARCHHEIGHTbc_ + _ωc_ + _μbc._ ( _B_ 1) (1) Note that we include 1,593 locality fixed effects ( _ωc_ ). Hence, the comparison is restricted to buildings within the same locality (the locality fixed effects also control for how measurement
3 error could vary across localities). For buildings that we know architectural heights but not roof height, we can use our estimates of _α_ and _β_ to predict roof height. Note that we obtain that _α_ = 1.54 (significant at 1%) and _β_ = 0.96 (ditto). _β_ being lower than 1.00 makes sense since roof height is by construction lower than architectural height. The adjusted R-squared is 0.99, which shows the predictive power of our imputation method. Doing so, we know roof height (in meters) for 739,938 buildings. It is then still missing for 8,713 buildings.

The next height variable that we can use to impute roof height is “highest occupied floor height,” which is “the elevation from a building’s base to the top of the floor slab of the highest interior level which contains usable floor space.” Its correlation with roof height (including the roof height estimates based on architectural height) is 0.99 (N = 2,532). We then estimate a similar to eq. (B1). We obtain that _α_ = 4.84 (significant at 1%) and _β_ = 1.04 (ditto). The adjusted R-squared is 0.99. This allows us to add 10 buildings. We then proceed similarly with tip height, “the vertical elevation from the base to the highest man-made part of the building, or any fixed attachment thereto, whichever is higher” (correlation with roof height = 0.99). This adds 189 buildings. For the remaining 8,514 tall buildings (out of 748,651) without direct or indirect roof height information, we use the number of floors to predict roof height, as it is available for many buildings. But in order to do that, it is important to first understand the relationship between roof height and the number of floors. To do so for buildings b in localities c, we simply regress roof height on the number of floors while also adding locality fixed effects ( _ωc_ ): _ROOFHEIGHTbc_ = _α_ + _β ∗ NUMFLOORSbc_ + _ωc_ + _μbc._ (2) For N = 719,622 buildings, we obtain _α_ = 1.77 (significant at 1%) and _β_ = 3.51 (ditto), implying an average height of about 3.5 m per floor. The adjusted R-squared is 0.98 (the correlation between roof height and the number of floors was also 0.98). Of course, an average height per floor of 3.5 m does not imply that the average ceiling height is 3.5 m (it is typically more around 2.5 m). Lobbies and top floor apartments have tall ceilings. Also, average height per floor includes the space between floors, for example for mechanical, electrical, and plumbing systems. This relationship is also shown visually in Appendix Section B Figure B.1 below.

In the data, most tall buildings in the world are less than 100 m tall in terms of roof height (the 95th percentile is about 110 m). As seen, the relationship is mostly linear. Indeed, below 100 m, the linear and quadratic fits are barely distinguishable. Another way to examine the linearity of the relationship between roof height and the number of floors is to estimate eq. (B2) for different segments of the building height distribution. More precisely, for buildings below 35 m, buildings between 35 and 100 m, and buildings above 100 m, we find a _β_ of 3.3, 3.3 and 3.5, respectively. Since the difference is rather minimal (20 cm per floor), and since _β_ = 3.5 for the full sample, we use _β_ = 3.5 (and _α_ = 1.77) to impute roof height when only the number of floors is available. Ultimately, we have 748,640 tall buildings with available height information.

# **B4. Second-step selection of the tall buildings based on the completion year**

We aim to select buildings that existed as of 2019. To do so, we primarily use information on the year of completion of each building. Among the 748,640 tall buildings, 539,455
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6 The mode of the distribution is about 50 m (about 14 floors). Since countries are likely to have more buildings below 50 m than above 50 m, and since the distribution of buildings is smooth after 50 m, this suggests that the data set mostly captures buildings above 50 m. Thus, the data set is likely less reliable for buildings below 50 m. Given that the satellite-based data that we use should capture buildings up to 50 m, we believe that we still capture most of the buildings in the world when combining the two datasets. Nonetheless, we can investigate if some regions of the world might have better data. Comparing the six continents (as defined by the United Nations), the mode is around 45-50 m for Africa, 50-55 m for Asia, 40-45 m for Europe, 15 m for North America, 45 m in Oceania and 45 m in South America. Therefore, we are confident that we can use information from the Emporis database to update WSF3Dv1 and create WSF3Dv2.

# **C Methods**

**C1. Classifying countries into 4 groups: heights vs. areas, high-rises vs. low-rises** First of all, we “residualize” the log of the outward based volume per capita (i.e., built-up area x 2.5 meters) with respect to log per capita GDP and its square (using country population as weights). As such, the residuals that we obtain capture to what extent a country uses a lot of area per capita given its income level, i.e., relative to the world’s quadratic fit. In layman’s terms, we obtain for each country the absolute distance from the country’s value to the world’s relation. A positive (negative) value implies more (less) outward volume per capita relative to the world.

Second, we similarly residualize the log of the upward volume per capita (= total volume - outward volume). The resulting residuals capture to what extent a country has a lot of (low-rise + high-rise) heights per capita given its income level. In layman’s terms, we obtain for each country the absolute distance from the country’s value to the world’s relation. A positive (negative) value implies more (less) upward volume per capita relative to the world.

Third, countries with higher area residuals tend to have higher heights residuals (correlation _≈_ 0.7), implying that countries that are “good” in one dimension are also “good” in the other dimension. However, since we are interested in the comparative rather than absolute advantage of each country, we residualize the height residuals with respect to the area residuals (using country populations as weights). In layman’s terms, we obtain for each country the distance from the country’s value to the world’s relation. A positive (negative) value implies more (less) heights per capita (rather than area per capita) relative to the world. The final residuals thus indicate to what extent a country is relatively pro-height or pro-area for a given income level.

We proceed likewise for high-rises vs. low-rises, first residualizing high-rise and low-rise volumes with respect to income, then residualizing the high-rise residuals with respect to the low-rise residuals. The final residuals indicate to what extent a country is relatively pro-highrises rather than relatively pro-low-rises for a given income level.

## **C2. Relation between city economic development and city building stocks**

To study how city building stocks vary with income, we use the 2015 city GDP data of Zhou et al. (2022) who provide “real GDP” data (2017 dollars) based on unbounded night lights data. We use this data in the absence of global city income data. City GDP is total lights within a UC boundary.
7 Finally, log(city GDP) / log (city pop.) is our income measure instead of log (city GDP / city pop.). We believe that the latter measure does not properly capture city incomes due to non-linearities in the relation between lights and population (see Appendix Section C3. below).

Appendix Figure C.3 shows a positive volume-income relation. For a given income level, there is more variation across cities than across countries. For example, volume per capita dramatically varies across U.S. cities despite them having similar incomes when compared to other world cities (e.g., 311m<sup>3</sup> per resident in New York vs. 569 in Dallas).

Note that this analysis indirectly controls for the effect of city population size. In the U.S., city incomes and sizes strongly correlate (Appendix Fig. C.5). That is also true globally conditional on country indicator variables (see Appendix Section C4. below). Indeed, within the same economy, higher-wage cities attract workers. Conversely, larger cities are denser, which generates productivity-enhancing agglomeration economies (Combes and Gobillon, 2015).

Based on the same analysis as at the country level, heights explain between two thirds and three fourths of the volume-income relation (vs. 65% at the country level) (Appx. Section C5. and Appx. Fig. C.4-C.6). Low-rises and high-rises account for 88% and 12% of the heights-income relation, hence 65% and 10% of the volume-income relation (25% for areas). At the country level and including rural areas, we found 60% for high-rises, 5% for low-rises, and 35% for areas.

**C3. City per capita income measure** To study how city stocks vary with respect to income, we use the 2015 city GDP data from Chen et al. (2022). More precisely, they provide high-resolution “real GDP” data (in 2017 dollars) based on (not top-coded) night lights data as reported by the NPP/VIIRS satellite series. While night lights data could capture infrastructure (including electrification) and past economic development in addition to current economic development as infrastructure and urban structures are durable, we use this data in the absence of better data on city incomes for the whole world. To obtain a measure of city GDP, we rely on the total sum of lights within each city’s boundary as defined by GHS-UCDB (Florczyk et al., 2019). Finally, we use log(city GDP) / log (city pop.) as our city per capita income measure instead of log (city GDP / city pop.).

Indeed, the latter measure does not, in our view, properly capture city incomes due to nonlinearities in the relationship between lights and population. As shown for 324 U.S. metro areas in Appendix Figure C.5, log (city GDP / city pop.) decreases with city population size for larger cities, for example due to street lighting being a non-rivalrous good. Indeed, the use of street lighting by some individuals does not diminish its availability to other individuals. As such, the number of street lights per capita should increase less than proportionally with respect to population. There could be of course other reasons. In contrast and as can be seen in Appendix Figure C.5, log (city GDP) / log(city pop.) increases (slightly concavely) with city size.

# **C4. Relation between city per capita income and city population size**

As shown in Appendix Figure C.5 for 324 U.S. metro areas, city per capita incomes and city population sizes are very strongly correlated (correlation about 0.9 and R-squared of 0.90). That is also the case in large countries with many cities, for example China and India (not shown).
8 Globally, conditional on country indicator variables capturing country-specific factors, we also find that this is the case (correlation about 0.7 and adjusted R-squared of 0.83). Note that we consider 12,516 world (GHS-UCBD) cities in 168 countries for this analysis.

## **C5. Decomposing built-up volumes at the city level**

The higher levels of volume per capita in richer/larger cities are driven by both larger areas and taller buildings in them. To obtain their respective contributions to total volumes, we rely on equation (C4.1) and use simple econometric regressions where the dependent variable is the unlogged per capita volume variable considered and the variable of interest is the per capita income measure based on night lights in 2015 (N = 12,516 world cities).

Total Volume = outward volume (area) + upward volume (heights) (C4.1) We obtain the following slopes for total volume, outward volume and upward volume: 444***, 152*** and 292***, respectively (*** implies significance at 1%). Using country populations as weights, we get 283***, 74*** and 209***, respectively. The implication of these results is that heights contribute to between two thirds and three fourths of the volume-income relation.

We then obtain the following slopes for upward volumes based on low-rises or high-rises: 281*** (184*** with population weights) and 12*** (25***), respectively. Giving more weight to larger cities since they account for most of the world’s urban population, low-rises and highrises respectively account for 88% and 12% of the heights-income relation, hence 65% and 10% of the volume-income relation (25% for areas). In contrast, at the country level and including rural areas, we found 60% for high-rises, 5% for low-rises, and 35% for areas.

**C6. Classifying regions into 4 groups for primate & secondary cities & rural areas**

For each subregion, Appx. Fig. C.7-C.9 show the (locality) population-weighted average residuals when only considering large cities (defined as cities in the top 15 of each country), small and medium-sized cities (cities not in the top 15 of each country) or rural areas & towns (localities _<_ 50,000 c. 2015). Comparing the three figures, one can see how some regions exhibit similar patterns for each type of locality. The coefficient of correlation between the pro-height residuals based on large cities and the same residuals but based on small and medium-sized cities or rural areas & towns is _∼_ 0.7-0.9. Correlation is less high but still positive, at _∼_ 0.45-0.6, for the pro-highrises residuals. Thus, regions tend to be similarly “specialised” across all localities.

# **REFERENCES**

> Chen, Jiandong, Ming Gao, Shulei Cheng, Wenxuan Hou, Malin Song, Xin Liu, and Yu Liu, “Global 1 km _×_ 1 km gridded revised real gross domestic product and electricity consumption during 1992–2019 based on calibrated nighttime light data,” _Scientific Data_ , 2022, _9_ (1), 202.

> Combes, Pierre-Philippe and Laurent Gobillon, “The empirics of agglomeration economies,” in “Handbook of regional and urban economics,” Vol. 5, Elsevier, 2015, pp. 247–348. Esch, Thomas, Elisabeth Brzoska, Stefan Dech, Benjamin Leutner, Daniela Palacios-Lopez, Annekatrin Metz-Marconcini, Mattia Marconcini, Achim Roth, and Julian Zeidler, “World Settlement Footprint 3D-A first three-dimensional survey of the global building stock,” _Remote Sensing of Environment_ , 2022, _270_ , 112877. Florczyk, AJ, Michele Melchiorri, Christina Corbane, Marcello Schiavina, M Maffenini, Martino Pesaresi, Panagiotis Politis, S Sabo, S Freire, Daniele Ehrlich et al., “Description of the GHS urban centre database 2015,” _Public release_ , 2019, _1_ , 1–75. Zhou, Yuyu, Xuecao Li, Wei Chen, Lin Meng, Qiusheng Wu, Peng Gong, and Karen C Seto, “Satellite mapping of urban builtup heights reveals extreme infrastructure gaps and inequalities in the Global South,” _Proceedings of the National Academy of Sciences_ , 2022, _119_ (46), e2214813119.
9

# **C. Appendix Figures and Appendix Tables (NOT FOR PUBLICATION)**

Figure C.1: Built-Up Volume for Selected Urban Agglomerations, 2012/2019.

_Notes:_ The map shows the spatial distribution of building volumes (m<sup>3</sup> ) as given by WSF3Dv2 (resolution of 90 m).
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