|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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